Finite Group Databasebeta

← C2×#22592018 #32166102

Subgroups — C2×#22592018 #32166102

Order 18176.

3006 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556105C211yesmaximal, characteristic
2C22×#14556087C211yesmaximal, characteristic
3#22592018C2116yesmaximal, direct product factor
4C2×#17985941C211yesmaximal, characteristic, complemented
5C2×#17985933C211yesmaximal, characteristic, complemented
6C2×#17985931C211yesmaximal, characteristic, complemented
7C2×#17985920C211yesmaximal, characteristic, complemented
8C2×#17985903C211yesmaximal, characteristic, complemented
9C2×#17985896C211yesmaximal, characteristic, complemented
10C2×#17985886C211yesmaximal, characteristic, complemented
11C2×#17985882C211yesmaximal, characteristic, complemented
12C2×#17985874C211yesmaximal, characteristic
13C2×#17985871C211yesmaximal, characteristic
14C2×#17985857C211yesmaximal, characteristic
15C22×C71⋊#95C211yesmaximal, characteristic
16C2×#381×C71C211yesmaximal, characteristic
17C23×Dic142C2211yescharacteristic
18C24×Dic71C2211yescharacteristic
19C24×Dic71C2211yescharacteristic
20C2×#14556105—28no—
21C2×#14556105C2218yes—
22C2×#14556087—28no—
23C2×#14556087C2218yes—
24C22×C4⋊Dic71C2211yescharacteristic
25C22×C4⋊Dic71C2211yescharacteristic
26C22×C4⋊Dic71C2211yescharacteristic
27C22×C4⋊Dic71C2211yescharacteristic
28C22×C4⋊Dic71C2211yescharacteristic
29C22×Dic71⋊C4C2211yescharacteristic
30C22×Dic71⋊C4C2211yescharacteristic
31C22×Dic71⋊C4C2211yescharacteristic
32C22×Dic71⋊C4C2211yescharacteristic
33C22×Dic71⋊C4C2211yescharacteristic
34C22×Dic71⋊C4C2211yescharacteristic
35C22×C22⋊Dic71C2211yescharacteristic
36C22×C22⋊Dic71C2211yescharacteristic
37C22×C4×Dic71C2211yescharacteristic
38C22×C4×Dic71C2211yescharacteristic
39#17985941C2218yescomplemented
40#17985933C2218yescomplemented
41#17985931C2218yescomplemented
42#17985920C2218yescomplemented
43#17985903C2218yescomplemented
44#17985896C2218yescomplemented
45#17985886C2218yescomplemented
46#17985882C2218yescomplemented
47#17985874C2218yes—
48#17985871C2218yes—
49#17985857C2218yes—
50C2×C71⋊#95C2218yes—
51C2×C71⋊#95C2211yescharacteristic
52C2×C71⋊#95C2211yescharacteristic
53C2×C71⋊#95C2211yescharacteristic
54C2×C71⋊#95C2211yescharacteristic
55C2×C71⋊#95C2211yescharacteristic
56C2×C71⋊#95C2211yescharacteristic
57C2×C71⋊#95C2211yescharacteristic
58C2×C71⋊#95C2211yescharacteristic
59C2×C71⋊#95C2211yescharacteristic
60C2×C71⋊#95C2211yescharacteristic
61C24×C4×C71C2211yescharacteristic
62C22×C22⋊C4×C71C2211yescharacteristic
63C22×C22⋊C4×C71C2211yescharacteristic
64#381×C71C2218yes—
65C2×#95×C71C2211yescharacteristic
66C2×#95×C71C2211yescharacteristic
67C2×#95×C71C2211yescharacteristic
68C2×#95×C71C2211yescharacteristic
69C22×Dic142—24no—
70C22×Dic142—24no—
71C22×Dic142—42no—
72C22×Dic142C2314yes—
73C23×Dic71—24no—
74C23×Dic71—24no—
75C23×Dic71—24no—
76C23×Dic71—24no—
77C23×Dic71—42no—
78C23×Dic71—42no—
79C23×Dic71C2311yescharacteristic
80C23×Dic71C2311yescharacteristic
81C23×Dic71C2311yescharacteristic
82C23×Dic71C2311yescharacteristic
83C23×Dic71C2314yes—
84C23×Dic71C2314yes—
85C23×Dic71C2311yescharacteristic
86C23×Dic71C2311yescharacteristic
87C23×Dic71C2311yescharacteristic
88C23×Dic71C2311yescharacteristic
89#14556105—232no—
90#14556087—232no—
91C2×C4⋊Dic71—24no—
92C2×C4⋊Dic71—24no—
93C2×C4⋊Dic71—24no—
94C2×C4⋊Dic71—24no—
95C2×C4⋊Dic71—42no—
96C2×C4⋊Dic71C2314yes—
97C2×C4⋊Dic71C2314yes—
98C2×C4⋊Dic71C2314yes—
99C2×C4⋊Dic71C2314yes—
100C2×C4⋊Dic71C2314yes—
101C2×Dic71⋊C4—24no—
102C2×Dic71⋊C4—24no—
103C2×Dic71⋊C4—24no—
104C2×Dic71⋊C4—24no—
105C2×Dic71⋊C4—42no—
106C2×Dic71⋊C4—42no—
107C2×Dic71⋊C4C2314yes—
108C2×Dic71⋊C4C2314yes—
109C2×Dic71⋊C4C2314yes—
110C2×Dic71⋊C4C2314yes—
111C2×Dic71⋊C4C2314yes—
112C2×Dic71⋊C4C2314yes—
113C2×C22⋊Dic71—24no—
114C2×C22⋊Dic71D418yes—
115C2×C22⋊Dic71C2314yes—
116C2×C22⋊Dic71C2314yes—
117C2×C4×Dic71—24no—
118C2×C4×Dic71—24no—
119C2×C4×Dic71C2314yes—
120C2×C4×Dic71C2314yes—
121C71⋊#95C2314yes—
122C71⋊#95C2314yes—
123C71⋊#95C2314yes—
124C71⋊#95C2314yes—
125C71⋊#95C2314yes—
126C71⋊#95C2314yes—
127C71⋊#95C2314yes—
128C71⋊#95C2314yes—
129C71⋊#95C2314yes—
130C71⋊#95C2314yes—
131C25×C71C2311yescharacteristic
132C23×C4×C71—24no—
133C23×C4×C71—24no—
134C23×C4×C71Q818yescomplemented
135C23×C4×C71C2311yescharacteristic
136C23×C4×C71C2311yescharacteristic
137C23×C4×C71C2311yescharacteristic
138C23×C4×C71C2311yescharacteristic
139C23×C4×C71C2311yescharacteristic
140C23×C4×C71C2311yescharacteristic
141C23×C4×C71C2314yes—
142C2×C22⋊C4×C71—24no—
143C2×C22⋊C4×C71—24no—
144C2×C22⋊C4×C71C2314yes—
145C2×C22⋊C4×C71C2314yes—
146#95×C71C2314yes—
147#95×C71C2314yes—
148#95×C71C2314yes—
149#95×C71C2314yes—
150C2×Dic142—28no—
151C2×Dic142—28no—
152C2×Dic142—44no—
153C2×Dic142—416no—
154C22×Dic71—22no—
155C22×Dic71—22no—
156C22×Dic71—22no—
157C22×Dic71—22no—
158C22×Dic71—22no—
159C22×Dic71—22no—
160C22×Dic71—22no—
161C22×Dic71—22no—
162C22×Dic71—22no—
163C22×Dic71—28no—
164C22×Dic71—22no—
165C22×Dic71—22no—
166C22×Dic71—22no—
167C22×Dic71—22no—
168C22×Dic71—28no—
169C22×Dic71—22no—
170C22×Dic71—22no—
171C22×Dic71—22no—
172C22×Dic71—22no—
173C22×Dic71—22no—
174C22×Dic71—22no—
175C22×Dic71—22no—
176C22×Dic71—28no—
177C22×Dic71—28no—
178C22×Dic71—44no—
179C22×Dic71—44no—
180C22×Dic71—416no—
181C22×Dic71—416no—
182C22×Dic71C2×D414yes—
183C22×Dic71C2×D414yes—
184C22×Dic71#4114yes—
185C22×Dic71#4114yes—
186C22×Dic71C2412yes—
187C22×Dic71C2412yes—
188C22×Dic71C2412yes—
189C22×Dic71C2412yes—
190C22×Dic71C2412yes—
191C22×Dic71C2412yes—
192C22×Dic71C2412yes—
193C22×Dic71C2412yes—
194C4⋊Dic71—28no—
195C4⋊Dic71—28no—
196C4⋊Dic71—28no—
197C4⋊Dic71—28no—
198C4⋊Dic71—44no—
199Dic71⋊C4—28no—
200Dic71⋊C4—28no—
201Dic71⋊C4—28no—
202Dic71⋊C4—28no—
203Dic71⋊C4—44no—
204Dic71⋊C4—44no—
205C22⋊Dic71—28no—
206C22⋊Dic71C2×D4116yes—
207C4×Dic71—28no—
208C4×Dic71—28no—
209C24×C71—22no—
210C24×C71—22no—
211C24×C71—22no—
212C24×C71—22no—
213C24×C71C2×D414yes—
214C24×C71C2×Q814yes—
215C24×C71#4114yes—
216C24×C71C2412yes—
217C24×C71C2411yescharacteristic
218C22×C4×C71—232no—
219C22×C4×C71—22no—
220C22×C4×C71—22no—
221C22×C4×C71—28no—
222C22×C4×C71—22no—
223C22×C4×C71—22no—
224C22×C4×C71—28no—
225C22×C4×C71—22no—
226C22×C4×C71—22no—
227C22×C4×C71—22no—
228C22×C4×C71—22no—
229C22×C4×C71—22no—
230C22×C4×C71—22no—
231C22×C4×C71—22no—
232C22×C4×C71—22no—
233C22×C4×C71—22no—
234C22×C4×C71—22no—
235C22×C4×C71—22no—
236C22×C4×C71—22no—
237C22×C4×C71C2×Q814yes—
238C22×C4×C71C2×Q814yes—
239C22×C4×C71C2×Q8116yescomplemented
240C22×C4×C71C2412yes—
241C22×C4×C71C2412yes—
242C22×C4×C71C2412yes—
243C22×C4×C71C2412yes—
244C22×C4×C71C2412yes—
245C22×C4×C71C2412yes—
246C22⋊C4×C71—28no—
247C22⋊C4×C71—28no—
248C23×C71—28no—
249C23×C71—28no—
250C23×C71—28no—
251C23×C71—28no—
252C23×C71—28no—
253C23×C71—28no—
254C23×C71—22no—
255C23×C71—22no—
256C23×C71—22no—
257C23×C71—22no—
258C23×C71C22⋊Q8116yes—
259C23×C71C22×D414yes—
260C23×C71C22×D412yes—
261C23×C71C22×Q814yes—
262C23×C71C22×Q812yes—
263C23×C71C2×#4112yes—
264C23×C71C2×#4112yes—
265C23×C71C2×#4114yes—
266C23×C71C2×#4112yes—
267C23×C71H(5,𝔽2)12yes—
268C23×C712−1+412yes—
269C23×C71C2511yescharacteristic
270C2×C4×C71—28no—
271C2×C4×C71—28no—
272C2×C4×C71—232no—
273C2×C4×C71—22no—
274C2×C4×C71—22no—
275C2×C4×C71—22no—
276C2×C4×C71—22no—
277C2×C4×C71—22no—
278C2×C4×C71—22no—
279C2×C4×C71—22no—
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—22no—
287C2×C4×C71—22no—
288C2×C4×C71—22no—
289C2×C4×C71—44no—
290C2×C4×C71—44no—
291C2×C4×C71—44no—
292C2×C4×C71—44no—
293C2×C4×C71C22×Q814yes—
294C2×C4×C71C22×Q814yes—
295C2×Dic71—28no—
296C2×Dic71—28no—
297C2×Dic71—28no—
298C2×Dic71—28no—
299C2×Dic71—22no—
300C2×Dic71—22no—
301C2×Dic71—22no—
302C2×Dic71—22no—
303C2×Dic71—22no—
304C2×Dic71—22no—
305C2×Dic71—22no—
306C2×Dic71—22no—
307C2×Dic71—22no—
308C2×Dic71—22no—
309C2×Dic71—22no—
310C2×Dic71—22no—
311C2×Dic71—22no—
312C2×Dic71—22no—
313C2×Dic71—22no—
314C2×Dic71—22no—
315C2×Dic71—22no—
316C2×Dic71—22no—
317C2×Dic71—22no—
318C2×Dic71—22no—
319C2×Dic71—416no—
320C2×Dic71—416no—
321C2×Dic71—44no—
322C2×Dic71—44no—
323C2×Dic71—44no—
324C2×Dic71—44no—
325C2×Dic71C22×D414yes—
326C2×Dic71C22×D414yes—
327C2×Dic71C2×#4114yes—
328C2×Dic71C2×#4114yes—
329Dic142—416no—
330C22×C71—24no—
331C22×C71—24no—
332C22×C71—232no—
333C22×C71—24no—
334C22×C71—24no—
335C22×C71—24no—
336C22×C71—24no—
337C22×C71C2×C22⋊Q818yes—
338C22×C71C2×C22⋊Q814yes—
339C22×C71#53314yes—
340C22×C71#54414yes—
341C22×C71#54614yes—
342C22×C71#54714yes—
343C22×C71#55114yes—
344C22×C71#55214yes—
345C22×C71C23×D411yescharacteristic
346C22×C71C23×Q811yescharacteristic
347C22×C71C22×#4111yescharacteristic
348C22×C71C22×#4111yescharacteristic
349C22×C71C22×#4111yescharacteristic
350C22×C71C2×H(5,𝔽2)11yescharacteristic
351C22×C71C2×2−1+411yescharacteristic
352C4×C71—24no—
353C4×C71—24no—
354C4×C71—42no—
355C4×C71—42no—
356C4×C71—42no—
357C4×C71—42no—
358Dic71—24no—
359Dic71—24no—
360Dic71—24no—
361Dic71—24no—
362Dic71—42no—
363Dic71—42no—
364Dic71—42no—
365Dic71—42no—
366C2×#2438—711nomaximal, Sylow
367C2×C71—28no—
368C2×C71#243818yescomplemented
369C2×C71C22×C22⋊Q811yescharacteristic
370C2×C71C2×#53311yescharacteristic
371C2×C71C2×#54411yescharacteristic
372C2×C71C2×#54611yescharacteristic
373C2×C71C2×#54711yescharacteristic
374C2×C71C2×#55111yescharacteristic
375C2×C71C2×#55211yescharacteristic
376C22×C22⋊Q8—711no—
377C22×#117—711no—
378#2438—7116no—
379C2×#400—711no—
380C2×#398—711no—
381C2×#398—711no—
382C2×#395—711no—
383C2×#391—711no—
384C2×#389—711no—
385C2×#387—711no—
386C2×#387—711no—
387C2×#385—711no—
388C2×#385—711no—
389C2×#381D7111yescharacteristic
390C2×#380—711no—
391C22×#95—711no—
392C71C2×#243811yescharacteristic, complemented, Sylow
393C23×Q8—711no—
394C24×C4—711no—
395C24×C4—711no—
396C24×C4C2×D7111yescharacteristic
397C2×C22⋊Q8—718no—
398C2×C22⋊Q8—1428no—
399C2×#117—718no—
400C2×#117—1428no—
401C22×C4⋊C4—711no—
402C22×C4⋊C4—711no—
403C22×C4⋊C4—711no—
404C22×C4⋊C4—711no—
405C22×C4⋊C4—711no—
406C22×C4⋊C4—711no—
407C22×C4⋊C4—711no—
408C22×C4⋊C4—711no—
409C22×C4⋊C4—711no—
410C22×C4⋊C4—711no—
411C22×C4⋊C4—711no—
412C22×C22⋊C4—711no—
413C22×C22⋊C4—711no—
414C22×C22⋊C4C2×D7111yescharacteristic
415C22×C22⋊C4C2×D7111yescharacteristic
416C22×C42—711no—
417C22×C42—711no—
418#400—718no—
419#398—718no—
420#398—718no—
421#395—718no—
422#391—718no—
423#389—718no—
424#387—718no—
425#387—718no—
426#385—718no—
427#385—718no—
428#381C2×D7118yes—
429#380—718no—
430C2×#95—711no—
431C2×#95—711no—
432C2×#95—711no—
433C2×#95—711no—
434C2×#95—711no—
435C2×#95—711no—
436C2×#95—711no—
437C2×#95—711no—
438C2×#95—718no—
439C2×#95—711no—
440C2×#95—711no—
441C2×#95C2×D7111yescharacteristic
442C2×#95C2×D7111yescharacteristic
443C2×#95C2×D7111yescharacteristic
444C2×#95C2×D7111yescharacteristic
445C25C22×D7111yescharacteristic
446C22×Q8—2842no—
447C22×Q8—714no—
448C22×Q8—1424no—
449C22×Q8—1424no—
450C23×C4—24no—
451C23×C4—24no—
452C23×C4—2842no—
453C23×C4—2842no—
454C23×C4—714no—
455C23×C4—714no—
456C23×C4—711no—
457C23×C4—711no—
458C23×C4—711no—
459C23×C4—711no—
460C23×C4—711no—
461C23×C4—711no—
462C23×C4—711no—
463C23×C4—711no—
464C23×C4—1424no—
465C23×C4—1424no—
466C23×C4—1424no—
467C23×C4—1424no—
468C23×C4Dic14218yescomplemented
469C23×C4C22×D7111yescharacteristic
470C23×C4C22×D7111yescharacteristic
471C23×C4C22×D7111yescharacteristic
472C23×C4C22×D7111yescharacteristic
473C23×C4C22×D7111yescharacteristic
474C23×C4C22×D7111yescharacteristic
475C23×C4C22×D7114yes—
476C22⋊Q8—14232no—
477#117—14232no—
478C2×C4⋊C4—2842no—
479C2×C4⋊C4—2842no—
480C2×C4⋊C4—2842no—
481C2×C4⋊C4—714no—
482C2×C4⋊C4—714no—
483C2×C4⋊C4—714no—
484C2×C4⋊C4—714no—
485C2×C4⋊C4—714no—
486C2×C4⋊C4—714no—
487C2×C4⋊C4—714no—
488C2×C4⋊C4—714no—
489C2×C4⋊C4—714no—
490C2×C4⋊C4—714no—
491C2×C4⋊C4—714no—
492C2×C4⋊C4—1424no—
493C2×C4⋊C4—1424no—
494C2×C4⋊C4—1424no—
495C2×C4⋊C4—1424no—
496C2×C4⋊C4—1424no—
497C2×C4⋊C4—1424no—
498C2×C4⋊C4—1424no—
499C2×C4⋊C4—1424no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—718no—
503C2×C22⋊C4—714no—
504C2×C22⋊C4—714no—
505C2×C22⋊C4—1424no—
506C2×C22⋊C4C22×D7114yes—
507C2×C22⋊C4C22×D7114yes—
508C2×C42—714no—
509C2×C42—714no—
510C2×C42—1424no—
511C2×C42—1424no—
512#95—714no—
513#95—714no—
514#95—714no—
515#95—714no—
516#95—714no—
517#95—714no—
518#95—714no—
519#95—714no—
520#95—714no—
521#95—714no—
522#95C22×D7114yes—
523#95C22×D7114yes—
524#95C22×D7114yes—
525#95C22×D7114yes—
526C24—22no—
527C24—22no—
528C24—22no—
529C24—22no—
530C24D4×D7114yes—
531C24C2×Dic14214yes—
532C24#1176586414yes—
533C24C23×D7112yes—
534C24C23×D7111yescharacteristic
535C2×Q8—2844no—
536C2×Q8—28416no—
537C2×Q8—1428no—
538C2×Q8—1428no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—28no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—28no—
545C22×C4—232no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—28416no—
559C22×C4—28416no—
560C22×C4—2844no—
561C22×C4—2844no—
562C22×C4—714no—
563C22×C4—714no—
564C22×C4—714no—
565C22×C4—714no—
566C22×C4—712no—
567C22×C4—712no—
568C22×C4—712no—
569C22×C4—712no—
570C22×C4—712no—
571C22×C4—712no—
572C22×C4—712no—
573C22×C4—712no—
574C22×C4—1428no—
575C22×C4—1428no—
576C22×C4—1422no—
577C22×C4—1422no—
578C22×C4—1422no—
579C22×C4—1428no—
580C22×C4—1422no—
581C22×C4—1422no—
582C22×C4—1422no—
583C22×C4—1422no—
584C22×C4—1422no—
585C22×C4—1428no—
586C22×C4—1422no—
587C22×C4—1422no—
588C22×C4—1422no—
589C22×C4—1422no—
590C22×C4—1422no—
591C22×C4—1422no—
592C22×C4—1422no—
593C22×C4—1422no—
594C22×C4—1422no—
595C22×C4—1422no—
596C22×C4—1422no—
597C22×C4—1422no—
598C22×C4C2×Dic14214yes—
599C22×C4C2×Dic14214yes—
600C22×C4C2×Dic142116yescomplemented
601C22×C4C23×D7112yes—
602C22×C4C23×D7112yes—
603C22×C4C23×D7112yes—
604C22×C4C23×D7112yes—
605C22×C4C23×D7112yes—
606C22×C4C23×D7112yes—
607C4⋊C4—2844no—
608C4⋊C4—2844no—
609C4⋊C4—2844no—
610C4⋊C4—1428no—
611C4⋊C4—1428no—
612C4⋊C4—1428no—
613C4⋊C4—1428no—
614C4⋊C4—1428no—
615C4⋊C4—1428no—
616C4⋊C4—1428no—
617C4⋊C4—1428no—
618C22⋊C4—28no—
619C22⋊C4—28no—
620C22⋊C4—7116no—
621C22⋊C4—1428no—
622C42—1428no—
623C42—1428no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—28no—
629C23—28no—
630C23—28no—
631C23—28no—
632C23—28no—
633C23—28no—
634C23#14556105116yes—
635C23C2×D4×D7114yes—
636C23C2×D4×D7112yes—
637C23C22×Dic14214yes—
638C23C22×Dic14212yes—
639C23#41×D7112yes—
640C23#41×D7112yes—
641C23C2×#1176586414yes—
642C23C2×#1176586412yes—
643C23#1455617412yes—
644C23#1455617512yes—
645C23C24×D7111yescharacteristic
646Q8—28416no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—28no—
652C2×C4—28no—
653C2×C4—232no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—44no—
667C2×C4—44no—
668C2×C4—44no—
669C2×C4—44no—
670C2×C4—2844no—
671C2×C4—2844no—
672C2×C4—2844no—
673C2×C4—2844no—
674C2×C4—28416no—
675C2×C4—28416no—
676C2×C4—714no—
677C2×C4—714no—
678C2×C4—714no—
679C2×C4—714no—
680C2×C4—1422no—
681C2×C4—1422no—
682C2×C4—1422no—
683C2×C4—1422no—
684C2×C4—1422no—
685C2×C4—1422no—
686C2×C4—1422no—
687C2×C4—1422no—
688C2×C4—1422no—
689C2×C4—1422no—
690C2×C4—1422no—
691C2×C4—1422no—
692C2×C4—1422no—
693C2×C4—1422no—
694C2×C4—1422no—
695C2×C4—1422no—
696C2×C4—1422no—
697C2×C4—1422no—
698C2×C4—1422no—
699C2×C4—1422no—
700C2×C4—1428no—
701C2×C4—1428no—
702C2×C4—1428no—
703C2×C4—1428no—
704C2×C4C22×Dic14214yes—
705C2×C4C22×Dic14214yes—
706C22—24no—
707C22—232no—
708C22—24no—
709C22—24no—
710C22—24no—
711C22—24no—
712C22—24no—
713C22C2×#1455610518yes—
714C22C2×#1455610514yes—
715C22#1798655214yes—
716C22#1798662714yes—
717C22#1798664114yes—
718C22#1798664714yes—
719C22#1798667214yes—
720C22#1798668614yes—
721C22C22×D4×D7111yescharacteristic
722C22C23×Dic14211yescharacteristic
723C22C2×#41×D7111yescharacteristic
724C22C2×#41×D7111yescharacteristic
725C22C22×#1176586411yescharacteristic
726C22C2×#1455617411yescharacteristic
727C22C2×#1455617511yescharacteristic
728C4—24no—
729C4—24no—
730C4—42no—
731C4—42no—
732C4—42no—
733C4—42no—
734C4—2842no—
735C4—2842no—
736C4—2842no—
737C4—2842no—
738C4—1424no—
739C4—1424no—
740C4—1424no—
741C4—1424no—
742C2—28no—
743C2#2259201818yesdirect product factor
744C2C22×#1455610511yescharacteristic
745C2C2×#1798655211yescharacteristic
746C2C2×#1798662711yescharacteristic
747C2C2×#1798664111yescharacteristic
748C2C2×#1798664711yescharacteristic
749C2C2×#1798667211yescharacteristic
750C2C2×#1798668611yescharacteristic
subgroupG/H
centerC24C23×D71
commutator, cosocleC23×C71C25
FrattiniC23C24×D71
FittingC2×#381×C71C2
socleC24×C71C24
prime radicalC25×C71C23
hypercenterC2×#381D71
hypocenterC71C2×#2438
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×#381

Complements

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

NH ≅ G/Ntype
3. #22592018C2direct (N × H)
4. C2×#17985941C2semidirect
5. C2×#17985933C2semidirect
6. C2×#17985931C2semidirect
7. C2×#17985920C2semidirect
8. C2×#17985903C2semidirect
9. C2×#17985896C2semidirect
10. C2×#17985886C2semidirect
11. C2×#17985882C2semidirect
39. #17985941C22semidirect
40. #17985933C22semidirect
41. #17985931C22semidirect
42. #17985920C22semidirect
43. #17985903C22semidirect
44. #17985896C22semidirect
45. #17985886C22semidirect
46. #17985882C22semidirect
134. C23×C4×C71Q8semidirect
239. C22×C4×C71C2×Q8semidirect
368. C2×C71#2438semidirect
392. C71C2×#2438semidirect
468. C23×C4Dic142semidirect
600. C22×C4C2×Dic142semidirect
743. C2#22592018direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145561052
C22×#145560872
#225920182
C2×#179859412
C2×#179859332
C2×#179859312
C2×#179859202
C2×#179859032
C2×#179858962
C2×#179858862
C2×#179858822
C2×#179858742
C2×#179858712
C2×#179858572
C22×C71⋊#952
C2×#381×C712
C2×#243871