Finite Group Databasebeta

← C131×#25029 #45710913

Subgroups — C131×#25029 #45710913

Order 33536.

834 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#485×C131C211yesmaximal, characteristic, complemented
2C2×#483×C131C211yesmaximal, characteristic, complemented
3#2538×C131C211yesmaximal, characteristic
4#2352×C131C211yesmaximal, characteristic
5#2077×C131C211yesmaximal, characteristic, complemented
6#2076×C131C211yesmaximal, characteristic, complemented
7#2036×C131C211yesmaximal, characteristic, complemented
8#2035×C131C211yesmaximal, characteristic, complemented
9#1955×C131C211yesmaximal, characteristic
10#1948×C131C211yesmaximal, characteristic, complemented
11#1854×C131C211yesmaximal, characteristic, complemented
12#1853×C131C211yesmaximal, characteristic, complemented
13#1847×C131C211yesmaximal, characteristic, complemented
14#1805×C131C211yesmaximal, characteristic, complemented
15#1763×C131C211yesmaximal, characteristic, complemented
16C2×C22⋊Q8×C131C2211yescharacteristic
17C2×C22⋊Q8×C131C2211yescharacteristic
18C2×C4×Q8×C131C2211yescharacteristic
19C2×C4×D4×C131C2211yescharacteristic
20C2×#117×C131C2211yescharacteristic
21C22×C4⋊C4×C131C2211yescharacteristic
22#485×C131—24no—
23#483×C131—24no—
24C2×#107×C131C2211yescharacteristic
25C2×#107×C131C2211yescharacteristic
26C2×#106×C131C2211yescharacteristic
27C2×#106×C131C2211yescharacteristic
28C2×#106×C131C2211yescharacteristic
29C2×#106×C131C2211yescharacteristic
30C2×C4⋊C8×C131C2211yescharacteristic
31C2×#103×C131C2211yescharacteristic
32C2×#103×C131C2211yescharacteristic
33C2×#103×C131C2211yescharacteristic
34C2×#103×C131C2211yescharacteristic
35C2×C22⋊C8×C131C2211yescharacteristic
36C2×C22⋊C8×C131C2211yescharacteristic
37C2×C22⋊C8×C131C2211yescharacteristic
38C2×C22⋊C8×C131C2211yescharacteristic
39C2×#97×C131C2211yescharacteristic
40#396×C131—21no—
41#396×C131—21no—
42#390×C131—21no—
43#389×C131—21no—
44#388×C131—21no—
45#387×C131—21no—
46#386×C131—21no—
47#384×C131C2211yescharacteristic
48#382×C131C2211yescharacteristic
49#380×C131C2211yescharacteristic
50#380×C131C2211yescharacteristic
51#380×C131C2211yescharacteristic
52#380×C131C2211yescharacteristic
53C4×C4⋊C4×C131C2211yescharacteristic
54C4×C22⋊C4×C131—21no—
55#340×C131C2211yescharacteristic
56#340×C131C2211yescharacteristic
57#340×C131C2211yescharacteristic
58#340×C131C2211yescharacteristic
59#340×C131C2211yescharacteristic
60#340×C131C2211yescharacteristic
61C22×Q8×C131C2311yescharacteristic
62C22×D4×C131D411yescharacteristic
63C23×C4×C131—21no—
64C23×C4×C131C2311yescharacteristic
65C23×C4×C131C2311yescharacteristic
66C22×C8×C131C2311yescharacteristic
67C22×C8×C131C2311yescharacteristic
68C22×C8×C131C2311yescharacteristic
69C22×C8×C131C2311yescharacteristic
70C22⋊Q8×C131—22no—
71C22⋊Q8×C131—22no—
72C22⋊Q8×C131—41no—
73C22⋊Q8×C131—41no—
74C4×Q8×C131—22no—
75C4×Q8×C131—22no—
76C4×D4×C131—22no—
77C4×D4×C131—22no—
78#117×C131—22no—
79#117×C131—41no—
80C2×C4⋊C4×C131—22no—
81C2×C4⋊C4×C131—21no—
82C2×C4⋊C4×C131—21no—
83C2×C4⋊C4×C131—21no—
84C2×C4⋊C4×C131—21no—
85C2×C4⋊C4×C131—21no—
86C2×C4⋊C4×C131—21no—
87C2×C4⋊C4×C131—41no—
88C2×C4⋊C4×C131D411yescharacteristic
89C2×C4⋊C4×C131C2311yescharacteristic
90C2×C4⋊C4×C131C2311yescharacteristic
91C2×C4⋊C4×C131C2311yescharacteristic
92C2×C4⋊C4×C131C2311yescharacteristic
93C2×C4⋊C4×C131C2311yescharacteristic
94C2×C4⋊C4×C131C2311yescharacteristic
95C2×C4⋊C4×C131C2311yescharacteristic
96C2×C22⋊C4×C131—21no—
97C2×C22⋊C4×C131—21no—
98C2×C22⋊C4×C131—21no—
99C2×C22⋊C4×C131—21no—
100C2×C22⋊C4×C131—21no—
101C2×C22⋊C4×C131—21no—
102C2×C22⋊C4×C131—21no—
103C2×C22⋊C4×C131D411yescharacteristic
104C2×C22⋊C4×C131D411yescharacteristic
105C2×C42×C131—21no—
106C2×C42×C131—21no—
107C2×C42×C131—21no—
108C2×C42×C131C2311yescharacteristic
109#107×C131—22no—
110#107×C131—41no—
111#106×C131—22no—
112#106×C131—22no—
113#106×C131—22no—
114#106×C131—41no—
115C4⋊C8×C131—22no—
116#103×C131—22no—
117#103×C131—22no—
118#103×C131—22no—
119#103×C131D414yescomplemented
120C22⋊C8×C131—22no—
121C22⋊C8×C131—22no—
122C22⋊C8×C131—22no—
123C22⋊C8×C131—22no—
124#97×C131—22no—
125#95×C131—21no—
126#95×C131—21no—
127#95×C131—21no—
128#95×C131—21no—
129#95×C131—21no—
130#95×C131—21no—
131#95×C131—21no—
132C24×C131C2×D411yescharacteristic
133C24×C131C2×D411yescharacteristic
134C2×Q8×C131—21no—
135C2×Q8×C131—21no—
136C2×Q8×C131—21no—
137C2×Q8×C131—21no—
138C2×Q8×C131—21no—
139C2×Q8×C131C2×D412yes—
140C2×D4×C131—22no—
141C2×D4×C131—22no—
142C2×D4×C131—41no—
143C22×C4×C131—21no—
144C22×C4×C131—21no—
145C22×C4×C131—21no—
146C22×C4×C131—21no—
147C22×C4×C131—21no—
148C22×C4×C131—21no—
149C22×C4×C131—21no—
150C22×C4×C131—21no—
151C22×C4×C131—21no—
152C22×C4×C131—21no—
153C22×C4×C131—21no—
154C22×C4×C131—21no—
155C22×C4×C131—21no—
156C22×C4×C131—21no—
157C22×C4×C131—21no—
158C22×C4×C131—21no—
159C22×C4×C131—21no—
160C22×C4×C131—21no—
161C22×C4×C131—21no—
162C22×C4×C131—21no—
163C22×C4×C131—42no—
164C22×C4×C131—42no—
165C22×C4×C131—81no—
166C22×C4×C131C2×D411yescharacteristic
167C22×C4×C131C2×D411yescharacteristic
168C22×C4×C131C2×D411yescharacteristic
169C22×C4×C131C2×D411yescharacteristic
170C22×C4×C131C2411yescharacteristic
171C2×C8×C131—21no—
172C2×C8×C131—21no—
173C2×C8×C131—21no—
174C2×C8×C131—21no—
175C2×C8×C131—21no—
176C2×C8×C131—21no—
177C2×C8×C131—21no—
178C2×C8×C131—21no—
179C2×C8×C131—21no—
180C2×C8×C131—21no—
181C2×C8×C131C2×D412yes—
182C2×C8×C131#4112yes—
183C4⋊C4×C131—22no—
184C4⋊C4×C131—21no—
185C4⋊C4×C131—21no—
186C4⋊C4×C131—21no—
187C4⋊C4×C131—21no—
188C4⋊C4×C131—21no—
189C4⋊C4×C131—21no—
190C4⋊C4×C131—21no—
191C4⋊C4×C131—21no—
192C4⋊C4×C131—21no—
193C4⋊C4×C131—21no—
194C4⋊C4×C131—21no—
195C4⋊C4×C131—21no—
196C4⋊C4×C131—21no—
197C4⋊C4×C131—42no—
198C4⋊C4×C131—42no—
199C4⋊C4×C131—42no—
200C4⋊C4×C131—42no—
201C4⋊C4×C131—42no—
202C4⋊C4×C131—81no—
203C4⋊C4×C131C2×D412yes—
204C22⋊C4×C131—22no—
205C22⋊C4×C131—22no—
206C22⋊C4×C131—42no—
207C22⋊C4×C131—42no—
208C22⋊C4×C131—42no—
209C22⋊C4×C131—42no—
210C22⋊C4×C131—81no—
211C22⋊C4×C131—81no—
212C22⋊C4×C131—81no—
213C42×C131—42no—
214C42×C131—42no—
215C42×C131—81no—
216C42×C131#4112yes—
217C42×C131#4112yes—
218C23×C131—21no—
219C23×C131—21no—
220C23×C131—21no—
221C23×C131—21no—
222C23×C131—21no—
223C23×C131—21no—
224C23×C131—21no—
225C23×C131—21no—
226C23×C131—21no—
227C23×C131—21no—
228C23×C131—21no—
229C23×C131—21no—
230C23×C131—21no—
231C23×C131#13712yes—
232C23×C131C22×D411yescharacteristic
233Q8×C131—22no—
234Q8×C131—22no—
235Q8×C131—41no—
236Q8×C131—41no—
237D4×C131—44no—
238C2×C4×C131—21no—
239C2×C4×C131—21no—
240C2×C4×C131—21no—
241C2×C4×C131—21no—
242C2×C4×C131—21no—
243C2×C4×C131—21no—
244C2×C4×C131—21no—
245C2×C4×C131—22no—
246C2×C4×C131—22no—
247C2×C4×C131—21no—
248C2×C4×C131—21no—
249C2×C4×C131—21no—
250C2×C4×C131—41no—
251C2×C4×C131—41no—
252C2×C4×C131—41no—
253C2×C4×C131—41no—
254C2×C4×C131—41no—
255C2×C4×C131—41no—
256C2×C4×C131—41no—
257C2×C4×C131—41no—
258C2×C4×C131—41no—
259C2×C4×C131—41no—
260C2×C4×C131—41no—
261C2×C4×C131—41no—
262C2×C4×C131—41no—
263C2×C4×C131—41no—
264C2×C4×C131—41no—
265C2×C4×C131—41no—
266C2×C4×C131—41no—
267C2×C4×C131—41no—
268C2×C4×C131—41no—
269C2×C4×C131—41no—
270C2×C4×C131—41no—
271C2×C4×C131—41no—
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—84no—
281C2×C4×C131#12312yes—
282C2×C4×C131#12312yes—
283C2×C4×C131C22×D411yescharacteristic
284C2×C4×C131C2×#4111yescharacteristic
285C2×C4×C131C2×#4111yescharacteristic
286C2×C4×C131C2×#4111yescharacteristic
287C2×C4×C131H(5,𝔽2)11yescharacteristic
288C2×C4×C1312−1+411yescharacteristic
289C8×C131—22no—
290C8×C131—22no—
291C8×C131—41no—
292C8×C131—41no—
293C22×C131—22no—
294C22×C131—22no—
295C22×C131—22no—
296C22×C131—41no—
297C22×C131—41no—
298C22×C131—41no—
299C22×C131—41no—
300C22×C131—41no—
301C22×C131—41no—
302C22×C131—41no—
303C22×C131—41no—
304C22×C131—41no—
305C22×C131—41no—
306C22×C131—41no—
307C22×C131C2×#12311yescharacteristic
308C22×C131D4211yescharacteristic
309C22×C131#54711yescharacteristic
310C22×C131C2×#13711yescharacteristic
311C22×C131#57511yescharacteristic
312C22×C131#57711yescharacteristic
313C22×C131#57711yescharacteristic
314C4×C131—22no—
315C4×C131—22no—
316C4×C131—41no—
317C4×C131—41no—
318C4×C131—42no—
319C4×C131—42no—
320C4×C131—81no—
321C4×C131—81no—
322C4×C131—81no—
323C4×C131—81no—
324C4×C131—81no—
325C4×C131—81no—
326C4×C131#53211yescharacteristic
327C4×C131#54211yescharacteristic
328C4×C131#54711yescharacteristic
329C4×C131#55311yescharacteristic
330C2×C131—42no—
331C2×C131—81no—
332C2×C131#242211yescharacteristic
333C2×C131#309511yescharacteristic
334C2×C131#309911yescharacteristic
335C2×C131#326611yescharacteristic
336C2×C131#327111yescharacteristic
337C2×C131#334411yescharacteristic
338C2×C131#335011yescharacteristic
339#25029C13111yesmaximal, characteristic, direct product factor, Sylow
340C131#2502911yescharacteristic, direct product factor, Sylow
341C2×#485C2×C13111yescharacteristic, complemented
342C2×#483C2×C13111yescharacteristic, complemented
343#2538C2×C13111yescharacteristic
344#2352C2×C13111yescharacteristic
345#2077C2×C13111yescharacteristic, complemented
346#2076C2×C13111yescharacteristic, complemented
347#2036C2×C13111yescharacteristic, complemented
348#2035C2×C13111yescharacteristic, complemented
349#1955C2×C13111yescharacteristic
350#1948C2×C13111yescharacteristic, complemented
351#1854C2×C13111yescharacteristic, complemented
352#1853C2×C13111yescharacteristic, complemented
353#1847C2×C13111yescharacteristic, complemented
354#1805C2×C13111yescharacteristic, complemented
355#1763C2×C13111yescharacteristic, complemented
356C2×C22⋊Q8C22×C13111yescharacteristic
357C2×C22⋊Q8C22×C13111yescharacteristic
358C2×C4×Q8C22×C13111yescharacteristic
359C2×C4×D4C22×C13111yescharacteristic
360C2×#117C22×C13111yescharacteristic
361C22×C4⋊C4C22×C13111yescharacteristic
362#485—24no—
363#483—24no—
364C2×#107C22×C13111yescharacteristic
365C2×#107C22×C13111yescharacteristic
366C2×#106C22×C13111yescharacteristic
367C2×#106C22×C13111yescharacteristic
368C2×#106C22×C13111yescharacteristic
369C2×#106C22×C13111yescharacteristic
370C2×C4⋊C8C22×C13111yescharacteristic
371C2×#103C22×C13111yescharacteristic
372C2×#103C22×C13111yescharacteristic
373C2×#103C22×C13111yescharacteristic
374C2×#103C22×C13111yescharacteristic
375C2×C22⋊C8C22×C13111yescharacteristic
376C2×C22⋊C8C22×C13111yescharacteristic
377C2×C22⋊C8C22×C13111yescharacteristic
378C2×C22⋊C8C22×C13111yescharacteristic
379C2×#97C22×C13111yescharacteristic
380#396—21no—
381#396—21no—
382#390—21no—
383#389—21no—
384#388—21no—
385#387—21no—
386#386—21no—
387#384C22×C13111yescharacteristic
388#382C22×C13111yescharacteristic
389#380C22×C13111yescharacteristic
390#380C22×C13111yescharacteristic
391#380C22×C13111yescharacteristic
392#380C22×C13111yescharacteristic
393C4×C4⋊C4C22×C13111yescharacteristic
394C4×C22⋊C4—21no—
395#340C22×C13111yescharacteristic
396#340C22×C13111yescharacteristic
397#340C22×C13111yescharacteristic
398#340C22×C13111yescharacteristic
399#340C22×C13111yescharacteristic
400#340C22×C13111yescharacteristic
401C22×Q8C23×C13111yescharacteristic
402C22×D4D4×C13111yescharacteristic
403C23×C4—21no—
404C23×C4C23×C13111yescharacteristic
405C23×C4C23×C13111yescharacteristic
406C22×C8C23×C13111yescharacteristic
407C22×C8C23×C13111yescharacteristic
408C22×C8C23×C13111yescharacteristic
409C22×C8C23×C13111yescharacteristic
410C22⋊Q8—22no—
411C22⋊Q8—22no—
412C22⋊Q8—41no—
413C22⋊Q8—41no—
414C4×Q8—22no—
415C4×Q8—22no—
416C4×D4—22no—
417C4×D4—22no—
418#117—22no—
419#117—41no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—41no—
428C2×C4⋊C4D4×C13111yescharacteristic
429C2×C4⋊C4C23×C13111yescharacteristic
430C2×C4⋊C4C23×C13111yescharacteristic
431C2×C4⋊C4C23×C13111yescharacteristic
432C2×C4⋊C4C23×C13111yescharacteristic
433C2×C4⋊C4C23×C13111yescharacteristic
434C2×C4⋊C4C23×C13111yescharacteristic
435C2×C4⋊C4C23×C13111yescharacteristic
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4D4×C13111yescharacteristic
444C2×C22⋊C4D4×C13111yescharacteristic
445C2×C42—21no—
446C2×C42—21no—
447C2×C42—21no—
448C2×C42C23×C13111yescharacteristic
449#107—22no—
450#107—41no—
451#106—22no—
452#106—22no—
453#106—22no—
454#106—41no—
455C4⋊C8—22no—
456#103—22no—
457#103—22no—
458#103—22no—
459#103D4×C13114yescomplemented
460C22⋊C8—22no—
461C22⋊C8—22no—
462C22⋊C8—22no—
463C22⋊C8—22no—
464#97—22no—
465#95—21no—
466#95—21no—
467#95—21no—
468#95—21no—
469#95—21no—
470#95—21no—
471#95—21no—
472C24C2×D4×C13111yescharacteristic
473C24C2×D4×C13111yescharacteristic
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8C2×D4×C13112yes—
480C2×D4—22no—
481C2×D4—22no—
482C2×D4—41no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—42no—
504C22×C4—42no—
505C22×C4—81no—
506C22×C4C2×D4×C13111yescharacteristic
507C22×C4C2×D4×C13111yescharacteristic
508C22×C4C2×D4×C13111yescharacteristic
509C22×C4C2×D4×C13111yescharacteristic
510C22×C4C24×C13111yescharacteristic
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8C2×D4×C13112yes—
522C2×C8#41×C13112yes—
523C4⋊C4—22no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—42no—
538C4⋊C4—42no—
539C4⋊C4—42no—
540C4⋊C4—42no—
541C4⋊C4—42no—
542C4⋊C4—81no—
543C4⋊C4C2×D4×C13112yes—
544C22⋊C4—22no—
545C22⋊C4—22no—
546C22⋊C4—42no—
547C22⋊C4—42no—
548C22⋊C4—42no—
549C22⋊C4—42no—
550C22⋊C4—81no—
551C22⋊C4—81no—
552C22⋊C4—81no—
553C42—42no—
554C42—42no—
555C42—81no—
556C42#41×C13112yes—
557C42#41×C13112yes—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23#137×C13112yes—
572C23C22×D4×C13111yescharacteristic
573Q8—22no—
574Q8—22no—
575Q8—41no—
576Q8—41no—
577D4—44no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—84no—
621C2×C4#123×C13112yes—
622C2×C4#123×C13112yes—
623C2×C4C22×D4×C13111yescharacteristic
624C2×C4C2×#41×C13111yescharacteristic
625C2×C4C2×#41×C13111yescharacteristic
626C2×C4C2×#41×C13111yescharacteristic
627C2×C4H(5,𝔽2)×C13111yescharacteristic
628C2×C42−1+4×C13111yescharacteristic
629C8—22no—
630C8—22no—
631C8—41no—
632C8—41no—
633C22—22no—
634C22—22no—
635C22—22no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22—41no—
642C22—41no—
643C22—41no—
644C22—41no—
645C22—41no—
646C22—41no—
647C22C2×#123×C13111yescharacteristic
648C22D42×C13111yescharacteristic
649C22#547×C13111yescharacteristic
650C22C2×#137×C13111yescharacteristic
651C22#575×C13111yescharacteristic
652C22#577×C13111yescharacteristic
653C22#577×C13111yescharacteristic
654C4—22no—
655C4—22no—
656C4—42no—
657C4—41no—
658C4—41no—
659C4—42no—
660C4—81no—
661C4—81no—
662C4—81no—
663C4—81no—
664C4—81no—
665C4—81no—
666C4#532×C13111yescharacteristic
667C4#542×C13111yescharacteristic
668C4#547×C13111yescharacteristic
669C4#553×C13111yescharacteristic
670C2—42no—
671C2—81no—
672C2#2422×C13111yescharacteristic
673C2#3095×C13111yescharacteristic
674C2#3099×C13111yescharacteristic
675C2#3266×C13111yescharacteristic
676C2#3271×C13111yescharacteristic
677C2#3344×C13111yescharacteristic
678C2#3350×C13111yescharacteristic
subgroupG/H
center, socleC23×C131C22×D4
commutator, Frattini, cosocleC22×C4C24×C131
prime radicalC22×D4×C131D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C131 ◁ C2×C4×D4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#485×C131C2semidirect
2. C2×#483×C131C2semidirect
5. #2077×C131C2semidirect
6. #2076×C131C2semidirect
7. #2036×C131C2semidirect
8. #2035×C131C2semidirect
10. #1948×C131C2semidirect
11. #1854×C131C2semidirect
12. #1853×C131C2semidirect
13. #1847×C131C2semidirect
14. #1805×C131C2semidirect
15. #1763×C131C2semidirect
119. #103×C131D4semidirect
339. #25029C131direct (N × H)
340. C131#25029direct (N × H)
341. C2×#485C2×C131semidirect
342. C2×#483C2×C131semidirect
345. #2077C2×C131semidirect
346. #2076C2×C131semidirect
347. #2036C2×C131semidirect
348. #2035C2×C131semidirect
350. #1948C2×C131semidirect
351. #1854C2×C131semidirect
352. #1853C2×C131semidirect
353. #1847C2×C131semidirect
354. #1805C2×C131semidirect
355. #1763C2×C131semidirect
459. #103D4×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#485×C1312
C2×#483×C1312
#2538×C1312
#2352×C1312
#2077×C1312
#2076×C1312
#2036×C1312
#2035×C1312
#1955×C1312
#1948×C1312
#1854×C1312
#1853×C1312
#1847×C1312
#1805×C1312
#1763×C1312
#25029131