Finite Group Databasebeta

← C2×#22599428 #32868801

Subgroups — C2×#22599428 #32868801

Order 18176.

2278 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986568C211yesmaximal, characteristic, complemented
2#22599428C2116yesmaximal, direct product factor
3C2×#17986389C211yesmaximal, characteristic, complemented
4C2×#17986381C211yesmaximal, characteristic, complemented
5C2×#17986361C211yesmaximal, characteristic, complemented
6C2×#17986347C211yesmaximal, characteristic, complemented
7C2×#17986221C211yesmaximal, characteristic, complemented
8C2×#17986199C211yesmaximal, characteristic, complemented
9C2×#17986214C211yesmaximal, characteristic, complemented
10C2×#17986194C211yesmaximal, characteristic, complemented
11C2×#17986159C211yesmaximal, characteristic, complemented
12C2×#17986142C211yesmaximal, characteristic, complemented
13C2×#17986149C211yesmaximal, characteristic, complemented
14C2×#17986132C211yesmaximal, characteristic, complemented
15C2×#17986060C211yesmaximal, characteristic, complemented
16C2×#542×C71C211yesmaximal, characteristic, complemented
17C22×#11765865C2211yescharacteristic
18C23×D284C2211yescharacteristic
19C22×#11765855C2211yescharacteristic, complemented
20C22×#11765853C2211yescharacteristic, complemented
21C22×#11765852C2211yescharacteristic
22C22×#11765852C2211yescharacteristic
23C22×#11765852C2211yescharacteristic, complemented
24C22×#11765850C2211yescharacteristic
25C22×#11765850C2211yescharacteristic
26C22×#11765850C2211yescharacteristic, complemented
27#17986568—24no—
28#17986568C2218yescomplemented
29C2×#14556125C2211yescharacteristic
30C2×#14556125C2211yescharacteristic
31C2×#14556116C2211yescharacteristic
32C2×#14556116C2211yescharacteristic
33C2×#14556103—21no—
34C2×#14556103—21no—
35C2×#14556098—21no—
36C2×#14556098—21no—
37#17986389C2218yescomplemented
38#17986381C2218yescomplemented
39#17986361C2218yescomplemented
40#17986347C2218yescomplemented
41#17986221C2218yescomplemented
42#17986214C2218yescomplemented
43#17986199C2218yescomplemented
44#17986194C2218yescomplemented
45#17986159C2218yescomplemented
46#17986149C2218yescomplemented
47#17986142C2218yescomplemented
48#17986132C2218yescomplemented
49#17986060C2218yescomplemented
50C2×C4⋊(C71⋊C8)C2211yescharacteristic, complemented
51C2×C4⋊(C71⋊C8)C2211yescharacteristic, complemented
52C2×#14556051C2211yescharacteristic, complemented
53C2×#14556051C2211yescharacteristic, complemented
54C2×#14556048C2211yescharacteristic
55C2×#14556048C2211yescharacteristic
56C2×#14556048C2211yescharacteristic
57C2×#14556048C2211yescharacteristic
58C2×#14556048C2211yescharacteristic, complemented
59C2×#14556048C2211yescharacteristic, complemented
60C2×C22⋊(C71⋊C8)C2211yescharacteristic
61C2×C22⋊(C71⋊C8)C2211yescharacteristic
62C2×#14556039C2211yescharacteristic, complemented
63C2×C4×C71⋊C8C2211yescharacteristic, complemented
64#542×C71—24no—
65#542×C71C2218yescomplemented
66C2×C4⋊Q8×C71C2211yescharacteristic, complemented
67C2×#126×C71—21no—
68C2×#124×C71—21no—
69C2×#124×C71C2211yescharacteristic, complemented
70C2×#123×C71—21no—
71C2×C22⋊Q8×C71—21no—
72C2×C22⋊Q8×C71C2211yescharacteristic
73C2×#121×C71C2211yescharacteristic
74C2×C4×Q8×C71C2211yescharacteristic, complemented
75C2×C4×D4×C71C2211yescharacteristic, complemented
76C2×#117×C71C2211yescharacteristic
77C24×D71—21no—
78C2×#11765865—22no—
79C2×#11765865—42no—
80C2×#11765865—42no—
81C2×#11765865C2314yes—
82C22×Dic142C2311yescharacteristic
83C22×D284—22no—
84C22×D284—21no—
85C22×D284—21no—
86C22×D284—21no—
87C22×D284—21no—
88C22×D284—21no—
89C22×D284—42no—
90C22×D284—42no—
91C22×D284C2311yescharacteristic
92C22×D284C2311yescharacteristic
93C22×D284C2311yescharacteristic
94C22×D284C2314yes—
95C22×C22⋊D71—21no—
96C22×C4×D71—21no—
97C2×#11765855—42no—
98C2×#11765855C2314yescomplemented
99C2×#11765853—42no—
100C2×#11765853C2314yescomplemented
101C2×#11765852—42no—
102C2×#11765852—42no—
103C2×#11765852—42no—
104C2×#11765852C2314yes—
105C2×#11765852C2314yes—
106C2×#11765852C2314yescomplemented
107C2×#11765850—42no—
108C2×#11765850—42no—
109C2×#11765850—42no—
110C2×#11765850C2314yes—
111C2×#11765850C2314yes—
112C2×#11765850C2314yescomplemented
113C22×C71⋊C8C2311yescharacteristic
114C22×C71⋊C8C2311yescharacteristic
115C22×C71⋊C8C2311yescharacteristic
116C22×C71⋊C8C2311yescharacteristic
117#14556125—22no—
118#14556125—22no—
119#14556125C2314yes—
120#14556125C2314yes—
121#14556116—22no—
122#14556116—22no—
123#14556116C2314yes—
124#14556116C2314yes—
125#14556103—28no—
126#14556103—28no—
127#14556098—28no—
128#14556098—28no—
129C2×(C2×D71)⋊C4—21no—
130C2×(C2×D71)⋊C4—21no—
131C2×(C2×D71)⋊C4—21no—
132C2×(C2×D71)⋊C4—21no—
133C4⋊(C71⋊C8)C2314yescomplemented
134C4⋊(C71⋊C8)C2314yescomplemented
135#14556051C2314yescomplemented
136#14556051C2314yescomplemented
137#14556048C2314yes—
138#14556048C2314yes—
139#14556048C2314yes—
140#14556048C2314yes—
141#14556048C2314yescomplemented
142#14556048C2314yescomplemented
143C22⋊(C71⋊C8)C2314yes—
144C22⋊(C71⋊C8)C2314yes—
145#14556039C2314yescomplemented
146C4×C71⋊C8C2314yescomplemented
147C22×Q8×C71—21no—
148C22×Q8×C71C2311yescharacteristic
149C22×D4×C71—21no—
150C22×D4×C71C2311yescharacteristic
151C23×C4×C71—21no—
152C23×C4×C71C2311yescharacteristic
153C4⋊Q8×C71—22no—
154C4⋊Q8×C71C2314yescomplemented
155#126×C71—28no—
156#124×C71—28no—
157#124×C71—22no—
158#124×C71C2314yescomplemented
159#123×C71—28no—
160C22⋊Q8×C71—22no—
161C22⋊Q8×C71—28no—
162C22⋊Q8×C71C2314yes—
163#121×C71—22no—
164#121×C71C2314yes—
165C4×Q8×C71—22no—
166C4×Q8×C71C2314yescomplemented
167C4×D4×C71—22no—
168C4×D4×C71C2314yescomplemented
169#117×C71D414yes—
170#117×C71C2314yes—
171C2×C4⋊C4×C71—21no—
172C2×C4⋊C4×C71—21no—
173C2×C4⋊C4×C71—21no—
174C2×C4⋊C4×C71D411yescharacteristic
175C2×C4⋊C4×C71D411yescharacteristic
176C2×C4⋊C4×C71C2311yescharacteristic
177C2×C4⋊C4×C71C2311yescharacteristic
178C2×C22⋊C4×C71—21no—
179C2×C22⋊C4×C71—21no—
180C2×C22⋊C4×C71—21no—
181C2×C22⋊C4×C71—21no—
182C2×C22⋊C4×C71—21no—
183C2×C22⋊C4×C71D411yescharacteristic
184C2×C22⋊C4×C71D411yescharacteristic
185C2×C42×C71—21no—
186C2×C42×C71C2311yescharacteristic
187C2×C42×C71C2311yescharacteristic
188C23×D71—21no—
189C23×D71—21no—
190C23×D71—21no—
191C23×D71—24no—
192C23×D71—44no—
193C23×D71—82no—
194C23×D71—82no—
195#11765865—44no—
196#11765865—44no—
197#11765865—48no—
198C2×Dic142—22no—
199C2×Dic142—22no—
200C2×Dic142—21no—
201C2×Dic142C2412yes—
202C2×D284—22no—
203C2×D284—22no—
204C2×D284—22no—
205C2×D284—22no—
206C2×D284—22no—
207C2×D284—22no—
208C2×D284—24no—
209C2×D284—21no—
210C2×D284—21no—
211C2×D284—21no—
212C2×D284—24no—
213C2×D284—24no—
214C2×D284—24no—
215C2×D284—24no—
216C2×D284—44no—
217C2×D284—44no—
218C2×D284—44no—
219C2×D284—48no—
220C2×D284—82no—
221C2×D284—82no—
222C2×D284—82no—
223C2×D284—82no—
224C2×D284C2412yes—
225C2×D284C2412yes—
226C2×D284C2412yes—
227C2×C22⋊D71—24no—
228C2×C22⋊D71—44no—
229C22×Dic71—21no—
230C2×C4×D71—24no—
231C2×C4×D71—44no—
232#11765855—44no—
233#11765853—44no—
234#11765852—44no—
235#11765852—44no—
236#11765852—44no—
237#11765850—44no—
238#11765850—44no—
239#11765850—44no—
240C2×C71⋊C8—22no—
241C2×C71⋊C8—22no—
242C2×C71⋊C8—22no—
243C2×C71⋊C8—22no—
244C2×C71⋊C8C2412yes—
245C2×C71⋊C8C2412yes—
246C2×C71⋊C8C2412yes—
247C2×C71⋊C8C2412yes—
248(C2×D71)⋊C4—24no—
249(C2×D71)⋊C4—24no—
250(C2×D71)⋊C4—24no—
251(C2×D71)⋊C4—24no—
252C24×C71—21no—
253C24×C71C2×D411yescharacteristic
254C2×Q8×C71—21no—
255C2×Q8×C71—24no—
256C2×Q8×C71—22no—
257C2×Q8×C71—22no—
258C2×Q8×C71—82no—
259C2×Q8×C71C2412yes—
260C2×D4×C71—24no—
261C2×D4×C71—21no—
262C2×D4×C71—22no—
263C2×D4×C71—22no—
264C2×D4×C71—82no—
265C2×D4×C71C2412yes—
266C22×C4×C71—22no—
267C22×C4×C71—22no—
268C22×C4×C71—21no—
269C22×C4×C71—21no—
270C22×C4×C71—21no—
271C22×C4×C71—24no—
272C22×C4×C71—82no—
273C22×C4×C71C2×D411yescharacteristic
274C22×C4×C71C2×D412yes—
275C22×C4×C71C2×D411yescharacteristic
276C22×C4×C71C2×D411yescharacteristic
277C22×C4×C71C2×D411yescharacteristic
278C22×C4×C71C2×D411yescharacteristic
279C22×C4×C71C2412yes—
280C22×C4×C71C2411yescharacteristic
281C4⋊C4×C71—24no—
282C4⋊C4×C71—24no—
283C4⋊C4×C71—24no—
284C4⋊C4×C71—21no—
285C4⋊C4×C71—21no—
286C4⋊C4×C71C2×D414yes—
287C4⋊C4×C71C2×D414yes—
288C4⋊C4×C71C2412yes—
289C4⋊C4×C71C2412yes—
290C22⋊C4×C71—24no—
291C22⋊C4×C71—24no—
292C22⋊C4×C71—24no—
293C22⋊C4×C71—24no—
294C22⋊C4×C71—24no—
295C22⋊C4×C71C2×D414yes—
296C22⋊C4×C71C2×D414yes—
297C42×C71—24no—
298C42×C71C2×D412yes—
299C42×C71C2×D412yes—
300C42×C71C2412yes—
301C42×C71C2412yes—
302C23×C71—22no—
303C23×C71—22no—
304C23×C71—22no—
305C23×C71—22no—
306C23×C71—42no—
307C23×C71—42no—
308C23×C71—42no—
309C23×C71C22×D412yes—
310C23×C71C22×D411yescharacteristic
311C22×D71—22no—
312C22×D71—22no—
313C22×D71—22no—
314C22×D71—48no—
315C22×D71—42no—
316C22×D71—42no—
317C22×D71—42no—
318C22×D71—42no—
319C22×D71—42no—
320C22×D71—42no—
321C22×D71—42no—
322C22×D71—42no—
323C22×D71—42no—
324C22×D71—84no—
325C22×D71—84no—
326C22×D71—816no—
327Q8×C71—22no—
328Q8×C71—22no—
329Q8×C71—42no—
330Q8×C71—84no—
331D4×C71—22no—
332D4×C71—22no—
333D4×C71—42no—
334D4×C71—84no—
335C2×C4×C71—22no—
336C2×C4×C71—22no—
337C2×C4×C71—22no—
338C2×C4×C71—22no—
339C2×C4×C71—22no—
340C2×C4×C71—24no—
341C2×C4×C71—22no—
342C2×C4×C71—22no—
343C2×C4×C71—22no—
344C2×C4×C71—22no—
345C2×C4×C71—22no—
346C2×C4×C71—42no—
347C2×C4×C71—42no—
348C2×C4×C71—42no—
349C2×C4×C71—84no—
350C2×C4×C71C22×D412yes—
351C2×C4×C71C22×D412yes—
352C2×C4×C71C22×D412yes—
353C2×C4×C71C22×D412yes—
354C2×C4×C71C22×D412yes—
355C2×C4×C71C22×D411yescharacteristic
356C2×C4×C71H(5,𝔽2)12yes—
357C2×C4×C71H(5,𝔽2)12yes—
358C2×C4×C71C2511yescharacteristic
359C22⋊D71—48no—
360C2×Dic71—22no—
361C2×Dic71—42no—
362D284—22no—
363D284—22no—
364D284—22no—
365D284—22no—
366D284—22no—
367D284—22no—
368D284—48no—
369D284—42no—
370D284—42no—
371D284—42no—
372D284—84no—
373D284—84no—
374D284—84no—
375D284—84no—
376C4×D71—48no—
377Dic142—22no—
378Dic142—22no—
379Dic142—42no—
380C71⋊C8—22no—
381C71⋊C8—22no—
382C71⋊C8—22no—
383C71⋊C8—22no—
384C22×C71—22no—
385C22×C71—22no—
386C22×C71—22no—
387C22×C71—44no—
388C22×C71—42no—
389C22×C71—42no—
390C22×C71—42no—
391C22×C71—84no—
392C22×C71#53512yes—
393C22×C71#57612yes—
394C22×C71#57712yes—
395C22×C71C23×D411yescharacteristic
396C2×D71—42no—
397C2×D71—42no—
398C2×D71—42no—
399C2×D71—42no—
400C2×D71—42no—
401C2×D71—42no—
402C2×D71—42no—
403C2×D71—42no—
404C2×D71—42no—
405C2×D71—816no—
406C2×D71—84no—
407C2×D71—84no—
408C2×D71—84no—
409C4×C71—22no—
410C4×C71—22no—
411C4×C71—22no—
412C4×C71—22no—
413C4×C71—22no—
414C4×C71—42no—
415C4×C71—42no—
416C4×C71—42no—
417C4×C71#53512yes—
418C4×C71C2×H(5,𝔽2)11yescharacteristic
419C4×C71C2×H(5,𝔽2)11yescharacteristic
420Dic71—42no—
421C2×#3224—711nomaximal, Sylow
422C2×C71—42no—
423C2×C71—82no—
424C2×C71#322414yescomplemented
425C2×C71C2×#53511yescharacteristic
426C2×C71C2×#57611yescharacteristic
427C2×C71C2×#57711yescharacteristic
428D71—82no—
429D71—82no—
430D71—82no—
431C2×#542D7111yescharacteristic, complemented
432C2×#535—711no—
433#3224—7116no—
434C2×#496—711no—
435C2×#495—711no—
436C2×#489—711no—
437C2×#486—711no—
438C2×#464—711no—
439C2×#460—711no—
440C2×#463—711no—
441C2×#459—711no—
442C2×#452—711no—
443C2×#449—711no—
444C2×#450—711no—
445C2×#447—711no—
446C2×#433—711no—
447C71C2×#322411yescharacteristic, complemented, Sylow
448C22×#41—711no—
449C23×D4—711no—
450C22×Q16—711no—
451C22×SD16—711no—
452C22×SD16—711no—
453C22×SD16—711no—
454C22×SD16—711no—
455C22×D8—711no—
456C22×D8—711no—
457C22×D8—711no—
458#542—24no—
459#542C2×D7118yescomplemented
460#535—718no—
461#535—1424no—
462C2×C4⋊Q8C2×D7111yescharacteristic, complemented
463C2×#127—711no—
464C2×#127—711no—
465C2×#126—21no—
466C2×#124—21no—
467C2×#124—711no—
468C2×#124—711no—
469C2×#124C2×D7111yescharacteristic, complemented
470C2×#123—21no—
471C2×C22⋊Q8—21no—
472C2×C22⋊Q8C2×D7111yescharacteristic
473C2×#121—1421no—
474C2×#121—1421no—
475C2×#121C2×D7111yescharacteristic
476C2×#120—1421no—
477C2×#120—1421no—
478C2×C4×Q8C2×D7111yescharacteristic, complemented
479C2×C4×D4C2×D7111yescharacteristic, complemented
480C2×#117C2×D7111yescharacteristic
481#496—718no—
482#495—718no—
483#489—718no—
484#486—718no—
485#464—718no—
486#463—718no—
487#460—718no—
488#459—718no—
489#452—718no—
490#450—718no—
491#449—718no—
492#447—718no—
493#433—718no—
494C2×C4⋊C8—711no—
495C2×C4⋊C8—711no—
496C2×#103—711no—
497C2×#103—711no—
498C2×#102—711no—
499C2×#102—711no—
500C2×#102—711no—
501C2×#102—711no—
502C2×#102—711no—
503C2×#102—711no—
504C2×C22⋊C8—711no—
505C2×C22⋊C8—711no—
506C2×#97—711no—
507C2×C4×C8—711no—
508C25—1421no—
509C2×#41—2842no—
510C2×#41—2842no—
511C2×#41—714no—
512C2×#41—1422no—
513C22×Q8—21no—
514C22×Q8—711no—
515C22×Q8C22×D7111yescharacteristic
516C22×D4—21no—
517C22×D4—2842no—
518C22×D4—2842no—
519C22×D4—714no—
520C22×D4—711no—
521C22×D4—711no—
522C22×D4—711no—
523C22×D4—1421no—
524C22×D4—1421no—
525C22×D4—1422no—
526C22×D4—1421no—
527C22×D4—1421no—
528C22×D4—1421no—
529C22×D4—1421no—
530C22×D4C22×D7111yescharacteristic
531C23×C4—21no—
532C23×C4—1421no—
533C23×C4C22×D7111yescharacteristic
534C2×Q16—2842no—
535C2×Q16—714no—
536C2×SD16—2842no—
537C2×SD16—2842no—
538C2×SD16—2842no—
539C2×SD16—2842no—
540C2×SD16—714no—
541C2×SD16—714no—
542C2×SD16—714no—
543C2×SD16—714no—
544C2×D8—2842no—
545C2×D8—2842no—
546C2×D8—2842no—
547C2×D8—714no—
548C2×D8—714no—
549C2×D8—714no—
550C22×C8—711no—
551C22×C8—711no—
552C22×C8—711no—
553C22×C8—711no—
554C4⋊Q8—22no—
555C4⋊Q8C22×D7114yescomplemented
556#127—714no—
557#127—714no—
558#127—1422no—
559#127—1422no—
560#126—28no—
561#124—28no—
562#124—22no—
563#124—714no—
564#124—714no—
565#124—1422no—
566#124—1422no—
567#124C22×D7114yescomplemented
568#123—28no—
569C22⋊Q8—22no—
570C22⋊Q8—28no—
571C22⋊Q8C22×D7114yes—
572#121—22no—
573#121—1428no—
574#121—1428no—
575#121C22×D7114yes—
576#120—1428no—
577#120—1428no—
578C4×Q8—22no—
579C4×Q8C22×D7114yescomplemented
580C4×D4—22no—
581C4×D4C22×D7114yescomplemented
582#117C22⋊D7114yes—
583#117C22×D7114yes—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4C22⋊D7111yescharacteristic
588C2×C4⋊C4C22⋊D7111yescharacteristic
589C2×C4⋊C4C22×D7111yescharacteristic
590C2×C4⋊C4C22×D7111yescharacteristic
591C2×C22⋊C4—21no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—1421no—
597C2×C22⋊C4—1421no—
598C2×C22⋊C4—1421no—
599C2×C22⋊C4—1421no—
600C2×C22⋊C4C22⋊D7111yescharacteristic
601C2×C22⋊C4C22⋊D7111yescharacteristic
602C2×C42—21no—
603C2×C42C22×D7111yescharacteristic
604C2×C42C22×D7111yescharacteristic
605C4⋊C8—714no—
606C4⋊C8—714no—
607#103—714no—
608#103—714no—
609#102—714no—
610#102—714no—
611#102—714no—
612#102—714no—
613#102—714no—
614#102—714no—
615C22⋊C8—714no—
616C22⋊C8—714no—
617#97—714no—
618C4×C8—714no—
619C24—21no—
620C24—2844no—
621C24—5682no—
622C24—5682no—
623C24—1421no—
624C24—1421no—
625C24—1421no—
626C24—1424no—
627C24C2×C22⋊D7111yescharacteristic
628#41—2848no—
629#41—2844no—
630#41—2844no—
631C2×Q8—21no—
632C2×Q8—24no—
633C2×Q8—22no—
634C2×Q8—22no—
635C2×Q8—82no—
636C2×Q8—712no—
637C2×Q8—1422no—
638C2×Q8—1422no—
639C2×Q8—1421no—
640C2×Q8C23×D7112yes—
641C2×D4—24no—
642C2×D4—21no—
643C2×D4—22no—
644C2×D4—22no—
645C2×D4—82no—
646C2×D4—2844no—
647C2×D4—2848no—
648C2×D4—2844no—
649C2×D4—2844no—
650C2×D4—2844no—
651C2×D4—5682no—
652C2×D4—5682no—
653C2×D4—5682no—
654C2×D4—5682no—
655C2×D4—712no—
656C2×D4—712no—
657C2×D4—712no—
658C2×D4—1424no—
659C2×D4—1424no—
660C2×D4—1421no—
661C2×D4—1421no—
662C2×D4—1421no—
663C2×D4—1424no—
664C2×D4—1424no—
665C2×D4—1424no—
666C2×D4—1424no—
667C2×D4—1422no—
668C2×D4—1422no—
669C2×D4—1422no—
670C2×D4—1422no—
671C2×D4—1422no—
672C2×D4—1422no—
673C2×D4C23×D7112yes—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—24no—
680C22×C4—82no—
681C22×C4—2844no—
682C22×C4—1421no—
683C22×C4—1424no—
684C22×C4C2×C22⋊D7112yes—
685C22×C4C2×C22⋊D7111yescharacteristic
686C22×C4C2×C22⋊D7111yescharacteristic
687C22×C4C2×C22⋊D7111yescharacteristic
688C22×C4C2×C22⋊D7111yescharacteristic
689C22×C4C2×C22⋊D7111yescharacteristic
690C22×C4C23×D7112yes—
691C22×C4C23×D7111yescharacteristic
692Q16—2844no—
693SD16—2844no—
694SD16—2844no—
695SD16—2844no—
696SD16—2844no—
697D8—2844no—
698D8—2844no—
699D8—2844no—
700C2×C8—712no—
701C2×C8—712no—
702C2×C8—712no—
703C2×C8—712no—
704C2×C8—1422no—
705C2×C8—1422no—
706C2×C8—1422no—
707C2×C8—1422no—
708C4⋊C4—24no—
709C4⋊C4—24no—
710C4⋊C4—24no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4C2×C22⋊D7114yes—
714C4⋊C4C2×C22⋊D7114yes—
715C4⋊C4C23×D7112yes—
716C4⋊C4C23×D7112yes—
717C22⋊C4—24no—
718C22⋊C4—24no—
719C22⋊C4—24no—
720C22⋊C4—24no—
721C22⋊C4—24no—
722C22⋊C4—1424no—
723C22⋊C4—1424no—
724C22⋊C4—1424no—
725C22⋊C4—1424no—
726C22⋊C4C2×C22⋊D7114yes—
727C22⋊C4C2×C22⋊D7114yes—
728C42—24no—
729C42C2×C22⋊D7112yes—
730C42C2×C22⋊D7112yes—
731C42C23×D7112yes—
732C42C23×D7112yes—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—42no—
738C23—42no—
739C23—42no—
740C23—2848no—
741C23—2842no—
742C23—2842no—
743C23—2842no—
744C23—2842no—
745C23—2842no—
746C23—2842no—
747C23—2842no—
748C23—2842no—
749C23—2842no—
750C23—5684no—
751C23—5684no—
752C23—56816no—
753C23—1422no—
754C23—1422no—
755C23—1422no—
756C23C22×C22⋊D7112yes—
757C23C22×C22⋊D7111yescharacteristic
758Q8—22no—
759Q8—22no—
760Q8—42no—
761Q8—84no—
762Q8—2842no—
763Q8—1422no—
764Q8—1422no—
765D4—22no—
766D4—22no—
767D4—42no—
768D4—84no—
769D4—2848no—
770D4—2848no—
771D4—2842no—
772D4—2842no—
773D4—2842no—
774D4—5684no—
775D4—5684no—
776D4—5684no—
777D4—5684no—
778D4—1422no—
779D4—1422no—
780D4—1422no—
781D4—1422no—
782D4—1422no—
783D4—1422no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—24no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—42no—
796C2×C4—42no—
797C2×C4—42no—
798C2×C4—84no—
799C2×C4—2848no—
800C2×C4—2842no—
801C2×C4—1422no—
802C2×C4C22×C22⋊D7112yes—
803C2×C4C22×C22⋊D7112yes—
804C2×C4C22×C22⋊D7112yes—
805C2×C4C22×C22⋊D7112yes—
806C2×C4C22×C22⋊D7112yes—
807C2×C4C22×C22⋊D7111yescharacteristic
808C2×C4#1455617412yes—
809C2×C4#1455617412yes—
810C2×C4C24×D7111yescharacteristic
811C8—1422no—
812C8—1422no—
813C8—1422no—
814C8—1422no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—44no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—84no—
823C22—2842no—
824C22—2842no—
825C22—2842no—
826C22—2842no—
827C22—2842no—
828C22—2842no—
829C22—2842no—
830C22—2842no—
831C22—2842no—
832C22—56816no—
833C22—5684no—
834C22—5684no—
835C22—5684no—
836C22#1798656312yes—
837C22#1798680212yes—
838C22#1798680712yes—
839C22C23×C22⋊D7111yescharacteristic
840C4—22no—
841C4—22no—
842C4—22no—
843C4—22no—
844C4—22no—
845C4—42no—
846C4—42no—
847C4—42no—
848C4—2842no—
849C4#1798656312yes—
850C4C2×#1455617411yescharacteristic
851C4C2×#1455617411yescharacteristic
852C2—42no—
853C2—82no—
854C2—5682no—
855C2—5682no—
856C2—5682no—
857C2#2259942814yesdirect product factor
858C2C2×#1798656311yescharacteristic
859C2C2×#1798680211yescharacteristic
860C2C2×#1798680711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#542×C71C2
socleC23×C71C22×D4
hypercenterC2×#542D71
hypocenterC71C2×#3224
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#17986568C2semidirect
2. #22599428C2direct (N × H)
3. C2×#17986389C2semidirect
4. C2×#17986381C2semidirect
5. C2×#17986361C2semidirect
6. C2×#17986347C2semidirect
7. C2×#17986221C2semidirect
8. C2×#17986199C2semidirect
9. C2×#17986214C2semidirect
10. C2×#17986194C2semidirect
11. C2×#17986159C2semidirect
12. C2×#17986142C2semidirect
13. C2×#17986149C2semidirect
14. C2×#17986132C2semidirect
15. C2×#17986060C2semidirect
16. C2×#542×C71C2semidirect
19. C22×#11765855C22semidirect
20. C22×#11765853C22semidirect
23. C22×#11765852C22semidirect
26. C22×#11765850C22semidirect
28. #17986568C22semidirect
37. #17986389C22semidirect
38. #17986381C22semidirect
39. #17986361C22semidirect
40. #17986347C22semidirect
41. #17986221C22semidirect
42. #17986214C22semidirect
43. #17986199C22semidirect
44. #17986194C22semidirect
45. #17986159C22semidirect
46. #17986149C22semidirect
47. #17986142C22semidirect
48. #17986132C22semidirect
49. #17986060C22semidirect
50. C2×C4⋊(C71⋊C8)C22semidirect
51. C2×C4⋊(C71⋊C8)C22semidirect
52. C2×#14556051C22semidirect
53. C2×#14556051C22semidirect
58. C2×#14556048C22semidirect
59. C2×#14556048C22semidirect
62. C2×#14556039C22semidirect
63. C2×C4×C71⋊C8C22semidirect
65. #542×C71C22semidirect
66. C2×C4⋊Q8×C71C22semidirect
69. C2×#124×C71C22semidirect
74. C2×C4×Q8×C71C22semidirect
75. C2×C4×D4×C71C22semidirect
98. C2×#11765855C23semidirect
100. C2×#11765853C23semidirect
106. C2×#11765852C23semidirect
112. C2×#11765850C23semidirect
133. C4⋊(C71⋊C8)C23semidirect
134. C4⋊(C71⋊C8)C23semidirect
135. #14556051C23semidirect
136. #14556051C23semidirect
141. #14556048C23semidirect
142. #14556048C23semidirect
145. #14556039C23semidirect
146. C4×C71⋊C8C23semidirect
154. C4⋊Q8×C71C23semidirect
158. #124×C71C23semidirect
166. C4×Q8×C71C23semidirect
168. C4×D4×C71C23semidirect
424. C2×C71#3224semidirect
431. C2×#542D71semidirect
447. C71C2×#3224semidirect
459. #542C2×D71semidirect
462. C2×C4⋊Q8C2×D71semidirect
469. C2×#124C2×D71semidirect
478. C2×C4×Q8C2×D71semidirect
479. C2×C4×D4C2×D71semidirect
555. C4⋊Q8C22×D71semidirect
567. #124C22×D71semidirect
579. C4×Q8C22×D71semidirect
581. C4×D4C22×D71semidirect
857. C2#22599428direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179865682
#225994282
C2×#179863892
C2×#179863812
C2×#179863612
C2×#179863472
C2×#179862212
C2×#179861992
C2×#179862142
C2×#179861942
C2×#179861592
C2×#179861422
C2×#179861492
C2×#179861322
C2×#179860602
C2×#542×C712
C2×#322471