Finite Group Databasebeta

← C131×#14758 #45700642

Subgroups — C131×#14758 #45700642

Order 33536.

2242 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊Q8×C131C211yesmaximal, characteristic
2C2×#395×C131C211yesmaximal, characteristic, complemented
3C2×#385×C131C211yesmaximal, characteristic
4C2×#380×C131C212yesmaximal
5C22×#95×C131C211yesmaximal, characteristic
6#1446×C131C211yesmaximal, characteristic, complemented
7#1444×C131C212yesmaximal, complemented
8#1444×C131C211yesmaximal, characteristic, complemented
9#1441×C131C211yesmaximal, characteristic, complemented
10#1441×C131C212yesmaximal, complemented
11C22⋊#95×C131C212yesmaximal
12C23×Q8×C131C2211yescharacteristic
13C24×C4×C131C2211yescharacteristic
14C24×C4×C131C2212yes—
15C2×C22⋊Q8×C131—24no—
16C2×C22⋊Q8×C131—28no—
17C22×C4⋊C4×C131C2211yescharacteristic
18C22×C4⋊C4×C131C2211yescharacteristic
19C22×C4⋊C4×C131C2212yes—
20C22×C4⋊C4×C131C2212yes—
21C22×C4⋊C4×C131C2212yes—
22C22×C4⋊C4×C131C2211yescharacteristic
23C22×C22⋊C4×C131C2211yescharacteristic
24C22×C22⋊C4×C131C2212yes—
25C22×C22⋊C4×C131C2211yescharacteristic
26#395×C131—24no—
27#385×C131—24no—
28#380×C131—28no—
29C2×#95×C131—24no—
30C2×#95×C131C2212yes—
31C2×#95×C131C2211yescharacteristic
32C2×#95×C131C2212yes—
33C2×#95×C131C2212yes—
34C2×#95×C131C2211yescharacteristic
35C2×#95×C131C2211yescharacteristic
36C2×#95×C131C2212yes—
37C2×#95×C131C2212yes—
38C2×#95×C131C2212yes—
39C2×#95×C131C2212yes—
40C2×#95×C131C2211yescharacteristic
41C25×C131C2311yescharacteristic
42C22×Q8×C131—24no—
43C22×Q8×C131—22no—
44C22×Q8×C131—22no—
45C22×Q8×C131—22no—
46C22×Q8×C131—42no—
47C23×C4×C131—24no—
48C23×C4×C131—24no—
49C23×C4×C131—24no—
50C23×C4×C131—22no—
51C23×C4×C131—24no—
52C23×C4×C131—22no—
53C23×C4×C131—24no—
54C23×C4×C131—42no—
55C23×C4×C131—42no—
56C23×C4×C131—42no—
57C23×C4×C131D414yes—
58C23×C4×C131Q818yescomplemented
59C23×C4×C131C2311yescharacteristic
60C23×C4×C131C2311yescharacteristic
61C23×C4×C131C2312yes—
62C23×C4×C131C2312yes—
63C23×C4×C131C2311yescharacteristic
64C23×C4×C131C2311yescharacteristic
65C23×C4×C131C2311yescharacteristic
66C23×C4×C131C2312yes—
67C23×C4×C131C2311yescharacteristic
68C23×C4×C131C2312yes—
69C22⋊Q8×C131—232no—
70C2×C4⋊C4×C131—24no—
71C2×C4⋊C4×C131—22no—
72C2×C4⋊C4×C131—24no—
73C2×C4⋊C4×C131—24no—
74C2×C4⋊C4×C131—24no—
75C2×C4⋊C4×C131—24no—
76C2×C4⋊C4×C131—22no—
77C2×C4⋊C4×C131—24no—
78C2×C4⋊C4×C131—24no—
79C2×C4⋊C4×C131—22no—
80C2×C4⋊C4×C131—22no—
81C2×C4⋊C4×C131—24no—
82C2×C4⋊C4×C131—22no—
83C2×C4⋊C4×C131—42no—
84C2×C4⋊C4×C131—42no—
85C2×C4⋊C4×C131—42no—
86C2×C22⋊C4×C131—24no—
87C2×C22⋊C4×C131—24no—
88C2×C22⋊C4×C131—22no—
89C2×C22⋊C4×C131—22no—
90C2×C22⋊C4×C131—24no—
91C2×C22⋊C4×C131—22no—
92C2×C22⋊C4×C131D418yes—
93C2×C22⋊C4×C131Q814yescomplemented
94#95×C131—24no—
95#95×C131—22no—
96#95×C131—24no—
97#95×C131—24no—
98#95×C131—24no—
99#95×C131—22no—
100#95×C131—22no—
101#95×C131—24no—
102#95×C131—42no—
103#95×C131—42no—
104#95×C131D414yes—
105C24×C131—21no—
106C24×C131—21no—
107C24×C131—22no—
108C24×C131—22no—
109C24×C131—21no—
110C24×C131—21no—
111C24×C131C2×D412yes—
112C24×C131C2×D414yes—
113C24×C131C2×Q812yes—
114C24×C131C2×Q814yes—
115C24×C131#4112yes—
116C24×C131C2411yescharacteristic
117C2×Q8×C131—28no—
118C2×Q8×C131—48no—
119C2×Q8×C131—48no—
120C2×Q8×C131—44no—
121C2×Q8×C131—44no—
122C22×C4×C131—22no—
123C22×C4×C131—22no—
124C22×C4×C131—22no—
125C22×C4×C131—22no—
126C22×C4×C131—22no—
127C22×C4×C131—22no—
128C22×C4×C131—28no—
129C22×C4×C131—216no—
130C22×C4×C131—21no—
131C22×C4×C131—21no—
132C22×C4×C131—22no—
133C22×C4×C131—22no—
134C22×C4×C131—21no—
135C22×C4×C131—21no—
136C22×C4×C131—22no—
137C22×C4×C131—22no—
138C22×C4×C131—22no—
139C22×C4×C131—22no—
140C22×C4×C131—22no—
141C22×C4×C131—22no—
142C22×C4×C131—22no—
143C22×C4×C131—22no—
144C22×C4×C131—21no—
145C22×C4×C131—21no—
146C22×C4×C131—22no—
147C22×C4×C131—21no—
148C22×C4×C131—21no—
149C22×C4×C131—22no—
150C22×C4×C131—22no—
151C22×C4×C131—22no—
152C22×C4×C131—21no—
153C22×C4×C131—22no—
154C22×C4×C131—22no—
155C22×C4×C131—22no—
156C22×C4×C131—22no—
157C22×C4×C131—22no—
158C22×C4×C131—22no—
159C22×C4×C131—22no—
160C22×C4×C131—22no—
161C22×C4×C131—21no—
162C22×C4×C131—28no—
163C22×C4×C131—216no—
164C22×C4×C131—21no—
165C22×C4×C131—22no—
166C22×C4×C131—22no—
167C22×C4×C131—21no—
168C22×C4×C131—21no—
169C22×C4×C131—21no—
170C22×C4×C131—22no—
171C22×C4×C131—22no—
172C22×C4×C131—21no—
173C22×C4×C131—21no—
174C22×C4×C131—44no—
175C22×C4×C131—48no—
176C22×C4×C131—48no—
177C22×C4×C131—48no—
178C22×C4×C131—48no—
179C22×C4×C131—48no—
180C22×C4×C131—48no—
181C22×C4×C131—48no—
182C22×C4×C131C2×D414yes—
183C22×C4×C131C2×D414yes—
184C22×C4×C131C2×D412yes—
185C22×C4×C131C2×D412yes—
186C22×C4×C131C2×D412yes—
187C22×C4×C131C2×D414yes—
188C22×C4×C131C2×Q812yes—
189C22×C4×C131C2×Q812yes—
190C22×C4×C131C2×Q814yes—
191C22×C4×C131C2×Q814yes—
192C22×C4×C131#4112yes—
193C22×C4×C131#4114yes—
194C4⋊C4×C131—28no—
195C4⋊C4×C131—216no—
196C4⋊C4×C131—48no—
197C4⋊C4×C131—48no—
198C4⋊C4×C131—44no—
199C4⋊C4×C131—44no—
200C22⋊C4×C131—216no—
201C22⋊C4×C131—28no—
202C22⋊C4×C131—44no—
203C23×C131—22no—
204C23×C131—24no—
205C23×C131—22no—
206C23×C131—24no—
207C23×C131—22no—
208C23×C131—22no—
209C23×C131—24no—
210C23×C131—24no—
211C23×C131—24no—
212C23×C131—22no—
213C23×C131—24no—
214C23×C131—24no—
215C23×C131—24no—
216C23×C131—22no—
217C23×C131—24no—
218C23×C131—22no—
219C23×C131—24no—
220C23×C131—22no—
221C23×C131#12014yes—
222C23×C131C22⋊Q814yes—
223C23×C131C22⋊Q818yes—
224C23×C131C4⋊Q814yes—
225C23×C131C4⋊Q818yes—
226C23×C131C22×D411yescharacteristic
227C23×C131C22×D412yes—
228C23×C131C22×D411yescharacteristic
229C23×C131C22×Q812yes—
230C23×C131C22×Q811yescharacteristic
231C23×C131C2×#4111yescharacteristic
232C23×C131C2×#4111yescharacteristic
233C23×C131C2×#4112yes—
234C23×C131H(5,𝔽2)12yes—
235C23×C131H(5,𝔽2)11yescharacteristic
236C23×C1312−1+411yescharacteristic
237Q8×C131—416no—
238C2×C4×C131—22no—
239C2×C4×C131—24no—
240C2×C4×C131—22no—
241C2×C4×C131—24no—
242C2×C4×C131—24no—
243C2×C4×C131—24no—
244C2×C4×C131—24no—
245C2×C4×C131—24no—
246C2×C4×C131—24no—
247C2×C4×C131—24no—
248C2×C4×C131—24no—
249C2×C4×C131—24no—
250C2×C4×C131—22no—
251C2×C4×C131—22no—
252C2×C4×C131—22no—
253C2×C4×C131—22no—
254C2×C4×C131—24no—
255C2×C4×C131—24no—
256C2×C4×C131—22no—
257C2×C4×C131—24no—
258C2×C4×C131—24no—
259C2×C4×C131—24no—
260C2×C4×C131—24no—
261C2×C4×C131—24no—
262C2×C4×C131—22no—
263C2×C4×C131—24no—
264C2×C4×C131—22no—
265C2×C4×C131—416no—
266C2×C4×C131—432no—
267C2×C4×C131—41no—
268C2×C4×C131—42no—
269C2×C4×C131—41no—
270C2×C4×C131—42no—
271C2×C4×C131—41no—
272C2×C4×C131—42no—
273C2×C4×C131—41no—
274C2×C4×C131—42no—
275C2×C4×C131—42no—
276C2×C4×C131—42no—
277C2×C4×C131—42no—
278C2×C4×C131—41no—
279C2×C4×C131—42no—
280C2×C4×C131—42no—
281C2×C4×C131—42no—
282C2×C4×C131—42no—
283C2×C4×C131—42no—
284C2×C4×C131—42no—
285C2×C4×C131—42no—
286C2×C4×C131—42no—
287C2×C4×C131—41no—
288C2×C4×C131—41no—
289C2×C4×C131—41no—
290C2×C4×C131—41no—
291C2×C4×C131—41no—
292C2×C4×C131—41no—
293C2×C4×C131—41no—
294C2×C4×C131—42no—
295C2×C4×C131—42no—
296C2×C4×C131—42no—
297C2×C4×C131—42no—
298C2×C4×C131#12114yes—
299C2×C4×C131C22⋊Q818yescomplemented
300C22×C131—24no—
301C22×C131—24no—
302C22×C131—24no—
303C22×C131—24no—
304C22×C131—24no—
305C22×C131—24no—
306C22×C131—28no—
307C22×C131—28no—
308C22×C131—28no—
309C22×C131—28no—
310C22×C131#39518yescomplemented
311C22×C131C2×#12011yescharacteristic
312C22×C131C2×#12111yescharacteristic
313C22×C131C2×C22⋊Q811yescharacteristic
314C22×C131C2×C22⋊Q812yes—
315C22×C131C2×C22⋊Q812yes—
316C22×C131C2×C4⋊Q811yescharacteristic
317C22×C131C2×C4⋊Q812yes—
318C22×C131#53211yescharacteristic
319C22×C131#53312yes—
320C22×C131#53411yescharacteristic
321C22×C131#53711yescharacteristic
322C22×C131#54312yes—
323C22×C131#54412yes—
324C22×C131D4212yes—
325C22×C131#54612yes—
326C22×C131#54611yescharacteristic
327C22×C131#54612yes—
328C22×C131#54712yes—
329C22×C131D4×Q811yescharacteristic
330C22×C131#55112yes—
331C22×C131#55211yescharacteristic
332C22×C131#55412yes—
333C22×C131#55411yescharacteristic
334C4×C131—24no—
335C4×C131—28no—
336C4×C131—42no—
337C4×C131—42no—
338C4×C131—44no—
339C4×C131—42no—
340C4×C131—44no—
341C4×C131—44no—
342C4×C131—81no—
343C4×C131—81no—
344C2×C131—28no—
345C2×C131C2×#39511yescharacteristic
346C2×C131#241011yescharacteristic
347C2×C131#241711yescharacteristic
348C2×C131#243011yescharacteristic
349C2×C131#243712yes—
350C2×C131#243812yes—
351C2×C131#244012yes—
352C2×C131#254912yes—
353C2×C131#256411yescharacteristic
354C2×C131#265911yescharacteristic
355C2×C131#285711yescharacteristic
356#14758C13111yesmaximal, characteristic, direct product factor, Sylow
357C131#1475811yescharacteristic, direct product factor, Sylow
358C22×C22⋊Q8C2×C13111yescharacteristic
359C2×#395C2×C13111yescharacteristic, complemented
360C2×#385C2×C13111yescharacteristic
361C2×#380C2×C13112yes—
362C22×#95C2×C13111yescharacteristic
363#1446C2×C13111yescharacteristic, complemented
364#1444C2×C13112yescomplemented
365#1444C2×C13111yescharacteristic, complemented
366#1441C2×C13111yescharacteristic, complemented
367#1441C2×C13112yescomplemented
368C22⋊#95C2×C13112yes—
369C23×Q8C22×C13111yescharacteristic
370C24×C4C22×C13111yescharacteristic
371C24×C4C22×C13112yes—
372C2×C22⋊Q8—24no—
373C2×C22⋊Q8—28no—
374C22×C4⋊C4C22×C13111yescharacteristic
375C22×C4⋊C4C22×C13111yescharacteristic
376C22×C4⋊C4C22×C13112yes—
377C22×C4⋊C4C22×C13112yes—
378C22×C4⋊C4C22×C13112yes—
379C22×C4⋊C4C22×C13111yescharacteristic
380C22×C22⋊C4C22×C13111yescharacteristic
381C22×C22⋊C4C22×C13112yes—
382C22×C22⋊C4C22×C13111yescharacteristic
383#395—24no—
384#385—24no—
385#380—28no—
386C2×#95—24no—
387C2×#95C22×C13112yes—
388C2×#95C22×C13112yes—
389C2×#95C22×C13111yescharacteristic
390C2×#95C22×C13112yes—
391C2×#95C22×C13112yes—
392C2×#95C22×C13111yescharacteristic
393C2×#95C22×C13112yes—
394C2×#95C22×C13111yescharacteristic
395C2×#95C22×C13112yes—
396C2×#95C22×C13112yes—
397C2×#95C22×C13111yescharacteristic
398C25C23×C13111yescharacteristic
399C22×Q8—24no—
400C22×Q8—22no—
401C22×Q8—22no—
402C22×Q8—22no—
403C22×Q8—42no—
404C23×C4—24no—
405C23×C4—24no—
406C23×C4—24no—
407C23×C4—22no—
408C23×C4—24no—
409C23×C4—22no—
410C23×C4—24no—
411C23×C4—42no—
412C23×C4—42no—
413C23×C4—42no—
414C23×C4D4×C13114yes—
415C23×C4Q8×C13118yescomplemented
416C23×C4C23×C13111yescharacteristic
417C23×C4C23×C13111yescharacteristic
418C23×C4C23×C13112yes—
419C23×C4C23×C13112yes—
420C23×C4C23×C13111yescharacteristic
421C23×C4C23×C13111yescharacteristic
422C23×C4C23×C13111yescharacteristic
423C23×C4C23×C13112yes—
424C23×C4C23×C13111yescharacteristic
425C23×C4C23×C13112yes—
426C22⋊Q8—232no—
427C2×C4⋊C4—24no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—24no—
430C2×C4⋊C4—24no—
431C2×C4⋊C4—24no—
432C2×C4⋊C4—24no—
433C2×C4⋊C4—24no—
434C2×C4⋊C4—22no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—24no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—24no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4—42no—
441C2×C4⋊C4—42no—
442C2×C4⋊C4—42no—
443C2×C22⋊C4—24no—
444C2×C22⋊C4—24no—
445C2×C22⋊C4—22no—
446C2×C22⋊C4—22no—
447C2×C22⋊C4—24no—
448C2×C22⋊C4—22no—
449C2×C22⋊C4D4×C13118yes—
450C2×C22⋊C4Q8×C13114yescomplemented
451#95—22no—
452#95—24no—
453#95—24no—
454#95—24no—
455#95—22no—
456#95—22no—
457#95—24no—
458#95—24no—
459#95—42no—
460#95—42no—
461#95D4×C13114yes—
462C24—21no—
463C24—21no—
464C24—22no—
465C24—22no—
466C24—21no—
467C24—21no—
468C24C2×D4×C13112yes—
469C24C2×D4×C13114yes—
470C24C2×Q8×C13112yes—
471C24C2×Q8×C13114yes—
472C24#41×C13112yes—
473C24C24×C13111yescharacteristic
474C2×Q8—28no—
475C2×Q8—48no—
476C2×Q8—48no—
477C2×Q8—44no—
478C2×Q8—44no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—28no—
486C22×C4—216no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—22no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—21no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—21no—
519C22×C4—28no—
520C22×C4—216no—
521C22×C4—21no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—44no—
532C22×C4—48no—
533C22×C4—48no—
534C22×C4—48no—
535C22×C4—48no—
536C22×C4—48no—
537C22×C4—48no—
538C22×C4—48no—
539C22×C4C2×D4×C13114yes—
540C22×C4C2×D4×C13114yes—
541C22×C4C2×D4×C13112yes—
542C22×C4C2×D4×C13112yes—
543C22×C4C2×D4×C13112yes—
544C22×C4C2×D4×C13114yes—
545C22×C4C2×Q8×C13112yes—
546C22×C4C2×Q8×C13112yes—
547C22×C4C2×Q8×C13114yes—
548C22×C4C2×Q8×C13114yes—
549C22×C4#41×C13112yes—
550C22×C4#41×C13114yes—
551C4⋊C4—28no—
552C4⋊C4—216no—
553C4⋊C4—48no—
554C4⋊C4—48no—
555C4⋊C4—44no—
556C4⋊C4—44no—
557C22⋊C4—216no—
558C22⋊C4—28no—
559C22⋊C4—44no—
560C23—22no—
561C23—24no—
562C23—22no—
563C23—24no—
564C23—22no—
565C23—22no—
566C23—24no—
567C23—24no—
568C23—24no—
569C23—22no—
570C23—24no—
571C23—24no—
572C23—24no—
573C23—22no—
574C23—24no—
575C23—22no—
576C23—22no—
577C23—24no—
578C23#120×C13114yes—
579C23C22⋊Q8×C13114yes—
580C23C22⋊Q8×C13118yes—
581C23C4⋊Q8×C13118yes—
582C23C4⋊Q8×C13114yes—
583C23C22×D4×C13111yescharacteristic
584C23C22×D4×C13112yes—
585C23C22×D4×C13111yescharacteristic
586C23C22×Q8×C13112yes—
587C23C22×Q8×C13111yescharacteristic
588C23C2×#41×C13111yescharacteristic
589C23C2×#41×C13111yescharacteristic
590C23C2×#41×C13112yes—
591C23H(5,𝔽2)×C13112yes—
592C23H(5,𝔽2)×C13111yescharacteristic
593C232−1+4×C13111yescharacteristic
594Q8—416no—
595C2×C4—22no—
596C2×C4—24no—
597C2×C4—22no—
598C2×C4—24no—
599C2×C4—24no—
600C2×C4—24no—
601C2×C4—24no—
602C2×C4—24no—
603C2×C4—24no—
604C2×C4—24no—
605C2×C4—24no—
606C2×C4—24no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—24no—
612C2×C4—24no—
613C2×C4—22no—
614C2×C4—24no—
615C2×C4—24no—
616C2×C4—24no—
617C2×C4—24no—
618C2×C4—24no—
619C2×C4—22no—
620C2×C4—24no—
621C2×C4—22no—
622C2×C4—416no—
623C2×C4—432no—
624C2×C4—41no—
625C2×C4—42no—
626C2×C4—41no—
627C2×C4—42no—
628C2×C4—41no—
629C2×C4—42no—
630C2×C4—41no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—41no—
640C2×C4—42no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4#121×C13114yes—
656C2×C4C22⋊Q8×C13118yescomplemented
657C22—28no—
658C22—24no—
659C22—24no—
660C22—24no—
661C22—24no—
662C22—24no—
663C22—24no—
664C22—28no—
665C22—28no—
666C22—28no—
667C22#395×C13118yescomplemented
668C22C2×#120×C13111yescharacteristic
669C22C2×#121×C13111yescharacteristic
670C22C2×C22⋊Q8×C13111yescharacteristic
671C22C2×C22⋊Q8×C13112yes—
672C22C2×C22⋊Q8×C13112yes—
673C22C2×C4⋊Q8×C13112yes—
674C22C2×C4⋊Q8×C13111yescharacteristic
675C22#532×C13111yescharacteristic
676C22#533×C13112yes—
677C22#534×C13111yescharacteristic
678C22#537×C13111yescharacteristic
679C22#543×C13112yes—
680C22#544×C13112yes—
681C22D42×C13112yes—
682C22#546×C13112yes—
683C22#546×C13112yes—
684C22#546×C13111yescharacteristic
685C22#547×C13112yes—
686C22D4×Q8×C13111yescharacteristic
687C22#551×C13112yes—
688C22#552×C13111yescharacteristic
689C22#554×C13111yescharacteristic
690C22#554×C13112yes—
691C4—24no—
692C4—28no—
693C4—42no—
694C4—42no—
695C4—44no—
696C4—42no—
697C4—44no—
698C4—44no—
699C4—81no—
700C4—81no—
701C2—28no—
702C2C2×#395×C13111yescharacteristic
703C2#2410×C13111yescharacteristic
704C2#2417×C13111yescharacteristic
705C2#2430×C13111yescharacteristic
706C2#2437×C13112yes—
707C2#2438×C13112yes—
708C2#2440×C13112yes—
709C2#2549×C13112yes—
710C2#2564×C13111yescharacteristic
711C2#2659×C13111yescharacteristic
712C2#2857×C13111yescharacteristic
subgroupG/H
center, socleC24×C131C24
commutator, Frattini, cosocleC24C24×C131
prime radicalC25×C131C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#395×C131C2semidirect
6. #1446×C131C2semidirect
7. #1444×C131C2semidirect
8. #1444×C131C2semidirect
9. #1441×C131C2semidirect
10. #1441×C131C2semidirect
58. C23×C4×C131Q8semidirect
93. C2×C22⋊C4×C131Q8semidirect
299. C2×C4×C131C22⋊Q8semidirect
310. C22×C131#395semidirect
356. #14758C131direct (N × H)
357. C131#14758direct (N × H)
359. C2×#395C2×C131semidirect
363. #1446C2×C131semidirect
364. #1444C2×C131semidirect
365. #1444C2×C131semidirect
366. #1441C2×C131semidirect
367. #1441C2×C131semidirect
415. C23×C4Q8×C131semidirect
450. C2×C22⋊C4Q8×C131semidirect
656. C2×C4C22⋊Q8×C131semidirect
667. C22#395×C131semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊Q8×C1312
C2×#395×C1312
C2×#385×C1312
C2×#380×C1312
C22×#95×C1312
#1446×C1312
#1444×C1312
#1441×C1312
C22⋊#95×C1312
#14758131