Finite Group Databasebeta

← C131×#21420 #45707304

Subgroups — C131×#21420 #45707304

Order 33536.

1678 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#525×C131C211yesmaximal, characteristic
2#2280×C131C211yesmaximal, characteristic, complemented
3C2×C4×C22⋊C4×C131C211yesmaximal, characteristic, complemented
4#1996×C131C212yesmaximal, complemented
5#1964×C131C212yesmaximal, complemented
6#1898×C131C214yesmaximal, complemented
7C4×#99×C131C214yesmaximal, complemented
8C22×#41×C131C411yescharacteristic, complemented
9C24×C4×C131C2211yescharacteristic
10#525×C131—21no—
11#525×C131—21no—
12#525×C131—21no—
13#525×C131—21no—
14#525×C131—21no—
15#525×C131—21no—
16#525×C131—21no—
17#525×C131—21no—
18C2×#123×C131C412yescomplemented
19C2×C22⋊Q8×C131C411yescharacteristic, complemented
20C2×C22⋊Q8×C131C2211yescharacteristic
21C2×#121×C131C411yescharacteristic, complemented
22C2×#121×C131C2211yescharacteristic
23C2×#120×C131C2212yes—
24C2×C4×D4×C131C412yescomplemented
25C2×C4×D4×C131C2212yes—
26C2×#117×C131—21no—
27C2×#117×C131C411yescharacteristic, complemented
28C22×C22⋊C4×C131C2212yes—
29C22×C42×C131—21no—
30C2×#99×C131C2218yes—
31#381×C131—21no—
32#380×C131—21no—
33#380×C131C2212yes—
34#379×C131C2212yes—
35C4×C22⋊C4×C131—21no—
36C4×C22⋊C4×C131—21no—
37C4×C22⋊C4×C131—21no—
38C4×C22⋊C4×C131C2212yes—
39C4×C22⋊C4×C131C2212yes—
40C4×C22⋊C4×C131C2212yes—
41C2×#95×C131—21no—
42#342×C131C2218yes—
43C25×C131C2311yescharacteristic
44C2×#41×C131—21no—
45C2×#41×C131—21no—
46C2×#41×C131—21no—
47C2×#41×C131—21no—
48C2×#41×C131—44no—
49C22×Q8×C131C2×C411yescharacteristic, complemented
50C22×D4×C131C2×C412yes—
51C22×D4×C131C2×C412yes—
52C22×D4×C131C2×C411yescharacteristic, complemented
53C22×D4×C131C2312yes—
54C23×C4×C131—22no—
55C23×C4×C131—44no—
56C23×C4×C131C2×C411yescharacteristic
57C23×C4×C131C2×C411yescharacteristic
58C23×C4×C131C2×C411yescharacteristic
59C23×C4×C131C2×C411yescharacteristic
60C23×C4×C131C2×C412yescomplemented
61C23×C4×C131D411yescharacteristic
62C23×C4×C131D411yescharacteristic
63C23×C4×C131D411yescharacteristic
64C23×C4×C131D411yescharacteristic
65C23×C4×C131D411yescharacteristic
66C23×C4×C131D411yescharacteristic
67C23×C4×C131D411yescharacteristic
68C23×C4×C131D411yescharacteristic
69C23×C4×C131C2311yescharacteristic
70C23×C4×C131C2311yescharacteristic
71#123×C131—22no—
72#123×C131—22no—
73#123×C131—22no—
74#123×C131—22no—
75C22⋊Q8×C131—21no—
76C22⋊Q8×C131—21no—
77C22⋊Q8×C131—21no—
78C22⋊Q8×C131—21no—
79C22⋊Q8×C131—21no—
80C22⋊Q8×C131—21no—
81C22⋊Q8×C131—21no—
82C22⋊Q8×C131—21no—
83#121×C131—21no—
84#121×C131—21no—
85#121×C131—21no—
86#121×C131—21no—
87#121×C131—21no—
88#121×C131—21no—
89#121×C131—21no—
90#121×C131—21no—
91#120×C131—22no—
92#120×C131—22no—
93#120×C131—22no—
94#120×C131—22no—
95C4×D4×C131—22no—
96C4×D4×C131—22no—
97C4×D4×C131—22no—
98C4×D4×C131—22no—
99C4×D4×C131—22no—
100C4×D4×C131—22no—
101C4×D4×C131—22no—
102C4×D4×C131—22no—
103#117×C131—21no—
104#117×C131—21no—
105#117×C131—21no—
106#117×C131—21no—
107#117×C131—44no—
108C2×C4⋊C4×C131—22no—
109C2×C4⋊C4×C131C2×C411yescharacteristic, complemented
110C2×C4⋊C4×C131C2×C411yescharacteristic, complemented
111C2×C4⋊C4×C131C2×C412yescomplemented
112C2×C4⋊C4×C131C2×C412yescomplemented
113C2×C22⋊C4×C131—22no—
114C2×C22⋊C4×C131—28no—
115C2×C22⋊C4×C131—22no—
116C2×C22⋊C4×C131—22no—
117C2×C22⋊C4×C131C2×C412yes—
118C2×C22⋊C4×C131C2×C412yes—
119C2×C22⋊C4×C131C2×C412yescomplemented
120C2×C22⋊C4×C131C2×C412yescomplemented
121C2×C22⋊C4×C131C2314yes—
122C2×C22⋊C4×C131C2312yes—
123C2×C22⋊C4×C131C2314yes—
124C2×C42×C131—22no—
125C2×C42×C131—22no—
126C2×C42×C131—22no—
127C2×C42×C131—44no—
128C2×C42×C131C2×C412yescomplemented
129#99×C131—216no—
130#95×C131—22no—
131#95×C131—22no—
132#95×C131—22no—
133#95×C131—22no—
134C24×C131—24no—
135C24×C131—42no—
136C24×C131—42no—
137C24×C131C22×C411yescharacteristic
138C24×C131C22×C411yescharacteristic
139C24×C131C22×C412yes—
140C24×C131C2×D411yescharacteristic
141C24×C131C2×D411yescharacteristic
142C24×C131C2×D411yescharacteristic
143C24×C131C2×D411yescharacteristic
144C24×C131C2411yescharacteristic
145#41×C131—44no—
146#41×C131—44no—
147#41×C131—44no—
148#41×C131—44no—
149C2×Q8×C131—21no—
150C2×Q8×C131—21no—
151C2×Q8×C131—42no—
152C2×D4×C131—22no—
153C2×D4×C131—22no—
154C2×D4×C131—22no—
155C2×D4×C131—22no—
156C2×D4×C131—22no—
157C2×D4×C131—22no—
158C2×D4×C131—28no—
159C2×D4×C131—21no—
160C2×D4×C131—21no—
161C2×D4×C131—42no—
162C2×D4×C131—44no—
163C2×D4×C131—44no—
164C22×C4×C131—24no—
165C22×C4×C131—24no—
166C22×C4×C131—24no—
167C22×C4×C131—28no—
168C22×C4×C131—24no—
169C22×C4×C131—22no—
170C22×C4×C131—22no—
171C22×C4×C131—24no—
172C22×C4×C131—42no—
173C22×C4×C131—42no—
174C22×C4×C131—42no—
175C22×C4×C131—42no—
176C22×C4×C131—42no—
177C22×C4×C131—42no—
178C22×C4×C131—42no—
179C22×C4×C131—42no—
180C22×C4×C131—42no—
181C22×C4×C131—42no—
182C22×C4×C131—42no—
183C22×C4×C131—44no—
184C22×C4×C131—44no—
185C22×C4×C131—44no—
186C22×C4×C131C22⋊C411yescharacteristic
187C22×C4×C131C22⋊C411yescharacteristic
188C22×C4×C131C22⋊C411yescharacteristic
189C22×C4×C131C22⋊C411yescharacteristic
190C22×C4×C131C22⋊C411yescharacteristic
191C22×C4×C131C22⋊C411yescharacteristic
192C22×C4×C131C22⋊C411yescharacteristic
193C22×C4×C131C22⋊C411yescharacteristic
194C22×C4×C131C22⋊C411yescharacteristic
195C22×C4×C131C22⋊C411yescharacteristic
196C22×C4×C131C22⋊C411yescharacteristic
197C22×C4×C131C22⋊C411yescharacteristic
198C22×C4×C131C22⋊C411yescharacteristic
199C22×C4×C131C22⋊C411yescharacteristic
200C22×C4×C131C22⋊C411yescharacteristic
201C22×C4×C131C22⋊C411yescharacteristic
202C22×C4×C131C22×C412yes—
203C22×C4×C131C22×C411yescharacteristic
204C22×C4×C131C22×C411yescharacteristic
205C22×C4×C131C22×C412yes—
206C22×C4×C131C22×C412yes—
207C22×C4×C131C22×C411yescharacteristic
208C22×C4×C131C22×C411yescharacteristic
209C22×C4×C131C2×D411yescharacteristic
210C22×C4×C131C2×D411yescharacteristic
211C22×C4×C131C2×D411yescharacteristic
212C22×C4×C131C2×D411yescharacteristic
213C22×C4×C131C2×D411yescharacteristic
214C22×C4×C131C2×D411yescharacteristic
215C22×C4×C131C2×D411yescharacteristic
216C22×C4×C131C2×D411yescharacteristic
217C4⋊C4×C131—21no—
218C4⋊C4×C131—21no—
219C4⋊C4×C131—21no—
220C4⋊C4×C131—21no—
221C4⋊C4×C131—22no—
222C4⋊C4×C131—22no—
223C4⋊C4×C131—22no—
224C4⋊C4×C131—22no—
225C4⋊C4×C131—44no—
226C22⋊C4×C131—28no—
227C22⋊C4×C131—22no—
228C22⋊C4×C131—22no—
229C22⋊C4×C131—22no—
230C22⋊C4×C131—22no—
231C22⋊C4×C131—22no—
232C22⋊C4×C131—22no—
233C22⋊C4×C131—24no—
234C22⋊C4×C131—22no—
235C22⋊C4×C131—22no—
236C22⋊C4×C131—22no—
237C22⋊C4×C131—22no—
238C22⋊C4×C131—28no—
239C22⋊C4×C131—44no—
240C22⋊C4×C131—44no—
241C22⋊C4×C131#4118yescomplemented
242C42×C131—22no—
243C42×C131—22no—
244C42×C131—44no—
245C42×C131—44no—
246C42×C131—44no—
247C23×C131—22no—
248C23×C131—22no—
249C23×C131—22no—
250C23×C131—22no—
251C23×C131—22no—
252C23×C131—22no—
253C23×C131—22no—
254C23×C131—22no—
255C23×C131—22no—
256C23×C131—22no—
257C23×C131—22no—
258C23×C131—22no—
259C23×C131—22no—
260C23×C131—24no—
261C23×C131—41no—
262C23×C131—41no—
263C23×C131—41no—
264C23×C131—41no—
265C23×C131—41no—
266C23×C131—41no—
267C23×C131—41no—
268C23×C131—41no—
269C23×C131—416no—
270C23×C131—42no—
271C23×C131—42no—
272C23×C131C2×C22⋊C411yescharacteristic
273C23×C131C2×C22⋊C411yescharacteristic
274C23×C131C2×C22⋊C411yescharacteristic
275C23×C131C2×C22⋊C411yescharacteristic
276C23×C131C23×C411yescharacteristic
277C23×C131C22×D411yescharacteristic
278C23×C131C22×D411yescharacteristic
279C23×C131C2×#4114yes—
280Q8×C131—42no—
281Q8×C131—42no—
282D4×C131—42no—
283D4×C131—44no—
284D4×C131—44no—
285D4×C131—44no—
286D4×C131—44no—
287D4×C131—44no—
288D4×C131—44no—
289D4×C131—42no—
290C2×C4×C131—22no—
291C2×C4×C131—22no—
292C2×C4×C131—22no—
293C2×C4×C131—22no—
294C2×C4×C131—22no—
295C2×C4×C131—22no—
296C2×C4×C131—22no—
297C2×C4×C131—22no—
298C2×C4×C131—22no—
299C2×C4×C131—22no—
300C2×C4×C131—22no—
301C2×C4×C131—22no—
302C2×C4×C131—22no—
303C2×C4×C131—22no—
304C2×C4×C131—22no—
305C2×C4×C131—22no—
306C2×C4×C131—22no—
307C2×C4×C131—22no—
308C2×C4×C131—24no—
309C2×C4×C131—28no—
310C2×C4×C131—41no—
311C2×C4×C131—41no—
312C2×C4×C131—41no—
313C2×C4×C131—41no—
314C2×C4×C131—41no—
315C2×C4×C131—41no—
316C2×C4×C131—41no—
317C2×C4×C131—41no—
318C2×C4×C131—41no—
319C2×C4×C131—41no—
320C2×C4×C131—41no—
321C2×C4×C131—41no—
322C2×C4×C131—44no—
323C2×C4×C131—44no—
324C2×C4×C131—416no—
325C2×C4×C131—44no—
326C2×C4×C131—44no—
327C2×C4×C131—42no—
328C2×C4×C131—42no—
329C2×C4×C131—44no—
330C2×C4×C131—44no—
331C2×C4×C131—44no—
332C2×C4×C131#9914yescomplemented
333C2×C4×C131C2×C22⋊C411yescharacteristic
334C2×C4×C131C2×C22⋊C411yescharacteristic
335C2×C4×C131C2×C22⋊C411yescharacteristic
336C2×C4×C131C2×C22⋊C411yescharacteristic
337C2×C4×C131C2×C22⋊C411yescharacteristic
338C2×C4×C131C2×C22⋊C411yescharacteristic
339C2×C4×C131C2×C22⋊C411yescharacteristic
340C2×C4×C131C2×C22⋊C411yescharacteristic
341C22×C131—28no—
342C22×C131—21no—
343C22×C131—21no—
344C22×C131—21no—
345C22×C131—21no—
346C22×C131—21no—
347C22×C131—21no—
348C22×C131—21no—
349C22×C131—21no—
350C22×C131—21no—
351C22×C131—21no—
352C22×C131—21no—
353C22×C131—21no—
354C22×C131—21no—
355C22×C131—21no—
356C22×C131—21no—
357C22×C131—21no—
358C22×C131—44no—
359C22×C131—44no—
360C22×C131—44no—
361C22×C131—44no—
362C22×C131—44no—
363C22×C131—44no—
364C22×C131—42no—
365C22×C131—42no—
366C22×C131—42no—
367C22×C131—84no—
368C22×C131C2×#9912yes—
369C22×C131#41012yes—
370C22×C131C22×C22⋊C411yescharacteristic
371C22×C131C4×#4112yes—
372C22×C131#52512yes—
373C22×C131#53212yes—
374C4×C131—21no—
375C4×C131—21no—
376C4×C131—21no—
377C4×C131—21no—
378C4×C131—21no—
379C4×C131—21no—
380C4×C131—48no—
381C4×C131—42no—
382C4×C131—42no—
383C4×C131—42no—
384C4×C131—84no—
385C4×C131C2×#9912yes—
386C4×C131C2×#9912yes—
387C2×C131—22no—
388C2×C131—22no—
389C2×C131—22no—
390C2×C131—22no—
391C2×C131—22no—
392C2×C131—41no—
393C2×C131—41no—
394C2×C131—82no—
395C2×C131#229711yescharacteristic
396C2×C131C22×#9911yescharacteristic
397C2×C131C2×#41011yescharacteristic
398#21420C13111yesmaximal, characteristic, direct product factor, Sylow
399C131#2142011yescharacteristic, direct product factor, Sylow
400C2×#525C2×C13111yescharacteristic
401#2280C2×C13111yescharacteristic, complemented
402C2×C4×C22⋊C4C2×C13111yescharacteristic, complemented
403#1996C2×C13112yescomplemented
404#1964C2×C13112yescomplemented
405#1898C2×C13114yescomplemented
406C4×#99C2×C13114yescomplemented
407C22×#41C4×C13111yescharacteristic, complemented
408C24×C4C22×C13111yescharacteristic
409#525—21no—
410#525—21no—
411#525—21no—
412#525—21no—
413#525—21no—
414#525—21no—
415#525—21no—
416#525—21no—
417C2×#123C4×C13112yescomplemented
418C2×C22⋊Q8C4×C13111yescharacteristic, complemented
419C2×C22⋊Q8C22×C13111yescharacteristic
420C2×#121C4×C13111yescharacteristic, complemented
421C2×#121C22×C13111yescharacteristic
422C2×#120C22×C13112yes—
423C2×C4×D4C4×C13112yescomplemented
424C2×C4×D4C22×C13112yes—
425C2×#117—21no—
426C2×#117C4×C13111yescharacteristic, complemented
427C22×C22⋊C4C22×C13112yes—
428C22×C42—21no—
429C2×#99C22×C13118yes—
430#381—21no—
431#380—21no—
432#380C22×C13112yes—
433#379C22×C13112yes—
434C4×C22⋊C4—21no—
435C4×C22⋊C4—21no—
436C4×C22⋊C4—21no—
437C4×C22⋊C4C22×C13112yes—
438C4×C22⋊C4C22×C13112yes—
439C4×C22⋊C4C22×C13112yes—
440C2×#95—21no—
441#342C22×C13118yes—
442C25C23×C13111yescharacteristic
443C2×#41—21no—
444C2×#41—21no—
445C2×#41—21no—
446C2×#41—21no—
447C2×#41—44no—
448C22×Q8C2×C4×C13111yescharacteristic, complemented
449C22×D4C2×C4×C13112yes—
450C22×D4C2×C4×C13112yes—
451C22×D4C2×C4×C13111yescharacteristic, complemented
452C22×D4C23×C13112yes—
453C23×C4—22no—
454C23×C4—44no—
455C23×C4C2×C4×C13111yescharacteristic
456C23×C4C2×C4×C13111yescharacteristic
457C23×C4C2×C4×C13111yescharacteristic
458C23×C4C2×C4×C13111yescharacteristic
459C23×C4C2×C4×C13112yescomplemented
460C23×C4D4×C13111yescharacteristic
461C23×C4D4×C13111yescharacteristic
462C23×C4D4×C13111yescharacteristic
463C23×C4D4×C13111yescharacteristic
464C23×C4D4×C13111yescharacteristic
465C23×C4D4×C13111yescharacteristic
466C23×C4D4×C13111yescharacteristic
467C23×C4D4×C13111yescharacteristic
468C23×C4C23×C13111yescharacteristic
469C23×C4C23×C13111yescharacteristic
470#123—22no—
471#123—22no—
472#123—22no—
473#123—22no—
474C22⋊Q8—21no—
475C22⋊Q8—21no—
476C22⋊Q8—21no—
477C22⋊Q8—21no—
478C22⋊Q8—21no—
479C22⋊Q8—21no—
480C22⋊Q8—21no—
481C22⋊Q8—21no—
482#121—21no—
483#121—21no—
484#121—21no—
485#121—21no—
486#121—21no—
487#121—21no—
488#121—21no—
489#121—21no—
490#120—22no—
491#120—22no—
492#120—22no—
493#120—22no—
494C4×D4—22no—
495C4×D4—22no—
496C4×D4—22no—
497C4×D4—22no—
498C4×D4—22no—
499C4×D4—22no—
500C4×D4—22no—
501C4×D4—22no—
502#117—21no—
503#117—21no—
504#117—21no—
505#117—21no—
506#117—44no—
507C2×C4⋊C4—22no—
508C2×C4⋊C4C2×C4×C13111yescharacteristic, complemented
509C2×C4⋊C4C2×C4×C13111yescharacteristic, complemented
510C2×C4⋊C4C2×C4×C13112yescomplemented
511C2×C4⋊C4C2×C4×C13112yescomplemented
512C2×C22⋊C4—22no—
513C2×C22⋊C4—28no—
514C2×C22⋊C4—22no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4C2×C4×C13112yes—
517C2×C22⋊C4C2×C4×C13112yes—
518C2×C22⋊C4C2×C4×C13112yescomplemented
519C2×C22⋊C4C2×C4×C13112yescomplemented
520C2×C22⋊C4C23×C13114yes—
521C2×C22⋊C4C23×C13112yes—
522C2×C22⋊C4C23×C13114yes—
523C2×C42—22no—
524C2×C42—22no—
525C2×C42—22no—
526C2×C42—44no—
527C2×C42C2×C4×C13112yescomplemented
528#99—216no—
529#95—22no—
530#95—22no—
531#95—22no—
532#95—22no—
533C24—24no—
534C24—42no—
535C24—42no—
536C24C22×C4×C13111yescharacteristic
537C24C22×C4×C13111yescharacteristic
538C24C22×C4×C13112yes—
539C24C2×D4×C13111yescharacteristic
540C24C2×D4×C13111yescharacteristic
541C24C2×D4×C13111yescharacteristic
542C24C2×D4×C13111yescharacteristic
543C24C24×C13111yescharacteristic
544#41—44no—
545#41—44no—
546#41—44no—
547#41—44no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—42no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—22no—
557C2×D4—28no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—42no—
561C2×D4—44no—
562C2×D4—44no—
563C22×C4—24no—
564C22×C4—24no—
565C22×C4—24no—
566C22×C4—28no—
567C22×C4—24no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—24no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—42no—
581C22×C4—42no—
582C22×C4—44no—
583C22×C4—44no—
584C22×C4—44no—
585C22×C4C22⋊C4×C13111yescharacteristic
586C22×C4C22⋊C4×C13111yescharacteristic
587C22×C4C22⋊C4×C13111yescharacteristic
588C22×C4C22⋊C4×C13111yescharacteristic
589C22×C4C22⋊C4×C13111yescharacteristic
590C22×C4C22⋊C4×C13111yescharacteristic
591C22×C4C22⋊C4×C13111yescharacteristic
592C22×C4C22⋊C4×C13111yescharacteristic
593C22×C4C22⋊C4×C13111yescharacteristic
594C22×C4C22⋊C4×C13111yescharacteristic
595C22×C4C22⋊C4×C13111yescharacteristic
596C22×C4C22⋊C4×C13111yescharacteristic
597C22×C4C22⋊C4×C13111yescharacteristic
598C22×C4C22⋊C4×C13111yescharacteristic
599C22×C4C22⋊C4×C13111yescharacteristic
600C22×C4C22⋊C4×C13111yescharacteristic
601C22×C4C22×C4×C13112yes—
602C22×C4C22×C4×C13111yescharacteristic
603C22×C4C22×C4×C13111yescharacteristic
604C22×C4C22×C4×C13112yes—
605C22×C4C22×C4×C13112yes—
606C22×C4C22×C4×C13111yescharacteristic
607C22×C4C22×C4×C13111yescharacteristic
608C22×C4C2×D4×C13111yescharacteristic
609C22×C4C2×D4×C13111yescharacteristic
610C22×C4C2×D4×C13111yescharacteristic
611C22×C4C2×D4×C13111yescharacteristic
612C22×C4C2×D4×C13111yescharacteristic
613C22×C4C2×D4×C13111yescharacteristic
614C22×C4C2×D4×C13111yescharacteristic
615C22×C4C2×D4×C13111yescharacteristic
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—22no—
621C4⋊C4—22no—
622C4⋊C4—22no—
623C4⋊C4—22no—
624C4⋊C4—44no—
625C22⋊C4—28no—
626C22⋊C4—22no—
627C22⋊C4—22no—
628C22⋊C4—22no—
629C22⋊C4—22no—
630C22⋊C4—22no—
631C22⋊C4—22no—
632C22⋊C4—24no—
633C22⋊C4—22no—
634C22⋊C4—22no—
635C22⋊C4—22no—
636C22⋊C4—22no—
637C22⋊C4—28no—
638C22⋊C4—44no—
639C22⋊C4—44no—
640C22⋊C4#41×C13118yescomplemented
641C42—22no—
642C42—22no—
643C42—44no—
644C42—44no—
645C42—44no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—24no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—416no—
669C23—42no—
670C23—42no—
671C23C2×C22⋊C4×C13111yescharacteristic
672C23C2×C22⋊C4×C13111yescharacteristic
673C23C2×C22⋊C4×C13111yescharacteristic
674C23C2×C22⋊C4×C13111yescharacteristic
675C23C23×C4×C13111yescharacteristic
676C23C22×D4×C13111yescharacteristic
677C23C22×D4×C13111yescharacteristic
678C23C2×#41×C13114yes—
679Q8—42no—
680Q8—42no—
681D4—42no—
682D4—44no—
683D4—44no—
684D4—44no—
685D4—44no—
686D4—44no—
687D4—44no—
688D4—42no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—28no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—44no—
722C2×C4—44no—
723C2×C4—416no—
724C2×C4—44no—
725C2×C4—44no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—44no—
729C2×C4—44no—
730C2×C4—44no—
731C2×C4#99×C13114yescomplemented
732C2×C4C2×C22⋊C4×C13111yescharacteristic
733C2×C4C2×C22⋊C4×C13111yescharacteristic
734C2×C4C2×C22⋊C4×C13111yescharacteristic
735C2×C4C2×C22⋊C4×C13111yescharacteristic
736C2×C4C2×C22⋊C4×C13111yescharacteristic
737C2×C4C2×C22⋊C4×C13111yescharacteristic
738C2×C4C2×C22⋊C4×C13111yescharacteristic
739C2×C4C2×C22⋊C4×C13111yescharacteristic
740C22—28no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—21no—
745C22—21no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22—21no—
753C22—21no—
754C22—21no—
755C22—21no—
756C22—21no—
757C22—44no—
758C22—44no—
759C22—44no—
760C22—44no—
761C22—44no—
762C22—44no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—84no—
767C22C2×#99×C13112yes—
768C22#410×C13112yes—
769C22C22×C22⋊C4×C13111yescharacteristic
770C22C4×#41×C13112yes—
771C22#525×C13112yes—
772C22#532×C13112yes—
773C4—21no—
774C4—21no—
775C4—21no—
776C4—21no—
777C4—21no—
778C4—21no—
779C4—48no—
780C4—42no—
781C4—42no—
782C4—42no—
783C4—84no—
784C4C2×#99×C13112yes—
785C4C2×#99×C13112yes—
786C2—22no—
787C2—22no—
788C2—22no—
789C2—22no—
790C2—22no—
791C2—41no—
792C2—41no—
793C2—82no—
794C2#2297×C13111yescharacteristic
795C2C22×#99×C13111yescharacteristic
796C2C2×#410×C13111yescharacteristic
subgroupG/H
centerC2×C4×C131C2×C22⋊C4
commutatorC23C23×C4×C131
Frattini, cosocleC24C24×C131
socleC22×C131C22×C22⋊C4
prime radicalC2×#525×C131C2
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C131 ◁ C24×C4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2280×C131C2semidirect
3. C2×C4×C22⋊C4×C131C2semidirect
4. #1996×C131C2semidirect
5. #1964×C131C2semidirect
6. #1898×C131C2semidirect
7. C4×#99×C131C2semidirect
8. C22×#41×C131C4semidirect
18. C2×#123×C131C4semidirect
19. C2×C22⋊Q8×C131C4semidirect
21. C2×#121×C131C4semidirect
24. C2×C4×D4×C131C4semidirect
27. C2×#117×C131C4semidirect
49. C22×Q8×C131C2×C4semidirect
52. C22×D4×C131C2×C4semidirect
60. C23×C4×C131C2×C4semidirect
109. C2×C4⋊C4×C131C2×C4semidirect
110. C2×C4⋊C4×C131C2×C4semidirect
111. C2×C4⋊C4×C131C2×C4semidirect
112. C2×C4⋊C4×C131C2×C4semidirect
119. C2×C22⋊C4×C131C2×C4semidirect
120. C2×C22⋊C4×C131C2×C4semidirect
128. C2×C42×C131C2×C4semidirect
241. C22⋊C4×C131#41semidirect
332. C2×C4×C131#99semidirect
398. #21420C131direct (N × H)
399. C131#21420direct (N × H)
401. #2280C2×C131semidirect
402. C2×C4×C22⋊C4C2×C131semidirect
403. #1996C2×C131semidirect
404. #1964C2×C131semidirect
405. #1898C2×C131semidirect
406. C4×#99C2×C131semidirect
407. C22×#41C4×C131semidirect
417. C2×#123C4×C131semidirect
418. C2×C22⋊Q8C4×C131semidirect
420. C2×#121C4×C131semidirect
423. C2×C4×D4C4×C131semidirect
426. C2×#117C4×C131semidirect
448. C22×Q8C2×C4×C131semidirect
451. C22×D4C2×C4×C131semidirect
459. C23×C4C2×C4×C131semidirect
508. C2×C4⋊C4C2×C4×C131semidirect
509. C2×C4⋊C4C2×C4×C131semidirect
510. C2×C4⋊C4C2×C4×C131semidirect
511. C2×C4⋊C4C2×C4×C131semidirect
518. C2×C22⋊C4C2×C4×C131semidirect
519. C2×C22⋊C4C2×C4×C131semidirect
527. C2×C42C2×C4×C131semidirect
640. C22⋊C4#41×C131semidirect
731. C2×C4#99×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#525×C1312
#2280×C1312
C2×C4×C22⋊C4×C1312
#1996×C1312
#1964×C1312
#1898×C1312
C4×#99×C1312
#21420131