Finite Group Databasebeta

← C2×#22601093 #32877201

Subgroups — C2×#22601093 #32877201

Order 18176.

1950 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986734C211yesmaximal, characteristic, complemented
2#22601093C2116yesmaximal, direct product factor
3C2×#17986365C211yesmaximal, characteristic, complemented
4C2×#17986361C211yesmaximal, characteristic, complemented
5C2×#17986356C211yesmaximal, characteristic, complemented
6C2×#17986303C211yesmaximal, characteristic, complemented
7C2×#17986296C211yesmaximal, characteristic, complemented
8C2×#17986276C211yesmaximal, characteristic, complemented
9C2×#17986214C211yesmaximal, characteristic, complemented
10C2×#17986214C211yesmaximal, characteristic, complemented
11C2×#17986194C211yesmaximal, characteristic
12C2×#17986130C211yesmaximal, characteristic, complemented
13C2×#17986109C211yesmaximal, characteristic, complemented
14C2×#17986099C211yesmaximal, characteristic, complemented
15C2×C4×#11765850C211yesmaximal, characteristic, complemented
16C2×#554×C71C211yesmaximal, characteristic, complemented
17C22×#11765853C2211yescharacteristic
18C22×#11765850C2211yescharacteristic
19C22×#11765850C2211yescharacteristic
20#17986734—24no—
21#17986734C2218yescomplemented
22C2×#14556125C2211yescharacteristic
23C2×#14556117—21no—
24C2×#14556116C2211yescharacteristic
25C2×#14556116C2211yescharacteristic
26C2×#14556113—21no—
27C2×#14556113—21no—
28C2×C4×Dic142C2211yescharacteristic
29C2×C4×D284C2211yescharacteristic
30C2×C4×D284C2211yescharacteristic
31C2×#14556090—21no—
32#17986365C2218yescomplemented
33#17986361C2218yescomplemented
34#17986356C2218yescomplemented
35#17986303C2218yescomplemented
36#17986296C2218yescomplemented
37#17986276C2218yescomplemented
38#17986214C2218yescomplemented
39#17986214C2218yescomplemented
40#17986194C2218yes—
41#17986130C2218yescomplemented
42#17986109C2218yescomplemented
43#17986099C2218yescomplemented
44C4×#11765850C2218yescomplemented
45C2×#14556061C2211yescharacteristic
46C2×#14556061C2211yescharacteristic
47C2×#14556059C2211yescharacteristic
48C2×C4⋊(C71⋊C8)C2211yescharacteristic
49C2×C4⋊(C71⋊C8)C2211yescharacteristic
50C2×C4⋊(C71⋊C8)C2211yescharacteristic
51C2×#14556051C2211yescharacteristic
52C2×#14556051C2211yescharacteristic
53C2×#14556051C2211yescharacteristic
54C2×#14556049C2211yescharacteristic
55C2×#14556048C2211yescharacteristic
56C2×#14556048C2211yescharacteristic
57C2×#14556048C2211yescharacteristic
58C2×#14556048C2211yescharacteristic
59C2×#14556048C2211yescharacteristic
60C2×#14556048C2211yescharacteristic
61C2×#14556039C2211yescharacteristic
62C2×#14556039C2211yescharacteristic
63C2×C4×C71⋊C8C2211yescharacteristic
64#554×C71—24no—
65#554×C71C2218yescomplemented
66C2×C4⋊Q8×C71C2211yescharacteristic
67C2×#125×C71C2211yescharacteristic
68C2×#125×C71C2211yescharacteristic
69C2×C22⋊Q8×C71—21no—
70C2×C22⋊Q8×C71—21no—
71C2×C22⋊Q8×C71—21no—
72C2×C4×Q8×C71C2211yescharacteristic
73C2×C4×D4×C71C2211yescharacteristic
74C2×C4×D4×C71C2211yescharacteristic
75C2×C4×D4×C71C2211yescharacteristic
76C22×C4⋊C4×C71—21no—
77C22×Dic142C2311yescharacteristic
78C22×D284—21no—
79C22×D284—21no—
80C22×D284C2311yescharacteristic
81C22×D284C2311yescharacteristic
82C22×C4×D71—21no—
83C22×C4×D71—21no—
84C2×#11765853—24no—
85C2×#11765853C2314yes—
86C2×#11765850—24no—
87C2×#11765850—24no—
88C2×#11765850C2314yes—
89C2×#11765850C2314yes—
90C22×C71⋊C8C2311yescharacteristic
91C22×C71⋊C8C2311yescharacteristic
92C22×C71⋊C8C2311yescharacteristic
93C22×C71⋊C8C2311yescharacteristic
94#14556125—22no—
95#14556125C2314yes—
96#14556117—28no—
97#14556116—22no—
98#14556116—22no—
99#14556116C2314yes—
100#14556116C2314yes—
101#14556113—28no—
102#14556113—28no—
103C4×Dic142—22no—
104C4×Dic142C2314yes—
105C4×D284—22no—
106C4×D284—22no—
107C4×D284C2314yes—
108C4×D284C2314yes—
109#14556090—28no—
110C2×C4⋊Dic71C2311yescharacteristic
111C2×Dic71⋊C4—21no—
112C2×(C2×D71)⋊C4—21no—
113C2×(C2×D71)⋊C4—21no—
114C2×(C2×D71)⋊C4—21no—
115C2×(C2×D71)⋊C4—21no—
116C2×(C2×D71)⋊C4—21no—
117C2×(C2×D71)⋊C4—21no—
118C2×C4×Dic71—21no—
119#14556061C2314yes—
120#14556061C2314yes—
121#14556059C2314yes—
122C4⋊(C71⋊C8)C2314yes—
123C4⋊(C71⋊C8)C2314yes—
124C4⋊(C71⋊C8)C2314yes—
125#14556051C2314yes—
126#14556051C2314yes—
127#14556051C2314yes—
128#14556049C2314yes—
129#14556048C2314yes—
130#14556048C2314yes—
131#14556048C2314yes—
132#14556048C2314yes—
133#14556048C2314yes—
134#14556048C2314yes—
135#14556039C2314yes—
136#14556039C2314yes—
137C4×C71⋊C8C2314yes—
138C22×Q8×C71—21no—
139C22×Q8×C71D411yescharacteristic
140C22×D4×C71C2311yescharacteristic
141C23×C4×C71—21no—
142C23×C4×C71—21no—
143C23×C4×C71—21no—
144C4⋊Q8×C71—22no—
145C4⋊Q8×C71C2314yes—
146#125×C71—22no—
147#125×C71—22no—
148#125×C71C2314yes—
149#125×C71C2314yes—
150C22⋊Q8×C71—28no—
151C22⋊Q8×C71—28no—
152C22⋊Q8×C71—28no—
153C4×Q8×C71D414yes—
154C4×Q8×C71C2314yes—
155C4×D4×C71—22no—
156C4×D4×C71—22no—
157C4×D4×C71—22no—
158C4×D4×C71C2314yes—
159C4×D4×C71C2314yes—
160C4×D4×C71C2314yes—
161C2×C4⋊C4×C71—21no—
162C2×C4⋊C4×C71—21no—
163C2×C4⋊C4×C71—21no—
164C2×C4⋊C4×C71—21no—
165C2×C4⋊C4×C71—21no—
166C2×C4⋊C4×C71—28no—
167C2×C4⋊C4×C71D411yescharacteristic
168C2×C4⋊C4×C71D411yescharacteristic
169C2×C4⋊C4×C71D411yescharacteristic
170C2×C4⋊C4×C71C2311yescharacteristic
171C2×C4⋊C4×C71C2311yescharacteristic
172C2×C4⋊C4×C71C2311yescharacteristic
173C2×C22⋊C4×C71—21no—
174C2×C22⋊C4×C71—21no—
175C2×C22⋊C4×C71—21no—
176C2×C42×C71C2311yescharacteristic
177C2×C42×C71C2311yescharacteristic
178C2×C42×C71C2311yescharacteristic
179C23×D71—21no—
180C23×D71—21no—
181C2×Dic142—22no—
182C2×Dic142—22no—
183C2×Dic142—21no—
184C2×Dic142C2412yes—
185C2×D284—22no—
186C2×D284—22no—
187C2×D284—22no—
188C2×D284—22no—
189C2×D284—24no—
190C2×D284—21no—
191C2×D284—21no—
192C2×D284—24no—
193C2×D284—44no—
194C2×D284—82no—
195C2×D284C2412yes—
196C2×D284C2412yes—
197C22×Dic71—21no—
198C22×Dic71—21no—
199C2×C4×D71—24no—
200C2×C4×D71—24no—
201C2×C4×D71—82no—
202C2×C4×D71—82no—
203#11765853—28no—
204#11765850—28no—
205#11765850—28no—
206C2×C71⋊C8—22no—
207C2×C71⋊C8—22no—
208C2×C71⋊C8—22no—
209C2×C71⋊C8—22no—
210C2×C71⋊C8C2412yes—
211C2×C71⋊C8C2412yes—
212C2×C71⋊C8C2412yes—
213C2×C71⋊C8C2412yes—
214C4⋊Dic71—21no—
215C4⋊Dic71C2412yes—
216Dic71⋊C4—24no—
217(C2×D71)⋊C4—24no—
218(C2×D71)⋊C4—24no—
219(C2×D71)⋊C4—24no—
220(C2×D71)⋊C4—24no—
221(C2×D71)⋊C4—24no—
222(C2×D71)⋊C4—24no—
223C4×Dic71—24no—
224C24×C71—21no—
225C2×Q8×C71—24no—
226C2×Q8×C71—42no—
227C2×Q8×C71—82no—
228C2×Q8×C71C2×D414yes—
229C2×D4×C71—21no—
230C2×D4×C71—22no—
231C2×D4×C71#4114yes—
232C2×D4×C71C2412yes—
233C22×C4×C71—21no—
234C22×C4×C71—21no—
235C22×C4×C71—21no—
236C22×C4×C71—24no—
237C22×C4×C71—24no—
238C22×C4×C71—24no—
239C22×C4×C71—44no—
240C22×C4×C71—82no—
241C22×C4×C71—82no—
242C22×C4×C71C2×D411yescharacteristic
243C22×C4×C71C2×D411yescharacteristic
244C22×C4×C71C2×D411yescharacteristic
245C22×C4×C71C2×D411yescharacteristic
246C22×C4×C71C2×D411yescharacteristic
247C22×C4×C71C2×D411yescharacteristic
248C22×C4×C71C2411yescharacteristic
249C4⋊C4×C71—24no—
250C4⋊C4×C71—24no—
251C4⋊C4×C71—24no—
252C4⋊C4×C71—24no—
253C4⋊C4×C71—24no—
254C4⋊C4×C71—21no—
255C4⋊C4×C71—21no—
256C4⋊C4×C71—21no—
257C4⋊C4×C71C2×D414yes—
258C4⋊C4×C71C2×D414yes—
259C4⋊C4×C71C2×D414yes—
260C4⋊C4×C71C2412yes—
261C4⋊C4×C71C2412yes—
262C4⋊C4×C71C2412yes—
263C22⋊C4×C71—24no—
264C22⋊C4×C71—24no—
265C22⋊C4×C71—24no—
266C42×C71C2×D412yes—
267C42×C71C2×D412yes—
268C42×C71C2×D412yes—
269C42×C71C2412yes—
270C42×C71C2412yes—
271C42×C71C2412yes—
272C23×C71—24no—
273C23×C71—22no—
274C23×C71—42no—
275C23×C71—42no—
276C23×C71C22×D411yescharacteristic
277C22×D71—22no—
278C22×D71—22no—
279C22×D71—42no—
280C22×D71—42no—
281C22×D71—42no—
282C22×D71—42no—
283C22×D71—42no—
284C22×D71—42no—
285Q8×C71—44no—
286Q8×C71—84no—
287D4×C71—24no—
288D4×C71—22no—
289D4×C71C2×#4114yes—
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—22no—
299C2×C4×C71—48no—
300C2×C4×C71—42no—
301C2×C4×C71—42no—
302C2×C4×C71—42no—
303C2×C4×C71—84no—
304C2×C4×C71—84no—
305C2×C4×C71C22×D412yes—
306C2×C4×C71C22×D412yes—
307C2×C4×C71C22×D412yes—
308C2×C4×C71C22×D412yes—
309C2×C4×C71C22×D412yes—
310C2×C4×C71C22×D412yes—
311C2×C4×C71C22×D411yescharacteristic
312C2×C4×C71C2×#4112yes—
313C2×C4×C712−1+412yes—
314C2×C4×C71C2511yescharacteristic
315C2×Dic71—22no—
316C2×Dic71—22no—
317C2×Dic71—42no—
318C2×Dic71—42no—
319D284—22no—
320D284—22no—
321D284—22no—
322D284—22no—
323D284—48no—
324D284—42no—
325D284—42no—
326D284—84no—
327C4×D71—84no—
328C4×D71—84no—
329Dic142—22no—
330Dic142—22no—
331Dic142—42no—
332C71⋊C8—22no—
333C71⋊C8—22no—
334C71⋊C8—22no—
335C71⋊C8—22no—
336C22×C71—24no—
337C22×C71—48no—
338C22×C71—42no—
339C22×C71—42no—
340C22×C71#54812yes—
341C22×C71#57512yes—
342C22×C71#57612yes—
343C22×C71C23×D411yescharacteristic
344C2×D71—42no—
345C2×D71—42no—
346C2×D71—42no—
347C2×D71—42no—
348C2×D71—42no—
349C2×D71—42no—
350C2×D71—84no—
351C2×D71—84no—
352C4×C71—22no—
353C4×C71—22no—
354C4×C71—22no—
355C4×C71—22no—
356C4×C71—22no—
357C4×C71—22no—
358C4×C71—42no—
359C4×C71—42no—
360C4×C71—42no—
361C4×C71#54812yes—
362C4×C71C22×#4111yescharacteristic
363C4×C71C2×2−1+411yescharacteristic
364Dic71—42no—
365Dic71—42no—
366C2×#3370—711nomaximal, Sylow
367C2×C71—44no—
368C2×C71#337014yescomplemented
369C2×C71C2×#54811yescharacteristic
370C2×C71C2×#57511yescharacteristic
371C2×C71C2×#57611yescharacteristic
372D71—82no—
373D71—82no—
374C2×#559—711no—
375C2×#554D7111yescharacteristic, complemented
376#3370—7116no—
377C2×#490—711no—
378C2×#489—711no—
379C2×#488—711no—
380C2×#479—711no—
381C2×#478—711no—
382C2×#474—711no—
383C2×#463—711no—
384C2×#463—711no—
385C2×#459—711no—
386C2×#446—711no—
387C2×#442—711no—
388C2×#440—711no—
389C2×C4×D8—711no—
390C71C2×#337011yescharacteristic, complemented, Sylow
391C22×SD16—711no—
392C22×D8—711no—
393C22×D8—711no—
394#559—718no—
395#559—1424no—
396#554—24no—
397#554C2×D7118yescomplemented
398C2×C4⋊Q8C2×D7111yescharacteristic
399C2×#127—711no—
400C2×#125C2×D7111yescharacteristic
401C2×#125C2×D7111yescharacteristic
402C2×#124—711no—
403C2×#124—711no—
404C2×#124—1421no—
405C2×#123—1421no—
406C2×#123—1421no—
407C2×C22⋊Q8—21no—
408C2×C22⋊Q8—21no—
409C2×C22⋊Q8—21no—
410C2×C4×Q8—711no—
411C2×C4×Q8C2×D7111yescharacteristic
412C2×C4×D4—711no—
413C2×C4×D4—711no—
414C2×C4×D4—1421no—
415C2×C4×D4C2×D7111yescharacteristic
416C2×C4×D4C2×D7111yescharacteristic
417C2×C4×D4C2×D7111yescharacteristic
418C22×C4⋊C4—21no—
419#490—718no—
420#489—718no—
421#488—718no—
422#479—718no—
423#478—718no—
424#474—718no—
425#463—718no—
426#463—718no—
427#459—718no—
428#446—718no—
429#442—718no—
430#440—718no—
431C4×D8—718no—
432C2×#107—711no—
433C2×#107—711no—
434C2×#106—711no—
435C2×C4⋊C8—711no—
436C2×C4⋊C8—711no—
437C2×C4⋊C8—711no—
438C2×#103—711no—
439C2×#103—711no—
440C2×#103—711no—
441C2×#102—711no—
442C2×#102—711no—
443C2×#102—711no—
444C2×#102—711no—
445C2×#102—711no—
446C2×#102—711no—
447C2×#102—711no—
448C2×#97—711no—
449C2×#97—711no—
450C2×C4×C8—711no—
451C22×Q8—21no—
452C22×Q8—711no—
453C22×Q8C22⋊D7111yescharacteristic
454C22×D4—711no—
455C22×D4—711no—
456C22×D4—1421no—
457C22×D4—1421no—
458C22×D4C22×D7111yescharacteristic
459C23×C4—21no—
460C23×C4—21no—
461C23×C4—21no—
462C23×C4—1421no—
463C23×C4—1421no—
464C2×SD16—714no—
465C2×SD16—1424no—
466C2×D8—714no—
467C2×D8—714no—
468C2×D8—1424no—
469C2×D8—1424no—
470C22×C8—711no—
471C22×C8—711no—
472C22×C8—711no—
473C22×C8—711no—
474C4⋊Q8—22no—
475C4⋊Q8C22×D7114yes—
476#127—714no—
477#127—1422no—
478#125—22no—
479#125—22no—
480#125C22×D7114yes—
481#125C22×D7114yes—
482#124—714no—
483#124—714no—
484#124—1428no—
485#124—1422no—
486#124—1422no—
487#123—1428no—
488#123—1428no—
489C22⋊Q8—28no—
490C22⋊Q8—28no—
491C22⋊Q8—28no—
492C4×Q8—714no—
493C4×Q8—1422no—
494C4×Q8C22⋊D7114yes—
495C4×Q8C22×D7114yes—
496C4×D4—22no—
497C4×D4—22no—
498C4×D4—22no—
499C4×D4—714no—
500C4×D4—714no—
501C4×D4—1428no—
502C4×D4—1422no—
503C4×D4—1422no—
504C4×D4C22×D7114yes—
505C4×D4C22×D7114yes—
506C4×D4C22×D7114yes—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—28no—
513C2×C4⋊C4—711no—
514C2×C4⋊C4—1421no—
515C2×C4⋊C4C22⋊D7111yescharacteristic
516C2×C4⋊C4C22⋊D7111yescharacteristic
517C2×C4⋊C4C22⋊D7111yescharacteristic
518C2×C4⋊C4C22×D7111yescharacteristic
519C2×C4⋊C4C22×D7111yescharacteristic
520C2×C4⋊C4C22×D7111yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—1421no—
525C2×C22⋊C4—1421no—
526C2×C22⋊C4—1421no—
527C2×C22⋊C4—1421no—
528C2×C22⋊C4—1421no—
529C2×C22⋊C4—1421no—
530C2×C42—1421no—
531C2×C42C22×D7111yescharacteristic
532C2×C42C22×D7111yescharacteristic
533C2×C42C22×D7111yescharacteristic
534#107—714no—
535#107—714no—
536#106—714no—
537C4⋊C8—714no—
538C4⋊C8—714no—
539C4⋊C8—714no—
540#103—714no—
541#103—714no—
542#103—714no—
543#102—714no—
544#102—714no—
545#102—714no—
546#102—714no—
547#102—714no—
548#102—714no—
549#102—714no—
550#97—714no—
551#97—714no—
552C4×C8—714no—
553C24—21no—
554C24—1421no—
555C24—1421no—
556C2×Q8—24no—
557C2×Q8—42no—
558C2×Q8—82no—
559C2×Q8—712no—
560C2×Q8—1422no—
561C2×Q8—1422no—
562C2×Q8—1421no—
563C2×Q8C2×C22⋊D7114yes—
564C2×D4—21no—
565C2×D4—22no—
566C2×D4—2844no—
567C2×D4—5682no—
568C2×D4—712no—
569C2×D4—712no—
570C2×D4—1424no—
571C2×D4—1421no—
572C2×D4—1421no—
573C2×D4—1424no—
574C2×D4—1422no—
575C2×D4—1422no—
576C2×D4—1422no—
577C2×D4—1422no—
578C2×D4#1176586614yes—
579C2×D4C23×D7112yes—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—24no—
584C22×C4—24no—
585C22×C4—24no—
586C22×C4—44no—
587C22×C4—82no—
588C22×C4—82no—
589C22×C4—5682no—
590C22×C4—5682no—
591C22×C4—1421no—
592C22×C4—1421no—
593C22×C4—1424no—
594C22×C4—1424no—
595C22×C4C2×C22⋊D7111yescharacteristic
596C22×C4C2×C22⋊D7111yescharacteristic
597C22×C4C2×C22⋊D7111yescharacteristic
598C22×C4C2×C22⋊D7111yescharacteristic
599C22×C4C2×C22⋊D7111yescharacteristic
600C22×C4C2×C22⋊D7111yescharacteristic
601C22×C4C23×D7111yescharacteristic
602SD16—1428no—
603D8—1428no—
604D8—1428no—
605C2×C8—712no—
606C2×C8—712no—
607C2×C8—712no—
608C2×C8—712no—
609C2×C8—1422no—
610C2×C8—1422no—
611C2×C8—1422no—
612C2×C8—1422no—
613C4⋊C4—24no—
614C4⋊C4—24no—
615C4⋊C4—24no—
616C4⋊C4—24no—
617C4⋊C4—24no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—712no—
622C4⋊C4—1424no—
623C4⋊C4—1421no—
624C4⋊C4C2×C22⋊D7114yes—
625C4⋊C4C2×C22⋊D7114yes—
626C4⋊C4C2×C22⋊D7114yes—
627C4⋊C4C23×D7112yes—
628C4⋊C4C23×D7112yes—
629C4⋊C4C23×D7112yes—
630C22⋊C4—24no—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—1424no—
634C22⋊C4—1424no—
635C22⋊C4—1424no—
636C22⋊C4—1424no—
637C22⋊C4—1424no—
638C22⋊C4—1424no—
639C42—1424no—
640C42C2×C22⋊D7112yes—
641C42C2×C22⋊D7112yes—
642C42C2×C22⋊D7112yes—
643C42C23×D7112yes—
644C42C23×D7112yes—
645C42C23×D7112yes—
646C23—22no—
647C23—24no—
648C23—42no—
649C23—42no—
650C23—2842no—
651C23—2842no—
652C23—2842no—
653C23—2842no—
654C23—2842no—
655C23—2842no—
656C23—1422no—
657C23—1422no—
658C23C22×C22⋊D7111yescharacteristic
659Q8—44no—
660Q8—84no—
661Q8—2842no—
662Q8—1422no—
663Q8—1422no—
664D4—22no—
665D4—24no—
666D4—2848no—
667D4—2842no—
668D4—2842no—
669D4—5684no—
670D4—1422no—
671D4—1422no—
672D4—1422no—
673D4—1422no—
674D4C2×#1176586614yes—
675C2×C4—22no—
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—48no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—84no—
689C2×C4—84no—
690C2×C4—2842no—
691C2×C4—2842no—
692C2×C4—5684no—
693C2×C4—5684no—
694C2×C4—1422no—
695C2×C4—1422no—
696C2×C4C22×C22⋊D7112yes—
697C2×C4C22×C22⋊D7112yes—
698C2×C4C22×C22⋊D7112yes—
699C2×C4C22×C22⋊D7112yes—
700C2×C4C22×C22⋊D7112yes—
701C2×C4C22×C22⋊D7112yes—
702C2×C4C22×C22⋊D7111yescharacteristic
703C2×C4C2×#1176586612yes—
704C2×C4#1455617612yes—
705C2×C4C24×D7111yescharacteristic
706C8—1422no—
707C8—1422no—
708C8—1422no—
709C8—1422no—
710C22—24no—
711C22—42no—
712C22—42no—
713C22—48no—
714C22—2842no—
715C22—2842no—
716C22—2842no—
717C22—2842no—
718C22—2842no—
719C22—2842no—
720C22—5684no—
721C22—5684no—
722C22#1798666012yes—
723C22#1798679712yes—
724C22#1798680212yes—
725C22C23×C22⋊D7111yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—22no—
731C4—22no—
732C4—42no—
733C4—42no—
734C4—42no—
735C4—2842no—
736C4—2842no—
737C4#1798666012yes—
738C4C22×#1176586611yescharacteristic
739C4C2×#1455617611yescharacteristic
740C2—44no—
741C2—5682no—
742C2—5682no—
743C2#2260109314yesdirect product factor
744C2C2×#1798666011yescharacteristic
745C2C2×#1798679711yescharacteristic
746C2C2×#1798680211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#554×C71C2
socleC23×C71C22×D4
prime radicalC2×#17986194C2
hypercenterC2×#554D71
hypocenterC71C2×#3370
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. C2×#17986734C2semidirect
2. #22601093C2direct (N × H)
3. C2×#17986365C2semidirect
4. C2×#17986361C2semidirect
5. C2×#17986356C2semidirect
6. C2×#17986303C2semidirect
7. C2×#17986296C2semidirect
8. C2×#17986276C2semidirect
9. C2×#17986214C2semidirect
10. C2×#17986214C2semidirect
12. C2×#17986130C2semidirect
13. C2×#17986109C2semidirect
14. C2×#17986099C2semidirect
15. C2×C4×#11765850C2semidirect
16. C2×#554×C71C2semidirect
21. #17986734C22semidirect
32. #17986365C22semidirect
33. #17986361C22semidirect
34. #17986356C22semidirect
35. #17986303C22semidirect
36. #17986296C22semidirect
37. #17986276C22semidirect
38. #17986214C22semidirect
39. #17986214C22semidirect
41. #17986130C22semidirect
42. #17986109C22semidirect
43. #17986099C22semidirect
44. C4×#11765850C22semidirect
65. #554×C71C22semidirect
368. C2×C71#3370semidirect
375. C2×#554D71semidirect
390. C71C2×#3370semidirect
397. #554C2×D71semidirect
743. C2#22601093direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179867342
#226010932
C2×#179863652
C2×#179863612
C2×#179863562
C2×#179863032
C2×#179862962
C2×#179862762
C2×#179862142
C2×#179861942
C2×#179861302
C2×#179861092
C2×#179860992
C2×C4×#117658502
C2×#554×C712
C2×#337071