Finite Group Databasebeta

← C2×#22593348 #32167491

Subgroups — C2×#22593348 #32167491

Order 18176.

3094 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556105C211yesmaximal, characteristic
2#22593348C2116yesmaximal, direct product factor
3C2×#17985930C211yesmaximal, characteristic, complemented
4C2×#17985929C211yesmaximal, characteristic, complemented
5C2×#17985919C211yesmaximal, characteristic, complemented
6C2×#17985918C211yesmaximal, characteristic, complemented
7C2×#17985906C211yesmaximal, characteristic, complemented
8C2×#17985904C211yesmaximal, characteristic, complemented
9C2×#17985894C211yesmaximal, characteristic, complemented
10C2×#17985894C211yesmaximal, characteristic, complemented
11C2×#17985872C211yesmaximal, characteristic
12C2×#17985871C211yesmaximal, characteristic
13C2×#17985857C211yesmaximal, characteristic
14C2×C22⋊C4×Dic71C211yesmaximal, characteristic
15C22×C71⋊#95C211yesmaximal, characteristic
16C22×C22⋊Q8×C71C211yesmaximal, characteristic
17C23×Dic142C2211yescharacteristic
18C24×Dic71C2211yescharacteristic
19C24×Dic71C2211yescharacteristic
20C2×#14556105—28no—
21C2×#14556105C2218yes—
22C22×C4⋊Dic71C2211yescharacteristic
23C22×Dic71⋊C4C2211yescharacteristic
24C22×Dic71⋊C4C2211yescharacteristic
25C22×Dic71⋊C4C2211yescharacteristic
26C22×Dic71⋊C4C2211yescharacteristic
27C22×Dic71⋊C4C2211yescharacteristic
28C22×Dic71⋊C4C2211yescharacteristic
29C22×Dic71⋊C4C2211yescharacteristic
30C22×Dic71⋊C4C2211yescharacteristic
31C22×C22⋊Dic71C2211yescharacteristic
32C22×C22⋊Dic71C2211yescharacteristic
33C22×C4×Dic71C2211yescharacteristic
34C22×C4×Dic71C2211yescharacteristic
35#17985930C2218yescomplemented
36#17985929C2218yescomplemented
37#17985919C2218yescomplemented
38#17985918C2218yescomplemented
39#17985906C2218yescomplemented
40#17985904C2218yescomplemented
41#17985894C2218yescomplemented
42#17985894C2218yescomplemented
43#17985872C2218yes—
44#17985871C2218yes—
45#17985857C2218yes—
46C22⋊C4×Dic71C2218yes—
47C2×C71⋊#95C2211yescharacteristic
48C2×C71⋊#95C2211yescharacteristic
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⋊#95C2218yes—
58C2×C71⋊#95C2211yescharacteristic
59C2×C71⋊#95C2211yescharacteristic
60C23×Q8×C71C2211yescharacteristic
61C24×C4×C71C2211yescharacteristic
62C2×C22⋊Q8×C71—28no—
63C2×C22⋊Q8×C71C2218yes—
64C22×C4⋊C4×C71C2211yescharacteristic
65C22×C4⋊C4×C71C2211yescharacteristic
66C22×C4⋊C4×C71C2211yescharacteristic
67C22×C22⋊C4×C71C2211yescharacteristic
68C22×C22⋊C4×C71C2211yescharacteristic
69C22×Dic142—24no—
70C22×Dic142—24no—
71C22×Dic142—42no—
72C22×Dic142C2314yes—
73C23×Dic71—24no—
74C23×Dic71—24no—
75C23×Dic71—42no—
76C23×Dic71—42no—
77C23×Dic71—42no—
78C23×Dic71Q818yescomplemented
79C23×Dic71C2311yescharacteristic
80C23×Dic71C2311yescharacteristic
81C23×Dic71C2311yescharacteristic
82C23×Dic71C2314yes—
83C23×Dic71C2311yescharacteristic
84C23×Dic71C2311yescharacteristic
85C23×Dic71C2311yescharacteristic
86C23×Dic71C2311yescharacteristic
87C23×Dic71C2311yescharacteristic
88C23×Dic71C2314yes—
89#14556105—232no—
90C2×C4⋊Dic71—24no—
91C2×C4⋊Dic71C2314yes—
92C2×Dic71⋊C4—24no—
93C2×Dic71⋊C4—24no—
94C2×Dic71⋊C4—24no—
95C2×Dic71⋊C4—24no—
96C2×Dic71⋊C4—42no—
97C2×Dic71⋊C4—42no—
98C2×Dic71⋊C4—42no—
99C2×Dic71⋊C4—42no—
100C2×Dic71⋊C4C2314yes—
101C2×Dic71⋊C4C2314yes—
102C2×Dic71⋊C4C2314yes—
103C2×Dic71⋊C4C2314yes—
104C2×Dic71⋊C4C2314yes—
105C2×Dic71⋊C4C2314yes—
106C2×Dic71⋊C4C2314yes—
107C2×Dic71⋊C4C2314yes—
108C2×C22⋊Dic71—24no—
109C2×C22⋊Dic71Q818yescomplemented
110C2×C22⋊Dic71C2314yes—
111C2×C22⋊Dic71C2314yes—
112C2×C4×Dic71—42no—
113C2×C4×Dic71—42no—
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—
126C71⋊#95C2314yes—
127C71⋊#95C2314yes—
128C25×C71C2311yescharacteristic
129C22×Q8×C71—24no—
130C22×Q8×C71—24no—
131C22×Q8×C71—42no—
132C22×Q8×C71C2314yes—
133C23×C4×C71—24no—
134C23×C4×C71—24no—
135C23×C4×C71—42no—
136C23×C4×C71C2311yescharacteristic
137C23×C4×C71C2311yescharacteristic
138C23×C4×C71C2311yescharacteristic
139C23×C4×C71C2314yes—
140C23×C4×C71C2311yescharacteristic
141C23×C4×C71C2311yescharacteristic
142C23×C4×C71C2311yescharacteristic
143C22⋊Q8×C71—232no—
144C2×C4⋊C4×C71—24no—
145C2×C4⋊C4×C71—24no—
146C2×C4⋊C4×C71—24no—
147C2×C4⋊C4×C71C2314yes—
148C2×C4⋊C4×C71C2314yes—
149C2×C4⋊C4×C71C2314yes—
150C2×C22⋊C4×C71—24no—
151C2×C22⋊C4×C71D418yes—
152C2×C22⋊C4×C71C2314yes—
153C2×C22⋊C4×C71C2314yes—
154C2×Dic142—28no—
155C2×Dic142—28no—
156C2×Dic142—44no—
157C2×Dic142—416no—
158C22×Dic71—22no—
159C22×Dic71—22no—
160C22×Dic71—22no—
161C22×Dic71—22no—
162C22×Dic71—22no—
163C22×Dic71—22no—
164C22×Dic71—22no—
165C22×Dic71—22no—
166C22×Dic71—22no—
167C22×Dic71—22no—
168C22×Dic71—22no—
169C22×Dic71—28no—
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—28no—
179C22×Dic71—416no—
180C22×Dic71—44no—
181C22×Dic71—44no—
182C22×Dic71—44no—
183C22×Dic71—416no—
184C22×Dic71C2×Q814yes—
185C22×Dic71C2×Q814yes—
186C22×Dic71C2×Q814yes—
187C22×Dic71C2×Q814yes—
188C22×Dic71C2×Q8116yescomplemented
189C22×Dic71#4114yes—
190C22×Dic71C2412yes—
191C22×Dic71C2412yes—
192C22×Dic71C2412yes—
193C22×Dic71C2412yes—
194C22×Dic71C2412yes—
195C22×Dic71C2412yes—
196C22×Dic71C2412yes—
197C22×Dic71C2412yes—
198C4⋊Dic71—28no—
199Dic71⋊C4—28no—
200Dic71⋊C4—28no—
201Dic71⋊C4—28no—
202Dic71⋊C4—28no—
203Dic71⋊C4—44no—
204Dic71⋊C4—44no—
205Dic71⋊C4—44no—
206Dic71⋊C4—44no—
207C22⋊Dic71—28no—
208C22⋊Dic71C2×Q8116yescomplemented
209C4×Dic71—44no—
210C4×Dic71—44no—
211C24×C71—22no—
212C24×C71—22no—
213C24×C71—22no—
214C24×C71—22no—
215C24×C71C2×D414yes—
216C24×C71C2×Q814yes—
217C24×C71C2×Q814yes—
218C24×C71C2412yes—
219C24×C71C2411yescharacteristic
220C2×Q8×C71—28no—
221C2×Q8×C71—28no—
222C2×Q8×C71—44no—
223C2×Q8×C71—416no—
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—28no—
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—28no—
241C22×C4×C71—44no—
242C22×C4×C71—416no—
243C22×C4×C71C2×D414yes—
244C22×C4×C71C2×D414yes—
245C22×C4×C71#4114yes—
246C22×C4×C71C2412yes—
247C22×C4×C71C2412yes—
248C22×C4×C71C2412yes—
249C22×C4×C71C2412yes—
250C22×C4×C71C2412yes—
251C22×C4×C71C2412yes—
252C4⋊C4×C71—28no—
253C4⋊C4×C71—28no—
254C4⋊C4×C71—28no—
255C22⋊C4×C71—28no—
256C22⋊C4×C71C2×D4116yes—
257C23×C71—28no—
258C23×C71—28no—
259C23×C71—28no—
260C23×C71—28no—
261C23×C71—28no—
262C23×C71—28no—
263C23×C71—22no—
264C23×C71—22no—
265C23×C71—22no—
266C23×C71—22no—
267C23×C71C4⋊Q8116yes—
268C23×C71C22×D414yes—
269C23×C71C22×D412yes—
270C23×C71C22×Q814yes—
271C23×C71C22×Q814yes—
272C23×C71C22×Q812yes—
273C23×C71C22×Q812yes—
274C23×C71C2×#4112yes—
275C23×C71C2×#4112yes—
276C23×C71H(5,𝔽2)12yes—
277C23×C71H(5,𝔽2)12yes—
278C23×C71C2511yescharacteristic
279Q8×C71—416no—
280C2×C4×C71—28no—
281C2×C4×C71—28no—
282C2×C4×C71—28no—
283C2×C4×C71—22no—
284C2×C4×C71—22no—
285C2×C4×C71—22no—
286C2×C4×C71—22no—
287C2×C4×C71—22no—
288C2×C4×C71—22no—
289C2×C4×C71—22no—
290C2×C4×C71—22no—
291C2×C4×C71—22no—
292C2×C4×C71—22no—
293C2×C4×C71—22no—
294C2×C4×C71—22no—
295C2×C4×C71—22no—
296C2×C4×C71—22no—
297C2×C4×C71—22no—
298C2×C4×C71—416no—
299C2×C4×C71—44no—
300C2×C4×C71—44no—
301C2×C4×C71—44no—
302C2×C4×C71C22×D414yes—
303C2×C4×C71C22×D414yes—
304C2×C4×C71C2×#4114yes—
305C2×Dic71—28no—
306C2×Dic71—28no—
307C2×Dic71—28no—
308C2×Dic71—28no—
309C2×Dic71—28no—
310C2×Dic71—22no—
311C2×Dic71—22no—
312C2×Dic71—22no—
313C2×Dic71—22no—
314C2×Dic71—22no—
315C2×Dic71—22no—
316C2×Dic71—22no—
317C2×Dic71—22no—
318C2×Dic71—22no—
319C2×Dic71—22no—
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—416no—
330C2×Dic71—416no—
331C2×Dic71—44no—
332C2×Dic71—44no—
333C2×Dic71—44no—
334C2×Dic71C22×Q814yes—
335C2×Dic71C22×Q814yes—
336C2×Dic71C22×Q814yes—
337C2×Dic71C22×Q814yes—
338C2×Dic71C2×#4114yes—
339Dic142—416no—
340C22×C71—24no—
341C22×C71—24no—
342C22×C71—24no—
343C22×C71—24no—
344C22×C71—24no—
345C22×C71—24no—
346C22×C71—232no—
347C22×C71C2×C4⋊Q818yes—
348C22×C71C2×C4⋊Q814yes—
349C22×C71#53314yes—
350C22×C71#54314yes—
351C22×C71#54614yes—
352C22×C71#54614yes—
353C22×C71#55414yes—
354C22×C71#55414yes—
355C22×C71C23×D411yescharacteristic
356C22×C71C23×Q811yescharacteristic
357C22×C71C23×Q811yescharacteristic
358C22×C71C22×#4111yescharacteristic
359C22×C71C22×#4111yescharacteristic
360C22×C71C2×H(5,𝔽2)11yescharacteristic
361C22×C71C2×H(5,𝔽2)11yescharacteristic
362C4×C71—24no—
363C4×C71—24no—
364C4×C71—24no—
365C4×C71—42no—
366C4×C71—42no—
367C4×C71—42no—
368Dic71—24no—
369Dic71—24no—
370Dic71—24no—
371Dic71—24no—
372Dic71—24no—
373Dic71—42no—
374Dic71—42no—
375Dic71—42no—
376C2×#2549—711nomaximal, Sylow
377C2×C71—28no—
378C2×C71#254918yescomplemented
379C2×C71C22×C4⋊Q811yescharacteristic
380C2×C71C2×#53311yescharacteristic
381C2×C71C2×#54311yescharacteristic
382C2×C71C2×#54611yescharacteristic
383C2×C71C2×#54611yescharacteristic
384C2×C71C2×#55411yescharacteristic
385C2×C71C2×#55411yescharacteristic
386C22×C22⋊Q8—711no—
387C22×C22⋊Q8D7111yescharacteristic
388#2549—7116no—
389C2×#398—711no—
390C2×#398—711no—
391C2×#395—711no—
392C2×#395—711no—
393C2×#391—711no—
394C2×#391—711no—
395C2×#389—711no—
396C2×#389—711no—
397C2×#385—711no—
398C2×#385—711no—
399C2×#380—711no—
400C2×C4×C22⋊C4—711no—
401C22×#95—711no—
402C71C2×#254911yescharacteristic, complemented, Sylow
403C23×Q8—711no—
404C23×Q8C2×D7111yescharacteristic
405C24×C4—711no—
406C24×C4—711no—
407C24×C4C2×D7111yescharacteristic
408C2×C22⋊Q8—28no—
409C2×C22⋊Q8—718no—
410C2×C22⋊Q8—1428no—
411C2×C22⋊Q8C2×D7118yes—
412C22×C4⋊C4—711no—
413C22×C4⋊C4—711no—
414C22×C4⋊C4—711no—
415C22×C4⋊C4—711no—
416C22×C4⋊C4—711no—
417C22×C4⋊C4—711no—
418C22×C4⋊C4—711no—
419C22×C4⋊C4—711no—
420C22×C4⋊C4—711no—
421C22×C4⋊C4C2×D7111yescharacteristic
422C22×C4⋊C4C2×D7111yescharacteristic
423C22×C4⋊C4C2×D7111yescharacteristic
424C22×C22⋊C4—711no—
425C22×C22⋊C4—711no—
426C22×C22⋊C4C2×D7111yescharacteristic
427C22×C22⋊C4C2×D7111yescharacteristic
428C22×C42—711no—
429C22×C42—711no—
430#398—718no—
431#398—718no—
432#395—718no—
433#395—718no—
434#391—718no—
435#391—718no—
436#389—718no—
437#389—718no—
438#385—718no—
439#385—718no—
440#380—718no—
441C4×C22⋊C4—718no—
442C2×#95—711no—
443C2×#95—711no—
444C2×#95—711no—
445C2×#95—711no—
446C2×#95—711no—
447C2×#95—711no—
448C2×#95—711no—
449C2×#95—711no—
450C2×#95—711no—
451C2×#95—711no—
452C2×#95—718no—
453C2×#95—711no—
454C2×#95—711no—
455C25C22×D7111yescharacteristic
456C22×Q8—24no—
457C22×Q8—24no—
458C22×Q8—42no—
459C22×Q8—2842no—
460C22×Q8—714no—
461C22×Q8—1424no—
462C22×Q8—1424no—
463C22×Q8C22×D7114yes—
464C23×C4—24no—
465C23×C4—24no—
466C23×C4—42no—
467C23×C4—2842no—
468C23×C4—2842no—
469C23×C4—2842no—
470C23×C4—718no—
471C23×C4—714no—
472C23×C4—714no—
473C23×C4—711no—
474C23×C4—711no—
475C23×C4—711no—
476C23×C4—711no—
477C23×C4—711no—
478C23×C4—711no—
479C23×C4—711no—
480C23×C4—711no—
481C23×C4—1424no—
482C23×C4—1424no—
483C23×C4C22×D7111yescharacteristic
484C23×C4C22×D7111yescharacteristic
485C23×C4C22×D7111yescharacteristic
486C23×C4C22×D7114yes—
487C23×C4C22×D7111yescharacteristic
488C23×C4C22×D7111yescharacteristic
489C23×C4C22×D7111yescharacteristic
490C22⋊Q8—232no—
491C22⋊Q8—14232no—
492C2×C4⋊C4—24no—
493C2×C4⋊C4—24no—
494C2×C4⋊C4—24no—
495C2×C4⋊C4—2842no—
496C2×C4⋊C4—2842no—
497C2×C4⋊C4—2842no—
498C2×C4⋊C4—2842no—
499C2×C4⋊C4—714no—
500C2×C4⋊C4—714no—
501C2×C4⋊C4—714no—
502C2×C4⋊C4—714no—
503C2×C4⋊C4—714no—
504C2×C4⋊C4—714no—
505C2×C4⋊C4—714no—
506C2×C4⋊C4—714no—
507C2×C4⋊C4—714no—
508C2×C4⋊C4—1424no—
509C2×C4⋊C4—1424no—
510C2×C4⋊C4—1424no—
511C2×C4⋊C4—1424no—
512C2×C4⋊C4—1424no—
513C2×C4⋊C4C22×D7114yes—
514C2×C4⋊C4C22×D7114yes—
515C2×C4⋊C4C22×D7114yes—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—718no—
518C2×C22⋊C4—714no—
519C2×C22⋊C4—714no—
520C2×C22⋊C4—1424no—
521C2×C22⋊C4C22⋊D7118yes—
522C2×C22⋊C4C22×D7114yes—
523C2×C22⋊C4C22×D7114yes—
524C2×C42—2842no—
525C2×C42—2842no—
526C2×C42—714no—
527C2×C42—714no—
528#95—714no—
529#95—714no—
530#95—714no—
531#95—714no—
532#95—714no—
533#95—714no—
534#95—714no—
535#95—714no—
536#95—714no—
537#95—714no—
538#95—714no—
539#95—714no—
540C24—22no—
541C24—22no—
542C24—22no—
543C24—22no—
544C24C2×C22⋊D7114yes—
545C24Q8×D7114yes—
546C24Q8×D7114yes—
547C24C23×D7112yes—
548C24C23×D7111yescharacteristic
549C2×Q8—28no—
550C2×Q8—28no—
551C2×Q8—44no—
552C2×Q8—416no—
553C2×Q8—28416no—
554C2×Q8—2844no—
555C2×Q8—1428no—
556C2×Q8—1428no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—28no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—28no—
574C22×C4—44no—
575C22×C4—416no—
576C22×C4—28416no—
577C22×C4—2844no—
578C22×C4—2844no—
579C22×C4—2844no—
580C22×C4—28416no—
581C22×C4—7116no—
582C22×C4—714no—
583C22×C4—714no—
584C22×C4—714no—
585C22×C4—714no—
586C22×C4—714no—
587C22×C4—712no—
588C22×C4—712no—
589C22×C4—712no—
590C22×C4—712no—
591C22×C4—712no—
592C22×C4—712no—
593C22×C4—712no—
594C22×C4—712no—
595C22×C4—1428no—
596C22×C4—1422no—
597C22×C4—1422no—
598C22×C4—1422no—
599C22×C4—1428no—
600C22×C4—1422no—
601C22×C4—1422no—
602C22×C4—1422no—
603C22×C4—1422no—
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×C4C2×C22⋊D7114yes—
617C22×C4C2×C22⋊D7114yes—
618C22×C4#1176586414yes—
619C22×C4C23×D7112yes—
620C22×C4C23×D7112yes—
621C22×C4C23×D7112yes—
622C22×C4C23×D7112yes—
623C22×C4C23×D7112yes—
624C22×C4C23×D7112yes—
625C4⋊C4—28no—
626C4⋊C4—28no—
627C4⋊C4—28no—
628C4⋊C4—2844no—
629C4⋊C4—2844no—
630C4⋊C4—2844no—
631C4⋊C4—2844no—
632C4⋊C4—1428no—
633C4⋊C4—1428no—
634C4⋊C4—1428no—
635C4⋊C4—1428no—
636C4⋊C4—1428no—
637C22⋊C4—28no—
638C22⋊C4—7116no—
639C22⋊C4—1428no—
640C22⋊C4C2×C22⋊D71116yes—
641C42—2844no—
642C42—2844no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—28no—
648C23—28no—
649C23—28no—
650C23—28no—
651C23—28no—
652C23—28no—
653C23#14556126116yes—
654C23C22×C22⋊D7114yes—
655C23C22×C22⋊D7112yes—
656C23C2×Q8×D7114yes—
657C23C2×Q8×D7114yes—
658C23C2×Q8×D7112yes—
659C23C2×Q8×D7112yes—
660C23#41×D7112yes—
661C23C2×#1176586412yes—
662C23#1455617312yes—
663C23#1455617412yes—
664C23C24×D7111yescharacteristic
665Q8—416no—
666Q8—28416no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—28no—
674C2×C4—28no—
675C2×C4—28no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—416no—
686C2×C4—44no—
687C2×C4—44no—
688C2×C4—44no—
689C2×C4—2844no—
690C2×C4—2844no—
691C2×C4—2844no—
692C2×C4—28416no—
693C2×C4—28416no—
694C2×C4—714no—
695C2×C4—714no—
696C2×C4—714no—
697C2×C4—714no—
698C2×C4—714no—
699C2×C4—1422no—
700C2×C4—1422no—
701C2×C4—1422no—
702C2×C4—1422no—
703C2×C4—1422no—
704C2×C4—1422no—
705C2×C4—1422no—
706C2×C4—1422no—
707C2×C4—1422no—
708C2×C4—1422no—
709C2×C4—1422no—
710C2×C4—1422no—
711C2×C4—1422no—
712C2×C4—1422no—
713C2×C4—1422no—
714C2×C4—1422no—
715C2×C4—1422no—
716C2×C4—1422no—
717C2×C4—1422no—
718C2×C4—1428no—
719C2×C4—1428no—
720C2×C4—1428no—
721C2×C4—1428no—
722C2×C4—1428no—
723C2×C4C22×C22⋊D7114yes—
724C2×C4C22×C22⋊D7114yes—
725C2×C4C2×#1176586414yes—
726C22—24no—
727C22—24no—
728C22—24no—
729C22—232no—
730C22—24no—
731C22—24no—
732C22—24no—
733C22C2×#1455612618yes—
734C22C2×#1455612614yes—
735C22#1798655114yes—
736C22#1798662414yes—
737C22#1798663714yes—
738C22#1798664314yes—
739C22#1798670314yes—
740C22#1798670714yes—
741C22C23×C22⋊D7111yescharacteristic
742C22C22×Q8×D7111yescharacteristic
743C22C22×Q8×D7111yescharacteristic
744C22C2×#41×D7111yescharacteristic
745C22C22×#1176586411yescharacteristic
746C22C2×#1455617311yescharacteristic
747C22C2×#1455617411yescharacteristic
748C4—24no—
749C4—24no—
750C4—24no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—2842no—
755C4—2842no—
756C4—2842no—
757C4—1424no—
758C4—1424no—
759C4—1424no—
760C4—1424no—
761C4—1424no—
762C2—28no—
763C2#2259334818yesdirect product factor
764C2C22×#1455612611yescharacteristic
765C2C2×#1798655111yescharacteristic
766C2C2×#1798662411yescharacteristic
767C2C2×#1798663711yescharacteristic
768C2C2×#1798664311yescharacteristic
769C2C2×#1798670311yescharacteristic
770C2C2×#1798670711yescharacteristic
subgroupG/H
centerC24C23×D71
commutator, cosocleC23×C71C25
FrattiniC23C24×D71
FittingC22×C22⋊Q8×C71C2
socleC24×C71C24
prime radicalC25×C71C23
hypercenterC22×C22⋊Q8D71
hypocenterC71C2×#2549
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #22593348C2direct (N × H)
3. C2×#17985930C2semidirect
4. C2×#17985929C2semidirect
5. C2×#17985919C2semidirect
6. C2×#17985918C2semidirect
7. C2×#17985906C2semidirect
8. C2×#17985904C2semidirect
9. C2×#17985894C2semidirect
10. C2×#17985894C2semidirect
35. #17985930C22semidirect
36. #17985929C22semidirect
37. #17985919C22semidirect
38. #17985918C22semidirect
39. #17985906C22semidirect
40. #17985904C22semidirect
41. #17985894C22semidirect
42. #17985894C22semidirect
78. C23×Dic71Q8semidirect
109. C2×C22⋊Dic71Q8semidirect
188. C22×Dic71C2×Q8semidirect
208. C22⋊Dic71C2×Q8semidirect
378. C2×C71#2549semidirect
402. C71C2×#2549semidirect
763. C2#22593348direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145561052
#225933482
C2×#179859302
C2×#179859292
C2×#179859192
C2×#179859182
C2×#179859062
C2×#179859042
C2×#179858942
C2×#179858722
C2×#179858712
C2×#179858572
C2×C22⋊C4×Dic712
C22×C71⋊#952
C22×C22⋊Q8×C712
C2×#254971