Finite Group Databasebeta

← C2×#22596481 #32203831

Subgroups — C2×#22596481 #32203831

Order 18176.

2174 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22596481C2116yesmaximal, direct product factor
2C2×#17985932C211yesmaximal, characteristic, complemented
3C2×#17985928C211yesmaximal, characteristic, complemented
4C2×#17985928C211yesmaximal, characteristic, complemented
5C2×#17985926C211yesmaximal, characteristic, complemented
6C2×#17985925C211yesmaximal, characteristic, complemented
7C2×#17985923C211yesmaximal, characteristic, complemented
8C2×#17985921C211yesmaximal, characteristic, complemented
9C2×#17985920C211yesmaximal, characteristic, complemented
10C2×#17985917C211yesmaximal, characteristic
11C2×#17985916C211yesmaximal, characteristic
12C2×#17985912C211yesmaximal, characteristic, complemented
13C2×#17985912C211yesmaximal, characteristic, complemented
14C2×#17985901C211yesmaximal, characteristic
15C2×#17985883C211yesmaximal, characteristic, complemented
16C2×#387×C71C211yesmaximal, characteristic, complemented
17C23×Dic142C2211yescharacteristic
18C23×D284C2211yescharacteristic
19C22×C4⋊Dic71C2211yescharacteristic
20C22×C4⋊Dic71C2211yescharacteristic
21C22×Dic71⋊C4C2211yescharacteristic
22C22×Dic71⋊C4C2211yescharacteristic
23C22×Dic71⋊C4C2211yescharacteristic
24C22×Dic71⋊C4C2211yescharacteristic
25C22×(C2×D71)⋊C4C2211yescharacteristic
26C22×(C2×D71)⋊C4C2211yescharacteristic
27C22×(C2×D71)⋊C4C2211yescharacteristic
28C22×(C2×D71)⋊C4C2211yescharacteristic
29C22×(C2×D71)⋊C4C2211yescharacteristic
30C22×(C2×D71)⋊C4C2211yescharacteristic
31C22×(C2×D71)⋊C4C2211yescharacteristic
32C22×(C2×D71)⋊C4C2211yescharacteristic
33C22×(C2×D71)⋊C4C2211yescharacteristic
34C22×(C2×D71)⋊C4C2211yescharacteristic
35C22×(C2×D71)⋊C4C2211yescharacteristic
36C22×(C2×D71)⋊C4C2211yescharacteristic
37#17985932C2218yescomplemented
38#17985928C2218yescomplemented
39#17985928C2218yescomplemented
40#17985926C2218yescomplemented
41#17985925C2218yescomplemented
42#17985923C2218yescomplemented
43#17985921C2218yescomplemented
44#17985920C2218yescomplemented
45#17985917C2218yes—
46#17985916C2218yes—
47#17985912C2218yescomplemented
48#17985912C2218yescomplemented
49#17985901C2218yes—
50#17985883C2218yescomplemented
51C2×C71⋊#95C2211yescharacteristic
52C2×C71⋊#95C2211yescharacteristic
53C2×C71⋊#95C2211yescharacteristic
54C2×C71⋊#95C2211yescharacteristic
55C2×C71⋊#95C2211yescharacteristic
56C2×C71⋊#95C2211yescharacteristic
57C2×C71⋊#95C2211yescharacteristic
58C2×C71⋊#95C2211yescharacteristic
59C22×C4⋊C4×C71C2211yescharacteristic
60C22×C4⋊C4×C71C2211yescharacteristic
61C22×C42×C71C2211yescharacteristic
62#387×C71C2218yescomplemented
63C2×#95×C71C2211yescharacteristic
64C2×#95×C71C2211yescharacteristic
65C2×#95×C71C2211yescharacteristic
66C2×#95×C71C2211yescharacteristic
67C24×D71C2311yescharacteristic
68C24×D71C2311yescharacteristic
69C22×Dic142—42no—
70C22×Dic142—42no—
71C22×Dic142—42no—
72C22×Dic142C2314yes—
73C22×D284—24no—
74C22×D284—42no—
75C22×D284—42no—
76C22×D284C2314yes—
77C23×Dic71C2311yescharacteristic
78C23×Dic71C2311yescharacteristic
79C23×Dic71C2311yescharacteristic
80C23×Dic71C2311yescharacteristic
81C23×Dic71C2311yescharacteristic
82C23×Dic71C2311yescharacteristic
83C2×C4⋊Dic71—42no—
84C2×C4⋊Dic71—42no—
85C2×C4⋊Dic71C2314yes—
86C2×C4⋊Dic71C2314yes—
87C2×Dic71⋊C4—24no—
88C2×Dic71⋊C4—42no—
89C2×Dic71⋊C4—42no—
90C2×Dic71⋊C4—42no—
91C2×Dic71⋊C4C2314yes—
92C2×Dic71⋊C4C2314yes—
93C2×Dic71⋊C4C2314yes—
94C2×Dic71⋊C4C2314yes—
95C2×(C2×D71)⋊C4—42no—
96C2×(C2×D71)⋊C4—42no—
97C2×(C2×D71)⋊C4—42no—
98C2×(C2×D71)⋊C4—42no—
99C2×(C2×D71)⋊C4—42no—
100C2×(C2×D71)⋊C4—42no—
101C2×(C2×D71)⋊C4—42no—
102C2×(C2×D71)⋊C4—42no—
103C2×(C2×D71)⋊C4—42no—
104C2×(C2×D71)⋊C4—42no—
105C2×(C2×D71)⋊C4—42no—
106C2×(C2×D71)⋊C4—42no—
107C2×(C2×D71)⋊C4C2314yes—
108C2×(C2×D71)⋊C4C2314yes—
109C2×(C2×D71)⋊C4C2314yes—
110C2×(C2×D71)⋊C4C2314yes—
111C2×(C2×D71)⋊C4C2314yes—
112C2×(C2×D71)⋊C4C2314yes—
113C2×(C2×D71)⋊C4C2314yes—
114C2×(C2×D71)⋊C4C2314yes—
115C2×(C2×D71)⋊C4C2314yes—
116C2×(C2×D71)⋊C4C2314yes—
117C2×(C2×D71)⋊C4C2314yes—
118C2×(C2×D71)⋊C4C2314yes—
119C71⋊#95C2314yes—
120C71⋊#95C2314yes—
121C71⋊#95C2314yes—
122C71⋊#95C2314yes—
123C71⋊#95C2314yes—
124C71⋊#95C2314yes—
125C71⋊#95C2314yes—
126C71⋊#95C2314yes—
127C23×C4×C71C2311yescharacteristic
128C23×C4×C71C2311yescharacteristic
129C23×C4×C71C2311yescharacteristic
130C23×C4×C71C2311yescharacteristic
131C23×C4×C71C2311yescharacteristic
132C23×C4×C71C2311yescharacteristic
133C23×C4×C71C2311yescharacteristic
134C2×C4⋊C4×C71—24no—
135C2×C4⋊C4×C71—42no—
136C2×C4⋊C4×C71C2314yes—
137C2×C4⋊C4×C71C2314yes—
138C2×C42×C71—42no—
139C2×C42×C71C2314yes—
140#95×C71C2314yes—
141#95×C71C2314yes—
142#95×C71C2314yes—
143#95×C71C2314yes—
144C23×D71—22no—
145C23×D71—22no—
146C23×D71—22no—
147C23×D71—22no—
148C23×D71—22no—
149C23×D71—22no—
150C23×D71—22no—
151C23×D71—22no—
152C23×D71—22no—
153C23×D71—22no—
154C23×D71—22no—
155C23×D71—22no—
156C23×D71—22no—
157C23×D71—22no—
158C23×D71C2412yes—
159C23×D71C2412yes—
160C2×Dic142—44no—
161C2×Dic142—44no—
162C2×Dic142—44no—
163C2×Dic142—416no—
164C2×D284—28no—
165C2×D284—44no—
166C2×D284—44no—
167C2×D284—416no—
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×Dic71—22no—
182C22×Dic71—22no—
183C22×Dic71—22no—
184C22×Dic71—22no—
185C22×Dic71—22no—
186C22×Dic71C2412yes—
187C22×Dic71C2412yes—
188C22×Dic71C2412yes—
189C22×Dic71C2412yes—
190C22×Dic71C2412yes—
191C22×Dic71C2412yes—
192C4⋊Dic71—44no—
193C4⋊Dic71—44no—
194Dic71⋊C4—28no—
195Dic71⋊C4—44no—
196Dic71⋊C4—44no—
197Dic71⋊C4—44no—
198(C2×D71)⋊C4—44no—
199(C2×D71)⋊C4—44no—
200(C2×D71)⋊C4—44no—
201(C2×D71)⋊C4—44no—
202(C2×D71)⋊C4—44no—
203(C2×D71)⋊C4—44no—
204(C2×D71)⋊C4—44no—
205(C2×D71)⋊C4—44no—
206(C2×D71)⋊C4—44no—
207(C2×D71)⋊C4—44no—
208(C2×D71)⋊C4—44no—
209(C2×D71)⋊C4—44no—
210C24×C71C2411yescharacteristic
211C22×C4×C71—22no—
212C22×C4×C71—22no—
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#4114yes—
232C22×C4×C71C2412yes—
233C22×C4×C71C2412yes—
234C22×C4×C71C2412yes—
235C22×C4×C71C2412yes—
236C22×C4×C71C2412yes—
237C22×C4×C71C2412yes—
238C22×C4×C71C2412yes—
239C4⋊C4×C71—28no—
240C4⋊C4×C71—44no—
241C42×C71—44no—
242C23×C71C2×#4112yes—
243C23×C71H(5,𝔽2)12yes—
244C23×C71H(5,𝔽2)12yes—
245C23×C71H(5,𝔽2)12yes—
246C23×C71H(5,𝔽2)12yes—
247C23×C712−1+412yes—
248C23×C712−1+412yes—
249C23×C71C2511yescharacteristic
250C22×D71—22no—
251C22×D71—22no—
252C22×D71—22no—
253C22×D71—22no—
254C22×D71—22no—
255C22×D71—22no—
256C22×D71—22no—
257C22×D71—22no—
258C22×D71—22no—
259C22×D71—22no—
260C22×D71—22no—
261C22×D71—22no—
262C22×D71—22no—
263C22×D71—22no—
264C22×D71—44no—
265C22×D71—44no—
266C22×D71—44no—
267C22×D71—44no—
268C22×D71—44no—
269C22×D71—44no—
270C22×D71—44no—
271C22×D71—44no—
272C22×D71—44no—
273C22×D71—44no—
274C22×D71—44no—
275C22×D71—44no—
276C22×D71—44no—
277C22×D71—44no—
278C2×C4×C71—28no—
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—22no—
290C2×C4×C71—22no—
291C2×C4×C71—22no—
292C2×C4×C71—22no—
293C2×C4×C71—22no—
294C2×C4×C71—22no—
295C2×C4×C71—22no—
296C2×C4×C71—22no—
297C2×C4×C71—22no—
298C2×C4×C71—22no—
299C2×C4×C71—44no—
300C2×C4×C71—44no—
301C2×C4×C71—44no—
302C2×C4×C71—44no—
303C2×C4×C71—44no—
304C2×C4×C71—44no—
305C2×C4×C71C2×#4114yes—
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—22no—
320C2×Dic71—22no—
321C2×Dic71—22no—
322C2×Dic71—22no—
323C2×Dic71—22no—
324C2×Dic71—44no—
325C2×Dic71—44no—
326C2×Dic71—44no—
327C2×Dic71—44no—
328C2×Dic71—44no—
329C2×Dic71—44no—
330D284—416no—
331Dic142—416no—
332C22×C71#53814yes—
333C22×C71#54214yes—
334C22×C71#54214yes—
335C22×C71#56014yes—
336C22×C71#56214yes—
337C22×C71#56214yes—
338C22×C71#56314yes—
339C22×C71C22×#4111yescharacteristic
340C22×C71C2×H(5,𝔽2)11yescharacteristic
341C22×C71C2×H(5,𝔽2)11yescharacteristic
342C22×C71C2×H(5,𝔽2)11yescharacteristic
343C22×C71C2×H(5,𝔽2)11yescharacteristic
344C22×C71C2×2−1+411yescharacteristic
345C22×C71C2×2−1+411yescharacteristic
346C2×D71—42no—
347C2×D71—42no—
348C2×D71—42no—
349C2×D71—42no—
350C2×D71—42no—
351C2×D71—42no—
352C2×D71—42no—
353C2×D71—42no—
354C2×D71—42no—
355C2×D71—42no—
356C2×D71—42no—
357C2×D71—42no—
358C2×D71—42no—
359C2×D71—42no—
360C2×D71—88no—
361C2×D71—88no—
362C4×C71—24no—
363C4×C71—42no—
364C4×C71—42no—
365C4×C71—42no—
366C4×C71—42no—
367C4×C71—42no—
368C4×C71—42no—
369Dic71—42no—
370Dic71—42no—
371Dic71—42no—
372Dic71—42no—
373Dic71—42no—
374Dic71—42no—
375C2×#2830—711nomaximal, Sylow
376C2×C71#283018yescomplemented
377C2×C71C2×#53811yescharacteristic
378C2×C71C2×#54211yescharacteristic
379C2×C71C2×#54211yescharacteristic
380C2×C71C2×#56011yescharacteristic
381C2×C71C2×#56211yescharacteristic
382C2×C71C2×#56211yescharacteristic
383C2×C71C2×#56311yescharacteristic
384D71—82no—
385D71—82no—
386#2830—7116no—
387C2×#398—711no—
388C2×#397—711no—
389C2×#397—711no—
390C2×#397—711no—
391C2×#397—711no—
392C2×#396—711no—
393C2×#396—711no—
394C2×#395—711no—
395C2×#394—711no—
396C2×#394—711no—
397C2×#393—711no—
398C2×#393—711no—
399C2×#390—711no—
400C2×#387—711no—
401C2×#387D7111yescharacteristic, complemented
402C71C2×#283011yescharacteristic, complemented, Sylow
403C23×Q8—711no—
404C23×D4—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⋊C4C2×D7111yescharacteristic
412C22×C4⋊C4C2×D7111yescharacteristic
413C22×C22⋊C4—711no—
414C22×C22⋊C4—711no—
415C22×C22⋊C4—711no—
416C22×C22⋊C4—711no—
417C22×C22⋊C4—711no—
418C22×C22⋊C4—711no—
419C22×C22⋊C4—711no—
420C22×C22⋊C4—711no—
421C22×C22⋊C4—711no—
422C22×C22⋊C4—711no—
423C22×C22⋊C4—711no—
424C22×C22⋊C4—711no—
425C22×C42C2×D7111yescharacteristic
426#398—718no—
427#397—718no—
428#397—718no—
429#397—718no—
430#397—718no—
431#396—718no—
432#396—718no—
433#395—718no—
434#394—718no—
435#394—718no—
436#393—718no—
437#393—718no—
438#390—718no—
439#387—718no—
440#387C2×D7118yescomplemented
441C2×#95—711no—
442C2×#95—711no—
443C2×#95—711no—
444C2×#95—711no—
445C2×#95—711no—
446C2×#95—711no—
447C2×#95—711no—
448C2×#95—711no—
449C2×#95C2×D7111yescharacteristic
450C2×#95C2×D7111yescharacteristic
451C2×#95C2×D7111yescharacteristic
452C2×#95C2×D7111yescharacteristic
453C25—711no—
454C25—711no—
455C22×Q8—2842no—
456C22×Q8—2842no—
457C22×Q8—2842no—
458C22×Q8—714no—
459C22×D4—2842no—
460C22×D4—2842no—
461C22×D4—714no—
462C22×D4—1424no—
463C23×C4—711no—
464C23×C4—711no—
465C23×C4—711no—
466C23×C4—711no—
467C23×C4—711no—
468C23×C4—711no—
469C23×C4C22×D7111yescharacteristic
470C23×C4C22×D7111yescharacteristic
471C23×C4C22×D7111yescharacteristic
472C23×C4C22×D7111yescharacteristic
473C23×C4C22×D7111yescharacteristic
474C23×C4C22×D7111yescharacteristic
475C23×C4C22×D7111yescharacteristic
476C2×C4⋊C4—24no—
477C2×C4⋊C4—42no—
478C2×C4⋊C4—2842no—
479C2×C4⋊C4—2842no—
480C2×C4⋊C4—2842no—
481C2×C4⋊C4—2842no—
482C2×C4⋊C4—2842no—
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—1424no—
490C2×C4⋊C4C22×D7114yes—
491C2×C4⋊C4C22×D7114yes—
492C2×C22⋊C4—2842no—
493C2×C22⋊C4—2842no—
494C2×C22⋊C4—2842no—
495C2×C22⋊C4—2842no—
496C2×C22⋊C4—2842no—
497C2×C22⋊C4—2842no—
498C2×C22⋊C4—2842no—
499C2×C22⋊C4—2842no—
500C2×C22⋊C4—2842no—
501C2×C22⋊C4—2842no—
502C2×C22⋊C4—2842no—
503C2×C22⋊C4—2842no—
504C2×C22⋊C4—714no—
505C2×C22⋊C4—714no—
506C2×C22⋊C4—714no—
507C2×C22⋊C4—714no—
508C2×C22⋊C4—714no—
509C2×C22⋊C4—714no—
510C2×C22⋊C4—714no—
511C2×C22⋊C4—714no—
512C2×C22⋊C4—714no—
513C2×C22⋊C4—714no—
514C2×C22⋊C4—714no—
515C2×C22⋊C4—714no—
516C2×C42—42no—
517C2×C42C22×D7114yes—
518#95—714no—
519#95—714no—
520#95—714no—
521#95—714no—
522#95—714no—
523#95—714no—
524#95—714no—
525#95—714no—
526#95C22×D7114yes—
527#95C22×D7114yes—
528#95C22×D7114yes—
529#95C22×D7114yes—
530C24—712no—
531C24—712no—
532C24—1422no—
533C24—1422no—
534C24—1422no—
535C24—1422no—
536C24—1422no—
537C24—1422no—
538C24—1422no—
539C24—1422no—
540C24—1422no—
541C24—1422no—
542C24—1422no—
543C24—1422no—
544C24—1422no—
545C24—1422no—
546C24C23×D7111yescharacteristic
547C2×Q8—2844no—
548C2×Q8—2844no—
549C2×Q8—2844no—
550C2×Q8—28416no—
551C2×D4—28416no—
552C2×D4—2844no—
553C2×D4—2844no—
554C2×D4—1428no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—712no—
576C22×C4—712no—
577C22×C4—712no—
578C22×C4—712no—
579C22×C4—712no—
580C22×C4—712no—
581C22×C4—1422no—
582C22×C4—1422no—
583C22×C4—1422no—
584C22×C4—1422no—
585C22×C4—1422no—
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×C4—1422no—
599C22×C4#1176586514yes—
600C22×C4C23×D7112yes—
601C22×C4C23×D7112yes—
602C22×C4C23×D7112yes—
603C22×C4C23×D7112yes—
604C22×C4C23×D7112yes—
605C22×C4C23×D7112yes—
606C22×C4C23×D7112yes—
607C4⋊C4—28no—
608C4⋊C4—44no—
609C4⋊C4—2844no—
610C4⋊C4—2844no—
611C4⋊C4—2844no—
612C4⋊C4—2844no—
613C4⋊C4—2844no—
614C4⋊C4—1428no—
615C22⋊C4—2844no—
616C22⋊C4—2844no—
617C22⋊C4—2844no—
618C22⋊C4—2844no—
619C22⋊C4—2844no—
620C22⋊C4—2844no—
621C22⋊C4—2844no—
622C22⋊C4—2844no—
623C22⋊C4—2844no—
624C22⋊C4—2844no—
625C22⋊C4—2844no—
626C22⋊C4—2844no—
627C42—44no—
628C23—2844no—
629C23—2844no—
630C23—2844no—
631C23—2844no—
632C23—2844no—
633C23—2844no—
634C23—2844no—
635C23—2844no—
636C23—2844no—
637C23—2844no—
638C23—2844no—
639C23—2844no—
640C23—2844no—
641C23—2844no—
642C23—1422no—
643C23—1422no—
644C23—1422no—
645C23—1422no—
646C23—1422no—
647C23—1422no—
648C23—1422no—
649C23—1422no—
650C23—1422no—
651C23—1422no—
652C23—1422no—
653C23—1422no—
654C23—1422no—
655C23—1422no—
656C23C2×#1176586512yes—
657C23#1455617312yes—
658C23#1455617412yes—
659C23#1455617412yes—
660C23#1455617412yes—
661C23#1455617512yes—
662C23#1455617612yes—
663C23C24×D7111yescharacteristic
664Q8—28416no—
665D4—28416no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—28no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—44no—
688C2×C4—44no—
689C2×C4—44no—
690C2×C4—44no—
691C2×C4—44no—
692C2×C4—44no—
693C2×C4—2844no—
694C2×C4—2844no—
695C2×C4—2844no—
696C2×C4—2844no—
697C2×C4—2844no—
698C2×C4—2844no—
699C2×C4—1422no—
700C2×C4—1422no—
701C2×C4—1422no—
702C2×C4—1422no—
703C2×C4—1422no—
704C2×C4—1422no—
705C2×C4—1422no—
706C2×C4—1422no—
707C2×C4—1422no—
708C2×C4—1422no—
709C2×C4—1422no—
710C2×C4—1422no—
711C2×C4—1422no—
712C2×C4—1422no—
713C2×C4—1422no—
714C2×C4—1422no—
715C2×C4—1422no—
716C2×C4—1422no—
717C2×C4C2×#1176586514yes—
718C22—2842no—
719C22—2842no—
720C22—2842no—
721C22—2842no—
722C22—2842no—
723C22—2842no—
724C22—2842no—
725C22—2842no—
726C22—2842no—
727C22—2842no—
728C22—2842no—
729C22—2842no—
730C22—2842no—
731C22—2842no—
732C22—5688no—
733C22—5688no—
734C22#1798658214yes—
735C22#1798662014yes—
736C22#1798662114yes—
737C22#1798674014yes—
738C22#1798674514yes—
739C22#1798674614yes—
740C22#1798675314yes—
741C22C22×#1176586511yescharacteristic
742C22C2×#1455617311yescharacteristic
743C22C2×#1455617411yescharacteristic
744C22C2×#1455617411yescharacteristic
745C22C2×#1455617411yescharacteristic
746C22C2×#1455617511yescharacteristic
747C22C2×#1455617611yescharacteristic
748C4—24no—
749C4—42no—
750C4—42no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—2842no—
756C4—2842no—
757C4—2842no—
758C4—2842no—
759C4—2842no—
760C4—2842no—
761C2—5682no—
762C2—5682no—
763C2#2259648118yesdirect product factor
764C2C2×#1798658211yescharacteristic
765C2C2×#1798662011yescharacteristic
766C2C2×#1798662111yescharacteristic
767C2C2×#1798674011yescharacteristic
768C2C2×#1798674511yescharacteristic
769C2C2×#1798674611yescharacteristic
770C2C2×#1798675311yescharacteristic
subgroupG/H
centerC24C23×D71
commutator, cosocleC23×C71C25
FrattiniC23C24×D71
FittingC2×#387×C71C2
socleC24×C71C24
prime radicalC23×D284C22
hypercenterC2×#387D71
hypocenterC71C2×#2830
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
1. #22596481C2direct (N × H)
2. C2×#17985932C2semidirect
3. C2×#17985928C2semidirect
4. C2×#17985928C2semidirect
5. C2×#17985926C2semidirect
6. C2×#17985925C2semidirect
7. C2×#17985923C2semidirect
8. C2×#17985921C2semidirect
9. C2×#17985920C2semidirect
12. C2×#17985912C2semidirect
13. C2×#17985912C2semidirect
15. C2×#17985883C2semidirect
16. C2×#387×C71C2semidirect
37. #17985932C22semidirect
38. #17985928C22semidirect
39. #17985928C22semidirect
40. #17985926C22semidirect
41. #17985925C22semidirect
42. #17985923C22semidirect
43. #17985921C22semidirect
44. #17985920C22semidirect
47. #17985912C22semidirect
48. #17985912C22semidirect
50. #17985883C22semidirect
62. #387×C71C22semidirect
376. C2×C71#2830semidirect
401. C2×#387D71semidirect
402. C71C2×#2830semidirect
440. #387C2×D71semidirect
763. C2#22596481direct (N × H)

Maximal subgroups

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

subgroupindex
#225964812
C2×#179859322
C2×#179859282
C2×#179859262
C2×#179859252
C2×#179859232
C2×#179859212
C2×#179859202
C2×#179859172
C2×#179859162
C2×#179859122
C2×#179859012
C2×#179858832
C2×#387×C712
C2×#283071