Finite Group Databasebeta

← C131×#25150 #45711034

Subgroups — C131×#25150 #45711034

Order 33536.

1154 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#463×C131C211yesmaximal, characteristic, complemented
2C2×#452×C131C211yesmaximal, characteristic, complemented
3C2×#449×C131C211yesmaximal, characteristic
4C2×C4×D8×C131C211yesmaximal, characteristic, complemented
5#2427×C131C211yesmaximal, characteristic, complemented
6#2339×C131C211yesmaximal, characteristic, complemented
7#2068×C131C211yesmaximal, characteristic, complemented
8#2036×C131C211yesmaximal, characteristic, complemented
9#2033×C131C211yesmaximal, characteristic, complemented
10#2015×C131C211yesmaximal, characteristic, complemented
11#1969×C131C211yesmaximal, characteristic, complemented
12#1923×C131C211yesmaximal, characteristic, complemented
13#1877×C131C211yesmaximal, characteristic, complemented
14#1877×C131C211yesmaximal, characteristic, complemented
15#1862×C131C211yesmaximal, characteristic, complemented
16C22×#41×C131C2211yescharacteristic
17C22×Q16×C131C2211yescharacteristic
18C22×SD16×C131C2211yescharacteristic
19C22×SD16×C131C2211yescharacteristic
20C22×D8×C131C2211yescharacteristic
21C2×#124×C131C2211yescharacteristic
22C2×C22⋊Q8×C131C2211yescharacteristic
23C2×#121×C131C2211yescharacteristic
24C2×C4×D4×C131C2211yescharacteristic
25C2×C4×D4×C131C2211yescharacteristic
26C2×C4×D4×C131C2211yescharacteristic
27#463×C131—24no—
28#452×C131—24no—
29#449×C131—24no—
30C4×D8×C131—24no—
31C2×#107×C131C2211yescharacteristic
32C2×#107×C131C2211yescharacteristic
33C2×C4⋊C8×C131C2211yescharacteristic
34C2×#103×C131C2211yescharacteristic
35C2×#103×C131C2211yescharacteristic
36C2×#103×C131C2211yescharacteristic
37C2×#103×C131C2211yescharacteristic
38C2×#102×C131C2211yescharacteristic
39C2×#102×C131C2211yescharacteristic
40C2×#102×C131C2211yescharacteristic
41C2×#102×C131C2211yescharacteristic
42C2×C22⋊C8×C131C2211yescharacteristic
43C2×C22⋊C8×C131C2211yescharacteristic
44C2×C4×C8×C131C2211yescharacteristic
45#397×C131—21no—
46#394×C131—21no—
47#391×C131C2211yescharacteristic
48#391×C131C2211yescharacteristic
49#391×C131C2211yescharacteristic
50#389×C131C2211yescharacteristic
51#386×C131—21no—
52#386×C131—21no—
53#386×C131—21no—
54#381×C131—21no—
55#380×C131—21no—
56#380×C131C2211yescharacteristic
57C4×C22⋊C4×C131C2211yescharacteristic
58C2×#95×C131—21no—
59#340×C131C2211yescharacteristic
60#340×C131C2211yescharacteristic
61#336×C131C2211yescharacteristic
62#336×C131C2211yescharacteristic
63C2×#41×C131—22no—
64C2×#41×C131—22no—
65C2×#41×C131—22no—
66C2×#41×C131—22no—
67C2×#41×C131—41no—
68C2×#41×C131—41no—
69C22×Q8×C131C2311yescharacteristic
70C22×Q8×C131C2311yescharacteristic
71C22×D4×C131—21no—
72C22×D4×C131—21no—
73C22×D4×C131C2311yescharacteristic
74C22×D4×C131C2311yescharacteristic
75C23×C4×C131—21no—
76C23×C4×C131—21no—
77C23×C4×C131—21no—
78C23×C4×C131—21no—
79C23×C4×C131C2311yescharacteristic
80C2×Q16×C131—22no—
81C2×Q16×C131—22no—
82C2×Q16×C131—41no—
83C2×SD16×C131—22no—
84C2×SD16×C131—22no—
85C2×SD16×C131—22no—
86C2×SD16×C131—22no—
87C2×SD16×C131—22no—
88C2×SD16×C131—41no—
89C2×D8×C131—22no—
90C2×D8×C131—22no—
91C2×D8×C131D414yes—
92C22×C8×C131C2311yescharacteristic
93C22×C8×C131C2311yescharacteristic
94C22×C8×C131C2311yescharacteristic
95C22×C8×C131C2311yescharacteristic
96#124×C131—22no—
97#124×C131—41no—
98C22⋊Q8×C131—22no—
99C22⋊Q8×C131—41no—
100#121×C131—22no—
101#121×C131—41no—
102C4×D4×C131—22no—
103C4×D4×C131—22no—
104C4×D4×C131—22no—
105C4×D4×C131—41no—
106C4×D4×C131—41no—
107C4×D4×C131—41no—
108C2×C4⋊C4×C131—21no—
109C2×C4⋊C4×C131—21no—
110C2×C4⋊C4×C131C2311yescharacteristic
111C2×C4⋊C4×C131C2311yescharacteristic
112C2×C4⋊C4×C131C2311yescharacteristic
113C2×C4⋊C4×C131C2311yescharacteristic
114C2×C22⋊C4×C131—21no—
115C2×C22⋊C4×C131—21no—
116C2×C22⋊C4×C131—21no—
117C2×C22⋊C4×C131—21no—
118C2×C22⋊C4×C131—21no—
119C2×C22⋊C4×C131—21no—
120C2×C22⋊C4×C131—21no—
121C2×C22⋊C4×C131—21no—
122C2×C22⋊C4×C131D411yescharacteristic
123C2×C22⋊C4×C131D411yescharacteristic
124C2×C42×C131C2311yescharacteristic
125C2×C42×C131C2311yescharacteristic
126#107×C131—22no—
127#107×C131—41no—
128C4⋊C8×C131—22no—
129#103×C131—22no—
130#103×C131—22no—
131#103×C131—22no—
132#103×C131—41no—
133#102×C131—22no—
134#102×C131—22no—
135#102×C131—22no—
136#102×C131D414yescomplemented
137C22⋊C8×C131—22no—
138C22⋊C8×C131—22no—
139C4×C8×C131—22no—
140#95×C131—21no—
141#95×C131—21no—
142#95×C131—21no—
143#95×C131—21no—
144#95×C131—21no—
145#95×C131—21no—
146#95×C131—21no—
147#95×C131—21no—
148#95×C131D411yescharacteristic
149#95×C131D411yescharacteristic
150C24×C131—21no—
151C24×C131—21no—
152C24×C131C2×D411yescharacteristic
153#41×C131—44no—
154#41×C131—44no—
155#41×C131—44no—
156#41×C131—44no—
157C2×Q8×C131—21no—
158C2×Q8×C131—21no—
159C2×Q8×C131—21no—
160C2×Q8×C131—21no—
161C2×Q8×C131—21no—
162C2×Q8×C131—21no—
163C2×Q8×C131—21no—
164C2×Q8×C131—21no—
165C2×Q8×C131—21no—
166C2×Q8×C131—21no—
167C2×Q8×C131—21no—
168C2×Q8×C131#4112yes—
169C2×D4×C131—24no—
170C2×D4×C131—21no—
171C2×D4×C131—21no—
172C2×D4×C131—21no—
173C2×D4×C131—21no—
174C2×D4×C131—21no—
175C2×D4×C131—21no—
176C2×D4×C131—21no—
177C2×D4×C131—21no—
178C2×D4×C131—42no—
179C2×D4×C131—42no—
180C2×D4×C131—42no—
181C2×D4×C131—42no—
182C2×D4×C131—81no—
183C2×D4×C131C2×D412yes—
184C2×D4×C131C2×D412yes—
185C2×D4×C131C2×D412yes—
186C2×D4×C131#4112yes—
187C22×C4×C131—24no—
188C22×C4×C131—21no—
189C22×C4×C131—21no—
190C22×C4×C131—21no—
191C22×C4×C131—21no—
192C22×C4×C131—21no—
193C22×C4×C131—21no—
194C22×C4×C131—21no—
195C22×C4×C131—21no—
196C22×C4×C131—21no—
197C22×C4×C131—21no—
198C22×C4×C131—21no—
199C22×C4×C131—21no—
200C22×C4×C131—42no—
201C22×C4×C131—42no—
202C22×C4×C131—42no—
203C22×C4×C131—42no—
204C22×C4×C131—42no—
205C22×C4×C131—42no—
206C22×C4×C131—42no—
207C22×C4×C131—42no—
208C22×C4×C131—81no—
209C22×C4×C131—81no—
210C22×C4×C131—81no—
211C22×C4×C131C2×D411yescharacteristic
212C22×C4×C131C2×D411yescharacteristic
213C22×C4×C131C2×D411yescharacteristic
214C22×C4×C131C2×D411yescharacteristic
215C22×C4×C131C2×D411yescharacteristic
216C22×C4×C131C2411yescharacteristic
217Q16×C131—44no—
218SD16×C131—44no—
219SD16×C131—44no—
220D8×C131—28no—
221C2×C8×C131—21no—
222C2×C8×C131—21no—
223C2×C8×C131—21no—
224C2×C8×C131—21no—
225C2×C8×C131—21no—
226C2×C8×C131—21no—
227C2×C8×C131—21no—
228C2×C8×C131—21no—
229C2×C8×C131—21no—
230C2×C8×C131—21no—
231C2×C8×C131C2×D412yes—
232C2×C8×C131C2×D412yes—
233C4⋊C4×C131—21no—
234C4⋊C4×C131—21no—
235C4⋊C4×C131—21no—
236C4⋊C4×C131—21no—
237C4⋊C4×C131—21no—
238C4⋊C4×C131—21no—
239C4⋊C4×C131—21no—
240C4⋊C4×C131—42no—
241C4⋊C4×C131—81no—
242C4⋊C4×C131C2×D412yes—
243C22⋊C4×C131—22no—
244C22⋊C4×C131—41no—
245C22⋊C4×C131—42no—
246C22⋊C4×C131—42no—
247C22⋊C4×C131—42no—
248C22⋊C4×C131—42no—
249C22⋊C4×C131—42no—
250C22⋊C4×C131—42no—
251C22⋊C4×C131—42no—
252C22⋊C4×C131—81no—
253C42×C131—21no—
254C42×C131—21no—
255C42×C131—21no—
256C42×C131—21no—
257C23×C131—22no—
258C23×C131—22no—
259C23×C131—22no—
260C23×C131—21no—
261C23×C131—22no—
262C23×C131—21no—
263C23×C131—21no—
264C23×C131—21no—
265C23×C131—21no—
266C23×C131—21no—
267C23×C131—21no—
268C23×C131—41no—
269C23×C131—41no—
270C23×C131—41no—
271C23×C131—41no—
272C23×C131—41no—
273C23×C131—41no—
274C23×C131—41no—
275C23×C131—41no—
276C23×C131—41no—
277C23×C131—41no—
278C23×C131C22×D411yescharacteristic
279Q8×C131—22no—
280Q8×C131—22no—
281Q8×C131—41no—
282Q8×C131—41no—
283Q8×C131—41no—
284Q8×C131—41no—
285Q8×C131—41no—
286Q8×C131—41no—
287D4×C131—22no—
288D4×C131—22no—
289D4×C131—22no—
290D4×C131—22no—
291D4×C131—22no—
292D4×C131—48no—
293D4×C131—41no—
294D4×C131—41no—
295D4×C131—84no—
296D4×C131#12114yes—
297C2×C4×C131—21no—
298C2×C4×C131—21no—
299C2×C4×C131—21no—
300C2×C4×C131—22no—
301C2×C4×C131—21no—
302C2×C4×C131—21no—
303C2×C4×C131—21no—
304C2×C4×C131—22no—
305C2×C4×C131—21no—
306C2×C4×C131—21no—
307C2×C4×C131—21no—
308C2×C4×C131—21no—
309C2×C4×C131—21no—
310C2×C4×C131—21no—
311C2×C4×C131—21no—
312C2×C4×C131—21no—
313C2×C4×C131—48no—
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—41no—
323C2×C4×C131—41no—
324C2×C4×C131—41no—
325C2×C4×C131—41no—
326C2×C4×C131—41no—
327C2×C4×C131—41no—
328C2×C4×C131—41no—
329C2×C4×C131—41no—
330C2×C4×C131—41no—
331C2×C4×C131—41no—
332C2×C4×C131—41no—
333C2×C4×C131—41no—
334C2×C4×C131—84no—
335C2×C4×C131—84no—
336C2×C4×C131—84no—
337C2×C4×C131#13512yes—
338C2×C4×C131C22×D411yescharacteristic
339C2×C4×C131C22×D411yescharacteristic
340C2×C4×C131C2×#4111yescharacteristic
341C2×C4×C131C2×#4111yescharacteristic
342C2×C4×C131H(5,𝔽2)11yescharacteristic
343C2×C4×C131H(5,𝔽2)11yescharacteristic
344C8×C131—22no—
345C8×C131—22no—
346C8×C131—41no—
347C8×C131—41no—
348C22×C131—24no—
349C22×C131—42no—
350C22×C131—42no—
351C22×C131—42no—
352C22×C131—42no—
353C22×C131—42no—
354C22×C131—42no—
355C22×C131—41no—
356C22×C131—41no—
357C22×C131—41no—
358C22×C131—42no—
359C22×C131—41no—
360C22×C131—41no—
361C22×C131—42no—
362C22×C131—41no—
363C22×C131—41no—
364C22×C131—42no—
365C22×C131—81no—
366C22×C131—81no—
367C22×C131—81no—
368C22×C131—81no—
369C22×C131#52511yescharacteristic
370C22×C131D4211yescharacteristic
371C22×C131D4211yescharacteristic
372C22×C131C2×#13511yescharacteristic
373C22×C131#57511yescharacteristic
374C22×C131#57611yescharacteristic
375C22×C131#57811yescharacteristic
376C4×C131—22no—
377C4×C131—41no—
378C4×C131—42no—
379C4×C131—41no—
380C4×C131—41no—
381C4×C131—42no—
382C4×C131—41no—
383C4×C131—81no—
384C4×C131—81no—
385C4×C131—81no—
386C4×C131—81no—
387C4×C131C2×#12111yescharacteristic
388C4×C131#53811yescharacteristic
389C4×C131#54611yescharacteristic
390C4×C131#54611yescharacteristic
391C2×C131—44no—
392C2×C131—81no—
393C2×C131—82no—
394C2×C131#242411yescharacteristic
395C2×C131#310211yescharacteristic
396C2×C131#312411yescharacteristic
397C2×C131#326911yescharacteristic
398C2×C131#327311yescharacteristic
399C2×C131#328011yescharacteristic
400C2×C131#328311yescharacteristic
401#25150C13111yesmaximal, characteristic, direct product factor, Sylow
402C131#2515011yescharacteristic, direct product factor, Sylow
403C2×#463C2×C13111yescharacteristic, complemented
404C2×#452C2×C13111yescharacteristic, complemented
405C2×#449C2×C13111yescharacteristic
406C2×C4×D8C2×C13111yescharacteristic, complemented
407#2427C2×C13111yescharacteristic, complemented
408#2339C2×C13111yescharacteristic, complemented
409#2068C2×C13111yescharacteristic, complemented
410#2036C2×C13111yescharacteristic, complemented
411#2033C2×C13111yescharacteristic, complemented
412#2015C2×C13111yescharacteristic, complemented
413#1969C2×C13111yescharacteristic, complemented
414#1923C2×C13111yescharacteristic, complemented
415#1877C2×C13111yescharacteristic, complemented
416#1877C2×C13111yescharacteristic, complemented
417#1862C2×C13111yescharacteristic, complemented
418C22×#41C22×C13111yescharacteristic
419C22×Q16C22×C13111yescharacteristic
420C22×SD16C22×C13111yescharacteristic
421C22×SD16C22×C13111yescharacteristic
422C22×D8C22×C13111yescharacteristic
423C2×#124C22×C13111yescharacteristic
424C2×C22⋊Q8C22×C13111yescharacteristic
425C2×#121C22×C13111yescharacteristic
426C2×C4×D4C22×C13111yescharacteristic
427C2×C4×D4C22×C13111yescharacteristic
428C2×C4×D4C22×C13111yescharacteristic
429#463—24no—
430#452—24no—
431#449—24no—
432C4×D8—24no—
433C2×#107C22×C13111yescharacteristic
434C2×#107C22×C13111yescharacteristic
435C2×C4⋊C8C22×C13111yescharacteristic
436C2×#103C22×C13111yescharacteristic
437C2×#103C22×C13111yescharacteristic
438C2×#103C22×C13111yescharacteristic
439C2×#103C22×C13111yescharacteristic
440C2×#102C22×C13111yescharacteristic
441C2×#102C22×C13111yescharacteristic
442C2×#102C22×C13111yescharacteristic
443C2×#102C22×C13111yescharacteristic
444C2×C22⋊C8C22×C13111yescharacteristic
445C2×C22⋊C8C22×C13111yescharacteristic
446C2×C4×C8C22×C13111yescharacteristic
447#397—21no—
448#394—21no—
449#391C22×C13111yescharacteristic
450#391C22×C13111yescharacteristic
451#391C22×C13111yescharacteristic
452#389C22×C13111yescharacteristic
453#386—21no—
454#386—21no—
455#386—21no—
456#381—21no—
457#380—21no—
458#380C22×C13111yescharacteristic
459C4×C22⋊C4C22×C13111yescharacteristic
460C2×#95—21no—
461#340C22×C13111yescharacteristic
462#340C22×C13111yescharacteristic
463#336C22×C13111yescharacteristic
464#336C22×C13111yescharacteristic
465C2×#41—22no—
466C2×#41—22no—
467C2×#41—22no—
468C2×#41—22no—
469C2×#41—41no—
470C2×#41—41no—
471C22×Q8C23×C13111yescharacteristic
472C22×Q8C23×C13111yescharacteristic
473C22×D4—21no—
474C22×D4—21no—
475C22×D4C23×C13111yescharacteristic
476C22×D4C23×C13111yescharacteristic
477C23×C4—21no—
478C23×C4—21no—
479C23×C4—21no—
480C23×C4—21no—
481C23×C4C23×C13111yescharacteristic
482C2×Q16—22no—
483C2×Q16—22no—
484C2×Q16—41no—
485C2×SD16—22no—
486C2×SD16—22no—
487C2×SD16—22no—
488C2×SD16—22no—
489C2×SD16—22no—
490C2×SD16—41no—
491C2×D8—22no—
492C2×D8—22no—
493C2×D8D4×C13114yes—
494C22×C8C23×C13111yescharacteristic
495C22×C8C23×C13111yescharacteristic
496C22×C8C23×C13111yescharacteristic
497C22×C8C23×C13111yescharacteristic
498#124—22no—
499#124—41no—
500C22⋊Q8—22no—
501C22⋊Q8—41no—
502#121—22no—
503#121—41no—
504C4×D4—22no—
505C4×D4—22no—
506C4×D4—22no—
507C4×D4—41no—
508C4×D4—41no—
509C4×D4—41no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4C23×C13111yescharacteristic
513C2×C4⋊C4C23×C13111yescharacteristic
514C2×C4⋊C4C23×C13111yescharacteristic
515C2×C4⋊C4C23×C13111yescharacteristic
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C22⋊C4—21no—
519C2×C22⋊C4—21no—
520C2×C22⋊C4—21no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4D4×C13111yescharacteristic
525C2×C22⋊C4D4×C13111yescharacteristic
526C2×C42C23×C13111yescharacteristic
527C2×C42C23×C13111yescharacteristic
528#107—22no—
529#107—41no—
530C4⋊C8—22no—
531#103—22no—
532#103—22no—
533#103—22no—
534#103—41no—
535#102—22no—
536#102—22no—
537#102—22no—
538#102D4×C13114yescomplemented
539C22⋊C8—22no—
540C22⋊C8—22no—
541C4×C8—22no—
542#95—21no—
543#95—21no—
544#95—21no—
545#95—21no—
546#95—21no—
547#95—21no—
548#95—21no—
549#95—21no—
550#95D4×C13111yescharacteristic
551#95D4×C13111yescharacteristic
552C24—21no—
553C24—21no—
554C24C2×D4×C13111yescharacteristic
555#41—44no—
556#41—44no—
557#41—44no—
558#41—44no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8—21no—
568C2×Q8—21no—
569C2×Q8—21no—
570C2×Q8#41×C13112yes—
571C2×D4—24no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—42no—
581C2×D4—42no—
582C2×D4—42no—
583C2×D4—42no—
584C2×D4—81no—
585C2×D4C2×D4×C13112yes—
586C2×D4C2×D4×C13112yes—
587C2×D4C2×D4×C13112yes—
588C2×D4#41×C13112yes—
589C22×C4—24no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—42no—
603C22×C4—42no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4—42no—
607C22×C4—42no—
608C22×C4—42no—
609C22×C4—42no—
610C22×C4—81no—
611C22×C4—81no—
612C22×C4—81no—
613C22×C4C2×D4×C13111yescharacteristic
614C22×C4C2×D4×C13111yescharacteristic
615C22×C4C2×D4×C13111yescharacteristic
616C22×C4C2×D4×C13111yescharacteristic
617C22×C4C2×D4×C13111yescharacteristic
618C22×C4C24×C13111yescharacteristic
619Q16—44no—
620SD16—44no—
621SD16—44no—
622D8—28no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8C2×D4×C13112yes—
634C2×C8C2×D4×C13112yes—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—42no—
643C4⋊C4—81no—
644C4⋊C4C2×D4×C13112yes—
645C22⋊C4—22no—
646C22⋊C4—41no—
647C22⋊C4—42no—
648C22⋊C4—42no—
649C22⋊C4—42no—
650C22⋊C4—42no—
651C22⋊C4—42no—
652C22⋊C4—42no—
653C22⋊C4—42no—
654C22⋊C4—81no—
655C42—21no—
656C42—21no—
657C42—21no—
658C42—21no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—21no—
663C23—22no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23C22×D4×C13111yescharacteristic
681Q8—22no—
682Q8—22no—
683Q8—41no—
684Q8—41no—
685Q8—41no—
686Q8—41no—
687Q8—41no—
688Q8—41no—
689D4—22no—
690D4—22no—
691D4—22no—
692D4—22no—
693D4—22no—
694D4—48no—
695D4—41no—
696D4—41no—
697D4—84no—
698D4#121×C13114yes—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—22no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—22no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—48no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—84no—
737C2×C4—84no—
738C2×C4—84no—
739C2×C4#135×C13112yes—
740C2×C4C22×D4×C13111yescharacteristic
741C2×C4C22×D4×C13111yescharacteristic
742C2×C4C2×#41×C13111yescharacteristic
743C2×C4C2×#41×C13111yescharacteristic
744C2×C4H(5,𝔽2)×C13111yescharacteristic
745C2×C4H(5,𝔽2)×C13111yescharacteristic
746C8—22no—
747C8—22no—
748C8—41no—
749C8—41no—
750C22—24no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—41no—
758C22—41no—
759C22—42no—
760C22—41no—
761C22—41no—
762C22—42no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—42no—
767C22—81no—
768C22—81no—
769C22—81no—
770C22—81no—
771C22#525×C13111yescharacteristic
772C22D42×C13111yescharacteristic
773C22D42×C13111yescharacteristic
774C22C2×#135×C13111yescharacteristic
775C22#575×C13111yescharacteristic
776C22#576×C13111yescharacteristic
777C22#578×C13111yescharacteristic
778C4—22no—
779C4—41no—
780C4—41no—
781C4—42no—
782C4—41no—
783C4—41no—
784C4—42no—
785C4—81no—
786C4—81no—
787C4—81no—
788C4—81no—
789C4C2×#121×C13111yescharacteristic
790C4#538×C13111yescharacteristic
791C4#546×C13111yescharacteristic
792C4#546×C13111yescharacteristic
793C2—44no—
794C2—81no—
795C2—82no—
796C2#2424×C13111yescharacteristic
797C2#3102×C13111yescharacteristic
798C2#3124×C13111yescharacteristic
799C2#3269×C13111yescharacteristic
800C2#3273×C13111yescharacteristic
801C2#3280×C13111yescharacteristic
802C2#3283×C13111yescharacteristic
subgroupG/H
center, socleC23×C131C22×D4
commutator, Frattini, cosocleC22×C4C24×C131
prime radicalC2×#449×C131C2
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×#463×C131C2semidirect
2. C2×#452×C131C2semidirect
4. C2×C4×D8×C131C2semidirect
5. #2427×C131C2semidirect
6. #2339×C131C2semidirect
7. #2068×C131C2semidirect
8. #2036×C131C2semidirect
9. #2033×C131C2semidirect
10. #2015×C131C2semidirect
11. #1969×C131C2semidirect
12. #1923×C131C2semidirect
13. #1877×C131C2semidirect
14. #1877×C131C2semidirect
15. #1862×C131C2semidirect
136. #102×C131D4semidirect
401. #25150C131direct (N × H)
402. C131#25150direct (N × H)
403. C2×#463C2×C131semidirect
404. C2×#452C2×C131semidirect
406. C2×C4×D8C2×C131semidirect
407. #2427C2×C131semidirect
408. #2339C2×C131semidirect
409. #2068C2×C131semidirect
410. #2036C2×C131semidirect
411. #2033C2×C131semidirect
412. #2015C2×C131semidirect
413. #1969C2×C131semidirect
414. #1923C2×C131semidirect
415. #1877C2×C131semidirect
416. #1877C2×C131semidirect
417. #1862C2×C131semidirect
538. #102D4×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#463×C1312
C2×#452×C1312
C2×#449×C1312
C2×C4×D8×C1312
#2427×C1312
#2339×C1312
#2068×C1312
#2036×C1312
#2033×C1312
#2015×C1312
#1969×C1312
#1923×C1312
#1877×C1312
#1862×C1312
#25150131