Finite Group Databasebeta

← C2×#22593688 #32167657

Subgroups — C2×#22593688 #32167657

Order 18176.

3374 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556090C211yesmaximal, characteristic
2C22×C4⋊C4×D71C211yesmaximal, characteristic, complemented
3#22593688C2116yesmaximal, direct product factor
4C2×#17985932C211yesmaximal, characteristic, complemented
5C2×#17985921C211yesmaximal, characteristic, complemented
6C2×#17985921C211yesmaximal, characteristic, complemented
7C2×#17985886C211yesmaximal, characteristic, complemented
8C2×#17985882C211yesmaximal, characteristic, complemented
9C2×#17985877C211yesmaximal, characteristic
10C2×#17985877C211yesmaximal, characteristic
11C2×#17985873C211yesmaximal, characteristic, complemented
12C2×#17985873C211yesmaximal, characteristic, complemented
13C2×#17985870C211yesmaximal, characteristic, complemented
14C2×#17985870C211yesmaximal, characteristic, complemented
15C2×#17985856C211yesmaximal, characteristic, complemented
16C2×#398×C71C211yesmaximal, characteristic, complemented
17C23×D284C2211yescharacteristic
18C23×C4×D71C2211yescharacteristic
19C23×C4×D71C2211yescharacteristic
20C23×C4×D71C2211yescharacteristic
21C23×C4×D71C2211yescharacteristic
22C2×#14556090—28no—
23C2×#14556090C2218yes—
24C22×C4⋊Dic71C2211yescharacteristic
25C22×C4⋊Dic71C2211yescharacteristic
26C22×C4⋊Dic71C2211yescharacteristic
27C22×Dic71⋊C4C2211yescharacteristic
28C22×Dic71⋊C4C2211yescharacteristic
29C22×Dic71⋊C4C2211yescharacteristic
30C22×Dic71⋊C4C2211yescharacteristic
31C2×C4⋊C4×D71—28no—
32C2×C4⋊C4×D71C2218yescomplemented
33C22×(C2×D71)⋊C4C2211yescharacteristic
34C22×(C2×D71)⋊C4C2211yescharacteristic
35C22×(C2×D71)⋊C4C2211yescharacteristic
36C22×(C2×D71)⋊C4C2211yescharacteristic
37C22×(C2×D71)⋊C4C2211yescharacteristic
38C22×(C2×D71)⋊C4C2211yescharacteristic
39C22×(C2×D71)⋊C4C2211yescharacteristic
40C22×(C2×D71)⋊C4C2211yescharacteristic
41C22×C4×Dic71C2211yescharacteristic
42#17985932C2218yescomplemented
43#17985921C2218yescomplemented
44#17985921C2218yescomplemented
45#17985886C2218yescomplemented
46#17985882C2218yescomplemented
47#17985877C2218yes—
48#17985877C2218yes—
49#17985873C2218yescomplemented
50#17985873C2218yescomplemented
51#17985870C2218yescomplemented
52#17985870C2218yescomplemented
53#17985856C2218yescomplemented
54C2×C71⋊#95C2211yescharacteristic
55C2×C71⋊#95C2211yescharacteristic
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×C4⋊C4×C71C2211yescharacteristic
65#398×C71C2218yescomplemented
66C2×#95×C71C2211yescharacteristic
67C2×#95×C71C2211yescharacteristic
68C2×#95×C71C2211yescharacteristic
69C24×D71C2311yescharacteristic
70C24×D71C2311yescharacteristic
71C22×D284—24no—
72C22×D284—24no—
73C22×D284Q818yes—
74C22×D284C2314yes—
75C23×Dic71C2311yescharacteristic
76C23×Dic71C2311yescharacteristic
77C23×Dic71C2311yescharacteristic
78C23×Dic71C2311yescharacteristic
79C23×Dic71C2311yescharacteristic
80C23×Dic71C2311yescharacteristic
81C22×C4×D71—24no—
82C22×C4×D71—24no—
83C22×C4×D71—24no—
84C22×C4×D71—24no—
85C22×C4×D71—24no—
86C22×C4×D71—42no—
87C22×C4×D71—42no—
88C22×C4×D71—42no—
89C22×C4×D71—42no—
90C22×C4×D71—42no—
91C22×C4×D71—42no—
92C22×C4×D71D418yes—
93C22×C4×D71C2314yes—
94C22×C4×D71C2314yes—
95C22×C4×D71C2314yes—
96C22×C4×D71C2314yes—
97#14556090—232no—
98C2×C4⋊Dic71—24no—
99C2×C4⋊Dic71—24no—
100C2×C4⋊Dic71—42no—
101C2×C4⋊Dic71C2314yes—
102C2×C4⋊Dic71C2314yes—
103C2×C4⋊Dic71C2314yes—
104C2×Dic71⋊C4—24no—
105C2×Dic71⋊C4—24no—
106C2×Dic71⋊C4—24no—
107C2×Dic71⋊C4—42no—
108C2×Dic71⋊C4C2314yes—
109C2×Dic71⋊C4C2314yes—
110C2×Dic71⋊C4C2314yes—
111C2×Dic71⋊C4C2314yes—
112C4⋊C4×D71—232no—
113C2×(C2×D71)⋊C4—24no—
114C2×(C2×D71)⋊C4—24no—
115C2×(C2×D71)⋊C4—24no—
116C2×(C2×D71)⋊C4—24no—
117C2×(C2×D71)⋊C4—24no—
118C2×(C2×D71)⋊C4—24no—
119C2×(C2×D71)⋊C4—42no—
120C2×(C2×D71)⋊C4—42no—
121C2×(C2×D71)⋊C4C2314yes—
122C2×(C2×D71)⋊C4C2314yes—
123C2×(C2×D71)⋊C4C2314yes—
124C2×(C2×D71)⋊C4C2314yes—
125C2×(C2×D71)⋊C4C2314yes—
126C2×(C2×D71)⋊C4C2314yes—
127C2×(C2×D71)⋊C4C2314yes—
128C2×(C2×D71)⋊C4C2314yes—
129C2×C4×Dic71—24no—
130C2×C4×Dic71C2314yes—
131C71⋊#95C2314yes—
132C71⋊#95C2314yes—
133C71⋊#95C2314yes—
134C71⋊#95C2314yes—
135C71⋊#95C2314yes—
136C71⋊#95C2314yes—
137C71⋊#95C2314yes—
138C23×C4×C71C2311yescharacteristic
139C23×C4×C71C2311yescharacteristic
140C23×C4×C71C2311yescharacteristic
141C23×C4×C71C2311yescharacteristic
142C23×C4×C71C2311yescharacteristic
143C23×C4×C71C2311yescharacteristic
144C23×C4×C71C2311yescharacteristic
145C2×C4⋊C4×C71—24no—
146C2×C4⋊C4×C71—24no—
147C2×C4⋊C4×C71—42no—
148C2×C4⋊C4×C71—42no—
149C2×C4⋊C4×C71C2314yes—
150C2×C4⋊C4×C71C2314yes—
151C2×C4⋊C4×C71C2314yes—
152C2×C4⋊C4×C71C2314yes—
153#95×C71C2314yes—
154#95×C71C2314yes—
155#95×C71C2314yes—
156C23×D71—22no—
157C23×D71—22no—
158C23×D71—22no—
159C23×D71—22no—
160C23×D71—22no—
161C23×D71—22no—
162C23×D71—22no—
163C23×D71—22no—
164C23×D71—22no—
165C23×D71—22no—
166C23×D71C2×D414yes—
167C23×D71C2×Q814yes—
168C23×D71C2×Q814yes—
169C23×D71#4114yes—
170C23×D71C2412yes—
171C23×D71C2412yes—
172C2×D284—232no—
173C2×D284—28no—
174C2×D284—28no—
175C2×D284C2×Q8116yes—
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×Dic71—22no—
187C22×Dic71—22no—
188C22×Dic71—22no—
189C22×Dic71—22no—
190C22×Dic71—22no—
191C22×Dic71—22no—
192C22×Dic71C2×D414yes—
193C22×Dic71#4114yes—
194C22×Dic71C2412yes—
195C22×Dic71C2412yes—
196C22×Dic71C2412yes—
197C22×Dic71C2412yes—
198C22×Dic71C2412yes—
199C22×Dic71C2412yes—
200C2×C4×D71—232no—
201C2×C4×D71—28no—
202C2×C4×D71—28no—
203C2×C4×D71—28no—
204C2×C4×D71—28no—
205C2×C4×D71—28no—
206C2×C4×D71—416no—
207C2×C4×D71—44no—
208C2×C4×D71—44no—
209C2×C4×D71—44no—
210C2×C4×D71—44no—
211C2×C4×D71—44no—
212C2×C4×D71—44no—
213C2×C4×D71—416no—
214C2×C4×D71—416no—
215C2×C4×D71C2×D4116yes—
216C4⋊Dic71—28no—
217C4⋊Dic71—28no—
218C4⋊Dic71—44no—
219Dic71⋊C4—28no—
220Dic71⋊C4—28no—
221Dic71⋊C4—28no—
222Dic71⋊C4—44no—
223(C2×D71)⋊C4—28no—
224(C2×D71)⋊C4—28no—
225(C2×D71)⋊C4—28no—
226(C2×D71)⋊C4—28no—
227(C2×D71)⋊C4—28no—
228(C2×D71)⋊C4—28no—
229(C2×D71)⋊C4—44no—
230(C2×D71)⋊C4—44no—
231C4×Dic71—28no—
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×C71—22no—
250C22×C4×C71—22no—
251C22×C4×C71C2×D414yes—
252C22×C4×C71C2×Q814yes—
253C22×C4×C71#4114yes—
254C22×C4×C71C2412yes—
255C22×C4×C71C2412yes—
256C22×C4×C71C2412yes—
257C22×C4×C71C2412yes—
258C22×C4×C71C2412yes—
259C22×C4×C71C2412yes—
260C22×C4×C71C2412yes—
261C4⋊C4×C71—28no—
262C4⋊C4×C71—28no—
263C4⋊C4×C71—44no—
264C4⋊C4×C71—44no—
265C23×C71C22×D412yes—
266C23×C71C22×Q812yes—
267C23×C71C2×#4112yes—
268C23×C71C2×#4112yes—
269C23×C71C2×#4112yes—
270C23×C71H(5,𝔽2)12yes—
271C23×C71H(5,𝔽2)12yes—
272C23×C71C2511yescharacteristic
273C22×D71—28no—
274C22×D71—28no—
275C22×D71—28no—
276C22×D71—28no—
277C22×D71—28no—
278C22×D71—28no—
279C22×D71—22no—
280C22×D71—22no—
281C22×D71—22no—
282C22×D71—22no—
283C22×D71—28no—
284C22×D71—28no—
285C22×D71—28no—
286C22×D71—22no—
287C22×D71—22no—
288C22×D71—22no—
289C22×D71—22no—
290C22×D71—22no—
291C22×D71—22no—
292C22×D71—44no—
293C22×D71—44no—
294C22×D71—44no—
295C22×D71—44no—
296C22×D71C22⋊Q8116yes—
297C22×D71C22×D414yes—
298C22×D71C22×Q814yes—
299C22×D71C22×Q814yes—
300C22×D71C2×#4114yes—
301C2×C4×C71—28no—
302C2×C4×C71—28no—
303C2×C4×C71—28no—
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—22no—
318C2×C4×C71—22no—
319C2×C4×C71—22no—
320C2×C4×C71—22no—
321C2×C4×C71—22no—
322C2×C4×C71—44no—
323C2×C4×C71—44no—
324C2×C4×C71—44no—
325C2×C4×C71—44no—
326C2×C4×C71C22×D414yes—
327C2×C4×C71C22×Q814yes—
328C2×C4×C71C2×#4114yes—
329C2×Dic71—28no—
330C2×Dic71—28no—
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—22no—
343C2×Dic71—22no—
344C2×Dic71—22no—
345C2×Dic71—22no—
346C2×Dic71—22no—
347C2×Dic71—44no—
348C2×Dic71—44no—
349C2×Dic71—44no—
350C2×Dic71—44no—
351C2×Dic71C22×D414yes—
352C2×Dic71C2×#4114yes—
353D284—232no—
354C4×D71—232no—
355C4×D71—416no—
356C4×D71—416no—
357C4×D71—416no—
358C22×C71C2×C22⋊Q814yes—
359C22×C71#52514yes—
360C22×C71#53414yes—
361C22×C71#55314yes—
362C22×C71#55314yes—
363C22×C71#55414yes—
364C22×C71#55414yes—
365C22×C71C23×D411yescharacteristic
366C22×C71C23×Q811yescharacteristic
367C22×C71C22×#4111yescharacteristic
368C22×C71C22×#4111yescharacteristic
369C22×C71C22×#4111yescharacteristic
370C22×C71C2×H(5,𝔽2)11yescharacteristic
371C22×C71C2×H(5,𝔽2)11yescharacteristic
372C2×D71—232no—
373C2×D71—24no—
374C2×D71—24no—
375C2×D71—24no—
376C2×D71—24no—
377C2×D71—24no—
378C2×D71—24no—
379C2×D71—24no—
380C2×D71—24no—
381C2×D71—24no—
382C2×D71—416no—
383C2×D71—42no—
384C2×D71—42no—
385C2×D71—42no—
386C2×D71—42no—
387C2×D71C2×C22⋊Q818yes—
388C4×C71—24no—
389C4×C71—24no—
390C4×C71—24no—
391C4×C71—42no—
392C4×C71—42no—
393C4×C71—42no—
394C4×C71—42no—
395Dic71—24no—
396Dic71—24no—
397Dic71—42no—
398Dic71—42no—
399Dic71—42no—
400Dic71—42no—
401C2×#2579—711nomaximal, Sylow
402C2×C71#257918yescomplemented
403C2×C71C22×C22⋊Q811yescharacteristic
404C2×C71C2×#52511yescharacteristic
405C2×C71C2×#53411yescharacteristic
406C2×C71C2×#55311yescharacteristic
407C2×C71C2×#55311yescharacteristic
408C2×C71C2×#55411yescharacteristic
409C2×C71C2×#55411yescharacteristic
410D71—28no—
411D71—44no—
412C22×C4×D4—711no—
413C23×C4⋊C4—711no—
414#2579—7116no—
415C2×#398—711no—
416C2×#398D7111yescharacteristic, complemented
417C2×#396—711no—
418C2×#396—711no—
419C2×#387—711no—
420C2×#387—711no—
421C2×#386—711no—
422C2×#386—711no—
423C2×#385—711no—
424C2×#385—711no—
425C2×#385—711no—
426C2×#385—711no—
427C2×#380—711no—
428C71C2×#257911yescharacteristic, complemented, Sylow
429C23×D4—711no—
430C24×C4—711no—
431C24×C4—711no—
432C24×C4—711no—
433C24×C4—711no—
434C2×C4×D4—718no—
435C2×C4×D4—1428no—
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⋊C4—711no—
443C22×C4⋊C4—718no—
444C22×C4⋊C4—1428no—
445C22×C4⋊C4C2×D7111yescharacteristic
446C22×C4⋊C4C2×D7111yescharacteristic
447C22×C4⋊C4C2×D7111yescharacteristic
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⋊C4—711no—
456C22×C22⋊C4—711no—
457C22×C42—711no—
458#398—718no—
459#398C2×D7118yescomplemented
460#396—718no—
461#396—718no—
462#387—718no—
463#387—718no—
464#386—718no—
465#386—718no—
466#385—718no—
467#385—718no—
468#385—718no—
469#385—718no—
470#380—718no—
471C2×#95—711no—
472C2×#95—711no—
473C2×#95—711no—
474C2×#95—711no—
475C2×#95—711no—
476C2×#95—711no—
477C2×#95—711no—
478C2×#95C2×D7111yescharacteristic
479C2×#95C2×D7111yescharacteristic
480C2×#95C2×D7111yescharacteristic
481C25—711no—
482C25—711no—
483C22×D4—718no—
484C22×D4—714no—
485C22×D4—1424no—
486C22×D4—1424no—
487C23×C4—2842no—
488C23×C4—2842no—
489C23×C4—2842no—
490C23×C4—2842no—
491C23×C4—2842no—
492C23×C4—2842no—
493C23×C4—718no—
494C23×C4—714no—
495C23×C4—714no—
496C23×C4—714no—
497C23×C4—711no—
498C23×C4—711no—
499C23×C4—711no—
500C23×C4—711no—
501C23×C4—711no—
502C23×C4—711no—
503C23×C4—714no—
504C23×C4—1424no—
505C23×C4—1424no—
506C23×C4—1424no—
507C23×C4—1424no—
508C23×C4—1424no—
509C23×C4C22×D7111yescharacteristic
510C23×C4C22×D7111yescharacteristic
511C23×C4C22×D7111yescharacteristic
512C23×C4C22×D7111yescharacteristic
513C23×C4C22×D7111yescharacteristic
514C23×C4C22×D7111yescharacteristic
515C23×C4C22×D7111yescharacteristic
516C4×D4—14232no—
517C2×C4⋊C4—24no—
518C2×C4⋊C4—24no—
519C2×C4⋊C4—42no—
520C2×C4⋊C4—42no—
521C2×C4⋊C4—2842no—
522C2×C4⋊C4—2842no—
523C2×C4⋊C4—714no—
524C2×C4⋊C4—714no—
525C2×C4⋊C4—714no—
526C2×C4⋊C4—714no—
527C2×C4⋊C4—714no—
528C2×C4⋊C4—714no—
529C2×C4⋊C4—714no—
530C2×C4⋊C4—14232no—
531C2×C4⋊C4—1424no—
532C2×C4⋊C4—1424no—
533C2×C4⋊C4—1424no—
534C2×C4⋊C4—1424no—
535C2×C4⋊C4—1424no—
536C2×C4⋊C4C22×D7114yes—
537C2×C4⋊C4C22×D7114yes—
538C2×C4⋊C4C22×D7114yes—
539C2×C4⋊C4C22×D7114yes—
540C2×C22⋊C4—2842no—
541C2×C22⋊C4—2842no—
542C2×C22⋊C4—714no—
543C2×C22⋊C4—714no—
544C2×C22⋊C4—714no—
545C2×C22⋊C4—714no—
546C2×C22⋊C4—714no—
547C2×C22⋊C4—714no—
548C2×C22⋊C4—714no—
549C2×C22⋊C4—714no—
550C2×C22⋊C4—1424no—
551C2×C22⋊C4—1424no—
552C2×C22⋊C4—1424no—
553C2×C22⋊C4—1424no—
554C2×C22⋊C4—1424no—
555C2×C22⋊C4—1424no—
556C2×C42—714no—
557C2×C42—1424no—
558#95—714no—
559#95—714no—
560#95—714no—
561#95—714no—
562#95—714no—
563#95—714no—
564#95—714no—
565#95C22×D7114yes—
566#95C22×D7114yes—
567#95C22×D7114yes—
568C24—714no—
569C24—714no—
570C24—714no—
571C24—712no—
572C24—714no—
573C24—712no—
574C24—1422no—
575C24—1422no—
576C24—1422no—
577C24—1422no—
578C24—1422no—
579C24—1422no—
580C24—1422no—
581C24—1422no—
582C24—1422no—
583C24—1422no—
584C24C23×D7111yescharacteristic
585C2×D4—7116no—
586C2×D4—1428no—
587C2×D4—1428no—
588C2×D4—14232no—
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—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—2844no—
608C22×C4—2844no—
609C22×C4—28416no—
610C22×C4—2844no—
611C22×C4—2844no—
612C22×C4—2844no—
613C22×C4—2844no—
614C22×C4—28416no—
615C22×C4—28416no—
616C22×C4—7116no—
617C22×C4—714no—
618C22×C4—714no—
619C22×C4—712no—
620C22×C4—712no—
621C22×C4—712no—
622C22×C4—712no—
623C22×C4—712no—
624C22×C4—712no—
625C22×C4—1428no—
626C22×C4—1428no—
627C22×C4—1428no—
628C22×C4—1428no—
629C22×C4—14232no—
630C22×C4—1422no—
631C22×C4—1422no—
632C22×C4—1422no—
633C22×C4—1422no—
634C22×C4—1422no—
635C22×C4—1422no—
636C22×C4—1422no—
637C22×C4—1422no—
638C22×C4—1422no—
639C22×C4—1422no—
640C22×C4—1422no—
641C22×C4—1422no—
642C22×C4—1422no—
643C22×C4—1422no—
644C22×C4—1422no—
645C22×C4—1422no—
646C22×C4—1428no—
647C22×C4D4×D7114yes—
648C22×C4Q8×D7114yes—
649C22×C4#1176586614yes—
650C22×C4C23×D7112yes—
651C22×C4C23×D7112yes—
652C22×C4C23×D7112yes—
653C22×C4C23×D7112yes—
654C22×C4C23×D7112yes—
655C22×C4C23×D7112yes—
656C22×C4C23×D7112yes—
657C4⋊C4—28no—
658C4⋊C4—28no—
659C4⋊C4—44no—
660C4⋊C4—44no—
661C4⋊C4—2844no—
662C4⋊C4—2844no—
663C4⋊C4—1428no—
664C4⋊C4—1428no—
665C4⋊C4—1428no—
666C4⋊C4—1428no—
667C4⋊C4—1428no—
668C22⋊C4—2844no—
669C22⋊C4—2844no—
670C22⋊C4—1428no—
671C22⋊C4—1428no—
672C22⋊C4—1428no—
673C22⋊C4—1428no—
674C22⋊C4—1428no—
675C22⋊C4—1428no—
676C42—1428no—
677C23—2844no—
678C23—2844no—
679C23—2844no—
680C23—2844no—
681C23—714no—
682C23—714no—
683C23—714no—
684C23—7116no—
685C23—714no—
686C23—1422no—
687C23—1422no—
688C23—1422no—
689C23—1422no—
690C23—1422no—
691C23—1422no—
692C23—1428no—
693C23—1428no—
694C23—1428no—
695C23—1422no—
696C23—1422no—
697C23—1422no—
698C23—1422no—
699C23—1428no—
700C23—1428no—
701C23—1428no—
702C23—1428no—
703C23—1428no—
704C23—1428no—
705C23C2×D4×D7112yes—
706C23C2×Q8×D7112yes—
707C23#41×D7112yes—
708C23#41×D7112yes—
709C23C2×#1176586612yes—
710C23#1455617312yes—
711C23#1455617412yes—
712C23C24×D7111yescharacteristic
713D4—14232no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—28no—
721C2×C4—28no—
722C2×C4—28no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—44no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—28416no—
740C2×C4—28416no—
741C2×C4—28416no—
742C2×C4—2844no—
743C2×C4—2844no—
744C2×C4—2844no—
745C2×C4—2844no—
746C2×C4—714no—
747C2×C4—714no—
748C2×C4—14232no—
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—1422no—
765C2×C4—1428no—
766C2×C4—1428no—
767C2×C4C2×D4×D7114yes—
768C2×C4C2×Q8×D7114yes—
769C2×C4C2×#1176586614yes—
770C22—2842no—
771C22—2842no—
772C22—2842no—
773C22—28416no—
774C22—2842no—
775C22—718no—
776C22—1424no—
777C22—1424no—
778C22—1424no—
779C22—1424no—
780C22—1424no—
781C22—1424no—
782C22—1424no—
783C22—1424no—
784C22—14232no—
785C22—1424no—
786C22C22⋊Q8×D7114yes—
787C22#1798651214yes—
788C22#1798655714yes—
789C22#1798669414yes—
790C22#1798670214yes—
791C22#1798670514yes—
792C22#1798671014yes—
793C22C22×D4×D7111yescharacteristic
794C22C22×Q8×D7111yescharacteristic
795C22C2×#41×D7111yescharacteristic
796C22C2×#41×D7111yescharacteristic
797C22C22×#1176586611yescharacteristic
798C22C2×#1455617311yescharacteristic
799C22C2×#1455617411yescharacteristic
800C4—24no—
801C4—24no—
802C4—24no—
803C4—42no—
804C4—42no—
805C4—42no—
806C4—42no—
807C4—2842no—
808C4—2842no—
809C4—2842no—
810C4—2842no—
811C4—1424no—
812C4—1424no—
813C2—2844no—
814C2—1428no—
815C2#2259368818yesdirect product factor
816C2C2×C22⋊Q8×D7111yescharacteristic
817C2C2×#1798651211yescharacteristic
818C2C2×#1798655711yescharacteristic
819C2C2×#1798669411yescharacteristic
820C2C2×#1798670211yescharacteristic
821C2C2×#1798670511yescharacteristic
822C2C2×#1798671011yescharacteristic
subgroupG/H
centerC24C23×D71
commutator, cosocleC23×C71C25
FrattiniC23C24×D71
FittingC2×#398×C71C2
socleC24×C71C24
prime radicalC23×D284C22
hypercenterC2×#398D71
hypocenterC71C2×#2579
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊C4×D71C2semidirect
3. #22593688C2direct (N × H)
4. C2×#17985932C2semidirect
5. C2×#17985921C2semidirect
6. C2×#17985921C2semidirect
7. C2×#17985886C2semidirect
8. C2×#17985882C2semidirect
11. C2×#17985873C2semidirect
12. C2×#17985873C2semidirect
13. C2×#17985870C2semidirect
14. C2×#17985870C2semidirect
15. C2×#17985856C2semidirect
16. C2×#398×C71C2semidirect
32. C2×C4⋊C4×D71C22semidirect
42. #17985932C22semidirect
43. #17985921C22semidirect
44. #17985921C22semidirect
45. #17985886C22semidirect
46. #17985882C22semidirect
49. #17985873C22semidirect
50. #17985873C22semidirect
51. #17985870C22semidirect
52. #17985870C22semidirect
53. #17985856C22semidirect
65. #398×C71C22semidirect
402. C2×C71#2579semidirect
416. C2×#398D71semidirect
428. C71C2×#2579semidirect
459. #398C2×D71semidirect
815. C2#22593688direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145560902
C22×C4⋊C4×D712
#225936882
C2×#179859322
C2×#179859212
C2×#179858862
C2×#179858822
C2×#179858772
C2×#179858732
C2×#179858702
C2×#179858562
C2×#398×C712
C2×#257971