Finite Group Databasebeta

← C2×#22600804 #32876009

Subgroups — C2×#22600804 #32876009

Order 18176.

2158 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986653C211yesmaximal, characteristic, complemented
2#22600804C2116yesmaximal, direct product factor
3C2×#17986409C211yesmaximal, characteristic, complemented
4C2×#17986317C211yesmaximal, characteristic, complemented
5C2×#17986315C211yesmaximal, characteristic, complemented
6C2×#17986323C211yesmaximal, characteristic, complemented
7C2×#17986310C211yesmaximal, characteristic, complemented
8C2×#17986296C211yesmaximal, characteristic, complemented
9C2×#17986289C211yesmaximal, characteristic, complemented
10C2×#17986250C211yesmaximal, characteristic, complemented
11C2×#17986233C211yesmaximal, characteristic, complemented
12C2×#17986109C211yesmaximal, characteristic, complemented
13C2×#17986071C211yesmaximal, characteristic, complemented
14C2×#17986042C211yesmaximal, characteristic, complemented
15C22×#14556059C211yesmaximal, characteristic, complemented
16C2×#553×C71C211yesmaximal, characteristic, complemented
17C22×#11765864—21no—
18C22×#11765850C2211yescharacteristic
19C22×#11765849C2211yescharacteristic
20C23×C71⋊C8C2211yescharacteristic
21#17986653—24no—
22#17986653C2218yescomplemented
23C2×#14556128C2211yescharacteristic
24C2×#14556112—21no—
25C2×#14556112—21no—
26C2×#14556108—21no—
27C2×#14556102C2211yescharacteristic
28C2×#14556102C2211yescharacteristic
29C2×C4×D284C2211yescharacteristic
30C22×C4⋊Dic71C2211yescharacteristic
31C22×C4⋊Dic71C2211yescharacteristic
32#17986409C2218yescomplemented
33#17986323C2218yescomplemented
34#17986317C2218yescomplemented
35#17986315C2218yescomplemented
36#17986310C2218yescomplemented
37#17986296C2218yescomplemented
38#17986289C2218yescomplemented
39#17986250C2218yescomplemented
40#17986233C2218yescomplemented
41#17986109C2218yescomplemented
42#17986071C2218yescomplemented
43#17986042C2218yescomplemented
44C2×#14556061C2211yescharacteristic
45C2×#14556061C2211yescharacteristic
46C2×#14556061C2211yescharacteristic
47C2×#14556059C2211yescharacteristic
48C2×#14556059C2211yescharacteristic
49C2×#14556059C2211yescharacteristic
50C2×#14556059C2211yescharacteristic
51C2×#14556059C2211yescharacteristic
52C2×#14556059C2211yescharacteristic
53C2×#14556059C2218yescomplemented
54C2×C4⋊(C71⋊C8)C2211yescharacteristic
55C2×#14556049C2211yescharacteristic
56C2×#14556049C2211yescharacteristic
57C2×#14556049C2211yescharacteristic
58C2×#14556048C2211yescharacteristic
59C2×#14556048C2211yescharacteristic
60C2×#14556048C2211yescharacteristic
61C2×C22⋊(C71⋊C8)C2211yescharacteristic
62C2×C22⋊(C71⋊C8)C2211yescharacteristic
63C2×#14556039C2211yescharacteristic
64#553×C71—24no—
65#553×C71C2218yescomplemented
66C2×#126×C71—21no—
67C2×#125×C71C2211yescharacteristic
68C2×#123×C71—21no—
69C2×#121×C71—21no—
70C2×#121×C71C2211yescharacteristic
71C2×#121×C71C2211yescharacteristic
72C2×C4×D4×C71—21no—
73C2×C4×D4×C71C2211yescharacteristic
74C2×C4×D4×C71C2211yescharacteristic
75C2×#117×C71C2211yescharacteristic
76C22×C4⋊C4×C71C2211yescharacteristic
77C2×#11765864—28no—
78C2×#11765864—48no—
79C22×Dic142—21no—
80C22×D284C2311yescharacteristic
81C22×C22⋊D71—21no—
82C22×C22⋊D71—21no—
83C23×Dic71—21no—
84C23×Dic71—21no—
85C22×C4×D71—21no—
86C2×#11765850—24no—
87C2×#11765850C2314yes—
88C2×#11765849—24no—
89C2×#11765849C2314yes—
90C22×C71⋊C8—24no—
91C22×C71⋊C8C2314yes—
92C22×C71⋊C8C2311yescharacteristic
93C22×C71⋊C8C2311yescharacteristic
94C22×C71⋊C8C2311yescharacteristic
95C22×C71⋊C8C2311yescharacteristic
96#14556128—22no—
97#14556128C2314yes—
98#14556112—28no—
99#14556112—28no—
100#14556108—28no—
101#14556102—22no—
102#14556102—22no—
103#14556102C2314yes—
104#14556102C2314yes—
105C4×D284—22no—
106C4×D284C2314yes—
107C2×C4⋊Dic71—22no—
108C2×C4⋊Dic71—22no—
109C2×C4⋊Dic71—21no—
110C2×C4⋊Dic71—21no—
111C2×C4⋊Dic71—21no—
112C2×C4⋊Dic71C2314yes—
113C2×C4⋊Dic71C2314yes—
114C2×C4⋊Dic71C2311yescharacteristic
115C2×C4⋊Dic71C2311yescharacteristic
116C2×C4⋊Dic71C2311yescharacteristic
117C2×(C2×D71)⋊C4—21no—
118C2×(C2×D71)⋊C4—21no—
119C2×(C2×D71)⋊C4—21no—
120#14556061C2314yes—
121#14556061C2314yes—
122#14556061C2314yes—
123#14556059C2314yes—
124#14556059C2314yes—
125#14556059C2314yes—
126#14556059C2314yes—
127#14556059C2314yes—
128#14556059C2314yes—
129C4⋊(C71⋊C8)C2314yes—
130#14556049C2314yes—
131#14556049C2314yes—
132#14556049C2314yes—
133#14556048C2314yes—
134#14556048C2314yes—
135#14556048C2314yes—
136C22⋊(C71⋊C8)C2314yes—
137C22⋊(C71⋊C8)C2314yes—
138#14556039C2314yes—
139C22×D4×C71—21no—
140C22×D4×C71—21no—
141C22×D4×C71D411yescharacteristic
142C22×D4×C71C2311yescharacteristic
143C23×C4×C71—21no—
144C23×C4×C71—21no—
145C23×C4×C71C2311yescharacteristic
146C23×C4×C71C2311yescharacteristic
147#126×C71—28no—
148#125×C71—22no—
149#125×C71C2314yes—
150#123×C71—28no—
151#121×C71—28no—
152#121×C71—22no—
153#121×C71—22no—
154#121×C71C2314yes—
155#121×C71C2314yes—
156C4×D4×C71—28no—
157C4×D4×C71—22no—
158C4×D4×C71D414yes—
159C4×D4×C71C2314yes—
160C4×D4×C71C2314yes—
161#117×C71—22no—
162#117×C71C2314yes—
163C2×C4⋊C4×C71—21no—
164C2×C4⋊C4×C71—22no—
165C2×C4⋊C4×C71—21no—
166C2×C4⋊C4×C71—21no—
167C2×C4⋊C4×C71D411yescharacteristic
168C2×C4⋊C4×C71C2314yes—
169C2×C4⋊C4×C71C2311yescharacteristic
170C2×C4⋊C4×C71C2311yescharacteristic
171C2×C4⋊C4×C71C2311yescharacteristic
172C2×C22⋊C4×C71—21no—
173C2×C22⋊C4×C71—21no—
174C2×C22⋊C4×C71—21no—
175C2×C22⋊C4×C71—21no—
176C2×C22⋊C4×C71D411yescharacteristic
177C2×C22⋊C4×C71D411yescharacteristic
178C2×C42×C71—21no—
179C2×C42×C71C2311yescharacteristic
180C23×D71—21no—
181#11765864—432no—
182C2×Dic142—24no—
183C2×Dic142—44no—
184C2×D284—22no—
185C2×D284—22no—
186C2×D284—21no—
187C2×D284C2412yes—
188C2×C22⋊D71—24no—
189C2×C22⋊D71—24no—
190C2×C22⋊D71—44no—
191C2×C22⋊D71—44no—
192C22×Dic71—21no—
193C22×Dic71—21no—
194C22×Dic71—21no—
195C22×Dic71—24no—
196C22×Dic71—24no—
197C22×Dic71—44no—
198C22×Dic71—44no—
199C2×C4×D71—24no—
200C2×C4×D71—44no—
201#11765850—28no—
202#11765849—28no—
203C2×C71⋊C8—22no—
204C2×C71⋊C8—22no—
205C2×C71⋊C8—22no—
206C2×C71⋊C8—28no—
207C2×C71⋊C8#4114yescomplemented
208C2×C71⋊C8C2412yes—
209C2×C71⋊C8C2412yes—
210C2×C71⋊C8C2412yes—
211C2×C71⋊C8C2412yes—
212C4⋊Dic71—21no—
213C4⋊Dic71—21no—
214C4⋊Dic71—21no—
215C4⋊Dic71—24no—
216C4⋊Dic71—24no—
217C4⋊Dic71—24no—
218C4⋊Dic71C2412yes—
219C4⋊Dic71C2412yes—
220C4⋊Dic71C2412yes—
221(C2×D71)⋊C4—24no—
222(C2×D71)⋊C4—24no—
223(C2×D71)⋊C4—24no—
224C24×C71—21no—
225C24×C71C2×D411yescharacteristic
226C24×C71C2×D411yescharacteristic
227C2×D4×C71—24no—
228C2×D4×C71—24no—
229C2×D4×C71—24no—
230C2×D4×C71—21no—
231C2×D4×C71—22no—
232C2×D4×C71—22no—
233C2×D4×C71—44no—
234C2×D4×C71—82no—
235C2×D4×C71C2×D414yes—
236C2×D4×C71C2412yes—
237C22×C4×C71—22no—
238C22×C4×C71—22no—
239C22×C4×C71—22no—
240C22×C4×C71—22no—
241C22×C4×C71—21no—
242C22×C4×C71—21no—
243C22×C4×C71—21no—
244C22×C4×C71—24no—
245C22×C4×C71—24no—
246C22×C4×C71—82no—
247C22×C4×C71—82no—
248C22×C4×C71C2×D411yescharacteristic
249C22×C4×C71C2×D411yescharacteristic
250C22×C4×C71C2×D411yescharacteristic
251C22×C4×C71C2×D411yescharacteristic
252C22×C4×C71C2×D412yes—
253C22×C4×C71C2×D412yes—
254C22×C4×C71C2412yes—
255C22×C4×C71C2412yes—
256C22×C4×C71C2411yescharacteristic
257C4⋊C4×C71—21no—
258C4⋊C4×C71—21no—
259C4⋊C4×C71—24no—
260C4⋊C4×C71—24no—
261C4⋊C4×C71—24no—
262C4⋊C4×C71—21no—
263C4⋊C4×C71C2×D414yes—
264C4⋊C4×C71C2412yes—
265C4⋊C4×C71C2412yes—
266C4⋊C4×C71C2412yes—
267C22⋊C4×C71—24no—
268C22⋊C4×C71—24no—
269C22⋊C4×C71—24no—
270C22⋊C4×C71—24no—
271C22⋊C4×C71C2×D414yes—
272C22⋊C4×C71C2×D414yes—
273C42×C71—24no—
274C42×C71C2×D412yes—
275C42×C71C2412yes—
276C23×C71—22no—
277C23×C71—22no—
278C23×C71—22no—
279C23×C71—22no—
280C23×C71—22no—
281C23×C71—22no—
282C23×C71—42no—
283C23×C71—42no—
284C23×C71—42no—
285C23×C71AGL(1,ℤ/8)14yes—
286C23×C71C22×D412yes—
287C23×C71C22×D412yes—
288C23×C71C22×D411yescharacteristic
289C22×D71—22no—
290C22×D71—42no—
291C22×D71—42no—
292C22×D71—42no—
293D4×C71—28no—
294D4×C71—22no—
295D4×C71—22no—
296D4×C71—48no—
297D4×C71—42no—
298D4×C71—84no—
299C2×C4×C71—22no—
300C2×C4×C71—22no—
301C2×C4×C71—22no—
302C2×C4×C71—22no—
303C2×C4×C71—24no—
304C2×C4×C71—24no—
305C2×C4×C71—22no—
306C2×C4×C71—22no—
307C2×C4×C71—22no—
308C2×C4×C71—22no—
309C2×C4×C71—22no—
310C2×C4×C71—22no—
311C2×C4×C71—22no—
312C2×C4×C71—42no—
313C2×C4×C71—42no—
314C2×C4×C71—42no—
315C2×C4×C71—84no—
316C2×C4×C71—84no—
317C2×C4×C71C22×D412yes—
318C2×C4×C71C22×D412yes—
319C2×C4×C71C22×D412yes—
320C2×C4×C71C22×D412yes—
321C2×C4×C71C22×D411yescharacteristic
322C2×C4×C71C2×#4112yes—
323C2×C4×C712−1+412yes—
324C2×C4×C71C2511yescharacteristic
325C22⋊D71—48no—
326C22⋊D71—48no—
327C2×Dic71—22no—
328C2×Dic71—22no—
329C2×Dic71—22no—
330C2×Dic71—48no—
331C2×Dic71—42no—
332C2×Dic71—42no—
333C2×Dic71—42no—
334C2×Dic71—48no—
335D284—22no—
336D284—22no—
337D284—42no—
338C4×D71—48no—
339Dic142—48no—
340C71⋊C8—22no—
341C71⋊C8—22no—
342C71⋊C8—22no—
343C71⋊C8C2×#4114yescomplemented
344C22×C71—28no—
345C22×C71—22no—
346C22×C71—22no—
347C22×C71—22no—
348C22×C71—22no—
349C22×C71—22no—
350C22×C71—44no—
351C22×C71—42no—
352C22×C71—42no—
353C22×C71—42no—
354C22×C71—84no—
355C22×C71#54712yes—
356C22×C71C2×AGL(1,ℤ/8)14yes—
357C22×C71C2×AGL(1,ℤ/8)12yes—
358C22×C71#57712yes—
359C22×C71C23×D411yescharacteristic
360C2×D71—42no—
361C2×D71—42no—
362C2×D71—42no—
363C2×D71—84no—
364C4×C71—22no—
365C4×C71—22no—
366C4×C71—22no—
367C4×C71—22no—
368C4×C71—42no—
369C4×C71—42no—
370C4×C71—42no—
371C4×C71#54712yes—
372C4×C71C22×#4111yescharacteristic
373C4×C71C2×2−1+411yescharacteristic
374Dic71—42no—
375Dic71—42no—
376Dic71—42no—
377C2×#3345—711nomaximal, Sylow
378C2×C71—24no—
379C2×C71—42no—
380C2×C71—82no—
381C2×C71#334514yescomplemented
382C2×C71C2×#54711yescharacteristic
383C2×C71C22×AGL(1,ℤ/8)11yescharacteristic
384C2×C71C2×#57711yescharacteristic
385D71—82no—
386C2×#553D7111yescharacteristic, complemented
387C2×#547—711no—
388#3345—7116no—
389C2×#501—711no—
390C2×#481—711no—
391C2×#481—711no—
392C2×#482—711no—
393C2×#480—711no—
394C2×#478—711no—
395C2×#476—711no—
396C2×#469—711no—
397C2×#466—711no—
398C2×#442—711no—
399C2×#435—711no—
400C2×#428—711no—
401C22×#106—711no—
402C71C2×#334511yescharacteristic, complemented, Sylow
403C22×#41—1421no—
404C22×D8—711no—
405C22×M16—711no—
406C23×C8—711no—
407#553—24no—
408#553C2×D7118yescomplemented
409#547—718no—
410#547—1424no—
411C2×C4⋊Q8—711no—
412C2×#126—21no—
413C2×#125C2×D7111yescharacteristic
414C2×#123—21no—
415C2×#123—1421no—
416C2×#123—1421no—
417C2×C22⋊Q8—1421no—
418C2×#121—21no—
419C2×#121—711no—
420C2×#121—711no—
421C2×#121C2×D7111yescharacteristic
422C2×#121C2×D7111yescharacteristic
423C2×C4×D4—21no—
424C2×C4×D4—711no—
425C2×C4×D4C2×D7111yescharacteristic
426C2×C4×D4C2×D7111yescharacteristic
427C2×#117C2×D7111yescharacteristic
428C22×C4⋊C4—711no—
429C22×C4⋊C4—711no—
430C22×C4⋊C4C2×D7111yescharacteristic
431#501—718no—
432#482—718no—
433#481—718no—
434#481—718no—
435#480—718no—
436#478—718no—
437#476—718no—
438#469—718no—
439#466—718no—
440#442—718no—
441#435—718no—
442#428—718no—
443C2×#107—711no—
444C2×#107—711no—
445C2×#107—711no—
446C2×#106—711no—
447C2×#106—711no—
448C2×#106—711no—
449C2×#106—711no—
450C2×#106—718no—
451C2×#106—711no—
452C2×#106—711no—
453C2×C4⋊C8—711no—
454C2×#102—711no—
455C2×#102—711no—
456C2×#102—711no—
457C2×#102—711no—
458C2×#102—711no—
459C2×#102—711no—
460C2×C22⋊C8—711no—
461C2×C22⋊C8—711no—
462C2×#97—711no—
463C2×#41—2848no—
464C2×#41—1428no—
465C22×Q8—1421no—
466C22×D4—21no—
467C22×D4—21no—
468C22×D4—711no—
469C22×D4—1421no—
470C22×D4—1421no—
471C22×D4C22⋊D7111yescharacteristic
472C22×D4C22×D7111yescharacteristic
473C23×C4—21no—
474C23×C4—21no—
475C23×C4—1421no—
476C23×C4—1421no—
477C23×C4—1421no—
478C23×C4C22×D7111yescharacteristic
479C23×C4C22×D7111yescharacteristic
480C2×D8—714no—
481C2×D8—1424no—
482C2×M16—714no—
483C2×M16—1424no—
484C22×C8—711no—
485C22×C8—711no—
486C22×C8—714no—
487C22×C8—711no—
488C22×C8—711no—
489C22×C8—1424no—
490C4⋊Q8—714no—
491C4⋊Q8—1422no—
492#126—28no—
493#125—22no—
494#125C22×D7114yes—
495#123—28no—
496#123—1428no—
497#123—1428no—
498C22⋊Q8—1428no—
499#121—28no—
500#121—22no—
501#121—22no—
502#121—714no—
503#121—714no—
504#121—1422no—
505#121—1422no—
506#121C22×D7114yes—
507#121C22×D7114yes—
508C4×D4—28no—
509C4×D4—22no—
510C4×D4—714no—
511C4×D4—1422no—
512C4×D4C22⋊D7114yes—
513C4×D4C22×D7114yes—
514C4×D4C22×D7114yes—
515#117—22no—
516#117C22×D7114yes—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—22no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—711no—
522C2×C4⋊C4—711no—
523C2×C4⋊C4—711no—
524C2×C4⋊C4—714no—
525C2×C4⋊C4—714no—
526C2×C4⋊C4—1421no—
527C2×C4⋊C4—1421no—
528C2×C4⋊C4—1422no—
529C2×C4⋊C4—1422no—
530C2×C4⋊C4—1421no—
531C2×C4⋊C4C22⋊D7111yescharacteristic
532C2×C4⋊C4C22×D7111yescharacteristic
533C2×C4⋊C4C22×D7111yescharacteristic
534C2×C4⋊C4C22×D7114yes—
535C2×C4⋊C4C22×D7111yescharacteristic
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—1421no—
541C2×C22⋊C4—1421no—
542C2×C22⋊C4—1421no—
543C2×C22⋊C4C22⋊D7111yescharacteristic
544C2×C22⋊C4C22⋊D7111yescharacteristic
545C2×C42—21no—
546C2×C42C22×D7111yescharacteristic
547#107—714no—
548#107—714no—
549#107—714no—
550#106—714no—
551#106—714no—
552#106—714no—
553#106—714no—
554#106—714no—
555#106—714no—
556C4⋊C8—714no—
557#102—714no—
558#102—714no—
559#102—714no—
560#102—714no—
561#102—714no—
562#102—714no—
563C22⋊C8—714no—
564C22⋊C8—714no—
565#97—714no—
566C24—21no—
567C24—1421no—
568C24C2×C22⋊D7111yescharacteristic
569C24C2×C22⋊D7111yescharacteristic
570#41—28432no—
571C2×Q8—2844no—
572C2×Q8—1424no—
573C2×D4—24no—
574C2×D4—24no—
575C2×D4—24no—
576C2×D4—21no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—44no—
580C2×D4—82no—
581C2×D4—2844no—
582C2×D4—2844no—
583C2×D4—712no—
584C2×D4—1424no—
585C2×D4—1424no—
586C2×D4—1421no—
587C2×D4—1422no—
588C2×D4—1422no—
589C2×D4C2×C22⋊D7114yes—
590C2×D4C23×D7112yes—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—24no—
599C22×C4—24no—
600C22×C4—82no—
601C22×C4—82no—
602C22×C4—2844no—
603C22×C4—2844no—
604C22×C4—2844no—
605C22×C4—1424no—
606C22×C4—1424no—
607C22×C4—1421no—
608C22×C4—1421no—
609C22×C4—1421no—
610C22×C4—1424no—
611C22×C4C2×C22⋊D7112yes—
612C22×C4C2×C22⋊D7112yes—
613C22×C4C2×C22⋊D7111yescharacteristic
614C22×C4C2×C22⋊D7111yescharacteristic
615C22×C4C2×C22⋊D7111yescharacteristic
616C22×C4C2×C22⋊D7111yescharacteristic
617C22×C4C23×D7112yes—
618C22×C4C23×D7112yes—
619C22×C4C23×D7111yescharacteristic
620D8—1428no—
621M16—1428no—
622C2×C8—714no—
623C2×C8—712no—
624C2×C8—712no—
625C2×C8—712no—
626C2×C8—712no—
627C2×C8—1428no—
628C2×C8—1422no—
629C2×C8—1422no—
630C2×C8—1422no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—24no—
634C4⋊C4—24no—
635C4⋊C4—24no—
636C4⋊C4—21no—
637C4⋊C4—712no—
638C4⋊C4—712no—
639C4⋊C4—712no—
640C4⋊C4—1421no—
641C4⋊C4—1421no—
642C4⋊C4—1421no—
643C4⋊C4—1424no—
644C4⋊C4—1424no—
645C4⋊C4—1424no—
646C4⋊C4C2×C22⋊D7114yes—
647C4⋊C4C23×D7112yes—
648C4⋊C4C23×D7112yes—
649C4⋊C4C23×D7112yes—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—24no—
653C22⋊C4—24no—
654C22⋊C4—1424no—
655C22⋊C4—1424no—
656C22⋊C4—1424no—
657C22⋊C4C2×C22⋊D7114yes—
658C22⋊C4C2×C22⋊D7114yes—
659C42—24no—
660C42C2×C22⋊D7112yes—
661C42C23×D7112yes—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—2842no—
672C23—2842no—
673C23—2842no—
674C23—1422no—
675C23#1455615314yes—
676C23C22×C22⋊D7112yes—
677C23C22×C22⋊D7112yes—
678C23C22×C22⋊D7111yescharacteristic
679Q8—2848no—
680D4—28no—
681D4—22no—
682D4—22no—
683D4—48no—
684D4—42no—
685D4—84no—
686D4—2848no—
687D4—2848no—
688D4—2842no—
689D4—1422no—
690D4—1422no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—84no—
708C2×C4—84no—
709C2×C4—2848no—
710C2×C4—2848no—
711C2×C4—2842no—
712C2×C4—2842no—
713C2×C4—2842no—
714C2×C4—2848no—
715C2×C4—1422no—
716C2×C4—1422no—
717C2×C4—1422no—
718C2×C4C22×C22⋊D7112yes—
719C2×C4C22×C22⋊D7112yes—
720C2×C4C22×C22⋊D7112yes—
721C2×C4C22×C22⋊D7112yes—
722C2×C4C22×C22⋊D7111yescharacteristic
723C2×C4#41×D7112yes—
724C2×C4#1455617512yes—
725C2×C4C24×D7111yescharacteristic
726C8—714no—
727C8—1422no—
728C8—1422no—
729C8—1422no—
730C22—22no—
731C22—22no—
732C22—28no—
733C22—22no—
734C22—22no—
735C22—22no—
736C22—44no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—84no—
741C22—2842no—
742C22—2842no—
743C22—2842no—
744C22—5684no—
745C22#1798664812yes—
746C22C2×#1455615314yes—
747C22C2×#1455615312yes—
748C22#1798681012yes—
749C22C23×C22⋊D7111yescharacteristic
750C4—22no—
751C4—22no—
752C4—22no—
753C4—22no—
754C4—42no—
755C4—42no—
756C4—42no—
757C4—2842no—
758C4—2842no—
759C4—2842no—
760C4#1798664812yes—
761C4C2×#41×D7111yescharacteristic
762C4C2×#1455617511yescharacteristic
763C2—24no—
764C2—42no—
765C2—82no—
766C2—5682no—
767C2#2260080414yesdirect product factor
768C2C2×#1798664811yescharacteristic
769C2C22×#1455615311yescharacteristic
770C2C2×#1798681011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#553×C71C2
socleC23×C71C22×D4
hypercenterC2×#553D71
hypocenterC71C2×#3345
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. C2×#17986653C2semidirect
2. #22600804C2direct (N × H)
3. C2×#17986409C2semidirect
4. C2×#17986317C2semidirect
5. C2×#17986315C2semidirect
6. C2×#17986323C2semidirect
7. C2×#17986310C2semidirect
8. C2×#17986296C2semidirect
9. C2×#17986289C2semidirect
10. C2×#17986250C2semidirect
11. C2×#17986233C2semidirect
12. C2×#17986109C2semidirect
13. C2×#17986071C2semidirect
14. C2×#17986042C2semidirect
15. C22×#14556059C2semidirect
16. C2×#553×C71C2semidirect
22. #17986653C22semidirect
32. #17986409C22semidirect
33. #17986323C22semidirect
34. #17986317C22semidirect
35. #17986315C22semidirect
36. #17986310C22semidirect
37. #17986296C22semidirect
38. #17986289C22semidirect
39. #17986250C22semidirect
40. #17986233C22semidirect
41. #17986109C22semidirect
42. #17986071C22semidirect
43. #17986042C22semidirect
53. C2×#14556059C22semidirect
65. #553×C71C22semidirect
207. C2×C71⋊C8#41semidirect
343. C71⋊C8C2×#41semidirect
381. C2×C71#3345semidirect
386. C2×#553D71semidirect
402. C71C2×#3345semidirect
408. #553C2×D71semidirect
767. C2#22600804direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179866532
#226008042
C2×#179864092
C2×#179863172
C2×#179863152
C2×#179863232
C2×#179863102
C2×#179862962
C2×#179862892
C2×#179862502
C2×#179862332
C2×#179861092
C2×#179860712
C2×#179860422
C22×#145560592
C2×#553×C712
C2×#334571