Finite Group Databasebeta

← C2×#22592041 #32165281

Subgroups — C2×#22592041 #32165281

Order 18176.

3550 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×#14556127C211yesmaximal, characteristic, complemented
2C22×#14556107C211yesmaximal, characteristic
3C22×#14556105C211yesmaximal, characteristic
4C23×Dic71⋊C4C211yesmaximal, characteristic
5#22592041C2116yesmaximal, direct product factor
6C2×#17985933C211yesmaximal, characteristic, complemented
7C2×#17985932C211yesmaximal, characteristic, complemented
8C2×#17985920C211yesmaximal, characteristic, complemented
9C2×#17985919C211yesmaximal, characteristic, complemented
10C2×#17985896C211yesmaximal, characteristic, complemented
11C2×#17985896C211yesmaximal, characteristic, complemented
12C2×#17985874C211yesmaximal, characteristic
13C2×#17985868C211yesmaximal, characteristic, complemented
14C2×#17985857C211yesmaximal, characteristic
15C2×C22⋊C4×Dic71C211yesmaximal, characteristic
16C2×#385×C71C211yesmaximal, characteristic
17C23×Dic142C2211yescharacteristic
18C23×Dic142C2211yescharacteristic
19C24×Dic71C2211yescharacteristic
20C24×Dic71C2211yescharacteristic
21C2×#14556127—28no—
22C2×#14556127C2218yescomplemented
23C2×#14556107—28no—
24C2×#14556107C2218yes—
25C2×#14556105—28no—
26C2×#14556105C2218yes—
27C22×C4⋊Dic71C2211yescharacteristic
28C22×C4⋊Dic71C2211yescharacteristic
29C22×C4⋊Dic71C2211yescharacteristic
30C22×C4⋊Dic71C2211yescharacteristic
31C22×Dic71⋊C4—28no—
32C22×Dic71⋊C4C2211yescharacteristic
33C22×Dic71⋊C4C2211yescharacteristic
34C22×Dic71⋊C4C2211yescharacteristic
35C22×Dic71⋊C4C2211yescharacteristic
36C22×Dic71⋊C4C2218yes—
37C22×Dic71⋊C4C2211yescharacteristic
38C22×Dic71⋊C4C2211yescharacteristic
39C22×Dic71⋊C4C2211yescharacteristic
40C22×Dic71⋊C4C2211yescharacteristic
41C22×Dic71⋊C4C2211yescharacteristic
42C22×Dic71⋊C4C2211yescharacteristic
43C22×C22⋊Dic71C2211yescharacteristic
44C22×C22⋊Dic71C2211yescharacteristic
45C22×C4×Dic71C2211yescharacteristic
46C22×C4×Dic71C2211yescharacteristic
47#17985933C2218yescomplemented
48#17985932C2218yescomplemented
49#17985920C2218yescomplemented
50#17985919C2218yescomplemented
51#17985896C2218yescomplemented
52#17985896C2218yescomplemented
53#17985874C2218yes—
54#17985868C2218yescomplemented
55#17985857C2218yes—
56C22⋊C4×Dic71C2218yes—
57C2×C71⋊#95C2211yescharacteristic
58C2×C71⋊#95C2211yescharacteristic
59C2×C71⋊#95C2211yescharacteristic
60C2×C71⋊#95C2211yescharacteristic
61C2×C71⋊#95C2211yescharacteristic
62C2×C71⋊#95C2211yescharacteristic
63C24×C4×C71C2211yescharacteristic
64C22×C4⋊C4×C71C2211yescharacteristic
65C22×C4⋊C4×C71C2211yescharacteristic
66C22×C22⋊C4×C71C2211yescharacteristic
67C22×C22⋊C4×C71C2211yescharacteristic
68#385×C71C2218yes—
69C2×#95×C71C2211yescharacteristic
70C2×#95×C71C2211yescharacteristic
71C22×Dic142—24no—
72C22×Dic142—24no—
73C22×Dic142—24no—
74C22×Dic142—24no—
75C22×Dic142—42no—
76C22×Dic142—42no—
77C22×Dic142C2314yes—
78C22×Dic142C2314yes—
79C23×Dic71—24no—
80C23×Dic71—24no—
81C23×Dic71—24no—
82C23×Dic71—24no—
83C23×Dic71—42no—
84C23×Dic71Q818yescomplemented
85C23×Dic71C2311yescharacteristic
86C23×Dic71C2311yescharacteristic
87C23×Dic71C2311yescharacteristic
88C23×Dic71C2314yes—
89C23×Dic71C2311yescharacteristic
90C23×Dic71C2311yescharacteristic
91C23×Dic71C2311yescharacteristic
92C23×Dic71C2311yescharacteristic
93C23×Dic71C2314yes—
94C23×Dic71C2311yescharacteristic
95#14556127—232no—
96#14556107—232no—
97#14556105—232no—
98C2×C4⋊Dic71—24no—
99C2×C4⋊Dic71—24no—
100C2×C4⋊Dic71—24no—
101C2×C4⋊Dic71—42no—
102C2×C4⋊Dic71C2314yes—
103C2×C4⋊Dic71C2314yes—
104C2×C4⋊Dic71C2314yes—
105C2×C4⋊Dic71C2314yes—
106C2×Dic71⋊C4—24no—
107C2×Dic71⋊C4—24no—
108C2×Dic71⋊C4—24no—
109C2×Dic71⋊C4—24no—
110C2×Dic71⋊C4—24no—
111C2×Dic71⋊C4—24no—
112C2×Dic71⋊C4—24no—
113C2×Dic71⋊C4—24no—
114C2×Dic71⋊C4—232no—
115C2×Dic71⋊C4—24no—
116C2×Dic71⋊C4D418yes—
117C2×Dic71⋊C4C2314yes—
118C2×Dic71⋊C4C2314yes—
119C2×Dic71⋊C4C2314yes—
120C2×Dic71⋊C4C2314yes—
121C2×Dic71⋊C4C2314yes—
122C2×Dic71⋊C4C2314yes—
123C2×Dic71⋊C4C2314yes—
124C2×Dic71⋊C4C2314yes—
125C2×Dic71⋊C4C2314yes—
126C2×Dic71⋊C4C2314yes—
127C2×C22⋊Dic71—24no—
128C2×C22⋊Dic71D418yes—
129C2×C22⋊Dic71C2314yes—
130C2×C22⋊Dic71C2314yes—
131C2×C4×Dic71—24no—
132C2×C4×Dic71—24no—
133C2×C4×Dic71C2314yes—
134C2×C4×Dic71C2314yes—
135C71⋊#95C2314yes—
136C71⋊#95C2314yes—
137C71⋊#95C2314yes—
138C71⋊#95C2314yes—
139C71⋊#95C2314yes—
140C71⋊#95C2314yes—
141C25×C71C2311yescharacteristic
142C23×C4×C71—24no—
143C23×C4×C71—24no—
144C23×C4×C71—42no—
145C23×C4×C71C2311yescharacteristic
146C23×C4×C71C2311yescharacteristic
147C23×C4×C71C2311yescharacteristic
148C23×C4×C71C2314yes—
149C23×C4×C71C2311yescharacteristic
150C23×C4×C71C2311yescharacteristic
151C23×C4×C71C2311yescharacteristic
152C2×C4⋊C4×C71—24no—
153C2×C4⋊C4×C71—42no—
154C2×C4⋊C4×C71C2314yes—
155C2×C4⋊C4×C71C2314yes—
156C2×C22⋊C4×C71—24no—
157C2×C22⋊C4×C71Q818yescomplemented
158C2×C22⋊C4×C71C2314yes—
159C2×C22⋊C4×C71C2314yes—
160#95×C71C2314yes—
161#95×C71C2314yes—
162C2×Dic142—28no—
163C2×Dic142—28no—
164C2×Dic142—28no—
165C2×Dic142—28no—
166C2×Dic142—44no—
167C2×Dic142—44no—
168C2×Dic142—416no—
169C2×Dic142—416no—
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—232no—
179C22×Dic71—28no—
180C22×Dic71—28no—
181C22×Dic71—22no—
182C22×Dic71—22no—
183C22×Dic71—28no—
184C22×Dic71—22no—
185C22×Dic71—22no—
186C22×Dic71—22no—
187C22×Dic71—22no—
188C22×Dic71—22no—
189C22×Dic71—22no—
190C22×Dic71—22no—
191C22×Dic71—28no—
192C22×Dic71—44no—
193C22×Dic71—416no—
194C22×Dic71C2×D414yes—
195C22×Dic71C2×D414yes—
196C22×Dic71C2×D414yes—
197C22×Dic71C2×D414yes—
198C22×Dic71C2×Q814yes—
199C22×Dic71C2×Q814yes—
200C22×Dic71C2×Q8116yescomplemented
201C22×Dic71#4114yes—
202C22×Dic71C2412yes—
203C22×Dic71C2412yes—
204C22×Dic71C2412yes—
205C22×Dic71C2412yes—
206C22×Dic71C2412yes—
207C22×Dic71C2412yes—
208C22×Dic71C2412yes—
209C22×Dic71C2412yes—
210C4⋊Dic71—28no—
211C4⋊Dic71—28no—
212C4⋊Dic71—28no—
213C4⋊Dic71—44no—
214Dic71⋊C4—28no—
215Dic71⋊C4—28no—
216Dic71⋊C4—28no—
217Dic71⋊C4—28no—
218Dic71⋊C4—28no—
219Dic71⋊C4—28no—
220Dic71⋊C4—28no—
221Dic71⋊C4—28no—
222Dic71⋊C4—28no—
223Dic71⋊C4C2×D4116yes—
224C22⋊Dic71—28no—
225C22⋊Dic71C2×D4116yes—
226C4×Dic71—28no—
227C4×Dic71—28no—
228C24×C71—22no—
229C24×C71—22no—
230C24×C71—22no—
231C24×C71—22no—
232C24×C71C2×D414yes—
233C24×C71C2×Q814yes—
234C24×C71C2×Q814yes—
235C24×C71C2412yes—
236C24×C71C2411yescharacteristic
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—28no—
249C22×C4×C71—22no—
250C22×C4×C71—22no—
251C22×C4×C71—22no—
252C22×C4×C71—22no—
253C22×C4×C71—28no—
254C22×C4×C71—44no—
255C22×C4×C71—416no—
256C22×C4×C71C2×D414yes—
257C22×C4×C71C2×Q814yes—
258C22×C4×C71C2×Q814yes—
259C22×C4×C71C2412yes—
260C22×C4×C71C2412yes—
261C22×C4×C71C2412yes—
262C22×C4×C71C2412yes—
263C22×C4×C71C2412yes—
264C22×C4×C71C2412yes—
265C4⋊C4×C71—28no—
266C4⋊C4×C71—44no—
267C22⋊C4×C71—28no—
268C22⋊C4×C71C2×Q8116yescomplemented
269C23×C71—28no—
270C23×C71—28no—
271C23×C71—28no—
272C23×C71—28no—
273C23×C71—28no—
274C23×C71—28no—
275C23×C71—22no—
276C23×C71—22no—
277C23×C71—22no—
278C23×C71—22no—
279C23×C71C4⋊Q8116yescomplemented
280C23×C71C22×D414yes—
281C23×C71C22×D412yes—
282C23×C71C22×D412yes—
283C23×C71C22×Q814yes—
284C23×C71C22×Q812yes—
285C23×C71C22×Q814yes—
286C23×C71C22×Q812yes—
287C23×C71C2×#4112yes—
288C23×C71H(5,𝔽2)12yes—
289C23×C712−1+412yes—
290C23×C71C2511yescharacteristic
291C2×C4×C71—28no—
292C2×C4×C71—28no—
293C2×C4×C71—28no—
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—22no—
308C2×C4×C71—22no—
309C2×C4×C71—416no—
310C2×C4×C71—44no—
311C2×C4×C71—44no—
312C2×C4×C71—44no—
313C2×C4×C71C22×D414yes—
314C2×C4×C71C22×Q814yes—
315C2×C4×C71C22×Q814yes—
316C2×Dic71—28no—
317C2×Dic71—28no—
318C2×Dic71—28no—
319C2×Dic71—28no—
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—232no—
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—416no—
339C2×Dic71—44no—
340C2×Dic71—44no—
341C2×Dic71—44no—
342C2×Dic71C22⋊Q8116yescomplemented
343C2×Dic71C22×D414yes—
344C2×Dic71C22×D414yes—
345C2×Dic71C22×D414yes—
346C2×Dic71C22×D414yes—
347C2×Dic71C22×Q814yes—
348C2×Dic71C22×Q814yes—
349C2×Dic71C2×#4114yes—
350Dic142—416no—
351Dic142—416no—
352C22×C71—24no—
353C22×C71—24no—
354C22×C71—24no—
355C22×C71—232no—
356C22×C71—24no—
357C22×C71—24no—
358C22×C71—24no—
359C22×C71C2×C22⋊Q814yes—
360C22×C71C2×C4⋊Q814yes—
361C22×C71C2×C4⋊Q818yescomplemented
362C22×C71#54414yes—
363C22×C71D4214yes—
364C22×C71#54714yes—
365C22×C71D4×Q814yes—
366C22×C71#55414yes—
367C22×C71C23×D411yescharacteristic
368C22×C71C23×D411yescharacteristic
369C22×C71C23×Q811yescharacteristic
370C22×C71C23×Q811yescharacteristic
371C22×C71C22×#4111yescharacteristic
372C22×C71C2×H(5,𝔽2)11yescharacteristic
373C22×C71C2×2−1+411yescharacteristic
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—
387Dic71C2×C22⋊Q818yescomplemented
388C2×#2440—711nomaximal, Sylow
389C2×C71—28no—
390C2×C71#244018yescomplemented
391C2×C71C22×C22⋊Q811yescharacteristic
392C2×C71C22×C4⋊Q811yescharacteristic
393C2×C71C2×#54411yescharacteristic
394C2×C71C2×D4211yescharacteristic
395C2×C71C2×#54711yescharacteristic
396C2×C71C2×D4×Q811yescharacteristic
397C2×C71C2×#55411yescharacteristic
398C22×C4⋊Q8—711no—
399C22×C22⋊Q8—711no—
400C22×C22⋊Q8—711no—
401C23×C4⋊C4—711no—
402#2440—7116no—
403C2×#398—711no—
404C2×#398—711no—
405C2×#395—711no—
406C2×#395—711no—
407C2×#389—711no—
408C2×#389—711no—
409C2×#385—711no—
410C2×#385D7111yescharacteristic
411C2×#384—711no—
412C2×#380—711no—
413C2×C4×C22⋊C4—711no—
414C71C2×#244011yescharacteristic, complemented, Sylow
415C23×Q8—711no—
416C23×Q8—711no—
417C24×C4—711no—
418C24×C4—711no—
419C24×C4C2×D7111yescharacteristic
420C2×C4⋊Q8—718no—
421C2×C4⋊Q8—1428no—
422C2×C22⋊Q8—718no—
423C2×C22⋊Q8—718no—
424C2×C22⋊Q8—1428no—
425C2×C22⋊Q8—1428no—
426C22×C4⋊C4—711no—
427C22×C4⋊C4—711no—
428C22×C4⋊C4—711no—
429C22×C4⋊C4—711no—
430C22×C4⋊C4—711no—
431C22×C4⋊C4—711no—
432C22×C4⋊C4—711no—
433C22×C4⋊C4—711no—
434C22×C4⋊C4—711no—
435C22×C4⋊C4—711no—
436C22×C4⋊C4—711no—
437C22×C4⋊C4—718no—
438C22×C4⋊C4—711no—
439C22×C4⋊C4—711no—
440C22×C4⋊C4—711no—
441C22×C4⋊C4—1428no—
442C22×C4⋊C4C2×D7111yescharacteristic
443C22×C4⋊C4C2×D7111yescharacteristic
444C22×C22⋊C4—711no—
445C22×C22⋊C4—711no—
446C22×C22⋊C4C2×D7111yescharacteristic
447C22×C22⋊C4C2×D7111yescharacteristic
448C22×C42—711no—
449C22×C42—711no—
450#398—718no—
451#398—718no—
452#395—718no—
453#395—718no—
454#389—718no—
455#389—718no—
456#385—718no—
457#385C2×D7118yes—
458#384—718no—
459#380—718no—
460C4×C22⋊C4—718no—
461C2×#95—711no—
462C2×#95—711no—
463C2×#95—711no—
464C2×#95—711no—
465C2×#95—711no—
466C2×#95—711no—
467C2×#95C2×D7111yescharacteristic
468C2×#95C2×D7111yescharacteristic
469C25C22×D7111yescharacteristic
470C22×Q8—2842no—
471C22×Q8—2842no—
472C22×Q8—714no—
473C22×Q8—714no—
474C22×Q8—1424no—
475C22×Q8—1424no—
476C22×Q8—1424no—
477C22×Q8—1424no—
478C23×C4—24no—
479C23×C4—24no—
480C23×C4—42no—
481C23×C4—2842no—
482C23×C4—714no—
483C23×C4—711no—
484C23×C4—718no—
485C23×C4—714no—
486C23×C4—711no—
487C23×C4—711no—
488C23×C4—711no—
489C23×C4—711no—
490C23×C4—711no—
491C23×C4—711no—
492C23×C4—711no—
493C23×C4—1424no—
494C23×C4—1424no—
495C23×C4—1424no—
496C23×C4—1424no—
497C23×C4C22×D7111yescharacteristic
498C23×C4C22×D7111yescharacteristic
499C23×C4C22×D7111yescharacteristic
500C23×C4C22×D7114yes—
501C23×C4C22×D7111yescharacteristic
502C23×C4C22×D7111yescharacteristic
503C23×C4C22×D7111yescharacteristic
504C4⋊Q8—14232no—
505C22⋊Q8—14232no—
506C22⋊Q8—14232no—
507C2×C4⋊C4—24no—
508C2×C4⋊C4—42no—
509C2×C4⋊C4—2842no—
510C2×C4⋊C4—714no—
511C2×C4⋊C4—718no—
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—714no—
523C2×C4⋊C4—714no—
524C2×C4⋊C4—714no—
525C2×C4⋊C4—14232no—
526C2×C4⋊C4—1424no—
527C2×C4⋊C4—1424no—
528C2×C4⋊C4—1424no—
529C2×C4⋊C4—1424no—
530C2×C4⋊C4—1424no—
531C2×C4⋊C4—1424no—
532C2×C4⋊C4—1424no—
533C2×C4⋊C4—1424no—
534C2×C4⋊C4—1424no—
535C2×C4⋊C4—1424no—
536C2×C4⋊C4—1424no—
537C2×C4⋊C4—1424no—
538C2×C4⋊C4C22×D7114yes—
539C2×C4⋊C4C22×D7114yes—
540C2×C22⋊C4—24no—
541C2×C22⋊C4—718no—
542C2×C22⋊C4—714no—
543C2×C22⋊C4—714no—
544C2×C22⋊C4—1424no—
545C2×C22⋊C4Dic14218yescomplemented
546C2×C22⋊C4C22×D7114yes—
547C2×C22⋊C4C22×D7114yes—
548C2×C42—714no—
549C2×C42—714no—
550C2×C42—1424no—
551C2×C42—1424no—
552#95—714no—
553#95—714no—
554#95—714no—
555#95—714no—
556#95—714no—
557#95—714no—
558#95C22×D7114yes—
559#95C22×D7114yes—
560C24—22no—
561C24—22no—
562C24—22no—
563C24—22no—
564C24D4×D7114yes—
565C24Q8×D7114yes—
566C24C2×Dic14214yes—
567C24C23×D7112yes—
568C24C23×D7111yescharacteristic
569C2×Q8—28416no—
570C2×Q8—2844no—
571C2×Q8—2844no—
572C2×Q8—28416no—
573C2×Q8—1428no—
574C2×Q8—1428no—
575C2×Q8—1428no—
576C2×Q8—1428no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—28no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—28no—
594C22×C4—44no—
595C22×C4—416no—
596C22×C4—28416no—
597C22×C4—2844no—
598C22×C4—714no—
599C22×C4—714no—
600C22×C4—714no—
601C22×C4—712no—
602C22×C4—714no—
603C22×C4—714no—
604C22×C4—714no—
605C22×C4—714no—
606C22×C4—7116no—
607C22×C4—712no—
608C22×C4—712no—
609C22×C4—712no—
610C22×C4—712no—
611C22×C4—712no—
612C22×C4—712no—
613C22×C4—712no—
614C22×C4—1428no—
615C22×C4—1422no—
616C22×C4—1422no—
617C22×C4—1422no—
618C22×C4—1422no—
619C22×C4—1422no—
620C22×C4—1428no—
621C22×C4—1422no—
622C22×C4—1422no—
623C22×C4—1422no—
624C22×C4—1422no—
625C22×C4—1428no—
626C22×C4—1428no—
627C22×C4—14232no—
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×C4D4×D7114yes—
637C22×C4C2×Dic14214yes—
638C22×C4C2×Dic14214yes—
639C22×C4C23×D7112yes—
640C22×C4C23×D7112yes—
641C22×C4C23×D7112yes—
642C22×C4C23×D7112yes—
643C22×C4C23×D7112yes—
644C22×C4C23×D7112yes—
645C4⋊C4—28no—
646C4⋊C4—44no—
647C4⋊C4—2844no—
648C4⋊C4—7116no—
649C4⋊C4—1428no—
650C4⋊C4—1428no—
651C4⋊C4—1428no—
652C4⋊C4—1428no—
653C4⋊C4—1428no—
654C4⋊C4—1428no—
655C4⋊C4—1428no—
656C4⋊C4—1428no—
657C4⋊C4—1428no—
658C4⋊C4—1428no—
659C4⋊C4—1428no—
660C4⋊C4—1428no—
661C22⋊C4—28no—
662C22⋊C4—7116no—
663C22⋊C4—1428no—
664C22⋊C4C2×Dic142116yescomplemented
665C42—1428no—
666C42—1428no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—28no—
672C23—28no—
673C23—28no—
674C23—28no—
675C23—28no—
676C23—28no—
677C23#14556127116yescomplemented
678C23C2×D4×D7114yes—
679C23C2×D4×D7112yes—
680C23C2×D4×D7112yes—
681C23C2×Q8×D7114yes—
682C23C2×Q8×D7112yes—
683C23C22×Dic14214yes—
684C23C22×Dic14212yes—
685C23#41×D7112yes—
686C23#1455617312yes—
687C23#1455617512yes—
688C23C24×D7111yescharacteristic
689Q8—28416no—
690Q8—28416no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—28no—
698C2×C4—28no—
699C2×C4—28no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—416no—
710C2×C4—44no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—2844no—
714C2×C4—2844no—
715C2×C4—2844no—
716C2×C4—28416no—
717C2×C4—714no—
718C2×C4—714no—
719C2×C4—714no—
720C2×C4—7116no—
721C2×C4—714no—
722C2×C4—714no—
723C2×C4—714no—
724C2×C4—714no—
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—14232no—
735C2×C4—1422no—
736C2×C4—1422no—
737C2×C4—1422no—
738C2×C4—1422no—
739C2×C4—1422no—
740C2×C4—1422no—
741C2×C4—1422no—
742C2×C4—1422no—
743C2×C4—1428no—
744C2×C4—1428no—
745C2×C4—1428no—
746C2×C4—1428no—
747C2×C4C2×D4×D7114yes—
748C2×C4C22×Dic14214yes—
749C2×C4C22×Dic14214yes—
750C22—24no—
751C22—232no—
752C22—24no—
753C22—24no—
754C22—24no—
755C22—24no—
756C22—24no—
757C22C22⋊Q8×D7114yes—
758C22C2×#1455612714yes—
759C22C2×#1455612718yescomplemented
760C22#1798662814yes—
761C22#1798663114yes—
762C22#1798664714yes—
763C22D4×Dic14214yes—
764C22#1798670814yes—
765C22C22×D4×D7111yescharacteristic
766C22C22×D4×D7111yescharacteristic
767C22C22×Q8×D7111yescharacteristic
768C22C23×Dic14211yescharacteristic
769C22C2×#41×D7111yescharacteristic
770C22C2×#1455617311yescharacteristic
771C22C2×#1455617511yescharacteristic
772C4—24no—
773C4—24no—
774C4—24no—
775C4—42no—
776C4—42no—
777C4—42no—
778C4—2842no—
779C4—2842no—
780C4—2842no—
781C4—718no—
782C4—1424no—
783C4—1424no—
784C4—1424no—
785C4—1424no—
786C2—28no—
787C2#2259204118yesdirect product factor
788C2C2×C22⋊Q8×D7111yescharacteristic
789C2C22×#1455612711yescharacteristic
790C2C2×#1798662811yescharacteristic
791C2C2×#1798663111yescharacteristic
792C2C2×#1798664711yescharacteristic
793C2C2×D4×Dic14211yescharacteristic
794C2C2×#1798670811yescharacteristic
subgroupG/H
centerC24C23×D71
commutator, cosocleC23×C71C25
FrattiniC23C24×D71
FittingC2×#385×C71C2
socleC24×C71C24
prime radicalC25×C71C23
hypercenterC2×#385D71
hypocenterC71C2×#2440
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C22×#14556127C2semidirect
5. #22592041C2direct (N × H)
6. C2×#17985933C2semidirect
7. C2×#17985932C2semidirect
8. C2×#17985920C2semidirect
9. C2×#17985919C2semidirect
10. C2×#17985896C2semidirect
11. C2×#17985896C2semidirect
13. C2×#17985868C2semidirect
22. C2×#14556127C22semidirect
47. #17985933C22semidirect
48. #17985932C22semidirect
49. #17985920C22semidirect
50. #17985919C22semidirect
51. #17985896C22semidirect
52. #17985896C22semidirect
54. #17985868C22semidirect
84. C23×Dic71Q8semidirect
157. C2×C22⋊C4×C71Q8semidirect
200. C22×Dic71C2×Q8semidirect
268. C22⋊C4×C71C2×Q8semidirect
279. C23×C71C4⋊Q8semidirect
342. C2×Dic71C22⋊Q8semidirect
361. C22×C71C2×C4⋊Q8semidirect
387. Dic71C2×C22⋊Q8semidirect
390. C2×C71#2440semidirect
414. C71C2×#2440semidirect
545. C2×C22⋊C4Dic142semidirect
664. C22⋊C4C2×Dic142semidirect
677. C23#14556127semidirect
759. C22C2×#14556127semidirect
787. C2#22592041direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145561272
C22×#145561072
C22×#145561052
C23×Dic71⋊C42
#225920412
C2×#179859332
C2×#179859322
C2×#179859202
C2×#179859192
C2×#179858962
C2×#179858742
C2×#179858682
C2×#179858572
C2×C22⋊C4×Dic712
C2×#385×C712
C2×#244071