Finite Group Databasebeta

← C2×#22591485 #32160036

Subgroups — C2×#22591485 #32160036

Order 18176.

2870 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556113C211yesmaximal, characteristic
2#22591485C2116yesmaximal, direct product factor
3C2×#17985900C211yesmaximal, characteristic
4C2×#17985894C211yesmaximal, characteristic, complemented
5C2×#17985891C211yesmaximal, characteristic, complemented
6C2×#17985890C211yesmaximal, characteristic, complemented
7C2×#17985890C211yesmaximal, characteristic, complemented
8C2×#17985889C211yesmaximal, characteristic, complemented
9C2×#17985885C211yesmaximal, characteristic, complemented
10C2×#17985881C211yesmaximal, characteristic, complemented
11C2×#17985877C211yesmaximal, characteristic
12C2×#17985870C211yesmaximal, characteristic, complemented
13C2×#17985870C211yesmaximal, characteristic, complemented
14C2×#17985858C211yesmaximal, characteristic, complemented
15C2×#17985856C211yesmaximal, characteristic, complemented
16C2×#389×C71C211yesmaximal, characteristic, complemented
17C23×D284C2211yescharacteristic
18C23×C4×D71C2211yescharacteristic
19C23×C4×D71C2211yescharacteristic
20C2×#14556113C4116yescomplemented
21C2×#14556113C2218yes—
22C22×C4⋊Dic71C2211yescharacteristic
23C22×Dic71⋊C4C2211yescharacteristic
24C22×Dic71⋊C4C2211yescharacteristic
25C22×Dic71⋊C4C2211yescharacteristic
26C22×Dic71⋊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
37C22×C4×Dic71C2211yescharacteristic
38C22×C4×Dic71C2211yescharacteristic
39#17985900C2218yes—
40#17985894C2218yescomplemented
41#17985891C2218yescomplemented
42#17985890C2218yescomplemented
43#17985890C2218yescomplemented
44#17985889C2218yescomplemented
45#17985885C2218yescomplemented
46#17985881C2218yescomplemented
47#17985877C2218yes—
48#17985870C2218yescomplemented
49#17985870C2218yescomplemented
50#17985858C2218yescomplemented
51#17985856C2218yescomplemented
52C2×C71⋊#95C2211yescharacteristic
53C2×C71⋊#95C2211yescharacteristic
54C2×C71⋊#95C2211yescharacteristic
55C2×C71⋊#95C2211yescharacteristic
56C2×C71⋊#95C2211yescharacteristic
57C2×C71⋊#95C2211yescharacteristic
58C2×C71⋊#95C2211yescharacteristic
59C2×C71⋊#95C2211yescharacteristic
60C22×C4⋊C4×C71C2211yescharacteristic
61C22×C4⋊C4×C71C2211yescharacteristic
62C22×C4⋊C4×C71C2211yescharacteristic
63C22×C4⋊C4×C71C2211yescharacteristic
64C22×C42×C71C2211yescharacteristic
65#389×C71C2218yescomplemented
66C2×#95×C71C2211yescharacteristic
67C2×#95×C71C2211yescharacteristic
68C24×D71C2311yescharacteristic
69C24×D71C2311yescharacteristic
70C22×D284—42no—
71C22×D284—42no—
72C22×D284C2×C418yes—
73C22×D284C2314yes—
74C23×Dic71C2311yescharacteristic
75C23×Dic71C2311yescharacteristic
76C23×Dic71C2311yescharacteristic
77C23×Dic71C2311yescharacteristic
78C23×Dic71C2311yescharacteristic
79C23×Dic71C2311yescharacteristic
80C22×C4×D71—42no—
81C22×C4×D71—42no—
82C22×C4×D71—42no—
83C22×C4×D71—42no—
84C22×C4×D71—42no—
85C22×C4×D71C2×C418yescomplemented
86C22×C4×D71C2314yes—
87C22×C4×D71C2314yes—
88#14556113C2×C4164yescomplemented
89C2×C4⋊Dic71—42no—
90C2×C4⋊Dic71C2314yes—
91C2×Dic71⋊C4—42no—
92C2×Dic71⋊C4—42no—
93C2×Dic71⋊C4—42no—
94C2×Dic71⋊C4C2×C418yescomplemented
95C2×Dic71⋊C4C2314yes—
96C2×Dic71⋊C4C2314yes—
97C2×Dic71⋊C4C2314yes—
98C2×Dic71⋊C4C2314yes—
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)⋊C4C2×C418yes—
107C2×(C2×D71)⋊C4C2×C418yes—
108C2×(C2×D71)⋊C4C2×C418yescomplemented
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—
119C2×C4×Dic71—42no—
120C2×C4×Dic71—42no—
121C2×C4×Dic71C2314yes—
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—42no—
139C2×C4⋊C4×C71—42no—
140C2×C4⋊C4×C71—42no—
141C2×C4⋊C4×C71C2×C418yescomplemented
142C2×C4⋊C4×C71C2314yes—
143C2×C4⋊C4×C71C2314yes—
144C2×C4⋊C4×C71C2314yes—
145C2×C4⋊C4×C71C2314yes—
146C2×C42×C71—42no—
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×D71—22no—
157C23×D71—22no—
158C23×D71—22no—
159C23×D71—22no—
160C23×D71—22no—
161C23×D71—22no—
162C23×D71C22×C414yes—
163C23×D71C22×C414yes—
164C23×D71C2412yes—
165C23×D71C2412yes—
166C2×D284—416no—
167C2×D284—44no—
168C2×D284—44no—
169C2×D284C22×C4116yes—
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×Dic71C22×C414yes—
187C22×Dic71C22×C414yes—
188C22×Dic71C2412yes—
189C22×Dic71C2412yes—
190C22×Dic71C2412yes—
191C22×Dic71C2412yes—
192C22×Dic71C2412yes—
193C22×Dic71C2412yes—
194C2×C4×D71—416no—
195C2×C4×D71—44no—
196C2×C4×D71—44no—
197C2×C4×D71—44no—
198C2×C4×D71—44no—
199C2×C4×D71—44no—
200C2×C4×D71—416no—
201C2×C4×D71C22×C4116yescomplemented
202C4⋊Dic71—44no—
203Dic71⋊C4—44no—
204Dic71⋊C4—44no—
205Dic71⋊C4—44no—
206Dic71⋊C4C22×C4116yescomplemented
207(C2×D71)⋊C4—44no—
208(C2×D71)⋊C4—44no—
209(C2×D71)⋊C4—44no—
210(C2×D71)⋊C4—44no—
211(C2×D71)⋊C4—44no—
212(C2×D71)⋊C4—44no—
213(C2×D71)⋊C4—44no—
214(C2×D71)⋊C4C22×C4116yes—
215(C2×D71)⋊C4C22×C4116yes—
216(C2×D71)⋊C4C22×C4116yescomplemented
217C4×Dic71—44no—
218C4×Dic71—44no—
219C24×C71C2411yescharacteristic
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×C71—22no—
233C22×C4×C71—22no—
234C22×C4×C71—22no—
235C22×C4×C71—22no—
236C22×C4×C71—22no—
237C22×C4×C71—22no—
238C22×C4×C71C22×C414yes—
239C22×C4×C71C22×C414yes—
240C22×C4×C71C22×C414yes—
241C22×C4×C71C2412yes—
242C22×C4×C71C2412yes—
243C22×C4×C71C2412yes—
244C22×C4×C71C2412yes—
245C22×C4×C71C2412yes—
246C22×C4×C71C2412yes—
247C22×C4×C71C2412yes—
248C4⋊C4×C71—44no—
249C4⋊C4×C71—44no—
250C4⋊C4×C71—44no—
251C4⋊C4×C71C22×C4116yescomplemented
252C42×C71—44no—
253C23×C71C23×C412yes—
254C23×C71H(5,𝔽2)12yes—
255C23×C71H(5,𝔽2)12yes—
256C23×C71H(5,𝔽2)12yes—
257C23×C71H(5,𝔽2)12yes—
258C23×C712−1+412yes—
259C23×C712−1+412yes—
260C23×C71C2511yescharacteristic
261C22×D71—28no—
262C22×D71—28no—
263C22×D71—28no—
264C22×D71—28no—
265C22×D71—28no—
266C22×D71—28no—
267C22×D71—22no—
268C22×D71—22no—
269C22×D71—22no—
270C22×D71—22no—
271C22×D71—22no—
272C22×D71—22no—
273C22×D71—22no—
274C22×D71—22no—
275C22×D71—22no—
276C22×D71—22no—
277C22×D71—22no—
278C22×D71—22no—
279C22×D71—44no—
280C22×D71—44no—
281C22×D71—44no—
282C22×D71—44no—
283C22×D71—44no—
284C22×D71—44no—
285C22×D71—44no—
286C22×D71—44no—
287C22×D71C23×C414yes—
288C22×D71C23×C414yes—
289C2×C4×C71—28no—
290C2×C4×C71—28no—
291C2×C4×C71—28no—
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—22no—
300C2×C4×C71—22no—
301C2×C4×C71—22no—
302C2×C4×C71—22no—
303C2×C4×C71—22no—
304C2×C4×C71—22no—
305C2×C4×C71—22no—
306C2×C4×C71—22no—
307C2×C4×C71—22no—
308C2×C4×C71—22no—
309C2×C4×C71—22no—
310C2×C4×C71—44no—
311C2×C4×C71—44no—
312C2×C4×C71—44no—
313C2×C4×C71—44no—
314C2×C4×C71C23×C414yes—
315C2×C4×C71C23×C414yes—
316C2×C4×C71C23×C414yes—
317C2×Dic71—28no—
318C2×Dic71—28no—
319C2×Dic71—22no—
320C2×Dic71—22no—
321C2×Dic71—22no—
322C2×Dic71—22no—
323C2×Dic71—22no—
324C2×Dic71—22no—
325C2×Dic71—22no—
326C2×Dic71—22no—
327C2×Dic71—22no—
328C2×Dic71—22no—
329C2×Dic71—22no—
330C2×Dic71—22no—
331C2×Dic71—22no—
332C2×Dic71—22no—
333C2×Dic71—22no—
334C2×Dic71—22no—
335C2×Dic71—44no—
336C2×Dic71—44no—
337C2×Dic71—44no—
338C2×Dic71—44no—
339C2×Dic71C23×C414yes—
340C2×Dic71C23×C414yes—
341D284—416no—
342C4×D71—416no—
343C4×D71—416no—
344C22×C71#51814yes—
345C22×C71#52014yes—
346C22×C71#52014yes—
347C22×C71#56014yes—
348C22×C71#56214yes—
349C22×C71#56214yes—
350C22×C71#56314yes—
351C22×C71C24×C411yescharacteristic
352C22×C71C2×H(5,𝔽2)11yescharacteristic
353C22×C71C2×H(5,𝔽2)11yescharacteristic
354C22×C71C2×H(5,𝔽2)11yescharacteristic
355C22×C71C2×H(5,𝔽2)11yescharacteristic
356C22×C71C2×2−1+411yescharacteristic
357C22×C71C2×2−1+411yescharacteristic
358C2×D71—24no—
359C2×D71—24no—
360C2×D71—24no—
361C2×D71—24no—
362C2×D71—24no—
363C2×D71—24no—
364C2×D71—416no—
365C2×D71—416no—
366C2×D71—42no—
367C2×D71—42no—
368C2×D71—42no—
369C2×D71—42no—
370C2×D71—42no—
371C2×D71—42no—
372C2×D71—42no—
373C2×D71—42no—
374C4×C71—24no—
375C4×C71—24no—
376C4×C71—24no—
377C4×C71—42no—
378C4×C71—42no—
379C4×C71—42no—
380C4×C71—42no—
381Dic71—24no—
382Dic71—24no—
383Dic71—42no—
384Dic71—42no—
385Dic71—42no—
386Dic71—42no—
387C2×#2376—711nomaximal, Sylow
388C2×C71#237618yescomplemented
389C2×C71C2×#51811yescharacteristic
390C2×C71C2×#52011yescharacteristic
391C2×C71C2×#52011yescharacteristic
392C2×C71C2×#56011yescharacteristic
393C2×C71C2×#56211yescharacteristic
394C2×C71C2×#56211yescharacteristic
395C2×C71C2×#56311yescharacteristic
396D71—44no—
397D71—44no—
398C22×#123—711no—
399#2376—7116no—
400C2×#390—711no—
401C2×#389—711no—
402C2×#389D7111yescharacteristic, complemented
403C2×#388—711no—
404C2×#388—711no—
405C2×#388—711no—
406C2×#388—711no—
407C2×#387—711no—
408C2×#387—711no—
409C2×#386—711no—
410C2×#385—711no—
411C2×#385—711no—
412C2×#380—711no—
413C2×#380—711no—
414C71C2×#237611yescharacteristic, complemented, Sylow
415C23×D4—711no—
416C24×C4—711no—
417C24×C4—711no—
418C2×#123—7116no—
419C2×#123—718no—
420C22×C4⋊C4—711no—
421C22×C4⋊C4—711no—
422C22×C4⋊C4—711no—
423C22×C4⋊C4—711no—
424C22×C4⋊C4—711no—
425C22×C4⋊C4C2×D7111yescharacteristic
426C22×C4⋊C4C2×D7111yescharacteristic
427C22×C4⋊C4C2×D7111yescharacteristic
428C22×C4⋊C4C2×D7111yescharacteristic
429C22×C22⋊C4—711no—
430C22×C22⋊C4—711no—
431C22×C22⋊C4—711no—
432C22×C22⋊C4—711no—
433C22×C22⋊C4—711no—
434C22×C22⋊C4—711no—
435C22×C22⋊C4—711no—
436C22×C22⋊C4—711no—
437C22×C22⋊C4—711no—
438C22×C22⋊C4—711no—
439C22×C42—711no—
440C22×C42—711no—
441C22×C42C2×D7111yescharacteristic
442#390—718no—
443#389—718no—
444#389C2×D7118yescomplemented
445#388—718no—
446#388—718no—
447#388—718no—
448#388—718no—
449#387—718no—
450#387—718no—
451#386—718no—
452#385—718no—
453#385—718no—
454#380—718no—
455#380—718no—
456C2×#95—711no—
457C2×#95—711no—
458C2×#95—711no—
459C2×#95—711no—
460C2×#95—711no—
461C2×#95—711no—
462C2×#95—711no—
463C2×#95—711no—
464C2×#95C2×D7111yescharacteristic
465C2×#95C2×D7111yescharacteristic
466C25—711no—
467C25—711no—
468C22×D4—2842no—
469C22×D4—2842no—
470C22×D4—718no—
471C22×D4—714no—
472C23×C4—2842no—
473C23×C4—2842no—
474C23×C4—2842no—
475C23×C4—2842no—
476C23×C4—2842no—
477C23×C4—714no—
478C23×C4—718no—
479C23×C4—714no—
480C23×C4—711no—
481C23×C4—711no—
482C23×C4—711no—
483C23×C4—711no—
484C23×C4—711no—
485C23×C4—711no—
486C23×C4C22×D7111yescharacteristic
487C23×C4C22×D7111yescharacteristic
488C23×C4C22×D7111yescharacteristic
489C23×C4C22×D7111yescharacteristic
490C23×C4C22×D7111yescharacteristic
491C23×C4C22×D7111yescharacteristic
492C23×C4C22×D7111yescharacteristic
493#123—7164no—
494C2×C4⋊C4—42no—
495C2×C4⋊C4—42no—
496C2×C4⋊C4—42no—
497C2×C4⋊C4—2842no—
498C2×C4⋊C4—2842no—
499C2×C4⋊C4—2842no—
500C2×C4⋊C4—2842no—
501C2×C4⋊C4—714no—
502C2×C4⋊C4—714no—
503C2×C4⋊C4—714no—
504C2×C4⋊C4—714no—
505C2×C4⋊C4—718no—
506C2×C4⋊C4—714no—
507C2×C4⋊C4C4×D7118yescomplemented
508C2×C4⋊C4C22×D7114yes—
509C2×C4⋊C4C22×D7114yes—
510C2×C4⋊C4C22×D7114yes—
511C2×C4⋊C4C22×D7114yes—
512C2×C22⋊C4—2842no—
513C2×C22⋊C4—2842no—
514C2×C22⋊C4—2842no—
515C2×C22⋊C4—2842no—
516C2×C22⋊C4—2842no—
517C2×C22⋊C4—2842no—
518C2×C22⋊C4—2842no—
519C2×C22⋊C4—714no—
520C2×C22⋊C4—714no—
521C2×C22⋊C4—714no—
522C2×C22⋊C4—714no—
523C2×C22⋊C4—714no—
524C2×C22⋊C4—714no—
525C2×C22⋊C4—714no—
526C2×C22⋊C4—718no—
527C2×C22⋊C4—718no—
528C2×C22⋊C4—718no—
529C2×C22⋊C4—714no—
530C2×C22⋊C4—714no—
531C2×C22⋊C4—714no—
532C2×C42—42no—
533C2×C42—2842no—
534C2×C42—2842no—
535C2×C42—714no—
536C2×C42—714no—
537C2×C42C22×D7114yes—
538#95—714no—
539#95—714no—
540#95—714no—
541#95—714no—
542#95—714no—
543#95—714no—
544#95—714no—
545#95—714no—
546#95C22×D7114yes—
547#95C22×D7114yes—
548C24—714no—
549C24—714no—
550C24—712no—
551C24—712no—
552C24—1422no—
553C24—1422no—
554C24—1422no—
555C24—1422no—
556C24—1422no—
557C24—1422no—
558C24—1422no—
559C24—1422no—
560C24—1422no—
561C24—1422no—
562C24—1422no—
563C24—1422no—
564C24C23×D7111yescharacteristic
565C2×D4—2844no—
566C2×D4—2844no—
567C2×D4—28416no—
568C2×D4—7116no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—2844no—
588C22×C4—2844no—
589C22×C4—28416no—
590C22×C4—2844no—
591C22×C4—2844no—
592C22×C4—2844no—
593C22×C4—28416no—
594C22×C4—7116no—
595C22×C4—714no—
596C22×C4—714no—
597C22×C4—712no—
598C22×C4—712no—
599C22×C4—712no—
600C22×C4—712no—
601C22×C4—712no—
602C22×C4—712no—
603C22×C4—1422no—
604C22×C4—1422no—
605C22×C4—1422no—
606C22×C4—1422no—
607C22×C4—1422no—
608C22×C4—1422no—
609C22×C4—1422no—
610C22×C4—1422no—
611C22×C4—1422no—
612C22×C4—1422no—
613C22×C4—1422no—
614C22×C4—1422no—
615C22×C4—1422no—
616C22×C4—1422no—
617C22×C4—1422no—
618C22×C4—1422no—
619C22×C4C2×C4×D7114yes—
620C22×C4C2×C4×D7114yes—
621C22×C4C2×C4×D7114yes—
622C22×C4C23×D7112yes—
623C22×C4C23×D7112yes—
624C22×C4C23×D7112yes—
625C22×C4C23×D7112yes—
626C22×C4C23×D7112yes—
627C22×C4C23×D7112yes—
628C22×C4C23×D7112yes—
629C4⋊C4—44no—
630C4⋊C4—44no—
631C4⋊C4—44no—
632C4⋊C4—2844no—
633C4⋊C4—2844no—
634C4⋊C4—2844no—
635C4⋊C4—2844no—
636C4⋊C4—7116no—
637C4⋊C4C2×C4×D71116yescomplemented
638C22⋊C4—2844no—
639C22⋊C4—2844no—
640C22⋊C4—2844no—
641C22⋊C4—2844no—
642C22⋊C4—2844no—
643C22⋊C4—2844no—
644C22⋊C4—2844no—
645C22⋊C4—7116no—
646C22⋊C4—7116no—
647C22⋊C4—7116no—
648C42—44no—
649C42—2844no—
650C42—2844no—
651C23—2844no—
652C23—2844no—
653C23—2844no—
654C23—2844no—
655C23—2844no—
656C23—2844no—
657C23—2844no—
658C23—2844no—
659C23—714no—
660C23—714no—
661C23—1422no—
662C23—1422no—
663C23—1422no—
664C23—1422no—
665C23—1422no—
666C23—1422no—
667C23—1422no—
668C23—1422no—
669C23—1422no—
670C23—1422no—
671C23—1422no—
672C23—1422no—
673C23—1428no—
674C23—1428no—
675C23—1428no—
676C23—1428no—
677C23—1428no—
678C23—1428no—
679C23C22×C4×D7112yes—
680C23#1455617312yes—
681C23#1455617312yes—
682C23#1455617412yes—
683C23#1455617412yes—
684C23#1455617612yes—
685C23#1455617612yes—
686C23C24×D7111yescharacteristic
687D4—28416no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—28no—
695C2×C4—28no—
696C2×C4—28no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—44no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—28416no—
714C2×C4—28416no—
715C2×C4—2844no—
716C2×C4—2844no—
717C2×C4—2844no—
718C2×C4—2844no—
719C2×C4—714no—
720C2×C4—714no—
721C2×C4—1422no—
722C2×C4—1422no—
723C2×C4—1422no—
724C2×C4—1422no—
725C2×C4—1422no—
726C2×C4—1422no—
727C2×C4—1422no—
728C2×C4—1422no—
729C2×C4—1422no—
730C2×C4—1422no—
731C2×C4—1422no—
732C2×C4—1422no—
733C2×C4—1422no—
734C2×C4—1422no—
735C2×C4—1422no—
736C2×C4—1422no—
737C2×C4—1428no—
738C2×C4—1428no—
739C2×C4C22×C4×D7114yes—
740C2×C4C22×C4×D7114yes—
741C2×C4C22×C4×D7114yes—
742C22—2842no—
743C22—2842no—
744C22—2842no—
745C22—2842no—
746C22—2842no—
747C22—2842no—
748C22—2842no—
749C22—2842no—
750C22—28416no—
751C22—28416no—
752C22—1424no—
753C22—1424no—
754C22—1424no—
755C22—1424no—
756C22—1424no—
757C22—1424no—
758C22#1798647114yes—
759C22#1798648014yes—
760C22#1798648114yes—
761C22#1798673714yes—
762C22#1798674514yes—
763C22#1798674714yes—
764C22#1798674814yes—
765C22C23×C4×D7111yescharacteristic
766C22C2×#1455617311yescharacteristic
767C22C2×#1455617311yescharacteristic
768C22C2×#1455617411yescharacteristic
769C22C2×#1455617411yescharacteristic
770C22C2×#1455617611yescharacteristic
771C22C2×#1455617611yescharacteristic
772C4—24no—
773C4—24no—
774C4—24no—
775C4—42no—
776C4—42no—
777C4—42no—
778C4—42no—
779C4—2842no—
780C4—2842no—
781C4—2842no—
782C4—2842no—
783C4—1424no—
784C4—1424no—
785C2—2844no—
786C2—2844no—
787C2#2259148518yesdirect product factor
788C2C2×#1798647111yescharacteristic
789C2C2×#1798648011yescharacteristic
790C2C2×#1798648111yescharacteristic
791C2C2×#1798673711yescharacteristic
792C2C2×#1798674511yescharacteristic
793C2C2×#1798674711yescharacteristic
794C2C2×#1798674811yescharacteristic
subgroupG/H
centerC24C23×D71
commutatorC22×C71C24×C4
FrattiniC23C24×D71
FittingC2×#389×C71C2
socleC24×C71C24
prime radicalC23×D284C22
cosocleC23×C71C25
hypercenterC2×#389D71
hypocenterC71C2×#2376
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
2. #22591485C2direct (N × H)
4. C2×#17985894C2semidirect
5. C2×#17985891C2semidirect
6. C2×#17985890C2semidirect
7. C2×#17985890C2semidirect
8. C2×#17985889C2semidirect
9. C2×#17985885C2semidirect
10. C2×#17985881C2semidirect
12. C2×#17985870C2semidirect
13. C2×#17985870C2semidirect
14. C2×#17985858C2semidirect
15. C2×#17985856C2semidirect
16. C2×#389×C71C2semidirect
20. C2×#14556113C4semidirect
40. #17985894C22semidirect
41. #17985891C22semidirect
42. #17985890C22semidirect
43. #17985890C22semidirect
44. #17985889C22semidirect
45. #17985885C22semidirect
46. #17985881C22semidirect
48. #17985870C22semidirect
49. #17985870C22semidirect
50. #17985858C22semidirect
51. #17985856C22semidirect
65. #389×C71C22semidirect
85. C22×C4×D71C2×C4semidirect
88. #14556113C2×C4semidirect
94. C2×Dic71⋊C4C2×C4semidirect
108. C2×(C2×D71)⋊C4C2×C4semidirect
141. C2×C4⋊C4×C71C2×C4semidirect
201. C2×C4×D71C22×C4semidirect
206. Dic71⋊C4C22×C4semidirect
216. (C2×D71)⋊C4C22×C4semidirect
251. C4⋊C4×C71C22×C4semidirect
388. C2×C71#2376semidirect
402. C2×#389D71semidirect
414. C71C2×#2376semidirect
444. #389C2×D71semidirect
507. C2×C4⋊C4C4×D71semidirect
637. C4⋊C4C2×C4×D71semidirect
787. C2#22591485direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145561132
#225914852
C2×#179859002
C2×#179858942
C2×#179858912
C2×#179858902
C2×#179858892
C2×#179858852
C2×#179858812
C2×#179858772
C2×#179858702
C2×#179858582
C2×#179858562
C2×#389×C712
C2×#237671