Finite Group Databasebeta

← C2×#22591326 #32156949

Subgroups — C2×#22591326 #32156949

Order 18176.

3830 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556109C211yesmaximal, characteristic
2C22×#14556084C211yesmaximal, characteristic, complemented
3#22591326C2116yesmaximal, direct product factor
4C2×#17985894C211yesmaximal, characteristic, complemented
5C2×#17985893C211yesmaximal, characteristic, complemented
6C2×#17985887C211yesmaximal, characteristic, complemented
7C2×#17985883C211yesmaximal, characteristic, complemented
8C2×#17985880C211yesmaximal, characteristic, complemented
9C2×#17985879C211yesmaximal, characteristic
10C2×#17985872C211yesmaximal, characteristic, complemented
11C2×#17985872C211yesmaximal, characteristic, complemented
12C2×C4×Dic71⋊C4C211yesmaximal, characteristic, complemented
13C2×C22⋊C4×Dic71C211yesmaximal, characteristic, complemented
14C2×C4×C22⋊Dic71C211yesmaximal, characteristic, complemented
15C22×C71⋊#95C211yesmaximal, characteristic, complemented
16C22×C4×D4×C71C211yesmaximal, characteristic
17C24×Dic71C2211yescharacteristic
18C24×Dic71C2211yescharacteristic
19C2×#14556109C4116yescomplemented
20C2×#14556109C2218yes—
21C2×#14556084—28no—
22C2×#14556084C2218yescomplemented
23C22×Dic71⋊C4C2211yescharacteristic
24C22×Dic71⋊C4C2211yescharacteristic
25C22×Dic71⋊C4C2211yescharacteristic
26C22×Dic71⋊C4C2211yescharacteristic
27C22×Dic71⋊C4C2211yescharacteristic
28C22×Dic71⋊C4C2211yescharacteristic
29C22×C22⋊Dic71C2211yescharacteristic
30C22×C22⋊Dic71C2211yescharacteristic
31C22×C22⋊Dic71C2211yescharacteristic
32C22×C22⋊Dic71C2211yescharacteristic
33C22×C22⋊Dic71C2211yescharacteristic
34C22×C22⋊Dic71C2211yescharacteristic
35C22×C4×Dic71C2211yescharacteristic
36C22×C4×Dic71C2211yescharacteristic
37C22×C4×Dic71C2211yescharacteristic
38C22×C4×Dic71C2211yescharacteristic
39#17985894C2218yescomplemented
40#17985893C2218yescomplemented
41#17985887C2218yescomplemented
42#17985883C2218yescomplemented
43#17985880C2218yescomplemented
44#17985879C2218yes—
45#17985872C2218yescomplemented
46#17985872C2218yescomplemented
47C4×Dic71⋊C4C2218yescomplemented
48C22⋊C4×Dic71C2218yescomplemented
49C4×C22⋊Dic71C2218yescomplemented
50C2×C71⋊#95C2211yescharacteristic
51C2×C71⋊#95C2211yescharacteristic
52C2×C71⋊#95C2211yescharacteristic
53C2×C71⋊#95C2211yescharacteristic
54C2×C71⋊#95C2211yescharacteristic
55C2×C71⋊#95C2211yescharacteristic
56C2×C71⋊#95C2211yescharacteristic
57C2×C71⋊#95C2211yescharacteristic
58C2×C71⋊#95C2211yescharacteristic
59C2×C71⋊#95C2211yescharacteristic
60C2×C71⋊#95C2218yescomplemented
61C23×D4×C71C2211yescharacteristic
62C24×C4×C71C2211yescharacteristic
63C24×C4×C71C2211yescharacteristic
64C2×C4×D4×C71—28no—
65C2×C4×D4×C71C2218yes—
66C22×C4⋊C4×C71C2211yescharacteristic
67C22×C22⋊C4×C71C2211yescharacteristic
68C22×C22⋊C4×C71C2211yescharacteristic
69C22×C42×C71C2211yescharacteristic
70C23×Dic71—24no—
71C23×Dic71—24no—
72C23×Dic71—24no—
73C23×Dic71—24no—
74C23×Dic71—42no—
75C23×Dic71C2×C418yescomplemented
76C23×Dic71C2311yescharacteristic
77C23×Dic71C2311yescharacteristic
78C23×Dic71C2311yescharacteristic
79C23×Dic71C2314yes—
80C23×Dic71C2311yescharacteristic
81C23×Dic71C2311yescharacteristic
82C23×Dic71C2311yescharacteristic
83C23×Dic71C2311yescharacteristic
84C23×Dic71C2314yes—
85C23×Dic71C2311yescharacteristic
86#14556109C2×C4164yescomplemented
87#14556084—232no—
88C2×Dic71⋊C4—24no—
89C2×Dic71⋊C4—24no—
90C2×Dic71⋊C4—24no—
91C2×Dic71⋊C4—42no—
92C2×Dic71⋊C4C2×C418yescomplemented
93C2×Dic71⋊C4C2×C418yescomplemented
94C2×Dic71⋊C4C2314yes—
95C2×Dic71⋊C4C2314yes—
96C2×Dic71⋊C4C2314yes—
97C2×Dic71⋊C4C2314yes—
98C2×Dic71⋊C4C2314yes—
99C2×Dic71⋊C4C2314yes—
100C2×C22⋊Dic71—24no—
101C2×C22⋊Dic71—24no—
102C2×C22⋊Dic71—42no—
103C2×C22⋊Dic71C2×C418yescomplemented
104C2×C22⋊Dic71C2×C418yescomplemented
105C2×C22⋊Dic71C2×C418yescomplemented
106C2×C22⋊Dic71C2314yes—
107C2×C22⋊Dic71C2314yes—
108C2×C22⋊Dic71C2314yes—
109C2×C22⋊Dic71C2314yes—
110C2×C22⋊Dic71C2314yes—
111C2×C22⋊Dic71C2314yes—
112C2×C4×Dic71—24no—
113C2×C4×Dic71—24no—
114C2×C4×Dic71—24no—
115C2×C4×Dic71—42no—
116C2×C4×Dic71C2314yes—
117C2×C4×Dic71C2314yes—
118C2×C4×Dic71C2314yes—
119C2×C4×Dic71C2314yes—
120C71⋊#95C2314yes—
121C71⋊#95C2314yes—
122C71⋊#95C2314yes—
123C71⋊#95C2314yes—
124C71⋊#95C2314yes—
125C71⋊#95C2314yes—
126C71⋊#95C2314yes—
127C71⋊#95C2314yes—
128C71⋊#95C2314yes—
129C71⋊#95C2314yes—
130C25×C71C2311yescharacteristic
131C25×C71C2311yescharacteristic
132C22×D4×C71—24no—
133C22×D4×C71—24no—
134C22×D4×C71C2×C418yes—
135C22×D4×C71C2314yes—
136C23×C4×C71—24no—
137C23×C4×C71—24no—
138C23×C4×C71—24no—
139C23×C4×C71—24no—
140C23×C4×C71—42no—
141C23×C4×C71—42no—
142C23×C4×C71C2311yescharacteristic
143C23×C4×C71C2314yes—
144C23×C4×C71C2314yes—
145C23×C4×C71C2311yescharacteristic
146C23×C4×C71C2311yescharacteristic
147C23×C4×C71C2311yescharacteristic
148C23×C4×C71C2311yescharacteristic
149C4×D4×C71—232no—
150C2×C4⋊C4×C71—24no—
151C2×C4⋊C4×C71C2314yes—
152C2×C22⋊C4×C71—24no—
153C2×C22⋊C4×C71D418yes—
154C2×C22⋊C4×C71C2314yes—
155C2×C22⋊C4×C71C2314yes—
156C2×C42×C71—24no—
157C2×C42×C71C2314yes—
158C22×Dic71—232no—
159C22×Dic71—22no—
160C22×Dic71—22no—
161C22×Dic71—28no—
162C22×Dic71—22no—
163C22×Dic71—22no—
164C22×Dic71—28no—
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—28no—
175C22×Dic71—22no—
176C22×Dic71—22no—
177C22×Dic71—22no—
178C22×Dic71—22no—
179C22×Dic71—22no—
180C22×Dic71—22no—
181C22×Dic71—28no—
182C22×Dic71—44no—
183C22×Dic71—416no—
184C22×Dic71C22×C414yes—
185C22×Dic71C22×C414yes—
186C22×Dic71C22×C414yes—
187C22×Dic71C22×C414yes—
188C22×Dic71C22×C4116yescomplemented
189C22×Dic71#4114yes—
190C22×Dic71C2412yes—
191C22×Dic71C2412yes—
192C22×Dic71C2412yes—
193C22×Dic71C2412yes—
194C22×Dic71C2412yes—
195C22×Dic71C2412yes—
196C22×Dic71C2412yes—
197C22×Dic71C2412yes—
198Dic71⋊C4—28no—
199Dic71⋊C4—28no—
200Dic71⋊C4—28no—
201Dic71⋊C4—44no—
202Dic71⋊C4C22×C4116yescomplemented
203Dic71⋊C4C22×C4116yescomplemented
204C22⋊Dic71—28no—
205C22⋊Dic71—28no—
206C22⋊Dic71—44no—
207C22⋊Dic71C22×C4116yescomplemented
208C22⋊Dic71C22×C4116yescomplemented
209C22⋊Dic71C22×C4116yescomplemented
210C4×Dic71—28no—
211C4×Dic71—28no—
212C4×Dic71—28no—
213C4×Dic71—44no—
214C24×C71—22no—
215C24×C71—22no—
216C24×C71—22no—
217C24×C71—22no—
218C24×C71—22no—
219C24×C71—22no—
220C24×C71—22no—
221C24×C71—22no—
222C24×C71—22no—
223C24×C71—22no—
224C24×C71C22×C414yes—
225C24×C71C22×C414yes—
226C24×C71C2×D414yes—
227C24×C71#4114yes—
228C24×C71C2412yes—
229C24×C71C2412yes—
230C24×C71C2411yescharacteristic
231C2×D4×C71—232no—
232C2×D4×C71—28no—
233C2×D4×C71—28no—
234C2×D4×C71C22×C4116yes—
235C22×C4×C71—22no—
236C22×C4×C71—22no—
237C22×C4×C71—22no—
238C22×C4×C71—22no—
239C22×C4×C71—22no—
240C22×C4×C71—22no—
241C22×C4×C71—22no—
242C22×C4×C71—22no—
243C22×C4×C71—22no—
244C22×C4×C71—28no—
245C22×C4×C71—22no—
246C22×C4×C71—22no—
247C22×C4×C71—28no—
248C22×C4×C71—28no—
249C22×C4×C71—28no—
250C22×C4×C71—44no—
251C22×C4×C71—44no—
252C22×C4×C71—416no—
253C22×C4×C71—416no—
254C22×C4×C71C22×C414yes—
255C22×C4×C71C2×D414yes—
256C22×C4×C71C2×D414yes—
257C22×C4×C71#4114yes—
258C22×C4×C71C2412yes—
259C22×C4×C71C2412yes—
260C22×C4×C71C2412yes—
261C22×C4×C71C2412yes—
262C22×C4×C71C2412yes—
263C4⋊C4×C71—28no—
264C22⋊C4×C71—28no—
265C22⋊C4×C71C2×D4116yes—
266C42×C71—28no—
267C23×C71—28no—
268C23×C71—28no—
269C23×C71—28no—
270C23×C71—28no—
271C23×C71—28no—
272C23×C71—28no—
273C23×C71—22no—
274C23×C71—22no—
275C23×C71—22no—
276C23×C71—22no—
277C23×C71—28no—
278C23×C71—28no—
279C23×C71—28no—
280C23×C71—22no—
281C23×C71—22no—
282C23×C71—22no—
283C23×C71—22no—
284C23×C71—22no—
285C23×C71—22no—
286C23×C71—44no—
287C23×C71—44no—
288C23×C71—44no—
289C23×C71—44no—
290C23×C71C4×D4116yes—
291C23×C71C23×C414yes—
292C23×C71C23×C414yes—
293C23×C71C23×C412yes—
294C23×C71C22×D414yes—
295C23×C71C22×D412yes—
296C23×C71C2×#4112yes—
297C23×C71C2×#4112yes—
298C23×C71C2×#4114yes—
299C23×C71C2×#4112yes—
300C23×C71H(5,𝔽2)12yes—
301C23×C712−1+412yes—
302C23×C71C2511yescharacteristic
303D4×C71—232no—
304C2×C4×C71—28no—
305C2×C4×C71—28no—
306C2×C4×C71—28no—
307C2×C4×C71—28no—
308C2×C4×C71—22no—
309C2×C4×C71—22no—
310C2×C4×C71—22no—
311C2×C4×C71—22no—
312C2×C4×C71—22no—
313C2×C4×C71—22no—
314C2×C4×C71—22no—
315C2×C4×C71—22no—
316C2×C4×C71—22no—
317C2×C4×C71—22no—
318C2×C4×C71—22no—
319C2×C4×C71—416no—
320C2×C4×C71—416no—
321C2×C4×C71—44no—
322C2×C4×C71C23×C414yes—
323C2×C4×C71C22×D414yes—
324C2×C4×C71C22×D414yes—
325C2×C4×C71C2×#4114yes—
326C2×Dic71—28no—
327C2×Dic71—28no—
328C2×Dic71—232no—
329C2×Dic71—28no—
330C2×Dic71—28no—
331C2×Dic71—28no—
332C2×Dic71—22no—
333C2×Dic71—22no—
334C2×Dic71—22no—
335C2×Dic71—22no—
336C2×Dic71—22no—
337C2×Dic71—22no—
338C2×Dic71—22no—
339C2×Dic71—22no—
340C2×Dic71—22no—
341C2×Dic71—22no—
342C2×Dic71—22no—
343C2×Dic71—22no—
344C2×Dic71—22no—
345C2×Dic71—22no—
346C2×Dic71—22no—
347C2×Dic71—22no—
348C2×Dic71—22no—
349C2×Dic71—22no—
350C2×Dic71—22no—
351C2×Dic71—416no—
352C2×Dic71—44no—
353C2×Dic71—44no—
354C2×Dic71—44no—
355C2×Dic71C23×C414yes—
356C2×Dic71C23×C414yes—
357C2×Dic71C23×C414yes—
358C2×Dic71C23×C414yes—
359C2×Dic71C2×#4114yes—
360C22×C71—232no—
361C22×C71—24no—
362C22×C71—24no—
363C22×C71—24no—
364C22×C71—24no—
365C22×C71—24no—
366C22×C71—24no—
367C22×C71—24no—
368C22×C71—24no—
369C22×C71—24no—
370C22×C71—416no—
371C22×C71—42no—
372C22×C71—42no—
373C22×C71—42no—
374C22×C71—42no—
375C22×C71C2×C4×D418yes—
376C22×C71C2×C4×D414yes—
377C22×C71C4×#4114yes—
378C22×C71#52014yes—
379C22×C71#54614yes—
380C22×C71#54714yes—
381C22×C71#55114yes—
382C22×C71#55214yes—
383C22×C71C24×C411yescharacteristic
384C22×C71C23×D411yescharacteristic
385C22×C71C22×#4111yescharacteristic
386C22×C71C22×#4111yescharacteristic
387C22×C71C22×#4111yescharacteristic
388C22×C71C2×H(5,𝔽2)11yescharacteristic
389C22×C71C2×2−1+411yescharacteristic
390C4×C71—24no—
391C4×C71—24no—
392C4×C71—24no—
393C4×C71—24no—
394C4×C71—42no—
395Dic71—24no—
396Dic71—24no—
397Dic71—24no—
398Dic71—24no—
399Dic71—24no—
400Dic71—42no—
401Dic71—42no—
402Dic71—42no—
403C2×#2359—711nomaximal, Sylow
404C2×C71—28no—
405C2×C71—44no—
406C2×C71#235918yescomplemented
407C2×C71C22×C4×D411yescharacteristic
408C2×C71C2×C4×#4111yescharacteristic
409C2×C71C2×#52011yescharacteristic
410C2×C71C2×#54611yescharacteristic
411C2×C71C2×#54711yescharacteristic
412C2×C71C2×#55111yescharacteristic
413C2×C71C2×#55211yescharacteristic
414C22×#123—711no—
415C22×C4×D4D7111yescharacteristic
416C22×#117—711no—
417#2359—7116no—
418C2×#389—711no—
419C2×#388—711no—
420C2×#388—711no—
421C2×#387—711no—
422C2×#387—711no—
423C2×#386—711no—
424C2×#385—711no—
425C2×#385—711no—
426C2×C4×C4⋊C4—711no—
427C2×C4×C22⋊C4—711no—
428C2×C4×C22⋊C4—711no—
429C22×#95—711no—
430C71C2×#235911yescharacteristic, complemented, Sylow
431C23×D4C2×D7111yescharacteristic
432C24×C4—711no—
433C24×C4—711no—
434C24×C4C2×D7111yescharacteristic
435C24×C4C2×D7111yescharacteristic
436C2×#123—7116no—
437C2×#123—718no—
438C2×C4×D4—28no—
439C2×C4×D4C2×D7118yes—
440C2×#117—718no—
441C2×#117—1428no—
442C22×C4⋊C4—711no—
443C22×C4⋊C4—711no—
444C22×C4⋊C4—711no—
445C22×C4⋊C4—711no—
446C22×C4⋊C4—711no—
447C22×C4⋊C4—711no—
448C22×C4⋊C4C2×D7111yescharacteristic
449C22×C22⋊C4—711no—
450C22×C22⋊C4—711no—
451C22×C22⋊C4—711no—
452C22×C22⋊C4—711no—
453C22×C22⋊C4—711no—
454C22×C22⋊C4—711no—
455C22×C22⋊C4C2×D7111yescharacteristic
456C22×C22⋊C4C2×D7111yescharacteristic
457C22×C42—711no—
458C22×C42—711no—
459C22×C42—711no—
460C22×C42—711no—
461C22×C42C2×D7111yescharacteristic
462#389—718no—
463#388—718no—
464#388—718no—
465#387—718no—
466#387—718no—
467#386—718no—
468#385—718no—
469#385—718no—
470C4×C4⋊C4—718no—
471C4×C22⋊C4—718no—
472C4×C22⋊C4—718no—
473C2×#95—711no—
474C2×#95—711no—
475C2×#95—711no—
476C2×#95—711no—
477C2×#95—711no—
478C2×#95—711no—
479C2×#95—711no—
480C2×#95—711no—
481C2×#95—711no—
482C2×#95—711no—
483C2×#95—718no—
484C25C22×D7111yescharacteristic
485C25C22×D7111yescharacteristic
486C22×D4—24no—
487C22×D4—24no—
488C22×D4C4×D7118yes—
489C22×D4C22×D7114yes—
490C23×C4—24no—
491C23×C4—24no—
492C23×C4—24no—
493C23×C4—24no—
494C23×C4—42no—
495C23×C4—42no—
496C23×C4—2842no—
497C23×C4—714no—
498C23×C4—718no—
499C23×C4—714no—
500C23×C4—711no—
501C23×C4—711no—
502C23×C4—711no—
503C23×C4—711no—
504C23×C4—711no—
505C23×C4—711no—
506C23×C4—711no—
507C23×C4—711no—
508C23×C4—1424no—
509C23×C4—1424no—
510C23×C4—1424no—
511C23×C4—1424no—
512C23×C4C22×D7111yescharacteristic
513C23×C4C22×D7114yes—
514C23×C4C22×D7114yes—
515C23×C4C22×D7111yescharacteristic
516C23×C4C22×D7111yescharacteristic
517C23×C4C22×D7111yescharacteristic
518C23×C4C22×D7111yescharacteristic
519#123—7164no—
520C4×D4—232no—
521#117—14232no—
522C2×C4⋊C4—24no—
523C2×C4⋊C4—2842no—
524C2×C4⋊C4—714no—
525C2×C4⋊C4—718no—
526C2×C4⋊C4—718no—
527C2×C4⋊C4—714no—
528C2×C4⋊C4—714no—
529C2×C4⋊C4—714no—
530C2×C4⋊C4—714no—
531C2×C4⋊C4—714no—
532C2×C4⋊C4—1424no—
533C2×C4⋊C4—1424no—
534C2×C4⋊C4—1424no—
535C2×C4⋊C4C22×D7114yes—
536C2×C22⋊C4—24no—
537C2×C22⋊C4—2842no—
538C2×C22⋊C4—714no—
539C2×C22⋊C4—718no—
540C2×C22⋊C4—718no—
541C2×C22⋊C4—718no—
542C2×C22⋊C4—714no—
543C2×C22⋊C4—714no—
544C2×C22⋊C4—714no—
545C2×C22⋊C4—714no—
546C2×C22⋊C4—714no—
547C2×C22⋊C4—1424no—
548C2×C22⋊C4—1424no—
549C2×C22⋊C4C22⋊D7118yes—
550C2×C22⋊C4C22×D7114yes—
551C2×C22⋊C4C22×D7114yes—
552C2×C42—24no—
553C2×C42—2842no—
554C2×C42—714no—
555C2×C42—714no—
556C2×C42—714no—
557C2×C42—714no—
558C2×C42—1424no—
559C2×C42—1424no—
560C2×C42—1424no—
561C2×C42C22×D7114yes—
562#95—714no—
563#95—714no—
564#95—714no—
565#95—714no—
566#95—714no—
567#95—714no—
568#95—714no—
569#95—714no—
570#95—714no—
571#95—714no—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—22no—
577C24—22no—
578C24—22no—
579C24—22no—
580C24—22no—
581C24—22no—
582C24C2×C4×D7114yes—
583C24C2×C4×D7114yes—
584C24C2×C22⋊D7114yes—
585C24#1176586514yes—
586C24C23×D7112yes—
587C24C23×D7112yes—
588C24C23×D7111yescharacteristic
589C2×D4—28no—
590C2×D4—28no—
591C2×D4—232no—
592C2×D4C2×C4×D71116yes—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—28no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—28no—
606C22×C4—28no—
607C22×C4—28no—
608C22×C4—44no—
609C22×C4—44no—
610C22×C4—416no—
611C22×C4—416no—
612C22×C4—28416no—
613C22×C4—2844no—
614C22×C4—714no—
615C22×C4—714no—
616C22×C4—714no—
617C22×C4—714no—
618C22×C4—7116no—
619C22×C4—714no—
620C22×C4—712no—
621C22×C4—712no—
622C22×C4—712no—
623C22×C4—712no—
624C22×C4—712no—
625C22×C4—712no—
626C22×C4—712no—
627C22×C4—712no—
628C22×C4—1428no—
629C22×C4—1422no—
630C22×C4—1422no—
631C22×C4—1422no—
632C22×C4—1422no—
633C22×C4—1422no—
634C22×C4—1422no—
635C22×C4—1428no—
636C22×C4—1422no—
637C22×C4—1422no—
638C22×C4—1422no—
639C22×C4—1422no—
640C22×C4—1422no—
641C22×C4—1428no—
642C22×C4—1422no—
643C22×C4—1422no—
644C22×C4—1422no—
645C22×C4—1428no—
646C22×C4—1422no—
647C22×C4—1422no—
648C22×C4—1422no—
649C22×C4—1422no—
650C22×C4—1422no—
651C22×C4—14232no—
652C22×C4C2×C4×D7114yes—
653C22×C4C2×C22⋊D7114yes—
654C22×C4C2×C22⋊D7114yes—
655C22×C4#1176586414yes—
656C22×C4C23×D7112yes—
657C22×C4C23×D7112yes—
658C22×C4C23×D7112yes—
659C22×C4C23×D7112yes—
660C22×C4C23×D7112yes—
661C4⋊C4—28no—
662C4⋊C4—2844no—
663C4⋊C4—7116no—
664C4⋊C4—7116no—
665C4⋊C4—1428no—
666C4⋊C4—1428no—
667C4⋊C4—1428no—
668C22⋊C4—28no—
669C22⋊C4—2844no—
670C22⋊C4—7116no—
671C22⋊C4—7116no—
672C22⋊C4—7116no—
673C22⋊C4—1428no—
674C22⋊C4—1428no—
675C22⋊C4C2×C22⋊D71116yes—
676C42—28no—
677C42—2844no—
678C42—1428no—
679C42—1428no—
680C42—1428no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—28no—
686C23—28no—
687C23—28no—
688C23—28no—
689C23—28no—
690C23—28no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—22no—
695C23—22no—
696C23—22no—
697C23—28no—
698C23—28no—
699C23—28no—
700C23—44no—
701C23—44no—
702C23—44no—
703C23—44no—
704C23C4×C22⋊D71116yes—
705C23C22×C4×D7114yes—
706C23C22×C4×D7114yes—
707C23C22×C4×D7112yes—
708C23C22×C22⋊D7114yes—
709C23C22×C22⋊D7112yes—
710C23#41×D7112yes—
711C23C2×#1176586412yes—
712C23C2×#1176586514yes—
713C23C2×#1176586512yes—
714C23#1455617312yes—
715C23#1455617512yes—
716C23C24×D7111yescharacteristic
717D4—232no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—28no—
727C2×C4—28no—
728C2×C4—28no—
729C2×C4—28no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—416no—
734C2×C4—416no—
735C2×C4—44no—
736C2×C4—2844no—
737C2×C4—2844no—
738C2×C4—2844no—
739C2×C4—28416no—
740C2×C4—714no—
741C2×C4—714no—
742C2×C4—714no—
743C2×C4—714no—
744C2×C4—714no—
745C2×C4—1422no—
746C2×C4—1422no—
747C2×C4—1422no—
748C2×C4—1422no—
749C2×C4—1422no—
750C2×C4—1422no—
751C2×C4—1422no—
752C2×C4—1422no—
753C2×C4—1422no—
754C2×C4—1422no—
755C2×C4—1422no—
756C2×C4—1422no—
757C2×C4—1422no—
758C2×C4—1422no—
759C2×C4—1422no—
760C2×C4—1422no—
761C2×C4—1422no—
762C2×C4—1422no—
763C2×C4—1422no—
764C2×C4—1428no—
765C2×C4—14232no—
766C2×C4—1428no—
767C2×C4—1428no—
768C2×C4—1428no—
769C2×C4—1428no—
770C2×C4C22×C4×D7114yes—
771C2×C4C22×C22⋊D7114yes—
772C2×C4C22×C22⋊D7114yes—
773C2×C4C2×#1176586414yes—
774C22—24no—
775C22—24no—
776C22—24no—
777C22—24no—
778C22—232no—
779C22—24no—
780C22—24no—
781C22—24no—
782C22—24no—
783C22—24no—
784C22—42no—
785C22—42no—
786C22—416no—
787C22—42no—
788C22—42no—
789C22C2×C4×C22⋊D7118yes—
790C22C2×C4×C22⋊D7114yes—
791C22C4×#1176586414yes—
792C22#1798647814yes—
793C22#1798664314yes—
794C22#1798664814yes—
795C22#1798667814yes—
796C22#1798668914yes—
797C22C23×C4×D7111yescharacteristic
798C22C23×C22⋊D7111yescharacteristic
799C22C2×#41×D7111yescharacteristic
800C22C22×#1176586411yescharacteristic
801C22C22×#1176586511yescharacteristic
802C22C2×#1455617311yescharacteristic
803C22C2×#1455617511yescharacteristic
804C4—24no—
805C4—24no—
806C4—24no—
807C4—24no—
808C4—42no—
809C4—2842no—
810C4—2842no—
811C4—2842no—
812C4—1424no—
813C4—1424no—
814C4—1424no—
815C4—1424no—
816C4—1424no—
817C2—28no—
818C2—44no—
819C2#2259132618yesdirect product factor
820C2C22×C4×C22⋊D7111yescharacteristic
821C2C2×C4×#1176586411yescharacteristic
822C2C2×#1798647811yescharacteristic
823C2C2×#1798664311yescharacteristic
824C2C2×#1798664811yescharacteristic
825C2C2×#1798667811yescharacteristic
826C2C2×#1798668911yescharacteristic
subgroupG/H
centerC24C23×D71
commutatorC22×C71C24×C4
FrattiniC23C24×D71
FittingC22×C4×D4×C71C2
socleC24×C71C24
prime radicalC23×D4×C71C22
cosocleC23×C71C25
hypercenterC22×C4×D4D71
hypocenterC71C2×#2359
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
2. C22×#14556084C2semidirect
3. #22591326C2direct (N × H)
4. C2×#17985894C2semidirect
5. C2×#17985893C2semidirect
6. C2×#17985887C2semidirect
7. C2×#17985883C2semidirect
8. C2×#17985880C2semidirect
10. C2×#17985872C2semidirect
11. C2×#17985872C2semidirect
12. C2×C4×Dic71⋊C4C2semidirect
13. C2×C22⋊C4×Dic71C2semidirect
14. C2×C4×C22⋊Dic71C2semidirect
15. C22×C71⋊#95C2semidirect
19. C2×#14556109C4semidirect
22. C2×#14556084C22semidirect
39. #17985894C22semidirect
40. #17985893C22semidirect
41. #17985887C22semidirect
42. #17985883C22semidirect
43. #17985880C22semidirect
45. #17985872C22semidirect
46. #17985872C22semidirect
47. C4×Dic71⋊C4C22semidirect
48. C22⋊C4×Dic71C22semidirect
49. C4×C22⋊Dic71C22semidirect
60. C2×C71⋊#95C22semidirect
75. C23×Dic71C2×C4semidirect
86. #14556109C2×C4semidirect
92. C2×Dic71⋊C4C2×C4semidirect
93. C2×Dic71⋊C4C2×C4semidirect
103. C2×C22⋊Dic71C2×C4semidirect
104. C2×C22⋊Dic71C2×C4semidirect
105. C2×C22⋊Dic71C2×C4semidirect
188. C22×Dic71C22×C4semidirect
202. Dic71⋊C4C22×C4semidirect
203. Dic71⋊C4C22×C4semidirect
207. C22⋊Dic71C22×C4semidirect
208. C22⋊Dic71C22×C4semidirect
209. C22⋊Dic71C22×C4semidirect
406. C2×C71#2359semidirect
430. C71C2×#2359semidirect
819. C2#22591326direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145561092
C22×#145560842
#225913262
C2×#179858942
C2×#179858932
C2×#179858872
C2×#179858832
C2×#179858802
C2×#179858792
C2×#179858722
C2×C4×Dic71⋊C42
C2×C22⋊C4×Dic712
C2×C4×C22⋊Dic712
C22×C71⋊#952
C22×C4×D4×C712
C2×#235971