Finite Group Databasebeta

← C2×#22592159 #32165207

Subgroups — C2×#22592159 #32165207

Order 18176.

3374 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×#14556106C211yesmaximal, characteristic, complemented
2C22×(C22⋊D71)⋊C4C211yesmaximal, characteristic
3#22592159C2116yesmaximal, direct product factor
4C2×#17985940C211yesmaximal, characteristic, complemented
5C2×#17985930C211yesmaximal, characteristic, complemented
6C2×#17985911C211yesmaximal, characteristic, complemented
7C2×#17985904C211yesmaximal, characteristic, complemented
8C2×#17985880C211yesmaximal, characteristic, complemented
9C2×#17985875C211yesmaximal, characteristic
10C2×#17985875C211yesmaximal, characteristic
11C2×#17985871C211yesmaximal, characteristic, complemented
12C2×#17985870C211yesmaximal, characteristic, complemented
13C2×#17985870C211yesmaximal, characteristic, complemented
14C2×#17985857C211yesmaximal, characteristic, complemented
15C2×#95×D71C211yesmaximal, characteristic, complemented
16C2×#396×C71C211yesmaximal, characteristic, complemented
17C23×Dic142C2211yescharacteristic
18C23×C22⋊D71C2211yescharacteristic
19C24×Dic71C2211yescharacteristic
20C23×C4×D71C2211yescharacteristic
21C23×C4×D71C2211yescharacteristic
22C23×C4×D71C2211yescharacteristic
23C2×#14556106—28no—
24C2×#14556106C2218yescomplemented
25C2×(C22⋊D71)⋊C4—28no—
26C2×(C22⋊D71)⋊C4C2218yes—
27C22×Dic71⋊C4C2211yescharacteristic
28C22×Dic71⋊C4C2211yescharacteristic
29C22×Dic71⋊C4C2211yescharacteristic
30C22×Dic71⋊C4C2211yescharacteristic
31C22×Dic71⋊C4C2211yescharacteristic
32C22×C22⋊Dic71C2211yescharacteristic
33C22×C22⋊Dic71C2211yescharacteristic
34C22×(C2×D71)⋊C4C2211yescharacteristic
35C22×(C2×D71)⋊C4C2211yescharacteristic
36C22×(C2×D71)⋊C4C2211yescharacteristic
37C22×C4×Dic71C2211yescharacteristic
38#17985940C2218yescomplemented
39#17985930C2218yescomplemented
40#17985911C2218yescomplemented
41#17985904C2218yescomplemented
42#17985880C2218yescomplemented
43#17985875C2218yes—
44#17985875C2218yes—
45#17985871C2218yescomplemented
46#17985870C2218yescomplemented
47#17985870C2218yescomplemented
48#17985857C2218yescomplemented
49C2×C71⋊#95C2211yescharacteristic
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
60#95×D71C2218yescomplemented
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×Dic142—24no—
71C22×Dic142—24no—
72C22×Dic142—42no—
73C22×Dic142C2314yes—
74C22×C22⋊D71—24no—
75C22×C22⋊D71—24no—
76C22×C22⋊D71Q818yescomplemented
77C22×C22⋊D71C2314yes—
78C23×Dic71—24no—
79C23×Dic71—24no—
80C23×Dic71—42no—
81C23×Dic71C2311yescharacteristic
82C23×Dic71C2311yescharacteristic
83C23×Dic71C2311yescharacteristic
84C23×Dic71C2314yes—
85C23×Dic71C2311yescharacteristic
86C23×Dic71C2311yescharacteristic
87C23×Dic71C2311yescharacteristic
88C23×Dic71C2311yescharacteristic
89C22×C4×D71—24no—
90C22×C4×D71—24no—
91C22×C4×D71—24no—
92C22×C4×D71—24no—
93C22×C4×D71—24no—
94C22×C4×D71—42no—
95C22×C4×D71—42no—
96C22×C4×D71—42no—
97C22×C4×D71—42no—
98C22×C4×D71C2314yes—
99C22×C4×D71C2314yes—
100C22×C4×D71C2314yes—
101#14556106—232no—
102(C22⋊D71)⋊C4—232no—
103C2×Dic71⋊C4—24no—
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—
112C2×Dic71⋊C4C2314yes—
113C2×C22⋊Dic71—24no—
114C2×C22⋊Dic71—42no—
115C2×C22⋊Dic71C2314yes—
116C2×C22⋊Dic71C2314yes—
117C2×(C2×D71)⋊C4—24no—
118C2×(C2×D71)⋊C4—24no—
119C2×(C2×D71)⋊C4D418yes—
120C2×(C2×D71)⋊C4C2314yes—
121C2×(C2×D71)⋊C4C2314yes—
122C2×(C2×D71)⋊C4C2314yes—
123C2×C4×Dic71—24no—
124C2×C4×Dic71C2314yes—
125C71⋊#95C2314yes—
126C71⋊#95C2314yes—
127C71⋊#95C2314yes—
128C71⋊#95C2314yes—
129C71⋊#95C2314yes—
130C71⋊#95C2314yes—
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—42no—
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—42no—
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×D71C2×D414yes—
161C23×D71C2×Q814yes—
162C23×D71#4114yes—
163C23×D71C2412yes—
164C2×Dic142—28no—
165C2×Dic142—28no—
166C2×Dic142—44no—
167C2×Dic142—416no—
168C2×C22⋊D71—232no—
169C2×C22⋊D71—28no—
170C2×C22⋊D71—28no—
171C2×C22⋊D71C2×Q8116yescomplemented
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×Dic71—22no—
187C22×Dic71—22no—
188C22×Dic71—22no—
189C22×Dic71—28no—
190C22×Dic71—28no—
191C22×Dic71—44no—
192C22×Dic71—416no—
193C22×Dic71C2×D414yes—
194C22×Dic71C2×Q814yes—
195C22×Dic71#4114yes—
196C22×Dic71#4114yes—
197C22×Dic71C2412yes—
198C22×Dic71C2412yes—
199C22×Dic71C2412yes—
200C22×Dic71C2412yes—
201C22×Dic71C2412yes—
202C22×Dic71C2412yes—
203C22×Dic71C2412yes—
204C2×C4×D71—28no—
205C2×C4×D71—28no—
206C2×C4×D71—28no—
207C2×C4×D71—28no—
208C2×C4×D71—28no—
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×D71—416no—
216Dic71⋊C4—28no—
217Dic71⋊C4—28no—
218Dic71⋊C4—28no—
219Dic71⋊C4—28no—
220Dic71⋊C4—44no—
221C22⋊Dic71—28no—
222C22⋊Dic71—44no—
223(C2×D71)⋊C4—28no—
224(C2×D71)⋊C4—28no—
225(C2×D71)⋊C4C2×D4116yes—
226C4×Dic71—28no—
227C24×C71—22no—
228C24×C71—22no—
229C24×C71—22no—
230C24×C71—22no—
231C24×C71—22no—
232C24×C71—22no—
233C24×C71C2×Q814yes—
234C24×C71C2412yes—
235C24×C71C2411yescharacteristic
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×C71—22no—
252C22×C4×C71—22no—
253C22×C4×C71C2×D414yes—
254C22×C4×C71C2412yes—
255C22×C4×C71C2412yes—
256C22×C4×C71C2412yes—
257C22×C4×C71C2412yes—
258C22×C4×C71C2412yes—
259C22×C4×C71C2412yes—
260C4⋊C4×C71—28no—
261C4⋊C4×C71—44no—
262C4⋊C4×C71—44no—
263C22⋊C4×C71—28no—
264C22⋊C4×C71—44no—
265C22⋊C4×C71—44no—
266C23×C71—28no—
267C23×C71—28no—
268C23×C71—28no—
269C23×C71—22no—
270C23×C71—22no—
271C23×C71—22no—
272C23×C71—22no—
273C23×C71—22no—
274C23×C71—22no—
275C23×C71—44no—
276C23×C71—44no—
277C23×C71—44no—
278C23×C71—44no—
279C23×C71C22×D412yes—
280C23×C71C22×Q814yes—
281C23×C71C22×Q812yes—
282C23×C71C2×#4112yes—
283C23×C71C2×#4112yes—
284C23×C71C2×#4112yes—
285C23×C71H(5,𝔽2)12yes—
286C23×C71H(5,𝔽2)12yes—
287C23×C71C2511yescharacteristic
288C22×D71—28no—
289C22×D71—28no—
290C22×D71—28no—
291C22×D71—28no—
292C22×D71—28no—
293C22×D71—28no—
294C22×D71—22no—
295C22×D71—22no—
296C22×D71—22no—
297C22×D71—22no—
298C22×D71C22⋊Q8116yes—
299C22×D71C22×D414yes—
300C22×D71C22×Q814yes—
301C22×D71C2×#4114yes—
302C2×C4×C71—28no—
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—22no—
318C2×C4×C71—22no—
319C2×C4×C71—22no—
320C2×C4×C71—44no—
321C2×C4×C71—44no—
322C2×C4×C71—44no—
323C2×C4×C71—44no—
324C2×C4×C71—44no—
325C2×C4×C71C22×D414yes—
326C22⋊D71—232no—
327C2×Dic71—28no—
328C2×Dic71—28no—
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—22no—
348C2×Dic71—416no—
349C2×Dic71—44no—
350C2×Dic71—44no—
351C2×Dic71—44no—
352C2×Dic71C22×D414yes—
353C2×Dic71C22×Q814yes—
354C2×Dic71C2×#4114yes—
355C2×Dic71C2×#4114yes—
356C4×D71—416no—
357C4×D71—416no—
358C4×D71—416no—
359Dic142—416no—
360C22×C71—24no—
361C22×C71—24no—
362C22×C71—24no—
363C22×C71—42no—
364C22×C71—42no—
365C22×C71—42no—
366C22×C71—42no—
367C22×C71—416no—
368C22×C71C2×C22⋊Q814yes—
369C22×C71#52914yes—
370C22×C71#53814yes—
371C22×C71#54614yes—
372C22×C71#54614yes—
373C22×C71#55414yes—
374C22×C71#55414yes—
375C22×C71C23×D411yescharacteristic
376C22×C71C23×Q811yescharacteristic
377C22×C71C22×#4111yescharacteristic
378C22×C71C22×#4111yescharacteristic
379C22×C71C22×#4111yescharacteristic
380C22×C71C2×H(5,𝔽2)11yescharacteristic
381C22×C71C2×H(5,𝔽2)11yescharacteristic
382C2×D71—24no—
383C2×D71—24no—
384C2×D71—24no—
385C2×D71—24no—
386C2×D71—24no—
387C2×D71—24no—
388C2×D71—232no—
389C2×D71C2×C22⋊Q818yes—
390C4×C71—24no—
391C4×C71—42no—
392C4×C71—42no—
393C4×C71—42no—
394C4×C71—42no—
395C4×C71—42no—
396Dic71—24no—
397Dic71—24no—
398Dic71—24no—
399Dic71—24no—
400Dic71—42no—
401Dic71—42no—
402Dic71—42no—
403C2×#2450—711nomaximal, Sylow
404C2×C71—44no—
405C2×C71#245018yescomplemented
406C2×C71C22×C22⋊Q811yescharacteristic
407C2×C71C2×#52911yescharacteristic
408C2×C71C2×#53811yescharacteristic
409C2×C71C2×#54611yescharacteristic
410C2×C71C2×#54611yescharacteristic
411C2×C71C2×#55411yescharacteristic
412C2×C71C2×#55411yescharacteristic
413D71—28no—
414C22×C22⋊Q8—711no—
415C22×C4×D4—711no—
416#2450—7116no—
417C2×#400—711no—
418C2×#398—711no—
419C2×#396D7111yescharacteristic, complemented
420C2×#393—711no—
421C2×#391—711no—
422C2×#387—711no—
423C2×#386—711no—
424C2×#386—711no—
425C2×#385—711no—
426C2×#385—711no—
427C2×#385—711no—
428C2×#380—711no—
429C22×#95—711no—
430C71C2×#245011yescharacteristic, complemented, Sylow
431C23×Q8—711no—
432C23×D4—711no—
433C24×C4—711no—
434C24×C4—711no—
435C24×C4—711no—
436C24×C4—711no—
437C2×C22⋊Q8—718no—
438C2×C22⋊Q8—1428no—
439C2×C4×D4—718no—
440C2×C4×D4—1428no—
441C22×C4⋊C4—711no—
442C22×C4⋊C4—711no—
443C22×C4⋊C4—711no—
444C22×C4⋊C4—711no—
445C22×C4⋊C4—711no—
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⋊C4C2×D7111yescharacteristic
455C22×C22⋊C4C2×D7111yescharacteristic
456C22×C22⋊C4C2×D7111yescharacteristic
457C22×C42—711no—
458#400—718no—
459#398—718no—
460#396C2×D7118yescomplemented
461#393—718no—
462#391—718no—
463#387—718no—
464#386—718no—
465#386—718no—
466#385—718no—
467#385—718no—
468#385—718no—
469#380—718no—
470C2×#95—711no—
471C2×#95—711no—
472C2×#95—711no—
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—718no—
482C2×#95C2×D7111yescharacteristic
483C25—711no—
484C25C22×D7111yescharacteristic
485C22×Q8—2842no—
486C22×Q8—714no—
487C22×Q8—1424no—
488C22×Q8—1424no—
489C22×D4—718no—
490C22×D4—714no—
491C22×D4—1424no—
492C22×D4—1424no—
493C23×C4—2842no—
494C23×C4—2842no—
495C23×C4—2842no—
496C23×C4—2842no—
497C23×C4—2842no—
498C23×C4—714no—
499C23×C4—714no—
500C23×C4—714no—
501C23×C4—714no—
502C23×C4—711no—
503C23×C4—711no—
504C23×C4—711no—
505C23×C4—711no—
506C23×C4—711no—
507C23×C4—711no—
508C23×C4—711no—
509C23×C4—1424no—
510C23×C4—1424no—
511C23×C4—1424no—
512C23×C4—1424no—
513C23×C4—1424no—
514C23×C4—1424no—
515C23×C4—1424no—
516C23×C4C22×D7111yescharacteristic
517C23×C4C22×D7111yescharacteristic
518C23×C4C22×D7111yescharacteristic
519C23×C4C22×D7111yescharacteristic
520C23×C4C22×D7111yescharacteristic
521C23×C4C22×D7111yescharacteristic
522C22⋊Q8—14232no—
523C4×D4—14232no—
524C2×C4⋊C4—24no—
525C2×C4⋊C4—42no—
526C2×C4⋊C4—42no—
527C2×C4⋊C4—2842no—
528C2×C4⋊C4—714no—
529C2×C4⋊C4—714no—
530C2×C4⋊C4—714no—
531C2×C4⋊C4—714no—
532C2×C4⋊C4—714no—
533C2×C4⋊C4—1424no—
534C2×C4⋊C4—1424no—
535C2×C4⋊C4—1424no—
536C2×C4⋊C4—1424no—
537C2×C4⋊C4C22×D7114yes—
538C2×C4⋊C4C22×D7114yes—
539C2×C4⋊C4C22×D7114yes—
540C2×C22⋊C4—24no—
541C2×C22⋊C4—42no—
542C2×C22⋊C4—42no—
543C2×C22⋊C4—2842no—
544C2×C22⋊C4—714no—
545C2×C22⋊C4—718no—
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⋊C4C22×D7114yes—
554C2×C22⋊C4C22×D7114yes—
555C2×C22⋊C4C22×D7114yes—
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#95—714no—
566#95—714no—
567#95—714no—
568#95—714no—
569#95C22×D7114yes—
570C24—22no—
571C24—22no—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—714no—
577C24—714no—
578C24—714no—
579C24—712no—
580C24—1422no—
581C24—1422no—
582C24—1422no—
583C24—1422no—
584C24Q8×D7114yes—
585C24C23×D7112yes—
586C24C23×D7111yescharacteristic
587C2×Q8—28416no—
588C2×Q8—2844no—
589C2×Q8—1428no—
590C2×Q8—1428no—
591C2×D4—7116no—
592C2×D4—1428no—
593C2×D4—1428no—
594C2×D4—14232no—
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—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—2844no—
613C22×C4—2844no—
614C22×C4—2844no—
615C22×C4—2844no—
616C22×C4—28416no—
617C22×C4—28416no—
618C22×C4—28416no—
619C22×C4—2844no—
620C22×C4—28416no—
621C22×C4—714no—
622C22×C4—714no—
623C22×C4—714no—
624C22×C4—714no—
625C22×C4—712no—
626C22×C4—712no—
627C22×C4—712no—
628C22×C4—712no—
629C22×C4—712no—
630C22×C4—712no—
631C22×C4—712no—
632C22×C4—1428no—
633C22×C4—1428no—
634C22×C4—1428no—
635C22×C4—1428no—
636C22×C4—1428no—
637C22×C4—1428no—
638C22×C4—1428no—
639C22×C4—1422no—
640C22×C4—1422no—
641C22×C4—1422no—
642C22×C4—1422no—
643C22×C4—1422no—
644C22×C4—1422no—
645C22×C4—1422no—
646C22×C4—1422no—
647C22×C4—1422no—
648C22×C4—1422no—
649C22×C4—1422no—
650C22×C4—1422no—
651C22×C4—1422no—
652C22×C4—1422no—
653C22×C4—1422no—
654C22×C4—1422no—
655C22×C4—1422no—
656C22×C4D4×D7114yes—
657C22×C4C23×D7112yes—
658C22×C4C23×D7112yes—
659C22×C4C23×D7112yes—
660C22×C4C23×D7112yes—
661C22×C4C23×D7112yes—
662C22×C4C23×D7112yes—
663C4⋊C4—28no—
664C4⋊C4—44no—
665C4⋊C4—44no—
666C4⋊C4—2844no—
667C4⋊C4—1428no—
668C4⋊C4—1428no—
669C4⋊C4—1428no—
670C4⋊C4—1428no—
671C22⋊C4—28no—
672C22⋊C4—44no—
673C22⋊C4—44no—
674C22⋊C4—2844no—
675C22⋊C4—7116no—
676C22⋊C4—1428no—
677C22⋊C4—1428no—
678C22⋊C4—1428no—
679C42—1428no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—28no—
687C23—28no—
688C23—28no—
689C23—44no—
690C23—44no—
691C23—44no—
692C23—44no—
693C23—714no—
694C23—714no—
695C23—714no—
696C23—7116no—
697C23—1422no—
698C23—1422no—
699C23—1422no—
700C23—1422no—
701C23—1428no—
702C23—1428no—
703C23—1428no—
704C23—1428no—
705C23—1428no—
706C23—1428no—
707C23C2×D4×D7112yes—
708C23C2×Q8×D7114yes—
709C23C2×Q8×D7112yes—
710C23#41×D7112yes—
711C23#41×D7112yes—
712C23#41×D7112yes—
713C23#1455617312yes—
714C23#1455617312yes—
715C23C24×D7111yescharacteristic
716Q8—28416no—
717D4—14232no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—28no—
721C2×C4—22no—
722C2×C4—22no—
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—22no—
736C2×C4—44no—
737C2×C4—44no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—44no—
741C2×C4—28416no—
742C2×C4—28416no—
743C2×C4—28416no—
744C2×C4—2844no—
745C2×C4—2844no—
746C2×C4—2844no—
747C2×C4—28416no—
748C2×C4—714no—
749C2×C4—714no—
750C2×C4—714no—
751C2×C4—714no—
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—1422no—
766C2×C4—1422no—
767C2×C4—1422no—
768C2×C4—1422no—
769C2×C4—1428no—
770C2×C4—1428no—
771C2×C4—1428no—
772C2×C4—1428no—
773C2×C4C2×D4×D7114yes—
774C22—24no—
775C22—24no—
776C22—24no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—416no—
781C22—42no—
782C22—718no—
783C22—1424no—
784C22—1424no—
785C22—1424no—
786C22—1424no—
787C22—1424no—
788C22—14232no—
789C22—1424no—
790C22C22⋊Q8×D7114yes—
791C22#1798653214yes—
792C22#1798658114yes—
793C22#1798663814yes—
794C22#1798664614yes—
795C22#1798670314yes—
796C22#1798670314yes—
797C22C22×D4×D7111yescharacteristic
798C22C22×Q8×D7111yescharacteristic
799C22C2×#41×D7111yescharacteristic
800C22C2×#41×D7111yescharacteristic
801C22C2×#41×D7111yescharacteristic
802C22C2×#1455617311yescharacteristic
803C22C2×#1455617311yescharacteristic
804C4—24no—
805C4—42no—
806C4—42no—
807C4—42no—
808C4—42no—
809C4—42no—
810C4—2842no—
811C4—2842no—
812C4—2842no—
813C4—1424no—
814C4—1424no—
815C4—1424no—
816C4—1424no—
817C2—44no—
818C2—1428no—
819C2#2259215918yesdirect product factor
820C2C2×C22⋊Q8×D7111yescharacteristic
821C2C2×#1798653211yescharacteristic
822C2C2×#1798658111yescharacteristic
823C2C2×#1798663811yescharacteristic
824C2C2×#1798664611yescharacteristic
825C2C2×#1798670311yescharacteristic
826C2C2×#1798670311yescharacteristic
subgroupG/H
centerC24C23×D71
commutator, cosocleC23×C71C25
FrattiniC23C24×D71
FittingC2×#396×C71C2
socleC24×C71C24
prime radicalC23×C22⋊D71C22
hypercenterC2×#396D71
hypocenterC71C2×#2450
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. C22×#14556106C2semidirect
3. #22592159C2direct (N × H)
4. C2×#17985940C2semidirect
5. C2×#17985930C2semidirect
6. C2×#17985911C2semidirect
7. C2×#17985904C2semidirect
8. C2×#17985880C2semidirect
11. C2×#17985871C2semidirect
12. C2×#17985870C2semidirect
13. C2×#17985870C2semidirect
14. C2×#17985857C2semidirect
15. C2×#95×D71C2semidirect
16. C2×#396×C71C2semidirect
24. C2×#14556106C22semidirect
38. #17985940C22semidirect
39. #17985930C22semidirect
40. #17985911C22semidirect
41. #17985904C22semidirect
42. #17985880C22semidirect
45. #17985871C22semidirect
46. #17985870C22semidirect
47. #17985870C22semidirect
48. #17985857C22semidirect
60. #95×D71C22semidirect
67. #396×C71C22semidirect
76. C22×C22⋊D71Q8semidirect
171. C2×C22⋊D71C2×Q8semidirect
405. C2×C71#2450semidirect
419. C2×#396D71semidirect
430. C71C2×#2450semidirect
460. #396C2×D71semidirect
819. C2#22592159direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145561062
C22×(C22⋊D71)⋊C42
#225921592
C2×#179859402
C2×#179859302
C2×#179859112
C2×#179859042
C2×#179858802
C2×#179858752
C2×#179858712
C2×#179858702
C2×#179858572
C2×#95×D712
C2×#396×C712
C2×#245071