Finite Group Databasebeta

← C2×#22600765 #32875950

Subgroups — C2×#22600765 #32875950

Order 18176.

1854 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×#17986720C211yesmaximal, characteristic
2C2×#17986717C211yesmaximal, characteristic
3#22600765C2116yesmaximal, direct product factor
4C2×#17986403C211yesmaximal, characteristic, complemented
5C2×#17986342C211yesmaximal, characteristic, complemented
6C2×#17986341C211yesmaximal, characteristic, complemented
7C2×#17986339C211yesmaximal, characteristic, complemented
8C2×#17986283C211yesmaximal, characteristic, complemented
9C2×#17986282C211yesmaximal, characteristic, complemented
10C2×#17986239C211yesmaximal, characteristic, complemented
11C2×#17986238C211yesmaximal, characteristic, complemented
12C2×#17986091C211yesmaximal, characteristic, complemented
13C2×(C22⋊D71)⋊C8C211yesmaximal, characteristic
14C2×#17986035C211yesmaximal, characteristic, complemented
15C2×#17986034C211yesmaximal, characteristic, complemented
16C2×#485×C71C211yesmaximal, characteristic, complemented
17C22×#11765855C2211yescharacteristic
18C23×C71⋊C8C2211yescharacteristic
19C22×C8×D71C2211yescharacteristic
20#17986720—24no—
21#17986720C2218yes—
22#17986717—24no—
23#17986717C2218yes—
24C2×#14556127C2211yescharacteristic
25C2×#14556127C2211yescharacteristic
26C2×#14556123—21no—
27C2×#14556122—21no—
28C2×#14556121—21no—
29C2×#14556121—21no—
30C2×#14556114—21no—
31C2×#14556114—21no—
32C2×#14556108C2211yescharacteristic
33C2×#14556107C2211yescharacteristic
34C2×#14556104C2211yescharacteristic
35C2×Q8×Dic71C2211yescharacteristic
36C2×C4×Dic142—21no—
37C2×#14556093—21no—
38C2×#14556093C2211yescharacteristic
39C2×C4×C22⋊D71C2211yescharacteristic
40C2×#14556087C2211yescharacteristic
41C2×#14556086C2211yescharacteristic
42C2×#14556086C2211yescharacteristic
43#17986403C2218yescomplemented
44#17986342C2218yescomplemented
45#17986341C2218yescomplemented
46#17986339C2218yescomplemented
47#17986283C2218yescomplemented
48#17986282C2218yescomplemented
49#17986239C2218yescomplemented
50#17986238C2218yescomplemented
51#17986091C2218yescomplemented
52(C22⋊D71)⋊C8C2218yes—
53#17986035C2218yescomplemented
54#17986034C2218yescomplemented
55C2×#14556062C2211yescharacteristic
56C2×#14556061C2211yescharacteristic
57C2×#14556061C2211yescharacteristic
58C2×#14556061C2211yescharacteristic
59C2×#14556060C2211yescharacteristic
60C2×#14556059C2211yescharacteristic
61C2×#14556059C2211yescharacteristic
62C2×Dic71⋊C8C2211yescharacteristic
63C2×#14556053C2211yescharacteristic
64C2×#14556053C2211yescharacteristic
65C2×#14556052C2211yescharacteristic
66C2×#14556051C2211yescharacteristic
67C2×(C2×D71)⋊C8C2211yescharacteristic
68C2×C8×Dic71C2211yescharacteristic
69C2×C22⋊Q8×C71C2211yescharacteristic
70C2×#117×C71C2211yescharacteristic
71#485×C71C2218yescomplemented
72C2×#107×C71C2211yescharacteristic
73C2×#106×C71C2211yescharacteristic
74C2×#103×C71C2211yescharacteristic
75C2×#103×C71C2211yescharacteristic
76C2×C22⋊C8×C71C2211yescharacteristic
77C22×Dic142—21no—
78C22×Dic142—21no—
79C22×Dic142C2311yescharacteristic
80C22×C22⋊D71D411yescharacteristic
81C22×C4×D71C2311yescharacteristic
82C2×#11765855—24no—
83C2×#11765855C2314yes—
84C22×C71⋊C8—24no—
85C22×C71⋊C8C2314yes—
86C22×C71⋊C8C2311yescharacteristic
87C22×C71⋊C8C2311yescharacteristic
88C2×C8×D71—24no—
89C2×C8×D71C2314yes—
90#14556127—22no—
91#14556127—22no—
92#14556127C2314yes—
93#14556127C2314yes—
94#14556123—28no—
95#14556122—28no—
96#14556121—28no—
97#14556121—28no—
98#14556114—28no—
99#14556114—28no—
100#14556108—22no—
101#14556108C2314yes—
102#14556107—22no—
103#14556107C2314yes—
104#14556104—22no—
105#14556104C2314yes—
106Q8×Dic71—22no—
107Q8×Dic71C2314yes—
108C4×Dic142—28no—
109#14556093—28no—
110#14556093—22no—
111#14556093C2314yes—
112C4×C22⋊D71D414yes—
113C4×C22⋊D71C2314yes—
114#14556087—22no—
115#14556087C2314yes—
116#14556086—22no—
117#14556086—22no—
118#14556086C2314yes—
119#14556086C2314yes—
120C2×C4⋊Dic71—21no—
121C2×C4⋊Dic71—21no—
122C2×C4⋊Dic71C2311yescharacteristic
123C2×C4⋊Dic71C2311yescharacteristic
124C2×C4⋊Dic71C2311yescharacteristic
125C2×Dic71⋊C4—21no—
126C2×Dic71⋊C4—21no—
127C2×Dic71⋊C4—21no—
128C2×Dic71⋊C4—21no—
129C2×Dic71⋊C4—21no—
130C2×Dic71⋊C4D411yescharacteristic
131C2×C22⋊Dic71—21no—
132C2×C22⋊Dic71—21no—
133C2×C22⋊Dic71D411yescharacteristic
134C2×(C2×D71)⋊C4—21no—
135C2×(C2×D71)⋊C4—21no—
136C2×(C2×D71)⋊C4—21no—
137C2×(C2×D71)⋊C4—21no—
138C2×(C2×D71)⋊C4D411yescharacteristic
139C2×C4×Dic71—21no—
140C2×C4×Dic71—21no—
141C2×C4×Dic71—21no—
142C2×C4×Dic71—21no—
143C2×C4×Dic71—21no—
144C2×C4×Dic71C2311yescharacteristic
145#14556062C2314yes—
146#14556061C2314yes—
147#14556061C2314yes—
148#14556061C2314yes—
149#14556060C2314yes—
150#14556059C2314yes—
151#14556059C2314yes—
152Dic71⋊C8C2314yes—
153#14556053C2314yes—
154#14556053C2314yes—
155#14556052C2314yes—
156#14556051C2314yes—
157(C2×D71)⋊C8C2314yes—
158C8×Dic71C2314yes—
159C22×Q8×C71C2311yescharacteristic
160C23×C4×C71C2311yescharacteristic
161C22×C8×C71C2311yescharacteristic
162C22×C8×C71C2311yescharacteristic
163C22⋊Q8×C71—22no—
164C22⋊Q8×C71C2314yes—
165#117×C71—22no—
166#117×C71C2314yes—
167C2×C4⋊C4×C71—21no—
168C2×C4⋊C4×C71C2311yescharacteristic
169C2×C4⋊C4×C71C2311yescharacteristic
170C2×C4⋊C4×C71C2311yescharacteristic
171C2×C22⋊C4×C71—21no—
172C2×C22⋊C4×C71—21no—
173C2×C42×C71—21no—
174#107×C71C2314yes—
175#106×C71C2314yes—
176#103×C71C2314yes—
177#103×C71C2314yes—
178C22⋊C8×C71C2314yes—
179C23×D71C2×D411yescharacteristic
180C2×Dic142—22no—
181C2×Dic142—22no—
182C2×Dic142—21no—
183C2×Dic142—24no—
184C2×Dic142—24no—
185C2×Dic142—44no—
186C2×Dic142—44no—
187C2×Dic142C2412yes—
188C2×C22⋊D71—24no—
189C2×C22⋊D71C2×D414yes—
190C22×Dic71—21no—
191C22×Dic71—21no—
192C22×Dic71—21no—
193C22×Dic71—21no—
194C22×Dic71C2×D411yescharacteristic
195C22×Dic71C2×D411yescharacteristic
196C22×Dic71C2×D411yescharacteristic
197C2×C4×D71—22no—
198C2×C4×D71—22no—
199C2×C4×D71C2×D412yes—
200C2×C4×D71C2412yes—
201#11765855—28no—
202C2×C71⋊C8—22no—
203C2×C71⋊C8—28no—
204C2×C71⋊C8#4114yes—
205C2×C71⋊C8C2412yes—
206C2×C71⋊C8C2412yes—
207C8×D71—28no—
208C4⋊Dic71—21no—
209C4⋊Dic71—21no—
210C4⋊Dic71—21no—
211C4⋊Dic71—24no—
212C4⋊Dic71—24no—
213C4⋊Dic71C2412yes—
214C4⋊Dic71C2412yes—
215C4⋊Dic71C2412yes—
216Dic71⋊C4—24no—
217Dic71⋊C4—24no—
218Dic71⋊C4—24no—
219Dic71⋊C4—24no—
220Dic71⋊C4—24no—
221Dic71⋊C4C2×D414yes—
222C22⋊Dic71—24no—
223C22⋊Dic71—24no—
224C22⋊Dic71C2×D414yes—
225(C2×D71)⋊C4—24no—
226(C2×D71)⋊C4—24no—
227(C2×D71)⋊C4—24no—
228(C2×D71)⋊C4—24no—
229(C2×D71)⋊C4C2×D414yes—
230C4×Dic71—24no—
231C4×Dic71—24no—
232C4×Dic71—24no—
233C4×Dic71—24no—
234C4×Dic71—24no—
235C4×Dic71C2×D412yes—
236C4×Dic71C2412yes—
237C24×C71C2×D411yescharacteristic
238C2×Q8×C71—21no—
239C2×Q8×C71—22no—
240C2×Q8×C71—22no—
241C2×Q8×C71C2412yes—
242C22×C4×C71—22no—
243C22×C4×C71—22no—
244C22×C4×C71—21no—
245C22×C4×C71—21no—
246C22×C4×C71—21no—
247C22×C4×C71—21no—
248C22×C4×C71C2×D411yescharacteristic
249C22×C4×C71C2×D412yes—
250C22×C4×C71C2412yes—
251C22×C4×C71C2411yescharacteristic
252C2×C8×C71—22no—
253C2×C8×C71—22no—
254C2×C8×C71C2412yes—
255C2×C8×C71C2412yes—
256C4⋊C4×C71—24no—
257C4⋊C4×C71—21no—
258C4⋊C4×C71—21no—
259C4⋊C4×C71—21no—
260C4⋊C4×C71C2412yes—
261C4⋊C4×C71C2412yes—
262C4⋊C4×C71C2412yes—
263C22⋊C4×C71—24no—
264C22⋊C4×C71—24no—
265C42×C71—24no—
266C23×C71—22no—
267C23×C71—22no—
268C23×C71—22no—
269C23×C71C22×D412yes—
270C23×C71C22×D411yescharacteristic
271C22×D71—22no—
272C22×D71—22no—
273C22×D71—22no—
274C22×D71C22×D412yes—
275Q8×C71—22no—
276Q8×C71—22no—
277Q8×C71—42no—
278C2×C4×C71—22no—
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×C71—42no—
290C2×C4×C71C22×D412yes—
291C2×C4×C71C22×D411yescharacteristic
292C2×C4×C71C2×#4112yes—
293C2×C4×C712−1+412yes—
294C2×C4×C71C2511yescharacteristic
295C22⋊D71—28no—
296C2×Dic71—22no—
297C2×Dic71—22no—
298C2×Dic71—22no—
299C2×Dic71—22no—
300C2×Dic71—22no—
301C2×Dic71—22no—
302C2×Dic71—42no—
303C2×Dic71—42no—
304C2×Dic71—42no—
305C2×Dic71—42no—
306C2×Dic71#13514yes—
307C2×Dic71C22×D412yes—
308C2×Dic71C22×D412yes—
309C2×Dic71C22×D412yes—
310C4×D71—24no—
311C4×D71—22no—
312C4×D71—22no—
313Dic142—22no—
314Dic142—22no—
315Dic142—42no—
316Dic142—48no—
317Dic142—48no—
318C8×C71—22no—
319C8×C71—22no—
320C71⋊C8—22no—
321C71⋊C8C2×#4114yes—
322C22×C71—22no—
323C22×C71—22no—
324C22×C71—22no—
325C22×C71—44no—
326C22×C71#54712yes—
327C22×C71C2×#13512yes—
328C22×C71#57812yes—
329C22×C71C23×D411yescharacteristic
330C2×D71—22no—
331C2×D71—22no—
332C2×D71—22no—
333C2×D71—44no—
334C4×C71—22no—
335C4×C71—42no—
336C4×C71—42no—
337C4×C71—42no—
338C4×C71—42no—
339C4×C71#54712yes—
340C4×C71C22×#4111yescharacteristic
341C4×C71C2×2−1+411yescharacteristic
342Dic71—22no—
343Dic71—22no—
344Dic71—42no—
345Dic71—42no—
346Dic71—42no—
347Dic71—42no—
348Dic71C2×#13514yes—
349C2×#3342—711nomaximal, Sylow
350C2×C71—42no—
351C2×C71#334214yescomplemented
352C2×C71C2×#54711yescharacteristic
353C2×C71C22×#13511yescharacteristic
354C2×C71C2×#57811yescharacteristic
355D71—42no—
356C2×#556—711no—
357C2×#556—711no—
358#3342—7116no—
359C2×#500—711no—
360C2×#485—711no—
361C2×#485—711no—
362C2×#485—711no—
363C2×#485D7111yescharacteristic, complemented
364C2×#475—711no—
365C2×#475—711no—
366C2×#467—711no—
367C2×#467—711no—
368C2×C4×Q16—711no—
369C2×C8×D4—711no—
370C2×#427—711no—
371C2×#427—711no—
372C71C2×#334211yescharacteristic, complemented, Sylow
373C22×Q16—711no—
374C23×C8—711no—
375C23×C8—711no—
376#556—718no—
377#556—718no—
378#556—1424no—
379#556—1424no—
380C2×C4⋊Q8—711no—
381C2×C4⋊Q8—711no—
382C2×#126—1421no—
383C2×#126—1421no—
384C2×#126—1421no—
385C2×#126—1421no—
386C2×#124—1421no—
387C2×#124—1421no—
388C2×C22⋊Q8—711no—
389C2×C22⋊Q8—711no—
390C2×C22⋊Q8—711no—
391C2×C22⋊Q8C2×D7111yescharacteristic
392C2×C4×Q8—711no—
393C2×C4×Q8—711no—
394C2×C4×Q8—1421no—
395C2×C4×Q8—1421no—
396C2×C4×D4—711no—
397C2×#117—711no—
398C2×#117—711no—
399C2×#117—711no—
400C2×#117C2×D7111yescharacteristic
401#500—718no—
402#485—718no—
403#485—718no—
404#485—718no—
405#485C2×D7118yescomplemented
406#475—718no—
407#475—718no—
408#467—718no—
409#467—718no—
410C4×Q16—718no—
411C8×D4—718no—
412#427—718no—
413#427—718no—
414C2×#107—711no—
415C2×#107—711no—
416C2×#107—711no—
417C2×#107—711no—
418C2×#107C2×D7111yescharacteristic
419C2×#106—711no—
420C2×#106—711no—
421C2×#106—711no—
422C2×#106C2×D7111yescharacteristic
423C2×C4⋊C8—711no—
424C2×#103—711no—
425C2×#103—711no—
426C2×#103—711no—
427C2×#103—711no—
428C2×#103C2×D7111yescharacteristic
429C2×#103C2×D7111yescharacteristic
430C2×C22⋊C8—711no—
431C2×C22⋊C8C2×D7111yescharacteristic
432C2×C4×C8—711no—
433C22×Q8—711no—
434C22×Q8—1421no—
435C22×Q8—1421no—
436C22×Q8C22×D7111yescharacteristic
437C22×D4—711no—
438C23×C4—711no—
439C23×C4C22×D7111yescharacteristic
440C2×Q16—714no—
441C2×Q16—1424no—
442C22×C8—711no—
443C22×C8—711no—
444C22×C8—714no—
445C22×C8—714no—
446C22×C8—1424no—
447C22×C8—1424no—
448C22×C8C22×D7111yescharacteristic
449C22×C8C22×D7111yescharacteristic
450C4⋊Q8—714no—
451C4⋊Q8—714no—
452C4⋊Q8—1422no—
453C4⋊Q8—1422no—
454#126—1428no—
455#126—1428no—
456#126—1428no—
457#126—1428no—
458#124—1428no—
459#124—1428no—
460C22⋊Q8—22no—
461C22⋊Q8—714no—
462C22⋊Q8—714no—
463C22⋊Q8—714no—
464C22⋊Q8—1422no—
465C22⋊Q8—1422no—
466C22⋊Q8—1422no—
467C22⋊Q8C22×D7114yes—
468C4×Q8—714no—
469C4×Q8—714no—
470C4×Q8—1428no—
471C4×Q8—1422no—
472C4×Q8—1422no—
473C4×Q8—1428no—
474C4×D4—714no—
475C4×D4—714no—
476#117—22no—
477#117—714no—
478#117—714no—
479#117—714no—
480#117—1422no—
481#117—1422no—
482#117—1422no—
483#117C22×D7114yes—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—711no—
486C2×C4⋊C4—711no—
487C2×C4⋊C4—711no—
488C2×C4⋊C4—711no—
489C2×C4⋊C4—1421no—
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⋊C4C22×D7111yescharacteristic
497C2×C4⋊C4C22×D7111yescharacteristic
498C2×C4⋊C4C22×D7111yescharacteristic
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—711no—
502C2×C22⋊C4—711no—
503C2×C22⋊C4—1421no—
504C2×C22⋊C4—1421no—
505C2×C22⋊C4—1421no—
506C2×C22⋊C4—1421no—
507C2×C22⋊C4—1421no—
508C2×C22⋊C4—1421no—
509C2×C42—21no—
510C2×C42—711no—
511C2×C42—1421no—
512C2×C42—1421no—
513C2×C42—1421no—
514C2×C42—1421no—
515C2×C42—1421no—
516#107—714no—
517#107—714no—
518#107—714no—
519#107—714no—
520#107C22×D7114yes—
521#106—714no—
522#106—714no—
523#106—714no—
524#106C22×D7114yes—
525C4⋊C8—714no—
526#103—714no—
527#103—714no—
528#103—714no—
529#103—714no—
530#103C22×D7114yes—
531#103C22×D7114yes—
532C22⋊C8—714no—
533C22⋊C8C22×D7114yes—
534C4×C8—714no—
535C24—711no—
536C24D4×D7111yescharacteristic
537C2×Q8—21no—
538C2×Q8—22no—
539C2×Q8—22no—
540C2×Q8—2844no—
541C2×Q8—2844no—
542C2×Q8—712no—
543C2×Q8—1424no—
544C2×Q8—1424no—
545C2×Q8—1422no—
546C2×Q8—1422no—
547C2×Q8—1421no—
548C2×Q8C23×D7112yes—
549C2×D4—714no—
550C2×D4—1424no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—711no—
558C22×C4—711no—
559C22×C4—711no—
560C22×C4—712no—
561C22×C4—712no—
562C22×C4—1421no—
563C22×C4—1421no—
564C22×C4—1421no—
565C22×C4—1421no—
566C22×C4—1422no—
567C22×C4—1422no—
568C22×C4D4×D7112yes—
569C22×C4D4×D7111yescharacteristic
570C22×C4C23×D7112yes—
571C22×C4C23×D7111yescharacteristic
572Q16—1428no—
573C2×C8—22no—
574C2×C8—22no—
575C2×C8—714no—
576C2×C8—712no—
577C2×C8—712no—
578C2×C8—1428no—
579C2×C8—1428no—
580C2×C8—1422no—
581C2×C8C23×D7112yes—
582C2×C8C23×D7112yes—
583C4⋊C4—24no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—714no—
588C4⋊C4—712no—
589C4⋊C4—712no—
590C4⋊C4—712no—
591C4⋊C4—1424no—
592C4⋊C4—1424no—
593C4⋊C4—1424no—
594C4⋊C4—1424no—
595C4⋊C4—1424no—
596C4⋊C4—1424no—
597C4⋊C4—1424no—
598C4⋊C4—1421no—
599C4⋊C4—1421no—
600C4⋊C4—1421no—
601C4⋊C4C23×D7112yes—
602C4⋊C4C23×D7112yes—
603C4⋊C4C23×D7112yes—
604C22⋊C4—24no—
605C22⋊C4—24no—
606C22⋊C4—714no—
607C22⋊C4—714no—
608C22⋊C4—1424no—
609C22⋊C4—1424no—
610C22⋊C4—1424no—
611C22⋊C4—1424no—
612C22⋊C4—1424no—
613C22⋊C4—1424no—
614C42—24no—
615C42—712no—
616C42—712no—
617C42—1424no—
618C42—1424no—
619C42—1424no—
620C42—1424no—
621C42—1424no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—712no—
626C23—1422no—
627C23—1422no—
628C23—1422no—
629C23C2×D4×D7112yes—
630C23C2×D4×D7111yescharacteristic
631Q8—22no—
632Q8—22no—
633Q8—42no—
634Q8—2848no—
635Q8—2848no—
636Q8—2842no—
637Q8—1422no—
638Q8—1422no—
639D4—1428no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—24no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—2842no—
653C2×C4—2842no—
654C2×C4—2842no—
655C2×C4—2842no—
656C2×C4—712no—
657C2×C4—714no—
658C2×C4—712no—
659C2×C4—712no—
660C2×C4—1422no—
661C2×C4—1422no—
662C2×C4—1422no—
663C2×C4—1422no—
664C2×C4—1422no—
665C2×C4—1422no—
666C2×C4—1422no—
667C2×C4—1422no—
668C2×C4—1424no—
669C2×C4C2×D4×D7112yes—
670C2×C4C2×D4×D7111yescharacteristic
671C2×C4#41×D7112yes—
672C2×C4#1455617512yes—
673C2×C4C24×D7111yescharacteristic
674C8—22no—
675C8—22no—
676C8—714no—
677C8—1422no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—44no—
682C22—2844no—
683C22—1422no—
684C22—1422no—
685C22—1422no—
686C22#1798664712yes—
687C22#135×D7112yes—
688C22#1798681512yes—
689C22C22×D4×D7111yescharacteristic
690C4—22no—
691C4—42no—
692C4—42no—
693C4—42no—
694C4—42no—
695C4—2842no—
696C4—2842no—
697C4—2842no—
698C4—2842no—
699C4—714no—
700C4—1422no—
701C4—1422no—
702C4#1798664712yes—
703C4C2×#41×D7111yescharacteristic
704C4C2×#1455617511yescharacteristic
705C2—42no—
706C2—2842no—
707C2#2260076514yesdirect product factor
708C2C2×#1798664711yescharacteristic
709C2C2×#135×D7111yescharacteristic
710C2C2×#1798681511yescharacteristic
subgroupG/H
centerC23C2×D4×D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#485×C71C2
socleC23×C71C22×D4
prime radicalC22×C22⋊D71D4
hypercenterC2×#485D71
hypocenterC71C2×#3342
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
3. #22600765C2direct (N × H)
4. C2×#17986403C2semidirect
5. C2×#17986342C2semidirect
6. C2×#17986341C2semidirect
7. C2×#17986339C2semidirect
8. C2×#17986283C2semidirect
9. C2×#17986282C2semidirect
10. C2×#17986239C2semidirect
11. C2×#17986238C2semidirect
12. C2×#17986091C2semidirect
14. C2×#17986035C2semidirect
15. C2×#17986034C2semidirect
16. C2×#485×C71C2semidirect
43. #17986403C22semidirect
44. #17986342C22semidirect
45. #17986341C22semidirect
46. #17986339C22semidirect
47. #17986283C22semidirect
48. #17986282C22semidirect
49. #17986239C22semidirect
50. #17986238C22semidirect
51. #17986091C22semidirect
53. #17986035C22semidirect
54. #17986034C22semidirect
71. #485×C71C22semidirect
351. C2×C71#3342semidirect
363. C2×#485D71semidirect
372. C71C2×#3342semidirect
405. #485C2×D71semidirect
707. C2#22600765direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179867202
C2×#179867172
#226007652
C2×#179864032
C2×#179863422
C2×#179863412
C2×#179863392
C2×#179862832
C2×#179862822
C2×#179862392
C2×#179862382
C2×#179860912
C2×(C22⋊D71)⋊C82
C2×#179860352
C2×#179860342
C2×#485×C712
C2×#334271