Finite Group Databasebeta

← C131×#26986 #45712870

Subgroups — C131×#26986 #45712870

Order 33536.

880 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#470×C131C211yesmaximal, characteristic, complemented
2C2×#440×C131C211yesmaximal, characteristic, complemented
3#2427×C131C211yesmaximal, characteristic
4#2421×C131C211yesmaximal, characteristic, complemented
5#2085×C131C211yesmaximal, characteristic, complemented
6#2036×C131C211yesmaximal, characteristic, complemented
7#2015×C131C211yesmaximal, characteristic, complemented
8#2000×C131C211yesmaximal, characteristic
9#1958×C131C211yesmaximal, characteristic, complemented
10#1935×C131C211yesmaximal, characteristic, complemented
11#1933×C131C211yesmaximal, characteristic, complemented
12#1895×C131C211yesmaximal, characteristic
13#1878×C131C211yesmaximal, characteristic, complemented
14#1864×C131C211yesmaximal, characteristic, complemented
15#1753×C131C211yesmaximal, characteristic, complemented
16C22×Q16×C131C2211yescharacteristic
17C22×SD16×C131C2211yescharacteristic
18C22×M16×C131C2211yescharacteristic
19C2×#124×C131C2211yescharacteristic
20C2×C22⋊Q8×C131C2211yescharacteristic
21C2×C22⋊Q8×C131C2211yescharacteristic
22C2×#121×C131C2211yescharacteristic
23C2×C4×Q8×C131C2211yescharacteristic
24C2×C4×D4×C131C2211yescharacteristic
25#470×C131—24no—
26#440×C131—24no—
27C2×#107×C131C2211yescharacteristic
28C2×#106×C131C2211yescharacteristic
29C2×#103×C131C2211yescharacteristic
30C2×#103×C131C2211yescharacteristic
31C2×#103×C131C2211yescharacteristic
32C2×#103×C131C2211yescharacteristic
33C2×#103×C131C2211yescharacteristic
34C2×#102×C131C2211yescharacteristic
35C2×#102×C131C2211yescharacteristic
36C2×#102×C131C2211yescharacteristic
37C2×C22⋊C8×C131C2211yescharacteristic
38C2×#97×C131C2211yescharacteristic
39C2×C4×C8×C131C2211yescharacteristic
40#400×C131—21no—
41#397×C131—21no—
42#397×C131—21no—
43#394×C131—21no—
44#391×C131C2211yescharacteristic
45#391×C131C2211yescharacteristic
46#389×C131C2211yescharacteristic
47#389×C131C2211yescharacteristic
48#388×C131—21no—
49#387×C131—21no—
50#386×C131—21no—
51#382×C131C2211yescharacteristic
52#380×C131—21no—
53#380×C131C2211yescharacteristic
54C4×C22⋊C4×C131C2211yescharacteristic
55#340×C131C2211yescharacteristic
56#340×C131C2211yescharacteristic
57#340×C131C2211yescharacteristic
58#340×C131C2211yescharacteristic
59#336×C131C2211yescharacteristic
60#336×C131C2211yescharacteristic
61C22×Q8×C131C2311yescharacteristic
62C22×Q8×C131C2311yescharacteristic
63C22×D4×C131—21no—
64C22×D4×C131C2311yescharacteristic
65C23×C4×C131—21no—
66C23×C4×C131C2311yescharacteristic
67C2×Q16×C131—22no—
68C2×Q16×C131—22no—
69C2×Q16×C131—41no—
70C2×SD16×C131—22no—
71C2×SD16×C131—22no—
72C2×SD16×C131—22no—
73C2×M16×C131—22no—
74C2×M16×C131—22no—
75C2×M16×C131—41no—
76C22×C8×C131C2311yescharacteristic
77C22×C8×C131C2311yescharacteristic
78C22×C8×C131C2311yescharacteristic
79C22×C8×C131C2311yescharacteristic
80#124×C131—22no—
81#124×C131—41no—
82C22⋊Q8×C131—22no—
83C22⋊Q8×C131—22no—
84C22⋊Q8×C131—41no—
85C22⋊Q8×C131—41no—
86#121×C131—22no—
87#121×C131—41no—
88C4×Q8×C131—22no—
89C4×Q8×C131—41no—
90C4×D4×C131—22no—
91C4×D4×C131—41no—
92C2×C4⋊C4×C131—21no—
93C2×C4⋊C4×C131—21no—
94C2×C4⋊C4×C131—21no—
95C2×C4⋊C4×C131—21no—
96C2×C4⋊C4×C131—21no—
97C2×C4⋊C4×C131C2311yescharacteristic
98C2×C4⋊C4×C131C2311yescharacteristic
99C2×C4⋊C4×C131C2311yescharacteristic
100C2×C4⋊C4×C131C2311yescharacteristic
101C2×C4⋊C4×C131C2311yescharacteristic
102C2×C22⋊C4×C131—21no—
103C2×C22⋊C4×C131—21no—
104C2×C22⋊C4×C131—21no—
105C2×C22⋊C4×C131—21no—
106C2×C22⋊C4×C131—21no—
107C2×C22⋊C4×C131—21no—
108C2×C22⋊C4×C131—21no—
109C2×C22⋊C4×C131D411yescharacteristic
110C2×C22⋊C4×C131D411yescharacteristic
111C2×C42×C131—21no—
112C2×C42×C131C2311yescharacteristic
113C2×C42×C131C2311yescharacteristic
114#107×C131—22no—
115#106×C131—22no—
116#103×C131—22no—
117#103×C131—22no—
118#103×C131—41no—
119#103×C131—41no—
120#103×C131D414yescomplemented
121#102×C131—22no—
122#102×C131—22no—
123#102×C131—41no—
124C22⋊C8×C131—22no—
125#97×C131—22no—
126C4×C8×C131—41no—
127#95×C131—21no—
128#95×C131—21no—
129#95×C131—21no—
130#95×C131—21no—
131#95×C131—21no—
132#95×C131—21no—
133#95×C131—21no—
134#95×C131—21no—
135#95×C131—21no—
136#95×C131D411yescharacteristic
137#95×C131D411yescharacteristic
138C24×C131—21no—
139C24×C131C2×D411yescharacteristic
140C2×Q8×C131—21no—
141C2×Q8×C131—21no—
142C2×Q8×C131—21no—
143C2×Q8×C131—21no—
144C2×Q8×C131—21no—
145C2×Q8×C131—21no—
146C2×Q8×C131—21no—
147C2×Q8×C131—21no—
148C2×Q8×C131—21no—
149C2×Q8×C131—21no—
150C2×Q8×C131—21no—
151C2×Q8×C131C2×D412yes—
152C2×D4×C131—21no—
153C2×D4×C131—21no—
154C2×D4×C131—21no—
155C2×D4×C131—21no—
156C2×D4×C131—21no—
157C2×D4×C131—42no—
158C2×D4×C131—42no—
159C2×D4×C131—81no—
160C2×D4×C131#4112yes—
161C22×C4×C131—21no—
162C22×C4×C131—21no—
163C22×C4×C131—21no—
164C22×C4×C131—21no—
165C22×C4×C131—21no—
166C22×C4×C131—21no—
167C22×C4×C131—21no—
168C22×C4×C131—21no—
169C22×C4×C131—21no—
170C22×C4×C131—21no—
171C22×C4×C131—21no—
172C22×C4×C131—21no—
173C22×C4×C131—21no—
174C22×C4×C131—42no—
175C22×C4×C131—42no—
176C22×C4×C131—81no—
177C22×C4×C131C2×D411yescharacteristic
178C22×C4×C131C2×D411yescharacteristic
179C22×C4×C131C2×D411yescharacteristic
180C22×C4×C131C2×D411yescharacteristic
181C22×C4×C131C2×D411yescharacteristic
182C22×C4×C131C2411yescharacteristic
183Q16×C131—44no—
184SD16×C131—28no—
185M16×C131—44no—
186C2×C8×C131—21no—
187C2×C8×C131—21no—
188C2×C8×C131—21no—
189C2×C8×C131—21no—
190C2×C8×C131—21no—
191C2×C8×C131—21no—
192C2×C8×C131—21no—
193C2×C8×C131—21no—
194C2×C8×C131—21no—
195C2×C8×C131C2×D412yes—
196C2×C8×C131#4112yes—
197C2×C8×C131#4112yes—
198C4⋊C4×C131—21no—
199C4⋊C4×C131—21no—
200C4⋊C4×C131—21no—
201C4⋊C4×C131—21no—
202C4⋊C4×C131—21no—
203C4⋊C4×C131—21no—
204C4⋊C4×C131—21no—
205C4⋊C4×C131—21no—
206C4⋊C4×C131—21no—
207C4⋊C4×C131—42no—
208C4⋊C4×C131—42no—
209C4⋊C4×C131—42no—
210C4⋊C4×C131—42no—
211C4⋊C4×C131—81no—
212C4⋊C4×C131C2×D412yes—
213C22⋊C4×C131—41no—
214C22⋊C4×C131—41no—
215C22⋊C4×C131—42no—
216C22⋊C4×C131—42no—
217C22⋊C4×C131—42no—
218C22⋊C4×C131—42no—
219C22⋊C4×C131—42no—
220C22⋊C4×C131—42no—
221C22⋊C4×C131—42no—
222C42×C131—21no—
223C42×C131—21no—
224C42×C131—21no—
225C42×C131—21no—
226C42×C131—42no—
227C23×C131—21no—
228C23×C131—21no—
229C23×C131—22no—
230C23×C131—21no—
231C23×C131—21no—
232C23×C131—21no—
233C23×C131—21no—
234C23×C131—21no—
235C23×C131—41no—
236C23×C131—41no—
237C23×C131—41no—
238C23×C131—41no—
239C23×C131—41no—
240C23×C131—41no—
241C23×C131C22×D411yescharacteristic
242Q8×C131—22no—
243Q8×C131—22no—
244Q8×C131—41no—
245Q8×C131—41no—
246Q8×C131—41no—
247Q8×C131—41no—
248Q8×C131—41no—
249Q8×C131—41no—
250D4×C131—22no—
251D4×C131—22no—
252D4×C131—41no—
253D4×C131—41no—
254D4×C131—84no—
255C2×C4×C131—21no—
256C2×C4×C131—21no—
257C2×C4×C131—21no—
258C2×C4×C131—22no—
259C2×C4×C131—22no—
260C2×C4×C131—21no—
261C2×C4×C131—21no—
262C2×C4×C131—21no—
263C2×C4×C131—21no—
264C2×C4×C131—21no—
265C2×C4×C131—21no—
266C2×C4×C131—21no—
267C2×C4×C131—21no—
268C2×C4×C131—21no—
269C2×C4×C131—21no—
270C2×C4×C131—21no—
271C2×C4×C131—21no—
272C2×C4×C131—41no—
273C2×C4×C131—41no—
274C2×C4×C131—41no—
275C2×C4×C131—41no—
276C2×C4×C131—41no—
277C2×C4×C131—41no—
278C2×C4×C131—41no—
279C2×C4×C131—41no—
280C2×C4×C131—41no—
281C2×C4×C131—41no—
282C2×C4×C131—41no—
283C2×C4×C131—41no—
284C2×C4×C131—41no—
285C2×C4×C131—41no—
286C2×C4×C131—41no—
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—41no—
295C2×C4×C131—84no—
296C2×C4×C131C22×D411yescharacteristic
297C2×C4×C131C2×#4111yescharacteristic
298C2×C4×C131C2×#4111yescharacteristic
299C2×C4×C131C2×#4111yescharacteristic
300C2×C4×C131H(5,𝔽2)11yescharacteristic
301C2×C4×C131H(5,𝔽2)11yescharacteristic
302C8×C131—22no—
303C8×C131—22no—
304C8×C131—22no—
305C8×C131—41no—
306C22×C131—41no—
307C22×C131—41no—
308C22×C131—41no—
309C22×C131—42no—
310C22×C131—41no—
311C22×C131—41no—
312C22×C131—41no—
313C22×C131—42no—
314C22×C131—41no—
315C22×C131—42no—
316C22×C131—81no—
317C22×C131—81no—
318C22×C131—81no—
319C22×C131—81no—
320C22×C131#53211yescharacteristic
321C22×C131D4211yescharacteristic
322C22×C131#54611yescharacteristic
323C22×C131#57511yescharacteristic
324C22×C131#57511yescharacteristic
325C22×C131#57711yescharacteristic
326C22×C131#57811yescharacteristic
327C4×C131—41no—
328C4×C131—42no—
329C4×C131—41no—
330C4×C131—42no—
331C4×C131—41no—
332C4×C131—41no—
333C4×C131—41no—
334C4×C131—81no—
335C4×C131—81no—
336C4×C131—81no—
337C4×C131—81no—
338C4×C131—81no—
339C4×C131#52511yescharacteristic
340C4×C131#54011yescharacteristic
341C4×C131#54611yescharacteristic
342C4×C131#55311yescharacteristic
343C2×C131—81no—
344C2×C131—82no—
345C2×C131#246411yescharacteristic
346C2×C131#317811yescharacteristic
347C2×C131#318311yescharacteristic
348C2×C131#327511yescharacteristic
349C2×C131#327711yescharacteristic
350C2×C131#331111yescharacteristic
351C2×C131#331511yescharacteristic
352#26986C13111yesmaximal, characteristic, direct product factor, Sylow
353C131#2698611yescharacteristic, direct product factor, Sylow
354C2×#470C2×C13111yescharacteristic, complemented
355C2×#440C2×C13111yescharacteristic, complemented
356#2427C2×C13111yescharacteristic
357#2421C2×C13111yescharacteristic, complemented
358#2085C2×C13111yescharacteristic, complemented
359#2036C2×C13111yescharacteristic, complemented
360#2015C2×C13111yescharacteristic, complemented
361#2000C2×C13111yescharacteristic
362#1958C2×C13111yescharacteristic, complemented
363#1935C2×C13111yescharacteristic, complemented
364#1933C2×C13111yescharacteristic, complemented
365#1895C2×C13111yescharacteristic
366#1878C2×C13111yescharacteristic, complemented
367#1864C2×C13111yescharacteristic, complemented
368#1753C2×C13111yescharacteristic, complemented
369C22×Q16C22×C13111yescharacteristic
370C22×SD16C22×C13111yescharacteristic
371C22×M16C22×C13111yescharacteristic
372C2×#124C22×C13111yescharacteristic
373C2×C22⋊Q8C22×C13111yescharacteristic
374C2×C22⋊Q8C22×C13111yescharacteristic
375C2×#121C22×C13111yescharacteristic
376C2×C4×Q8C22×C13111yescharacteristic
377C2×C4×D4C22×C13111yescharacteristic
378#470—24no—
379#440—24no—
380C2×#107C22×C13111yescharacteristic
381C2×#106C22×C13111yescharacteristic
382C2×#103C22×C13111yescharacteristic
383C2×#103C22×C13111yescharacteristic
384C2×#103C22×C13111yescharacteristic
385C2×#103C22×C13111yescharacteristic
386C2×#103C22×C13111yescharacteristic
387C2×#102C22×C13111yescharacteristic
388C2×#102C22×C13111yescharacteristic
389C2×#102C22×C13111yescharacteristic
390C2×C22⋊C8C22×C13111yescharacteristic
391C2×#97C22×C13111yescharacteristic
392C2×C4×C8C22×C13111yescharacteristic
393#400—21no—
394#397—21no—
395#397—21no—
396#394—21no—
397#391C22×C13111yescharacteristic
398#391C22×C13111yescharacteristic
399#389C22×C13111yescharacteristic
400#389C22×C13111yescharacteristic
401#388—21no—
402#387—21no—
403#386—21no—
404#382C22×C13111yescharacteristic
405#380—21no—
406#380C22×C13111yescharacteristic
407C4×C22⋊C4C22×C13111yescharacteristic
408#340C22×C13111yescharacteristic
409#340C22×C13111yescharacteristic
410#340C22×C13111yescharacteristic
411#340C22×C13111yescharacteristic
412#336C22×C13111yescharacteristic
413#336C22×C13111yescharacteristic
414C22×Q8C23×C13111yescharacteristic
415C22×Q8C23×C13111yescharacteristic
416C22×D4—21no—
417C22×D4C23×C13111yescharacteristic
418C23×C4—21no—
419C23×C4C23×C13111yescharacteristic
420C2×Q16—22no—
421C2×Q16—22no—
422C2×Q16—41no—
423C2×SD16—22no—
424C2×SD16—22no—
425C2×SD16—22no—
426C2×M16—22no—
427C2×M16—22no—
428C2×M16—41no—
429C22×C8C23×C13111yescharacteristic
430C22×C8C23×C13111yescharacteristic
431C22×C8C23×C13111yescharacteristic
432C22×C8C23×C13111yescharacteristic
433#124—22no—
434#124—41no—
435C22⋊Q8—22no—
436C22⋊Q8—22no—
437C22⋊Q8—41no—
438C22⋊Q8—41no—
439#121—22no—
440#121—41no—
441C4×Q8—22no—
442C4×Q8—41no—
443C4×D4—22no—
444C4×D4—41no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4C23×C13111yescharacteristic
451C2×C4⋊C4C23×C13111yescharacteristic
452C2×C4⋊C4C23×C13111yescharacteristic
453C2×C4⋊C4C23×C13111yescharacteristic
454C2×C4⋊C4C23×C13111yescharacteristic
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4D4×C13111yescharacteristic
463C2×C22⋊C4D4×C13111yescharacteristic
464C2×C42—21no—
465C2×C42C23×C13111yescharacteristic
466C2×C42C23×C13111yescharacteristic
467#107—22no—
468#106—22no—
469#103—22no—
470#103—22no—
471#103—41no—
472#103—41no—
473#103D4×C13114yescomplemented
474#102—22no—
475#102—22no—
476#102—41no—
477C22⋊C8—22no—
478#97—22no—
479C4×C8—41no—
480#95—21no—
481#95—21no—
482#95—21no—
483#95—21no—
484#95—21no—
485#95—21no—
486#95—21no—
487#95—21no—
488#95—21no—
489#95D4×C13111yescharacteristic
490#95D4×C13111yescharacteristic
491C24—21no—
492C24C2×D4×C13111yescharacteristic
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8C2×D4×C13112yes—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—21no—
509C2×D4—21no—
510C2×D4—42no—
511C2×D4—42no—
512C2×D4—81no—
513C2×D4#41×C13112yes—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—81no—
530C22×C4C2×D4×C13111yescharacteristic
531C22×C4C2×D4×C13111yescharacteristic
532C22×C4C2×D4×C13111yescharacteristic
533C22×C4C2×D4×C13111yescharacteristic
534C22×C4C2×D4×C13111yescharacteristic
535C22×C4C24×C13111yescharacteristic
536Q16—44no—
537SD16—28no—
538M16—44no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8C2×D4×C13112yes—
549C2×C8#41×C13112yes—
550C2×C8#41×C13112yes—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—42no—
561C4⋊C4—42no—
562C4⋊C4—42no—
563C4⋊C4—42no—
564C4⋊C4—81no—
565C4⋊C4C2×D4×C13112yes—
566C22⋊C4—41no—
567C22⋊C4—41no—
568C22⋊C4—42no—
569C22⋊C4—42no—
570C22⋊C4—42no—
571C22⋊C4—42no—
572C22⋊C4—42no—
573C22⋊C4—42no—
574C22⋊C4—42no—
575C42—21no—
576C42—21no—
577C42—21no—
578C42—21no—
579C42—42no—
580C23—21no—
581C23—21no—
582C23—22no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23C22×D4×C13111yescharacteristic
595Q8—22no—
596Q8—22no—
597Q8—41no—
598Q8—41no—
599Q8—41no—
600Q8—41no—
601Q8—41no—
602Q8—41no—
603D4—22no—
604D4—22no—
605D4—41no—
606D4—41no—
607D4—84no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—84no—
649C2×C4C22×D4×C13111yescharacteristic
650C2×C4C2×#41×C13111yescharacteristic
651C2×C4C2×#41×C13111yescharacteristic
652C2×C4C2×#41×C13111yescharacteristic
653C2×C4H(5,𝔽2)×C13111yescharacteristic
654C2×C4H(5,𝔽2)×C13111yescharacteristic
655C8—22no—
656C8—22no—
657C8—22no—
658C8—41no—
659C22—41no—
660C22—41no—
661C22—41no—
662C22—42no—
663C22—41no—
664C22—42no—
665C22—41no—
666C22—41no—
667C22—41no—
668C22—42no—
669C22—81no—
670C22—81no—
671C22—81no—
672C22—81no—
673C22#532×C13111yescharacteristic
674C22D42×C13111yescharacteristic
675C22#546×C13111yescharacteristic
676C22#575×C13111yescharacteristic
677C22#575×C13111yescharacteristic
678C22#577×C13111yescharacteristic
679C22#578×C13111yescharacteristic
680C4—41no—
681C4—42no—
682C4—41no—
683C4—41no—
684C4—41no—
685C4—41no—
686C4—42no—
687C4—81no—
688C4—81no—
689C4—81no—
690C4—81no—
691C4—81no—
692C4#525×C13111yescharacteristic
693C4#540×C13111yescharacteristic
694C4#546×C13111yescharacteristic
695C4#553×C13111yescharacteristic
696C2—81no—
697C2—82no—
698C2#2464×C13111yescharacteristic
699C2#3178×C13111yescharacteristic
700C2#3183×C13111yescharacteristic
701C2#3275×C13111yescharacteristic
702C2#3277×C13111yescharacteristic
703C2#3311×C13111yescharacteristic
704C2#3315×C13111yescharacteristic
subgroupG/H
center, socleC23×C131C22×D4
commutator, Frattini, cosocleC22×C4C24×C131
prime radicalC2×#121×C131C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C131 ◁ C4×C22⋊C4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#470×C131C2semidirect
2. C2×#440×C131C2semidirect
4. #2421×C131C2semidirect
5. #2085×C131C2semidirect
6. #2036×C131C2semidirect
7. #2015×C131C2semidirect
9. #1958×C131C2semidirect
10. #1935×C131C2semidirect
11. #1933×C131C2semidirect
13. #1878×C131C2semidirect
14. #1864×C131C2semidirect
15. #1753×C131C2semidirect
120. #103×C131D4semidirect
352. #26986C131direct (N × H)
353. C131#26986direct (N × H)
354. C2×#470C2×C131semidirect
355. C2×#440C2×C131semidirect
357. #2421C2×C131semidirect
358. #2085C2×C131semidirect
359. #2036C2×C131semidirect
360. #2015C2×C131semidirect
362. #1958C2×C131semidirect
363. #1935C2×C131semidirect
364. #1933C2×C131semidirect
366. #1878C2×C131semidirect
367. #1864C2×C131semidirect
368. #1753C2×C131semidirect
473. #103D4×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#470×C1312
C2×#440×C1312
#2427×C1312
#2421×C1312
#2085×C1312
#2036×C1312
#2015×C1312
#2000×C1312
#1958×C1312
#1935×C1312
#1933×C1312
#1895×C1312
#1878×C1312
#1864×C1312
#1753×C1312
#26986131