Finite Group Databasebeta

← C2×#22593535 #32168672

Subgroups — C2×#22593535 #32168672

Order 18176.

3094 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556118C211yesmaximal, characteristic, complemented
2C22×(C22⋊D71)⋊C4C211yesmaximal, characteristic
3#22593535C2116yesmaximal, direct product factor
4C2×#17985922C211yesmaximal, characteristic, complemented
5C2×#17985921C211yesmaximal, characteristic, complemented
6C2×#17985921C211yesmaximal, characteristic, complemented
7C2×#17985899C211yesmaximal, characteristic
8C2×#17985899C211yesmaximal, characteristic
9C2×#17985874C211yesmaximal, characteristic, complemented
10C2×#17985873C211yesmaximal, characteristic, complemented
11C2×#17985871C211yesmaximal, characteristic, complemented
12C2×#17985870C211yesmaximal, characteristic, complemented
13C2×#17985868C211yesmaximal, characteristic, complemented
14C2×#17985863C211yesmaximal, characteristic, complemented
15C2×C4⋊C4×Dic71C211yesmaximal, characteristic, complemented
16C2×#396×C71C211yesmaximal, characteristic, complemented
17C23×C22⋊D71C2211yescharacteristic
18C24×Dic71C2211yescharacteristic
19C23×C4×D71C2211yescharacteristic
20C2×#14556118—28no—
21C2×#14556118C2218yescomplemented
22C2×(C22⋊D71)⋊C4—28no—
23C2×(C22⋊D71)⋊C4C2218yes—
24C22×C4⋊Dic71C2211yescharacteristic
25C22×C4⋊Dic71C2211yescharacteristic
26C22×C4⋊Dic71C2211yescharacteristic
27C22×Dic71⋊C4C2211yescharacteristic
28C22×Dic71⋊C4C2211yescharacteristic
29C22×Dic71⋊C4C2211yescharacteristic
30C22×Dic71⋊C4C2211yescharacteristic
31C22×Dic71⋊C4C2211yescharacteristic
32C22×Dic71⋊C4C2211yescharacteristic
33C22×Dic71⋊C4C2211yescharacteristic
34C22×C22⋊Dic71C2211yescharacteristic
35C22×C22⋊Dic71C2211yescharacteristic
36C22×(C2×D71)⋊C4C2211yescharacteristic
37C22×(C2×D71)⋊C4C2211yescharacteristic
38C22×(C2×D71)⋊C4C2211yescharacteristic
39C22×(C2×D71)⋊C4C2211yescharacteristic
40C22×(C2×D71)⋊C4C2211yescharacteristic
41C22×C4×Dic71C2211yescharacteristic
42C22×C4×Dic71C2211yescharacteristic
43C22×C4×Dic71C2211yescharacteristic
44#17985922C2218yescomplemented
45#17985921C2218yescomplemented
46#17985921C2218yescomplemented
47#17985899C2218yes—
48#17985899C2218yes—
49#17985874C2218yescomplemented
50#17985873C2218yescomplemented
51#17985871C2218yescomplemented
52#17985870C2218yescomplemented
53#17985868C2218yescomplemented
54#17985863C2218yescomplemented
55C4⋊C4×Dic71C2218yescomplemented
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×C22⋊C4×C71C2211yescharacteristic
65C22×C22⋊C4×C71C2211yescharacteristic
66C22×C22⋊C4×C71C2211yescharacteristic
67#396×C71C2218yescomplemented
68C2×#95×C71C2211yescharacteristic
69C24×D71C2311yescharacteristic
70C22×C22⋊D71—24no—
71C22×C22⋊D71—24no—
72C22×C22⋊D71Q818yes—
73C22×C22⋊D71C2314yes—
74C23×Dic71—24no—
75C23×Dic71—42no—
76C23×Dic71—42no—
77C23×Dic71C2311yescharacteristic
78C23×Dic71C2311yescharacteristic
79C23×Dic71C2311yescharacteristic
80C23×Dic71C2311yescharacteristic
81C23×Dic71C2311yescharacteristic
82C23×Dic71C2311yescharacteristic
83C23×Dic71C2314yes—
84C23×Dic71C2311yescharacteristic
85C22×C4×D71—24no—
86C22×C4×D71—42no—
87C22×C4×D71—42no—
88C22×C4×D71C2314yes—
89#14556118—232no—
90(C22⋊D71)⋊C4—232no—
91C2×C4⋊Dic71—24no—
92C2×C4⋊Dic71—24no—
93C2×C4⋊Dic71—42no—
94C2×C4⋊Dic71C2314yes—
95C2×C4⋊Dic71C2314yes—
96C2×C4⋊Dic71C2314yes—
97C2×Dic71⋊C4—24no—
98C2×Dic71⋊C4—24no—
99C2×Dic71⋊C4—24no—
100C2×Dic71⋊C4—24no—
101C2×Dic71⋊C4—24no—
102C2×Dic71⋊C4—42no—
103C2×Dic71⋊C4—42no—
104C2×Dic71⋊C4C2314yes—
105C2×Dic71⋊C4C2314yes—
106C2×Dic71⋊C4C2314yes—
107C2×Dic71⋊C4C2314yes—
108C2×Dic71⋊C4C2314yes—
109C2×Dic71⋊C4C2314yes—
110C2×Dic71⋊C4C2314yes—
111C2×C22⋊Dic71—24no—
112C2×C22⋊Dic71—42no—
113C2×C22⋊Dic71C2314yes—
114C2×C22⋊Dic71C2314yes—
115C2×(C2×D71)⋊C4—24no—
116C2×(C2×D71)⋊C4—24no—
117C2×(C2×D71)⋊C4—24no—
118C2×(C2×D71)⋊C4—42no—
119C2×(C2×D71)⋊C4—42no—
120C2×(C2×D71)⋊C4C2314yes—
121C2×(C2×D71)⋊C4C2314yes—
122C2×(C2×D71)⋊C4C2314yes—
123C2×(C2×D71)⋊C4C2314yes—
124C2×(C2×D71)⋊C4C2314yes—
125C2×C4×Dic71—24no—
126C2×C4×Dic71—24no—
127C2×C4×Dic71D418yes—
128C2×C4×Dic71C2314yes—
129C2×C4×Dic71C2314yes—
130C2×C4×Dic71C2314yes—
131C71⋊#95C2314yes—
132C71⋊#95C2314yes—
133C71⋊#95C2314yes—
134C71⋊#95C2314yes—
135C71⋊#95C2314yes—
136C25×C71C2311yescharacteristic
137C23×C4×C71C2311yescharacteristic
138C23×C4×C71C2311yescharacteristic
139C23×C4×C71C2311yescharacteristic
140C23×C4×C71C2311yescharacteristic
141C23×C4×C71C2311yescharacteristic
142C23×C4×C71C2311yescharacteristic
143C2×C4⋊C4×C71—24no—
144C2×C4⋊C4×C71—24no—
145C2×C4⋊C4×C71—42no—
146C2×C4⋊C4×C71C2314yes—
147C2×C4⋊C4×C71C2314yes—
148C2×C4⋊C4×C71C2314yes—
149C2×C22⋊C4×C71—24no—
150C2×C22⋊C4×C71—24no—
151C2×C22⋊C4×C71—42no—
152C2×C22⋊C4×C71C2314yes—
153C2×C22⋊C4×C71C2314yes—
154C2×C22⋊C4×C71C2314yes—
155#95×C71C2314yes—
156C23×D71—22no—
157C23×D71—22no—
158C23×D71—22no—
159C23×D71—22no—
160C23×D71—22no—
161C23×D71—22no—
162C23×D71C2×Q814yes—
163C23×D71C2412yes—
164C2×C22⋊D71—232no—
165C2×C22⋊D71—28no—
166C2×C22⋊D71—28no—
167C2×C22⋊D71C2×Q8116yes—
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—28no—
185C22×Dic71—44no—
186C22×Dic71—44no—
187C22×Dic71—416no—
188C22×Dic71C2×D414yes—
189C22×Dic71C2×D414yes—
190C22×Dic71C2×Q814yes—
191C22×Dic71#4114yes—
192C22×Dic71#4114yes—
193C22×Dic71C2412yes—
194C22×Dic71C2412yes—
195C22×Dic71C2412yes—
196C22×Dic71C2412yes—
197C22×Dic71C2412yes—
198C22×Dic71C2412yes—
199C22×Dic71C2412yes—
200C2×C4×D71—28no—
201C2×C4×D71—44no—
202C2×C4×D71—44no—
203C2×C4×D71—416no—
204C4⋊Dic71—28no—
205C4⋊Dic71—28no—
206C4⋊Dic71—44no—
207Dic71⋊C4—28no—
208Dic71⋊C4—28no—
209Dic71⋊C4—28no—
210Dic71⋊C4—28no—
211Dic71⋊C4—28no—
212Dic71⋊C4—44no—
213Dic71⋊C4—44no—
214C22⋊Dic71—28no—
215C22⋊Dic71—44no—
216(C2×D71)⋊C4—28no—
217(C2×D71)⋊C4—28no—
218(C2×D71)⋊C4—28no—
219(C2×D71)⋊C4—44no—
220(C2×D71)⋊C4—44no—
221C4×Dic71—28no—
222C4×Dic71—28no—
223C4×Dic71C2×D4116yes—
224C24×C71—22no—
225C24×C71—22no—
226C24×C71—22no—
227C24×C71—22no—
228C24×C71—22no—
229C24×C71—22no—
230C24×C71C2×Q814yes—
231C24×C71C2412yes—
232C24×C71C2411yescharacteristic
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×C71—22no—
240C22×C4×C71—22no—
241C22×C4×C71—22no—
242C22×C4×C71—22no—
243C22×C4×C71—22no—
244C22×C4×C71—22no—
245C22×C4×C71—22no—
246C22×C4×C71—22no—
247C22×C4×C71—22no—
248C22×C4×C71—22no—
249C22×C4×C71C2×D414yes—
250C22×C4×C71#4114yes—
251C22×C4×C71C2412yes—
252C22×C4×C71C2412yes—
253C22×C4×C71C2412yes—
254C22×C4×C71C2412yes—
255C22×C4×C71C2412yes—
256C22×C4×C71C2412yes—
257C4⋊C4×C71—28no—
258C4⋊C4×C71—28no—
259C4⋊C4×C71—44no—
260C22⋊C4×C71—28no—
261C22⋊C4×C71—28no—
262C22⋊C4×C71—44no—
263C23×C71—28no—
264C23×C71—28no—
265C23×C71—28no—
266C23×C71—22no—
267C23×C71—22no—
268C23×C71—22no—
269C23×C71—22no—
270C23×C71—22no—
271C23×C71—22no—
272C23×C71—44no—
273C23×C71—44no—
274C23×C71—44no—
275C23×C71—44no—
276C23×C71C22×D412yes—
277C23×C71C22×Q814yes—
278C23×C71C22×Q812yes—
279C23×C71C2×#4112yes—
280C23×C71C2×#4112yes—
281C23×C71C2×#4112yes—
282C23×C71H(5,𝔽2)12yes—
283C23×C71H(5,𝔽2)12yes—
284C23×C71C2511yescharacteristic
285C22×D71—28no—
286C22×D71—28no—
287C22×D71—28no—
288C22×D71—22no—
289C22×D71—22no—
290C22×D71—22no—
291C22×D71—22no—
292C22×D71—22no—
293C22×D71—22no—
294C22×D71—44no—
295C22×D71—44no—
296C22×D71—44no—
297C22×D71—44no—
298C22×D71C22×Q814yes—
299C2×C4×C71—28no—
300C2×C4×C71—28no—
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—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—44no—
318C2×C4×C71—44no—
319C2×C4×C71—44no—
320C2×C4×C71—44no—
321C2×C4×C71C22×D414yes—
322C2×C4×C71C2×#4114yes—
323C22⋊D71—232no—
324C2×Dic71—28no—
325C2×Dic71—28no—
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—22no—
336C2×Dic71—22no—
337C2×Dic71—22no—
338C2×Dic71—22no—
339C2×Dic71—22no—
340C2×Dic71—22no—
341C2×Dic71—22no—
342C2×Dic71—416no—
343C2×Dic71—44no—
344C2×Dic71—44no—
345C2×Dic71—44no—
346C2×Dic71—44no—
347C2×Dic71C22⋊Q8116yes—
348C2×Dic71C22×D414yes—
349C2×Dic71C22×D414yes—
350C2×Dic71C22×Q814yes—
351C2×Dic71C2×#4114yes—
352C2×Dic71C2×#4114yes—
353C4×D71—416no—
354C22×C71—24no—
355C22×C71—24no—
356C22×C71—24no—
357C22×C71—416no—
358C22×C71—42no—
359C22×C71—42no—
360C22×C71—42no—
361C22×C71—42no—
362C22×C71C2×C22⋊Q814yes—
363C22×C71#53214yes—
364C22×C71#53514yes—
365C22×C71#55314yes—
366C22×C71#55314yes—
367C22×C71#55414yes—
368C22×C71#55414yes—
369C22×C71C23×D411yescharacteristic
370C22×C71C23×Q811yescharacteristic
371C22×C71C22×#4111yescharacteristic
372C22×C71C22×#4111yescharacteristic
373C22×C71C22×#4111yescharacteristic
374C22×C71C2×H(5,𝔽2)11yescharacteristic
375C22×C71C2×H(5,𝔽2)11yescharacteristic
376C2×D71—24no—
377C2×D71—24no—
378C2×D71—24no—
379C2×D71—416no—
380C2×D71—42no—
381C2×D71—42no—
382C2×D71—42no—
383C2×D71—42no—
384C4×C71—24no—
385C4×C71—24no—
386C4×C71—42no—
387C4×C71—42no—
388C4×C71—42no—
389C4×C71—42no—
390Dic71—24no—
391Dic71—24no—
392Dic71—42no—
393Dic71—42no—
394Dic71—42no—
395Dic71—42no—
396Dic71C2×C22⋊Q818yes—
397C2×#2566—711nomaximal, Sylow
398C2×C71—44no—
399C2×C71#256618yescomplemented
400C2×C71C22×C22⋊Q811yescharacteristic
401C2×C71C2×#53211yescharacteristic
402C2×C71C2×#53511yescharacteristic
403C2×C71C2×#55311yescharacteristic
404C2×C71C2×#55311yescharacteristic
405C2×C71C2×#55411yescharacteristic
406C2×C71C2×#55411yescharacteristic
407D71—44no—
408C22×#125—711no—
409C22×C4×D4—711no—
410#2566—7116no—
411C2×#396—711no—
412C2×#396—711no—
413C2×#396—711no—
414C2×#396D7111yescharacteristic, complemented
415C2×#390—711no—
416C2×#390—711no—
417C2×#385—711no—
418C2×#385—711no—
419C2×#385—711no—
420C2×#385—711no—
421C2×#384—711no—
422C2×#382—711no—
423C2×C4×C4⋊C4—711no—
424C71C2×#256611yescharacteristic, complemented, Sylow
425C23×D4—711no—
426C24×C4—711no—
427C24×C4—711no—
428C2×#125—718no—
429C2×#125—1428no—
430C2×C4×D4—718no—
431C2×C4×D4—1428no—
432C22×C4⋊C4—711no—
433C22×C4⋊C4—711no—
434C22×C4⋊C4—711no—
435C22×C4⋊C4—711no—
436C22×C4⋊C4—711no—
437C22×C4⋊C4—711no—
438C22×C4⋊C4—711no—
439C22×C4⋊C4—711no—
440C22×C4⋊C4—711no—
441C22×C4⋊C4—711no—
442C22×C4⋊C4C2×D7111yescharacteristic
443C22×C4⋊C4C2×D7111yescharacteristic
444C22×C4⋊C4C2×D7111yescharacteristic
445C22×C22⋊C4—711no—
446C22×C22⋊C4—711no—
447C22×C22⋊C4—711no—
448C22×C22⋊C4—711no—
449C22×C22⋊C4—711no—
450C22×C22⋊C4—711no—
451C22×C22⋊C4—711no—
452C22×C22⋊C4C2×D7111yescharacteristic
453C22×C22⋊C4C2×D7111yescharacteristic
454C22×C22⋊C4C2×D7111yescharacteristic
455C22×C42—711no—
456C22×C42—711no—
457C22×C42—711no—
458#396—718no—
459#396—718no—
460#396—718no—
461#396C2×D7118yescomplemented
462#390—718no—
463#390—718no—
464#385—718no—
465#385—718no—
466#385—718no—
467#385—718no—
468#384—718no—
469#382—718no—
470C4×C4⋊C4—718no—
471C2×#95—711no—
472C2×#95—711no—
473C2×#95—711no—
474C2×#95—711no—
475C2×#95—711no—
476C2×#95C2×D7111yescharacteristic
477C25—711no—
478C25C22×D7111yescharacteristic
479C22×D4—718no—
480C22×D4—714no—
481C22×D4—1424no—
482C22×D4—1424no—
483C23×C4—2842no—
484C23×C4—2842no—
485C23×C4—2842no—
486C23×C4—2842no—
487C23×C4—714no—
488C23×C4—714no—
489C23×C4—711no—
490C23×C4—711no—
491C23×C4—711no—
492C23×C4—711no—
493C23×C4—711no—
494C23×C4—711no—
495C23×C4—711no—
496C23×C4—1424no—
497C23×C4—1424no—
498C23×C4C22×D7111yescharacteristic
499C23×C4C22×D7111yescharacteristic
500C23×C4C22×D7111yescharacteristic
501C23×C4C22×D7111yescharacteristic
502C23×C4C22×D7111yescharacteristic
503C23×C4C22×D7111yescharacteristic
504#125—14232no—
505C4×D4—14232no—
506C2×C4⋊C4—24no—
507C2×C4⋊C4—24no—
508C2×C4⋊C4—42no—
509C2×C4⋊C4—2842no—
510C2×C4⋊C4—2842no—
511C2×C4⋊C4—2842no—
512C2×C4⋊C4—714no—
513C2×C4⋊C4—714no—
514C2×C4⋊C4—714no—
515C2×C4⋊C4—714no—
516C2×C4⋊C4—714no—
517C2×C4⋊C4—714no—
518C2×C4⋊C4—714no—
519C2×C4⋊C4—714no—
520C2×C4⋊C4—714no—
521C2×C4⋊C4—714no—
522C2×C4⋊C4—1424no—
523C2×C4⋊C4—1424no—
524C2×C4⋊C4—1424no—
525C2×C4⋊C4—1424no—
526C2×C4⋊C4—1424no—
527C2×C4⋊C4—1424no—
528C2×C4⋊C4—1424no—
529C2×C4⋊C4C22×D7114yes—
530C2×C4⋊C4C22×D7114yes—
531C2×C4⋊C4C22×D7114yes—
532C2×C22⋊C4—24no—
533C2×C22⋊C4—24no—
534C2×C22⋊C4—42no—
535C2×C22⋊C4—2842no—
536C2×C22⋊C4—2842no—
537C2×C22⋊C4—2842no—
538C2×C22⋊C4—714no—
539C2×C22⋊C4—714no—
540C2×C22⋊C4—714no—
541C2×C22⋊C4—714no—
542C2×C22⋊C4—714no—
543C2×C22⋊C4—714no—
544C2×C22⋊C4—714no—
545C2×C22⋊C4—1424no—
546C2×C22⋊C4—1424no—
547C2×C22⋊C4—1424no—
548C2×C22⋊C4—1424no—
549C2×C22⋊C4C22×D7114yes—
550C2×C22⋊C4C22×D7114yes—
551C2×C22⋊C4C22×D7114yes—
552C2×C42—718no—
553C2×C42—714no—
554C2×C42—714no—
555C2×C42—714no—
556C2×C42—1424no—
557C2×C42—1424no—
558#95—714no—
559#95—714no—
560#95—714no—
561#95—714no—
562#95—714no—
563#95C22×D7114yes—
564C24—22no—
565C24—22no—
566C24—22no—
567C24—22no—
568C24—22no—
569C24—22no—
570C24—714no—
571C24—712no—
572C24—1422no—
573C24—1422no—
574C24—1422no—
575C24—1422no—
576C24—1422no—
577C24—1422no—
578C24Q8×D7114yes—
579C24C23×D7112yes—
580C24C23×D7111yescharacteristic
581C2×D4—7116no—
582C2×D4—1428no—
583C2×D4—1428no—
584C2×D4—14232no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
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—2844no—
602C22×C4—2844no—
603C22×C4—28416no—
604C22×C4—28416no—
605C22×C4—2844no—
606C22×C4—2844no—
607C22×C4—714no—
608C22×C4—714no—
609C22×C4—714no—
610C22×C4—712no—
611C22×C4—714no—
612C22×C4—714no—
613C22×C4—712no—
614C22×C4—712no—
615C22×C4—712no—
616C22×C4—712no—
617C22×C4—712no—
618C22×C4—712no—
619C22×C4—1428no—
620C22×C4—1428no—
621C22×C4—1422no—
622C22×C4—1422no—
623C22×C4—1422no—
624C22×C4—1422no—
625C22×C4—1422no—
626C22×C4—1422no—
627C22×C4—1422no—
628C22×C4—1422no—
629C22×C4—1422no—
630C22×C4—1422no—
631C22×C4—1422no—
632C22×C4—1422no—
633C22×C4—1422no—
634C22×C4—1422no—
635C22×C4—1422no—
636C22×C4—1422no—
637C22×C4D4×D7114yes—
638C22×C4#1176586414yes—
639C22×C4C23×D7112yes—
640C22×C4C23×D7112yes—
641C22×C4C23×D7112yes—
642C22×C4C23×D7112yes—
643C22×C4C23×D7112yes—
644C22×C4C23×D7112yes—
645C4⋊C4—28no—
646C4⋊C4—28no—
647C4⋊C4—44no—
648C4⋊C4—2844no—
649C4⋊C4—2844no—
650C4⋊C4—2844no—
651C4⋊C4—1428no—
652C4⋊C4—1428no—
653C4⋊C4—1428no—
654C4⋊C4—1428no—
655C4⋊C4—1428no—
656C4⋊C4—1428no—
657C4⋊C4—1428no—
658C22⋊C4—28no—
659C22⋊C4—28no—
660C22⋊C4—44no—
661C22⋊C4—2844no—
662C22⋊C4—2844no—
663C22⋊C4—2844no—
664C22⋊C4—1428no—
665C22⋊C4—1428no—
666C22⋊C4—1428no—
667C22⋊C4—1428no—
668C42—7116no—
669C42—1428no—
670C42—1428no—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—28no—
678C23—28no—
679C23—28no—
680C23—44no—
681C23—44no—
682C23—44no—
683C23—44no—
684C23—2844no—
685C23—2844no—
686C23—2844no—
687C23—2844no—
688C23—714no—
689C23—1422no—
690C23—1422no—
691C23—1422no—
692C23—1422no—
693C23—1422no—
694C23—1422no—
695C23—1428no—
696C23—1428no—
697C23—1428no—
698C23C2×D4×D7112yes—
699C23C2×Q8×D7114yes—
700C23C2×Q8×D7112yes—
701C23#41×D7112yes—
702C23#41×D7112yes—
703C23C2×#1176586412yes—
704C23#1455617312yes—
705C23#1455617412yes—
706C23C24×D7111yescharacteristic
707D4—14232no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—28no—
713C2×C4—28no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
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—44no—
727C2×C4—44no—
728C2×C4—44no—
729C2×C4—44no—
730C2×C4—28416no—
731C2×C4—2844no—
732C2×C4—2844no—
733C2×C4—2844no—
734C2×C4—2844no—
735C2×C4—28416no—
736C2×C4—714no—
737C2×C4—714no—
738C2×C4—714no—
739C2×C4—7116no—
740C2×C4—714no—
741C2×C4—714no—
742C2×C4—1422no—
743C2×C4—1422no—
744C2×C4—1422no—
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—1428no—
755C2×C4—1422no—
756C2×C4—1422no—
757C2×C4—1422no—
758C2×C4—1422no—
759C2×C4—1428no—
760C2×C4C2×D4×D7114yes—
761C2×C4C2×#1176586414yes—
762C22—24no—
763C22—24no—
764C22—24no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—416no—
770C22—2842no—
771C22—2842no—
772C22—2842no—
773C22—2842no—
774C22—28416no—
775C22—1424no—
776C22—1424no—
777C22—1424no—
778C22C22⋊Q8×D7114yes—
779C22#1798654414yes—
780C22#1798656514yes—
781C22#1798669214yes—
782C22#1798670014yes—
783C22#1798670314yes—
784C22#1798670714yes—
785C22C22×D4×D7111yescharacteristic
786C22C22×Q8×D7111yescharacteristic
787C22C2×#41×D7111yescharacteristic
788C22C2×#41×D7111yescharacteristic
789C22C22×#1176586411yescharacteristic
790C22C2×#1455617311yescharacteristic
791C22C2×#1455617411yescharacteristic
792C4—24no—
793C4—24no—
794C4—42no—
795C4—42no—
796C4—42no—
797C4—42no—
798C4—2842no—
799C4—2842no—
800C4—2842no—
801C4—2842no—
802C4—718no—
803C4—1424no—
804C4—1424no—
805C2—44no—
806C2—2844no—
807C2#2259353518yesdirect product factor
808C2C2×C22⋊Q8×D7111yescharacteristic
809C2C2×#1798654411yescharacteristic
810C2C2×#1798656511yescharacteristic
811C2C2×#1798669211yescharacteristic
812C2C2×#1798670011yescharacteristic
813C2C2×#1798670311yescharacteristic
814C2C2×#1798670711yescharacteristic
subgroupG/H
centerC24C23×D71
commutator, cosocleC23×C71C25
FrattiniC23C24×D71
FittingC2×#396×C71C2
socleC24×C71C24
prime radicalC23×C22⋊D71C22
hypercenterC2×#396D71
hypocenterC71C2×#2566
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. C22×#14556118C2semidirect
3. #22593535C2direct (N × H)
4. C2×#17985922C2semidirect
5. C2×#17985921C2semidirect
6. C2×#17985921C2semidirect
9. C2×#17985874C2semidirect
10. C2×#17985873C2semidirect
11. C2×#17985871C2semidirect
12. C2×#17985870C2semidirect
13. C2×#17985868C2semidirect
14. C2×#17985863C2semidirect
15. C2×C4⋊C4×Dic71C2semidirect
16. C2×#396×C71C2semidirect
21. C2×#14556118C22semidirect
44. #17985922C22semidirect
45. #17985921C22semidirect
46. #17985921C22semidirect
49. #17985874C22semidirect
50. #17985873C22semidirect
51. #17985871C22semidirect
52. #17985870C22semidirect
53. #17985868C22semidirect
54. #17985863C22semidirect
55. C4⋊C4×Dic71C22semidirect
67. #396×C71C22semidirect
399. C2×C71#2566semidirect
414. C2×#396D71semidirect
424. C71C2×#2566semidirect
461. #396C2×D71semidirect
807. C2#22593535direct (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×(C22⋊D71)⋊C42
#225935352
C2×#179859222
C2×#179859212
C2×#179858992
C2×#179858742
C2×#179858732
C2×#179858712
C2×#179858702
C2×#179858682
C2×#179858632
C2×C4⋊C4×Dic712
C2×#396×C712
C2×#256671