Finite Group Databasebeta

← C2×#22598468 #32865653

Subgroups — C2×#22598468 #32865653

Order 18176.

2118 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986553C211yesmaximal, characteristic
2C2×C4×Q8×D71C211yesmaximal, characteristic
3#22598468C2116yesmaximal, direct product factor
4C2×#17986331C211yesmaximal, characteristic
5C2×#17986328C211yesmaximal, characteristic
6C2×#17986283C211yesmaximal, characteristic, complemented
7C2×#17986282C211yesmaximal, characteristic, complemented
8C2×#17986208C211yesmaximal, characteristic, complemented
9C2×#17986207C211yesmaximal, characteristic, complemented
10C2×#17986156C211yesmaximal, characteristic
11C2×#17986153C211yesmaximal, characteristic
12C2×#17986107C211yesmaximal, characteristic, complemented
13C2×#17986104C211yesmaximal, characteristic, complemented
14C2×#17986104C211yesmaximal, characteristic, complemented
15C2×#17986054C211yesmaximal, characteristic
16C2×#441×C71C211yesmaximal, characteristic, complemented
17C22×Q8×D71C2211yescharacteristic
18C22×Dic284C2211yescharacteristic
19C22×#11765855C2211yescharacteristic
20C22×#11765855C2211yescharacteristic
21#17986553—24no—
22#17986553C2218yes—
23C2×#14556127C2211yescharacteristic
24C2×#14556126C2211yescharacteristic
25C2×#14556118—21no—
26C2×#14556108C2211yescharacteristic
27C2×#14556106—21no—
28C2×#14556104C2211yescharacteristic
29C2×Q8×Dic71C2211yescharacteristic
30C2×C4×Dic142—21no—
31C2×C4×Dic142—21no—
32C2×C4×Dic142C2211yescharacteristic
33C2×C4×Dic142C2211yescharacteristic
34C2×#14556093—21no—
35C2×#14556093C2211yescharacteristic
36C4×Q8×D71—24no—
37C4×Q8×D71C2218yes—
38C2×#14556085—21no—
39C2×C4⋊C4×D71—21no—
40C2×C4⋊C4×D71C2211yescharacteristic
41C2×C42×D71—21no—
42C2×C42×D71C2211yescharacteristic
43#17986331C2218yes—
44#17986328C2218yes—
45#17986283C2218yescomplemented
46#17986282C2218yescomplemented
47#17986208C2218yescomplemented
48#17986207C2218yescomplemented
49#17986156C2218yes—
50#17986153C2218yes—
51#17986107C2218yescomplemented
52#17986104C2218yescomplemented
53#17986104C2218yescomplemented
54#17986054C2218yes—
55C2×#14556060C2211yescharacteristic
56C2×#14556059C2211yescharacteristic
57C2×#14556059C2211yescharacteristic
58C2×Dic71⋊C8C2211yescharacteristic
59C2×Dic71⋊C8C2211yescharacteristic
60C2×#14556053C2211yescharacteristic
61C2×#14556053C2211yescharacteristic
62C2×#14556052C2211yescharacteristic
63C2×#14556052C2211yescharacteristic
64C2×#14556051C2211yescharacteristic
65C2×#14556051C2211yescharacteristic
66C2×(C2×D71)⋊C8C2211yescharacteristic
67C2×(C2×D71)⋊C8C2211yescharacteristic
68C2×#14556039C2211yescharacteristic
69C22×Q16×C71C2211yescharacteristic
70C2×C4×Q8×C71C2211yescharacteristic
71C2×C4×Q8×C71C2211yescharacteristic
72#441×C71C2218yescomplemented
73C2×#106×C71C2211yescharacteristic
74C2×#103×C71C2211yescharacteristic
75C2×#103×C71C2211yescharacteristic
76C2×#97×C71C2211yescharacteristic
77C22×Dic142—21no—
78C22×Dic142—21no—
79C22×Dic142C2311yescharacteristic
80C22×Dic142C2311yescharacteristic
81C2×Q8×D71—24no—
82C2×Q8×D71—22no—
83C2×Q8×D71—24no—
84C2×Q8×D71C2314yes—
85C22×C4×D71—21no—
86C22×C4×D71—21no—
87C22×C4×D71D411yescharacteristic
88C22×C4×D71D411yescharacteristic
89C22×C4×D71C2311yescharacteristic
90C2×Dic284—24no—
91C2×Dic284C2314yes—
92C2×#11765855—24no—
93C2×#11765855—24no—
94C2×#11765855C2314yes—
95C2×#11765855C2314yes—
96C22×C71⋊C8C2311yescharacteristic
97C22×C71⋊C8C2311yescharacteristic
98#14556127—22no—
99#14556127C2314yes—
100#14556126—22no—
101#14556126C2314yes—
102#14556118—28no—
103#14556108—22no—
104#14556108C2314yes—
105#14556106—28no—
106#14556104—22no—
107#14556104C2314yes—
108Q8×Dic71—22no—
109Q8×Dic71C2314yes—
110C4×Dic142—28no—
111C4×Dic142—28no—
112C4×Dic142—22no—
113C4×Dic142—22no—
114C4×Dic142C2314yes—
115C4×Dic142C2314yes—
116#14556093—22no—
117#14556093—28no—
118#14556093C2314yes—
119#14556085—28no—
120C2×C4⋊Dic71—21no—
121C2×C4⋊Dic71—21no—
122C2×C4⋊Dic71C2311yescharacteristic
123C2×C4⋊Dic71C2311yescharacteristic
124C2×Dic71⋊C4—21no—
125C2×Dic71⋊C4—21no—
126C2×Dic71⋊C4—21no—
127C2×Dic71⋊C4—21no—
128C2×Dic71⋊C4—21no—
129C2×Dic71⋊C4—21no—
130C2×Dic71⋊C4—21no—
131C2×Dic71⋊C4—21no—
132C4⋊C4×D71—28no—
133C4⋊C4×D71—22no—
134C4⋊C4×D71C2314yes—
135C2×(C2×D71)⋊C4—21no—
136C2×(C2×D71)⋊C4—21no—
137C2×C4×Dic71—21no—
138C2×C4×Dic71—21no—
139C2×C4×Dic71—21no—
140C2×C4×Dic71—21no—
141C2×C4×Dic71D411yescharacteristic
142C2×C4×Dic71D411yescharacteristic
143C2×C4×Dic71C2311yescharacteristic
144C42×D71—28no—
145C42×D71D414yes—
146C42×D71C2314yes—
147#14556060C2314yes—
148#14556059C2314yes—
149#14556059C2314yes—
150Dic71⋊C8C2314yes—
151Dic71⋊C8C2314yes—
152#14556053C2314yes—
153#14556053C2314yes—
154#14556052C2314yes—
155#14556052C2314yes—
156#14556051C2314yes—
157#14556051C2314yes—
158(C2×D71)⋊C8C2314yes—
159(C2×D71)⋊C8C2314yes—
160#14556039C2314yes—
161C22×Q8×C71C2311yescharacteristic
162C22×Q8×C71C2311yescharacteristic
163C2×Q16×C71—24no—
164C2×Q16×C71C2314yes—
165C22×C8×C71C2311yescharacteristic
166C22×C8×C71C2311yescharacteristic
167C4×Q8×C71—22no—
168C4×Q8×C71—22no—
169C4×Q8×C71C2314yes—
170C4×Q8×C71C2314yes—
171C2×C4⋊C4×C71—21no—
172C2×C4⋊C4×C71—21no—
173C2×C4⋊C4×C71C2311yescharacteristic
174C2×C4⋊C4×C71C2311yescharacteristic
175C2×C42×C71—21no—
176C2×C42×C71—21no—
177C2×C42×C71C2311yescharacteristic
178#106×C71C2314yes—
179#103×C71C2314yes—
180#103×C71C2314yes—
181#97×C71C2314yes—
182C23×D71C2×D411yescharacteristic
183C2×Dic142—28no—
184C2×Dic142—21no—
185C2×Dic142—22no—
186C2×Dic142—24no—
187C2×Dic142—22no—
188C2×Dic142—22no—
189C2×Dic142—21no—
190C2×Dic142—24no—
191C2×Dic142—44no—
192C2×Dic142#4114yes—
193C2×Dic142C2412yes—
194C2×Dic142C2412yes—
195Q8×D71—216no—
196Q8×D71—28no—
197Q8×D71—28no—
198C22×Dic71—21no—
199C22×Dic71—21no—
200C22×Dic71—21no—
201C22×Dic71—21no—
202C22×Dic71C2×D411yescharacteristic
203C22×Dic71C2×D411yescharacteristic
204C22×Dic71C2×D411yescharacteristic
205C2×C4×D71—28no—
206C2×C4×D71—24no—
207C2×C4×D71—24no—
208C2×C4×D71—22no—
209C2×C4×D71—22no—
210C2×C4×D71—24no—
211C2×C4×D71—24no—
212C2×C4×D71—44no—
213C2×C4×D71C2×D414yes—
214C2×C4×D71C2×D414yes—
215C2×C4×D71C2×D412yes—
216C2×C4×D71C2412yes—
217Dic284—28no—
218#11765855—28no—
219#11765855—28no—
220C2×C71⋊C8—22no—
221C2×C71⋊C8—22no—
222C2×C71⋊C8C2412yes—
223C2×C71⋊C8C2412yes—
224C4⋊Dic71—21no—
225C4⋊Dic71—21no—
226C4⋊Dic71—24no—
227C4⋊Dic71—24no—
228C4⋊Dic71C2412yes—
229C4⋊Dic71C2412yes—
230Dic71⋊C4—24no—
231Dic71⋊C4—24no—
232Dic71⋊C4—24no—
233Dic71⋊C4—24no—
234Dic71⋊C4—24no—
235Dic71⋊C4—24no—
236Dic71⋊C4—24no—
237Dic71⋊C4—24no—
238(C2×D71)⋊C4—24no—
239(C2×D71)⋊C4—24no—
240C4×Dic71—24no—
241C4×Dic71—24no—
242C4×Dic71—24no—
243C4×Dic71—24no—
244C4×Dic71C2×D412yes—
245C4×Dic71C2×D414yes—
246C4×Dic71C2×D414yes—
247C4×Dic71C2412yes—
248C2×Q8×C71—21no—
249C2×Q8×C71—21no—
250C2×Q8×C71—22no—
251C2×Q8×C71—22no—
252C2×Q8×C71—22no—
253C2×Q8×C71#4114yes—
254C2×Q8×C71C2412yes—
255C2×Q8×C71C2412yes—
256C22×C4×C71—21no—
257C22×C4×C71—21no—
258C22×C4×C71—21no—
259C22×C4×C71—21no—
260C22×C4×C71C2×D411yescharacteristic
261C22×C4×C71C2×D411yescharacteristic
262C22×C4×C71C2411yescharacteristic
263Q16×C71—28no—
264C2×C8×C71—22no—
265C2×C8×C71—22no—
266C2×C8×C71C2412yes—
267C2×C8×C71C2412yes—
268C4⋊C4×C71—24no—
269C4⋊C4×C71—24no—
270C4⋊C4×C71—21no—
271C4⋊C4×C71—21no—
272C4⋊C4×C71C2412yes—
273C4⋊C4×C71C2412yes—
274C42×C71—24no—
275C42×C71—24no—
276C42×C71C2×D412yes—
277C42×C71C2412yes—
278C23×C71C22×D411yescharacteristic
279C22×D71—22no—
280C22×D71—22no—
281C22×D71#13714yes—
282C22×D71C22×D412yes—
283Q8×C71—24no—
284Q8×C71—22no—
285Q8×C71—22no—
286Q8×C71—22no—
287Q8×C71—42no—
288Q8×C71C2×#4114yes—
289C2×C4×C71—24no—
290C2×C4×C71—22no—
291C2×C4×C71—22no—
292C2×C4×C71—22no—
293C2×C4×C71—22no—
294C2×C4×C71—22no—
295C2×C4×C71—22no—
296C2×C4×C71—42no—
297C2×C4×C71—42no—
298C2×C4×C71—42no—
299C2×C4×C71C22×D412yes—
300C2×C4×C71C22×D412yes—
301C2×C4×C71C22×D411yescharacteristic
302C2×C4×C71C2×#4112yes—
303C2×C4×C71C2×#4112yes—
304C2×C4×C71C2511yescharacteristic
305C2×Dic71—24no—
306C2×Dic71—22no—
307C2×Dic71—22no—
308C2×Dic71—22no—
309C2×Dic71—22no—
310C2×Dic71—22no—
311C2×Dic71—22no—
312C2×Dic71—42no—
313C2×Dic71—42no—
314C2×Dic71—42no—
315C2×Dic71#13714yes—
316C2×Dic71C22×D412yes—
317C2×Dic71C22×D412yes—
318C2×Dic71C22×D412yes—
319C4×D71—216no—
320C4×D71—28no—
321C4×D71—24no—
322C4×D71—22no—
323C4×D71—22no—
324C4×D71—28no—
325C4×D71—48no—
326Dic142—216no—
327Dic142—24no—
328Dic142—22no—
329Dic142—22no—
330Dic142—22no—
331Dic142—42no—
332Dic142—48no—
333Dic142C2×#4114yes—
334C8×C71—22no—
335C8×C71—22no—
336C71⋊C8—22no—
337C71⋊C8—22no—
338C22×C71#52512yes—
339C22×C71C2×#13712yes—
340C22×C71C2×#13712yes—
341C22×C71C23×D411yescharacteristic
342C2×D71—28no—
343C2×D71—22no—
344C2×D71—22no—
345C2×D71C2×#13714yes—
346C4×C71—24no—
347C4×C71—22no—
348C4×C71—22no—
349C4×C71—42no—
350C4×C71—42no—
351C4×C71—42no—
352C4×C71#52512yes—
353C4×C71C22×#4111yescharacteristic
354C4×C71C22×#4111yescharacteristic
355Dic71—22no—
356Dic71—24no—
357Dic71—22no—
358Dic71—42no—
359Dic71—42no—
360Dic71—42no—
361Dic71C2×#13714yes—
362C2×#3113—711nomaximal, Sylow
363C2×C71#311314yescomplemented
364C2×C71C2×#52511yescharacteristic
365C2×C71C22×#13711yescharacteristic
366C2×C71C22×#13711yescharacteristic
367D71—24no—
368C2×#533—711no—
369C22×C4×Q8—711no—
370#3113—7116no—
371C2×#483—711no—
372C2×#483—711no—
373C2×#475—711no—
374C2×#475—711no—
375C2×#462—711no—
376C2×#462—711no—
377C2×#451—711no—
378C2×#451—711no—
379C2×#441—711no—
380C2×#441—711no—
381C2×#441—711no—
382C2×#441D7111yescharacteristic, complemented
383C2×#432—711no—
384C71C2×#311311yescharacteristic, complemented, Sylow
385C23×Q8—711no—
386C22×Q16—711no—
387C22×Q16—711no—
388C22×Q16—711no—
389C22×Q16C2×D7111yescharacteristic
390#533—718no—
391#533—1424no—
392C2×C4⋊Q8—711no—
393C2×C4⋊Q8—711no—
394C2×#125—1421no—
395C2×C22⋊Q8—711no—
396C2×C22⋊Q8—711no—
397C2×C22⋊Q8—1421no—
398C2×C4×Q8—711no—
399C2×C4×Q8—718no—
400C2×C4×Q8—711no—
401C2×C4×Q8—711no—
402C2×C4×Q8—711no—
403C2×C4×Q8—1421no—
404C2×C4×Q8—1421no—
405C2×C4×Q8—1421no—
406C2×C4×Q8—1424no—
407C2×C4×Q8C2×D7111yescharacteristic
408C2×C4×Q8C2×D7111yescharacteristic
409C2×#117—1421no—
410C22×C4⋊C4—711no—
411C22×C4⋊C4—1421no—
412C22×C42—711no—
413C22×C42—1421no—
414#483—718no—
415#483—718no—
416#475—718no—
417#475—718no—
418#462—718no—
419#462—718no—
420#451—718no—
421#451—718no—
422#441—718no—
423#441—718no—
424#441—718no—
425#441C2×D7118yescomplemented
426#432—718no—
427C2×#106—711no—
428C2×#106—711no—
429C2×#106—711no—
430C2×#106C2×D7111yescharacteristic
431C2×C4⋊C8—711no—
432C2×C4⋊C8—711no—
433C2×#103—711no—
434C2×#103—711no—
435C2×#103—711no—
436C2×#103—711no—
437C2×#103—711no—
438C2×#103—711no—
439C2×#103C2×D7111yescharacteristic
440C2×#103C2×D7111yescharacteristic
441C2×C22⋊C8—711no—
442C2×C22⋊C8—711no—
443C2×#97—711no—
444C2×#97C2×D7111yescharacteristic
445C22×Q8—714no—
446C22×Q8—711no—
447C22×Q8—711no—
448C22×Q8—1421no—
449C22×Q8—1421no—
450C22×Q8—1422no—
451C22×Q8—1424no—
452C22×Q8—1424no—
453C22×Q8C22×D7111yescharacteristic
454C22×Q8C22×D7111yescharacteristic
455C23×C4—711no—
456C23×C4—711no—
457C23×C4—711no—
458C23×C4—1421no—
459C23×C4—1421no—
460C2×Q16—24no—
461C2×Q16—714no—
462C2×Q16—714no—
463C2×Q16—714no—
464C2×Q16—1424no—
465C2×Q16—1424no—
466C2×Q16—1424no—
467C2×Q16C22×D7114yes—
468C22×C8—711no—
469C22×C8—711no—
470C22×C8C22×D7111yescharacteristic
471C22×C8C22×D7111yescharacteristic
472C4⋊Q8—714no—
473C4⋊Q8—714no—
474C4⋊Q8—1422no—
475C4⋊Q8—1422no—
476#125—1428no—
477C22⋊Q8—714no—
478C22⋊Q8—714no—
479C22⋊Q8—1422no—
480C22⋊Q8—1428no—
481C22⋊Q8—1422no—
482C4×Q8—22no—
483C4×Q8—22no—
484C4×Q8—714no—
485C4×Q8—714no—
486C4×Q8—714no—
487C4×Q8—714no—
488C4×Q8—1428no—
489C4×Q8—1428no—
490C4×Q8—1428no—
491C4×Q8—1422no—
492C4×Q8—1422no—
493C4×Q8—1422no—
494C4×Q8—1422no—
495C4×Q8C22×D7114yes—
496C4×Q8C22×D7114yes—
497#117—1428no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—711no—
501C2×C4⋊C4—711no—
502C2×C4⋊C4—714no—
503C2×C4⋊C4—1422no—
504C2×C4⋊C4—1428no—
505C2×C4⋊C4—1421no—
506C2×C4⋊C4—1421no—
507C2×C4⋊C4—1421no—
508C2×C4⋊C4—1421no—
509C2×C4⋊C4—1421no—
510C2×C4⋊C4—1421no—
511C2×C4⋊C4—1421no—
512C2×C4⋊C4—1421no—
513C2×C4⋊C4—1421no—
514C2×C4⋊C4—1421no—
515C2×C4⋊C4C22×D7111yescharacteristic
516C2×C4⋊C4C22×D7111yescharacteristic
517C2×C22⋊C4—1421no—
518C2×C22⋊C4—1421no—
519C2×C42—21no—
520C2×C42—21no—
521C2×C42—711no—
522C2×C42—711no—
523C2×C42—711no—
524C2×C42—714no—
525C2×C42—714no—
526C2×C42—1428no—
527C2×C42—1421no—
528C2×C42—1421no—
529C2×C42—1421no—
530C2×C42—1421no—
531C2×C42C22×D7111yescharacteristic
532#106—714no—
533#106—714no—
534#106—714no—
535#106C22×D7114yes—
536C4⋊C8—714no—
537C4⋊C8—714no—
538#103—714no—
539#103—714no—
540#103—714no—
541#103—714no—
542#103—714no—
543#103—714no—
544#103C22×D7114yes—
545#103C22×D7114yes—
546C22⋊C8—714no—
547C22⋊C8—714no—
548#97—714no—
549#97C22×D7114yes—
550C24—711no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—22no—
554C2×Q8—22no—
555C2×Q8—22no—
556C2×Q8—2844no—
557C2×Q8—714no—
558C2×Q8—712no—
559C2×Q8—712no—
560C2×Q8—1424no—
561C2×Q8—1424no—
562C2×Q8—1428no—
563C2×Q8—1422no—
564C2×Q8—1422no—
565C2×Q8—1428no—
566C2×Q8—14216no—
567C2×Q8—1428no—
568C2×Q8—1421no—
569C2×Q8—1421no—
570C2×Q8—1422no—
571C2×Q8#1176586514yes—
572C2×Q8C23×D7112yes—
573C2×Q8C23×D7112yes—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—2844no—
579C22×C4—711no—
580C22×C4—711no—
581C22×C4—711no—
582C22×C4—714no—
583C22×C4—714no—
584C22×C4—712no—
585C22×C4—712no—
586C22×C4—1424no—
587C22×C4—1424no—
588C22×C4—1424no—
589C22×C4—1424no—
590C22×C4—1428no—
591C22×C4—1421no—
592C22×C4—1421no—
593C22×C4—1421no—
594C22×C4—1421no—
595C22×C4—1422no—
596C22×C4—1422no—
597C22×C4D4×D7111yescharacteristic
598C22×C4D4×D7111yescharacteristic
599C22×C4C23×D7111yescharacteristic
600Q16—28no—
601Q16—1428no—
602Q16—1428no—
603Q16—1428no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—712no—
607C2×C8—712no—
608C2×C8—1422no—
609C2×C8—1422no—
610C2×C8C23×D7112yes—
611C2×C8C23×D7112yes—
612C4⋊C4—24no—
613C4⋊C4—24no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—712no—
617C4⋊C4—712no—
618C4⋊C4—1424no—
619C4⋊C4—1424no—
620C4⋊C4—1424no—
621C4⋊C4—1424no—
622C4⋊C4—1424no—
623C4⋊C4—1424no—
624C4⋊C4—1424no—
625C4⋊C4—1424no—
626C4⋊C4—1424no—
627C4⋊C4—1424no—
628C4⋊C4—1421no—
629C4⋊C4—1421no—
630C4⋊C4C23×D7112yes—
631C4⋊C4C23×D7112yes—
632C22⋊C4—1424no—
633C22⋊C4—1424no—
634C42—24no—
635C42—24no—
636C42—714no—
637C42—714no—
638C42—712no—
639C42—712no—
640C42—1424no—
641C42—1424no—
642C42—1424no—
643C42—1424no—
644C42D4×D7112yes—
645C42C23×D7112yes—
646C23—712no—
647C23—714no—
648C23—1422no—
649C23—1422no—
650C23C2×D4×D7111yescharacteristic
651Q8—22no—
652Q8—24no—
653Q8—22no—
654Q8—22no—
655Q8—42no—
656Q8—2848no—
657Q8—2842no—
658Q8—714no—
659Q8—14216no—
660Q8—1422no—
661Q8—1422no—
662Q8—1422no—
663Q8—1424no—
664Q8C2×#1176586514yes—
665C2×C4—22no—
666C2×C4—24no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—2848no—
676C2×C4—2842no—
677C2×C4—2842no—
678C2×C4—2842no—
679C2×C4—712no—
680C2×C4—714no—
681C2×C4—712no—
682C2×C4—712no—
683C2×C4—1428no—
684C2×C4—1428no—
685C2×C4—14216no—
686C2×C4—1422no—
687C2×C4—1422no—
688C2×C4—1422no—
689C2×C4—1422no—
690C2×C4—1422no—
691C2×C4—1424no—
692C2×C4—1422no—
693C2×C4—1422no—
694C2×C4—1422no—
695C2×C4—1424no—
696C2×C4C2×D4×D7112yes—
697C2×C4C2×D4×D7112yes—
698C2×C4C2×D4×D7111yescharacteristic
699C2×C4#41×D7112yes—
700C2×C4C2×#1176586512yes—
701C2×C4C24×D7111yescharacteristic
702C8—22no—
703C8—22no—
704C8—1422no—
705C8—1422no—
706C22—714no—
707C22—1428no—
708C22—1422no—
709C22—1422no—
710C22#1798650812yes—
711C22#137×D7112yes—
712C22#137×D7112yes—
713C22C22×D4×D7111yescharacteristic
714C4—22no—
715C4—22no—
716C4—24no—
717C4—42no—
718C4—42no—
719C4—42no—
720C4—2842no—
721C4—2842no—
722C4—2842no—
723C4—714no—
724C4—1422no—
725C4—1422no—
726C4—1424no—
727C4#1798650812yes—
728C4C2×#41×D7111yescharacteristic
729C4C22×#1176586511yescharacteristic
730C2—1424no—
731C2#2259846814yesdirect product factor
732C2C2×#1798650811yescharacteristic
733C2C2×#137×D7111yescharacteristic
734C2C2×#137×D7111yescharacteristic
subgroupG/H
centerC23C2×D4×D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#441×C71C2
socleC23×C71C22×D4
prime radicalC23×D71C2×D4
hypercenterC2×#441D71
hypocenterC71C2×#3113
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#441

Complements

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

NH ≅ G/Ntype
3. #22598468C2direct (N × H)
6. C2×#17986283C2semidirect
7. C2×#17986282C2semidirect
8. C2×#17986208C2semidirect
9. C2×#17986207C2semidirect
12. C2×#17986107C2semidirect
13. C2×#17986104C2semidirect
14. C2×#17986104C2semidirect
16. C2×#441×C71C2semidirect
45. #17986283C22semidirect
46. #17986282C22semidirect
47. #17986208C22semidirect
48. #17986207C22semidirect
51. #17986107C22semidirect
52. #17986104C22semidirect
53. #17986104C22semidirect
72. #441×C71C22semidirect
363. C2×C71#3113semidirect
382. C2×#441D71semidirect
384. C71C2×#3113semidirect
425. #441C2×D71semidirect
731. C2#22598468direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179865532
C2×C4×Q8×D712
#225984682
C2×#179863312
C2×#179863282
C2×#179862832
C2×#179862822
C2×#179862082
C2×#179862072
C2×#179861562
C2×#179861532
C2×#179861072
C2×#179861042
C2×#179860542
C2×#441×C712
C2×#311371