Finite Group Databasebeta

← C2×#22600800 #32876004

Subgroups — C2×#22600800 #32876004

Order 18176.

1878 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986709C211yesmaximal, characteristic
2C2×#17986690C211yesmaximal, characteristic
3#22600800C2116yesmaximal, direct product factor
4C2×#17986408C211yesmaximal, characteristic, complemented
5C2×#17986333C211yesmaximal, characteristic, complemented
6C2×#17986339C211yesmaximal, characteristic, complemented
7C2×#17986328C211yesmaximal, characteristic, complemented
8C2×#17986328C211yesmaximal, characteristic, complemented
9C2×#17986306C211yesmaximal, characteristic, complemented
10C2×#17986284C211yesmaximal, characteristic, complemented
11C2×#17986254C211yesmaximal, characteristic, complemented
12C2×#17986237C211yesmaximal, characteristic, complemented
13C2×#17986072C211yesmaximal, characteristic
14C2×#17986038C211yesmaximal, characteristic, complemented
15C2×#106×D71C211yesmaximal, characteristic, complemented
16C2×#441×C71C211yesmaximal, characteristic, complemented
17C22×#11765848C2211yescharacteristic
18C22×C8×D71C2211yescharacteristic
19#17986709—24no—
20#17986709C2218yes—
21#17986690—24no—
22#17986690C2218yes—
23C2×#14556128C2211yescharacteristic
24C2×#14556122—21no—
25C2×#14556120—21no—
26C2×#14556120C2211yescharacteristic
27C2×#14556118—21no—
28C2×#14556113—21no—
29C2×#14556106—21no—
30C2×#14556106—21no—
31C2×#14556104C2211yescharacteristic
32C2×#14556104C2211yescharacteristic
33C2×#14556104C2211yescharacteristic
34C2×#14556104C2211yescharacteristic
35C2×C4×D284—21no—
36C2×C4×D284C2211yescharacteristic
37C2×#14556086C2211yescharacteristic
38C2×#14556085—21no—
39C2×C4⋊C4×D71C2211yescharacteristic
40C2×C4⋊C4×D71C2211yescharacteristic
41C2×C4⋊C4×D71C2211yescharacteristic
42#17986408C2218yescomplemented
43#17986339C2218yescomplemented
44#17986333C2218yescomplemented
45#17986328C2218yescomplemented
46#17986328C2218yescomplemented
47#17986306C2218yescomplemented
48#17986284C2218yescomplemented
49#17986254C2218yescomplemented
50#17986237C2218yescomplemented
51#17986072C2218yes—
52#17986038C2218yescomplemented
53C2×#14556062C2211yescharacteristic
54C2×#14556062C2211yescharacteristic
55C2×#14556061C2211yescharacteristic
56C2×#14556060C2211yescharacteristic
57C2×#14556060C2211yescharacteristic
58C2×#14556059C2211yescharacteristic
59C2×#14556059C2211yescharacteristic
60C2×#14556059C2211yescharacteristic
61#106×D71C2218yescomplemented
62C2×C4⋊(C71⋊C8)C2211yescharacteristic
63C2×#14556052C2211yescharacteristic
64C2×#14556052C2211yescharacteristic
65C2×#14556052C2211yescharacteristic
66C2×#14556052C2211yescharacteristic
67C2×(C2×D71)⋊C8C2211yescharacteristic
68C2×(C2×D71)⋊C8C2211yescharacteristic
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×D284D411yescharacteristic
79C22×C4×D71—21no—
80C22×C4×D71—21no—
81C22×C4×D71—21no—
82C22×C4×D71C2311yescharacteristic
83C22×C4×D71C2311yescharacteristic
84C2×#11765848—24no—
85C2×#11765848C2314yes—
86C22×C71⋊C8C2311yescharacteristic
87C22×C71⋊C8C2311yescharacteristic
88C2×C8×D71—24no—
89C2×C8×D71C2314yes—
90#14556128—22no—
91#14556128C2314yes—
92#14556122—28no—
93#14556120—28no—
94#14556120—22no—
95#14556120C2314yes—
96#14556118—28no—
97#14556113—28no—
98#14556106—28no—
99#14556106—28no—
100#14556104—22no—
101#14556104—22no—
102#14556104—22no—
103#14556104—22no—
104#14556104C2314yes—
105#14556104C2314yes—
106#14556104C2314yes—
107#14556104C2314yes—
108C4×D284—28no—
109C4×D284D414yes—
110C4×D284C2314yes—
111#14556086—22no—
112#14556086C2314yes—
113#14556085—28no—
114C2×C4⋊Dic71—21no—
115C2×C4⋊Dic71D411yescharacteristic
116C2×C4⋊Dic71C2311yescharacteristic
117C2×C4⋊Dic71C2311yescharacteristic
118C2×C4⋊Dic71C2311yescharacteristic
119C2×C4⋊Dic71C2311yescharacteristic
120C2×Dic71⋊C4—21no—
121C2×Dic71⋊C4—21no—
122C2×Dic71⋊C4—21no—
123C2×Dic71⋊C4—21no—
124C2×Dic71⋊C4—21no—
125C2×Dic71⋊C4—21no—
126C2×Dic71⋊C4—21no—
127C2×Dic71⋊C4—21no—
128C2×Dic71⋊C4—21no—
129C4⋊C4×D71—22no—
130C4⋊C4×D71—22no—
131C4⋊C4×D71—22no—
132C4⋊C4×D71C2314yes—
133C4⋊C4×D71C2314yes—
134C4⋊C4×D71C2314yes—
135C2×(C2×D71)⋊C4—21no—
136C2×(C2×D71)⋊C4—21no—
137C2×(C2×D71)⋊C4—21no—
138C2×(C2×D71)⋊C4—21no—
139C2×(C2×D71)⋊C4—21no—
140C2×(C2×D71)⋊C4D411yescharacteristic
141C2×(C2×D71)⋊C4D411yescharacteristic
142C2×C4×Dic71—21no—
143#14556062C2314yes—
144#14556062C2314yes—
145#14556061C2314yes—
146#14556060C2314yes—
147#14556060C2314yes—
148#14556059C2314yes—
149#14556059C2314yes—
150#14556059C2314yes—
151C4⋊(C71⋊C8)C2314yes—
152#14556052C2314yes—
153#14556052C2314yes—
154#14556052C2314yes—
155#14556052C2314yes—
156(C2×D71)⋊C8C2314yes—
157(C2×D71)⋊C8C2314yes—
158C22×Q8×C71C2311yescharacteristic
159C22×Q8×C71C2311yescharacteristic
160C2×Q16×C71—24no—
161C2×Q16×C71C2314yes—
162C22×C8×C71C2311yescharacteristic
163C22×C8×C71C2311yescharacteristic
164C4×Q8×C71—22no—
165C4×Q8×C71—22no—
166C4×Q8×C71C2314yes—
167C4×Q8×C71C2314yes—
168C2×C4⋊C4×C71—21no—
169C2×C4⋊C4×C71—21no—
170C2×C4⋊C4×C71C2311yescharacteristic
171C2×C4⋊C4×C71C2311yescharacteristic
172C2×C42×C71—21no—
173C2×C42×C71—21no—
174C2×C42×C71C2311yescharacteristic
175#106×C71C2314yes—
176#103×C71C2314yes—
177#103×C71C2314yes—
178#97×C71C2314yes—
179C23×D71C2×D411yescharacteristic
180C23×D71C2×D411yescharacteristic
181C2×Dic142—24no—
182C2×Dic142—82no—
183C2×D284—24no—
184C2×D284C2×D414yes—
185C22×Dic71—21no—
186C22×Dic71—21no—
187C22×Dic71—21no—
188C22×Dic71—21no—
189C22×Dic71C2×D411yescharacteristic
190C22×Dic71C2×D411yescharacteristic
191C2×C4×D71—22no—
192C2×C4×D71—22no—
193C2×C4×D71—22no—
194C2×C4×D71—22no—
195C2×C4×D71—24no—
196C2×C4×D71—24no—
197C2×C4×D71—24no—
198C2×C4×D71—44no—
199C2×C4×D71—82no—
200C2×C4×D71—82no—
201C2×C4×D71C2×D412yes—
202C2×C4×D71C2×D412yes—
203C2×C4×D71C2412yes—
204C2×C4×D71C2412yes—
205#11765848—28no—
206C2×C71⋊C8—22no—
207C2×C71⋊C8—22no—
208C2×C71⋊C8C2412yes—
209C2×C71⋊C8C2412yes—
210C8×D71—28no—
211C4⋊Dic71—21no—
212C4⋊Dic71—21no—
213C4⋊Dic71—21no—
214C4⋊Dic71—24no—
215C4⋊Dic71—21no—
216C4⋊Dic71C2×D414yes—
217C4⋊Dic71C2412yes—
218C4⋊Dic71C2412yes—
219C4⋊Dic71C2412yes—
220C4⋊Dic71C2412yes—
221Dic71⋊C4—24no—
222Dic71⋊C4—24no—
223Dic71⋊C4—24no—
224Dic71⋊C4—24no—
225Dic71⋊C4—24no—
226Dic71⋊C4—24no—
227Dic71⋊C4—24no—
228Dic71⋊C4—24no—
229Dic71⋊C4—24no—
230(C2×D71)⋊C4—24no—
231(C2×D71)⋊C4—24no—
232(C2×D71)⋊C4—24no—
233(C2×D71)⋊C4—24no—
234(C2×D71)⋊C4—24no—
235(C2×D71)⋊C4C2×D414yes—
236(C2×D71)⋊C4C2×D414yes—
237C4×Dic71—24no—
238C2×Q8×C71—21no—
239C2×Q8×C71—21no—
240C2×Q8×C71—22no—
241C2×Q8×C71—22no—
242C2×Q8×C71—22no—
243C2×Q8×C71—22no—
244C2×Q8×C71C2412yes—
245C2×Q8×C71C2412yes—
246C22×C4×C71—21no—
247C22×C4×C71—21no—
248C22×C4×C71—21no—
249C22×C4×C71—21no—
250C22×C4×C71C2×D411yescharacteristic
251C22×C4×C71C2×D411yescharacteristic
252C22×C4×C71C2411yescharacteristic
253Q16×C71—28no—
254C2×C8×C71—22no—
255C2×C8×C71#4114yes—
256C2×C8×C71C2412yes—
257C2×C8×C71C2412yes—
258C4⋊C4×C71—24no—
259C4⋊C4×C71—24no—
260C4⋊C4×C71—21no—
261C4⋊C4×C71—21no—
262C4⋊C4×C71C2412yes—
263C4⋊C4×C71C2412yes—
264C42×C71—24no—
265C42×C71—24no—
266C42×C71C2×D412yes—
267C42×C71C2412yes—
268C23×C71C22×D411yescharacteristic
269C22×D71—22no—
270C22×D71—22no—
271C22×D71—22no—
272C22×D71—22no—
273C22×D71—22no—
274C22×D71#13714yes—
275C22×D71C22×D412yes—
276C22×D71C22×D412yes—
277Q8×C71—22no—
278Q8×C71—22no—
279Q8×C71—22no—
280Q8×C71—22no—
281Q8×C71—42no—
282Q8×C71—42no—
283C2×C4×C71—22no—
284C2×C4×C71—22no—
285C2×C4×C71—22no—
286C2×C4×C71—22no—
287C2×C4×C71—22no—
288C2×C4×C71—22no—
289C2×C4×C71—42no—
290C2×C4×C71—42no—
291C2×C4×C71—42no—
292C2×C4×C71—42no—
293C2×C4×C71C22×D412yes—
294C2×C4×C71C22×D412yes—
295C2×C4×C71C22×D411yescharacteristic
296C2×C4×C71C2×#4112yes—
297C2×C4×C712−1+412yes—
298C2×C4×C71C2511yescharacteristic
299C2×Dic71—22no—
300C2×Dic71—22no—
301C2×Dic71—22no—
302C2×Dic71—22no—
303C2×Dic71—22no—
304C2×Dic71—22no—
305C2×Dic71—42no—
306C2×Dic71—42no—
307C2×Dic71—42no—
308C2×Dic71—42no—
309C2×Dic71C22×D412yes—
310C2×Dic71C22×D412yes—
311D284—28no—
312C4×D71—24no—
313C4×D71—24no—
314C4×D71—22no—
315C4×D71—22no—
316C4×D71—22no—
317C4×D71—22no—
318C4×D71—48no—
319C4×D71—84no—
320C4×D71—84no—
321Dic142—84no—
322C8×C71—22no—
323C8×C71C2×#4114yes—
324C71⋊C8—22no—
325C71⋊C8—22no—
326C22×C71#54712yes—
327C22×C71C2×#13712yes—
328C22×C71#57712yes—
329C22×C71C23×D411yescharacteristic
330C2×D71—28no—
331C2×D71—22no—
332C2×D71—22no—
333C2×D71—22no—
334C2×D71—22no—
335C2×D71—22no—
336C2×D71—44no—
337C2×D71C2×#13714yes—
338C4×C71—22no—
339C4×C71—22no—
340C4×C71—42no—
341C4×C71—42no—
342C4×C71—42no—
343C4×C71—42no—
344C4×C71#54712yes—
345C4×C71C22×#4111yescharacteristic
346C4×C71C2×2−1+411yescharacteristic
347Dic71—22no—
348Dic71—22no—
349Dic71—42no—
350Dic71—42no—
351Dic71—42no—
352Dic71—42no—
353C2×#3344—711nomaximal, Sylow
354C2×C71#334414yescomplemented
355C2×C71C2×#54711yescharacteristic
356C2×C71C22×#13711yescharacteristic
357C2×C71C2×#57711yescharacteristic
358D71—24no—
359D71—42no—
360C2×#554—711no—
361C2×#552—711no—
362#3344—7116no—
363C2×#501—711no—
364C2×#484—711no—
365C2×#485—711no—
366C2×#483—711no—
367C2×#483—711no—
368C2×#479—711no—
369C2×#475—711no—
370C2×#470—711no—
371C2×#467—711no—
372C2×#441D7111yescharacteristic, complemented
373C2×#435—711no—
374C2×#428—711no—
375C22×#106—711no—
376C71C2×#334411yescharacteristic, complemented, Sylow
377C22×Q16C2×D7111yescharacteristic
378C22×M16—711no—
379C23×C8—711no—
380#554—718no—
381#554—1424no—
382#552—718no—
383#552—1424no—
384C2×C4⋊Q8—711no—
385C2×#126—1421no—
386C2×#125—711no—
387C2×#125—1421no—
388C2×#125—1421no—
389C2×#123—1421no—
390C2×C22⋊Q8—711no—
391C2×C22⋊Q8—711no—
392C2×C22⋊Q8—711no—
393C2×C22⋊Q8—711no—
394C2×C22⋊Q8—1421no—
395C2×C22⋊Q8—1421no—
396C2×C4×Q8C2×D7111yescharacteristic
397C2×C4×Q8C2×D7111yescharacteristic
398C2×C4×D4—711no—
399C2×C4×D4—1421no—
400C2×#117—711no—
401C2×#117—1421no—
402C22×C4⋊C4—711no—
403C22×C4⋊C4—711no—
404C22×C4⋊C4—711no—
405#501—718no—
406#485—718no—
407#484—718no—
408#483—718no—
409#483—718no—
410#479—718no—
411#475—718no—
412#470—718no—
413#467—718no—
414#441C2×D7118yescomplemented
415#435—718no—
416#428—718no—
417C2×#107—711no—
418C2×#107—711no—
419C2×#107—711no—
420C2×#106—711no—
421C2×#106—711no—
422C2×#106—711no—
423C2×#106—711no—
424C2×#106—711no—
425C2×#106—718no—
426C2×#106C2×D7111yescharacteristic
427C2×C4⋊C8—711no—
428C2×#103—711no—
429C2×#103—711no—
430C2×#103—711no—
431C2×#103—711no—
432C2×#103C2×D7111yescharacteristic
433C2×#103C2×D7111yescharacteristic
434C2×C22⋊C8—711no—
435C2×C22⋊C8—711no—
436C2×#97C2×D7111yescharacteristic
437C22×Q8—1421no—
438C22×Q8C22×D7111yescharacteristic
439C22×Q8C22×D7111yescharacteristic
440C22×D4—711no—
441C23×C4—711no—
442C23×C4—711no—
443C23×C4—1421no—
444C23×C4—1421no—
445C23×C4—1421no—
446C2×Q16—24no—
447C2×Q16C22×D7114yes—
448C2×M16—714no—
449C2×M16—1424no—
450C22×C8—711no—
451C22×C8—711no—
452C22×C8—714no—
453C22×C8—1424no—
454C22×C8C22×D7111yescharacteristic
455C22×C8C22×D7111yescharacteristic
456C4⋊Q8—714no—
457C4⋊Q8—1422no—
458#126—1428no—
459#125—714no—
460#125—1428no—
461#125—1428no—
462#125—1422no—
463#123—1428no—
464C22⋊Q8—714no—
465C22⋊Q8—714no—
466C22⋊Q8—714no—
467C22⋊Q8—714no—
468C22⋊Q8—1428no—
469C22⋊Q8—1428no—
470C22⋊Q8—1422no—
471C22⋊Q8—1422no—
472C22⋊Q8—1422no—
473C22⋊Q8—1422no—
474C4×Q8—22no—
475C4×Q8—22no—
476C4×Q8C22×D7114yes—
477C4×Q8C22×D7114yes—
478C4×D4—714no—
479C4×D4—714no—
480C4×D4—1428no—
481#117—714no—
482#117—1428no—
483#117—1422no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—711no—
487C2×C4⋊C4—711no—
488C2×C4⋊C4—711no—
489C2×C4⋊C4—711no—
490C2×C4⋊C4—711no—
491C2×C4⋊C4—714no—
492C2×C4⋊C4—714no—
493C2×C4⋊C4—714no—
494C2×C4⋊C4—1422no—
495C2×C4⋊C4—1422no—
496C2×C4⋊C4—1422no—
497C2×C4⋊C4—1421no—
498C2×C4⋊C4—1421no—
499C2×C4⋊C4—1421no—
500C2×C4⋊C4—1421no—
501C2×C4⋊C4—1421no—
502C2×C4⋊C4—1421no—
503C2×C4⋊C4—1421no—
504C2×C4⋊C4—1421no—
505C2×C4⋊C4—1421no—
506C2×C4⋊C4—1421no—
507C2×C4⋊C4C22×D7111yescharacteristic
508C2×C4⋊C4C22×D7111yescharacteristic
509C2×C22⋊C4—711no—
510C2×C22⋊C4—711no—
511C2×C22⋊C4—1421no—
512C2×C22⋊C4—1421no—
513C2×C22⋊C4—1421no—
514C2×C22⋊C4—1421no—
515C2×C22⋊C4—1421no—
516C2×C42—21no—
517C2×C42—21no—
518C2×C42—1421no—
519C2×C42C22×D7111yescharacteristic
520#107—714no—
521#107—714no—
522#107—714no—
523#106—714no—
524#106—714no—
525#106—714no—
526#106—714no—
527#106—714no—
528#106C22×D7114yes—
529C4⋊C8—714no—
530#103—714no—
531#103—714no—
532#103—714no—
533#103—714no—
534#103C22×D7114yes—
535#103C22×D7114yes—
536C22⋊C8—714no—
537C22⋊C8—714no—
538#97C22×D7114yes—
539C24—711no—
540C24—711no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—22no—
544C2×Q8—22no—
545C2×Q8—22no—
546C2×Q8—22no—
547C2×Q8—5682no—
548C2×Q8—1424no—
549C2×Q8C23×D7112yes—
550C2×Q8C23×D7112yes—
551C2×D4—714no—
552C2×D4—1424no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—2844no—
558C22×C4—5682no—
559C22×C4—5682no—
560C22×C4—711no—
561C22×C4—711no—
562C22×C4—712no—
563C22×C4—712no—
564C22×C4—712no—
565C22×C4—712no—
566C22×C4—1424no—
567C22×C4—1424no—
568C22×C4—1424no—
569C22×C4—1421no—
570C22×C4—1421no—
571C22×C4—1421no—
572C22×C4—1421no—
573C22×C4—1422no—
574C22×C4—1422no—
575C22×C4—1422no—
576C22×C4—1422no—
577C22×C4D4×D7111yescharacteristic
578C22×C4D4×D7111yescharacteristic
579C22×C4C23×D7111yescharacteristic
580Q16—28no—
581M16—1428no—
582C2×C8—22no—
583C2×C8—712no—
584C2×C8—712no—
585C2×C8—1422no—
586C2×C8—1422no—
587C2×C8—1428no—
588C2×C8#1176586514yes—
589C2×C8C23×D7112yes—
590C2×C8C23×D7112yes—
591C4⋊C4—24no—
592C4⋊C4—24no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—714no—
596C4⋊C4—712no—
597C4⋊C4—712no—
598C4⋊C4—712no—
599C4⋊C4—712no—
600C4⋊C4—1424no—
601C4⋊C4—1424no—
602C4⋊C4—1424no—
603C4⋊C4—1424no—
604C4⋊C4—1424no—
605C4⋊C4—1424no—
606C4⋊C4—1424no—
607C4⋊C4—1424no—
608C4⋊C4—1424no—
609C4⋊C4—1421no—
610C4⋊C4—1421no—
611C4⋊C4—1421no—
612C4⋊C4—1421no—
613C4⋊C4—1424no—
614C4⋊C4C23×D7112yes—
615C4⋊C4C23×D7112yes—
616C22⋊C4—714no—
617C22⋊C4—714no—
618C22⋊C4—1424no—
619C22⋊C4—1424no—
620C22⋊C4—1424no—
621C22⋊C4—1424no—
622C22⋊C4—1424no—
623C42—24no—
624C42—24no—
625C42—1424no—
626C42D4×D7112yes—
627C42C23×D7112yes—
628C23—712no—
629C23—714no—
630C23—712no—
631C23—1422no—
632C23—1422no—
633C23—1422no—
634C23—1422no—
635C23—1422no—
636C23C2×D4×D7111yescharacteristic
637Q8—22no—
638Q8—22no—
639Q8—22no—
640Q8—22no—
641Q8—42no—
642Q8—42no—
643Q8—5684no—
644D4—1428no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—2848no—
656C2×C4—2842no—
657C2×C4—2842no—
658C2×C4—2842no—
659C2×C4—2842no—
660C2×C4—5684no—
661C2×C4—5684no—
662C2×C4—712no—
663C2×C4—712no—
664C2×C4—1422no—
665C2×C4—1422no—
666C2×C4—1422no—
667C2×C4—1422no—
668C2×C4—1422no—
669C2×C4—1422no—
670C2×C4—1422no—
671C2×C4—1422no—
672C2×C4—1422no—
673C2×C4—1422no—
674C2×C4—1424no—
675C2×C4—1424no—
676C2×C4C2×D4×D7112yes—
677C2×C4C2×D4×D7112yes—
678C2×C4C2×D4×D7111yescharacteristic
679C2×C4C2×#1176586512yes—
680C2×C4#1455617512yes—
681C2×C4C24×D7111yescharacteristic
682C8—22no—
683C8—1422no—
684C8—1422no—
685C8C2×#1176586514yes—
686C22—2844no—
687C22—714no—
688C22—1422no—
689C22—1422no—
690C22—1422no—
691C22—1422no—
692C22—1422no—
693C22—1428no—
694C22#1798665412yes—
695C22#137×D7112yes—
696C22#1798680812yes—
697C22C22×D4×D7111yescharacteristic
698C4—22no—
699C4—22no—
700C4—42no—
701C4—42no—
702C4—42no—
703C4—42no—
704C4—2842no—
705C4—2842no—
706C4—2842no—
707C4—2842no—
708C4—1422no—
709C4—1422no—
710C4#1798665412yes—
711C4C22×#1176586511yescharacteristic
712C4C2×#1455617511yescharacteristic
713C2—2842no—
714C2—1424no—
715C2#2260080014yesdirect product factor
716C2C2×#1798665411yescharacteristic
717C2C2×#137×D7111yescharacteristic
718C2C2×#1798680811yescharacteristic
subgroupG/H
centerC23C2×D4×D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#441×C71C2
socleC23×C71C22×D4
prime radicalC22×D284D4
hypercenterC2×#441D71
hypocenterC71C2×#3344
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. #22600800C2direct (N × H)
4. C2×#17986408C2semidirect
5. C2×#17986333C2semidirect
6. C2×#17986339C2semidirect
7. C2×#17986328C2semidirect
8. C2×#17986328C2semidirect
9. C2×#17986306C2semidirect
10. C2×#17986284C2semidirect
11. C2×#17986254C2semidirect
12. C2×#17986237C2semidirect
14. C2×#17986038C2semidirect
15. C2×#106×D71C2semidirect
16. C2×#441×C71C2semidirect
42. #17986408C22semidirect
43. #17986339C22semidirect
44. #17986333C22semidirect
45. #17986328C22semidirect
46. #17986328C22semidirect
47. #17986306C22semidirect
48. #17986284C22semidirect
49. #17986254C22semidirect
50. #17986237C22semidirect
52. #17986038C22semidirect
61. #106×D71C22semidirect
72. #441×C71C22semidirect
354. C2×C71#3344semidirect
372. C2×#441D71semidirect
376. C71C2×#3344semidirect
414. #441C2×D71semidirect
715. C2#22600800direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179867092
C2×#179866902
#226008002
C2×#179864082
C2×#179863332
C2×#179863392
C2×#179863282
C2×#179863062
C2×#179862842
C2×#179862542
C2×#179862372
C2×#179860722
C2×#179860382
C2×#106×D712
C2×#441×C712
C2×#334471