Finite Group Databasebeta

← C2×#22598143 #32864970

Subgroups — C2×#22598143 #32864970

Order 18176.

2098 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986555C211yesmaximal, characteristic
2C2×C4×Q8×D71C211yesmaximal, characteristic
3#22598143C2116yesmaximal, direct product factor
4C2×#17986307C211yesmaximal, characteristic, complemented
5C2×#17986306C211yesmaximal, characteristic, complemented
6C2×#17986303C211yesmaximal, characteristic, complemented
7C2×#17986293C211yesmaximal, characteristic, complemented
8C2×#17986292C211yesmaximal, characteristic, complemented
9C2×#17986283C211yesmaximal, characteristic, complemented
10C2×#17986282C211yesmaximal, characteristic, complemented
11C2×#17986040C211yesmaximal, characteristic
12C2×#17986038C211yesmaximal, characteristic
13C2×#17986021C211yesmaximal, characteristic
14C2×#17986006C211yesmaximal, characteristic
15C2×#17986006C211yesmaximal, characteristic
16C2×#479×C71C211yesmaximal, characteristic, complemented
17C22×Q8×D71C2211yescharacteristic
18C22×#11765848C2211yescharacteristic
19C22×#11765848C2211yescharacteristic
20#17986555—24no—
21#17986555C2218yes—
22C2×#14556127C2211yescharacteristic
23C2×#14556127C2211yescharacteristic
24C2×#14556120C2211yescharacteristic
25C2×#14556106—21no—
26C2×#14556106—21no—
27C2×Q8×Dic71C2211yescharacteristic
28C2×C4×Dic142—21no—
29C2×C4×Dic142C2211yescharacteristic
30C2×#14556093—21no—
31C2×#14556093—21no—
32C2×#14556093—21no—
33C2×#14556093C2211yescharacteristic
34C4×Q8×D71—24no—
35C4×Q8×D71C2218yes—
36C2×#14556086C2211yescharacteristic
37C2×#14556086C2211yescharacteristic
38C2×C4⋊C4×D71—21no—
39C2×C4⋊C4×D71C2211yescharacteristic
40C2×C42×D71—21no—
41C2×C42×D71C2211yescharacteristic
42#17986307C2218yescomplemented
43#17986306C2218yescomplemented
44#17986303C2218yescomplemented
45#17986293C2218yescomplemented
46#17986292C2218yescomplemented
47#17986283C2218yescomplemented
48#17986282C2218yescomplemented
49#17986040C2218yes—
50#17986038C2218yes—
51C2×#14556062C2211yescharacteristic
52C2×#14556061C2211yescharacteristic
53C2×#14556061C2211yescharacteristic
54C2×#14556060C2211yescharacteristic
55C2×#14556059C2211yescharacteristic
56C2×#14556059C2211yescharacteristic
57#17986021C2218yes—
58C2×C4⋊(C71⋊C8)C2211yescharacteristic
59C2×Dic71⋊C8C2211yescharacteristic
60C2×Dic71⋊C8C2211yescharacteristic
61#17986006C2218yes—
62#17986006C2218yes—
63C2×#14556053C2211yescharacteristic
64C2×#14556053C2211yescharacteristic
65C2×#14556052C2211yescharacteristic
66C2×#14556052C2211yescharacteristic
67C2×#14556051C2211yescharacteristic
68C2×#14556051C2211yescharacteristic
69C2×#125×C71C2211yescharacteristic
70C2×C4×Q8×C71C2211yescharacteristic
71#479×C71C2218yescomplemented
72C2×#107×C71C2211yescharacteristic
73C2×#106×C71C2211yescharacteristic
74C2×C4⋊C8×C71C2211yescharacteristic
75C2×#103×C71C2211yescharacteristic
76C2×#103×C71C2211yescharacteristic
77C22×Dic142—21no—
78C22×Dic142—21no—
79C22×Dic142—21no—
80C22×Dic142C2311yescharacteristic
81C2×Q8×D71—22no—
82C2×Q8×D71—24no—
83C2×Q8×D71Q818yescomplemented
84C2×Q8×D71C2314yes—
85C22×C4×D71—21no—
86C22×C4×D71—21no—
87C22×C4×D71D411yescharacteristic
88C22×C4×D71D411yescharacteristic
89C22×C4×D71C2311yescharacteristic
90C2×#11765848—24no—
91C2×#11765848—24no—
92C2×#11765848C2314yes—
93C2×#11765848C2314yes—
94C22×C71⋊C8C2311yescharacteristic
95C22×C71⋊C8C2311yescharacteristic
96#14556127—22no—
97#14556127—22no—
98#14556127C2314yes—
99#14556127C2314yes—
100#14556120—22no—
101#14556120C2314yes—
102#14556106—28no—
103#14556106—28no—
104Q8×Dic71—22no—
105Q8×Dic71C2314yes—
106C4×Dic142—28no—
107C4×Dic142—22no—
108C4×Dic142C2314yes—
109#14556093—22no—
110#14556093—28no—
111#14556093—28no—
112#14556093—28no—
113#14556093C2314yes—
114#14556086—22no—
115#14556086—22no—
116#14556086C2314yes—
117#14556086C2314yes—
118C2×C4⋊Dic71—21no—
119C2×C4⋊Dic71C2311yescharacteristic
120C2×C4⋊Dic71C2311yescharacteristic
121C2×C4⋊Dic71C2311yescharacteristic
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—28no—
130C4⋊C4×D71—22no—
131C4⋊C4×D71C2314yes—
132C2×(C2×D71)⋊C4—21no—
133C2×(C2×D71)⋊C4—21no—
134C2×C4×Dic71—21no—
135C2×C4×Dic71—21no—
136C2×C4×Dic71—21no—
137C2×C4×Dic71—21no—
138C2×C4×Dic71—21no—
139C2×C4×Dic71D411yescharacteristic
140C2×C4×Dic71D411yescharacteristic
141C2×C4×Dic71C2311yescharacteristic
142C42×D71—28no—
143C42×D71D414yes—
144C42×D71C2314yes—
145#14556062C2314yes—
146#14556061C2314yes—
147#14556061C2314yes—
148#14556060C2314yes—
149#14556059C2314yes—
150#14556059C2314yes—
151C4⋊(C71⋊C8)C2314yes—
152Dic71⋊C8C2314yes—
153Dic71⋊C8C2314yes—
154#14556053C2314yes—
155#14556053C2314yes—
156#14556052C2314yes—
157#14556052C2314yes—
158#14556051C2314yes—
159#14556051C2314yes—
160C22×Q8×C71C2311yescharacteristic
161C22×C8×C71C2311yescharacteristic
162C22×C8×C71C2311yescharacteristic
163#125×C71—22no—
164#125×C71C2314yes—
165C4×Q8×C71—22no—
166C4×Q8×C71C2314yes—
167C2×C4⋊C4×C71—21no—
168C2×C4⋊C4×C71—21no—
169C2×C4⋊C4×C71—21no—
170C2×C4⋊C4×C71C2311yescharacteristic
171C2×C4⋊C4×C71C2311yescharacteristic
172C2×C4⋊C4×C71C2311yescharacteristic
173C2×C42×C71—21no—
174C2×C42×C71C2311yescharacteristic
175#107×C71C2314yes—
176#106×C71C2314yes—
177C4⋊C8×C71C2314yes—
178#103×C71C2314yes—
179#103×C71C2314yes—
180C23×D71C2×D411yescharacteristic
181C2×Dic142—21no—
182C2×Dic142—22no—
183C2×Dic142—28no—
184C2×Dic142—24no—
185C2×Dic142—24no—
186C2×Dic142—24no—
187C2×Dic142—44no—
188C2×Dic142—44no—
189C2×Dic142C2×Q814yes—
190C2×Dic142C2412yes—
191Q8×D71—216no—
192Q8×D71—28no—
193Q8×D71C2×Q8116yescomplemented
194C22×Dic71—21no—
195C22×Dic71—21no—
196C22×Dic71—21no—
197C22×Dic71—21no—
198C22×Dic71C2×D411yescharacteristic
199C22×Dic71C2×D411yescharacteristic
200C22×Dic71C2×D411yescharacteristic
201C2×C4×D71—28no—
202C2×C4×D71—24no—
203C2×C4×D71—24no—
204C2×C4×D71—24no—
205C2×C4×D71—42no—
206C2×C4×D71—44no—
207C2×C4×D71C2×D414yes—
208C2×C4×D71C2×D414yes—
209C2×C4×D71C2×D412yes—
210C2×C4×D71C2×Q814yes—
211C2×C4×D71#4114yes—
212C2×C4×D71C2412yes—
213#11765848—28no—
214#11765848—28no—
215C2×C71⋊C8—22no—
216C2×C71⋊C8—22no—
217C2×C71⋊C8C2412yes—
218C2×C71⋊C8C2412yes—
219C4⋊Dic71—21no—
220C4⋊Dic71—21no—
221C4⋊Dic71—21no—
222C4⋊Dic71—24no—
223C4⋊Dic71C2412yes—
224C4⋊Dic71C2412yes—
225C4⋊Dic71C2412yes—
226Dic71⋊C4—24no—
227Dic71⋊C4—24no—
228Dic71⋊C4—24no—
229Dic71⋊C4—24no—
230Dic71⋊C4—24no—
231Dic71⋊C4—24no—
232Dic71⋊C4—24no—
233(C2×D71)⋊C4—24no—
234(C2×D71)⋊C4—24no—
235C4×Dic71—24no—
236C4×Dic71—24no—
237C4×Dic71—24no—
238C4×Dic71—24no—
239C4×Dic71—24no—
240C4×Dic71C2×D412yes—
241C4×Dic71C2×D414yes—
242C4×Dic71C2×D414yes—
243C4×Dic71C2412yes—
244C2×Q8×C71—21no—
245C2×Q8×C71—22no—
246C2×Q8×C71C2×Q814yes—
247C2×Q8×C71C2412yes—
248C22×C4×C71—21no—
249C22×C4×C71—21no—
250C22×C4×C71—21no—
251C22×C4×C71—21no—
252C22×C4×C71C2×D411yescharacteristic
253C22×C4×C71C2×D411yescharacteristic
254C22×C4×C71C2411yescharacteristic
255C2×C8×C71—22no—
256C2×C8×C71—22no—
257C2×C8×C71C2412yes—
258C2×C8×C71C2412yes—
259C4⋊C4×C71—24no—
260C4⋊C4×C71—24no—
261C4⋊C4×C71—24no—
262C4⋊C4×C71—21no—
263C4⋊C4×C71—21no—
264C4⋊C4×C71—21no—
265C4⋊C4×C71C2412yes—
266C4⋊C4×C71C2412yes—
267C4⋊C4×C71C2412yes—
268C42×C71—24no—
269C42×C71C2×D412yes—
270C42×C71C2412yes—
271C23×C71C22×D411yescharacteristic
272C22×D71—22no—
273C22×D71—22no—
274C22×D71C22⋊Q814yes—
275C22×D71C22×D412yes—
276Q8×C71—24no—
277Q8×C71—22no—
278Q8×C71C22×Q814yes—
279C2×C4×C71—24no—
280C2×C4×C71—22no—
281C2×C4×C71—22no—
282C2×C4×C71—22no—
283C2×C4×C71—22no—
284C2×C4×C71—22no—
285C2×C4×C71—22no—
286C2×C4×C71—42no—
287C2×C4×C71—42no—
288C2×C4×C71—42no—
289C2×C4×C71C22×D412yes—
290C2×C4×C71C22×D412yes—
291C2×C4×C71C22×D411yescharacteristic
292C2×C4×C71C22×Q812yes—
293C2×C4×C71C2×#4112yes—
294C2×C4×C71C2511yescharacteristic
295C2×Dic71—24no—
296C2×Dic71—22no—
297C2×Dic71—22no—
298C2×Dic71—22no—
299C2×Dic71—22no—
300C2×Dic71—22no—
301C2×Dic71—42no—
302C2×Dic71—42no—
303C2×Dic71—42no—
304C2×Dic71C22⋊Q814yes—
305C2×Dic71#13714yes—
306C2×Dic71C22×D412yes—
307C2×Dic71C22×D412yes—
308C2×Dic71C22×D412yes—
309C4×D71—216no—
310C4×D71—28no—
311C4×D71—44no—
312C4×D71—48no—
313C4×D71C22⋊Q818yes—
314C4×D71C22×Q814yes—
315C4×D71C2×#4114yes—
316Dic142—24no—
317Dic142—22no—
318Dic142—216no—
319Dic142—48no—
320Dic142—48no—
321Dic142C22×Q814yes—
322C8×C71—22no—
323C8×C71—22no—
324C71⋊C8—22no—
325C71⋊C8—22no—
326C22×C71C2×C22⋊Q812yes—
327C22×C71C2×#13712yes—
328C22×C71#57512yes—
329C22×C71C23×D411yescharacteristic
330C2×D71—28no—
331C2×D71—22no—
332C2×D71—22no—
333C2×D71C2×C22⋊Q814yes—
334C4×C71—24no—
335C4×C71—22no—
336C4×C71—22no—
337C4×C71—42no—
338C4×C71—42no—
339C4×C71—42no—
340C4×C71C2×C22⋊Q812yes—
341C4×C71C23×Q811yescharacteristic
342C4×C71C22×#4111yescharacteristic
343Dic71—24no—
344Dic71—22no—
345Dic71—42no—
346Dic71—42no—
347Dic71—42no—
348Dic71C2×C22⋊Q814yes—
349Dic71C2×#13714yes—
350C2×#3078—711nomaximal, Sylow
351C2×C71#307814yescomplemented
352C2×C71C22×C22⋊Q811yescharacteristic
353C2×C71C22×#13711yescharacteristic
354C2×C71C2×#57511yescharacteristic
355D71—24no—
356C2×#533—711no—
357C22×C4×Q8—711no—
358#3078—7116no—
359C2×#479—711no—
360C2×#479—711no—
361C2×#479—711no—
362C2×#479D7111yescharacteristic, complemented
363C2×#477—711no—
364C2×#477—711no—
365C2×#475—711no—
366C2×#475—711no—
367C2×#428—711no—
368C2×#428—711no—
369C2×#423—711no—
370C2×#419—711no—
371C2×#419—711no—
372C71C2×#307811yescharacteristic, complemented, Sylow
373C23×Q8—711no—
374C22×M16—711no—
375C22×M16—711no—
376#533—718no—
377#533—1424no—
378C2×C4⋊Q8—711no—
379C2×C4⋊Q8—711no—
380C2×#125—711no—
381C2×#125C2×D7111yescharacteristic
382C2×C22⋊Q8—1421no—
383C2×C22⋊Q8—1421no—
384C2×C4×Q8—711no—
385C2×C4×Q8—718no—
386C2×C4×Q8—711no—
387C2×C4×Q8—711no—
388C2×C4×Q8—1421no—
389C2×C4×Q8—1421no—
390C2×C4×Q8—1421no—
391C2×C4×Q8—1421no—
392C2×C4×Q8—1424no—
393C2×C4×Q8C2×D7111yescharacteristic
394C2×#117—711no—
395C2×#117—711no—
396C22×C4⋊C4—711no—
397C22×C4⋊C4—1421no—
398C22×C42—711no—
399C22×C42—1421no—
400#479—718no—
401#479—718no—
402#479—718no—
403#479C2×D7118yescomplemented
404#477—718no—
405#477—718no—
406#475—718no—
407#475—718no—
408#428—718no—
409#428—718no—
410C2×#107—711no—
411C2×#107—711no—
412C2×#107—711no—
413C2×#107C2×D7111yescharacteristic
414C2×#106—711no—
415C2×#106—711no—
416C2×#106—711no—
417C2×#106C2×D7111yescharacteristic
418#423—718no—
419C2×C4⋊C8—711no—
420C2×C4⋊C8—711no—
421C2×C4⋊C8—711no—
422C2×C4⋊C8C2×D7111yescharacteristic
423#419—718no—
424#419—718no—
425C2×#103—711no—
426C2×#103—711no—
427C2×#103—711no—
428C2×#103—711no—
429C2×#103—711no—
430C2×#103—711no—
431C2×#103C2×D7111yescharacteristic
432C2×#103C2×D7111yescharacteristic
433C22×Q8—718no—
434C22×Q8—714no—
435C22×Q8—711no—
436C22×Q8—1421no—
437C22×Q8—1421no—
438C22×Q8—1421no—
439C22×Q8—1422no—
440C22×Q8—1424no—
441C22×Q8C22×D7111yescharacteristic
442C23×C4—711no—
443C23×C4—711no—
444C23×C4—711no—
445C23×C4—1421no—
446C23×C4—1421no—
447C2×M16—714no—
448C2×M16—714no—
449C2×M16—1424no—
450C2×M16—1424no—
451C22×C8—711no—
452C22×C8—711no—
453C22×C8C22×D7111yescharacteristic
454C22×C8C22×D7111yescharacteristic
455C4⋊Q8—714no—
456C4⋊Q8—714no—
457C4⋊Q8—1422no—
458C4⋊Q8—1422no—
459#125—22no—
460#125—714no—
461#125—1422no—
462#125C22×D7114yes—
463C22⋊Q8—1428no—
464C22⋊Q8—1428no—
465C4×Q8—22no—
466C4×Q8—714no—
467C4×Q8—714no—
468C4×Q8—714no—
469C4×Q8—1428no—
470C4×Q8—1428no—
471C4×Q8—1422no—
472C4×Q8—1428no—
473C4×Q8—1428no—
474C4×Q8—1422no—
475C4×Q8—1422no—
476C4×Q8C22×D7114yes—
477#117—714no—
478#117—714no—
479#117—1422no—
480#117—1422no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—711no—
485C2×C4⋊C4—711no—
486C2×C4⋊C4—711no—
487C2×C4⋊C4—714no—
488C2×C4⋊C4—1422no—
489C2×C4⋊C4—1428no—
490C2×C4⋊C4—1421no—
491C2×C4⋊C4—1421no—
492C2×C4⋊C4—1421no—
493C2×C4⋊C4—1421no—
494C2×C4⋊C4—1421no—
495C2×C4⋊C4—1421no—
496C2×C4⋊C4—1421no—
497C2×C4⋊C4—1421no—
498C2×C4⋊C4C22×D7111yescharacteristic
499C2×C4⋊C4C22×D7111yescharacteristic
500C2×C4⋊C4C22×D7111yescharacteristic
501C2×C22⋊C4—1421no—
502C2×C22⋊C4—1421no—
503C2×C42—21no—
504C2×C42—711no—
505C2×C42—711no—
506C2×C42—711no—
507C2×C42—714no—
508C2×C42—714no—
509C2×C42—1428no—
510C2×C42—1421no—
511C2×C42—1421no—
512C2×C42—1421no—
513C2×C42—1421no—
514C2×C42—1421no—
515C2×C42C22×D7111yescharacteristic
516#107—714no—
517#107—714no—
518#107—714no—
519#107C22×D7114yes—
520#106—714no—
521#106—714no—
522#106—714no—
523#106C22×D7114yes—
524C4⋊C8—714no—
525C4⋊C8—714no—
526C4⋊C8—714no—
527C4⋊C8C22×D7114yes—
528#103—714no—
529#103—714no—
530#103—714no—
531#103—714no—
532#103—714no—
533#103—714no—
534#103C22×D7114yes—
535#103C22×D7114yes—
536C24—711no—
537C2×Q8—21no—
538C2×Q8—22no—
539C2×Q8—2844no—
540C2×Q8—2844no—
541C2×Q8—7116no—
542C2×Q8—714no—
543C2×Q8—712no—
544C2×Q8—1424no—
545C2×Q8—1424no—
546C2×Q8—1424no—
547C2×Q8—1428no—
548C2×Q8—1428no—
549C2×Q8—14216no—
550C2×Q8—1421no—
551C2×Q8—1422no—
552C2×Q8Q8×D7114yes—
553C2×Q8C23×D7112yes—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—2842no—
559C22×C4—2844no—
560C22×C4—714no—
561C22×C4—711no—
562C22×C4—711no—
563C22×C4—712no—
564C22×C4—714no—
565C22×C4—714no—
566C22×C4—712no—
567C22×C4—711no—
568C22×C4—714no—
569C22×C4—1424no—
570C22×C4—1424no—
571C22×C4—1424no—
572C22×C4—1428no—
573C22×C4—1421no—
574C22×C4—1421no—
575C22×C4—1421no—
576C22×C4—1421no—
577C22×C4D4×D7111yescharacteristic
578C22×C4D4×D7111yescharacteristic
579C22×C4C23×D7111yescharacteristic
580M16—1428no—
581M16—1428no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—712no—
585C2×C8—712no—
586C2×C8—1422no—
587C2×C8—1422no—
588C2×C8C23×D7112yes—
589C2×C8C23×D7112yes—
590C4⋊C4—24no—
591C4⋊C4—24no—
592C4⋊C4—24no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—712no—
597C4⋊C4—712no—
598C4⋊C4—712no—
599C4⋊C4—1424no—
600C4⋊C4—1424no—
601C4⋊C4—1424no—
602C4⋊C4—1424no—
603C4⋊C4—1424no—
604C4⋊C4—1424no—
605C4⋊C4—1424no—
606C4⋊C4—1424no—
607C4⋊C4—1421no—
608C4⋊C4—1421no—
609C4⋊C4—1421no—
610C4⋊C4C23×D7112yes—
611C4⋊C4C23×D7112yes—
612C4⋊C4C23×D7112yes—
613C22⋊C4—1424no—
614C22⋊C4—1424no—
615C42—24no—
616C42—714no—
617C42—714no—
618C42—712no—
619C42—712no—
620C42—1424no—
621C42—1424no—
622C42—1424no—
623C42—1424no—
624C42—1424no—
625C42D4×D7112yes—
626C42C23×D7112yes—
627C23—712no—
628C23—714no—
629C23—1422no—
630C23—1422no—
631C23C2×D4×D7111yescharacteristic
632Q8—22no—
633Q8—24no—
634Q8—2848no—
635Q8—2848no—
636Q8—714no—
637Q8—14216no—
638Q8—1422no—
639Q8—1424no—
640Q8C2×Q8×D7114yes—
641C2×C4—22no—
642C2×C4—24no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—2844no—
652C2×C4—2848no—
653C2×C4—2842no—
654C2×C4—2842no—
655C2×C4—2842no—
656C2×C4—712no—
657C2×C4—712no—
658C2×C4—714no—
659C2×C4—714no—
660C2×C4—714no—
661C2×C4—714no—
662C2×C4—718no—
663C2×C4—712no—
664C2×C4—1428no—
665C2×C4—14216no—
666C2×C4—1422no—
667C2×C4—1422no—
668C2×C4—1422no—
669C2×C4—1422no—
670C2×C4—1424no—
671C2×C4—1422no—
672C2×C4C2×D4×D7112yes—
673C2×C4C2×D4×D7112yes—
674C2×C4C2×D4×D7111yescharacteristic
675C2×C4C2×Q8×D7112yes—
676C2×C4#41×D7112yes—
677C2×C4C24×D7111yescharacteristic
678C8—22no—
679C8—22no—
680C8—1422no—
681C8—1422no—
682C22—714no—
683C22—1422no—
684C22—1422no—
685C22—1428no—
686C22C22⋊Q8×D7112yes—
687C22#137×D7112yes—
688C22#1798679612yes—
689C22C22×D4×D7111yescharacteristic
690C4—22no—
691C4—22no—
692C4—24no—
693C4—42no—
694C4—42no—
695C4—42no—
696C4—2842no—
697C4—2842no—
698C4—2842no—
699C4—714no—
700C4—714no—
701C4—1422no—
702C4—1424no—
703C4C22⋊Q8×D7112yes—
704C4C22×Q8×D7111yescharacteristic
705C4C2×#41×D7111yescharacteristic
706C2—1424no—
707C2#2259814314yesdirect product factor
708C2C2×C22⋊Q8×D7111yescharacteristic
709C2C2×#137×D7111yescharacteristic
710C2C2×#1798679611yescharacteristic
subgroupG/H
centerC23C2×D4×D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#479×C71C2
socleC23×C71C22×D4
prime radicalC23×D71C2×D4
hypercenterC2×#479D71
hypocenterC71C2×#3078
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#479

Complements

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

NH ≅ G/Ntype
3. #22598143C2direct (N × H)
4. C2×#17986307C2semidirect
5. C2×#17986306C2semidirect
6. C2×#17986303C2semidirect
7. C2×#17986293C2semidirect
8. C2×#17986292C2semidirect
9. C2×#17986283C2semidirect
10. C2×#17986282C2semidirect
16. C2×#479×C71C2semidirect
42. #17986307C22semidirect
43. #17986306C22semidirect
44. #17986303C22semidirect
45. #17986293C22semidirect
46. #17986292C22semidirect
47. #17986283C22semidirect
48. #17986282C22semidirect
71. #479×C71C22semidirect
83. C2×Q8×D71Q8semidirect
193. Q8×D71C2×Q8semidirect
351. C2×C71#3078semidirect
362. C2×#479D71semidirect
372. C71C2×#3078semidirect
403. #479C2×D71semidirect
707. C2#22598143direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179865552
C2×C4×Q8×D712
#225981432
C2×#179863072
C2×#179863062
C2×#179863032
C2×#179862932
C2×#179862922
C2×#179862832
C2×#179862822
C2×#179860402
C2×#179860382
C2×#179860212
C2×#179860062
C2×#479×C712
C2×#307871