Finite Group Databasebeta

← C131×#17505 #45703389

Subgroups — C131×#17505 #45703389

Order 33536.

954 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3460×C131C211yesmaximal, characteristic
2#2989×C131C211yesmaximal, characteristic, complemented
3#2965×C131C211yesmaximal, characteristic, complemented
4#1496×C131C211yesmaximal, characteristic, complemented
5#1495×C131C211yesmaximal, characteristic, complemented
6#1494×C131C211yesmaximal, characteristic, complemented
7#1492×C131C211yesmaximal, characteristic, complemented
8#1490×C131C211yesmaximal, characteristic, complemented
9#1489×C131C211yesmaximal, characteristic, complemented
10#1488×C131C211yesmaximal, characteristic, complemented
11#1486×C131C211yesmaximal, characteristic, complemented
12#1484×C131C211yesmaximal, characteristic, complemented
13#1483×C131C211yesmaximal, characteristic, complemented
14#1482×C131C211yesmaximal, characteristic, complemented
15#1480×C131C211yesmaximal, characteristic, complemented
16#544×C131C411yescharacteristic
17#542×C131—21no—
18#542×C131C411yescharacteristic
19#542×C131C411yescharacteristic
20#540×C131—21no—
21#540×C131C411yescharacteristic
22#540×C131C411yescharacteristic
23#538×C131—21no—
24#538×C131—21no—
25#537×C131C411yescharacteristic
26#535×C131C411yescharacteristic
27#535×C131C411yescharacteristic
28#532×C131—21no—
29#532×C131C2211yescharacteristic
30#532×C131C2211yescharacteristic
31#529×C131—21no—
32#529×C131C2211yescharacteristic
33#529×C131C2211yescharacteristic
34#525×C131—21no—
35#525×C131—21no—
36C4×#41×C131C2211yescharacteristic
37C4×#41×C131C2211yescharacteristic
38C2×C4×D4×C131C2211yescharacteristic
39#446×C131—21no—
40#446×C131—21no—
41#436×C131—21no—
42#436×C131—21no—
43#435×C131—21no—
44#435×C131—21no—
45#435×C131—21no—
46#435×C131—21no—
47#432×C131C2211yescharacteristic
48#432×C131C2211yescharacteristic, complemented
49#431×C131C2211yescharacteristic
50#431×C131C2211yescharacteristic, complemented
51#431×C131C2211yescharacteristic, complemented
52#431×C131C2211yescharacteristic, complemented
53#423×C131C2211yescharacteristic
54#423×C131C2211yescharacteristic, complemented
55C2×C4⋊C8×C131C2211yescharacteristic, complemented
56C4×M16×C131C2211yescharacteristic
57C4×M16×C131C2211yescharacteristic, complemented
58C2×C4×C8×C131C2211yescharacteristic, complemented
59Q8⋊C8×C131C2211yescharacteristic, complemented
60Q8⋊C8×C131C2211yescharacteristic, complemented
61Q8⋊C8×C131C2211yescharacteristic, complemented
62Q8⋊C8×C131C2211yescharacteristic, complemented
63D4⋊C8×C131C2211yescharacteristic
64D4⋊C8×C131C2211yescharacteristic
65D4⋊C8×C131C2211yescharacteristic
66D4⋊C8×C131C2211yescharacteristic
67D4⋊C8×C131C2211yescharacteristic
68D4⋊C8×C131C2211yescharacteristic
69D4⋊C8×C131C2211yescharacteristic
70D4⋊C8×C131C2211yescharacteristic
71D4⋊C8×C131C2211yescharacteristic, complemented
72D4⋊C8×C131C2211yescharacteristic, complemented
73D4⋊C8×C131C2211yescharacteristic, complemented
74D4⋊C8×C131C2211yescharacteristic, complemented
75C2×#41×C131—21no—
76C2×#41×C131—21no—
77C2×#41×C131C2×C411yescharacteristic
78C2×#41×C131C2×C411yescharacteristic
79C22×D4×C131C2×C411yescharacteristic
80C23×C4×C131—21no—
81C2×M16×C131—21no—
82C2×M16×C131—21no—
83C2×M16×C131—21no—
84C2×M16×C131—21no—
85C22×C8×C131—21no—
86C22×C8×C131—21no—
87C4⋊Q8×C131—21no—
88C4⋊Q8×C131C2×C411yescharacteristic
89C4⋊Q8×C131C2×C411yescharacteristic
90#127×C131—21no—
91#127×C131C2×C411yescharacteristic
92#127×C131C2×C411yescharacteristic
93#126×C131—21no—
94#126×C131—21no—
95#126×C131—21no—
96#126×C131—21no—
97#125×C131—21no—
98#125×C131C2×C411yescharacteristic
99#125×C131C2×C411yescharacteristic
100#124×C131—21no—
101#124×C131—21no—
102#124×C131—21no—
103#124×C131—21no—
104#124×C131—21no—
105#124×C131C2×C411yescharacteristic
106#124×C131C2×C411yescharacteristic
107#123×C131—21no—
108#123×C131—21no—
109#123×C131—21no—
110#123×C131—21no—
111#123×C131—21no—
112#123×C131—21no—
113#123×C131—21no—
114#123×C131—21no—
115C22⋊Q8×C131—21no—
116C22⋊Q8×C131—21no—
117C22⋊Q8×C131—21no—
118C22⋊Q8×C131—21no—
119C22⋊Q8×C131—21no—
120C22⋊Q8×C131C2×C411yescharacteristic
121C22⋊Q8×C131C2×C411yescharacteristic
122#121×C131—21no—
123#121×C131—21no—
124#121×C131—21no—
125#121×C131—21no—
126#121×C131—21no—
127#121×C131—21no—
128#121×C131—21no—
129#121×C131—21no—
130#121×C131—21no—
131#121×C131—21no—
132#121×C131—21no—
133#121×C131C2×C411yescharacteristic
134#121×C131C2×C411yescharacteristic
135#121×C131C2×C411yescharacteristic
136#121×C131C2×C411yescharacteristic
137#121×C131C2×C411yescharacteristic
138#121×C131C2×C411yescharacteristic
139#120×C131—21no—
140#120×C131—21no—
141#120×C131—21no—
142#120×C131—21no—
143C4×Q8×C131C2×C411yescharacteristic
144C4×Q8×C131D411yescharacteristic
145C4×Q8×C131D411yescharacteristic
146C4×Q8×C131C2311yescharacteristic
147C4×D4×C131—21no—
148C4×D4×C131—21no—
149C4×D4×C131—21no—
150C4×D4×C131—21no—
151C4×D4×C131—21no—
152C4×D4×C131—21no—
153C4×D4×C131—21no—
154C4×D4×C131—21no—
155C4×D4×C131C2×C411yescharacteristic
156C4×D4×C131C2×C411yescharacteristic
157C4×D4×C131C2×C411yescharacteristic
158C4×D4×C131D411yescharacteristic
159C4×D4×C131D411yescharacteristic
160C4×D4×C131D411yescharacteristic
161C4×D4×C131D411yescharacteristic
162C4×D4×C131D411yescharacteristic
163C4×D4×C131D411yescharacteristic
164C4×D4×C131C2311yescharacteristic
165C4×D4×C131C2311yescharacteristic
166C4×D4×C131C2311yescharacteristic
167#117×C131—21no—
168#117×C131—21no—
169#117×C131—21no—
170#117×C131C2×C411yescharacteristic
171#117×C131C2×C411yescharacteristic
172#117×C131C2×C411yescharacteristic
173#117×C131C2×C411yescharacteristic
174C2×C4⋊C4×C131C2×C411yescharacteristic
175C2×C22⋊C4×C131—21no—
176C2×C42×C131—21no—
177C2×C42×C131C2311yescharacteristic
178C2×C42×C131C2311yescharacteristic
179C2×C42×C131C2311yescharacteristic
180C4⋊C8×C131—21no—
181C4⋊C8×C131—21no—
182C4⋊C8×C131—21no—
183C4⋊C8×C131—21no—
184C4⋊C8×C131—21no—
185C4⋊C8×C131—21no—
186C4⋊C8×C131C2311yescharacteristic
187C4⋊C8×C131C2311yescharacteristic
188C4⋊C8×C131C2311yescharacteristic
189C4⋊C8×C131C2311yescharacteristic
190C22⋊C8×C131—21no—
191C22⋊C8×C131—21no—
192C22⋊C8×C131—21no—
193C22⋊C8×C131—21no—
194C22⋊C8×C131—21no—
195C22⋊C8×C131—21no—
196#97×C131—21no—
197#97×C131—21no—
198#97×C131—21no—
199#97×C131—21no—
200C4×C8×C131—21no—
201C4×C8×C131—21no—
202C4×C8×C131C2311yescharacteristic
203C4×C8×C131C2311yescharacteristic
204C4×C8×C131C2311yescharacteristic
205C4×C8×C131C2311yescharacteristic
206C24×C131—21no—
207#41×C131—42no—
208#41×C131—42no—
209#41×C131—81no—
210#41×C131—81no—
211#41×C131—81no—
212#41×C131—81no—
213C2×Q8×C131—21no—
214C2×Q8×C131—21no—
215C2×Q8×C131C22⋊C411yescharacteristic
216C2×Q8×C131C22×C411yescharacteristic
217C2×D4×C131—21no—
218C2×D4×C131—21no—
219C2×D4×C131—21no—
220C2×D4×C131—21no—
221C2×D4×C131—21no—
222C2×D4×C131—21no—
223C2×D4×C131—21no—
224C2×D4×C131—21no—
225C2×D4×C131—21no—
226C2×D4×C131—21no—
227C2×D4×C131—21no—
228C2×D4×C131—21no—
229C2×D4×C131—42no—
230C2×D4×C131C22⋊C411yescharacteristic
231C2×D4×C131C22⋊C411yescharacteristic
232C2×D4×C131C22⋊C411yescharacteristic
233C2×D4×C131C22×C411yescharacteristic
234C2×D4×C131C22×C411yescharacteristic
235C2×D4×C131C22×C411yescharacteristic
236C22×C4×C131—21no—
237C22×C4×C131—21no—
238C22×C4×C131—21no—
239C22×C4×C131—21no—
240C22×C4×C131—21no—
241C22×C4×C131—21no—
242C22×C4×C131—21no—
243C22×C4×C131—21no—
244C22×C4×C131—81no—
245C22×C4×C131—81no—
246C22×C4×C131C22×C411yescharacteristic
247C22×C4×C131C22×C411yescharacteristic
248C22×C4×C131C22×C411yescharacteristic
249C22×C4×C131C2×D411yescharacteristic
250C22×C4×C131C2×D411yescharacteristic
251C22×C4×C131C2×D411yescharacteristic
252C22×C4×C131C2×D411yescharacteristic
253C22×C4×C131C2×D411yescharacteristic
254C22×C4×C131C2×D411yescharacteristic
255M16×C131—42no—
256M16×C131—42no—
257M16×C131—81no—
258M16×C131—81no—
259C2×C8×C131—21no—
260C2×C8×C131—21no—
261C2×C8×C131—21no—
262C2×C8×C131—21no—
263C2×C8×C131—21no—
264C2×C8×C131—21no—
265C2×C8×C131—21no—
266C2×C8×C131—21no—
267C2×C8×C131—42no—
268C2×C8×C131—81no—
269C4⋊C4×C131—21no—
270C4⋊C4×C131—21no—
271C4⋊C4×C131—21no—
272C4⋊C4×C131—21no—
273C4⋊C4×C131—21no—
274C4⋊C4×C131—21no—
275C4⋊C4×C131—21no—
276C4⋊C4×C131—21no—
277C4⋊C4×C131—21no—
278C4⋊C4×C131—21no—
279C4⋊C4×C131—21no—
280C4⋊C4×C131C22⋊C411yescharacteristic
281C4⋊C4×C131C22⋊C411yescharacteristic
282C4⋊C4×C131C22⋊C411yescharacteristic
283C4⋊C4×C131C22⋊C411yescharacteristic
284C4⋊C4×C131C22⋊C411yescharacteristic
285C4⋊C4×C131C22⋊C411yescharacteristic
286C4⋊C4×C131C22×C411yescharacteristic
287C4⋊C4×C131C22×C411yescharacteristic
288C4⋊C4×C131C22×C411yescharacteristic
289C4⋊C4×C131C22×C411yescharacteristic
290C22⋊C4×C131—21no—
291C22⋊C4×C131—21no—
292C22⋊C4×C131—21no—
293C22⋊C4×C131—21no—
294C22⋊C4×C131—21no—
295C22⋊C4×C131—21no—
296C22⋊C4×C131—21no—
297C22⋊C4×C131—21no—
298C22⋊C4×C131—21no—
299C22⋊C4×C131—21no—
300C22⋊C4×C131—21no—
301C22⋊C4×C131—21no—
302C22⋊C4×C131—21no—
303C22⋊C4×C131—21no—
304C22⋊C4×C131—21no—
305C22⋊C4×C131—21no—
306C22⋊C4×C131—21no—
307C22⋊C4×C131—21no—
308C22⋊C4×C131—21no—
309C22⋊C4×C131C22⋊C411yescharacteristic
310C22⋊C4×C131C22⋊C411yescharacteristic
311C22⋊C4×C131C22⋊C411yescharacteristic
312C22⋊C4×C131C22⋊C411yescharacteristic
313C22⋊C4×C131C22⋊C411yescharacteristic
314C22⋊C4×C131C22⋊C411yescharacteristic
315C42×C131—21no—
316C42×C131—21no—
317C42×C131—21no—
318C42×C131C22×C411yescharacteristic
319C42×C131C22×C411yescharacteristic
320C42×C131C22×C411yescharacteristic
321C42×C131C2×D411yescharacteristic
322C42×C131C2×D411yescharacteristic
323C42×C131C2×D411yescharacteristic
324C42×C131C2×D411yescharacteristic
325C42×C131C2×D411yescharacteristic
326C42×C131C2×D411yescharacteristic
327C42×C131C2411yescharacteristic
328C23×C131—21no—
329C23×C131—21no—
330C23×C131—21no—
331C23×C131—42no—
332C23×C131—81no—
333C23×C131—81no—
334C23×C131C2×C22⋊C411yescharacteristic
335C23×C131C2×C22⋊C411yescharacteristic
336C23×C131C2×C22⋊C411yescharacteristic
337Q8×C131—22no—
338Q8×C131—41no—
339Q8×C131—81no—
340Q8×C131—81no—
341D4×C131—22no—
342D4×C131—22no—
343D4×C131—22no—
344D4×C131—41no—
345D4×C131—41no—
346D4×C131—41no—
347D4×C131—42no—
348D4×C131—42no—
349D4×C131—81no—
350D4×C131—81no—
351D4×C131—81no—
352D4×C131—81no—
353D4×C131—81no—
354D4×C131—81no—
355D4×C131—81no—
356D4×C131—81no—
357D4×C131—81no—
358D4×C131—81no—
359C2×C4×C131—22no—
360C2×C4×C131—22no—
361C2×C4×C131—22no—
362C2×C4×C131—21no—
363C2×C4×C131—21no—
364C2×C4×C131—21no—
365C2×C4×C131—21no—
366C2×C4×C131—21no—
367C2×C4×C131—21no—
368C2×C4×C131—21no—
369C2×C4×C131—21no—
370C2×C4×C131—21no—
371C2×C4×C131—21no—
372C2×C4×C131—21no—
373C2×C4×C131—41no—
374C2×C4×C131—41no—
375C2×C4×C131—41no—
376C2×C4×C131—42no—
377C2×C4×C131—41no—
378C2×C4×C131—41no—
379C2×C4×C131—41no—
380C2×C4×C131—41no—
381C2×C4×C131—41no—
382C2×C4×C131—41no—
383C2×C4×C131—81no—
384C2×C4×C131—81no—
385C2×C4×C131—81no—
386C2×C4×C131—81no—
387C2×C4×C131C2×C22⋊C411yescharacteristic
388C2×C4×C131C2×C22⋊C411yescharacteristic
389C2×C4×C131C2×C22⋊C411yescharacteristic
390C2×C4×C131C2×C22⋊C411yescharacteristic
391C2×C4×C131C2×C22⋊C411yescharacteristic
392C2×C4×C131C2×C22⋊C411yescharacteristic
393C2×C4×C131C2×C22⋊C411yescharacteristic
394C2×C4×C131C2×C22⋊C411yescharacteristic
395C2×C4×C131C2×C22⋊C411yescharacteristic
396C2×C4×C131C23×C411yescharacteristic
397C2×C4×C131C22×D411yescharacteristic
398C2×C4×C131C22×D411yescharacteristic
399C8×C131—22no—
400C8×C131—41no—
401C8×C131—41no—
402C8×C131—41no—
403C8×C131—41no—
404C8×C131—41no—
405C8×C131—41no—
406C8×C131—41no—
407C22×C131—21no—
408C22×C131—21no—
409C22×C131—21no—
410C22×C131—21no—
411C22×C131—21no—
412C22×C131—21no—
413C22×C131—21no—
414C22×C131—21no—
415C22×C131—21no—
416C22×C131—41no—
417C22×C131—41no—
418C22×C131—41no—
419C22×C131—41no—
420C22×C131—41no—
421C22×C131—41no—
422C22×C131—41no—
423C22×C131—41no—
424C22×C131—41no—
425C22×C131—84no—
426C22×C131C22×C22⋊C411yescharacteristic
427C4×C131—21no—
428C4×C131—21no—
429C4×C131—21no—
430C4×C131—21no—
431C4×C131—21no—
432C4×C131—21no—
433C4×C131—21no—
434C4×C131—21no—
435C4×C131—21no—
436C4×C131—21no—
437C4×C131—41no—
438C4×C131—41no—
439C4×C131—41no—
440C4×C131—41no—
441C4×C131—41no—
442C4×C131#56812yes—
443C4×C131#57611yescharacteristic
444C4×C131#57711yescharacteristic
445C2×C131—41no—
446C2×C131—41no—
447C2×C131—41no—
448C2×C131—81no—
449C2×C131—81no—
450C2×C131—81no—
451C2×C131#287911yescharacteristic
452C2×C131#289711yescharacteristic
453C2×C131#290111yescharacteristic
454#17505C13111yesmaximal, characteristic, direct product factor, Sylow
455C131#1750511yescharacteristic, direct product factor, Sylow
456#3460C2×C13111yescharacteristic
457#2989C2×C13111yescharacteristic, complemented
458#2965C2×C13111yescharacteristic, complemented
459#1496C2×C13111yescharacteristic, complemented
460#1495C2×C13111yescharacteristic, complemented
461#1494C2×C13111yescharacteristic, complemented
462#1492C2×C13111yescharacteristic, complemented
463#1490C2×C13111yescharacteristic, complemented
464#1489C2×C13111yescharacteristic, complemented
465#1488C2×C13111yescharacteristic, complemented
466#1486C2×C13111yescharacteristic, complemented
467#1484C2×C13111yescharacteristic, complemented
468#1483C2×C13111yescharacteristic, complemented
469#1482C2×C13111yescharacteristic, complemented
470#1480C2×C13111yescharacteristic, complemented
471#544C4×C13111yescharacteristic
472#542—21no—
473#542C4×C13111yescharacteristic
474#542C4×C13111yescharacteristic
475#540—21no—
476#540C4×C13111yescharacteristic
477#540C4×C13111yescharacteristic
478#538—21no—
479#538—21no—
480#537C4×C13111yescharacteristic
481#535C4×C13111yescharacteristic
482#535C4×C13111yescharacteristic
483#532—21no—
484#532C22×C13111yescharacteristic
485#532C22×C13111yescharacteristic
486#529—21no—
487#529C22×C13111yescharacteristic
488#529C22×C13111yescharacteristic
489#525—21no—
490#525—21no—
491C4×#41C22×C13111yescharacteristic
492C4×#41C22×C13111yescharacteristic
493C2×C4×D4C22×C13111yescharacteristic
494#446—21no—
495#446—21no—
496#436—21no—
497#436—21no—
498#435—21no—
499#435—21no—
500#435—21no—
501#435—21no—
502#432C22×C13111yescharacteristic
503#432C22×C13111yescharacteristic, complemented
504#431C22×C13111yescharacteristic
505#431C22×C13111yescharacteristic, complemented
506#431C22×C13111yescharacteristic, complemented
507#431C22×C13111yescharacteristic, complemented
508#423C22×C13111yescharacteristic
509#423C22×C13111yescharacteristic, complemented
510C2×C4⋊C8C22×C13111yescharacteristic, complemented
511C4×M16C22×C13111yescharacteristic
512C4×M16C22×C13111yescharacteristic, complemented
513C2×C4×C8C22×C13111yescharacteristic, complemented
514Q8⋊C8C22×C13111yescharacteristic, complemented
515Q8⋊C8C22×C13111yescharacteristic, complemented
516Q8⋊C8C22×C13111yescharacteristic, complemented
517Q8⋊C8C22×C13111yescharacteristic, complemented
518D4⋊C8C22×C13111yescharacteristic
519D4⋊C8C22×C13111yescharacteristic
520D4⋊C8C22×C13111yescharacteristic
521D4⋊C8C22×C13111yescharacteristic
522D4⋊C8C22×C13111yescharacteristic
523D4⋊C8C22×C13111yescharacteristic
524D4⋊C8C22×C13111yescharacteristic
525D4⋊C8C22×C13111yescharacteristic
526D4⋊C8C22×C13111yescharacteristic, complemented
527D4⋊C8C22×C13111yescharacteristic, complemented
528D4⋊C8C22×C13111yescharacteristic, complemented
529D4⋊C8C22×C13111yescharacteristic, complemented
530C2×#41—21no—
531C2×#41—21no—
532C2×#41C2×C4×C13111yescharacteristic
533C2×#41C2×C4×C13111yescharacteristic
534C22×D4C2×C4×C13111yescharacteristic
535C23×C4—21no—
536C2×M16—21no—
537C2×M16—21no—
538C2×M16—21no—
539C2×M16—21no—
540C22×C8—21no—
541C22×C8—21no—
542C4⋊Q8—21no—
543C4⋊Q8C2×C4×C13111yescharacteristic
544C4⋊Q8C2×C4×C13111yescharacteristic
545#127—21no—
546#127C2×C4×C13111yescharacteristic
547#127C2×C4×C13111yescharacteristic
548#126—21no—
549#126—21no—
550#126—21no—
551#126—21no—
552#125—21no—
553#125C2×C4×C13111yescharacteristic
554#125C2×C4×C13111yescharacteristic
555#124—21no—
556#124—21no—
557#124—21no—
558#124—21no—
559#124—21no—
560#124C2×C4×C13111yescharacteristic
561#124C2×C4×C13111yescharacteristic
562#123—21no—
563#123—21no—
564#123—21no—
565#123—21no—
566#123—21no—
567#123—21no—
568#123—21no—
569#123—21no—
570C22⋊Q8—21no—
571C22⋊Q8—21no—
572C22⋊Q8—21no—
573C22⋊Q8—21no—
574C22⋊Q8—21no—
575C22⋊Q8C2×C4×C13111yescharacteristic
576C22⋊Q8C2×C4×C13111yescharacteristic
577#121—21no—
578#121—21no—
579#121—21no—
580#121—21no—
581#121—21no—
582#121—21no—
583#121—21no—
584#121—21no—
585#121—21no—
586#121—21no—
587#121—21no—
588#121C2×C4×C13111yescharacteristic
589#121C2×C4×C13111yescharacteristic
590#121C2×C4×C13111yescharacteristic
591#121C2×C4×C13111yescharacteristic
592#121C2×C4×C13111yescharacteristic
593#121C2×C4×C13111yescharacteristic
594#120—21no—
595#120—21no—
596#120—21no—
597#120—21no—
598C4×Q8C2×C4×C13111yescharacteristic
599C4×Q8D4×C13111yescharacteristic
600C4×Q8D4×C13111yescharacteristic
601C4×Q8C23×C13111yescharacteristic
602C4×D4—21no—
603C4×D4—21no—
604C4×D4—21no—
605C4×D4—21no—
606C4×D4—21no—
607C4×D4—21no—
608C4×D4—21no—
609C4×D4—21no—
610C4×D4C2×C4×C13111yescharacteristic
611C4×D4C2×C4×C13111yescharacteristic
612C4×D4C2×C4×C13111yescharacteristic
613C4×D4D4×C13111yescharacteristic
614C4×D4D4×C13111yescharacteristic
615C4×D4D4×C13111yescharacteristic
616C4×D4D4×C13111yescharacteristic
617C4×D4D4×C13111yescharacteristic
618C4×D4D4×C13111yescharacteristic
619C4×D4C23×C13111yescharacteristic
620C4×D4C23×C13111yescharacteristic
621C4×D4C23×C13111yescharacteristic
622#117—21no—
623#117—21no—
624#117—21no—
625#117C2×C4×C13111yescharacteristic
626#117C2×C4×C13111yescharacteristic
627#117C2×C4×C13111yescharacteristic
628#117C2×C4×C13111yescharacteristic
629C2×C4⋊C4C2×C4×C13111yescharacteristic
630C2×C22⋊C4—21no—
631C2×C42—21no—
632C2×C42C23×C13111yescharacteristic
633C2×C42C23×C13111yescharacteristic
634C2×C42C23×C13111yescharacteristic
635C4⋊C8—21no—
636C4⋊C8—21no—
637C4⋊C8—21no—
638C4⋊C8—21no—
639C4⋊C8—21no—
640C4⋊C8—21no—
641C4⋊C8C23×C13111yescharacteristic
642C4⋊C8C23×C13111yescharacteristic
643C4⋊C8C23×C13111yescharacteristic
644C4⋊C8C23×C13111yescharacteristic
645C22⋊C8—21no—
646C22⋊C8—21no—
647C22⋊C8—21no—
648C22⋊C8—21no—
649C22⋊C8—21no—
650C22⋊C8—21no—
651#97—21no—
652#97—21no—
653#97—21no—
654#97—21no—
655C4×C8—21no—
656C4×C8—21no—
657C4×C8C23×C13111yescharacteristic
658C4×C8C23×C13111yescharacteristic
659C4×C8C23×C13111yescharacteristic
660C4×C8C23×C13111yescharacteristic
661C24—21no—
662#41—42no—
663#41—42no—
664#41—81no—
665#41—81no—
666#41—81no—
667#41—81no—
668C2×Q8—21no—
669C2×Q8—21no—
670C2×Q8C22⋊C4×C13111yescharacteristic
671C2×Q8C22×C4×C13111yescharacteristic
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—42no—
685C2×D4C22⋊C4×C13111yescharacteristic
686C2×D4C22⋊C4×C13111yescharacteristic
687C2×D4C22⋊C4×C13111yescharacteristic
688C2×D4C22×C4×C13111yescharacteristic
689C2×D4C22×C4×C13111yescharacteristic
690C2×D4C22×C4×C13111yescharacteristic
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—81no—
700C22×C4—81no—
701C22×C4C22×C4×C13111yescharacteristic
702C22×C4C22×C4×C13111yescharacteristic
703C22×C4C22×C4×C13111yescharacteristic
704C22×C4C2×D4×C13111yescharacteristic
705C22×C4C2×D4×C13111yescharacteristic
706C22×C4C2×D4×C13111yescharacteristic
707C22×C4C2×D4×C13111yescharacteristic
708C22×C4C2×D4×C13111yescharacteristic
709C22×C4C2×D4×C13111yescharacteristic
710M16—42no—
711M16—42no—
712M16—81no—
713M16—81no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—21no—
717C2×C8—21no—
718C2×C8—21no—
719C2×C8—21no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—42no—
723C2×C8—81no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4C22⋊C4×C13111yescharacteristic
736C4⋊C4C22⋊C4×C13111yescharacteristic
737C4⋊C4C22⋊C4×C13111yescharacteristic
738C4⋊C4C22⋊C4×C13111yescharacteristic
739C4⋊C4C22⋊C4×C13111yescharacteristic
740C4⋊C4C22⋊C4×C13111yescharacteristic
741C4⋊C4C22×C4×C13111yescharacteristic
742C4⋊C4C22×C4×C13111yescharacteristic
743C4⋊C4C22×C4×C13111yescharacteristic
744C4⋊C4C22×C4×C13111yescharacteristic
745C22⋊C4—21no—
746C22⋊C4—21no—
747C22⋊C4—21no—
748C22⋊C4—21no—
749C22⋊C4—21no—
750C22⋊C4—21no—
751C22⋊C4—21no—
752C22⋊C4—21no—
753C22⋊C4—21no—
754C22⋊C4—21no—
755C22⋊C4—21no—
756C22⋊C4—21no—
757C22⋊C4—21no—
758C22⋊C4—21no—
759C22⋊C4—21no—
760C22⋊C4—21no—
761C22⋊C4—21no—
762C22⋊C4—21no—
763C22⋊C4—21no—
764C22⋊C4C22⋊C4×C13111yescharacteristic
765C22⋊C4C22⋊C4×C13111yescharacteristic
766C22⋊C4C22⋊C4×C13111yescharacteristic
767C22⋊C4C22⋊C4×C13111yescharacteristic
768C22⋊C4C22⋊C4×C13111yescharacteristic
769C22⋊C4C22⋊C4×C13111yescharacteristic
770C42—21no—
771C42—21no—
772C42—21no—
773C42C22×C4×C13111yescharacteristic
774C42C22×C4×C13111yescharacteristic
775C42C22×C4×C13111yescharacteristic
776C42C2×D4×C13111yescharacteristic
777C42C2×D4×C13111yescharacteristic
778C42C2×D4×C13111yescharacteristic
779C42C2×D4×C13111yescharacteristic
780C42C2×D4×C13111yescharacteristic
781C42C2×D4×C13111yescharacteristic
782C42C24×C13111yescharacteristic
783C23—21no—
784C23—21no—
785C23—21no—
786C23—42no—
787C23—81no—
788C23—81no—
789C23C2×C22⋊C4×C13111yescharacteristic
790C23C2×C22⋊C4×C13111yescharacteristic
791C23C2×C22⋊C4×C13111yescharacteristic
792Q8—22no—
793Q8—41no—
794Q8—81no—
795Q8—81no—
796D4—22no—
797D4—22no—
798D4—22no—
799D4—41no—
800D4—41no—
801D4—41no—
802D4—42no—
803D4—42no—
804D4—81no—
805D4—81no—
806D4—81no—
807D4—81no—
808D4—81no—
809D4—81no—
810D4—81no—
811D4—81no—
812D4—81no—
813D4—81no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—42no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—81no—
839C2×C4—81no—
840C2×C4—81no—
841C2×C4—81no—
842C2×C4C2×C22⋊C4×C13111yescharacteristic
843C2×C4C2×C22⋊C4×C13111yescharacteristic
844C2×C4C2×C22⋊C4×C13111yescharacteristic
845C2×C4C2×C22⋊C4×C13111yescharacteristic
846C2×C4C2×C22⋊C4×C13111yescharacteristic
847C2×C4C2×C22⋊C4×C13111yescharacteristic
848C2×C4C2×C22⋊C4×C13111yescharacteristic
849C2×C4C2×C22⋊C4×C13111yescharacteristic
850C2×C4C2×C22⋊C4×C13111yescharacteristic
851C2×C4C23×C4×C13111yescharacteristic
852C2×C4C22×D4×C13111yescharacteristic
853C2×C4C22×D4×C13111yescharacteristic
854C8—22no—
855C8—41no—
856C8—41no—
857C8—41no—
858C8—41no—
859C8—41no—
860C8—41no—
861C8—41no—
862C22—21no—
863C22—21no—
864C22—21no—
865C22—21no—
866C22—21no—
867C22—21no—
868C22—21no—
869C22—21no—
870C22—21no—
871C22—41no—
872C22—41no—
873C22—41no—
874C22—41no—
875C22—41no—
876C22—41no—
877C22—41no—
878C22—41no—
879C22—41no—
880C22—84no—
881C22C22×C22⋊C4×C13111yescharacteristic
882C4—21no—
883C4—21no—
884C4—21no—
885C4—21no—
886C4—21no—
887C4—21no—
888C4—21no—
889C4—21no—
890C4—21no—
891C4—21no—
892C4—41no—
893C4—41no—
894C4—41no—
895C4—41no—
896C4—41no—
897C4#568×C13112yes—
898C4#576×C13111yescharacteristic
899C4#577×C13111yescharacteristic
900C2—41no—
901C2—41no—
902C2—41no—
903C2—81no—
904C2—81no—
905C2—81no—
906C2#2879×C13111yescharacteristic
907C2#2897×C13111yescharacteristic
908C2#2901×C13111yescharacteristic
subgroupG/H
centerC2×C4×C131C22×D4
commutatorC2×C4C23×C4×C131
Frattini, cosocleC42C24×C131
socleC22×C131C22×C22⋊C4
prime radical#3460×C131C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C131 ◁ C4×#41×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2989×C131C2semidirect
3. #2965×C131C2semidirect
4. #1496×C131C2semidirect
5. #1495×C131C2semidirect
6. #1494×C131C2semidirect
7. #1492×C131C2semidirect
8. #1490×C131C2semidirect
9. #1489×C131C2semidirect
10. #1488×C131C2semidirect
11. #1486×C131C2semidirect
12. #1484×C131C2semidirect
13. #1483×C131C2semidirect
14. #1482×C131C2semidirect
15. #1480×C131C2semidirect
48. #432×C131C22semidirect
50. #431×C131C22semidirect
51. #431×C131C22semidirect
52. #431×C131C22semidirect
54. #423×C131C22semidirect
55. C2×C4⋊C8×C131C22semidirect
57. C4×M16×C131C22semidirect
58. C2×C4×C8×C131C22semidirect
59. Q8⋊C8×C131C22semidirect
60. Q8⋊C8×C131C22semidirect
61. Q8⋊C8×C131C22semidirect
62. Q8⋊C8×C131C22semidirect
71. D4⋊C8×C131C22semidirect
72. D4⋊C8×C131C22semidirect
73. D4⋊C8×C131C22semidirect
74. D4⋊C8×C131C22semidirect
454. #17505C131direct (N × H)
455. C131#17505direct (N × H)
457. #2989C2×C131semidirect
458. #2965C2×C131semidirect
459. #1496C2×C131semidirect
460. #1495C2×C131semidirect
461. #1494C2×C131semidirect
462. #1492C2×C131semidirect
463. #1490C2×C131semidirect
464. #1489C2×C131semidirect
465. #1488C2×C131semidirect
466. #1486C2×C131semidirect
467. #1484C2×C131semidirect
468. #1483C2×C131semidirect
469. #1482C2×C131semidirect
470. #1480C2×C131semidirect
503. #432C22×C131semidirect
505. #431C22×C131semidirect
506. #431C22×C131semidirect
507. #431C22×C131semidirect
509. #423C22×C131semidirect
510. C2×C4⋊C8C22×C131semidirect
512. C4×M16C22×C131semidirect
513. C2×C4×C8C22×C131semidirect
514. Q8⋊C8C22×C131semidirect
515. Q8⋊C8C22×C131semidirect
516. Q8⋊C8C22×C131semidirect
517. Q8⋊C8C22×C131semidirect
526. D4⋊C8C22×C131semidirect
527. D4⋊C8C22×C131semidirect
528. D4⋊C8C22×C131semidirect
529. D4⋊C8C22×C131semidirect

Maximal subgroups

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

subgroupindex
#3460×C1312
#2989×C1312
#2965×C1312
#1496×C1312
#1495×C1312
#1494×C1312
#1492×C1312
#1490×C1312
#1489×C1312
#1488×C1312
#1486×C1312
#1484×C1312
#1483×C1312
#1482×C1312
#1480×C1312
#17505131