Finite Group Databasebeta

← C2×#22593418 #32167549

Subgroups — C2×#22593418 #32167549

Order 18176.

2726 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556118C211yesmaximal, characteristic, complemented
2C22×#14556106C211yesmaximal, characteristic
3#22593418C2116yesmaximal, direct product factor
4C2×#17985936C211yesmaximal, characteristic
5C2×#17985929C211yesmaximal, characteristic, complemented
6C2×#17985921C211yesmaximal, characteristic
7C2×#17985920C211yesmaximal, characteristic, complemented
8C2×#17985905C211yesmaximal, characteristic, complemented
9C2×#17985897C211yesmaximal, characteristic, complemented
10C2×#17985897C211yesmaximal, characteristic, complemented
11C2×#17985890C211yesmaximal, characteristic
12C2×#17985890C211yesmaximal, characteristic
13C2×#17985884C211yesmaximal, characteristic, complemented
14C2×#17985873C211yesmaximal, characteristic
15C2×C4×(C2×D71)⋊C4C211yesmaximal, characteristic
16C2×C4×C4⋊C4×C71C211yesmaximal, characteristic, complemented
17C23×Dic142C2211yescharacteristic
18C23×C4×D71C2211yescharacteristic
19C2×#14556118—28no—
20C2×#14556118C2218yescomplemented
21C2×#14556106—28no—
22C2×#14556106C2218yes—
23C22×C4⋊Dic71C2211yescharacteristic
24C22×C4⋊Dic71C2211yescharacteristic
25C22×C4⋊Dic71C2211yescharacteristic
26C22×C4⋊Dic71C2211yescharacteristic
27C22×C4⋊Dic71C2211yescharacteristic
28C22×Dic71⋊C4C2211yescharacteristic
29C22×Dic71⋊C4C2211yescharacteristic
30C22×Dic71⋊C4C2211yescharacteristic
31C22×Dic71⋊C4C2211yescharacteristic
32C22×Dic71⋊C4C2211yescharacteristic
33C22×Dic71⋊C4C2211yescharacteristic
34C22×(C2×D71)⋊C4C2211yescharacteristic
35C22×(C2×D71)⋊C4C2211yescharacteristic
36C22×(C2×D71)⋊C4C2211yescharacteristic
37C22×(C2×D71)⋊C4C2211yescharacteristic
38C22×(C2×D71)⋊C4C2211yescharacteristic
39C22×(C2×D71)⋊C4C2211yescharacteristic
40C22×C4×Dic71C2211yescharacteristic
41#17985936C2218yes—
42#17985929C2218yescomplemented
43#17985921C2218yes—
44#17985920C2218yescomplemented
45#17985905C2218yescomplemented
46#17985897C2218yescomplemented
47#17985897C2218yescomplemented
48#17985890C2218yes—
49#17985890C2218yes—
50#17985884C2218yescomplemented
51#17985873C2218yes—
52C4×(C2×D71)⋊C4C2218yes—
53C2×C71⋊#95C2211yescharacteristic
54C2×C71⋊#95C2211yescharacteristic
55C2×C71⋊#95C2211yescharacteristic
56C2×C71⋊#95C2211yescharacteristic
57C2×C71⋊#95C2211yescharacteristic
58C2×C71⋊#95C2211yescharacteristic
59C2×C71⋊#95C2211yescharacteristic
60C2×C71⋊#95C2211yescharacteristic
61C22×C4⋊C4×C71C2211yescharacteristic
62C22×C4⋊C4×C71C2211yescharacteristic
63C22×C42×C71C2211yescharacteristic
64C22×C42×C71C2211yescharacteristic
65C22×C42×C71C2211yescharacteristic
66C4×C4⋊C4×C71C2218yescomplemented
67C2×#95×C71C2211yescharacteristic
68C2×#95×C71C2211yescharacteristic
69C24×D71C2311yescharacteristic
70C22×Dic142—24no—
71C22×Dic142—24no—
72C22×Dic142—42no—
73C22×Dic142C2314yes—
74C23×Dic71C2311yescharacteristic
75C23×Dic71C2311yescharacteristic
76C23×Dic71C2311yescharacteristic
77C23×Dic71C2311yescharacteristic
78C23×Dic71C2311yescharacteristic
79C23×Dic71C2311yescharacteristic
80C23×Dic71C2311yescharacteristic
81C22×C4×D71—24no—
82C22×C4×D71—24no—
83C22×C4×D71—42no—
84C22×C4×D71C2314yes—
85#14556118—232no—
86#14556106—232no—
87C2×C4⋊Dic71—24no—
88C2×C4⋊Dic71—24no—
89C2×C4⋊Dic71—24no—
90C2×C4⋊Dic71—24no—
91C2×C4⋊Dic71—42no—
92C2×C4⋊Dic71C2314yes—
93C2×C4⋊Dic71C2314yes—
94C2×C4⋊Dic71C2314yes—
95C2×C4⋊Dic71C2314yes—
96C2×C4⋊Dic71C2314yes—
97C2×Dic71⋊C4—24no—
98C2×Dic71⋊C4—24no—
99C2×Dic71⋊C4—24no—
100C2×Dic71⋊C4—24no—
101C2×Dic71⋊C4—24no—
102C2×Dic71⋊C4—24no—
103C2×Dic71⋊C4C2314yes—
104C2×Dic71⋊C4C2314yes—
105C2×Dic71⋊C4C2314yes—
106C2×Dic71⋊C4C2314yes—
107C2×Dic71⋊C4C2314yes—
108C2×Dic71⋊C4C2314yes—
109C2×(C2×D71)⋊C4—24no—
110C2×(C2×D71)⋊C4—24no—
111C2×(C2×D71)⋊C4—24no—
112C2×(C2×D71)⋊C4—24no—
113C2×(C2×D71)⋊C4—42no—
114C2×(C2×D71)⋊C4Q818yescomplemented
115C2×(C2×D71)⋊C4C2314yes—
116C2×(C2×D71)⋊C4C2314yes—
117C2×(C2×D71)⋊C4C2314yes—
118C2×(C2×D71)⋊C4C2314yes—
119C2×(C2×D71)⋊C4C2314yes—
120C2×(C2×D71)⋊C4C2314yes—
121C2×C4×Dic71—24no—
122C2×C4×Dic71C2314yes—
123C71⋊#95C2314yes—
124C71⋊#95C2314yes—
125C71⋊#95C2314yes—
126C71⋊#95C2314yes—
127C71⋊#95C2314yes—
128C71⋊#95C2314yes—
129C71⋊#95C2314yes—
130C71⋊#95C2314yes—
131C23×C4×C71C2311yescharacteristic
132C23×C4×C71C2311yescharacteristic
133C23×C4×C71C2311yescharacteristic
134C23×C4×C71C2311yescharacteristic
135C23×C4×C71C2311yescharacteristic
136C23×C4×C71C2311yescharacteristic
137C23×C4×C71C2311yescharacteristic
138C2×C4⋊C4×C71—24no—
139C2×C4⋊C4×C71D418yes—
140C2×C4⋊C4×C71C2314yes—
141C2×C4⋊C4×C71C2314yes—
142C2×C42×C71—24no—
143C2×C42×C71—42no—
144C2×C42×C71—42no—
145C2×C42×C71C2314yes—
146C2×C42×C71C2314yes—
147C2×C42×C71C2314yes—
148#95×C71C2314yes—
149#95×C71C2314yes—
150C23×D71—22no—
151C23×D71—22no—
152C23×D71—22no—
153C23×D71—22no—
154C23×D71—22no—
155C23×D71—22no—
156C23×D71C2×Q814yes—
157C23×D71C2412yes—
158C2×Dic142—28no—
159C2×Dic142—28no—
160C2×Dic142—44no—
161C2×Dic142—416no—
162C22×Dic71—22no—
163C22×Dic71—22no—
164C22×Dic71—22no—
165C22×Dic71—22no—
166C22×Dic71—22no—
167C22×Dic71—22no—
168C22×Dic71—22no—
169C22×Dic71—22no—
170C22×Dic71—22no—
171C22×Dic71—22no—
172C22×Dic71—22no—
173C22×Dic71—22no—
174C22×Dic71—22no—
175C22×Dic71—22no—
176C22×Dic71—22no—
177C22×Dic71—22no—
178C22×Dic71—22no—
179C22×Dic71—22no—
180C22×Dic71—22no—
181C22×Dic71C2×Q814yes—
182C22×Dic71#4114yes—
183C22×Dic71C2412yes—
184C22×Dic71C2412yes—
185C22×Dic71C2412yes—
186C22×Dic71C2412yes—
187C22×Dic71C2412yes—
188C22×Dic71C2412yes—
189C22×Dic71C2412yes—
190C2×C4×D71—28no—
191C2×C4×D71—28no—
192C2×C4×D71—44no—
193C2×C4×D71—416no—
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—28no—
204Dic71⋊C4—28no—
205(C2×D71)⋊C4—28no—
206(C2×D71)⋊C4—28no—
207(C2×D71)⋊C4—28no—
208(C2×D71)⋊C4—28no—
209(C2×D71)⋊C4—44no—
210(C2×D71)⋊C4C2×Q8116yescomplemented
211C4×Dic71—28no—
212C24×C71C2411yescharacteristic
213C22×C4×C71—22no—
214C22×C4×C71—22no—
215C22×C4×C71—22no—
216C22×C4×C71—22no—
217C22×C4×C71—22no—
218C22×C4×C71—22no—
219C22×C4×C71—22no—
220C22×C4×C71—22no—
221C22×C4×C71—22no—
222C22×C4×C71—22no—
223C22×C4×C71—22no—
224C22×C4×C71—22no—
225C22×C4×C71—22no—
226C22×C4×C71—22no—
227C22×C4×C71—22no—
228C22×C4×C71C2×D414yes—
229C22×C4×C71C2×D414yes—
230C22×C4×C71C2×D414yes—
231C22×C4×C71C2×Q814yes—
232C22×C4×C71#4114yes—
233C22×C4×C71#4114yes—
234C22×C4×C71C2412yes—
235C22×C4×C71C2412yes—
236C22×C4×C71C2412yes—
237C22×C4×C71C2412yes—
238C22×C4×C71C2412yes—
239C22×C4×C71C2412yes—
240C22×C4×C71C2412yes—
241C4⋊C4×C71—28no—
242C4⋊C4×C71C2×D4116yes—
243C42×C71—28no—
244C42×C71—44no—
245C42×C71—44no—
246C23×C71C22×D412yes—
247C23×C71C22×Q812yes—
248C23×C71C2×#4112yes—
249C23×C71C2×#4112yes—
250C23×C71C2×#4112yes—
251C23×C71H(5,𝔽2)12yes—
252C23×C712−1+412yes—
253C23×C71C2511yescharacteristic
254C22×D71—28no—
255C22×D71—28no—
256C22×D71—28no—
257C22×D71—22no—
258C22×D71—22no—
259C22×D71—22no—
260C22×D71—22no—
261C22×D71—22no—
262C22×D71—22no—
263C22×D71—44no—
264C22×D71—44no—
265C22×D71—44no—
266C22×D71—44no—
267C22×D71C22×Q814yes—
268C2×C4×C71—28no—
269C2×C4×C71—28no—
270C2×C4×C71—28no—
271C2×C4×C71—28no—
272C2×C4×C71—28no—
273C2×C4×C71—28no—
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×C71C22×D414yes—
291C2×C4×C71C22×D414yes—
292C2×C4×C71C22×D414yes—
293C2×C4×C71C22×Q814yes—
294C2×C4×C71C2×#4114yes—
295C2×C4×C71C2×#4114yes—
296C2×Dic71—28no—
297C2×Dic71—28no—
298C2×Dic71—22no—
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—44no—
318C2×Dic71—44no—
319C2×Dic71—44no—
320C2×Dic71—44no—
321C2×Dic71—44no—
322C2×Dic71C22×Q814yes—
323C2×Dic71C2×#4114yes—
324C4×D71—416no—
325Dic142—416no—
326C22×C71#53214yes—
327C22×C71#53314yes—
328C22×C71#53914yes—
329C22×C71#54614yes—
330C22×C71D4×Q814yes—
331C22×C71#55214yes—
332C22×C71#55414yes—
333C22×C71C23×D411yescharacteristic
334C22×C71C23×Q811yescharacteristic
335C22×C71C22×#4111yescharacteristic
336C22×C71C22×#4111yescharacteristic
337C22×C71C22×#4111yescharacteristic
338C22×C71C2×H(5,𝔽2)11yescharacteristic
339C22×C71C2×2−1+411yescharacteristic
340C2×D71—24no—
341C2×D71—24no—
342C2×D71—24no—
343C2×D71—42no—
344C2×D71—42no—
345C2×D71—42no—
346C2×D71—42no—
347C2×D71—416no—
348C4×C71—24no—
349C4×C71—24no—
350C4×C71—24no—
351C4×C71—24no—
352C4×C71—24no—
353C4×C71—24no—
354C4×C71—42no—
355Dic71—24no—
356Dic71—24no—
357Dic71—42no—
358Dic71—42no—
359Dic71—42no—
360Dic71—42no—
361Dic71—42no—
362C2×#2556—711nomaximal, Sylow
363C2×C71#255618yescomplemented
364C2×C71C2×#53211yescharacteristic
365C2×C71C2×#53311yescharacteristic
366C2×C71C2×#53911yescharacteristic
367C2×C71C2×#54611yescharacteristic
368C2×C71C2×D4×Q811yescharacteristic
369C2×C71C2×#55211yescharacteristic
370C2×C71C2×#55411yescharacteristic
371D71—44no—
372C22×#125—711no—
373C22×C22⋊Q8—711no—
374#2556—7116no—
375C2×#399—711no—
376C2×#398—711no—
377C2×#396—711no—
378C2×#395—711no—
379C2×#391—711no—
380C2×#389—711no—
381C2×#389—711no—
382C2×#388—711no—
383C2×#388—711no—
384C2×#387—711no—
385C2×#385—711no—
386C2×C4×C4⋊C4D7111yescharacteristic, complemented
387C2×C4×C22⋊C4—711no—
388C71C2×#255611yescharacteristic, complemented, Sylow
389C23×Q8—711no—
390C24×C4—711no—
391C2×#125—718no—
392C2×#125—1428no—
393C2×C22⋊Q8—718no—
394C2×C22⋊Q8—1428no—
395C22×C4⋊C4—711no—
396C22×C4⋊C4—711no—
397C22×C4⋊C4—711no—
398C22×C4⋊C4—711no—
399C22×C4⋊C4—711no—
400C22×C4⋊C4—711no—
401C22×C4⋊C4—711no—
402C22×C4⋊C4—711no—
403C22×C4⋊C4—711no—
404C22×C4⋊C4—711no—
405C22×C4⋊C4—711no—
406C22×C4⋊C4C2×D7111yescharacteristic
407C22×C4⋊C4C2×D7111yescharacteristic
408C22×C22⋊C4—711no—
409C22×C22⋊C4—711no—
410C22×C22⋊C4—711no—
411C22×C22⋊C4—711no—
412C22×C22⋊C4—711no—
413C22×C22⋊C4—711no—
414C22×C42—711no—
415C22×C42C2×D7111yescharacteristic
416C22×C42C2×D7111yescharacteristic
417C22×C42C2×D7111yescharacteristic
418#399—718no—
419#398—718no—
420#396—718no—
421#395—718no—
422#391—718no—
423#389—718no—
424#389—718no—
425#388—718no—
426#388—718no—
427#387—718no—
428#385—718no—
429C4×C4⋊C4C2×D7118yescomplemented
430C4×C22⋊C4—718no—
431C2×#95—711no—
432C2×#95—711no—
433C2×#95—711no—
434C2×#95—711no—
435C2×#95—711no—
436C2×#95—711no—
437C2×#95—711no—
438C2×#95—711no—
439C2×#95C2×D7111yescharacteristic
440C2×#95C2×D7111yescharacteristic
441C25—711no—
442C22×Q8—2842no—
443C22×Q8—714no—
444C22×Q8—1424no—
445C22×Q8—1424no—
446C23×C4—2842no—
447C23×C4—714no—
448C23×C4—711no—
449C23×C4—711no—
450C23×C4—711no—
451C23×C4—711no—
452C23×C4—711no—
453C23×C4—711no—
454C23×C4—711no—
455C23×C4—1424no—
456C23×C4—1424no—
457C23×C4C22×D7111yescharacteristic
458C23×C4C22×D7111yescharacteristic
459C23×C4C22×D7111yescharacteristic
460C23×C4C22×D7111yescharacteristic
461C23×C4C22×D7111yescharacteristic
462C23×C4C22×D7111yescharacteristic
463C23×C4C22×D7111yescharacteristic
464#125—14232no—
465C22⋊Q8—14232no—
466C2×C4⋊C4—24no—
467C2×C4⋊C4—2842no—
468C2×C4⋊C4—714no—
469C2×C4⋊C4—714no—
470C2×C4⋊C4—714no—
471C2×C4⋊C4—714no—
472C2×C4⋊C4—714no—
473C2×C4⋊C4—714no—
474C2×C4⋊C4—714no—
475C2×C4⋊C4—714no—
476C2×C4⋊C4—714no—
477C2×C4⋊C4—714no—
478C2×C4⋊C4—714no—
479C2×C4⋊C4—1424no—
480C2×C4⋊C4—1424no—
481C2×C4⋊C4—1424no—
482C2×C4⋊C4—1424no—
483C2×C4⋊C4—1424no—
484C2×C4⋊C4—1424no—
485C2×C4⋊C4—1424no—
486C2×C4⋊C4—1424no—
487C2×C4⋊C4—1424no—
488C2×C4⋊C4—1424no—
489C2×C4⋊C4D28418yes—
490C2×C4⋊C4C22×D7114yes—
491C2×C4⋊C4C22×D7114yes—
492C2×C22⋊C4—2842no—
493C2×C22⋊C4—714no—
494C2×C22⋊C4—718no—
495C2×C22⋊C4—714no—
496C2×C22⋊C4—714no—
497C2×C22⋊C4—714no—
498C2×C22⋊C4—714no—
499C2×C22⋊C4—714no—
500C2×C22⋊C4—1424no—
501C2×C22⋊C4—1424no—
502C2×C22⋊C4—1424no—
503C2×C22⋊C4—1424no—
504C2×C42—24no—
505C2×C42—42no—
506C2×C42—42no—
507C2×C42—714no—
508C2×C42—1424no—
509C2×C42C22×D7114yes—
510C2×C42C22×D7114yes—
511C2×C42C22×D7114yes—
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#95C22×D7114yes—
521#95C22×D7114yes—
522C24—714no—
523C24—712no—
524C24—1422no—
525C24—1422no—
526C24—1422no—
527C24—1422no—
528C24—1422no—
529C24—1422no—
530C24C23×D7111yescharacteristic
531C2×Q8—28416no—
532C2×Q8—2844no—
533C2×Q8—1428no—
534C2×Q8—1428no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—28416no—
551C22×C4—2844no—
552C22×C4—714no—
553C22×C4—714no—
554C22×C4—712no—
555C22×C4—712no—
556C22×C4—712no—
557C22×C4—712no—
558C22×C4—712no—
559C22×C4—712no—
560C22×C4—712no—
561C22×C4—1428no—
562C22×C4—1422no—
563C22×C4—1422no—
564C22×C4—1422no—
565C22×C4—1422no—
566C22×C4—1422no—
567C22×C4—1422no—
568C22×C4—1422no—
569C22×C4—1422no—
570C22×C4—1422no—
571C22×C4—1422no—
572C22×C4—1422no—
573C22×C4—1422no—
574C22×C4—1422no—
575C22×C4—1422no—
576C22×C4—1422no—
577C22×C4—1428no—
578C22×C4—1422no—
579C22×C4—1422no—
580C22×C4—1422no—
581C22×C4—1422no—
582C22×C4C2×D28414yes—
583C22×C4C2×D28414yes—
584C22×C4C2×D28414yes—
585C22×C4Q8×D7114yes—
586C22×C4#1176586514yes—
587C22×C4#1176586514yes—
588C22×C4C23×D7112yes—
589C22×C4C23×D7112yes—
590C22×C4C23×D7112yes—
591C22×C4C23×D7112yes—
592C22×C4C23×D7112yes—
593C22×C4C23×D7112yes—
594C22×C4C23×D7112yes—
595C4⋊C4—28no—
596C4⋊C4—2844no—
597C4⋊C4—1428no—
598C4⋊C4—1428no—
599C4⋊C4—1428no—
600C4⋊C4—1428no—
601C4⋊C4—1428no—
602C4⋊C4—1428no—
603C4⋊C4—1428no—
604C4⋊C4—1428no—
605C4⋊C4—1428no—
606C4⋊C4—1428no—
607C4⋊C4C2×D284116yes—
608C22⋊C4—2844no—
609C22⋊C4—7116no—
610C22⋊C4—1428no—
611C22⋊C4—1428no—
612C22⋊C4—1428no—
613C22⋊C4—1428no—
614C42—28no—
615C42—44no—
616C42—44no—
617C42—1428no—
618C23—2844no—
619C23—2844no—
620C23—2844no—
621C23—2844no—
622C23—714no—
623C23—1422no—
624C23—1422no—
625C23—1422no—
626C23—1422no—
627C23—1422no—
628C23—1422no—
629C23—1428no—
630C23—1428no—
631C23—1428no—
632C23C22×D28412yes—
633C23C2×Q8×D7112yes—
634C23#41×D7112yes—
635C23C2×#1176586512yes—
636C23C2×#1176586512yes—
637C23#1455617312yes—
638C23#1455617512yes—
639C23C24×D7111yescharacteristic
640Q8—28416no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—28no—
654C2×C4—28no—
655C2×C4—28no—
656C2×C4—28no—
657C2×C4—28no—
658C2×C4—28no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—44no—
663C2×C4—28416no—
664C2×C4—2844no—
665C2×C4—2844no—
666C2×C4—2844no—
667C2×C4—2844no—
668C2×C4—2844no—
669C2×C4—714no—
670C2×C4—714no—
671C2×C4—1422no—
672C2×C4—1422no—
673C2×C4—1422no—
674C2×C4—1422no—
675C2×C4—1422no—
676C2×C4—1422no—
677C2×C4—1422no—
678C2×C4—1422no—
679C2×C4—1422no—
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—1428no—
691C2×C4—1428no—
692C2×C4C22×D28414yes—
693C2×C4C22×D28414yes—
694C2×C4C22×D28414yes—
695C2×C4C2×Q8×D7114yes—
696C2×C4C2×#1176586514yes—
697C2×C4C2×#1176586514yes—
698C22—2842no—
699C22—2842no—
700C22—28416no—
701C22—2842no—
702C22—2842no—
703C22—1424no—
704C22—1424no—
705C22—1424no—
706C22#1798654914yes—
707C22#1798655314yes—
708C22#1798659114yes—
709C22#1798664414yes—
710C22Q8×D28414yes—
711C22#1798668214yes—
712C22#1798670414yes—
713C22C23×D28411yescharacteristic
714C22C22×Q8×D7111yescharacteristic
715C22C2×#41×D7111yescharacteristic
716C22C22×#1176586511yescharacteristic
717C22C22×#1176586511yescharacteristic
718C22C2×#1455617311yescharacteristic
719C22C2×#1455617511yescharacteristic
720C4—24no—
721C4—24no—
722C4—24no—
723C4—24no—
724C4—24no—
725C4—24no—
726C4—42no—
727C4—2842no—
728C4—2842no—
729C4—2842no—
730C4—2842no—
731C4—2842no—
732C4—1424no—
733C4—1424no—
734C2—2844no—
735C2#2259341818yesdirect product factor
736C2C2×#1798654911yescharacteristic
737C2C2×#1798655311yescharacteristic
738C2C2×#1798659111yescharacteristic
739C2C2×#1798664411yescharacteristic
740C2C2×Q8×D28411yescharacteristic
741C2C2×#1798668211yescharacteristic
742C2C2×#1798670411yescharacteristic
subgroupG/H
centerC24C23×D71
commutator, cosocleC23×C71C25
FrattiniC23C24×D71
FittingC2×C4×C4⋊C4×C71C2
socleC24×C71C24
prime radicalC24×D71C23
hypercenterC2×C4×C4⋊C4D71
hypocenterC71C2×#2556
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#14556118C2semidirect
3. #22593418C2direct (N × H)
5. C2×#17985929C2semidirect
7. C2×#17985920C2semidirect
8. C2×#17985905C2semidirect
9. C2×#17985897C2semidirect
10. C2×#17985897C2semidirect
13. C2×#17985884C2semidirect
16. C2×C4×C4⋊C4×C71C2semidirect
20. C2×#14556118C22semidirect
42. #17985929C22semidirect
44. #17985920C22semidirect
45. #17985905C22semidirect
46. #17985897C22semidirect
47. #17985897C22semidirect
50. #17985884C22semidirect
66. C4×C4⋊C4×C71C22semidirect
114. C2×(C2×D71)⋊C4Q8semidirect
210. (C2×D71)⋊C4C2×Q8semidirect
363. C2×C71#2556semidirect
386. C2×C4×C4⋊C4D71semidirect
388. C71C2×#2556semidirect
429. C4×C4⋊C4C2×D71semidirect
735. C2#22593418direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145561182
C22×#145561062
#225934182
C2×#179859362
C2×#179859292
C2×#179859212
C2×#179859202
C2×#179859052
C2×#179858972
C2×#179858902
C2×#179858842
C2×#179858732
C2×C4×(C2×D71)⋊C42
C2×C4×C4⋊C4×C712
C2×#255671