Finite Group Databasebeta

← C2×#22601415 #32878468

Subgroups — C2×#22601415 #32878468

Order 18176.

1938 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986722C211yesmaximal, characteristic, complemented
2#22601415C2116yesmaximal, direct product factor
3C2×#17986394C211yesmaximal, characteristic, complemented
4C2×#17986391C211yesmaximal, characteristic, complemented
5C2×#17986381C211yesmaximal, characteristic
6C2×#17986221C211yesmaximal, characteristic, complemented
7C2×#17986218C211yesmaximal, characteristic, complemented
8C2×#17986209C211yesmaximal, characteristic, complemented
9C2×#17986206C211yesmaximal, characteristic, complemented
10C2×#17986214C211yesmaximal, characteristic
11C2×#17986211C211yesmaximal, characteristic
12C2×#17986130C211yesmaximal, characteristic, complemented
13C2×#17986099C211yesmaximal, characteristic, complemented
14C2×#17986097C211yesmaximal, characteristic, complemented
15C2×C4×#11765855C211yesmaximal, characteristic, complemented
16C2×#556×C71C211yesmaximal, characteristic, complemented
17C22×#11765855C2211yescharacteristic
18C22×#11765855C2211yescharacteristic
19C22×#11765855C2211yescharacteristic
20C22×#11765855C2211yescharacteristic
21C22×#11765853C2211yescharacteristic
22C22×#11765853C2211yescharacteristic
23C22×#11765852C2211yescharacteristic
24C22×#11765852C2211yescharacteristic
25C22×#11765850C2211yescharacteristic
26#17986722—24no—
27#17986722C2218yescomplemented
28C2×#14556128C2211yescharacteristic
29C2×#14556123—21no—
30C2×#14556123—21no—
31C2×#14556116C2211yescharacteristic
32C2×#14556116C2211yescharacteristic
33C2×#14556104—21no—
34C2×C4×Dic142C2211yescharacteristic
35C2×C4×Dic142C2211yescharacteristic
36C2×C4×D284C2211yescharacteristic
37C2×#14556086—21no—
38#17986394C2218yescomplemented
39#17986391C2218yescomplemented
40#17986381C2218yes—
41#17986221C2218yescomplemented
42#17986218C2218yescomplemented
43#17986214C2218yes—
44#17986211C2218yes—
45#17986209C2218yescomplemented
46#17986206C2218yescomplemented
47#17986130C2218yescomplemented
48#17986099C2218yescomplemented
49#17986097C2218yescomplemented
50C4×#11765855C2218yescomplemented
51C2×#14556061C2211yescharacteristic
52C2×C4⋊(C71⋊C8)C2211yescharacteristic
53C2×C4⋊(C71⋊C8)C2211yescharacteristic
54C2×C4⋊(C71⋊C8)C2211yescharacteristic
55C2×#14556052C2211yescharacteristic
56C2×#14556052C2211yescharacteristic
57C2×#14556051C2211yescharacteristic
58C2×#14556051C2211yescharacteristic
59C2×#14556049C2211yescharacteristic
60C2×#14556048C2211yescharacteristic
61C2×#14556039C2211yescharacteristic
62C2×#14556039C2211yescharacteristic
63C2×C4×C71⋊C8C2211yescharacteristic
64#556×C71—24no—
65#556×C71C2218yescomplemented
66C2×C4⋊Q8×C71C2211yescharacteristic
67C2×#126×C71—21no—
68C2×#126×C71—21no—
69C2×#124×C71C2211yescharacteristic
70C2×#124×C71C2211yescharacteristic
71C2×C22⋊Q8×C71—21no—
72C2×C4×Q8×C71C2211yescharacteristic
73C2×C4×Q8×C71C2211yescharacteristic
74C2×C4×Q8×C71C2211yescharacteristic
75C2×C4×D4×C71C2211yescharacteristic
76C2×#117×C71—21no—
77C22×Dic142C2311yescharacteristic
78C22×Dic142C2311yescharacteristic
79C22×D284C2311yescharacteristic
80C22×C4×D71—21no—
81C2×#11765855—24no—
82C2×#11765855—42no—
83C2×#11765855—42no—
84C2×#11765855—42no—
85C2×#11765855C2314yes—
86C2×#11765855C2314yes—
87C2×#11765855C2314yes—
88C2×#11765855C2314yes—
89C2×#11765853—24no—
90C2×#11765853—42no—
91C2×#11765853C2314yes—
92C2×#11765853C2314yes—
93C2×#11765852—24no—
94C2×#11765852—42no—
95C2×#11765852C2314yes—
96C2×#11765852C2314yes—
97C2×#11765850—42no—
98C2×#11765850C2314yes—
99C22×C71⋊C8C2311yescharacteristic
100C22×C71⋊C8C2311yescharacteristic
101C22×C71⋊C8C2311yescharacteristic
102C22×C71⋊C8C2311yescharacteristic
103#14556128—22no—
104#14556128C2314yes—
105#14556123—28no—
106#14556123—28no—
107#14556116—22no—
108#14556116—22no—
109#14556116C2314yes—
110#14556116C2314yes—
111#14556104—28no—
112C4×Dic142—22no—
113C4×Dic142—22no—
114C4×Dic142C2314yes—
115C4×Dic142C2314yes—
116C4×D284—22no—
117C4×D284C2314yes—
118#14556086—28no—
119C2×C4⋊Dic71—21no—
120C2×C4⋊Dic71—21no—
121C2×C4⋊Dic71C2311yescharacteristic
122C2×Dic71⋊C4—21no—
123C2×Dic71⋊C4—21no—
124C2×(C2×D71)⋊C4—21no—
125C2×(C2×D71)⋊C4—21no—
126C2×(C2×D71)⋊C4—21no—
127C2×(C2×D71)⋊C4—21no—
128C2×(C2×D71)⋊C4—21no—
129C2×C4×Dic71—21no—
130C2×C4×Dic71—21no—
131#14556061C2314yes—
132C4⋊(C71⋊C8)C2314yes—
133C4⋊(C71⋊C8)C2314yes—
134C4⋊(C71⋊C8)C2314yes—
135#14556052C2314yes—
136#14556052C2314yes—
137#14556051C2314yes—
138#14556051C2314yes—
139#14556049C2314yes—
140#14556048C2314yes—
141#14556039C2314yes—
142#14556039C2314yes—
143C4×C71⋊C8C2314yes—
144C22×Q8×C71D411yescharacteristic
145C22×Q8×C71C2311yescharacteristic
146C22×Q8×C71C2311yescharacteristic
147C22×D4×C71C2311yescharacteristic
148C23×C4×C71—21no—
149C4⋊Q8×C71—22no—
150C4⋊Q8×C71C2314yes—
151#126×C71—28no—
152#126×C71—28no—
153#124×C71—22no—
154#124×C71—22no—
155#124×C71C2314yes—
156#124×C71C2314yes—
157C22⋊Q8×C71—28no—
158C4×Q8×C71—22no—
159C4×Q8×C71—22no—
160C4×Q8×C71D414yes—
161C4×Q8×C71C2314yes—
162C4×Q8×C71C2314yes—
163C4×Q8×C71C2314yes—
164C4×D4×C71—22no—
165C4×D4×C71C2314yes—
166#117×C71—28no—
167C2×C4⋊C4×C71—21no—
168C2×C4⋊C4×C71—21no—
169C2×C4⋊C4×C71—21no—
170C2×C4⋊C4×C71—21no—
171C2×C4⋊C4×C71D411yescharacteristic
172C2×C4⋊C4×C71D411yescharacteristic
173C2×C4⋊C4×C71D411yescharacteristic
174C2×C4⋊C4×C71C2311yescharacteristic
175C2×C22⋊C4×C71—21no—
176C2×C22⋊C4×C71—21no—
177C2×C22⋊C4×C71—21no—
178C2×C22⋊C4×C71—21no—
179C2×C22⋊C4×C71—21no—
180C2×C42×C71—21no—
181C2×C42×C71—21no—
182C2×C42×C71C2311yescharacteristic
183C2×C42×C71C2311yescharacteristic
184C2×C42×C71C2311yescharacteristic
185C23×D71—21no—
186C2×Dic142—22no—
187C2×Dic142—22no—
188C2×Dic142—22no—
189C2×Dic142—22no—
190C2×Dic142—21no—
191C2×Dic142—21no—
192C2×Dic142C2412yes—
193C2×Dic142C2412yes—
194C2×D284—22no—
195C2×D284—22no—
196C2×D284—21no—
197C2×D284C2412yes—
198C22×Dic71—21no—
199C22×Dic71—21no—
200C22×Dic71—21no—
201C2×C4×D71—24no—
202C2×C4×D71—44no—
203#11765855—28no—
204#11765855—44no—
205#11765855—44no—
206#11765855—44no—
207#11765853—28no—
208#11765853—44no—
209#11765852—28no—
210#11765852—44no—
211#11765850—44no—
212C2×C71⋊C8—22no—
213C2×C71⋊C8—22no—
214C2×C71⋊C8—22no—
215C2×C71⋊C8#4114yes—
216C2×C71⋊C8C2412yes—
217C2×C71⋊C8C2412yes—
218C2×C71⋊C8C2412yes—
219C2×C71⋊C8C2412yes—
220C4⋊Dic71—24no—
221C4⋊Dic71—24no—
222C4⋊Dic71—21no—
223C4⋊Dic71C2412yes—
224Dic71⋊C4—24no—
225Dic71⋊C4—24no—
226(C2×D71)⋊C4—24no—
227(C2×D71)⋊C4—24no—
228(C2×D71)⋊C4—24no—
229(C2×D71)⋊C4—24no—
230(C2×D71)⋊C4—24no—
231C4×Dic71—24no—
232C4×Dic71—24no—
233C24×C71—21no—
234C2×Q8×C71—21no—
235C2×Q8×C71—21no—
236C2×Q8×C71—22no—
237C2×Q8×C71—22no—
238C2×Q8×C71—22no—
239C2×Q8×C71—22no—
240C2×Q8×C71—42no—
241C2×Q8×C71C2×D414yes—
242C2×Q8×C71C2412yes—
243C2×Q8×C71C2412yes—
244C2×D4×C71—21no—
245C2×D4×C71—22no—
246C2×D4×C71—22no—
247C2×D4×C71C2412yes—
248C22×C4×C71—21no—
249C22×C4×C71—21no—
250C22×C4×C71—21no—
251C22×C4×C71—24no—
252C22×C4×C71—44no—
253C22×C4×C71C2×D411yescharacteristic
254C22×C4×C71C2×D411yescharacteristic
255C22×C4×C71C2×D411yescharacteristic
256C22×C4×C71C2×D411yescharacteristic
257C22×C4×C71C2×D411yescharacteristic
258C22×C4×C71C2×D411yescharacteristic
259C22×C4×C71C2411yescharacteristic
260C4⋊C4×C71—24no—
261C4⋊C4×C71—24no—
262C4⋊C4×C71—24no—
263C4⋊C4×C71—24no—
264C4⋊C4×C71—21no—
265C4⋊C4×C71C2×D414yes—
266C4⋊C4×C71C2×D414yes—
267C4⋊C4×C71C2×D414yes—
268C4⋊C4×C71C2412yes—
269C22⋊C4×C71—24no—
270C22⋊C4×C71—24no—
271C22⋊C4×C71—24no—
272C22⋊C4×C71—24no—
273C22⋊C4×C71—24no—
274C42×C71—24no—
275C42×C71—24no—
276C42×C71C2×D412yes—
277C42×C71C2×D412yes—
278C42×C71C2×D412yes—
279C42×C71C2412yes—
280C42×C71C2412yes—
281C42×C71C2412yes—
282C23×C71—22no—
283C23×C71—42no—
284C23×C71—42no—
285C23×C71—42no—
286C23×C71C22×D411yescharacteristic
287C22×D71—22no—
288C22×D71—42no—
289C22×D71—42no—
290C22×D71—42no—
291Q8×C71—22no—
292Q8×C71—22no—
293Q8×C71—22no—
294Q8×C71—22no—
295Q8×C71—44no—
296Q8×C71—42no—
297Q8×C71—42no—
298D4×C71—22no—
299D4×C71—22no—
300D4×C71—42no—
301C2×C4×C71—22no—
302C2×C4×C71—22no—
303C2×C4×C71—22no—
304C2×C4×C71—22no—
305C2×C4×C71—22no—
306C2×C4×C71—22no—
307C2×C4×C71—22no—
308C2×C4×C71—22no—
309C2×C4×C71—22no—
310C2×C4×C71—48no—
311C2×C4×C71—42no—
312C2×C4×C71—42no—
313C2×C4×C71—42no—
314C2×C4×C71C22×D412yes—
315C2×C4×C71C22×D412yes—
316C2×C4×C71C22×D412yes—
317C2×C4×C71C22×D412yes—
318C2×C4×C71C22×D412yes—
319C2×C4×C71C22×D412yes—
320C2×C4×C71C22×D411yescharacteristic
321C2×C4×C71C2×#4112yes—
322C2×C4×C71H(5,𝔽2)12yes—
323C2×C4×C71C2511yescharacteristic
324C2×Dic71—22no—
325C2×Dic71—22no—
326C2×Dic71—22no—
327C2×Dic71—42no—
328C2×Dic71—42no—
329C2×Dic71—42no—
330D284—22no—
331D284—22no—
332D284—42no—
333C4×D71—48no—
334Dic142—22no—
335Dic142—22no—
336Dic142—22no—
337Dic142—22no—
338Dic142—42no—
339Dic142—42no—
340C71⋊C8—22no—
341C71⋊C8—22no—
342C71⋊C8—22no—
343C71⋊C8C2×#4114yes—
344C22×C71—42no—
345C22×C71—42no—
346C22×C71—42no—
347C22×C71—84no—
348C22×C71#55012yes—
349C22×C71#57512yes—
350C22×C71#57812yes—
351C22×C71C23×D411yescharacteristic
352C2×D71—42no—
353C2×D71—42no—
354C2×D71—42no—
355C2×D71—84no—
356C4×C71—22no—
357C4×C71—22no—
358C4×C71—22no—
359C4×C71—22no—
360C4×C71—22no—
361C4×C71—22no—
362C4×C71—42no—
363C4×C71—42no—
364C4×C71—42no—
365C4×C71#55012yes—
366C4×C71C22×#4111yescharacteristic
367C4×C71C2×H(5,𝔽2)11yescharacteristic
368Dic71—42no—
369Dic71—42no—
370Dic71—42no—
371C2×#3402—711nomaximal, Sylow
372C2×C71—82no—
373C2×C71#340214yescomplemented
374C2×C71C2×#55011yescharacteristic
375C2×C71C2×#57511yescharacteristic
376C2×C71C2×#57811yescharacteristic
377D71—82no—
378C2×#556—711no—
379C2×#556D7111yescharacteristic, complemented
380#3402—7116no—
381C2×#497—711no—
382C2×#497—711no—
383C2×#495—711no—
384C2×#464—711no—
385C2×#464—711no—
386C2×#462—711no—
387C2×#462—711no—
388C2×#463—711no—
389C2×#463—711no—
390C2×#446—711no—
391C2×#440—711no—
392C2×#440—711no—
393C2×C4×Q16—711no—
394C71C2×#340211yescharacteristic, complemented, Sylow
395C22×Q16—711no—
396C22×Q16—711no—
397C22×Q16—711no—
398C22×Q16—711no—
399C22×SD16—711no—
400C22×SD16—711no—
401C22×SD16—711no—
402C22×SD16—711no—
403C22×D8—711no—
404#556—24no—
405#556—718no—
406#556—1424no—
407#556C2×D7118yescomplemented
408C2×C4⋊Q8—711no—
409C2×C4⋊Q8C2×D7111yescharacteristic
410C2×#126—21no—
411C2×#126—21no—
412C2×#126—1421no—
413C2×#126—1421no—
414C2×#124—711no—
415C2×#124—711no—
416C2×#124C2×D7111yescharacteristic
417C2×#124C2×D7111yescharacteristic
418C2×C22⋊Q8—21no—
419C2×C22⋊Q8—1421no—
420C2×C4×Q8—711no—
421C2×C4×Q8—711no—
422C2×C4×Q8C2×D7111yescharacteristic
423C2×C4×Q8C2×D7111yescharacteristic
424C2×C4×Q8C2×D7111yescharacteristic
425C2×C4×D4—711no—
426C2×C4×D4C2×D7111yescharacteristic
427C2×#117—21no—
428C2×#117—1421no—
429#497—718no—
430#497—718no—
431#495—718no—
432#464—718no—
433#464—718no—
434#463—718no—
435#463—718no—
436#462—718no—
437#462—718no—
438#446—718no—
439#440—718no—
440#440—718no—
441C4×Q16—718no—
442C2×#107—711no—
443C2×C4⋊C8—711no—
444C2×C4⋊C8—711no—
445C2×C4⋊C8—711no—
446C2×#103—711no—
447C2×#103—711no—
448C2×#103—711no—
449C2×#103—711no—
450C2×#102—711no—
451C2×#102—711no—
452C2×#97—711no—
453C2×#97—711no—
454C2×C4×C8—711no—
455C22×Q8—711no—
456C22×Q8—711no—
457C22×Q8C22⋊D7111yescharacteristic
458C22×Q8C22×D7111yescharacteristic
459C22×Q8C22×D7111yescharacteristic
460C22×D4—711no—
461C22×D4C22×D7111yescharacteristic
462C23×C4—21no—
463C23×C4—1421no—
464C2×Q16—2842no—
465C2×Q16—2842no—
466C2×Q16—2842no—
467C2×Q16—714no—
468C2×Q16—714no—
469C2×Q16—714no—
470C2×Q16—714no—
471C2×Q16—1424no—
472C2×SD16—2842no—
473C2×SD16—2842no—
474C2×SD16—714no—
475C2×SD16—714no—
476C2×SD16—714no—
477C2×SD16—714no—
478C2×SD16—1424no—
479C2×SD16—1424no—
480C2×D8—2842no—
481C2×D8—714no—
482C22×C8—711no—
483C22×C8—711no—
484C22×C8—711no—
485C22×C8—711no—
486C4⋊Q8—22no—
487C4⋊Q8—714no—
488C4⋊Q8—1422no—
489C4⋊Q8C22×D7114yes—
490#126—28no—
491#126—28no—
492#126—1428no—
493#126—1428no—
494#124—22no—
495#124—22no—
496#124—714no—
497#124—714no—
498#124—1422no—
499#124—1422no—
500#124C22×D7114yes—
501#124C22×D7114yes—
502C22⋊Q8—28no—
503C22⋊Q8—1428no—
504C4×Q8—22no—
505C4×Q8—22no—
506C4×Q8—714no—
507C4×Q8—714no—
508C4×Q8—1422no—
509C4×Q8—1422no—
510C4×Q8C22⋊D7114yes—
511C4×Q8C22×D7114yes—
512C4×Q8C22×D7114yes—
513C4×Q8C22×D7114yes—
514C4×D4—22no—
515C4×D4—714no—
516C4×D4—1422no—
517C4×D4C22×D7114yes—
518#117—28no—
519#117—1428no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4—21no—
524C2×C4⋊C4—711no—
525C2×C4⋊C4—1421no—
526C2×C4⋊C4—1421no—
527C2×C4⋊C4—1421no—
528C2×C4⋊C4—1421no—
529C2×C4⋊C4C22⋊D7111yescharacteristic
530C2×C4⋊C4C22⋊D7111yescharacteristic
531C2×C4⋊C4C22⋊D7111yescharacteristic
532C2×C4⋊C4C22×D7111yescharacteristic
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—1421no—
539C2×C22⋊C4—1421no—
540C2×C22⋊C4—1421no—
541C2×C22⋊C4—1421no—
542C2×C22⋊C4—1421no—
543C2×C42—21no—
544C2×C42—21no—
545C2×C42—1421no—
546C2×C42—1421no—
547C2×C42C22×D7111yescharacteristic
548C2×C42C22×D7111yescharacteristic
549C2×C42C22×D7111yescharacteristic
550#107—714no—
551C4⋊C8—714no—
552C4⋊C8—714no—
553C4⋊C8—714no—
554#103—714no—
555#103—714no—
556#103—714no—
557#103—714no—
558#102—714no—
559#102—714no—
560#97—714no—
561#97—714no—
562C4×C8—714no—
563C24—21no—
564C24—1421no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—22no—
568C2×Q8—22no—
569C2×Q8—22no—
570C2×Q8—22no—
571C2×Q8—42no—
572C2×Q8—712no—
573C2×Q8—712no—
574C2×Q8—1422no—
575C2×Q8—1422no—
576C2×Q8—1422no—
577C2×Q8—1422no—
578C2×Q8—1421no—
579C2×Q8—1421no—
580C2×Q8C2×C22⋊D7114yes—
581C2×Q8C23×D7112yes—
582C2×Q8C23×D7112yes—
583C2×D4—21no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—712no—
587C2×D4—1421no—
588C2×D4—1422no—
589C2×D4—1422no—
590C2×D4C23×D7112yes—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—24no—
595C22×C4—44no—
596C22×C4—2844no—
597C22×C4—1421no—
598C22×C4—1421no—
599C22×C4—1421no—
600C22×C4—1424no—
601C22×C4C2×C22⋊D7111yescharacteristic
602C22×C4C2×C22⋊D7111yescharacteristic
603C22×C4C2×C22⋊D7111yescharacteristic
604C22×C4C2×C22⋊D7111yescharacteristic
605C22×C4C2×C22⋊D7111yescharacteristic
606C22×C4C2×C22⋊D7111yescharacteristic
607C22×C4C23×D7111yescharacteristic
608Q16—2844no—
609Q16—2844no—
610Q16—2844no—
611Q16—1428no—
612SD16—2844no—
613SD16—2844no—
614SD16—1428no—
615SD16—1428no—
616D8—2844no—
617C2×C8—714no—
618C2×C8—712no—
619C2×C8—712no—
620C2×C8—712no—
621C2×C8—712no—
622C2×C8—1422no—
623C2×C8—1422no—
624C2×C8—1422no—
625C4⋊C4—24no—
626C4⋊C4—24no—
627C4⋊C4—24no—
628C4⋊C4—24no—
629C4⋊C4—21no—
630C4⋊C4—712no—
631C4⋊C4—1424no—
632C4⋊C4—1424no—
633C4⋊C4—1421no—
634C4⋊C4—1424no—
635C4⋊C4—1424no—
636C4⋊C4C2×C22⋊D7114yes—
637C4⋊C4C2×C22⋊D7114yes—
638C4⋊C4C2×C22⋊D7114yes—
639C4⋊C4C23×D7112yes—
640C22⋊C4—24no—
641C22⋊C4—24no—
642C22⋊C4—24no—
643C22⋊C4—24no—
644C22⋊C4—24no—
645C22⋊C4—1424no—
646C22⋊C4—1424no—
647C22⋊C4—1424no—
648C22⋊C4—1424no—
649C22⋊C4—1424no—
650C42—24no—
651C42—24no—
652C42—1424no—
653C42—1424no—
654C42C2×C22⋊D7112yes—
655C42C2×C22⋊D7112yes—
656C42C2×C22⋊D7112yes—
657C42C23×D7112yes—
658C42C23×D7112yes—
659C42C23×D7112yes—
660C23—22no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—2842no—
665C23—2842no—
666C23—2842no—
667C23—1422no—
668C23C22×C22⋊D7111yescharacteristic
669Q8—22no—
670Q8—22no—
671Q8—22no—
672Q8—22no—
673Q8—44no—
674Q8—42no—
675Q8—42no—
676Q8—2842no—
677Q8—2842no—
678Q8—1422no—
679Q8—1422no—
680Q8—1422no—
681Q8—1422no—
682D4—22no—
683D4—22no—
684D4—42no—
685D4—2842no—
686D4—1422no—
687D4—1422no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—48no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—2848no—
702C2×C4—2842no—
703C2×C4—2842no—
704C2×C4—2842no—
705C2×C4—1422no—
706C2×C4—1422no—
707C2×C4—1422no—
708C2×C4C22×C22⋊D7112yes—
709C2×C4C22×C22⋊D7112yes—
710C2×C4C22×C22⋊D7112yes—
711C2×C4C22×C22⋊D7112yes—
712C2×C4C22×C22⋊D7112yes—
713C2×C4C22×C22⋊D7112yes—
714C2×C4C22×C22⋊D7111yescharacteristic
715C2×C4#41×D7112yes—
716C2×C4#1455617412yes—
717C2×C4C24×D7111yescharacteristic
718C8—714no—
719C8—1422no—
720C8—1422no—
721C8—1422no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—84no—
726C22—2842no—
727C22—2842no—
728C22—2842no—
729C22—5684no—
730C22#1798666812yes—
731C22#1798679712yes—
732C22#1798681412yes—
733C22C23×C22⋊D7111yescharacteristic
734C4—22no—
735C4—22no—
736C4—22no—
737C4—22no—
738C4—22no—
739C4—22no—
740C4—42no—
741C4—42no—
742C4—42no—
743C4—2842no—
744C4—2842no—
745C4—2842no—
746C4#1798666812yes—
747C4C2×#41×D7111yescharacteristic
748C4C2×#1455617411yescharacteristic
749C2—82no—
750C2—5682no—
751C2#2260141514yesdirect product factor
752C2C2×#1798666811yescharacteristic
753C2C2×#1798679711yescharacteristic
754C2C2×#1798681411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#556×C71C2
socleC23×C71C22×D4
prime radicalC22×#11765850C22
hypercenterC2×#556D71
hypocenterC71C2×#3402
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. C2×#17986722C2semidirect
2. #22601415C2direct (N × H)
3. C2×#17986394C2semidirect
4. C2×#17986391C2semidirect
6. C2×#17986221C2semidirect
7. C2×#17986218C2semidirect
8. C2×#17986209C2semidirect
9. C2×#17986206C2semidirect
12. C2×#17986130C2semidirect
13. C2×#17986099C2semidirect
14. C2×#17986097C2semidirect
15. C2×C4×#11765855C2semidirect
16. C2×#556×C71C2semidirect
27. #17986722C22semidirect
38. #17986394C22semidirect
39. #17986391C22semidirect
41. #17986221C22semidirect
42. #17986218C22semidirect
45. #17986209C22semidirect
46. #17986206C22semidirect
47. #17986130C22semidirect
48. #17986099C22semidirect
49. #17986097C22semidirect
50. C4×#11765855C22semidirect
65. #556×C71C22semidirect
373. C2×C71#3402semidirect
379. C2×#556D71semidirect
394. C71C2×#3402semidirect
407. #556C2×D71semidirect
751. C2#22601415direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179867222
#226014152
C2×#179863942
C2×#179863912
C2×#179863812
C2×#179862212
C2×#179862182
C2×#179862092
C2×#179862062
C2×#179862142
C2×#179862112
C2×#179861302
C2×#179860992
C2×#179860972
C2×C4×#117658552
C2×#556×C712
C2×#340271