Finite Group Databasebeta

← #3500×D71 #32905916

Subgroups — #3500×D71 #32905916

Order 18176.

11534 conjugacy classes of subgroups.

The subgroup lattice has 1216 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×2−1+4×D71C211yesmaximal, characteristic, complemented
2C2×H(5,𝔽2)×D71C211yesmaximal, characteristic, complemented
3#22602134C211yesmaximal, characteristic, complemented
4#22602133C211yesmaximal, characteristic, complemented
5#22602132C213yesmaximal, complemented
6#22602131C214yesmaximal, complemented
7#22602130C213yesmaximal, complemented
8#22602129C213yesmaximal, complemented
9#22602128C211yesmaximal, characteristic, complemented
10#22602127C213yesmaximal, complemented
11#22602126C2112yesmaximal, complemented
12#548×D71C214yesmaximal, complemented
13#546×D71C2112yesmaximal, complemented
14#536×D71C213yesmaximal, complemented
15#535×D71C213yesmaximal, complemented
16#532×D71C213yesmaximal, complemented
17C2×#124×D71C213yesmaximal, complemented
18C4×#41×D71C211yesmaximal, characteristic, complemented
19C71×#3500C211yesmaximal, characteristic, complemented
20C2×#14556176C2213yescomplemented
21C2×#14556176C2212yescomplemented
22C2×#14556175C2216yescomplemented
23C2×#14556175C2213yescomplemented
24C2×#14556175C2211yescharacteristic, complemented
252−1+4×D71—216no—
26C2×#14556174C2213yescomplemented
27C2×#14556174C2212yescomplemented
28C2×#14556174C2211yescharacteristic, complemented
29C2×#14556173C2216yescomplemented
30C2×#14556173C2213yescomplemented
31H(5,𝔽2)×D71—216no—
32C2×#41×D71C2212yes—
33C2×#41×D71C2213yes—
34C2×#41×D71C2211yescharacteristic
35C2×#41×D71C2216yescomplemented
36C2×#41×D71C2213yescomplemented
37C22×Q8×D71C2212yescomplemented
38C22×Q8×D71C2213yescomplemented
39C22×D4×D71C2216yes—
40C22×D4×D71C2213yes—
41#17986661C2214yescomplemented
42#17986660C2214yescomplemented
43#17986659C22112yescomplemented
44#17986658C22112yescomplemented
45#17986657C22112yescomplemented
46#17986656C2214yescomplemented
47#17986655C22112yescomplemented
48#17986646C22112yescomplemented
49#17986645C22112yescomplemented
50#17986644C22112yescomplemented
51#17986643C22112yescomplemented
52#17986642C22112yescomplemented
53#17986641C22124yescomplemented
54#17986640C22112yescomplemented
55#17986639C22124yescomplemented
56#17986638C22124yescomplemented
57#17986637C22112yescomplemented
58#17986636C22124yescomplemented
59#17986575C2213yescomplemented
60#17986574C2216yescomplemented
61#17986573C2213yescomplemented
62#17986572C22112yescomplemented
63#17986571C22112yescomplemented
64#17986570C2213yescomplemented
65#17986569C2216yescomplemented
66#17986568C2213yescomplemented
67#17986567C2216yescomplemented
68#17986566C2213yescomplemented
69#17986565C22112yescomplemented
70#17986564C22112yescomplemented
71#17986563C2213yescomplemented
72#17986562C2216yescomplemented
73#17986550C2213yescomplemented
74#17986549C2213yescomplemented
75#17986548C2213yescomplemented
76#17986548C2213yescomplemented
77#17986547C2213yescomplemented
78#17986546C22112yescomplemented
79#17986545C2213yescomplemented
80#17986545C2213yescomplemented
81#17986544C22112yescomplemented
82C4⋊Q8×D71C2213yescomplemented
83#127×D71C2213yescomplemented
84C2×#14556117C2213yescomplemented
85C2×#14556116C2213yescomplemented
86C2×#14556115C2213yescomplemented
87C2×#14556114C22112yescomplemented
88#124×D71C22112yescomplemented
89#124×D71C2213yescomplemented
90#124×D71C2216yescomplemented
91#124×D71C2211yescharacteristic, complemented
92#124×D71C22112yescomplemented
93#124×D71C2216yescomplemented
94#124×D71C2216yescomplemented
95#123×D71C22112yescomplemented
96C22⋊Q8×D71C22112yescomplemented
97#121×D71C22112yescomplemented
98#121×D71C22112yescomplemented
99#120×D71C22112yescomplemented
100#41×Dic71C2211yescharacteristic, complemented
101C4×#11765866C2212yescomplemented
102C4×#11765865C2213yescomplemented
103#17986467C2213yescomplemented
104C4×#11765864C2216yescomplemented
105C4×Q8×D71C2212yescomplemented
106C4×D4×D71C2216yescomplemented
107C4×D4×D71C22112yescomplemented
108#117×D71C2213yescomplemented
109C2×C22⋊C4×D71C22112yescomplemented
110C2×C42×D71C2213yescomplemented
111C2×2−1+4×C71C2211yescharacteristic, complemented
112C2×H(5,𝔽2)×C71C2211yescharacteristic, complemented
113#548×C71C2214yescomplemented
114#546×C71C22112yescomplemented
115#536×C71C2213yescomplemented
116#535×C71C2213yescomplemented
117#532×C71C2213yescomplemented
118C2×#124×C71C2213yescomplemented
119C4×#41×C71C2211yescharacteristic, complemented
120C24×D71C2316yes—
121#14556176—216no—
122#14556176—224no—
123#14556175—224no—
124#14556175—248no—
125#14556175—28no—
126#14556174—216no—
127#14556174—224no—
128#14556174—28no—
129#14556173—224no—
130#14556173—248no—
131C2×#11765866C2313yes—
132C2×#11765866C2312yes—
133C2×#11765866C2311yescharacteristic
134C2×#11765866C2313yescomplemented
135C2×#11765866C2316yescomplemented
136C2×#11765865C2316yes—
137C2×#11765865C2313yes—
138C2×#11765865C2316yes—
139C2×#11765865C2313yes—
140C2×#11765865C2316yescomplemented
141C2×#11765865C2313yescomplemented
142C2×#11765865C23112yescomplemented
143C2×#11765865C2316yescomplemented
144C2×#11765864C2313yes—
145C2×#11765864C2316yes—
146C2×#11765864C2316yes—
147C2×#11765864C2313yes—
148C2×#11765864C2313yescomplemented
149C2×#11765864C2316yescomplemented
150C2×#11765864C23112yescomplemented
151C2×#11765864C2316yescomplemented
152#41×D71—216no—
153#41×D71—248no—
154#41×D71—224no—
155#41×D71—224no—
156#41×D71D4116yescomplemented
157C22×Dic142C2313yescomplemented
158C22×Dic142C2316yescomplemented
159C22×Dic142C2316yescomplemented
160C2×Q8×D71—216no—
161C2×Q8×D71—224no—
162C2×Q8×D71C2316yes—
163C2×Q8×D71C2313yes—
164C2×Q8×D71C2311yescharacteristic
165C2×Q8×D71C2311yescharacteristic
166C2×Q8×D71C2316yescomplemented
167C2×Q8×D71C2316yescomplemented
168C2×Q8×D71C2312yescomplemented
169C2×Q8×D71C2316yescomplemented
170C22×D284C2313yes—
171C22×D284C2316yes—
172C22×C22⋊D71C2316yes—
173C22×C22⋊D71C23112yes—
174C2×D4×D71—248no—
175C2×D4×D71—224no—
176C2×D4×D71C2316yes—
177C2×D4×D71C2316yes—
178C2×D4×D71C2316yes—
179C2×D4×D71C2313yes—
180C2×D4×D71C2316yes—
181C2×D4×D71C2316yes—
182C2×D4×D71C23112yes—
183C2×D4×D71C2316yes—
184C2×D4×D71C2316yes—
185C2×D4×D71C2311yescharacteristic
186C2×D4×D71C23112yes—
187C2×D4×D71C2313yes—
188C22×C4×D71C2316yes—
189C22×C4×D71C2316yes—
190C22×C4×D71C2316yes—
191C22×C4×D71C2316yes—
192C22×C4×D71C2313yes—
193#14556128C2313yescomplemented
194#14556127C23112yescomplemented
195#14556126C2313yescomplemented
196#14556126C2313yescomplemented
197#14556125C2313yescomplemented
198#14556124C2313yescomplemented
199#14556124C23112yescomplemented
200#14556124C2313yescomplemented
201#14556117C2316yescomplemented
202#14556117C23112yescomplemented
203#14556117C2313yescomplemented
204#14556117C2311yescharacteristic, complemented
205#14556116C2316yescomplemented
206#14556116C23112yescomplemented
207#14556116C2313yescomplemented
208#14556116C2311yescharacteristic, complemented
209#14556115C2316yescomplemented
210#14556115C23112yescomplemented
211#14556115C2313yescomplemented
212#14556115C2311yescharacteristic, complemented
213#14556114C23124yescomplemented
214#14556114C23124yescomplemented
215#14556114C23124yescomplemented
216#14556114C23112yescomplemented
217#14556114C2314yescomplemented
218#14556113C23124yescomplemented
219#14556112C23112yescomplemented
220#14556111C23112yescomplemented
221#14556110C23124yescomplemented
222#14556109C23112yescomplemented
223#14556108C23112yescomplemented
224#14556107C23112yescomplemented
225#14556106C23124yescomplemented
226#14556105C23124yescomplemented
227#14556104C23112yescomplemented
228#14556103C23112yescomplemented
229#14556103C23112yescomplemented
230#14556102C23112yescomplemented
231#14556102C23112yescomplemented
232#14556101C23124yescomplemented
233#14556101C23112yescomplemented
234#14556101C23112yescomplemented
235#14556100C23124yescomplemented
236#14556100C23112yescomplemented
237#14556100C23112yescomplemented
238#14556099C23112yescomplemented
239#14556099C23112yescomplemented
240#14556098C23112yescomplemented
241#14556098C23124yescomplemented
242#14556097C23112yescomplemented
243#14556096C23124yescomplemented
244#14556096C23112yescomplemented
245Q8×Dic71C2312yescomplemented
246C4×Dic142C2316yescomplemented
247#14556093C2316yescomplemented
248C4×D284C2316yescomplemented
249C4×D284C23112yescomplemented
250D4×Dic71C23112yescomplemented
251D4×Dic71C2316yescomplemented
252#14556090C2316yescomplemented
253#14556090C23112yescomplemented
254C4×C22⋊D71C23112yescomplemented
255C4×C22⋊D71C23112yescomplemented
256C4×C22⋊D71C23112yescomplemented
257(C22⋊D71)⋊C4C23112yescomplemented
258(C22⋊D71)⋊C4C23112yescomplemented
259(C22⋊D71)⋊C4C23112yescomplemented
260#14556087C2313yescomplemented
261#14556086C2316yescomplemented
262#14556085C2316yescomplemented
263#14556084C2316yescomplemented
264C4⋊C4×D71C2316yes—
265C4⋊C4×D71C23112yes—
266C2×C22⋊Dic71C23112yescomplemented
267C2×(C2×D71)⋊C4C23112yescomplemented
268C2×(C2×D71)⋊C4C23112yescomplemented
269C22⋊C4×D71C23112yes—
270C22⋊C4×D71C23124yes—
271C22⋊C4×D71C2316yes—
272C22⋊C4×D71C2314yes—
273C22⋊C4×D71C23124yescomplemented
274C22⋊C4×D71C23124yescomplemented
275C2×C4×Dic71C2316yescomplemented
276C2×C4×Dic71C2313yescomplemented
277C42×D71C2311yescharacteristic
278C42×D71C2313yes—
279C42×D71C2316yes—
280C42×D71C2316yescomplemented
281C42×D71C2313yescomplemented
282C42×D71C2313yescomplemented
2832−1+4×C71—28no—
284H(5,𝔽2)×C71—28no—
285C2×#41×C71C2313yes—
286C2×#41×C71C2312yes—
287C2×#41×C71C2311yescharacteristic
288C2×#41×C71C2313yescomplemented
289C2×#41×C71C2316yescomplemented
290C22×Q8×C71C2313yescomplemented
291C22×Q8×C71C2312yescomplemented
292C22×D4×C71C2313yes—
293C22×D4×C71C2316yes—
294C4⋊Q8×C71C2313yescomplemented
295#127×C71C2313yescomplemented
296#124×C71C2316yescomplemented
297#124×C71C23112yescomplemented
298#124×C71C2313yescomplemented
299#124×C71C2311yescharacteristic, complemented
300#123×C71C23112yescomplemented
301C22⋊Q8×C71C23112yescomplemented
302#121×C71C23112yescomplemented
303#121×C71C23112yescomplemented
304#120×C71C23112yescomplemented
305C4×Q8×C71C2312yescomplemented
306C4×D4×C71C2316yescomplemented
307C4×D4×C71C23112yescomplemented
308#117×C71C2313yescomplemented
309C2×C22⋊C4×C71C23112yescomplemented
310C2×C42×C71C2313yescomplemented
311C23×D71—224no—
312C23×D71—424no—
313C23×D71C2412yes—
314C23×D71C2416yes—
315C23×D71C2413yes—
316C23×D71C24112yes—
317C23×D71C2416yes—
318#11765866—28no—
319#11765866—224no—
320#11765866—212no—
321#11765866—212no—
322#11765866C2×D418yescomplemented
323#11765865—212no—
324#11765865—212no—
325#11765865—248no—
326#11765865—224no—
327#11765865—224no—
328#11765865—224no—
329#11765865—224no—
330#11765865C2×D4124yescomplemented
331#11765864—224no—
332#11765864—248no—
333#11765864—224no—
334#11765864—224no—
335#11765864—212no—
336#11765864—212no—
337#11765864—224no—
338#11765864C2×D4124yescomplemented
339C2×Dic142—212no—
340C2×Dic142—224no—
341C2×Dic142—224no—
342C2×Dic142C24112yes—
343C2×Dic142C2416yes—
344C2×Dic142C2416yes—
345C2×Dic142C2413yes—
346C2×Dic142C2412yes—
347C2×Dic142C2411yescharacteristic
348C2×Dic142C2413yes—
349Q8×D71—28no—
350Q8×D71—224no—
351Q8×D71—212no—
352Q8×D71—224no—
353Q8×D71—224no—
354Q8×D71—24no—
355Q8×D71—224no—
356Q8×D71C2×D418yes—
357C2×D284—212no—
358C2×D284—224no—
359C2×D284C2416yes—
360C2×D284C2416yes—
361C2×D284C2413yes—
362C2×D284C2416yes—
363C2×D284C2411yescharacteristic
364C2×D284C24112yes—
365C2×D284C2413yes—
366C2×C22⋊D71—248no—
367C2×C22⋊D71—224no—
368C2×C22⋊D71C2416yes—
369C2×C22⋊D71C24112yes—
370C2×C22⋊D71C2416yes—
371C2×C22⋊D71C2416yes—
372C2×C22⋊D71C2416yes—
373C2×C22⋊D71C2416yes—
374C2×C22⋊D71C2412yes—
375C2×C22⋊D71C24112yes—
376C2×C22⋊D71C24112yes—
377C2×C22⋊D71C2416yes—
378D4×D71—224no—
379D4×D71—224no—
380D4×D71—224no—
381D4×D71—248no—
382D4×D71—224no—
383D4×D71—224no—
384D4×D71—212no—
385D4×D71—224no—
386D4×D71—224no—
387D4×D71—24no—
388D4×D71—424no—
389D4×D71C2×D4124yes—
390C22×Dic71C2416yes—
391C22×Dic71C2416yes—
392C22×Dic71C2416yes—
393C22×Dic71C2416yes—
394C22×Dic71C2413yes—
395C2×C4×D71—224no—
396C2×C4×D71—224no—
397C2×C4×D71—224no—
398C2×C4×D71—412no—
399C2×C4×D71C2×D4124yes—
400C2×C4×D71C2412yes—
401C2×C4×D71C2416yes—
402C2×C4×D71C2412yes—
403C2×C4×D71C2416yes—
404C2×C4×D71C2416yes—
405C2×C4×D71C2416yes—
406C2×C4×D71C24112yes—
407C2×C4×D71C2416yes—
408C2×C4×D71C2416yes—
409C2×C4×D71C2416yes—
410C2×C4×D71C2416yes—
411C2×C4×D71C2413yes—
412C2×C4×D71C2411yescharacteristic
413C2×C4×D71C2413yes—
414C2×C4×D71C2413yes—
415C4⋊Dic71C2416yes—
416C4⋊Dic71C24112yes—
417Dic71⋊C4C24112yes—
418Dic71⋊C4C24112yes—
419Dic71⋊C4C24112yes—
420C22⋊Dic71C24112yes—
421C22⋊Dic71C24124yes—
422C22⋊Dic71C2416yes—
423C22⋊Dic71C2414yes—
424(C2×D71)⋊C4C24112yes—
425(C2×D71)⋊C4C24112yes—
426(C2×D71)⋊C4C24124yes—
427(C2×D71)⋊C4C24124yes—
428(C2×D71)⋊C4C24112yes—
429(C2×D71)⋊C4C2414yes—
430(C2×D71)⋊C4C2414yes—
431C4×Dic71C2412yes—
432C4×Dic71C2411yescharacteristic
433C4×Dic71C2416yes—
434C4×Dic71C2413yes—
435C4×Dic71C2416yes—
436C4×Dic71C2416yes—
437C4×Dic71C2416yes—
438C24×C71C2416yes—
439#41×C71—28no—
440#41×C71—224no—
441#41×C71—212no—
442#41×C71—212no—
443#41×C71C2×D418yescomplemented
444C2×Q8×C71—28no—
445C2×Q8×C71—212no—
446C2×Q8×C71C2416yes—
447C2×Q8×C71C2413yes—
448C2×Q8×C71C2411yescharacteristic
449C2×Q8×C71C2411yescharacteristic
450C2×D4×C71—224no—
451C2×D4×C71—212no—
452C2×D4×C71C2416yes—
453C2×D4×C71C2416yes—
454C2×D4×C71C2413yes—
455C2×D4×C71C2416yes—
456C2×D4×C71C2411yescharacteristic
457C2×D4×C71C24112yes—
458C2×D4×C71C2413yes—
459C22×C4×C71C2416yes—
460C22×C4×C71C2416yes—
461C22×C4×C71C2416yes—
462C22×C4×C71C2416yes—
463C22×C4×C71C2413yes—
464C4⋊C4×C71C2416yes—
465C4⋊C4×C71C24112yes—
466C22⋊C4×C71C24112yes—
467C22⋊C4×C71C24124yes—
468C22⋊C4×C71C2416yes—
469C22⋊C4×C71C2414yes—
470C42×C71C2411yescharacteristic
471C42×C71C2413yes—
472C42×C71C2416yes—
473C23×C71—212no—
474C23×C71—412no—
475C23×C71C2516yes—
476C23×C71C2512yes—
477C23×C71C2513yes—
478C22×D71—212no—
479C22×D71—212no—
480C22×D71—24no—
481C22×D71—212no—
482C22×D71—28no—
483C22×D71—224no—
484C22×D71—224no—
485C22×D71—424no—
486C22×D71—412no—
487C22×D71—848no—
488C22×D71C22×D4112yes—
489C22×D71C2516yes—
490C22×D71C2512yes—
491C22×D71C2513yes—
492C22×D71C2511yescharacteristic
493Q8×C71—26no—
494Q8×C71—212no—
495Q8×C71—22no—
496Q8×C71C22×D414yes—
497D4×C71—212no—
498D4×C71—212no—
499D4×C71—26no—
500D4×C71—212no—
501D4×C71—22no—
502D4×C71—412no—
503D4×C71C22×D4112yes—
504C2×C4×C71—212no—
505C2×C4×C71—212no—
506C2×C4×C71—212no—
507C2×C4×C71—46no—
508C2×C4×C71C22×D4112yes—
509C2×C4×C71C2512yes—
510C2×C4×C71C2516yes—
511C2×C4×C71C2516yes—
512C2×C4×C71C2512yes—
513C2×C4×C71C2511yescharacteristic
514C2×C4×C71C2513yes—
515C22⋊D71—212no—
516C22⋊D71—212no—
517C22⋊D71—212no—
518C22⋊D71—212no—
519C22⋊D71—212no—
520C22⋊D71—224no—
521C22⋊D71—24no—
522C22⋊D71—412no—
523C22⋊D71—412no—
524C22⋊D71C22×D4124yes—
525C2×Dic71—212no—
526C2×Dic71—212no—
527C2×Dic71—212no—
528C2×Dic71—46no—
529C2×Dic71C22×D4112yes—
530C2×Dic71C2512yes—
531C2×Dic71C2516yes—
532C2×Dic71C2516yes—
533C2×Dic71C2512yes—
534C2×Dic71C2511yescharacteristic
535C2×Dic71C2513yes—
536D284—212no—
537D284—212no—
538D284—26no—
539D284—212no—
540D284—22no—
541D284—412no—
542D284C22×D4112yes—
543C4×D71—24no—
544C4×D71—212no—
545C4×D71—224no—
546C4×D71—24no—
547C4×D71—212no—
548C4×D71—212no—
549C4×D71—212no—
550C4×D71—212no—
551C4×D71—212no—
552C4×D71—46no—
553C4×D71—46no—
554C4×D71C22×D4112yes—
555C4×D71C22×D414yes—
556C4×D71C22×D4112yes—
557C4×D71C22×D4112yes—
558Dic142—26no—
559Dic142—212no—
560Dic142—22no—
561Dic142—212no—
562Dic142—224no—
563Dic142—24no—
564Dic142C22×D4112yes—
565C22×C71—26no—
566C22×C71—22no—
567C22×C71—26no—
568C22×C71—24no—
569C22×C71—212no—
570C22×C71—812no—
571C22×C71C23×D416yes—
572C22×C71C2611yescharacteristic
573C2×D71—26no—
574C2×D71—224no—
575C2×D71—22no—
576C2×D71—26no—
577C2×D71—24no—
578C2×D71—212no—
579C2×D71—48no—
580C2×D71—424no—
581C2×D71—824no—
582C2×D71—812no—
583C2×D71C23×D416yes—
584C2×D71C23×D412yes—
585C2×D71#58514yes—
586C4×C71—26no—
587C4×C71—22no—
588C4×C71—22no—
589C4×C71—26no—
590C4×C71C23×D412yes—
591C4×C71C23×D416yes—
592Dic71—26no—
593Dic71—22no—
594Dic71—22no—
595Dic71—26no—
596Dic71C23×D412yes—
597Dic71C23×D416yes—
598C2×#3500—711nomaximal, Sylow
599C2×C71—26no—
600C2×C71—46no—
601C2×C71—42no—
602C2×C71C24×D411yescharacteristic
603C2×C71C2×#58512yes—
604D71—26no—
605D71—42no—
606D71—46no—
607D71#350014yesdirect product factor
608C22×2−1+4—711no—
609C22×H(5,𝔽2)—711no—
610#3500—711no—
611#3500—711no—
612#3500—714no—
613#3500—7112no—
614#3500—713no—
615#3500—713no—
616#3500—713no—
617#3500—713no—
618#3500—711no—
619#3500D7111yescharacteristic, direct product factor
620C2×#548—714no—
621C2×#546—7112no—
622C2×#536—713no—
623C2×#535—713no—
624C2×#532—713no—
625C22×#124—713no—
626C2×C4×#41—711no—
627C71C2×#350011yescharacteristic, complemented, Sylow
628C2×2−1+4—711no—
629C2×2−1+4—713no—
630C2×2−1+4—716no—
631C2×2−1+4—712no—
632C2×2−1+4—713no—
633C2×2−1+4—14216no—
634C2×2−1+4C2×D7111yescharacteristic, complemented
635C2×H(5,𝔽2)—712no—
636C2×H(5,𝔽2)—713no—
637C2×H(5,𝔽2)—711no—
638C2×H(5,𝔽2)—716no—
639C2×H(5,𝔽2)—713no—
640C2×H(5,𝔽2)—14216no—
641C2×H(5,𝔽2)C2×D7111yescharacteristic, complemented
642C22×#41—711no—
643C22×#41—713no—
644C22×#41—712no—
645C22×#41—713no—
646C22×#41—716no—
647C23×Q8—713no—
648C23×Q8—712no—
649C23×D4—713no—
650C23×D4—716no—
651#548—714no—
652#548—714no—
653#548—7112no—
654#548—7112no—
655#548—7112no—
656#548—714no—
657#548—7112no—
658#548C2×D7114yescomplemented
659#546—7112no—
660#546—7112no—
661#546—7112no—
662#546—7124no—
663#546—7112no—
664#546—7124no—
665#546—7112no—
666#546—7124no—
667#546—7112no—
668#546—7112no—
669#546—7124no—
670#546C2×D71112yescomplemented
671#536—713no—
672#536—713no—
673#536—716no—
674#536—716no—
675#536—7112no—
676#536—7112no—
677#536—713no—
678#536C2×D7113yescomplemented
679#535—713no—
680#535—713no—
681#535—716no—
682#535—716no—
683#535—7112no—
684#535—7112no—
685#535—713no—
686#535C2×D7113yescomplemented
687#532—713no—
688#532—713no—
689#532—713no—
690#532—713no—
691#532—713no—
692#532—713no—
693#532—7112no—
694#532—7112no—
695#532—713no—
696#532C2×D7113yescomplemented
697C2×C4⋊Q8—713no—
698C2×#127—713no—
699C2×#124—713no—
700C2×#124—713no—
701C2×#124—713no—
702C2×#124—716no—
703C2×#124—7112no—
704C2×#124—716no—
705C2×#124—716no—
706C2×#124—7112no—
707C2×#124—711no—
708C2×#124—7112no—
709C2×#124—713no—
710C2×#124C2×D7113yescomplemented
711C2×#123—7112no—
712C2×C22⋊Q8—7112no—
713C2×#121—7112no—
714C2×#121—7112no—
715C2×#120—7112no—
716C4×#41—711no—
717C4×#41—712no—
718C4×#41—716no—
719C4×#41—713no—
720C4×#41—713no—
721C4×#41C2×D7111yescharacteristic, complemented
722C2×C4×Q8—712no—
723C2×C4×D4—716no—
724C2×C4×D4—7112no—
725C2×#117—713no—
726C22×C22⋊C4—7112no—
727C22×C42—713no—
728C25—716no—
7292−1+4—28no—
7302−1+4—14216no—
7312−1+4—14224no—
7322−1+4—14248no—
7332−1+4—14224no—
7342−1+4—1428no—
735H(5,𝔽2)—28no—
736H(5,𝔽2)—14248no—
737H(5,𝔽2)—14224no—
738H(5,𝔽2)—14216no—
739H(5,𝔽2)—14224no—
740H(5,𝔽2)—1428no—
741C2×#41—7116no—
742C2×#41—711no—
743C2×#41—713no—
744C2×#41—712no—
745C2×#41—713no—
746C2×#41—716no—
747C2×#41—713no—
748C2×#41—716no—
749C2×#41—713no—
750C2×#41—716no—
751C2×#41—716no—
752C2×#41—713no—
753C2×#41—716no—
754C2×#41—7112no—
755C2×#41—713no—
756C2×#41—716no—
757C2×#41—713no—
758C2×#41—716no—
759C2×#41—716no—
760C2×#41—713no—
761C2×#41—716no—
762C2×#41—7112no—
763C2×#41—14224no—
764C2×#41—14224no—
765C2×#41—14248no—
766C2×#41—14216no—
767C2×#41C22×D7113yes—
768C2×#41C22×D7112yes—
769C2×#41C22×D7111yescharacteristic
770C2×#41C22×D7113yescomplemented
771C2×#41C22×D7116yescomplemented
772C22×Q8—711no—
773C22×Q8—716no—
774C22×Q8—713no—
775C22×Q8—711no—
776C22×Q8—716no—
777C22×Q8—716no—
778C22×Q8—716no—
779C22×Q8—712no—
780C22×Q8—716no—
781C22×Q8—713no—
782C22×Q8—716no—
783C22×Q8—14224no—
784C22×Q8—14216no—
785C22×Q8C22×D7113yescomplemented
786C22×Q8C22×D7112yescomplemented
787C22×D4—7112no—
788C22×D4—713no—
789C22×D4—716no—
790C22×D4—7112no—
791C22×D4—716no—
792C22×D4—716no—
793C22×D4—716no—
794C22×D4—713no—
795C22×D4—716no—
796C22×D4—716no—
797C22×D4—711no—
798C22×D4—7112no—
799C22×D4—716no—
800C22×D4—716no—
801C22×D4—713no—
802C22×D4—716no—
803C22×D4—14224no—
804C22×D4—14248no—
805C22×D4C22×D7113yes—
806C22×D4C22×D7116yes—
807C23×C4—716no—
808C23×C4—713no—
809C23×C4—716no—
810C23×C4—716no—
811C23×C4—716no—
812C4⋊Q8—713no—
813C4⋊Q8—713no—
814C4⋊Q8—7112no—
815C4⋊Q8—713no—
816C4⋊Q8C22×D7113yescomplemented
817#127—713no—
818#127—713no—
819#127—7112no—
820#127—713no—
821#127C22×D7113yescomplemented
822#124—713no—
823#124—716no—
824#124—7112no—
825#124—711no—
826#124—713no—
827#124—716no—
828#124—7112no—
829#124—711no—
830#124—7112no—
831#124—7124no—
832#124—7124no—
833#124—7124no—
834#124—714no—
835#124—713no—
836#124—716no—
837#124—7112no—
838#124—711no—
839#124C22×D7113yescomplemented
840#124C22×D7116yescomplemented
841#124C22×D71112yescomplemented
842#124C22×D7111yescharacteristic, complemented
843#123—7112no—
844#123—7112no—
845#123—7124no—
846#123—7124no—
847#123—7112no—
848#123C22×D71112yescomplemented
849C22⋊Q8—7112no—
850C22⋊Q8—7112no—
851C22⋊Q8—7124no—
852C22⋊Q8—7112no—
853C22⋊Q8—7124no—
854C22⋊Q8C22×D71112yescomplemented
855#121—7112no—
856#121—7112no—
857#121—7112no—
858#121—7112no—
859#121—7124no—
860#121—7112no—
861#121—7112no—
862#121—7112no—
863#121—7112no—
864#121—7112no—
865#121—7112no—
866#121—7124no—
867#121C22×D71112yescomplemented
868#121C22×D71112yescomplemented
869#120—7112no—
870#120—7124no—
871#120—7112no—
872#120—7112no—
873#120—7124no—
874#120C22×D71112yescomplemented
875C4×Q8—712no—
876C4×Q8—716no—
877C4×Q8—716no—
878C4×Q8C22×D7112yescomplemented
879C4×D4—716no—
880C4×D4—7112no—
881C4×D4—7112no—
882C4×D4—7112no—
883C4×D4—7112no—
884C4×D4—716no—
885C4×D4—7112no—
886C4×D4—7112no—
887C4×D4—7112no—
888C4×D4—7112no—
889C4×D4—716no—
890C4×D4—7112no—
891C4×D4C22×D7116yescomplemented
892C4×D4C22×D71112yescomplemented
893#117—713no—
894#117—716no—
895#117—716no—
896#117—716no—
897#117C22×D7113yescomplemented
898C2×C4⋊C4—716no—
899C2×C4⋊C4—7112no—
900C2×C22⋊C4—7112no—
901C2×C22⋊C4—7112no—
902C2×C22⋊C4—7112no—
903C2×C22⋊C4—7112no—
904C2×C22⋊C4—7124no—
905C2×C22⋊C4—7124no—
906C2×C22⋊C4—7124no—
907C2×C22⋊C4—716no—
908C2×C22⋊C4—714no—
909C2×C22⋊C4C22×D71112yescomplemented
910C2×C42—713no—
911C2×C42—716no—
912C2×C42—713no—
913C2×C42—716no—
914C2×C42—716no—
915C2×C42—713no—
916C2×C42—713no—
917C2×C42—711no—
918C2×C42C22×D7113yescomplemented
919C24—28424no—
920C24—7112no—
921C24—716no—
922C24—713no—
923C24—716no—
924C24—712no—
925C24—14224no—
926C24C23×D7116yes—
927#41—28no—
928#41—224no—
929#41—212no—
930#41—212no—
931#41—718no—
932#41—7124no—
933#41—7124no—
934#41—14224no—
935#41—14224no—
936#41—14248no—
937#41—14224no—
938#41—14224no—
939#41—14224no—
940#41—14212no—
941#41—14224no—
942#41—14212no—
943#41—14212no—
944#41—14212no—
945#41—14248no—
946#41—14224no—
947#41—14224no—
948#41—1428no—
949#41—14224no—
950#41—14212no—
951#41—14212no—
952#41D4×D7118yescomplemented
953C2×Q8—28no—
954C2×Q8—212no—
955C2×Q8—718no—
956C2×Q8—713no—
957C2×Q8—7112no—
958C2×Q8—716no—
959C2×Q8—716no—
960C2×Q8—713no—
961C2×Q8—712no—
962C2×Q8—711no—
963C2×Q8—14224no—
964C2×Q8—14224no—
965C2×Q8—14212no—
966C2×Q8—14224no—
967C2×Q8—14224no—
968C2×Q8—14224no—
969C2×Q8—1424no—
970C2×Q8—14224no—
971C2×Q8—1428no—
972C2×Q8—14212no—
973C2×Q8C23×D7116yes—
974C2×Q8C23×D7113yes—
975C2×Q8C23×D7111yescharacteristic
976C2×Q8C23×D7111yescharacteristic
977C2×D4—224no—
978C2×D4—212no—
979C2×D4—28424no—
980C2×D4—7112no—
981C2×D4—7112no—
982C2×D4—716no—
983C2×D4—7124no—
984C2×D4—716no—
985C2×D4—716no—
986C2×D4—716no—
987C2×D4—716no—
988C2×D4—7112no—
989C2×D4—716no—
990C2×D4—712no—
991C2×D4—7112no—
992C2×D4—713no—
993C2×D4—716no—
994C2×D4—716no—
995C2×D4—716no—
996C2×D4—713no—
997C2×D4—711no—
998C2×D4—14224no—
999C2×D4—14212no—
1000C2×D4—14224no—
1001C2×D4—14224no—
1002C2×D4—14224no—
1003C2×D4—1424no—
1004C2×D4—14224no—
1005C2×D4—14248no—
1006C2×D4—14224no—
1007C2×D4—14224no—
1008C2×D4—14224no—
1009C2×D4—14248no—
1010C2×D4—14224no—
1011C2×D4—14212no—
1012C2×D4C23×D7116yes—
1013C2×D4C23×D7116yes—
1014C2×D4C23×D7116yes—
1015C2×D4C23×D7113yes—
1016C2×D4C23×D7111yescharacteristic
1017C2×D4C23×D71112yes—
1018C2×D4C23×D7113yes—
1019C22×C4—28412no—
1020C22×C4—716no—
1021C22×C4—716no—
1022C22×C4—716no—
1023C22×C4—713no—
1024C22×C4—7124no—
1025C22×C4—711no—
1026C22×C4—713no—
1027C22×C4—713no—
1028C22×C4—713no—
1029C22×C4—716no—
1030C22×C4—716no—
1031C22×C4—716no—
1032C22×C4—712no—
1033C22×C4—716no—
1034C22×C4—716no—
1035C22×C4—7112no—
1036C22×C4—712no—
1037C22×C4—716no—
1038C22×C4—716no—
1039C22×C4—716no—
1040C22×C4—716no—
1041C22×C4—14224no—
1042C22×C4—14224no—
1043C22×C4—14224no—
1044C22×C4C23×D7116yes—
1045C22×C4C23×D7116yes—
1046C22×C4C23×D7116yes—
1047C22×C4C23×D7116yes—
1048C22×C4C23×D7113yes—
1049C4⋊C4—7112no—
1050C4⋊C4—7112no—
1051C4⋊C4—7112no—
1052C4⋊C4—716no—
1053C4⋊C4—7112no—
1054C4⋊C4C23×D7116yes—
1055C4⋊C4C23×D71112yes—
1056C22⋊C4—7112no—
1057C22⋊C4—7124no—
1058C22⋊C4—716no—
1059C22⋊C4—714no—
1060C22⋊C4—7112no—
1061C22⋊C4—7112no—
1062C22⋊C4—7124no—
1063C22⋊C4—7124no—
1064C22⋊C4—7112no—
1065C22⋊C4—714no—
1066C22⋊C4—714no—
1067C22⋊C4C23×D71112yes—
1068C22⋊C4C23×D71124yes—
1069C22⋊C4C23×D7116yes—
1070C22⋊C4C23×D7114yes—
1071C42—712no—
1072C42—711no—
1073C42—716no—
1074C42—713no—
1075C42—716no—
1076C42—716no—
1077C42—716no—
1078C42C23×D7111yescharacteristic
1079C42C23×D7113yes—
1080C42C23×D7116yes—
1081C23—212no—
1082C23—412no—
1083C23—28412no—
1084C23—28424no—
1085C23—56848no—
1086C23—711no—
1087C23—7112no—
1088C23—713no—
1089C23—716no—
1090C23—712no—
1091C23—1424no—
1092C23—14212no—
1093C23—1428no—
1094C23—14224no—
1095C23—14224no—
1096C23—14212no—
1097C23—14212no—
1098C23C24×D7116yes—
1099C23C24×D7112yes—
1100C23C24×D7113yes—
1101Q8—212no—
1102Q8—26no—
1103Q8—22no—
1104Q8—7112no—
1105Q8—14212no—
1106Q8—14224no—
1107Q8—1424no—
1108Q8—14212no—
1109Q8—1426no—
1110Q8—1422no—
1111Q8C2×D4×D7114yes—
1112D4—212no—
1113D4—212no—
1114D4—212no—
1115D4—26no—
1116D4—22no—
1117D4—412no—
1118D4—28412no—
1119D4—28412no—
1120D4—28412no—
1121D4—7124no—
1122D4—7112no—
1123D4—14212no—
1124D4—14212no—
1125D4—14212no—
1126D4—14224no—
1127D4—1424no—
1128D4—14212no—
1129D4—14212no—
1130D4—14212no—
1131D4—14212no—
1132D4—14212no—
1133D4—1426no—
1134D4—1422no—
1135D4C2×D4×D71112yes—
1136C2×C4—212no—
1137C2×C4—212no—
1138C2×C4—212no—
1139C2×C4—46no—
1140C2×C4—2846no—
1141C2×C4—2846no—
1142C2×C4—2846no—
1143C2×C4—7112no—
1144C2×C4—711no—
1145C2×C4—713no—
1146C2×C4—714no—
1147C2×C4—7112no—
1148C2×C4—7112no—
1149C2×C4—7112no—
1150C2×C4—712no—
1151C2×C4—716no—
1152C2×C4—716no—
1153C2×C4—712no—
1154C2×C4—14212no—
1155C2×C4—14212no—
1156C2×C4—1424no—
1157C2×C4—14212no—
1158C2×C4—1424no—
1159C2×C4—14212no—
1160C2×C4—14224no—
1161C2×C4—14212no—
1162C2×C4—14212no—
1163C2×C4—14212no—
1164C2×C4—14212no—
1165C2×C4—14212no—
1166C2×C4C2×D4×D71112yes—
1167C2×C4C24×D7112yes—
1168C2×C4C24×D7116yes—
1169C2×C4C24×D7116yes—
1170C2×C4C24×D7112yes—
1171C2×C4C24×D7111yescharacteristic
1172C2×C4C24×D7113yes—
1173C22—26no—
1174C22—22no—
1175C22—26no—
1176C22—24no—
1177C22—212no—
1178C22—812no—
1179C22—28424no—
1180C22—2848no—
1181C22—56812no—
1182C22—56824no—
1183C22—712no—
1184C22—714no—
1185C22—716no—
1186C22—14224no—
1187C22—1422no—
1188C22—1426no—
1189C22—1424no—
1190C22—14212no—
1191C22—1426no—
1192C22C22×D4×D7116yes—
1193C22C25×D7111yescharacteristic
1194C4—22no—
1195C4—26no—
1196C4—22no—
1197C4—26no—
1198C4—712no—
1199C4—716no—
1200C4—1422no—
1201C4—1426no—
1202C4—1422no—
1203C4—1426no—
1204C4C22×D4×D7116yes—
1205C4C22×D4×D7112yes—
1206C2—26no—
1207C2—46no—
1208C2—42no—
1209C2—2846no—
1210C2—2842no—
1211C2—714no—
1212C2—1426no—
1213C2C23×D4×D7111yescharacteristic
1214C2#585×D7112yes—
subgroupG/H
center, FrattiniC22C25×D71
commutator, socle, cosocleC22×C71C26
FittingC71×#3500C2
hypercenter#3500D71
hypocenterC71C2×#3500
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C22 ◁ #3500

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×2−1+4×D71C2semidirect
2. C2×H(5,𝔽2)×D71C2semidirect
3. #22602134C2semidirect
4. #22602133C2semidirect
5. #22602132C2semidirect
6. #22602131C2semidirect
7. #22602130C2semidirect
8. #22602129C2semidirect
9. #22602128C2semidirect
10. #22602127C2semidirect
11. #22602126C2semidirect
12. #548×D71C2semidirect
13. #546×D71C2semidirect
14. #536×D71C2semidirect
15. #535×D71C2semidirect
16. #532×D71C2semidirect
17. C2×#124×D71C2semidirect
18. C4×#41×D71C2semidirect
19. C71×#3500C2semidirect
20. C2×#14556176C22semidirect
21. C2×#14556176C22semidirect
22. C2×#14556175C22semidirect
23. C2×#14556175C22semidirect
24. C2×#14556175C22semidirect
26. C2×#14556174C22semidirect
27. C2×#14556174C22semidirect
28. C2×#14556174C22semidirect
29. C2×#14556173C22semidirect
30. C2×#14556173C22semidirect
35. C2×#41×D71C22semidirect
36. C2×#41×D71C22semidirect
37. C22×Q8×D71C22semidirect
38. C22×Q8×D71C22semidirect
41. #17986661C22semidirect
42. #17986660C22semidirect
43. #17986659C22semidirect
44. #17986658C22semidirect
45. #17986657C22semidirect
46. #17986656C22semidirect
47. #17986655C22semidirect
48. #17986646C22semidirect
49. #17986645C22semidirect
50. #17986644C22semidirect
51. #17986643C22semidirect
52. #17986642C22semidirect
53. #17986641C22semidirect
54. #17986640C22semidirect
55. #17986639C22semidirect
56. #17986638C22semidirect
57. #17986637C22semidirect
58. #17986636C22semidirect
59. #17986575C22semidirect
60. #17986574C22semidirect
61. #17986573C22semidirect
62. #17986572C22semidirect
63. #17986571C22semidirect
64. #17986570C22semidirect
65. #17986569C22semidirect
66. #17986568C22semidirect
67. #17986567C22semidirect
68. #17986566C22semidirect
69. #17986565C22semidirect
70. #17986564C22semidirect
71. #17986563C22semidirect
72. #17986562C22semidirect
73. #17986550C22semidirect
74. #17986549C22semidirect
75. #17986548C22semidirect
76. #17986548C22semidirect
77. #17986547C22semidirect
78. #17986546C22semidirect
79. #17986545C22semidirect
80. #17986545C22semidirect
81. #17986544C22semidirect
82. C4⋊Q8×D71C22semidirect
83. #127×D71C22semidirect
84. C2×#14556117C22semidirect
85. C2×#14556116C22semidirect
86. C2×#14556115C22semidirect
87. C2×#14556114C22semidirect
88. #124×D71C22semidirect
89. #124×D71C22semidirect
90. #124×D71C22semidirect
91. #124×D71C22semidirect
92. #124×D71C22semidirect
93. #124×D71C22semidirect
94. #124×D71C22semidirect
95. #123×D71C22semidirect
96. C22⋊Q8×D71C22semidirect
97. #121×D71C22semidirect
98. #121×D71C22semidirect
99. #120×D71C22semidirect
100. #41×Dic71C22semidirect
101. C4×#11765866C22semidirect
102. C4×#11765865C22semidirect
103. #17986467C22semidirect
104. C4×#11765864C22semidirect
105. C4×Q8×D71C22semidirect
106. C4×D4×D71C22semidirect
107. C4×D4×D71C22semidirect
108. #117×D71C22semidirect
109. C2×C22⋊C4×D71C22semidirect
110. C2×C42×D71C22semidirect
111. C2×2−1+4×C71C22semidirect
112. C2×H(5,𝔽2)×C71C22semidirect
113. #548×C71C22semidirect
114. #546×C71C22semidirect
115. #536×C71C22semidirect
116. #535×C71C22semidirect
117. #532×C71C22semidirect
118. C2×#124×C71C22semidirect
119. C4×#41×C71C22semidirect
134. C2×#11765866C23semidirect
135. C2×#11765866C23semidirect
140. C2×#11765865C23semidirect
141. C2×#11765865C23semidirect
142. C2×#11765865C23semidirect
143. C2×#11765865C23semidirect
148. C2×#11765864C23semidirect
149. C2×#11765864C23semidirect
150. C2×#11765864C23semidirect
151. C2×#11765864C23semidirect
156. #41×D71D4semidirect
157. C22×Dic142C23semidirect
158. C22×Dic142C23semidirect
159. C22×Dic142C23semidirect
166. C2×Q8×D71C23semidirect
167. C2×Q8×D71C23semidirect
168. C2×Q8×D71C23semidirect
169. C2×Q8×D71C23semidirect
193. #14556128C23semidirect
194. #14556127C23semidirect
195. #14556126C23semidirect
196. #14556126C23semidirect
197. #14556125C23semidirect
198. #14556124C23semidirect
199. #14556124C23semidirect
200. #14556124C23semidirect
201. #14556117C23semidirect
202. #14556117C23semidirect
203. #14556117C23semidirect
204. #14556117C23semidirect
205. #14556116C23semidirect
206. #14556116C23semidirect
207. #14556116C23semidirect
208. #14556116C23semidirect
209. #14556115C23semidirect
210. #14556115C23semidirect
211. #14556115C23semidirect
212. #14556115C23semidirect
213. #14556114C23semidirect
214. #14556114C23semidirect
215. #14556114C23semidirect
216. #14556114C23semidirect
217. #14556114C23semidirect
218. #14556113C23semidirect
219. #14556112C23semidirect
220. #14556111C23semidirect
221. #14556110C23semidirect
222. #14556109C23semidirect
223. #14556108C23semidirect
224. #14556107C23semidirect
225. #14556106C23semidirect
226. #14556105C23semidirect
227. #14556104C23semidirect
228. #14556103C23semidirect
229. #14556103C23semidirect
230. #14556102C23semidirect
231. #14556102C23semidirect
232. #14556101C23semidirect
233. #14556101C23semidirect
234. #14556101C23semidirect
235. #14556100C23semidirect
236. #14556100C23semidirect
237. #14556100C23semidirect
238. #14556099C23semidirect
239. #14556099C23semidirect
240. #14556098C23semidirect
241. #14556098C23semidirect
242. #14556097C23semidirect
243. #14556096C23semidirect
244. #14556096C23semidirect
245. Q8×Dic71C23semidirect
246. C4×Dic142C23semidirect
247. #14556093C23semidirect
248. C4×D284C23semidirect
249. C4×D284C23semidirect
250. D4×Dic71C23semidirect
251. D4×Dic71C23semidirect
252. #14556090C23semidirect
253. #14556090C23semidirect
254. C4×C22⋊D71C23semidirect
255. C4×C22⋊D71C23semidirect
256. C4×C22⋊D71C23semidirect
257. (C22⋊D71)⋊C4C23semidirect
258. (C22⋊D71)⋊C4C23semidirect
259. (C22⋊D71)⋊C4C23semidirect
260. #14556087C23semidirect
261. #14556086C23semidirect
262. #14556085C23semidirect
263. #14556084C23semidirect
266. C2×C22⋊Dic71C23semidirect
267. C2×(C2×D71)⋊C4C23semidirect
268. C2×(C2×D71)⋊C4C23semidirect
273. C22⋊C4×D71C23semidirect
274. C22⋊C4×D71C23semidirect
275. C2×C4×Dic71C23semidirect
276. C2×C4×Dic71C23semidirect
280. C42×D71C23semidirect
281. C42×D71C23semidirect
282. C42×D71C23semidirect
288. C2×#41×C71C23semidirect
289. C2×#41×C71C23semidirect
290. C22×Q8×C71C23semidirect
291. C22×Q8×C71C23semidirect
294. C4⋊Q8×C71C23semidirect
295. #127×C71C23semidirect
296. #124×C71C23semidirect
297. #124×C71C23semidirect
298. #124×C71C23semidirect
299. #124×C71C23semidirect
300. #123×C71C23semidirect
301. C22⋊Q8×C71C23semidirect
302. #121×C71C23semidirect
303. #121×C71C23semidirect
304. #120×C71C23semidirect
305. C4×Q8×C71C23semidirect
306. C4×D4×C71C23semidirect
307. C4×D4×C71C23semidirect
308. #117×C71C23semidirect
309. C2×C22⋊C4×C71C23semidirect
310. C2×C42×C71C23semidirect
322. #11765866C2×D4semidirect
330. #11765865C2×D4semidirect
338. #11765864C2×D4semidirect
443. #41×C71C2×D4semidirect
607. D71#3500direct (N × H)
619. #3500D71direct (N × H)
627. C71C2×#3500semidirect
634. C2×2−1+4C2×D71semidirect
641. C2×H(5,𝔽2)C2×D71semidirect
658. #548C2×D71semidirect
670. #546C2×D71semidirect
678. #536C2×D71semidirect
686. #535C2×D71semidirect
696. #532C2×D71semidirect
710. C2×#124C2×D71semidirect
721. C4×#41C2×D71semidirect
770. C2×#41C22×D71semidirect
771. C2×#41C22×D71semidirect
785. C22×Q8C22×D71semidirect
786. C22×Q8C22×D71semidirect
816. C4⋊Q8C22×D71semidirect
821. #127C22×D71semidirect
839. #124C22×D71semidirect
840. #124C22×D71semidirect
841. #124C22×D71semidirect
842. #124C22×D71semidirect
848. #123C22×D71semidirect
854. C22⋊Q8C22×D71semidirect
867. #121C22×D71semidirect
868. #121C22×D71semidirect
874. #120C22×D71semidirect
878. C4×Q8C22×D71semidirect
891. C4×D4C22×D71semidirect
892. C4×D4C22×D71semidirect
897. #117C22×D71semidirect
909. C2×C22⋊C4C22×D71semidirect
918. C2×C42C22×D71semidirect
952. #41D4×D71semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×2−1+4×D712
C2×H(5,𝔽2)×D712
#226021342
#226021332
#226021322
#226021312
#226021302
#226021292
#226021282
#226021272
#226021262
#548×D712
#546×D712
#536×D712
#535×D712
#532×D712
C2×#124×D712
C4×#41×D712
C71×#35002
C2×#350071