Finite Group Databasebeta

← C2×#22594172 #32164516

Subgroups — C2×#22594172 #32164516

Order 18176.

2614 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556118C211yesmaximal, characteristic, complemented
2C22×#14556086C211yesmaximal, characteristic
3#22594172C2116yesmaximal, direct product factor
4C2×#17985933C211yesmaximal, characteristic, complemented
5C2×#17985932C211yesmaximal, characteristic, complemented
6C2×#17985931C211yesmaximal, characteristic, complemented
7C2×#17985923C211yesmaximal, characteristic
8C2×#17985921C211yesmaximal, characteristic
9C2×#17985921C211yesmaximal, characteristic
10C2×#17985921C211yesmaximal, characteristic
11C2×#17985896C211yesmaximal, characteristic, complemented
12C2×#17985894C211yesmaximal, characteristic, complemented
13C2×#17985868C211yesmaximal, characteristic, complemented
14C2×#17985858C211yesmaximal, characteristic
15C2×#17985858C211yesmaximal, characteristic
16C2×#398×C71C211yesmaximal, characteristic, complemented
17C23×C4×D71C2211yescharacteristic
18C2×#14556118—28no—
19C2×#14556118C2218yescomplemented
20C2×#14556086—28no—
21C2×#14556086C2218yes—
22C22×C4⋊Dic71C2211yescharacteristic
23C22×C4⋊Dic71C2211yescharacteristic
24C22×C4⋊Dic71C2211yescharacteristic
25C22×C4⋊Dic71C2211yescharacteristic
26C22×Dic71⋊C4C2211yescharacteristic
27C22×Dic71⋊C4C2211yescharacteristic
28C22×Dic71⋊C4C2211yescharacteristic
29C22×Dic71⋊C4C2211yescharacteristic
30C22×Dic71⋊C4C2211yescharacteristic
31C22×Dic71⋊C4C2211yescharacteristic
32C22×Dic71⋊C4C2211yescharacteristic
33C22×Dic71⋊C4C2211yescharacteristic
34C22×Dic71⋊C4C2211yescharacteristic
35C22×Dic71⋊C4C2211yescharacteristic
36C22×(C2×D71)⋊C4C2211yescharacteristic
37C22×(C2×D71)⋊C4C2211yescharacteristic
38C22×(C2×D71)⋊C4C2211yescharacteristic
39C22×(C2×D71)⋊C4C2211yescharacteristic
40C22×(C2×D71)⋊C4C2211yescharacteristic
41C22×(C2×D71)⋊C4C2211yescharacteristic
42C22×C4×Dic71C2211yescharacteristic
43C22×C4×Dic71C2211yescharacteristic
44#17985933C2218yescomplemented
45#17985932C2218yescomplemented
46#17985931C2218yescomplemented
47#17985923C2218yes—
48#17985921C2218yes—
49#17985921C2218yes—
50#17985921C2218yes—
51#17985896C2218yescomplemented
52#17985894C2218yescomplemented
53#17985868C2218yescomplemented
54#17985858C2218yes—
55#17985858C2218yes—
56C2×C71⋊#95C2211yescharacteristic
57C2×C71⋊#95C2211yescharacteristic
58C2×C71⋊#95C2211yescharacteristic
59C2×C71⋊#95C2211yescharacteristic
60C2×C71⋊#95C2211yescharacteristic
61C22×C4⋊C4×C71C2211yescharacteristic
62C22×C4⋊C4×C71C2211yescharacteristic
63C22×C4⋊C4×C71C2211yescharacteristic
64C22×C4⋊C4×C71C2211yescharacteristic
65#398×C71C2218yescomplemented
66C2×#95×C71C2211yescharacteristic
67C2×#95×C71C2211yescharacteristic
68C2×#95×C71C2211yescharacteristic
69C24×D71C2311yescharacteristic
70C23×Dic71C2311yescharacteristic
71C23×Dic71C2311yescharacteristic
72C23×Dic71C2311yescharacteristic
73C23×Dic71C2311yescharacteristic
74C23×Dic71C2311yescharacteristic
75C23×Dic71C2311yescharacteristic
76C23×Dic71C2311yescharacteristic
77C22×C4×D71—24no—
78C22×C4×D71—24no—
79C22×C4×D71Q818yes—
80C22×C4×D71C2314yes—
81#14556118—232no—
82#14556086—232no—
83C2×C4⋊Dic71—24no—
84C2×C4⋊Dic71—24no—
85C2×C4⋊Dic71—42no—
86C2×C4⋊Dic71—42no—
87C2×C4⋊Dic71C2314yes—
88C2×C4⋊Dic71C2314yes—
89C2×C4⋊Dic71C2314yes—
90C2×C4⋊Dic71C2314yes—
91C2×Dic71⋊C4—24no—
92C2×Dic71⋊C4—24no—
93C2×Dic71⋊C4—24no—
94C2×Dic71⋊C4—24no—
95C2×Dic71⋊C4—24no—
96C2×Dic71⋊C4—24no—
97C2×Dic71⋊C4—42no—
98C2×Dic71⋊C4—42no—
99C2×Dic71⋊C4—42no—
100C2×Dic71⋊C4—42no—
101C2×Dic71⋊C4C2314yes—
102C2×Dic71⋊C4C2314yes—
103C2×Dic71⋊C4C2314yes—
104C2×Dic71⋊C4C2314yes—
105C2×Dic71⋊C4C2314yes—
106C2×Dic71⋊C4C2314yes—
107C2×Dic71⋊C4C2314yes—
108C2×Dic71⋊C4C2314yes—
109C2×Dic71⋊C4C2314yes—
110C2×Dic71⋊C4C2314yes—
111C2×(C2×D71)⋊C4—24no—
112C2×(C2×D71)⋊C4—24no—
113C2×(C2×D71)⋊C4—42no—
114C2×(C2×D71)⋊C4—42no—
115C2×(C2×D71)⋊C4—42no—
116C2×(C2×D71)⋊C4—42no—
117C2×(C2×D71)⋊C4C2314yes—
118C2×(C2×D71)⋊C4C2314yes—
119C2×(C2×D71)⋊C4C2314yes—
120C2×(C2×D71)⋊C4C2314yes—
121C2×(C2×D71)⋊C4C2314yes—
122C2×(C2×D71)⋊C4C2314yes—
123C2×C4×Dic71—24no—
124C2×C4×Dic71D418yes—
125C2×C4×Dic71C2314yes—
126C2×C4×Dic71C2314yes—
127C71⋊#95C2314yes—
128C71⋊#95C2314yes—
129C71⋊#95C2314yes—
130C71⋊#95C2314yes—
131C71⋊#95C2314yes—
132C23×C4×C71C2311yescharacteristic
133C23×C4×C71C2311yescharacteristic
134C23×C4×C71C2311yescharacteristic
135C23×C4×C71C2311yescharacteristic
136C23×C4×C71C2311yescharacteristic
137C23×C4×C71C2311yescharacteristic
138C23×C4×C71C2311yescharacteristic
139C2×C4⋊C4×C71—24no—
140C2×C4⋊C4×C71—24no—
141C2×C4⋊C4×C71—42no—
142C2×C4⋊C4×C71—42no—
143C2×C4⋊C4×C71C2314yes—
144C2×C4⋊C4×C71C2314yes—
145C2×C4⋊C4×C71C2314yes—
146C2×C4⋊C4×C71C2314yes—
147#95×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—
158C22×Dic71—22no—
159C22×Dic71—22no—
160C22×Dic71—22no—
161C22×Dic71—22no—
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×Dic71C2×D414yes—
176C22×Dic71C2×D414yes—
177C22×Dic71C2×Q814yes—
178C22×Dic71#4114yes—
179C22×Dic71C2412yes—
180C22×Dic71C2412yes—
181C22×Dic71C2412yes—
182C22×Dic71C2412yes—
183C22×Dic71C2412yes—
184C22×Dic71C2412yes—
185C22×Dic71C2412yes—
186C2×C4×D71—232no—
187C2×C4×D71—28no—
188C2×C4×D71—28no—
189C2×C4×D71C2×Q8116yes—
190C4⋊Dic71—28no—
191C4⋊Dic71—28no—
192C4⋊Dic71—44no—
193C4⋊Dic71—44no—
194Dic71⋊C4—28no—
195Dic71⋊C4—28no—
196Dic71⋊C4—28no—
197Dic71⋊C4—28no—
198Dic71⋊C4—28no—
199Dic71⋊C4—28no—
200Dic71⋊C4—44no—
201Dic71⋊C4—44no—
202Dic71⋊C4—44no—
203Dic71⋊C4—44no—
204(C2×D71)⋊C4—28no—
205(C2×D71)⋊C4—28no—
206(C2×D71)⋊C4—44no—
207(C2×D71)⋊C4—44no—
208(C2×D71)⋊C4—44no—
209(C2×D71)⋊C4—44no—
210C4×Dic71—28no—
211C4×Dic71C2×D4116yes—
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×C71—22no—
229C22×C4×C71—22no—
230C22×C4×C71—22no—
231C22×C4×C71—22no—
232C22×C4×C71C2×D414yes—
233C22×C4×C71C2×Q814yes—
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×C71—28no—
243C4⋊C4×C71—44no—
244C4⋊C4×C71—44no—
245C23×C71C22×D412yes—
246C23×C71C22×Q812yes—
247C23×C71C2×#4112yes—
248C23×C71H(5,𝔽2)12yes—
249C23×C71H(5,𝔽2)12yes—
250C23×C712−1+412yes—
251C23×C712−1+412yes—
252C23×C71C2511yescharacteristic
253C22×D71—28no—
254C22×D71—28no—
255C22×D71—28no—
256C22×D71—22no—
257C22×D71—22no—
258C22×D71—22no—
259C22×D71—22no—
260C22×D71—22no—
261C22×D71—22no—
262C22×D71—44no—
263C22×D71—44no—
264C22×D71—44no—
265C22×D71—44no—
266C22×D71C22×Q814yes—
267C2×C4×C71—28no—
268C2×C4×C71—28no—
269C2×C4×C71—22no—
270C2×C4×C71—22no—
271C2×C4×C71—22no—
272C2×C4×C71—22no—
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—44no—
289C2×C4×C71—44no—
290C2×C4×C71—44no—
291C2×C4×C71—44no—
292C2×C4×C71—44no—
293C2×C4×C71C22×D414yes—
294C2×C4×C71C22×Q814yes—
295C2×Dic71—28no—
296C2×Dic71—22no—
297C2×Dic71—22no—
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—44no—
314C2×Dic71—44no—
315C2×Dic71—44no—
316C2×Dic71—44no—
317C2×Dic71—44no—
318C2×Dic71C22⋊Q8116yes—
319C2×Dic71C22×D414yes—
320C2×Dic71C22×D414yes—
321C2×Dic71C22×Q814yes—
322C2×Dic71C2×#4114yes—
323C4×D71—232no—
324C22×C71C2×C22⋊Q814yes—
325C22×C71#53714yes—
326C22×C71#53714yes—
327C22×C71#54014yes—
328C22×C71#54114yes—
329C22×C71#54414yes—
330C22×C71#54414yes—
331C22×C71C23×D411yescharacteristic
332C22×C71C23×Q811yescharacteristic
333C22×C71C22×#4111yescharacteristic
334C22×C71C2×H(5,𝔽2)11yescharacteristic
335C22×C71C2×H(5,𝔽2)11yescharacteristic
336C22×C71C2×2−1+411yescharacteristic
337C22×C71C2×2−1+411yescharacteristic
338C2×D71—24no—
339C2×D71—24no—
340C2×D71—24no—
341C2×D71—416no—
342C2×D71—42no—
343C2×D71—42no—
344C2×D71—42no—
345C2×D71—42no—
346C4×C71—24no—
347C4×C71—24no—
348C4×C71—42no—
349C4×C71—42no—
350C4×C71—42no—
351C4×C71—42no—
352C4×C71—42no—
353Dic71—24no—
354Dic71—42no—
355Dic71—42no—
356Dic71—42no—
357Dic71—42no—
358Dic71—42no—
359Dic71C2×C22⋊Q818yes—
360C2×#2629—711nomaximal, Sylow
361C2×C71#262918yescomplemented
362C2×C71C22×C22⋊Q811yescharacteristic
363C2×C71C2×#53711yescharacteristic
364C2×C71C2×#53711yescharacteristic
365C2×C71C2×#54011yescharacteristic
366C2×C71C2×#54111yescharacteristic
367C2×C71C2×#54411yescharacteristic
368C2×C71C2×#54411yescharacteristic
369D71—44no—
370C22×#125—711no—
371C22×#117—711no—
372#2629—7116no—
373C2×#398—711no—
374C2×#398—711no—
375C2×#398—711no—
376C2×#398D7111yescharacteristic, complemented
377C2×#396—711no—
378C2×#396—711no—
379C2×#396—711no—
380C2×#396—711no—
381C2×#389—711no—
382C2×#389—711no—
383C2×#384—711no—
384C2×#380—711no—
385C2×#380—711no—
386C71C2×#262911yescharacteristic, complemented, Sylow
387C24×C4—711no—
388C2×#125—718no—
389C2×#125—1428no—
390C2×#117—718no—
391C2×#117—1428no—
392C22×C4⋊C4—711no—
393C22×C4⋊C4—711no—
394C22×C4⋊C4—711no—
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×C4⋊C4C2×D7111yescharacteristic
409C22×C4⋊C4C2×D7111yescharacteristic
410C22×C22⋊C4—711no—
411C22×C22⋊C4—711no—
412C22×C22⋊C4—711no—
413C22×C22⋊C4—711no—
414C22×C22⋊C4—711no—
415C22×C22⋊C4—711no—
416C22×C42—711no—
417C22×C42—711no—
418#398—718no—
419#398—718no—
420#398—718no—
421#398C2×D7118yescomplemented
422#396—718no—
423#396—718no—
424#396—718no—
425#396—718no—
426#389—718no—
427#389—718no—
428#384—718no—
429#380—718no—
430#380—718no—
431C2×#95—711no—
432C2×#95—711no—
433C2×#95—711no—
434C2×#95—711no—
435C2×#95—711no—
436C2×#95C2×D7111yescharacteristic
437C2×#95C2×D7111yescharacteristic
438C2×#95C2×D7111yescharacteristic
439C25—711no—
440C23×C4—711no—
441C23×C4—711no—
442C23×C4—718no—
443C23×C4—714no—
444C23×C4—711no—
445C23×C4—711no—
446C23×C4—711no—
447C23×C4—711no—
448C23×C4—711no—
449C23×C4—1424no—
450C23×C4—1424no—
451C23×C4C22×D7111yescharacteristic
452C23×C4C22×D7111yescharacteristic
453C23×C4C22×D7111yescharacteristic
454C23×C4C22×D7111yescharacteristic
455C23×C4C22×D7111yescharacteristic
456C23×C4C22×D7111yescharacteristic
457C23×C4C22×D7111yescharacteristic
458#125—14232no—
459#117—14232no—
460C2×C4⋊C4—24no—
461C2×C4⋊C4—24no—
462C2×C4⋊C4—42no—
463C2×C4⋊C4—42no—
464C2×C4⋊C4—2842no—
465C2×C4⋊C4—2842no—
466C2×C4⋊C4—2842no—
467C2×C4⋊C4—2842no—
468C2×C4⋊C4—2842no—
469C2×C4⋊C4—2842no—
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—714no—
480C2×C4⋊C4—714no—
481C2×C4⋊C4—714no—
482C2×C4⋊C4—714no—
483C2×C4⋊C4—714no—
484C2×C4⋊C4—1424no—
485C2×C4⋊C4—1424no—
486C2×C4⋊C4—1424no—
487C2×C4⋊C4—1424no—
488C2×C4⋊C4—1424no—
489C2×C4⋊C4—1424no—
490C2×C4⋊C4—1424no—
491C2×C4⋊C4—1424no—
492C2×C4⋊C4C22×D7114yes—
493C2×C4⋊C4C22×D7114yes—
494C2×C4⋊C4C22×D7114yes—
495C2×C4⋊C4C22×D7114yes—
496C2×C22⋊C4—2842no—
497C2×C22⋊C4—2842no—
498C2×C22⋊C4—2842no—
499C2×C22⋊C4—2842no—
500C2×C22⋊C4—714no—
501C2×C22⋊C4—714no—
502C2×C22⋊C4—714no—
503C2×C22⋊C4—714no—
504C2×C22⋊C4—714no—
505C2×C22⋊C4—714no—
506C2×C22⋊C4—1424no—
507C2×C22⋊C4—1424no—
508C2×C42—718no—
509C2×C42—714no—
510C2×C42—714no—
511C2×C42—1424no—
512#95—714no—
513#95—714no—
514#95—714no—
515#95—714no—
516#95—714no—
517#95C22×D7114yes—
518#95C22×D7114yes—
519#95C22×D7114yes—
520C24—714no—
521C24—712no—
522C24—1422no—
523C24—1422no—
524C24—1422no—
525C24—1422no—
526C24—1422no—
527C24—1422no—
528C24C23×D7111yescharacteristic
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
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—714no—
549C22×C4—714no—
550C22×C4—714no—
551C22×C4—712no—
552C22×C4—714no—
553C22×C4—712no—
554C22×C4—7116no—
555C22×C4—712no—
556C22×C4—712no—
557C22×C4—712no—
558C22×C4—712no—
559C22×C4—712no—
560C22×C4—1428no—
561C22×C4—1428no—
562C22×C4—14232no—
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—1422no—
578C22×C4—1422no—
579C22×C4—1422no—
580C22×C4D4×D7114yes—
581C22×C4Q8×D7114yes—
582C22×C4C23×D7112yes—
583C22×C4C23×D7112yes—
584C22×C4C23×D7112yes—
585C22×C4C23×D7112yes—
586C22×C4C23×D7112yes—
587C22×C4C23×D7112yes—
588C22×C4C23×D7112yes—
589C4⋊C4—28no—
590C4⋊C4—28no—
591C4⋊C4—44no—
592C4⋊C4—44no—
593C4⋊C4—2844no—
594C4⋊C4—2844no—
595C4⋊C4—2844no—
596C4⋊C4—2844no—
597C4⋊C4—2844no—
598C4⋊C4—2844no—
599C4⋊C4—1428no—
600C4⋊C4—1428no—
601C4⋊C4—1428no—
602C4⋊C4—1428no—
603C4⋊C4—1428no—
604C4⋊C4—1428no—
605C4⋊C4—1428no—
606C4⋊C4—1428no—
607C22⋊C4—2844no—
608C22⋊C4—2844no—
609C22⋊C4—2844no—
610C22⋊C4—2844no—
611C22⋊C4—1428no—
612C22⋊C4—1428no—
613C42—7116no—
614C42—1428no—
615C23—2844no—
616C23—2844no—
617C23—2844no—
618C23—2844no—
619C23—714no—
620C23—1422no—
621C23—1422no—
622C23—1422no—
623C23—1422no—
624C23—1422no—
625C23—1422no—
626C23—1428no—
627C23—1428no—
628C23—1428no—
629C23C2×D4×D7112yes—
630C23C2×Q8×D7112yes—
631C23#41×D7112yes—
632C23#1455617312yes—
633C23#1455617412yes—
634C23#1455617512yes—
635C23#1455617612yes—
636C23C24×D7111yescharacteristic
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—28no—
641C2×C4—22no—
642C2×C4—28no—
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—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—44no—
659C2×C4—44no—
660C2×C4—44no—
661C2×C4—44no—
662C2×C4—44no—
663C2×C4—2844no—
664C2×C4—2844no—
665C2×C4—2844no—
666C2×C4—2844no—
667C2×C4—2844no—
668C2×C4—714no—
669C2×C4—714no—
670C2×C4—714no—
671C2×C4—7116no—
672C2×C4—714no—
673C2×C4—14232no—
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—1422no—
691C2×C4—1428no—
692C2×C4C2×D4×D7114yes—
693C2×C4C2×Q8×D7114yes—
694C22—28416no—
695C22—2842no—
696C22—2842no—
697C22—2842no—
698C22—2842no—
699C22—1424no—
700C22—1424no—
701C22—1424no—
702C22C22⋊Q8×D7114yes—
703C22#1798657614yes—
704C22#1798657914yes—
705C22#1798660114yes—
706C22#1798660814yes—
707C22#1798662614yes—
708C22#1798662914yes—
709C22C22×D4×D7111yescharacteristic
710C22C22×Q8×D7111yescharacteristic
711C22C2×#41×D7111yescharacteristic
712C22C2×#1455617311yescharacteristic
713C22C2×#1455617411yescharacteristic
714C22C2×#1455617511yescharacteristic
715C22C2×#1455617611yescharacteristic
716C4—24no—
717C4—24no—
718C4—42no—
719C4—42no—
720C4—42no—
721C4—42no—
722C4—42no—
723C4—2842no—
724C4—2842no—
725C4—2842no—
726C4—2842no—
727C4—2842no—
728C4—718no—
729C4—1424no—
730C2—2844no—
731C2#2259417218yesdirect product factor
732C2C2×C22⋊Q8×D7111yescharacteristic
733C2C2×#1798657611yescharacteristic
734C2C2×#1798657911yescharacteristic
735C2C2×#1798660111yescharacteristic
736C2C2×#1798660811yescharacteristic
737C2C2×#1798662611yescharacteristic
738C2C2×#1798662911yescharacteristic
subgroupG/H
centerC24C23×D71
commutator, cosocleC23×C71C25
FrattiniC23C24×D71
FittingC2×#398×C71C2
socleC24×C71C24
prime radicalC24×D71C23
hypercenterC2×#398D71
hypocenterC71C2×#2629
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
1. C22×#14556118C2semidirect
3. #22594172C2direct (N × H)
4. C2×#17985933C2semidirect
5. C2×#17985932C2semidirect
6. C2×#17985931C2semidirect
11. C2×#17985896C2semidirect
12. C2×#17985894C2semidirect
13. C2×#17985868C2semidirect
16. C2×#398×C71C2semidirect
19. C2×#14556118C22semidirect
44. #17985933C22semidirect
45. #17985932C22semidirect
46. #17985931C22semidirect
51. #17985896C22semidirect
52. #17985894C22semidirect
53. #17985868C22semidirect
65. #398×C71C22semidirect
361. C2×C71#2629semidirect
376. C2×#398D71semidirect
386. C71C2×#2629semidirect
421. #398C2×D71semidirect
731. C2#22594172direct (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×#145560862
#225941722
C2×#179859332
C2×#179859322
C2×#179859312
C2×#179859232
C2×#179859212
C2×#179858962
C2×#179858942
C2×#179858682
C2×#179858582
C2×#398×C712
C2×#262971