Finite Group Databasebeta

← C2×#22592146 #32164933

Subgroups — C2×#22592146 #32164933

Order 18176.

3830 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556104C211yesmaximal, characteristic, complemented
2C22×C4×C22⋊D71C211yesmaximal, characteristic
3C22×C4⋊C4×D71C211yesmaximal, characteristic, complemented
4#22592146C2116yesmaximal, direct product factor
5C2×#17985935C211yesmaximal, characteristic, complemented
6C2×#17985929C211yesmaximal, characteristic, complemented
7C2×#17985922C211yesmaximal, characteristic, complemented
8C2×#17985918C211yesmaximal, characteristic, complemented
9C2×#17985894C211yesmaximal, characteristic, complemented
10C2×#17985885C211yesmaximal, characteristic, complemented
11C2×#17985875C211yesmaximal, characteristic
12C2×#17985875C211yesmaximal, characteristic
13C2×#17985872C211yesmaximal, characteristic, complemented
14C2×#17985870C211yesmaximal, characteristic, complemented
15C2×#17985870C211yesmaximal, characteristic, complemented
16C22×C22⋊Q8×C71C211yesmaximal, characteristic, complemented
17C23×C22⋊D71C2211yescharacteristic
18C23×C4×D71C2211yescharacteristic
19C23×C4×D71C2211yescharacteristic
20C23×C4×D71C2211yescharacteristic
21C2×#14556104—28no—
22C2×#14556104C2218yescomplemented
23C2×C4×C22⋊D71—28no—
24C2×C4×C22⋊D71C2218yes—
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
34C2×C4⋊C4×D71—28no—
35C2×C4⋊C4×D71C2218yescomplemented
36C22×C22⋊Dic71C2211yescharacteristic
37C22×C22⋊Dic71C2211yescharacteristic
38C22×C22⋊Dic71C2211yescharacteristic
39C22×(C2×D71)⋊C4C2211yescharacteristic
40C22×(C2×D71)⋊C4C2211yescharacteristic
41C22×(C2×D71)⋊C4C2211yescharacteristic
42C22×C4×Dic71C2211yescharacteristic
43#17985935C2218yescomplemented
44#17985929C2218yescomplemented
45#17985922C2218yescomplemented
46#17985918C2218yescomplemented
47#17985894C2218yescomplemented
48#17985885C2218yescomplemented
49#17985875C2218yes—
50#17985875C2218yes—
51#17985872C2218yescomplemented
52#17985870C2218yescomplemented
53#17985870C2218yescomplemented
54C2×C71⋊#95C2211yescharacteristic
55C2×C71⋊#95C2211yescharacteristic
56C2×C71⋊#95C2211yescharacteristic
57C2×C71⋊#95C2211yescharacteristic
58C2×C71⋊#95C2211yescharacteristic
59C2×C71⋊#95C2211yescharacteristic
60C2×C71⋊#95C2211yescharacteristic
61C2×C71⋊#95C2211yescharacteristic
62C23×Q8×C71C2211yescharacteristic
63C24×C4×C71C2211yescharacteristic
64C2×C22⋊Q8×C71—28no—
65C2×C22⋊Q8×C71C2218yescomplemented
66C22×C4⋊C4×C71C2211yescharacteristic
67C22×C4⋊C4×C71C2211yescharacteristic
68C22×C4⋊C4×C71C2211yescharacteristic
69C22×C22⋊C4×C71C2211yescharacteristic
70C22×C22⋊C4×C71C2211yescharacteristic
71C24×D71C2311yescharacteristic
72C22×C22⋊D71—24no—
73C22×C22⋊D71—24no—
74C22×C22⋊D71Q818yescomplemented
75C22×C22⋊D71C2314yes—
76C23×Dic71C2311yescharacteristic
77C23×Dic71C2311yescharacteristic
78C23×Dic71C2311yescharacteristic
79C23×Dic71C2311yescharacteristic
80C23×Dic71C2311yescharacteristic
81C23×Dic71C2311yescharacteristic
82C23×Dic71C2311yescharacteristic
83C22×C4×D71—24no—
84C22×C4×D71—24no—
85C22×C4×D71—24no—
86C22×C4×D71—24no—
87C22×C4×D71—24no—
88C22×C4×D71—24no—
89C22×C4×D71—24no—
90C22×C4×D71—42no—
91C22×C4×D71—42no—
92C22×C4×D71C2314yes—
93C22×C4×D71C2314yes—
94C22×C4×D71C2314yes—
95#14556104—232no—
96C4×C22⋊D71—232no—
97C2×C4⋊Dic71—24no—
98C2×C4⋊Dic71—24no—
99C2×C4⋊Dic71C2314yes—
100C2×C4⋊Dic71C2314yes—
101C2×Dic71⋊C4—24no—
102C2×Dic71⋊C4—24no—
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×Dic71⋊C4C2314yes—
114C2×Dic71⋊C4C2314yes—
115C4⋊C4×D71—232no—
116C2×C22⋊Dic71—24no—
117C2×C22⋊Dic71—24no—
118C2×C22⋊Dic71—42no—
119C2×C22⋊Dic71C2314yes—
120C2×C22⋊Dic71C2314yes—
121C2×C22⋊Dic71C2314yes—
122C2×(C2×D71)⋊C4—24no—
123C2×(C2×D71)⋊C4—24no—
124C2×(C2×D71)⋊C4D418yes—
125C2×(C2×D71)⋊C4C2314yes—
126C2×(C2×D71)⋊C4C2314yes—
127C2×(C2×D71)⋊C4C2314yes—
128C2×C4×Dic71—24no—
129C2×C4×Dic71C2314yes—
130C71⋊#95C2314yes—
131C71⋊#95C2314yes—
132C71⋊#95C2314yes—
133C71⋊#95C2314yes—
134C71⋊#95C2314yes—
135C71⋊#95C2314yes—
136C71⋊#95C2314yes—
137C71⋊#95C2314yes—
138C25×C71C2311yescharacteristic
139C22×Q8×C71—24no—
140C22×Q8×C71—24no—
141C22×Q8×C71—42no—
142C22×Q8×C71C2314yes—
143C23×C4×C71—24no—
144C23×C4×C71—24no—
145C23×C4×C71—42no—
146C23×C4×C71C2311yescharacteristic
147C23×C4×C71C2311yescharacteristic
148C23×C4×C71C2314yes—
149C23×C4×C71C2311yescharacteristic
150C23×C4×C71C2311yescharacteristic
151C23×C4×C71C2311yescharacteristic
152C23×C4×C71C2311yescharacteristic
153C22⋊Q8×C71—232no—
154C2×C4⋊C4×C71—24no—
155C2×C4⋊C4×C71—24no—
156C2×C4⋊C4×C71D418yescomplemented
157C2×C4⋊C4×C71C2314yes—
158C2×C4⋊C4×C71C2314yes—
159C2×C4⋊C4×C71C2314yes—
160C2×C22⋊C4×C71—24no—
161C2×C22⋊C4×C71—24no—
162C2×C22⋊C4×C71C2314yes—
163C2×C22⋊C4×C71C2314yes—
164C23×D71—22no—
165C23×D71—22no—
166C23×D71—22no—
167C23×D71—22no—
168C23×D71C2×D414yes—
169C23×D71C2×Q814yes—
170C23×D71#4114yes—
171C23×D71C2412yes—
172C2×C22⋊D71—232no—
173C2×C22⋊D71—28no—
174C2×C22⋊D71—28no—
175C2×C22⋊D71C2×Q8116yescomplemented
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×Dic71—22no—
193C22×Dic71—22no—
194C22×Dic71C2×D414yes—
195C22×Dic71C2×Q814yes—
196C22×Dic71#4114yes—
197C22×Dic71C2412yes—
198C22×Dic71C2412yes—
199C22×Dic71C2412yes—
200C22×Dic71C2412yes—
201C22×Dic71C2412yes—
202C22×Dic71C2412yes—
203C22×Dic71C2412yes—
204C2×C4×D71—232no—
205C2×C4×D71—28no—
206C2×C4×D71—28no—
207C2×C4×D71—28no—
208C2×C4×D71—28no—
209C2×C4×D71—28no—
210C2×C4×D71—28no—
211C2×C4×D71—28no—
212C2×C4×D71—44no—
213C2×C4×D71—44no—
214C2×C4×D71—416no—
215C2×C4×D71—416no—
216C4⋊Dic71—28no—
217C4⋊Dic71—28no—
218Dic71⋊C4—28no—
219Dic71⋊C4—28no—
220Dic71⋊C4—28no—
221Dic71⋊C4—28no—
222Dic71⋊C4—28no—
223Dic71⋊C4—28no—
224Dic71⋊C4—44no—
225C22⋊Dic71—28no—
226C22⋊Dic71—28no—
227C22⋊Dic71—44no—
228(C2×D71)⋊C4—28no—
229(C2×D71)⋊C4—28no—
230(C2×D71)⋊C4C2×D4116yes—
231C4×Dic71—28no—
232C24×C71—22no—
233C24×C71—22no—
234C24×C71—22no—
235C24×C71—22no—
236C24×C71—22no—
237C24×C71—22no—
238C24×C71C2×Q814yes—
239C24×C71C2412yes—
240C24×C71C2411yescharacteristic
241C2×Q8×C71—28no—
242C2×Q8×C71—28no—
243C2×Q8×C71—44no—
244C2×Q8×C71—416no—
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×C71—22no—
254C22×C4×C71—22no—
255C22×C4×C71—22no—
256C22×C4×C71—22no—
257C22×C4×C71—22no—
258C22×C4×C71—22no—
259C22×C4×C71—28no—
260C22×C4×C71—28no—
261C22×C4×C71—44no—
262C22×C4×C71—416no—
263C22×C4×C71C2×D414yes—
264C22×C4×C71C2×D414yes—
265C22×C4×C71C2×D414yes—
266C22×C4×C71C2×D414yes—
267C22×C4×C71C2412yes—
268C22×C4×C71C2412yes—
269C22×C4×C71C2412yes—
270C22×C4×C71C2412yes—
271C22×C4×C71C2412yes—
272C22×C4×C71C2412yes—
273C4⋊C4×C71—28no—
274C4⋊C4×C71—28no—
275C4⋊C4×C71C2×D4116yescomplemented
276C22⋊C4×C71—28no—
277C22⋊C4×C71—28no—
278C23×C71—28no—
279C23×C71—28no—
280C23×C71—28no—
281C23×C71—22no—
282C23×C71—22no—
283C23×C71—22no—
284C23×C71—22no—
285C23×C71—22no—
286C23×C71—22no—
287C23×C71—44no—
288C23×C71—44no—
289C23×C71—44no—
290C23×C71—44no—
291C23×C71C22×D412yes—
292C23×C71C22×D412yes—
293C23×C71C22×Q814yes—
294C23×C71C22×Q812yes—
295C23×C71C2×#4112yes—
296C23×C71C2×#4112yes—
297C23×C71H(5,𝔽2)12yes—
298C23×C712−1+412yes—
299C23×C71C2511yescharacteristic
300C22×D71—28no—
301C22×D71—28no—
302C22×D71—28no—
303C22×D71—28no—
304C22×D71—28no—
305C22×D71—28no—
306C22×D71—22no—
307C22×D71—22no—
308C22×D71—22no—
309C22×D71—22no—
310C22×D71C22⋊Q8116yescomplemented
311C22×D71C22×D414yes—
312C22×D71C22×Q814yes—
313C22×D71C2×#4114yes—
314Q8×C71—416no—
315C2×C4×C71—28no—
316C2×C4×C71—28no—
317C2×C4×C71—28no—
318C2×C4×C71—28no—
319C2×C4×C71—22no—
320C2×C4×C71—22no—
321C2×C4×C71—22no—
322C2×C4×C71—22no—
323C2×C4×C71—22no—
324C2×C4×C71—22no—
325C2×C4×C71—22no—
326C2×C4×C71—22no—
327C2×C4×C71—22no—
328C2×C4×C71—22no—
329C2×C4×C71—22no—
330C2×C4×C71—22no—
331C2×C4×C71—22no—
332C2×C4×C71—22no—
333C2×C4×C71—416no—
334C2×C4×C71—44no—
335C2×C4×C71—44no—
336C2×C4×C71C22×D414yes—
337C2×C4×C71C22×D414yes—
338C2×C4×C71C22×D414yes—
339C2×C4×C71C22×D414yes—
340C22⋊D71—232no—
341C2×Dic71—28no—
342C2×Dic71—28no—
343C2×Dic71—28no—
344C2×Dic71—22no—
345C2×Dic71—22no—
346C2×Dic71—22no—
347C2×Dic71—22no—
348C2×Dic71—22no—
349C2×Dic71—22no—
350C2×Dic71—22no—
351C2×Dic71—22no—
352C2×Dic71—22no—
353C2×Dic71—22no—
354C2×Dic71—22no—
355C2×Dic71—22no—
356C2×Dic71—22no—
357C2×Dic71—22no—
358C2×Dic71—22no—
359C2×Dic71—22no—
360C2×Dic71—22no—
361C2×Dic71—22no—
362C2×Dic71—44no—
363C2×Dic71—44no—
364C2×Dic71—44no—
365C2×Dic71—44no—
366C2×Dic71C22×D414yes—
367C2×Dic71C22×Q814yes—
368C2×Dic71C2×#4114yes—
369C4×D71—232no—
370C4×D71—416no—
371C4×D71—416no—
372C22×C71—24no—
373C22×C71—24no—
374C22×C71—24no—
375C22×C71—42no—
376C22×C71—42no—
377C22×C71—42no—
378C22×C71—42no—
379C22×C71—416no—
380C22×C71C2×C22⋊Q814yes—
381C22×C71#52514yes—
382C22×C71#53914yes—
383C22×C71D4214yes—
384C22×C71#54714yes—
385C22×C71D4×Q814yes—
386C22×C71#55414yes—
387C22×C71C23×D411yescharacteristic
388C22×C71C23×D411yescharacteristic
389C22×C71C23×Q811yescharacteristic
390C22×C71C22×#4111yescharacteristic
391C22×C71C22×#4111yescharacteristic
392C22×C71C2×H(5,𝔽2)11yescharacteristic
393C22×C71C2×2−1+411yescharacteristic
394C2×D71—24no—
395C2×D71—24no—
396C2×D71—24no—
397C2×D71—24no—
398C2×D71—24no—
399C2×D71—24no—
400C2×D71—232no—
401C2×D71C2×C22⋊Q818yescomplemented
402C4×C71—24no—
403C4×C71—24no—
404C4×C71—24no—
405C4×C71—24no—
406C4×C71—42no—
407C4×C71—42no—
408Dic71—24no—
409Dic71—24no—
410Dic71—24no—
411Dic71—42no—
412Dic71—42no—
413Dic71—42no—
414Dic71—42no—
415C2×#2449—711nomaximal, Sylow
416C2×C71—44no—
417C2×C71#244918yescomplemented
418C2×C71C22×C22⋊Q811yescharacteristic
419C2×C71C2×#52511yescharacteristic
420C2×C71C2×#53911yescharacteristic
421C2×C71C2×D4211yescharacteristic
422C2×C71C2×#54711yescharacteristic
423C2×C71C2×D4×Q811yescharacteristic
424C2×C71C2×#55411yescharacteristic
425D71—28no—
426C22×C22⋊Q8—711no—
427C22×C22⋊Q8D7111yescharacteristic, complemented
428C22×C4×D4—711no—
429C23×C4⋊C4—711no—
430#2449—7116no—
431C2×#399—711no—
432C2×#398—711no—
433C2×#396—711no—
434C2×#395—711no—
435C2×#389—711no—
436C2×#387—711no—
437C2×#386—711no—
438C2×#386—711no—
439C2×#385—711no—
440C2×#385—711no—
441C2×#385—711no—
442C71C2×#244911yescharacteristic, complemented, Sylow
443C23×Q8C2×D7111yescharacteristic
444C23×D4—711no—
445C24×C4—711no—
446C24×C4—711no—
447C24×C4—711no—
448C24×C4C2×D7111yescharacteristic
449C2×C22⋊Q8—28no—
450C2×C22⋊Q8—718no—
451C2×C22⋊Q8—1428no—
452C2×C22⋊Q8C2×D7118yescomplemented
453C2×C4×D4—718no—
454C2×C4×D4—1428no—
455C22×C4⋊C4—711no—
456C22×C4⋊C4—711no—
457C22×C4⋊C4—711no—
458C22×C4⋊C4—711no—
459C22×C4⋊C4—711no—
460C22×C4⋊C4—711no—
461C22×C4⋊C4—711no—
462C22×C4⋊C4—711no—
463C22×C4⋊C4—711no—
464C22×C4⋊C4—718no—
465C22×C4⋊C4—1428no—
466C22×C4⋊C4C2×D7111yescharacteristic
467C22×C4⋊C4C2×D7111yescharacteristic
468C22×C4⋊C4C2×D7111yescharacteristic
469C22×C22⋊C4—711no—
470C22×C22⋊C4—711no—
471C22×C22⋊C4—711no—
472C22×C22⋊C4—711no—
473C22×C22⋊C4—711no—
474C22×C22⋊C4—711no—
475C22×C22⋊C4C2×D7111yescharacteristic
476C22×C22⋊C4C2×D7111yescharacteristic
477C22×C42—711no—
478#399—718no—
479#398—718no—
480#396—718no—
481#395—718no—
482#389—718no—
483#387—718no—
484#386—718no—
485#386—718no—
486#385—718no—
487#385—718no—
488#385—718no—
489C2×#95—711no—
490C2×#95—711no—
491C2×#95—711no—
492C2×#95—711no—
493C2×#95—711no—
494C2×#95—711no—
495C2×#95—711no—
496C2×#95—711no—
497C25—711no—
498C25C22×D7111yescharacteristic
499C22×Q8—24no—
500C22×Q8—24no—
501C22×Q8—42no—
502C22×Q8C22×D7114yes—
503C22×D4—718no—
504C22×D4—714no—
505C22×D4—1424no—
506C22×D4—1424no—
507C23×C4—24no—
508C23×C4—24no—
509C23×C4—42no—
510C23×C4—2842no—
511C23×C4—2842no—
512C23×C4—714no—
513C23×C4—714no—
514C23×C4—711no—
515C23×C4—711no—
516C23×C4—711no—
517C23×C4—711no—
518C23×C4—711no—
519C23×C4—711no—
520C23×C4—711no—
521C23×C4—714no—
522C23×C4—1424no—
523C23×C4—1424no—
524C23×C4—1424no—
525C23×C4—1424no—
526C23×C4—1424no—
527C23×C4—1424no—
528C23×C4—1424no—
529C23×C4C22×D7111yescharacteristic
530C23×C4C22×D7111yescharacteristic
531C23×C4C22×D7114yes—
532C23×C4C22×D7111yescharacteristic
533C23×C4C22×D7111yescharacteristic
534C23×C4C22×D7111yescharacteristic
535C23×C4C22×D7111yescharacteristic
536C22⋊Q8—232no—
537C22⋊Q8—14232no—
538C4×D4—14232no—
539C2×C4⋊C4—24no—
540C2×C4⋊C4—24no—
541C2×C4⋊C4—2842no—
542C2×C4⋊C4—714no—
543C2×C4⋊C4—714no—
544C2×C4⋊C4—714no—
545C2×C4⋊C4—714no—
546C2×C4⋊C4—714no—
547C2×C4⋊C4—714no—
548C2×C4⋊C4—714no—
549C2×C4⋊C4—714no—
550C2×C4⋊C4—714no—
551C2×C4⋊C4—1424no—
552C2×C4⋊C4—1424no—
553C2×C4⋊C4—1424no—
554C2×C4⋊C4—1424no—
555C2×C4⋊C4—1424no—
556C2×C4⋊C4—1424no—
557C2×C4⋊C4—1424no—
558C2×C4⋊C4—1424no—
559C2×C4⋊C4—14232no—
560C2×C4⋊C4C22⋊D7118yescomplemented
561C2×C4⋊C4C22×D7114yes—
562C2×C4⋊C4C22×D7114yes—
563C2×C4⋊C4C22×D7114yes—
564C2×C22⋊C4—24no—
565C2×C22⋊C4—24no—
566C2×C22⋊C4—2842no—
567C2×C22⋊C4—714no—
568C2×C22⋊C4—718no—
569C2×C22⋊C4—714no—
570C2×C22⋊C4—714no—
571C2×C22⋊C4—714no—
572C2×C22⋊C4—714no—
573C2×C22⋊C4—714no—
574C2×C22⋊C4—1424no—
575C2×C22⋊C4—1424no—
576C2×C22⋊C4—1424no—
577C2×C22⋊C4—1424no—
578C2×C22⋊C4C22×D7114yes—
579C2×C22⋊C4C22×D7114yes—
580C2×C42—714no—
581C2×C42—1424no—
582#95—714no—
583#95—714no—
584#95—714no—
585#95—714no—
586#95—714no—
587#95—714no—
588#95—714no—
589#95—714no—
590C24—22no—
591C24—22no—
592C24—22no—
593C24—22no—
594C24—22no—
595C24—22no—
596C24—714no—
597C24—714no—
598C24—714no—
599C24—712no—
600C24—1422no—
601C24—1422no—
602C24—1422no—
603C24—1422no—
604C24Q8×D7114yes—
605C24C23×D7112yes—
606C24C23×D7111yescharacteristic
607C2×Q8—28no—
608C2×Q8—28no—
609C2×Q8—44no—
610C2×Q8—416no—
611C2×D4—7116no—
612C2×D4—1428no—
613C2×D4—1428no—
614C2×D4—14232no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—28no—
630C22×C4—28no—
631C22×C4—44no—
632C22×C4—416no—
633C22×C4—28416no—
634C22×C4—28416no—
635C22×C4—2844no—
636C22×C4—2844no—
637C22×C4—714no—
638C22×C4—714no—
639C22×C4—714no—
640C22×C4—712no—
641C22×C4—712no—
642C22×C4—712no—
643C22×C4—712no—
644C22×C4—712no—
645C22×C4—712no—
646C22×C4—712no—
647C22×C4—1428no—
648C22×C4—1428no—
649C22×C4—1428no—
650C22×C4—1428no—
651C22×C4—14232no—
652C22×C4—1422no—
653C22×C4—1422no—
654C22×C4—1422no—
655C22×C4—1422no—
656C22×C4—1422no—
657C22×C4—1422no—
658C22×C4—1422no—
659C22×C4—1422no—
660C22×C4—1422no—
661C22×C4—1422no—
662C22×C4—1422no—
663C22×C4—1422no—
664C22×C4—1428no—
665C22×C4—1428no—
666C22×C4—1422no—
667C22×C4—1422no—
668C22×C4—1422no—
669C22×C4—1422no—
670C22×C4—1422no—
671C22×C4—1422no—
672C22×C4—1428no—
673C22×C4D4×D7114yes—
674C22×C4C2×C22⋊D7114yes—
675C22×C4C2×C22⋊D7114yes—
676C22×C4C2×C22⋊D7114yes—
677C22×C4C23×D7112yes—
678C22×C4C23×D7112yes—
679C22×C4C23×D7112yes—
680C22×C4C23×D7112yes—
681C22×C4C23×D7112yes—
682C22×C4C23×D7112yes—
683C4⋊C4—28no—
684C4⋊C4—28no—
685C4⋊C4—2844no—
686C4⋊C4—1428no—
687C4⋊C4—1428no—
688C4⋊C4—1428no—
689C4⋊C4—1428no—
690C4⋊C4—1428no—
691C4⋊C4—1428no—
692C4⋊C4—1428no—
693C4⋊C4—1428no—
694C4⋊C4C2×C22⋊D71116yescomplemented
695C22⋊C4—28no—
696C22⋊C4—28no—
697C22⋊C4—2844no—
698C22⋊C4—7116no—
699C22⋊C4—1428no—
700C22⋊C4—1428no—
701C22⋊C4—1428no—
702C22⋊C4—1428no—
703C42—1428no—
704C23—22no—
705C23—22no—
706C23—22no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—28no—
711C23—28no—
712C23—28no—
713C23—44no—
714C23—44no—
715C23—44no—
716C23—44no—
717C23—714no—
718C23—714no—
719C23—714no—
720C23—7116no—
721C23—1422no—
722C23—1422no—
723C23—1422no—
724C23—1422no—
725C23—1428no—
726C23—1428no—
727C23—1428no—
728C23—1428no—
729C23—1428no—
730C23—1428no—
731C23C2×D4×D7112yes—
732C23C22×C22⋊D7112yes—
733C23C2×Q8×D7114yes—
734C23C2×Q8×D7112yes—
735C23#41×D7112yes—
736C23#41×D7112yes—
737C23#1455617312yes—
738C23#1455617612yes—
739C23C24×D7111yescharacteristic
740Q8—416no—
741D4—14232no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—28no—
751C2×C4—28no—
752C2×C4—28no—
753C2×C4—28no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—416no—
761C2×C4—44no—
762C2×C4—44no—
763C2×C4—28416no—
764C2×C4—28416no—
765C2×C4—2844no—
766C2×C4—2844no—
767C2×C4—2844no—
768C2×C4—2844no—
769C2×C4—714no—
770C2×C4—714no—
771C2×C4—714no—
772C2×C4—14232no—
773C2×C4—1422no—
774C2×C4—1422no—
775C2×C4—1422no—
776C2×C4—1422no—
777C2×C4—1422no—
778C2×C4—1422no—
779C2×C4—1422no—
780C2×C4—1422no—
781C2×C4—1422no—
782C2×C4—1422no—
783C2×C4—1422no—
784C2×C4—1422no—
785C2×C4—1422no—
786C2×C4—1422no—
787C2×C4—1422no—
788C2×C4—1422no—
789C2×C4—1422no—
790C2×C4—1422no—
791C2×C4—1428no—
792C2×C4—1428no—
793C2×C4—1428no—
794C2×C4C2×D4×D7114yes—
795C2×C4C22×C22⋊D7114yes—
796C2×C4C22×C22⋊D7114yes—
797C2×C4C22×C22⋊D7114yes—
798C22—24no—
799C22—24no—
800C22—24no—
801C22—42no—
802C22—42no—
803C22—42no—
804C22—416no—
805C22—42no—
806C22—718no—
807C22—1424no—
808C22—1424no—
809C22—1424no—
810C22—1424no—
811C22—1424no—
812C22—14232no—
813C22—1424no—
814C22C22⋊Q8×D7114yes—
815C22#1798650614yes—
816C22#1798659514yes—
817C22D4×C22⋊D7114yes—
818C22#1798665114yes—
819C22Q8×C22⋊D7114yes—
820C22#1798670314yes—
821C22C22×D4×D7111yescharacteristic
822C22C23×C22⋊D7111yescharacteristic
823C22C22×Q8×D7111yescharacteristic
824C22C2×#41×D7111yescharacteristic
825C22C2×#41×D7111yescharacteristic
826C22C2×#1455617311yescharacteristic
827C22C2×#1455617611yescharacteristic
828C4—24no—
829C4—24no—
830C4—24no—
831C4—24no—
832C4—42no—
833C4—42no—
834C4—2842no—
835C4—2842no—
836C4—2842no—
837C4—2842no—
838C4—1424no—
839C4—1424no—
840C4—1424no—
841C2—44no—
842C2—1428no—
843C2#2259214618yesdirect product factor
844C2C2×C22⋊Q8×D7111yescharacteristic
845C2C2×#1798650611yescharacteristic
846C2C2×#1798659511yescharacteristic
847C2C2×D4×C22⋊D7111yescharacteristic
848C2C2×#1798665111yescharacteristic
849C2C2×Q8×C22⋊D7111yescharacteristic
850C2C2×#1798670311yescharacteristic
subgroupG/H
centerC24C23×D71
commutator, cosocleC23×C71C25
FrattiniC23C24×D71
FittingC22×C22⋊Q8×C71C2
socleC24×C71C24
prime radicalC23×C22⋊D71C22
hypercenterC22×C22⋊Q8D71
hypocenterC71C2×#2449
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×#14556104C2semidirect
3. C22×C4⋊C4×D71C2semidirect
4. #22592146C2direct (N × H)
5. C2×#17985935C2semidirect
6. C2×#17985929C2semidirect
7. C2×#17985922C2semidirect
8. C2×#17985918C2semidirect
9. C2×#17985894C2semidirect
10. C2×#17985885C2semidirect
13. C2×#17985872C2semidirect
14. C2×#17985870C2semidirect
15. C2×#17985870C2semidirect
16. C22×C22⋊Q8×C71C2semidirect
22. C2×#14556104C22semidirect
35. C2×C4⋊C4×D71C22semidirect
43. #17985935C22semidirect
44. #17985929C22semidirect
45. #17985922C22semidirect
46. #17985918C22semidirect
47. #17985894C22semidirect
48. #17985885C22semidirect
51. #17985872C22semidirect
52. #17985870C22semidirect
53. #17985870C22semidirect
65. C2×C22⋊Q8×C71C22semidirect
74. C22×C22⋊D71Q8semidirect
156. C2×C4⋊C4×C71D4semidirect
175. C2×C22⋊D71C2×Q8semidirect
275. C4⋊C4×C71C2×D4semidirect
310. C22×D71C22⋊Q8semidirect
401. C2×D71C2×C22⋊Q8semidirect
417. C2×C71#2449semidirect
427. C22×C22⋊Q8D71semidirect
442. C71C2×#2449semidirect
452. C2×C22⋊Q8C2×D71semidirect
560. C2×C4⋊C4C22⋊D71semidirect
694. C4⋊C4C2×C22⋊D71semidirect
843. C2#22592146direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145561042
C22×C4×C22⋊D712
C22×C4⋊C4×D712
#225921462
C2×#179859352
C2×#179859292
C2×#179859222
C2×#179859182
C2×#179858942
C2×#179858852
C2×#179858752
C2×#179858722
C2×#179858702
C22×C22⋊Q8×C712
C2×#244971