Finite Group Databasebeta

← C2×#22591135 #32156351

Subgroups — C2×#22591135 #32156351

Order 18176.

2982 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×#14556112C211yesmaximal, characteristic
2#22591135C2116yesmaximal, direct product factor
3C2×#17985899C211yesmaximal, characteristic
4C2×#17985895C211yesmaximal, characteristic, complemented
5C2×#17985892C211yesmaximal, characteristic, complemented
6C2×#17985890C211yesmaximal, characteristic, complemented
7C2×#17985889C211yesmaximal, characteristic, complemented
8C2×#17985884C211yesmaximal, characteristic, complemented
9C2×#17985882C211yesmaximal, characteristic, complemented
10C2×#17985875C211yesmaximal, characteristic
11C2×#17985873C211yesmaximal, characteristic, complemented
12C2×#17985857C211yesmaximal, characteristic, complemented
13C2×C4×C4⋊Dic71C211yesmaximal, characteristic, complemented
14C2×C22⋊C4×Dic71C211yesmaximal, characteristic, complemented
15C2×#17985846C211yesmaximal, characteristic, complemented
16C2×#388×C71C211yesmaximal, characteristic, complemented
17C23×C22⋊D71C2211yescharacteristic
18C24×Dic71C2211yescharacteristic
19C23×C4×D71C2211yescharacteristic
20C2×#14556112C4116yescomplemented
21C2×#14556112C2218yes—
22C22×C4⋊Dic71C2211yescharacteristic
23C22×C4⋊Dic71C2211yescharacteristic
24C22×C4⋊Dic71C2211yescharacteristic
25C22×Dic71⋊C4C2211yescharacteristic
26C22×Dic71⋊C4C2211yescharacteristic
27C22×Dic71⋊C4C2211yescharacteristic
28C22×C22⋊Dic71C2211yescharacteristic
29C22×C22⋊Dic71C2211yescharacteristic
30C22×(C2×D71)⋊C4C2211yescharacteristic
31C22×(C2×D71)⋊C4C2211yescharacteristic
32C22×(C2×D71)⋊C4C2211yescharacteristic
33C22×(C2×D71)⋊C4C2211yescharacteristic
34C22×(C2×D71)⋊C4C2211yescharacteristic
35C22×C4×Dic71C2211yescharacteristic
36C22×C4×Dic71C2211yescharacteristic
37C22×C4×Dic71C2211yescharacteristic
38C22×C4×Dic71C2211yescharacteristic
39#17985899C2218yes—
40#17985895C2218yescomplemented
41#17985892C2218yescomplemented
42#17985890C2218yescomplemented
43#17985889C2218yescomplemented
44#17985884C2218yescomplemented
45#17985882C2218yescomplemented
46#17985875C2218yes—
47#17985873C2218yescomplemented
48#17985857C2218yescomplemented
49C4×C4⋊Dic71C2218yescomplemented
50C22⋊C4×Dic71C2218yescomplemented
51#17985846C2218yescomplemented
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×C22⋊C4×C71C2211yescharacteristic
62C22×C22⋊C4×C71C2211yescharacteristic
63C22×C22⋊C4×C71C2211yescharacteristic
64C22×C42×C71C2211yescharacteristic
65#388×C71C2218yescomplemented
66C2×#95×C71C2211yescharacteristic
67C2×#95×C71C2211yescharacteristic
68C24×D71C2311yescharacteristic
69C22×C22⋊D71—42no—
70C22×C22⋊D71—42no—
71C22×C22⋊D71C2×C418yes—
72C22×C22⋊D71C2314yes—
73C23×Dic71—42no—
74C23×Dic71—42no—
75C23×Dic71C2×C418yescomplemented
76C23×Dic71C2311yescharacteristic
77C23×Dic71C2311yescharacteristic
78C23×Dic71C2311yescharacteristic
79C23×Dic71C2311yescharacteristic
80C23×Dic71C2311yescharacteristic
81C23×Dic71C2311yescharacteristic
82C23×Dic71C2311yescharacteristic
83C23×Dic71C2314yes—
84C22×C4×D71—24no—
85C22×C4×D71—42no—
86C22×C4×D71—42no—
87C22×C4×D71C2314yes—
88#14556112C2×C4164yescomplemented
89C2×C4⋊Dic71—24no—
90C2×C4⋊Dic71C2×C418yescomplemented
91C2×C4⋊Dic71C2×C418yescomplemented
92C2×C4⋊Dic71C2314yes—
93C2×C4⋊Dic71C2314yes—
94C2×C4⋊Dic71C2314yes—
95C2×Dic71⋊C4—42no—
96C2×Dic71⋊C4—42no—
97C2×Dic71⋊C4—42no—
98C2×Dic71⋊C4C2314yes—
99C2×Dic71⋊C4C2314yes—
100C2×Dic71⋊C4C2314yes—
101C2×C22⋊Dic71—24no—
102C2×C22⋊Dic71—42no—
103C2×C22⋊Dic71C2314yes—
104C2×C22⋊Dic71C2314yes—
105C2×(C2×D71)⋊C4—24no—
106C2×(C2×D71)⋊C4—42no—
107C2×(C2×D71)⋊C4—42no—
108C2×(C2×D71)⋊C4C2×C418yes—
109C2×(C2×D71)⋊C4C2×C418yes—
110C2×(C2×D71)⋊C4C2314yes—
111C2×(C2×D71)⋊C4C2314yes—
112C2×(C2×D71)⋊C4C2314yes—
113C2×(C2×D71)⋊C4C2314yes—
114C2×(C2×D71)⋊C4C2314yes—
115C2×C4×Dic71—42no—
116C2×C4×Dic71—42no—
117C2×C4×Dic71—42no—
118C2×C4×Dic71—42no—
119C2×C4×Dic71C2314yes—
120C2×C4×Dic71C2314yes—
121C2×C4×Dic71C2314yes—
122C2×C4×Dic71C2314yes—
123C71⋊#95C2314yes—
124C71⋊#95C2314yes—
125C71⋊#95C2314yes—
126C71⋊#95C2314yes—
127C71⋊#95C2314yes—
128C71⋊#95C2314yes—
129C71⋊#95C2314yes—
130C71⋊#95C2314yes—
131C25×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×C71C2314yes—
140C2×C22⋊C4×C71—24no—
141C2×C22⋊C4×C71—42no—
142C2×C22⋊C4×C71C2×C418yescomplemented
143C2×C22⋊C4×C71C2314yes—
144C2×C22⋊C4×C71C2314yes—
145C2×C22⋊C4×C71C2314yes—
146C2×C42×C71—24no—
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×D71C22×C414yes—
157C23×D71C2412yes—
158C2×C22⋊D71—416no—
159C2×C22⋊D71—44no—
160C2×C22⋊D71—44no—
161C2×C22⋊D71C22×C4116yes—
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—416no—
180C22×Dic71—44no—
181C22×Dic71—44no—
182C22×Dic71C22×C414yes—
183C22×Dic71C22×C414yes—
184C22×Dic71C22×C414yes—
185C22×Dic71C22×C4116yescomplemented
186C22×Dic71#4114yes—
187C22×Dic71C2412yes—
188C22×Dic71C2412yes—
189C22×Dic71C2412yes—
190C22×Dic71C2412yes—
191C22×Dic71C2412yes—
192C22×Dic71C2412yes—
193C22×Dic71C2412yes—
194C2×C4×D71—28no—
195C2×C4×D71—44no—
196C2×C4×D71—44no—
197C2×C4×D71—416no—
198C4⋊Dic71—28no—
199C4⋊Dic71C22×C4116yescomplemented
200C4⋊Dic71C22×C4116yescomplemented
201Dic71⋊C4—44no—
202Dic71⋊C4—44no—
203Dic71⋊C4—44no—
204C22⋊Dic71—28no—
205C22⋊Dic71—44no—
206(C2×D71)⋊C4—28no—
207(C2×D71)⋊C4—44no—
208(C2×D71)⋊C4—44no—
209(C2×D71)⋊C4C22×C4116yes—
210(C2×D71)⋊C4C22×C4116yes—
211C4×Dic71—44no—
212C4×Dic71—44no—
213C4×Dic71—44no—
214C4×Dic71—44no—
215C24×C71—22no—
216C24×C71—22no—
217C24×C71—22no—
218C24×C71—22no—
219C24×C71—22no—
220C24×C71—22no—
221C24×C71C22×C414yes—
222C24×C71C2412yes—
223C24×C71C2411yescharacteristic
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×C71—22no—
239C22×C4×C71C22×C414yes—
240C22×C4×C71C22×C414yes—
241C22×C4×C71#4114yes—
242C22×C4×C71C2412yes—
243C22×C4×C71C2412yes—
244C22×C4×C71C2412yes—
245C22×C4×C71C2412yes—
246C22×C4×C71C2412yes—
247C22×C4×C71C2412yes—
248C4⋊C4×C71—44no—
249C22⋊C4×C71—28no—
250C22⋊C4×C71—44no—
251C22⋊C4×C71C22×C4116yescomplemented
252C42×C71—28no—
253C23×C71—28no—
254C23×C71—28no—
255C23×C71—28no—
256C23×C71—22no—
257C23×C71—22no—
258C23×C71—22no—
259C23×C71—22no—
260C23×C71—22no—
261C23×C71—22no—
262C23×C71—44no—
263C23×C71—44no—
264C23×C71—44no—
265C23×C71—44no—
266C23×C71C23×C414yes—
267C23×C71C23×C412yes—
268C23×C71C2×#4112yes—
269C23×C71C2×#4112yes—
270C23×C71H(5,𝔽2)12yes—
271C23×C71H(5,𝔽2)12yes—
272C23×C71H(5,𝔽2)12yes—
273C23×C712−1+412yes—
274C23×C71C2511yescharacteristic
275C22×D71—28no—
276C22×D71—28no—
277C22×D71—28no—
278C22×D71—22no—
279C22×D71—22no—
280C22×D71—22no—
281C22×D71—22no—
282C22×D71—22no—
283C22×D71—22no—
284C22×D71—44no—
285C22×D71—44no—
286C22×D71—44no—
287C22×D71—44no—
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—44no—
308C2×C4×C71—44no—
309C2×C4×C71—44no—
310C2×C4×C71C23×C414yes—
311C2×C4×C71C23×C414yes—
312C2×C4×C71C2×#4114yes—
313C22⋊D71—416no—
314C2×Dic71—28no—
315C2×Dic71—28no—
316C2×Dic71—28no—
317C2×Dic71—28no—
318C2×Dic71—22no—
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—416no—
336C2×Dic71—44no—
337C2×Dic71—44no—
338C2×Dic71—44no—
339C2×Dic71C23×C414yes—
340C2×Dic71C23×C414yes—
341C2×Dic71C23×C414yes—
342C2×Dic71C2×#4114yes—
343C4×D71—416no—
344C22×C71—24no—
345C22×C71—24no—
346C22×C71—24no—
347C22×C71—416no—
348C22×C71—42no—
349C22×C71—42no—
350C22×C71—42no—
351C22×C71—42no—
352C22×C71C4×#4114yes—
353C22×C71#51814yes—
354C22×C71#52014yes—
355C22×C71#53814yes—
356C22×C71#53914yes—
357C22×C71#54014yes—
358C22×C71#54214yes—
359C22×C71C24×C411yescharacteristic
360C22×C71C22×#4111yescharacteristic
361C22×C71C22×#4111yescharacteristic
362C22×C71C2×H(5,𝔽2)11yescharacteristic
363C22×C71C2×H(5,𝔽2)11yescharacteristic
364C22×C71C2×H(5,𝔽2)11yescharacteristic
365C22×C71C2×2−1+411yescharacteristic
366C2×D71—24no—
367C2×D71—24no—
368C2×D71—24no—
369C2×D71—416no—
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—
380Dic71—24no—
381Dic71—24no—
382Dic71—24no—
383Dic71—24no—
384Dic71—42no—
385Dic71—42no—
386Dic71—42no—
387C2×#2335—711nomaximal, Sylow
388C2×C71—44no—
389C2×C71#233518yescomplemented
390C2×C71C2×C4×#4111yescharacteristic
391C2×C71C2×#51811yescharacteristic
392C2×C71C2×#52011yescharacteristic
393C2×C71C2×#53811yescharacteristic
394C2×C71C2×#53911yescharacteristic
395C2×C71C2×#54011yescharacteristic
396C2×C71C2×#54211yescharacteristic
397D71—44no—
398C22×#123—711no—
399#2335—7116no—
400C2×#390—711no—
401C2×#389—711no—
402C2×#388—711no—
403C2×#388—711no—
404C2×#388—711no—
405C2×#388D7111yescharacteristic, complemented
406C2×#387—711no—
407C2×#387—711no—
408C2×#386—711no—
409C2×#385—711no—
410C2×#380—711no—
411C2×C4×C4⋊C4—711no—
412C2×C4×C22⋊C4—711no—
413C2×C4×C22⋊C4—711no—
414C71C2×#233511yescharacteristic, 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⋊C4—711no—
426C22×C4⋊C4C2×D7111yescharacteristic
427C22×C22⋊C4—711no—
428C22×C22⋊C4—711no—
429C22×C22⋊C4—711no—
430C22×C22⋊C4—711no—
431C22×C22⋊C4—711no—
432C22×C22⋊C4—711no—
433C22×C22⋊C4—711no—
434C22×C22⋊C4C2×D7111yescharacteristic
435C22×C22⋊C4C2×D7111yescharacteristic
436C22×C22⋊C4C2×D7111yescharacteristic
437C22×C42—711no—
438C22×C42—711no—
439C22×C42—711no—
440C22×C42—711no—
441C22×C42C2×D7111yescharacteristic
442#390—718no—
443#389—718no—
444#388—718no—
445#388—718no—
446#388—718no—
447#388C2×D7118yescomplemented
448#387—718no—
449#387—718no—
450#386—718no—
451#385—718no—
452#380—718no—
453C4×C4⋊C4—718no—
454C4×C22⋊C4—718no—
455C4×C22⋊C4—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—
467C25C22×D7111yescharacteristic
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—718no—
477C23×C4—714no—
478C23×C4—714no—
479C23×C4—711no—
480C23×C4—711no—
481C23×C4—711no—
482C23×C4—711no—
483C23×C4—711no—
484C23×C4—711no—
485C23×C4—711no—
486C23×C4—1424no—
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—2842no—
496C2×C4⋊C4—2842no—
497C2×C4⋊C4—2842no—
498C2×C4⋊C4—714no—
499C2×C4⋊C4—714no—
500C2×C4⋊C4—714no—
501C2×C4⋊C4—718no—
502C2×C4⋊C4—718no—
503C2×C4⋊C4—714no—
504C2×C4⋊C4—714no—
505C2×C4⋊C4—714no—
506C2×C4⋊C4—1424no—
507C2×C4⋊C4C22×D7114yes—
508C2×C22⋊C4—24no—
509C2×C22⋊C4—42no—
510C2×C22⋊C4—2842no—
511C2×C22⋊C4—2842no—
512C2×C22⋊C4—2842no—
513C2×C22⋊C4—714no—
514C2×C22⋊C4—714no—
515C2×C22⋊C4—714no—
516C2×C22⋊C4—718no—
517C2×C22⋊C4—718no—
518C2×C22⋊C4—714no—
519C2×C22⋊C4—714no—
520C2×C22⋊C4—714no—
521C2×C22⋊C4—714no—
522C2×C22⋊C4—1424no—
523C2×C22⋊C4—1424no—
524C2×C22⋊C4C4×D7118yescomplemented
525C2×C22⋊C4C22×D7114yes—
526C2×C22⋊C4C22×D7114yes—
527C2×C22⋊C4C22×D7114yes—
528C2×C42—24no—
529C2×C42—2842no—
530C2×C42—2842no—
531C2×C42—2842no—
532C2×C42—2842no—
533C2×C42—714no—
534C2×C42—714no—
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—22no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—714no—
555C24—712no—
556C24—1422no—
557C24—1422no—
558C24—1422no—
559C24—1422no—
560C24—1422no—
561C24—1422no—
562C24C2×C4×D7114yes—
563C24C23×D7112yes—
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—2844no—
585C22×C4—2844no—
586C22×C4—28416no—
587C22×C4—2844no—
588C22×C4—2844no—
589C22×C4—28416no—
590C22×C4—7116no—
591C22×C4—714no—
592C22×C4—714no—
593C22×C4—714no—
594C22×C4—714no—
595C22×C4—712no—
596C22×C4—712no—
597C22×C4—712no—
598C22×C4—712no—
599C22×C4—712no—
600C22×C4—712no—
601C22×C4—712no—
602C22×C4—1428no—
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×C4—1422no—
620C22×C4C2×C4×D7114yes—
621C22×C4C2×C4×D7114yes—
622C22×C4#1176586414yes—
623C22×C4C23×D7112yes—
624C22×C4C23×D7112yes—
625C22×C4C23×D7112yes—
626C22×C4C23×D7112yes—
627C22×C4C23×D7112yes—
628C22×C4C23×D7112yes—
629C4⋊C4—44no—
630C4⋊C4—2844no—
631C4⋊C4—2844no—
632C4⋊C4—2844no—
633C4⋊C4—7116no—
634C4⋊C4—7116no—
635C4⋊C4—1428no—
636C22⋊C4—28no—
637C22⋊C4—44no—
638C22⋊C4—2844no—
639C22⋊C4—2844no—
640C22⋊C4—2844no—
641C22⋊C4—7116no—
642C22⋊C4—7116no—
643C22⋊C4—1428no—
644C22⋊C4—1428no—
645C22⋊C4C2×C4×D71116yescomplemented
646C42—28no—
647C42—2844no—
648C42—2844no—
649C42—2844no—
650C42—2844no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—28no—
658C23—28no—
659C23—28no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—44no—
664C23—2844no—
665C23—2844no—
666C23—2844no—
667C23—2844no—
668C23—714no—
669C23—1422no—
670C23—1422no—
671C23—1422no—
672C23—1422no—
673C23—1422no—
674C23—1422no—
675C23—1428no—
676C23—1428no—
677C23—1428no—
678C23C22×C4×D7114yes—
679C23C22×C4×D7112yes—
680C23#41×D7112yes—
681C23C2×#1176586412yes—
682C23#1455617312yes—
683C23#1455617412yes—
684C23#1455617412yes—
685C23#1455617512yes—
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—44no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4—28416no—
710C2×C4—2844no—
711C2×C4—2844no—
712C2×C4—2844no—
713C2×C4—28416no—
714C2×C4—714no—
715C2×C4—714no—
716C2×C4—714no—
717C2×C4—714no—
718C2×C4—1422no—
719C2×C4—1422no—
720C2×C4—1422no—
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—1428no—
736C2×C4—1428no—
737C2×C4—1428no—
738C2×C4—1428no—
739C2×C4C22×C4×D7114yes—
740C2×C4C22×C4×D7114yes—
741C2×C4C2×#1176586414yes—
742C22—24no—
743C22—24no—
744C22—24no—
745C22—416no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—28416no—
751C22—2842no—
752C22—2842no—
753C22—2842no—
754C22—2842no—
755C22—1424no—
756C22—1424no—
757C22—1424no—
758C22C4×#1176586414yes—
759C22#1798647314yes—
760C22#1798647814yes—
761C22#1798658314yes—
762C22#1798659314yes—
763C22#1798660214yes—
764C22#1798661514yes—
765C22C23×C4×D7111yescharacteristic
766C22C2×#41×D7111yescharacteristic
767C22C22×#1176586411yescharacteristic
768C22C2×#1455617311yescharacteristic
769C22C2×#1455617411yescharacteristic
770C22C2×#1455617411yescharacteristic
771C22C2×#1455617511yescharacteristic
772C4—24no—
773C4—24no—
774C4—24no—
775C4—42no—
776C4—42no—
777C4—42no—
778C4—2842no—
779C4—2842no—
780C4—2842no—
781C4—1424no—
782C4—1424no—
783C4—1424no—
784C4—1424no—
785C2—44no—
786C2—2844no—
787C2#2259113518yesdirect product factor
788C2C2×C4×#1176586411yescharacteristic
789C2C2×#1798647311yescharacteristic
790C2C2×#1798647811yescharacteristic
791C2C2×#1798658311yescharacteristic
792C2C2×#1798659311yescharacteristic
793C2C2×#1798660211yescharacteristic
794C2C2×#1798661511yescharacteristic
subgroupG/H
centerC24C23×D71
commutatorC22×C71C24×C4
FrattiniC23C24×D71
FittingC2×#388×C71C2
socleC24×C71C24
prime radicalC23×C22⋊D71C22
cosocleC23×C71C25
hypercenterC2×#388D71
hypocenterC71C2×#2335
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. #22591135C2direct (N × H)
4. C2×#17985895C2semidirect
5. C2×#17985892C2semidirect
6. C2×#17985890C2semidirect
7. C2×#17985889C2semidirect
8. C2×#17985884C2semidirect
9. C2×#17985882C2semidirect
11. C2×#17985873C2semidirect
12. C2×#17985857C2semidirect
13. C2×C4×C4⋊Dic71C2semidirect
14. C2×C22⋊C4×Dic71C2semidirect
15. C2×#17985846C2semidirect
16. C2×#388×C71C2semidirect
20. C2×#14556112C4semidirect
40. #17985895C22semidirect
41. #17985892C22semidirect
42. #17985890C22semidirect
43. #17985889C22semidirect
44. #17985884C22semidirect
45. #17985882C22semidirect
47. #17985873C22semidirect
48. #17985857C22semidirect
49. C4×C4⋊Dic71C22semidirect
50. C22⋊C4×Dic71C22semidirect
51. #17985846C22semidirect
65. #388×C71C22semidirect
75. C23×Dic71C2×C4semidirect
88. #14556112C2×C4semidirect
90. C2×C4⋊Dic71C2×C4semidirect
91. C2×C4⋊Dic71C2×C4semidirect
142. C2×C22⋊C4×C71C2×C4semidirect
185. C22×Dic71C22×C4semidirect
199. C4⋊Dic71C22×C4semidirect
200. C4⋊Dic71C22×C4semidirect
251. C22⋊C4×C71C22×C4semidirect
389. C2×C71#2335semidirect
405. C2×#388D71semidirect
414. C71C2×#2335semidirect
447. #388C2×D71semidirect
524. C2×C22⋊C4C4×D71semidirect
645. C22⋊C4C2×C4×D71semidirect
787. C2#22591135direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145561122
#225911352
C2×#179858992
C2×#179858952
C2×#179858922
C2×#179858902
C2×#179858892
C2×#179858842
C2×#179858822
C2×#179858752
C2×#179858732
C2×#179858572
C2×C4×C4⋊Dic712
C2×C22⋊C4×Dic712
C2×#179858462
C2×#388×C712
C2×#233571