Finite Group Databasebeta

← C2×#22600331 #32874026

Subgroups — C2×#22600331 #32874026

Order 18176.

2374 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986653C211yesmaximal, characteristic, complemented
2#22600331C2116yesmaximal, direct product factor
3C2×#17986358C211yesmaximal, characteristic, complemented
4C2×#17986332C211yesmaximal, characteristic, complemented
5C2×#17986310C211yesmaximal, characteristic, complemented
6C2×#17986294C211yesmaximal, characteristic, complemented
7C2×#17986247C211yesmaximal, characteristic, complemented
8C2×#17986233C211yesmaximal, characteristic, complemented
9C2×#17986211C211yesmaximal, characteristic, complemented
10C2×#17986144C211yesmaximal, characteristic, complemented
11C2×#17986138C211yesmaximal, characteristic, complemented
12C2×#17986097C211yesmaximal, characteristic, complemented
13C2×#17986071C211yesmaximal, characteristic, complemented
14C2×#17986000C211yesmaximal, characteristic, complemented
15C22×#14556052C211yesmaximal, characteristic, complemented
16C2×#548×C71C211yesmaximal, characteristic, complemented
17C22×#11765864—21no—
18C22×#11765852C2211yescharacteristic
19C22×#11765852C2211yescharacteristic
20C22×#11765850C2211yescharacteristic
21C22×#11765849C2211yescharacteristic
22C23×C71⋊C8C2211yescharacteristic
23#17986653—24no—
24#17986653C2218yescomplemented
25C2×#14556128C2211yescharacteristic
26C2×#14556112—21no—
27C2×#14556112—21no—
28C2×#14556108—21no—
29C2×#14556102C2211yescharacteristic
30C2×#14556102C2211yescharacteristic
31C2×C4×D284C2211yescharacteristic
32C22×C4⋊Dic71C2211yescharacteristic
33C22×C4⋊Dic71C2211yescharacteristic
34#17986358C2218yescomplemented
35#17986332C2218yescomplemented
36#17986310C2218yescomplemented
37#17986294C2218yescomplemented
38#17986247C2218yescomplemented
39#17986233C2218yescomplemented
40#17986211C2218yescomplemented
41#17986144C2218yescomplemented
42#17986138C2218yescomplemented
43#17986097C2218yescomplemented
44#17986071C2218yescomplemented
45C2×#14556061C2211yescharacteristic
46C2×#14556061C2211yescharacteristic
47C2×#14556061C2211yescharacteristic
48C2×C4⋊(C71⋊C8)C2211yescharacteristic
49#17986000C2218yescomplemented
50C2×#14556052C2211yescharacteristic
51C2×#14556052C2211yescharacteristic
52C2×#14556052C2211yescharacteristic
53C2×#14556052C2211yescharacteristic
54C2×#14556052C2211yescharacteristic
55C2×#14556052C2211yescharacteristic
56C2×#14556052C2218yescomplemented
57C2×#14556049C2211yescharacteristic
58C2×#14556049C2211yescharacteristic
59C2×#14556049C2211yescharacteristic
60C2×#14556048C2211yescharacteristic
61C2×C22⋊(C71⋊C8)C2211yescharacteristic
62C2×C22⋊(C71⋊C8)C2211yescharacteristic
63C2×#14556039C2211yescharacteristic
64C22×#41×C71C2211yescharacteristic
65C23×Q8×C71C2211yescharacteristic
66#548×C71—24no—
67#548×C71C2218yescomplemented
68C2×#124×C71—21no—
69C2×#124×C71C2211yescharacteristic
70C2×C22⋊Q8×C71—21no—
71C2×C22⋊Q8×C71C2211yescharacteristic
72C2×#121×C71—21no—
73C2×#121×C71C2211yescharacteristic
74C2×C4×Q8×C71C2211yescharacteristic
75C2×C4×D4×C71—21no—
76C2×C4×D4×C71C2211yescharacteristic
77C2×#11765864—28no—
78C2×#11765864—48no—
79C22×Dic142—21no—
80C22×D284C2311yescharacteristic
81C22×C22⋊D71—21no—
82C22×C22⋊D71—21no—
83C23×Dic71—21no—
84C23×Dic71—21no—
85C22×C4×D71—21no—
86C2×#11765852—24no—
87C2×#11765852—42no—
88C2×#11765852C2314yes—
89C2×#11765852C2314yes—
90C2×#11765850—42no—
91C2×#11765850C2314yes—
92C2×#11765849—42no—
93C2×#11765849C2314yes—
94C22×C71⋊C8—42no—
95C22×C71⋊C8C2311yescharacteristic
96C22×C71⋊C8C2311yescharacteristic
97C22×C71⋊C8C2311yescharacteristic
98C22×C71⋊C8C2311yescharacteristic
99C22×C71⋊C8C2314yes—
100#14556128—22no—
101#14556128C2314yes—
102#14556112—28no—
103#14556112—28no—
104#14556108—28no—
105#14556102—22no—
106#14556102—22no—
107#14556102C2314yes—
108#14556102C2314yes—
109C4×D284—22no—
110C4×D284C2314yes—
111C2×C4⋊Dic71—22no—
112C2×C4⋊Dic71—22no—
113C2×C4⋊Dic71—21no—
114C2×C4⋊Dic71—21no—
115C2×C4⋊Dic71—21no—
116C2×C4⋊Dic71C2314yes—
117C2×C4⋊Dic71C2314yes—
118C2×C4⋊Dic71C2311yescharacteristic
119C2×C4⋊Dic71C2311yescharacteristic
120C2×C4⋊Dic71C2311yescharacteristic
121C2×(C2×D71)⋊C4—21no—
122C2×(C2×D71)⋊C4—21no—
123C2×(C2×D71)⋊C4—21no—
124#14556061C2314yes—
125#14556061C2314yes—
126#14556061C2314yes—
127C4⋊(C71⋊C8)C2314yes—
128#14556052C2314yes—
129#14556052C2314yes—
130#14556052C2314yes—
131#14556052C2314yes—
132#14556052C2314yes—
133#14556052C2314yes—
134#14556049C2314yes—
135#14556049C2314yes—
136#14556049C2314yes—
137#14556048C2314yes—
138C22⋊(C71⋊C8)C2314yes—
139C22⋊(C71⋊C8)C2314yes—
140#14556039C2314yes—
141C2×#41×C71—22no—
142C2×#41×C71—24no—
143C2×#41×C71—42no—
144C2×#41×C71C2314yes—
145C22×Q8×C71—21no—
146C22×Q8×C71—22no—
147C22×Q8×C71—24no—
148C22×Q8×C71—42no—
149C22×Q8×C71C2311yescharacteristic
150C22×Q8×C71C2314yes—
151C22×Q8×C71C2311yescharacteristic
152C22×D4×C71—21no—
153C22×D4×C71—21no—
154C22×D4×C71D411yescharacteristic
155C22×D4×C71C2311yescharacteristic
156C23×C4×C71—21no—
157C23×C4×C71—21no—
158C23×C4×C71C2311yescharacteristic
159C23×C4×C71C2311yescharacteristic
160#124×C71—28no—
161#124×C71—22no—
162#124×C71C2314yes—
163C22⋊Q8×C71—22no—
164C22⋊Q8×C71—28no—
165C22⋊Q8×C71C2314yes—
166#121×C71—28no—
167#121×C71—22no—
168#121×C71C2314yes—
169C4×Q8×C71—22no—
170C4×Q8×C71C2314yes—
171C4×D4×C71—28no—
172C4×D4×C71D414yes—
173C4×D4×C71C2314yes—
174C2×C4⋊C4×C71—21no—
175C2×C4⋊C4×C71—21no—
176C2×C4⋊C4×C71D411yescharacteristic
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×C71D411yescharacteristic
183C2×C22⋊C4×C71D411yescharacteristic
184C2×C42×C71—21no—
185C2×C42×C71C2311yescharacteristic
186C23×D71—21no—
187#11765864—432no—
188C2×Dic142—24no—
189C2×Dic142—44no—
190C2×D284—22no—
191C2×D284—22no—
192C2×D284—21no—
193C2×D284C2412yes—
194C2×C22⋊D71—24no—
195C2×C22⋊D71—24no—
196C2×C22⋊D71—44no—
197C2×C22⋊D71—44no—
198C22×Dic71—21no—
199C22×Dic71—21no—
200C22×Dic71—21no—
201C22×Dic71—24no—
202C22×Dic71—24no—
203C22×Dic71—44no—
204C22×Dic71—44no—
205C2×C4×D71—24no—
206C2×C4×D71—44no—
207#11765852—28no—
208#11765852—44no—
209#11765850—44no—
210#11765849—44no—
211C2×C71⋊C8—22no—
212C2×C71⋊C8—22no—
213C2×C71⋊C8—22no—
214C2×C71⋊C8—22no—
215C2×C71⋊C8—44no—
216C2×C71⋊C8C2412yes—
217C2×C71⋊C8C2412yes—
218C2×C71⋊C8C2412yes—
219C2×C71⋊C8C2412yes—
220C4⋊Dic71—21no—
221C4⋊Dic71—21no—
222C4⋊Dic71—21no—
223C4⋊Dic71—24no—
224C4⋊Dic71—24no—
225C4⋊Dic71—24no—
226C4⋊Dic71C2412yes—
227C4⋊Dic71C2412yes—
228C4⋊Dic71C2412yes—
229(C2×D71)⋊C4—24no—
230(C2×D71)⋊C4—24no—
231(C2×D71)⋊C4—24no—
232C24×C71—21no—
233C24×C71C2×D411yescharacteristic
234C24×C71C2×D411yescharacteristic
235#41×C71—28no—
236#41×C71—44no—
237#41×C71—48no—
238C2×Q8×C71—21no—
239C2×Q8×C71—24no—
240C2×Q8×C71—21no—
241C2×Q8×C71—22no—
242C2×Q8×C71—28no—
243C2×Q8×C71—22no—
244C2×Q8×C71—22no—
245C2×Q8×C71—44no—
246C2×Q8×C71—44no—
247C2×Q8×C71—48no—
248C2×Q8×C71#4114yescomplemented
249C2×Q8×C71C2412yes—
250C2×Q8×C71C2412yes—
251C2×D4×C71—24no—
252C2×D4×C71—24no—
253C2×D4×C71—24no—
254C2×D4×C71—21no—
255C2×D4×C71—22no—
256C2×D4×C71—22no—
257C2×D4×C71—44no—
258C2×D4×C71—44no—
259C2×D4×C71C2×D414yes—
260C2×D4×C71C2412yes—
261C22×C4×C71—21no—
262C22×C4×C71—22no—
263C22×C4×C71—22no—
264C22×C4×C71—22no—
265C22×C4×C71—22no—
266C22×C4×C71—21no—
267C22×C4×C71—21no—
268C22×C4×C71—24no—
269C22×C4×C71—24no—
270C22×C4×C71—44no—
271C22×C4×C71—44no—
272C22×C4×C71C2×D411yescharacteristic
273C22×C4×C71C2×D411yescharacteristic
274C22×C4×C71C2×D411yescharacteristic
275C22×C4×C71C2×D411yescharacteristic
276C22×C4×C71C2×D412yes—
277C22×C4×C71C2×D412yes—
278C22×C4×C71C2412yes—
279C22×C4×C71C2412yes—
280C22×C4×C71C2411yescharacteristic
281C4⋊C4×C71—24no—
282C4⋊C4×C71—24no—
283C4⋊C4×C71—21no—
284C4⋊C4×C71C2×D414yes—
285C4⋊C4×C71C2412yes—
286C22⋊C4×C71—24no—
287C22⋊C4×C71—24no—
288C22⋊C4×C71—24no—
289C22⋊C4×C71—24no—
290C22⋊C4×C71C2×D414yes—
291C22⋊C4×C71C2×D414yes—
292C42×C71—24no—
293C42×C71C2×D412yes—
294C42×C71C2412yes—
295C23×C71—22no—
296C23×C71—22no—
297C23×C71—22no—
298C23×C71—22no—
299C23×C71—22no—
300C23×C71—22no—
301C23×C71—42no—
302C23×C71—42no—
303C23×C71—42no—
304C23×C71AGL(1,ℤ/8)14yes—
305C23×C71C22×D412yes—
306C23×C71C22×D412yes—
307C23×C71C22×D411yescharacteristic
308C22×D71—22no—
309C22×D71—42no—
310C22×D71—42no—
311C22×D71—42no—
312Q8×C71—24no—
313Q8×C71—22no—
314Q8×C71—22no—
315Q8×C71—22no—
316Q8×C71—48no—
317Q8×C71—42no—
318Q8×C71C2×#4114yescomplemented
319D4×C71—28no—
320D4×C71—22no—
321D4×C71—22no—
322D4×C71—48no—
323D4×C71—48no—
324D4×C71—42no—
325C2×C4×C71—22no—
326C2×C4×C71—22no—
327C2×C4×C71—24no—
328C2×C4×C71—22no—
329C2×C4×C71—22no—
330C2×C4×C71—22no—
331C2×C4×C71—24no—
332C2×C4×C71—24no—
333C2×C4×C71—22no—
334C2×C4×C71—22no—
335C2×C4×C71—22no—
336C2×C4×C71—22no—
337C2×C4×C71—22no—
338C2×C4×C71—22no—
339C2×C4×C71—48no—
340C2×C4×C71—48no—
341C2×C4×C71—42no—
342C2×C4×C71—42no—
343C2×C4×C71C22×D412yes—
344C2×C4×C71C22×D412yes—
345C2×C4×C71C22×D412yes—
346C2×C4×C71C22×D412yes—
347C2×C4×C71C22×D411yescharacteristic
348C2×C4×C71C2×#4112yes—
349C2×C4×C71H(5,𝔽2)12yes—
350C2×C4×C71C2511yescharacteristic
351C22⋊D71—48no—
352C22⋊D71—48no—
353C2×Dic71—22no—
354C2×Dic71—22no—
355C2×Dic71—22no—
356C2×Dic71—48no—
357C2×Dic71—42no—
358C2×Dic71—42no—
359C2×Dic71—42no—
360C2×Dic71—48no—
361D284—22no—
362D284—22no—
363D284—42no—
364C4×D71—48no—
365Dic142—48no—
366C71⋊C8—22no—
367C71⋊C8—22no—
368C71⋊C8—22no—
369C71⋊C8—22no—
370C22×C71—22no—
371C22×C71—28no—
372C22×C71—22no—
373C22×C71—22no—
374C22×C71—22no—
375C22×C71—22no—
376C22×C71—44no—
377C22×C71—42no—
378C22×C71—42no—
379C22×C71—42no—
380C22×C71—84no—
381C22×C71#54612yes—
382C22×C71C2×AGL(1,ℤ/8)14yes—
383C22×C71C2×AGL(1,ℤ/8)12yes—
384C22×C71#57812yes—
385C22×C71C23×D411yescharacteristic
386C2×D71—42no—
387C2×D71—42no—
388C2×D71—42no—
389C2×D71—84no—
390C4×C71—22no—
391C4×C71—22no—
392C4×C71—24no—
393C4×C71—22no—
394C4×C71—22no—
395C4×C71—42no—
396C4×C71—42no—
397C4×C71#54612yes—
398C4×C71C22×#4111yescharacteristic
399C4×C71C2×H(5,𝔽2)11yescharacteristic
400Dic71—42no—
401Dic71—42no—
402Dic71—42no—
403C2×#3308—711nomaximal, Sylow
404C2×C71—24no—
405C2×C71—42no—
406C2×C71—82no—
407C2×C71#330814yescomplemented
408C2×C71C2×#54611yescharacteristic
409C2×C71C22×AGL(1,ℤ/8)11yescharacteristic
410C2×C71C2×#57811yescharacteristic
411D71—82no—
412C2×#548D7111yescharacteristic, complemented
413C2×#547—711no—
414#3308—7116no—
415C2×#489—711no—
416C2×#484—711no—
417C2×#480—711no—
418C2×#477—711no—
419C2×#468—711no—
420C2×#466—711no—
421C2×#463—711no—
422C2×#449—711no—
423C2×#448—711no—
424C2×#440—711no—
425C2×#435—711no—
426C2×#417—711no—
427C22×#103—711no—
428C71C2×#330811yescharacteristic, complemented, Sylow
429C22×#41—1421no—
430C22×#41C2×D7111yescharacteristic
431C23×Q8C2×D7111yescharacteristic
432C22×SD16—711no—
433C22×SD16—711no—
434C22×D8—711no—
435C22×M16—711no—
436C23×C8—711no—
437#548—24no—
438#548C2×D7118yescomplemented
439#547—718no—
440#547—1424no—
441C2×C4⋊Q8—711no—
442C2×#124—21no—
443C2×#124C2×D7111yescharacteristic
444C2×#123—1421no—
445C2×#123—1421no—
446C2×C22⋊Q8—21no—
447C2×C22⋊Q8—1421no—
448C2×C22⋊Q8C2×D7111yescharacteristic
449C2×#121—21no—
450C2×#121—711no—
451C2×#121—711no—
452C2×#121C2×D7111yescharacteristic
453C2×C4×Q8C2×D7111yescharacteristic
454C2×C4×D4—21no—
455C2×C4×D4—711no—
456C2×C4×D4C2×D7111yescharacteristic
457C22×C4⋊C4—711no—
458C22×C4⋊C4—711no—
459#489—718no—
460#484—718no—
461#480—718no—
462#477—718no—
463#468—718no—
464#466—718no—
465#463—718no—
466#449—718no—
467#448—718no—
468#440—718no—
469#435—718no—
470C2×#107—711no—
471C2×#107—711no—
472C2×#107—711no—
473C2×C4⋊C8—711no—
474#417—718no—
475C2×#103—711no—
476C2×#103—711no—
477C2×#103—711no—
478C2×#103—711no—
479C2×#103—711no—
480C2×#103—711no—
481C2×#103—718no—
482C2×#102—711no—
483C2×#102—711no—
484C2×#102—711no—
485C2×#102—711no—
486C2×C22⋊C8—711no—
487C2×C22⋊C8—711no—
488C2×#97—711no—
489C2×#41—22no—
490C2×#41—24no—
491C2×#41—42no—
492C2×#41—2848no—
493C2×#41—1428no—
494C2×#41C22×D7114yes—
495C22×Q8—21no—
496C22×Q8—22no—
497C22×Q8—24no—
498C22×Q8—42no—
499C22×Q8—1421no—
500C22×Q8C22×D7111yescharacteristic
501C22×Q8C22×D7114yes—
502C22×Q8C22×D7111yescharacteristic
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—711no—
506C22×D4—1421no—
507C22×D4—1421no—
508C22×D4C22⋊D7111yescharacteristic
509C22×D4C22×D7111yescharacteristic
510C23×C4—21no—
511C23×C4—21no—
512C23×C4—1421no—
513C23×C4—1421no—
514C23×C4—1421no—
515C23×C4C22×D7111yescharacteristic
516C23×C4C22×D7111yescharacteristic
517C2×SD16—2842no—
518C2×SD16—714no—
519C2×SD16—714no—
520C2×SD16—1424no—
521C2×D8—2842no—
522C2×D8—714no—
523C2×M16—2842no—
524C2×M16—714no—
525C22×C8—2842no—
526C22×C8—714no—
527C22×C8—711no—
528C22×C8—711no—
529C22×C8—711no—
530C22×C8—711no—
531C4⋊Q8—714no—
532C4⋊Q8—1422no—
533#124—28no—
534#124—22no—
535#124C22×D7114yes—
536#123—1428no—
537#123—1428no—
538C22⋊Q8—22no—
539C22⋊Q8—28no—
540C22⋊Q8—1428no—
541C22⋊Q8C22×D7114yes—
542#121—28no—
543#121—22no—
544#121—714no—
545#121—714no—
546#121—1422no—
547#121—1422no—
548#121C22×D7114yes—
549C4×Q8—22no—
550C4×Q8C22×D7114yes—
551C4×D4—28no—
552C4×D4—714no—
553C4×D4—1422no—
554C4×D4C22⋊D7114yes—
555C4×D4C22×D7114yes—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—711no—
559C2×C4⋊C4—711no—
560C2×C4⋊C4—711no—
561C2×C4⋊C4—714no—
562C2×C4⋊C4—714no—
563C2×C4⋊C4—1421no—
564C2×C4⋊C4—1421no—
565C2×C4⋊C4—1422no—
566C2×C4⋊C4—1422no—
567C2×C4⋊C4—1421no—
568C2×C4⋊C4C22⋊D7111yescharacteristic
569C2×C4⋊C4C22×D7111yescharacteristic
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—1421no—
575C2×C22⋊C4—1421no—
576C2×C22⋊C4—1421no—
577C2×C22⋊C4C22⋊D7111yescharacteristic
578C2×C22⋊C4C22⋊D7111yescharacteristic
579C2×C42—21no—
580C2×C42C22×D7111yescharacteristic
581#107—714no—
582#107—714no—
583#107—714no—
584C4⋊C8—714no—
585#103—714no—
586#103—714no—
587#103—714no—
588#103—714no—
589#103—714no—
590#103—714no—
591#102—714no—
592#102—714no—
593#102—714no—
594#102—714no—
595C22⋊C8—714no—
596C22⋊C8—714no—
597#97—714no—
598C24—21no—
599C24—1421no—
600C24C2×C22⋊D7111yescharacteristic
601C24C2×C22⋊D7111yescharacteristic
602#41—28no—
603#41—44no—
604#41—48no—
605#41—28432no—
606C2×Q8—21no—
607C2×Q8—24no—
608C2×Q8—21no—
609C2×Q8—22no—
610C2×Q8—28no—
611C2×Q8—22no—
612C2×Q8—22no—
613C2×Q8—44no—
614C2×Q8—44no—
615C2×Q8—48no—
616C2×Q8—2844no—
617C2×Q8—1424no—
618C2×Q8#1176586414yescomplemented
619C2×Q8C23×D7112yes—
620C2×Q8C23×D7112yes—
621C2×D4—24no—
622C2×D4—24no—
623C2×D4—24no—
624C2×D4—21no—
625C2×D4—22no—
626C2×D4—22no—
627C2×D4—44no—
628C2×D4—44no—
629C2×D4—2844no—
630C2×D4—2844no—
631C2×D4—712no—
632C2×D4—1424no—
633C2×D4—1424no—
634C2×D4—1421no—
635C2×D4—1422no—
636C2×D4—1422no—
637C2×D4C2×C22⋊D7114yes—
638C2×D4C23×D7112yes—
639C22×C4—21no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—24no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—24no—
648C22×C4—44no—
649C22×C4—44no—
650C22×C4—2844no—
651C22×C4—2844no—
652C22×C4—2844no—
653C22×C4—1424no—
654C22×C4—1424no—
655C22×C4—1421no—
656C22×C4—1421no—
657C22×C4—1421no—
658C22×C4—1424no—
659C22×C4C2×C22⋊D7112yes—
660C22×C4C2×C22⋊D7112yes—
661C22×C4C2×C22⋊D7111yescharacteristic
662C22×C4C2×C22⋊D7111yescharacteristic
663C22×C4C2×C22⋊D7111yescharacteristic
664C22×C4C2×C22⋊D7111yescharacteristic
665C22×C4C23×D7112yes—
666C22×C4C23×D7112yes—
667C22×C4C23×D7111yescharacteristic
668SD16—2844no—
669SD16—1428no—
670D8—2844no—
671M16—2844no—
672C2×C8—2844no—
673C2×C8—712no—
674C2×C8—712no—
675C2×C8—712no—
676C2×C8—712no—
677C2×C8—1422no—
678C2×C8—1422no—
679C2×C8—1422no—
680C2×C8—1422no—
681C4⋊C4—24no—
682C4⋊C4—24no—
683C4⋊C4—21no—
684C4⋊C4—712no—
685C4⋊C4—712no—
686C4⋊C4—712no—
687C4⋊C4—1421no—
688C4⋊C4—1421no—
689C4⋊C4—1421no—
690C4⋊C4—1424no—
691C4⋊C4—1424no—
692C4⋊C4—1424no—
693C4⋊C4C2×C22⋊D7114yes—
694C4⋊C4C23×D7112yes—
695C22⋊C4—24no—
696C22⋊C4—24no—
697C22⋊C4—24no—
698C22⋊C4—24no—
699C22⋊C4—1424no—
700C22⋊C4—1424no—
701C22⋊C4—1424no—
702C22⋊C4C2×C22⋊D7114yes—
703C22⋊C4C2×C22⋊D7114yes—
704C42—24no—
705C42C2×C22⋊D7112yes—
706C42C23×D7112yes—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—2842no—
717C23—2842no—
718C23—2842no—
719C23—1422no—
720C23#1455615314yes—
721C23C22×C22⋊D7112yes—
722C23C22×C22⋊D7112yes—
723C23C22×C22⋊D7111yescharacteristic
724Q8—22no—
725Q8—24no—
726Q8—22no—
727Q8—22no—
728Q8—48no—
729Q8—42no—
730Q8—2848no—
731Q8C2×#1176586414yescomplemented
732D4—28no—
733D4—22no—
734D4—22no—
735D4—48no—
736D4—48no—
737D4—42no—
738D4—2848no—
739D4—2848no—
740D4—2842no—
741D4—1422no—
742D4—1422no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—24no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—48no—
758C2×C4—48no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—2848no—
762C2×C4—2848no—
763C2×C4—2842no—
764C2×C4—2842no—
765C2×C4—2842no—
766C2×C4—2848no—
767C2×C4—1422no—
768C2×C4—1422no—
769C2×C4—1422no—
770C2×C4C22×C22⋊D7112yes—
771C2×C4C22×C22⋊D7112yes—
772C2×C4C22×C22⋊D7112yes—
773C2×C4C22×C22⋊D7112yes—
774C2×C4C22×C22⋊D7111yescharacteristic
775C2×C4C2×#1176586412yes—
776C2×C4#1455617312yes—
777C2×C4C24×D7111yescharacteristic
778C8—1422no—
779C8—1422no—
780C8—1422no—
781C8—1422no—
782C22—22no—
783C22—22no—
784C22—28no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—44no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—84no—
793C22—2842no—
794C22—2842no—
795C22—2842no—
796C22—5684no—
797C22#1798664312yes—
798C22C2×#1455615314yes—
799C22C2×#1455615312yes—
800C22#1798681412yes—
801C22C23×C22⋊D7111yescharacteristic
802C4—22no—
803C4—22no—
804C4—24no—
805C4—22no—
806C4—22no—
807C4—42no—
808C4—42no—
809C4—2842no—
810C4—2842no—
811C4—2842no—
812C4#1798664312yes—
813C4C22×#1176586411yescharacteristic
814C4C2×#1455617311yescharacteristic
815C2—24no—
816C2—42no—
817C2—82no—
818C2—5682no—
819C2#2260033114yesdirect product factor
820C2C2×#1798664311yescharacteristic
821C2C22×#1455615311yescharacteristic
822C2C2×#1798681411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#548×C71C2
socleC23×C71C22×D4
hypercenterC2×#548D71
hypocenterC71C2×#3308
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C2×#17986653C2semidirect
2. #22600331C2direct (N × H)
3. C2×#17986358C2semidirect
4. C2×#17986332C2semidirect
5. C2×#17986310C2semidirect
6. C2×#17986294C2semidirect
7. C2×#17986247C2semidirect
8. C2×#17986233C2semidirect
9. C2×#17986211C2semidirect
10. C2×#17986144C2semidirect
11. C2×#17986138C2semidirect
12. C2×#17986097C2semidirect
13. C2×#17986071C2semidirect
14. C2×#17986000C2semidirect
15. C22×#14556052C2semidirect
16. C2×#548×C71C2semidirect
24. #17986653C22semidirect
34. #17986358C22semidirect
35. #17986332C22semidirect
36. #17986310C22semidirect
37. #17986294C22semidirect
38. #17986247C22semidirect
39. #17986233C22semidirect
40. #17986211C22semidirect
41. #17986144C22semidirect
42. #17986138C22semidirect
43. #17986097C22semidirect
44. #17986071C22semidirect
49. #17986000C22semidirect
56. C2×#14556052C22semidirect
67. #548×C71C22semidirect
248. C2×Q8×C71#41semidirect
318. Q8×C71C2×#41semidirect
407. C2×C71#3308semidirect
412. C2×#548D71semidirect
428. C71C2×#3308semidirect
438. #548C2×D71semidirect
618. C2×Q8#11765864semidirect
731. Q8C2×#11765864semidirect
819. C2#22600331direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179866532
#226003312
C2×#179863582
C2×#179863322
C2×#179863102
C2×#179862942
C2×#179862472
C2×#179862332
C2×#179862112
C2×#179861442
C2×#179861382
C2×#179860972
C2×#179860712
C2×#179860002
C22×#145560522
C2×#548×C712
C2×#330871