Finite Group Databasebeta

← C2×#22600682 #32875859

Subgroups — C2×#22600682 #32875859

Order 18176.

2374 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986650C211yesmaximal, characteristic, complemented
2C2×#17986649C211yesmaximal, characteristic, complemented
3#22600682C2116yesmaximal, direct product factor
4C2×#17986403C211yesmaximal, characteristic, complemented
5C2×#17986314C211yesmaximal, characteristic, complemented
6C2×#17986313C211yesmaximal, characteristic, complemented
7C2×#17986311C211yesmaximal, characteristic, complemented
8C2×#17986278C211yesmaximal, characteristic, complemented
9C2×#17986277C211yesmaximal, characteristic, complemented
10C2×#17986234C211yesmaximal, characteristic, complemented
11C2×#17986233C211yesmaximal, characteristic, complemented
12C2×#17986079C211yesmaximal, characteristic, complemented
13C2×(C22⋊D71)⋊C8C211yesmaximal, characteristic, complemented
14C22×#14556061C211yesmaximal, characteristic, complemented
15C2×#107×D71C211yesmaximal, characteristic, complemented
16C2×#480×C71C211yesmaximal, characteristic, complemented
17C22×#11765865—21no—
18C22×#11765864—21no—
19C22×#11765850C2211yescharacteristic
20C23×C71⋊C8C2211yescharacteristic
21C22×C8×D71C2211yescharacteristic
22#17986650—24no—
23#17986650C2218yescomplemented
24#17986649—24no—
25#17986649C2218yescomplemented
26C2×#14556127C2211yescharacteristic
27C2×#14556127C2211yescharacteristic
28C2×#14556113—21no—
29C2×#14556111—21no—
30C2×#14556110—21no—
31C2×#14556109—21no—
32C2×#14556106—21no—
33C2×#14556105—21no—
34C2×#14556103C2211yescharacteristic
35C2×#14556102C2211yescharacteristic
36C2×#14556099C2211yescharacteristic
37C2×D4×Dic71C2211yescharacteristic
38C2×#14556090C2211yescharacteristic
39C2×C4×C22⋊D71C2211yescharacteristic
40C22×C4⋊Dic71C2211yescharacteristic
41C2×C4⋊C4×D71C2211yescharacteristic
42C2×C4⋊C4×D71C2211yescharacteristic
43#17986403C2218yescomplemented
44#17986314C2218yescomplemented
45#17986313C2218yescomplemented
46#17986311C2218yescomplemented
47#17986278C2218yescomplemented
48#17986277C2218yescomplemented
49#17986234C2218yescomplemented
50#17986233C2218yescomplemented
51#17986079C2218yescomplemented
52(C22⋊D71)⋊C8C2218yescomplemented
53C2×#14556062C2211yescharacteristic
54C2×#14556062C2211yescharacteristic
55C2×#14556061C2211yescharacteristic
56C2×#14556061C2211yescharacteristic
57C2×#14556061C2211yescharacteristic
58C2×#14556061C2211yescharacteristic
59C2×#14556061C2211yescharacteristic
60C2×#14556061C2218yescomplemented
61#107×D71C2218yescomplemented
62C2×Dic71⋊C8C2211yescharacteristic
63C2×#14556050C2211yescharacteristic
64C2×#14556050C2211yescharacteristic
65C2×#14556049C2211yescharacteristic
66C2×#14556048C2211yescharacteristic
67C2×(C2×D71)⋊C8C2211yescharacteristic
68C2×C8×Dic71C2211yescharacteristic
69C2×#121×C71C2211yescharacteristic
70C22×C4⋊C4×C71C2211yescharacteristic
71#480×C71C2218yescomplemented
72C2×#107×C71C2211yescharacteristic
73C2×#107×C71C2211yescharacteristic
74C2×#102×C71C2211yescharacteristic
75C2×#102×C71C2211yescharacteristic
76C2×C22⋊C8×C71C2211yescharacteristic
77C2×#11765865—28no—
78C2×#11765865—48no—
79C2×#11765864—28no—
80C2×#11765864—48no—
81C22×Dic142—21no—
82C22×Dic142—21no—
83C22×D284—21no—
84C22×D284C2311yescharacteristic
85C22×C22⋊D71—21no—
86C22×C22⋊D71—21no—
87C22×C22⋊D71D411yescharacteristic
88C23×Dic71—21no—
89C23×Dic71—21no—
90C22×C4×D71—21no—
91C22×C4×D71—21no—
92C22×C4×D71—21no—
93C22×C4×D71C2311yescharacteristic
94C2×#11765850—24no—
95C2×#11765850C2314yes—
96C22×C71⋊C8—24no—
97C22×C71⋊C8C2314yes—
98C22×C71⋊C8C2311yescharacteristic
99C22×C71⋊C8C2311yescharacteristic
100C2×C8×D71—24no—
101C2×C8×D71C2314yes—
102#14556127—22no—
103#14556127—22no—
104#14556127C2314yes—
105#14556127C2314yes—
106#14556113—28no—
107#14556111—28no—
108#14556110—28no—
109#14556109—28no—
110#14556106—28no—
111#14556105—28no—
112#14556103—22no—
113#14556103C2314yes—
114#14556102—22no—
115#14556102C2314yes—
116#14556099—22no—
117#14556099C2314yes—
118D4×Dic71—22no—
119D4×Dic71C2314yes—
120#14556090—22no—
121#14556090C2314yes—
122C4×C22⋊D71D414yes—
123C4×C22⋊D71C2314yes—
124C2×C4⋊Dic71—22no—
125C2×C4⋊Dic71—21no—
126C2×C4⋊Dic71C2314yes—
127C2×C4⋊Dic71C2311yescharacteristic
128C2×C4⋊Dic71C2311yescharacteristic
129C2×C4⋊Dic71C2311yescharacteristic
130C2×Dic71⋊C4—21no—
131C2×Dic71⋊C4—21no—
132C2×Dic71⋊C4—21no—
133C2×Dic71⋊C4—21no—
134C2×Dic71⋊C4D411yescharacteristic
135C4⋊C4×D71—22no—
136C4⋊C4×D71—22no—
137C4⋊C4×D71C2314yes—
138C4⋊C4×D71C2314yes—
139C2×C22⋊Dic71—21no—
140C2×C22⋊Dic71—21no—
141C2×C22⋊Dic71D411yescharacteristic
142C2×(C2×D71)⋊C4—21no—
143C2×(C2×D71)⋊C4—21no—
144C2×(C2×D71)⋊C4—21no—
145C2×(C2×D71)⋊C4D411yescharacteristic
146C2×C4×Dic71C2311yescharacteristic
147#14556062C2314yes—
148#14556062C2314yes—
149#14556061C2314yes—
150#14556061C2314yes—
151#14556061C2314yes—
152#14556061C2314yes—
153#14556061C2314yes—
154Dic71⋊C8C2314yes—
155#14556050C2314yes—
156#14556050C2314yes—
157#14556049C2314yes—
158#14556048C2314yes—
159(C2×D71)⋊C8C2314yes—
160C8×Dic71C2314yes—
161C22×D4×C71—21no—
162C22×D4×C71C2311yescharacteristic
163C23×C4×C71—21no—
164C23×C4×C71C2311yescharacteristic
165C22×C8×C71C2311yescharacteristic
166C22×C8×C71C2311yescharacteristic
167#121×C71—22no—
168#121×C71C2314yes—
169C2×C4⋊C4×C71—22no—
170C2×C4⋊C4×C71—21no—
171C2×C4⋊C4×C71C2311yescharacteristic
172C2×C4⋊C4×C71C2311yescharacteristic
173C2×C4⋊C4×C71C2311yescharacteristic
174C2×C4⋊C4×C71C2314yes—
175C2×C22⋊C4×C71—21no—
176#107×C71C2314yes—
177#107×C71C2314yes—
178#102×C71C2314yes—
179#102×C71C2314yes—
180C22⋊C8×C71C2314yes—
181C23×D71—21no—
182C23×D71C2×D411yescharacteristic
183#11765865—432no—
184#11765864—432no—
185C2×Dic142—24no—
186C2×Dic142—24no—
187C2×Dic142—44no—
188C2×Dic142—44no—
189C2×D284—22no—
190C2×D284—22no—
191C2×D284—24no—
192C2×D284—21no—
193C2×D284—44no—
194C2×D284C2412yes—
195C2×C22⋊D71—24no—
196C2×C22⋊D71—24no—
197C2×C22⋊D71—44no—
198C2×C22⋊D71—44no—
199C2×C22⋊D71D818yescomplemented
200C2×C22⋊D71C2×D414yes—
201C22×Dic71—21no—
202C22×Dic71—21no—
203C22×Dic71—21no—
204C22×Dic71—24no—
205C22×Dic71—24no—
206C22×Dic71—44no—
207C22×Dic71—44no—
208C22×Dic71C2×D411yescharacteristic
209C22×Dic71C2×D411yescharacteristic
210C22×Dic71C2×D411yescharacteristic
211C2×C4×D71—22no—
212C2×C4×D71—22no—
213C2×C4×D71—24no—
214C2×C4×D71—24no—
215C2×C4×D71—24no—
216C2×C4×D71—44no—
217C2×C4×D71—44no—
218C2×C4×D71—44no—
219C2×C4×D71C2×D412yes—
220C2×C4×D71C2412yes—
221#11765850—28no—
222C2×C71⋊C8—22no—
223C2×C71⋊C8—28no—
224C2×C71⋊C8#4114yescomplemented
225C2×C71⋊C8C2412yes—
226C2×C71⋊C8C2412yes—
227C8×D71—28no—
228C4⋊Dic71—21no—
229C4⋊Dic71—21no—
230C4⋊Dic71—21no—
231C4⋊Dic71—24no—
232C4⋊Dic71C2412yes—
233C4⋊Dic71C2412yes—
234C4⋊Dic71C2412yes—
235Dic71⋊C4—24no—
236Dic71⋊C4—24no—
237Dic71⋊C4—24no—
238Dic71⋊C4—24no—
239Dic71⋊C4C2×D414yes—
240C22⋊Dic71—24no—
241C22⋊Dic71—24no—
242C22⋊Dic71C2×D414yes—
243(C2×D71)⋊C4—24no—
244(C2×D71)⋊C4—24no—
245(C2×D71)⋊C4—24no—
246(C2×D71)⋊C4C2×D414yes—
247C4×Dic71C2×D412yes—
248C4×Dic71C2412yes—
249C24×C71—21no—
250C24×C71C2×D411yescharacteristic
251C2×D4×C71—24no—
252C2×D4×C71—21no—
253C2×D4×C71—22no—
254C2×D4×C71—22no—
255C2×D4×C71—44no—
256C2×D4×C71C2412yes—
257C22×C4×C71—22no—
258C22×C4×C71—22no—
259C22×C4×C71—21no—
260C22×C4×C71—21no—
261C22×C4×C71—21no—
262C22×C4×C71—24no—
263C22×C4×C71—44no—
264C22×C4×C71C2×D411yescharacteristic
265C22×C4×C71C2×D412yes—
266C22×C4×C71C2412yes—
267C22×C4×C71C2411yescharacteristic
268C2×C8×C71—22no—
269C2×C8×C71—22no—
270C2×C8×C71C2412yes—
271C2×C8×C71C2412yes—
272C4⋊C4×C71—21no—
273C4⋊C4×C71—21no—
274C4⋊C4×C71—24no—
275C4⋊C4×C71—21no—
276C4⋊C4×C71C2412yes—
277C4⋊C4×C71C2412yes—
278C4⋊C4×C71C2412yes—
279C22⋊C4×C71—24no—
280C23×C71—22no—
281C23×C71—22no—
282C23×C71—22no—
283C23×C71—42no—
284C23×C71—42no—
285C23×C71—42no—
286C23×C71C2×D814yes—
287C23×C71C22×D412yes—
288C23×C71C22×D411yescharacteristic
289C22×D71—22no—
290C22×D71—22no—
291C22×D71—22no—
292C22×D71—42no—
293C22×D71—42no—
294C22×D71—42no—
295C22×D71C2×D814yes—
296C22×D71C22×D412yes—
297D4×C71—22no—
298D4×C71—22no—
299D4×C71—48no—
300D4×C71—42no—
301C2×C4×C71—22no—
302C2×C4×C71—24no—
303C2×C4×C71—22no—
304C2×C4×C71—22no—
305C2×C4×C71—22no—
306C2×C4×C71—22no—
307C2×C4×C71—22no—
308C2×C4×C71—42no—
309C2×C4×C71—42no—
310C2×C4×C71—48no—
311C2×C4×C71—42no—
312C2×C4×C71C22×D412yes—
313C2×C4×C71C22×D411yescharacteristic
314C2×C4×C71C2×#4112yes—
315C2×C4×C712−1+412yes—
316C2×C4×C71C2511yescharacteristic
317C22⋊D71—48no—
318C22⋊D71—48no—
319C22⋊D71C2×D8116yescomplemented
320C2×Dic71—22no—
321C2×Dic71—22no—
322C2×Dic71—22no—
323C2×Dic71—22no—
324C2×Dic71—22no—
325C2×Dic71—42no—
326C2×Dic71—42no—
327C2×Dic71—42no—
328C2×Dic71—48no—
329C2×Dic71—48no—
330C2×Dic71C2×D814yes—
331C2×Dic71C22×D412yes—
332C2×Dic71C22×D412yes—
333C2×Dic71C22×D412yes—
334D284—22no—
335D284—22no—
336D284—48no—
337D284—42no—
338C4×D71—24no—
339C4×D71—22no—
340C4×D71—22no—
341C4×D71—48no—
342C4×D71—48no—
343C4×D71—48no—
344Dic142—48no—
345Dic142—48no—
346C8×C71—22no—
347C8×C71—22no—
348C71⋊C8—22no—
349C71⋊C8C2×#4114yescomplemented
350C22×C71—28no—
351C22×C71—22no—
352C22×C71—22no—
353C22×C71—42no—
354C22×C71—42no—
355C22×C71—42no—
356C22×C71—84no—
357C22×C71#54712yes—
358C22×C71C22×D814yes—
359C22×C71C22×D812yes—
360C22×C71#57812yes—
361C22×C71C23×D411yescharacteristic
362C2×D71—28no—
363C2×D71—22no—
364C2×D71—22no—
365C2×D71—42no—
366C2×D71—42no—
367C2×D71—42no—
368C2×D71—84no—
369C2×D71C22×D814yes—
370C4×C71—22no—
371C4×C71—42no—
372C4×C71—42no—
373C4×C71—42no—
374C4×C71#54712yes—
375C4×C71C22×#4111yescharacteristic
376C4×C71C2×2−1+411yescharacteristic
377Dic71—22no—
378Dic71—22no—
379Dic71—42no—
380Dic71—42no—
381Dic71—42no—
382Dic71C22×D814yes—
383C2×#3334—711nomaximal, Sylow
384C2×C71—24no—
385C2×C71—82no—
386C2×C71#333414yescomplemented
387C2×C71C2×#54711yescharacteristic
388C2×C71C23×D811yescharacteristic
389C2×C71C2×#57811yescharacteristic
390D71—24no—
391D71—82no—
392C2×#547—711no—
393C2×#547—711no—
394#3334—7116no—
395C2×#500—711no—
396C2×#480—711no—
397C2×#480—711no—
398C2×#480—711no—
399C2×#480D7111yescharacteristic, complemented
400C2×#474—711no—
401C2×#474—711no—
402C2×#466—711no—
403C2×#466—711no—
404C2×C4×D8—711no—
405C2×C8×D4—711no—
406C22×#107—711no—
407C22×#107—711no—
408C71C2×#333411yescharacteristic, complemented, Sylow
409C22×#41—1421no—
410C22×#41—1421no—
411C22×D8—711no—
412C23×C8—711no—
413C23×C8—711no—
414#547—718no—
415#547—718no—
416#547—1424no—
417#547—1424no—
418C2×C4⋊Q8—711no—
419C2×C4⋊Q8—711no—
420C2×#123—1421no—
421C2×#123—1421no—
422C2×#123—1421no—
423C2×#123—1421no—
424C2×C22⋊Q8—1421no—
425C2×C22⋊Q8—1421no—
426C2×#121—711no—
427C2×#121—711no—
428C2×#121—711no—
429C2×#121C2×D7111yescharacteristic
430C2×C4×D4—711no—
431C2×C4×D4—711no—
432C2×C4×D4—711no—
433C22×C4⋊C4—711no—
434C22×C4⋊C4—711no—
435C22×C4⋊C4—711no—
436C22×C4⋊C4C2×D7111yescharacteristic
437#500—718no—
438#480—718no—
439#480—718no—
440#480—718no—
441#480C2×D7118yescomplemented
442#474—718no—
443#474—718no—
444#466—718no—
445#466—718no—
446C4×D8—718no—
447C8×D4—718no—
448C2×#107—711no—
449C2×#107—711no—
450C2×#107—718no—
451C2×#107—711no—
452C2×#107—711no—
453C2×#107—711no—
454C2×#107—711no—
455C2×#107—711no—
456C2×#107—718no—
457C2×#107C2×D7111yescharacteristic
458C2×#107C2×D7111yescharacteristic
459C2×C4⋊C8—711no—
460C2×#102—711no—
461C2×#102—711no—
462C2×#102—711no—
463C2×#102—711no—
464C2×#102C2×D7111yescharacteristic
465C2×#102C2×D7111yescharacteristic
466C2×C22⋊C8—711no—
467C2×C22⋊C8C2×D7111yescharacteristic
468C2×C4×C8—711no—
469C2×#41—2848no—
470C2×#41—2848no—
471C2×#41—1428no—
472C2×#41—1428no—
473C22×Q8—1421no—
474C22×Q8—1421no—
475C22×D4—21no—
476C22×D4—711no—
477C22×D4—711no—
478C22×D4—1421no—
479C22×D4—1421no—
480C22×D4—1421no—
481C22×D4C22×D7111yescharacteristic
482C23×C4—21no—
483C23×C4—711no—
484C23×C4—1421no—
485C23×C4—1421no—
486C23×C4—1421no—
487C23×C4—1421no—
488C23×C4—1421no—
489C23×C4C22×D7111yescharacteristic
490C2×D8—714no—
491C2×D8—1424no—
492C22×C8—711no—
493C22×C8—711no—
494C22×C8—714no—
495C22×C8—714no—
496C22×C8—1424no—
497C22×C8—1424no—
498C22×C8C22×D7111yescharacteristic
499C22×C8C22×D7111yescharacteristic
500C4⋊Q8—714no—
501C4⋊Q8—714no—
502C4⋊Q8—1422no—
503C4⋊Q8—1422no—
504#123—1428no—
505#123—1428no—
506#123—1428no—
507#123—1428no—
508C22⋊Q8—1428no—
509C22⋊Q8—1428no—
510#121—22no—
511#121—714no—
512#121—714no—
513#121—714no—
514#121—1422no—
515#121—1422no—
516#121—1422no—
517#121C22×D7114yes—
518C4×D4—714no—
519C4×D4—714no—
520C4×D4—714no—
521C4×D4—714no—
522C4×D4—1422no—
523C4×D4—1422no—
524C2×C4⋊C4—21no—
525C2×C4⋊C4—22no—
526C2×C4⋊C4—711no—
527C2×C4⋊C4—711no—
528C2×C4⋊C4—711no—
529C2×C4⋊C4—711no—
530C2×C4⋊C4—714no—
531C2×C4⋊C4—714no—
532C2×C4⋊C4—714no—
533C2×C4⋊C4—1422no—
534C2×C4⋊C4—1422no—
535C2×C4⋊C4—1421no—
536C2×C4⋊C4—1421no—
537C2×C4⋊C4—1421no—
538C2×C4⋊C4—1421no—
539C2×C4⋊C4—1421no—
540C2×C4⋊C4—1422no—
541C2×C4⋊C4C22×D7111yescharacteristic
542C2×C4⋊C4C22×D7111yescharacteristic
543C2×C4⋊C4C22×D7111yescharacteristic
544C2×C4⋊C4C22×D7114yes—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—711no—
547C2×C22⋊C4—711no—
548C2×C22⋊C4—1421no—
549C2×C22⋊C4—1421no—
550C2×C22⋊C4—1421no—
551C2×C22⋊C4—1421no—
552C2×C22⋊C4—1421no—
553C2×C42—711no—
554#107—714no—
555#107—714no—
556#107—714no—
557#107—714no—
558#107—714no—
559#107—714no—
560#107—714no—
561#107C22×D7114yes—
562#107C22×D7114yes—
563C4⋊C8—714no—
564#102—714no—
565#102—714no—
566#102—714no—
567#102—714no—
568#102C22×D7114yes—
569#102C22×D7114yes—
570C22⋊C8—714no—
571C22⋊C8C22×D7114yes—
572C4×C8—714no—
573C24—21no—
574C24—711no—
575C24—1421no—
576C24D4×D7111yescharacteristic
577#41—28432no—
578#41—28432no—
579C2×Q8—2844no—
580C2×Q8—2844no—
581C2×Q8—1424no—
582C2×Q8—1424no—
583C2×D4—24no—
584C2×D4—21no—
585C2×D4—22no—
586C2×D4—22no—
587C2×D4—44no—
588C2×D4—2844no—
589C2×D4—2844no—
590C2×D4—2844no—
591C2×D4—714no—
592C2×D4—718no—
593C2×D4—712no—
594C2×D4—1424no—
595C2×D4—1424no—
596C2×D4—1424no—
597C2×D4—1421no—
598C2×D4—1422no—
599C2×D4—1422no—
600C2×D4C23×D7112yes—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—24no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—44no—
608C22×C4—2844no—
609C22×C4—2844no—
610C22×C4—2844no—
611C22×C4—2844no—
612C22×C4—2844no—
613C22×C4—711no—
614C22×C4—711no—
615C22×C4—711no—
616C22×C4—712no—
617C22×C4—712no—
618C22×C4—1424no—
619C22×C4—1424no—
620C22×C4—1424no—
621C22×C4—1424no—
622C22×C4—1424no—
623C22×C4—1421no—
624C22×C4—1421no—
625C22×C4—1421no—
626C22×C4—1422no—
627C22×C4—1422no—
628C22×C4D4×D7112yes—
629C22×C4D4×D7111yescharacteristic
630C22×C4C23×D7112yes—
631C22×C4C23×D7111yescharacteristic
632D8—1428no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—714no—
636C2×C8—712no—
637C2×C8—712no—
638C2×C8—1428no—
639C2×C8—1428no—
640C2×C8—1422no—
641C2×C8C23×D7112yes—
642C2×C8C23×D7112yes—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—24no—
646C4⋊C4—21no—
647C4⋊C4—714no—
648C4⋊C4—712no—
649C4⋊C4—712no—
650C4⋊C4—712no—
651C4⋊C4—1424no—
652C4⋊C4—1424no—
653C4⋊C4—1424no—
654C4⋊C4—1424no—
655C4⋊C4—1421no—
656C4⋊C4—1421no—
657C4⋊C4—1421no—
658C4⋊C4—1424no—
659C4⋊C4C23×D7112yes—
660C4⋊C4C23×D7112yes—
661C4⋊C4C23×D7112yes—
662C22⋊C4—24no—
663C22⋊C4—714no—
664C22⋊C4—714no—
665C22⋊C4—1424no—
666C22⋊C4—1424no—
667C22⋊C4—1424no—
668C22⋊C4—1424no—
669C22⋊C4—1424no—
670C42—712no—
671C42—712no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—2842no—
679C23—2842no—
680C23—2842no—
681C23—712no—
682C23—714no—
683C23—1422no—
684C23—1422no—
685C23—1422no—
686C23D8×D7114yes—
687C23C2×D4×D7112yes—
688C23C2×D4×D7111yescharacteristic
689Q8—2848no—
690Q8—2848no—
691D4—22no—
692D4—22no—
693D4—48no—
694D4—42no—
695D4—2848no—
696D4—2848no—
697D4—2848no—
698D4—2842no—
699D4—7116no—
700D4—1422no—
701D4—1422no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—24no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—48no—
712C2×C4—42no—
713C2×C4—2848no—
714C2×C4—2848no—
715C2×C4—2848no—
716C2×C4—2842no—
717C2×C4—2842no—
718C2×C4—2842no—
719C2×C4—2848no—
720C2×C4—2848no—
721C2×C4—712no—
722C2×C4—714no—
723C2×C4—712no—
724C2×C4—712no—
725C2×C4—1422no—
726C2×C4—1422no—
727C2×C4—1422no—
728C2×C4—1422no—
729C2×C4—1422no—
730C2×C4—1422no—
731C2×C4—1422no—
732C2×C4—1424no—
733C2×C4C2×D4×D7112yes—
734C2×C4C2×D4×D7111yescharacteristic
735C2×C4#41×D7112yes—
736C2×C4#1455617512yes—
737C2×C4C24×D7111yescharacteristic
738C8—22no—
739C8—22no—
740C8—714no—
741C8—1422no—
742C22—22no—
743C22—22no—
744C22—28no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—84no—
749C22—2842no—
750C22—2842no—
751C22—2842no—
752C22—5684no—
753C22—714no—
754C22—1422no—
755C22—1422no—
756C22—1428no—
757C22#1798664712yes—
758C22C2×D8×D7114yes—
759C22C2×D8×D7112yes—
760C22#1798681512yes—
761C22C22×D4×D7111yescharacteristic
762C4—22no—
763C4—42no—
764C4—42no—
765C4—42no—
766C4—2842no—
767C4—2842no—
768C4—2842no—
769C4—714no—
770C4—1422no—
771C4—1422no—
772C4#1798664712yes—
773C4C2×#41×D7111yescharacteristic
774C4C2×#1455617511yescharacteristic
775C2—24no—
776C2—82no—
777C2—5682no—
778C2—1424no—
779C2#2260068214yesdirect product factor
780C2C2×#1798664711yescharacteristic
781C2C22×D8×D7111yescharacteristic
782C2C2×#1798681511yescharacteristic
subgroupG/H
centerC23C2×D4×D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#480×C71C2
socleC23×C71C22×D4
hypercenterC2×#480D71
hypocenterC71C2×#3334
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#480

Complements

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

NH ≅ G/Ntype
1. C2×#17986650C2semidirect
2. C2×#17986649C2semidirect
3. #22600682C2direct (N × H)
4. C2×#17986403C2semidirect
5. C2×#17986314C2semidirect
6. C2×#17986313C2semidirect
7. C2×#17986311C2semidirect
8. C2×#17986278C2semidirect
9. C2×#17986277C2semidirect
10. C2×#17986234C2semidirect
11. C2×#17986233C2semidirect
12. C2×#17986079C2semidirect
13. C2×(C22⋊D71)⋊C8C2semidirect
14. C22×#14556061C2semidirect
15. C2×#107×D71C2semidirect
16. C2×#480×C71C2semidirect
23. #17986650C22semidirect
25. #17986649C22semidirect
43. #17986403C22semidirect
44. #17986314C22semidirect
45. #17986313C22semidirect
46. #17986311C22semidirect
47. #17986278C22semidirect
48. #17986277C22semidirect
49. #17986234C22semidirect
50. #17986233C22semidirect
51. #17986079C22semidirect
52. (C22⋊D71)⋊C8C22semidirect
60. C2×#14556061C22semidirect
61. #107×D71C22semidirect
71. #480×C71C22semidirect
199. C2×C22⋊D71D8semidirect
224. C2×C71⋊C8#41semidirect
319. C22⋊D71C2×D8semidirect
349. C71⋊C8C2×#41semidirect
386. C2×C71#3334semidirect
399. C2×#480D71semidirect
408. C71C2×#3334semidirect
441. #480C2×D71semidirect
779. C2#22600682direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179866502
C2×#179866492
#226006822
C2×#179864032
C2×#179863142
C2×#179863132
C2×#179863112
C2×#179862782
C2×#179862772
C2×#179862342
C2×#179862332
C2×#179860792
C2×(C22⋊D71)⋊C82
C22×#145560612
C2×#107×D712
C2×#480×C712
C2×#333471