Finite Group Databasebeta

← C2×#22593480 #32167607

Subgroups — C2×#22593480 #32167607

Order 18176.

2898 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556123C211yesmaximal, characteristic, complemented
2#22593480C2116yesmaximal, direct product factor
3C2×#17985932C211yesmaximal, characteristic, complemented
4C2×#17985924C211yesmaximal, characteristic, complemented
5C2×#17985915C211yesmaximal, characteristic
6C2×#17985910C211yesmaximal, characteristic, complemented
7C2×#17985906C211yesmaximal, characteristic, complemented
8C2×#17985899C211yesmaximal, characteristic
9C2×#17985893C211yesmaximal, characteristic, complemented
10C2×#17985889C211yesmaximal, characteristic, complemented
11C2×#17985889C211yesmaximal, characteristic, complemented
12C2×#17985880C211yesmaximal, characteristic, complemented
13C2×#17985878C211yesmaximal, characteristic
14C2×C4⋊C4×Dic71C211yesmaximal, characteristic, complemented
15C2×C4×C22⋊Dic71C211yesmaximal, characteristic, complemented
16C22×C22⋊Q8×C71C211yesmaximal, characteristic, complemented
17C23×C22⋊D71C2211yescharacteristic
18C2×#14556123—28no—
19C2×#14556123C2218yescomplemented
20C22×C4⋊Dic71C2211yescharacteristic
21C22×C4⋊Dic71C2211yescharacteristic
22C22×Dic71⋊C4C2211yescharacteristic
23C22×Dic71⋊C4C2211yescharacteristic
24C22×C22⋊Dic71C2211yescharacteristic
25C22×C22⋊Dic71C2211yescharacteristic
26C22×C22⋊Dic71C2211yescharacteristic
27C22×(C2×D71)⋊C4C2211yescharacteristic
28C22×(C2×D71)⋊C4C2211yescharacteristic
29C22×(C2×D71)⋊C4C2211yescharacteristic
30C22×(C2×D71)⋊C4C2211yescharacteristic
31C22×(C2×D71)⋊C4C2211yescharacteristic
32C22×(C2×D71)⋊C4C2211yescharacteristic
33C22×C4×Dic71C2211yescharacteristic
34C22×C4×Dic71C2211yescharacteristic
35C22×C4×Dic71C2211yescharacteristic
36C22×C4×Dic71C2211yescharacteristic
37#17985932C2218yescomplemented
38#17985924C2218yescomplemented
39#17985915C2218yes—
40#17985910C2218yescomplemented
41#17985906C2218yescomplemented
42#17985899C2218yes—
43#17985893C2218yescomplemented
44#17985889C2218yescomplemented
45#17985889C2218yescomplemented
46#17985880C2218yescomplemented
47#17985878C2218yes—
48C4⋊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
60C23×Q8×C71C2211yescharacteristic
61C24×C4×C71C2211yescharacteristic
62C2×C22⋊Q8×C71—28no—
63C2×C22⋊Q8×C71C2218yescomplemented
64C22×C4⋊C4×C71C2211yescharacteristic
65C22×C4⋊C4×C71C2211yescharacteristic
66C22×C4⋊C4×C71C2211yescharacteristic
67C22×C22⋊C4×C71C2211yescharacteristic
68C22×C22⋊C4×C71C2211yescharacteristic
69C24×D71C2311yescharacteristic
70C22×C22⋊D71—24no—
71C22×C22⋊D71—24no—
72C22×C22⋊D71—42no—
73C22×C22⋊D71C2314yes—
74C23×Dic71C2311yescharacteristic
75C23×Dic71C2311yescharacteristic
76C23×Dic71C2311yescharacteristic
77C23×Dic71C2311yescharacteristic
78C23×Dic71C2311yescharacteristic
79C23×Dic71C2311yescharacteristic
80C23×Dic71C2311yescharacteristic
81#14556123—232no—
82C2×C4⋊Dic71—24no—
83C2×C4⋊Dic71—24no—
84C2×C4⋊Dic71C2314yes—
85C2×C4⋊Dic71C2314yes—
86C2×Dic71⋊C4—24no—
87C2×Dic71⋊C4—24no—
88C2×Dic71⋊C4C2314yes—
89C2×Dic71⋊C4C2314yes—
90C2×C22⋊Dic71—24no—
91C2×C22⋊Dic71—24no—
92C2×C22⋊Dic71—24no—
93C2×C22⋊Dic71C2314yes—
94C2×C22⋊Dic71C2314yes—
95C2×C22⋊Dic71C2314yes—
96C2×(C2×D71)⋊C4—24no—
97C2×(C2×D71)⋊C4—24no—
98C2×(C2×D71)⋊C4—24no—
99C2×(C2×D71)⋊C4—24no—
100C2×(C2×D71)⋊C4—24no—
101C2×(C2×D71)⋊C4—42no—
102C2×(C2×D71)⋊C4C2314yes—
103C2×(C2×D71)⋊C4C2314yes—
104C2×(C2×D71)⋊C4C2314yes—
105C2×(C2×D71)⋊C4C2314yes—
106C2×(C2×D71)⋊C4C2314yes—
107C2×(C2×D71)⋊C4C2314yes—
108C2×C4×Dic71—24no—
109C2×C4×Dic71—24no—
110C2×C4×Dic71—42no—
111C2×C4×Dic71—42no—
112C2×C4×Dic71C2314yes—
113C2×C4×Dic71C2314yes—
114C2×C4×Dic71C2314yes—
115C2×C4×Dic71C2314yes—
116C71⋊#95C2314yes—
117C71⋊#95C2314yes—
118C71⋊#95C2314yes—
119C71⋊#95C2314yes—
120C71⋊#95C2314yes—
121C71⋊#95C2314yes—
122C71⋊#95C2314yes—
123C71⋊#95C2314yes—
124C71⋊#95C2314yes—
125C71⋊#95C2314yes—
126C25×C71C2311yescharacteristic
127C22×Q8×C71—24no—
128C22×Q8×C71—24no—
129C22×Q8×C71—42no—
130C22×Q8×C71C2314yes—
131C23×C4×C71—24no—
132C23×C4×C71—24no—
133C23×C4×C71—42no—
134C23×C4×C71C2311yescharacteristic
135C23×C4×C71C2311yescharacteristic
136C23×C4×C71C2314yes—
137C23×C4×C71C2311yescharacteristic
138C23×C4×C71C2311yescharacteristic
139C23×C4×C71C2311yescharacteristic
140C23×C4×C71C2311yescharacteristic
141C22⋊Q8×C71—232no—
142C2×C4⋊C4×C71—24no—
143C2×C4⋊C4×C71—24no—
144C2×C4⋊C4×C71D418yescomplemented
145C2×C4⋊C4×C71C2314yes—
146C2×C4⋊C4×C71C2314yes—
147C2×C4⋊C4×C71C2314yes—
148C2×C22⋊C4×C71—24no—
149C2×C22⋊C4×C71—24no—
150C2×C22⋊C4×C71C2314yes—
151C2×C22⋊C4×C71C2314yes—
152C23×D71—22no—
153C23×D71—22no—
154C23×D71—22no—
155C23×D71—22no—
156C23×D71—22no—
157C23×D71—22no—
158C23×D71—22no—
159C23×D71C2412yes—
160C2×C22⋊D71—28no—
161C2×C22⋊D71—28no—
162C2×C22⋊D71—44no—
163C2×C22⋊D71—416no—
164C22×Dic71—22no—
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—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#4114yes—
184C22×Dic71#4114yes—
185C22×Dic71C2412yes—
186C22×Dic71C2412yes—
187C22×Dic71C2412yes—
188C22×Dic71C2412yes—
189C22×Dic71C2412yes—
190C22×Dic71C2412yes—
191C22×Dic71C2412yes—
192C4⋊Dic71—28no—
193C4⋊Dic71—28no—
194Dic71⋊C4—28no—
195Dic71⋊C4—28no—
196C22⋊Dic71—28no—
197C22⋊Dic71—28no—
198C22⋊Dic71—28no—
199(C2×D71)⋊C4—28no—
200(C2×D71)⋊C4—28no—
201(C2×D71)⋊C4—28no—
202(C2×D71)⋊C4—28no—
203(C2×D71)⋊C4—28no—
204(C2×D71)⋊C4—44no—
205C4×Dic71—28no—
206C4×Dic71—28no—
207C4×Dic71—44no—
208C4×Dic71—44no—
209C24×C71—22no—
210C24×C71—22no—
211C24×C71—22no—
212C24×C71—22no—
213C24×C71—22no—
214C24×C71—22no—
215C24×C71#4114yes—
216C24×C71C2412yes—
217C24×C71C2411yescharacteristic
218C2×Q8×C71—28no—
219C2×Q8×C71—28no—
220C2×Q8×C71—44no—
221C2×Q8×C71—416no—
222C22×C4×C71—22no—
223C22×C4×C71—22no—
224C22×C4×C71—22no—
225C22×C4×C71—22no—
226C22×C4×C71—22no—
227C22×C4×C71—22no—
228C22×C4×C71—22no—
229C22×C4×C71—22no—
230C22×C4×C71—22no—
231C22×C4×C71—22no—
232C22×C4×C71—22no—
233C22×C4×C71—22no—
234C22×C4×C71—22no—
235C22×C4×C71—22no—
236C22×C4×C71—28no—
237C22×C4×C71—28no—
238C22×C4×C71—44no—
239C22×C4×C71—416no—
240C22×C4×C71C2×D414yes—
241C22×C4×C71C2×D414yes—
242C22×C4×C71C2×D414yes—
243C22×C4×C71#4114yes—
244C22×C4×C71C2412yes—
245C22×C4×C71C2412yes—
246C22×C4×C71C2412yes—
247C22×C4×C71C2412yes—
248C22×C4×C71C2412yes—
249C22×C4×C71C2412yes—
250C4⋊C4×C71—28no—
251C4⋊C4×C71—28no—
252C4⋊C4×C71C2×D4116yescomplemented
253C22⋊C4×C71—28no—
254C22⋊C4×C71—28no—
255C23×C71—28no—
256C23×C71—28no—
257C23×C71—28no—
258C23×C71—22no—
259C23×C71—22no—
260C23×C71—22no—
261C23×C71—22no—
262C23×C71—22no—
263C23×C71—22no—
264C23×C71—44no—
265C23×C71—44no—
266C23×C71—44no—
267C23×C71—44no—
268C23×C71C22×D412yes—
269C23×C71C2×#4112yes—
270C23×C71C2×#4112yes—
271C23×C71C2×#4112yes—
272C23×C71C2×#4114yes—
273C23×C71C2×#4112yes—
274C23×C71H(5,𝔽2)12yes—
275C23×C712−1+412yes—
276C23×C71C2511yescharacteristic
277C22×D71—22no—
278C22×D71—22no—
279C22×D71—22no—
280C22×D71—22no—
281C22×D71—22no—
282C22×D71—22no—
283C22×D71—22no—
284C22×D71—44no—
285C22×D71—44no—
286C22×D71—44no—
287C22×D71—44no—
288C22×D71—44no—
289C22×D71—44no—
290C22×D71—44no—
291Q8×C71—416no—
292C2×C4×C71—28no—
293C2×C4×C71—28no—
294C2×C4×C71—28no—
295C2×C4×C71—28no—
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—22no—
310C2×C4×C71—416no—
311C2×C4×C71—44no—
312C2×C4×C71—44no—
313C2×C4×C71C22×D414yes—
314C2×C4×C71C22×D414yes—
315C2×C4×C71C22×D414yes—
316C2×C4×C71C2×#4114yes—
317C22⋊D71—416no—
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—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—44no—
340C2×Dic71—44no—
341C2×Dic71—44no—
342C2×Dic71—44no—
343C2×Dic71—44no—
344C2×Dic71C2×#4114yes—
345C2×Dic71C2×#4114yes—
346C22×C71—24no—
347C22×C71—24no—
348C22×C71—24no—
349C22×C71—416no—
350C22×C71—42no—
351C22×C71—42no—
352C22×C71—42no—
353C22×C71—42no—
354C22×C71#52914yes—
355C22×C71#53214yes—
356C22×C71#53914yes—
357C22×C71#54614yes—
358C22×C71#54814yes—
359C22×C71#55114yes—
360C22×C71#55614yes—
361C22×C71C23×D411yescharacteristic
362C22×C71C22×#4111yescharacteristic
363C22×C71C22×#4111yescharacteristic
364C22×C71C22×#4111yescharacteristic
365C22×C71C22×#4111yescharacteristic
366C22×C71C2×H(5,𝔽2)11yescharacteristic
367C22×C71C2×2−1+411yescharacteristic
368C2×D71—42no—
369C2×D71—42no—
370C2×D71—42no—
371C2×D71—42no—
372C2×D71—42no—
373C2×D71—42no—
374C2×D71—42no—
375C2×D71—88no—
376C4×C71—24no—
377C4×C71—24no—
378C4×C71—24no—
379C4×C71—24no—
380C4×C71—42no—
381C4×C71—42no—
382Dic71—24no—
383Dic71—24no—
384Dic71—42no—
385Dic71—42no—
386Dic71—42no—
387Dic71—42no—
388Dic71—42no—
389C2×#2560—711nomaximal, Sylow
390C2×C71—44no—
391C2×C71#256018yescomplemented
392C2×C71C2×#52911yescharacteristic
393C2×C71C2×#53211yescharacteristic
394C2×C71C2×#53911yescharacteristic
395C2×C71C2×#54611yescharacteristic
396C2×C71C2×#54811yescharacteristic
397C2×C71C2×#55111yescharacteristic
398C2×C71C2×#55611yescharacteristic
399D71—82no—
400C22×#126—711no—
401C22×C22⋊Q8D7111yescharacteristic, complemented
402#2560—7116no—
403C2×#398—711no—
404C2×#397—711no—
405C2×#394—711no—
406C2×#393—711no—
407C2×#391—711no—
408C2×#390—711no—
409C2×#388—711no—
410C2×#388—711no—
411C2×#388—711no—
412C2×#387—711no—
413C2×#386—711no—
414C2×C4×C4⋊C4—711no—
415C2×C4×C22⋊C4—711no—
416C71C2×#256011yescharacteristic, complemented, Sylow
417C23×Q8C2×D7111yescharacteristic
418C23×D4—711no—
419C24×C4C2×D7111yescharacteristic
420C2×#126—718no—
421C2×#126—1428no—
422C2×C22⋊Q8—28no—
423C2×C22⋊Q8C2×D7118yescomplemented
424C22×C4⋊C4—711no—
425C22×C4⋊C4—711no—
426C22×C4⋊C4—711no—
427C22×C4⋊C4—711no—
428C22×C4⋊C4C2×D7111yescharacteristic
429C22×C4⋊C4C2×D7111yescharacteristic
430C22×C4⋊C4C2×D7111yescharacteristic
431C22×C22⋊C4—711no—
432C22×C22⋊C4—711no—
433C22×C22⋊C4—711no—
434C22×C22⋊C4—711no—
435C22×C22⋊C4—711no—
436C22×C22⋊C4—711no—
437C22×C22⋊C4—711no—
438C22×C22⋊C4—711no—
439C22×C22⋊C4—711no—
440C22×C22⋊C4C2×D7111yescharacteristic
441C22×C22⋊C4C2×D7111yescharacteristic
442C22×C42—711no—
443C22×C42—711no—
444C22×C42—711no—
445C22×C42—711no—
446#398—718no—
447#397—718no—
448#394—718no—
449#393—718no—
450#391—718no—
451#390—718no—
452#388—718no—
453#388—718no—
454#388—718no—
455#387—718no—
456#386—718no—
457C4×C4⋊C4—718no—
458C4×C22⋊C4—718no—
459C2×#95—711no—
460C2×#95—711no—
461C2×#95—711no—
462C2×#95—711no—
463C2×#95—711no—
464C2×#95—711no—
465C2×#95—711no—
466C2×#95—711no—
467C2×#95—711no—
468C2×#95—711no—
469C25—711no—
470C25C22×D7111yescharacteristic
471C22×Q8—24no—
472C22×Q8—24no—
473C22×Q8—42no—
474C22×Q8C22×D7114yes—
475C22×D4—2842no—
476C22×D4—714no—
477C22×D4—1424no—
478C22×D4—1424no—
479C23×C4—24no—
480C23×C4—24no—
481C23×C4—42no—
482C23×C4—711no—
483C23×C4—711no—
484C23×C4—711no—
485C23×C4—711no—
486C23×C4—711no—
487C23×C4—711no—
488C23×C4—711no—
489C23×C4C22×D7111yescharacteristic
490C23×C4C22×D7111yescharacteristic
491C23×C4C22×D7114yes—
492C23×C4C22×D7111yescharacteristic
493C23×C4C22×D7111yescharacteristic
494C23×C4C22×D7111yescharacteristic
495C23×C4C22×D7111yescharacteristic
496#126—14232no—
497C22⋊Q8—232no—
498C2×C4⋊C4—24no—
499C2×C4⋊C4—24no—
500C2×C4⋊C4—714no—
501C2×C4⋊C4—714no—
502C2×C4⋊C4—714no—
503C2×C4⋊C4—714no—
504C2×C4⋊C4—1424no—
505C2×C4⋊C4—1424no—
506C2×C4⋊C4—1424no—
507C2×C4⋊C4—1424no—
508C2×C4⋊C4C22⋊D7118yescomplemented
509C2×C4⋊C4C22×D7114yes—
510C2×C4⋊C4C22×D7114yes—
511C2×C4⋊C4C22×D7114yes—
512C2×C22⋊C4—24no—
513C2×C22⋊C4—24no—
514C2×C22⋊C4—2842no—
515C2×C22⋊C4—714no—
516C2×C22⋊C4—714no—
517C2×C22⋊C4—714no—
518C2×C22⋊C4—714no—
519C2×C22⋊C4—714no—
520C2×C22⋊C4—714no—
521C2×C22⋊C4—714no—
522C2×C22⋊C4—714no—
523C2×C22⋊C4—714no—
524C2×C22⋊C4—1424no—
525C2×C22⋊C4—1424no—
526C2×C22⋊C4—1424no—
527C2×C22⋊C4—1424no—
528C2×C22⋊C4—1424no—
529C2×C22⋊C4—1424no—
530C2×C22⋊C4—1424no—
531C2×C22⋊C4—1424no—
532C2×C22⋊C4C22×D7114yes—
533C2×C22⋊C4C22×D7114yes—
534C2×C42—2842no—
535C2×C42—2842no—
536C2×C42—714no—
537C2×C42—714no—
538C2×C42—714no—
539C2×C42—714no—
540C2×C42—1424no—
541C2×C42—1424no—
542#95—714no—
543#95—714no—
544#95—714no—
545#95—714no—
546#95—714no—
547#95—714no—
548#95—714no—
549#95—714no—
550#95—714no—
551#95—714no—
552C24—22no—
553C24—22no—
554C24—22no—
555C24—22no—
556C24—22no—
557C24—22no—
558C24—712no—
559C24—1422no—
560C24—1422no—
561C24—1422no—
562C24—1422no—
563C24—1422no—
564C24—1422no—
565C24—1422no—
566C24#1176586614yes—
567C24C23×D7112yes—
568C24C23×D7111yescharacteristic
569C2×Q8—28no—
570C2×Q8—28no—
571C2×Q8—44no—
572C2×Q8—416no—
573C2×D4—28416no—
574C2×D4—2844no—
575C2×D4—1428no—
576C2×D4—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—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—28no—
592C22×C4—28no—
593C22×C4—44no—
594C22×C4—416no—
595C22×C4—714no—
596C22×C4—714no—
597C22×C4—712no—
598C22×C4—712no—
599C22×C4—712no—
600C22×C4—712no—
601C22×C4—712no—
602C22×C4—712no—
603C22×C4—712no—
604C22×C4—1422no—
605C22×C4—1422no—
606C22×C4—1422no—
607C22×C4—1422no—
608C22×C4—1422no—
609C22×C4—1422no—
610C22×C4—1422no—
611C22×C4—1422no—
612C22×C4—1422no—
613C22×C4—1422no—
614C22×C4—1422no—
615C22×C4—1422no—
616C22×C4—1422no—
617C22×C4—1422no—
618C22×C4—1422no—
619C22×C4—1422no—
620C22×C4—1422no—
621C22×C4—1422no—
622C22×C4—1422no—
623C22×C4C2×C22⋊D7114yes—
624C22×C4C2×C22⋊D7114yes—
625C22×C4C2×C22⋊D7114yes—
626C22×C4#1176586414yes—
627C22×C4C23×D7112yes—
628C22×C4C23×D7112yes—
629C22×C4C23×D7112yes—
630C22×C4C23×D7112yes—
631C22×C4C23×D7112yes—
632C22×C4C23×D7112yes—
633C4⋊C4—28no—
634C4⋊C4—28no—
635C4⋊C4—1428no—
636C4⋊C4—1428no—
637C4⋊C4—1428no—
638C4⋊C4—1428no—
639C4⋊C4C2×C22⋊D71116yescomplemented
640C22⋊C4—28no—
641C22⋊C4—28no—
642C22⋊C4—2844no—
643C22⋊C4—1428no—
644C22⋊C4—1428no—
645C22⋊C4—1428no—
646C22⋊C4—1428no—
647C22⋊C4—1428no—
648C22⋊C4—1428no—
649C22⋊C4—1428no—
650C22⋊C4—1428no—
651C42—2844no—
652C42—2844no—
653C42—1428no—
654C42—1428no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—28no—
662C23—28no—
663C23—28no—
664C23—44no—
665C23—44no—
666C23—44no—
667C23—44no—
668C23—2844no—
669C23—2844no—
670C23—2844no—
671C23—2844no—
672C23—2844no—
673C23—2844no—
674C23—2844no—
675C23—1422no—
676C23—1422no—
677C23—1422no—
678C23—1422no—
679C23—1422no—
680C23—1422no—
681C23—1422no—
682C23C22×C22⋊D7112yes—
683C23#41×D7112yes—
684C23#41×D7112yes—
685C23C2×#1176586412yes—
686C23C2×#1176586614yes—
687C23C2×#1176586612yes—
688C23#1455617312yes—
689C23#1455617612yes—
690C23C24×D7111yescharacteristic
691Q8—416no—
692D4—28416no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—28no—
702C2×C4—28no—
703C2×C4—28no—
704C2×C4—28no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—416no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—2844no—
715C2×C4—2844no—
716C2×C4—2844no—
717C2×C4—2844no—
718C2×C4—2844no—
719C2×C4—714no—
720C2×C4—714no—
721C2×C4—1422no—
722C2×C4—1422no—
723C2×C4—1422no—
724C2×C4—1422no—
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—1422no—
735C2×C4—1422no—
736C2×C4—1422no—
737C2×C4—1422no—
738C2×C4—1422no—
739C2×C4—1422no—
740C2×C4—1428no—
741C2×C4—1428no—
742C2×C4C22×C22⋊D7114yes—
743C2×C4C22×C22⋊D7114yes—
744C2×C4C22×C22⋊D7114yes—
745C2×C4C2×#1176586414yes—
746C22—24no—
747C22—24no—
748C22—24no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—416no—
753C22—42no—
754C22—2842no—
755C22—2842no—
756C22—2842no—
757C22—2842no—
758C22—2842no—
759C22—2842no—
760C22—2842no—
761C22—5688no—
762C22#1798653514yes—
763C22#1798654514yes—
764C22#1798659514yes—
765C22#1798664314yes—
766C22#1798666014yes—
767C22#1798667614yes—
768C22#1798672014yes—
769C22C23×C22⋊D7111yescharacteristic
770C22C2×#41×D7111yescharacteristic
771C22C2×#41×D7111yescharacteristic
772C22C22×#1176586411yescharacteristic
773C22C22×#1176586611yescharacteristic
774C22C2×#1455617311yescharacteristic
775C22C2×#1455617611yescharacteristic
776C4—24no—
777C4—24no—
778C4—24no—
779C4—24no—
780C4—42no—
781C4—42no—
782C4—2842no—
783C4—2842no—
784C4—2842no—
785C4—2842no—
786C4—2842no—
787C4—1424no—
788C4—1424no—
789C2—44no—
790C2—5682no—
791C2#2259348018yesdirect product factor
792C2C2×#1798653511yescharacteristic
793C2C2×#1798654511yescharacteristic
794C2C2×#1798659511yescharacteristic
795C2C2×#1798664311yescharacteristic
796C2C2×#1798666011yescharacteristic
797C2C2×#1798667611yescharacteristic
798C2C2×#1798672011yescharacteristic
subgroupG/H
centerC24C23×D71
commutator, cosocleC23×C71C25
FrattiniC23C24×D71
FittingC22×C22⋊Q8×C71C2
socleC24×C71C24
prime radicalC23×C22⋊D71C22
hypercenterC22×C22⋊Q8D71
hypocenterC71C2×#2560
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×#14556123C2semidirect
2. #22593480C2direct (N × H)
3. C2×#17985932C2semidirect
4. C2×#17985924C2semidirect
6. C2×#17985910C2semidirect
7. C2×#17985906C2semidirect
9. C2×#17985893C2semidirect
10. C2×#17985889C2semidirect
11. C2×#17985889C2semidirect
12. C2×#17985880C2semidirect
14. C2×C4⋊C4×Dic71C2semidirect
15. C2×C4×C22⋊Dic71C2semidirect
16. C22×C22⋊Q8×C71C2semidirect
19. C2×#14556123C22semidirect
37. #17985932C22semidirect
38. #17985924C22semidirect
40. #17985910C22semidirect
41. #17985906C22semidirect
43. #17985893C22semidirect
44. #17985889C22semidirect
45. #17985889C22semidirect
46. #17985880C22semidirect
48. C4⋊C4×Dic71C22semidirect
49. C4×C22⋊Dic71C22semidirect
63. C2×C22⋊Q8×C71C22semidirect
144. C2×C4⋊C4×C71D4semidirect
252. C4⋊C4×C71C2×D4semidirect
391. C2×C71#2560semidirect
401. C22×C22⋊Q8D71semidirect
416. C71C2×#2560semidirect
423. C2×C22⋊Q8C2×D71semidirect
508. C2×C4⋊C4C22⋊D71semidirect
639. C4⋊C4C2×C22⋊D71semidirect
791. C2#22593480direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145561232
#225934802
C2×#179859322
C2×#179859242
C2×#179859152
C2×#179859102
C2×#179859062
C2×#179858992
C2×#179858932
C2×#179858892
C2×#179858802
C2×#179858782
C2×C4⋊C4×Dic712
C2×C4×C22⋊Dic712
C22×C22⋊Q8×C712
C2×#256071