Finite Group Databasebeta

← C131×#25091 #45710975

Subgroups — C131×#25091 #45710975

Order 33536.

1136 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#465×C131C211yesmaximal, characteristic, complemented
2C2×#464×C131C211yesmaximal, characteristic, complemented
3C2×#452×C131C211yesmaximal, characteristic, complemented
4C2×#416×C131C211yesmaximal, characteristic, complemented
5#2431×C131C211yesmaximal, characteristic
6#2362×C131C211yesmaximal, characteristic, complemented
7#2065×C131C211yesmaximal, characteristic, complemented
8#2056×C131C211yesmaximal, characteristic, complemented
9#2042×C131C211yesmaximal, characteristic, complemented
10#2014×C131C211yesmaximal, characteristic, complemented
11#1982×C131C211yesmaximal, characteristic, complemented
12#1927×C131C211yesmaximal, characteristic, complemented
13#1880×C131C211yesmaximal, characteristic, complemented
14#1875×C131C211yesmaximal, characteristic, complemented
15#1850×C131C211yesmaximal, characteristic, complemented
16C22×#41×C131C2211yescharacteristic
17C22×Q16×C131C2211yescharacteristic
18C22×SD16×C131C2211yescharacteristic
19C22×SD16×C131C2211yescharacteristic
20C23×C8×C131C2211yescharacteristic
21C2×#127×C131C2211yescharacteristic
22C2×#124×C131C2211yescharacteristic
23C2×C22⋊Q8×C131C2211yescharacteristic
24C2×#121×C131C2211yescharacteristic
25C2×C4×Q8×C131C2211yescharacteristic
26C2×#117×C131C2211yescharacteristic
27#465×C131—24no—
28#464×C131—24no—
29#452×C131—24no—
30C2×#106×C131C2211yescharacteristic
31C2×C4⋊C8×C131C2211yescharacteristic
32C2×C4⋊C8×C131C2211yescharacteristic
33#416×C131—24no—
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×#102×C131C2211yescharacteristic
43C2×#102×C131C2211yescharacteristic
44C2×C22⋊C8×C131C2211yescharacteristic
45#392×C131—21no—
46#392×C131—21no—
47#391×C131C2211yescharacteristic
48#391×C131C2211yescharacteristic
49#390×C131C2211yescharacteristic
50#389×C131C2211yescharacteristic
51#388×C131—21no—
52#388×C131—21no—
53#387×C131—21no—
54#386×C131—21no—
55#386×C131—21no—
56C4×C4⋊C4×C131—21no—
57C4×C4⋊C4×C131C2211yescharacteristic
58C4×C22⋊C4×C131C2211yescharacteristic
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×C131—21no—
74C22×D4×C131—21no—
75C22×D4×C131C2311yescharacteristic
76C22×D4×C131C2311yescharacteristic
77C23×C4×C131—21no—
78C23×C4×C131C2311yescharacteristic
79C2×Q16×C131—22no—
80C2×Q16×C131—22no—
81C2×Q16×C131—41no—
82C2×SD16×C131—22no—
83C2×SD16×C131—22no—
84C2×SD16×C131—22no—
85C2×SD16×C131—22no—
86C2×SD16×C131—41no—
87C2×SD16×C131—41no—
88C22×C8×C131—22no—
89C22×C8×C131—22no—
90C22×C8×C131—41no—
91C22×C8×C131C2311yescharacteristic
92C22×C8×C131C2311yescharacteristic
93C22×C8×C131C2311yescharacteristic
94C22×C8×C131C2311yescharacteristic
95#127×C131—22no—
96#127×C131—41no—
97#124×C131—22no—
98#124×C131—41no—
99C22⋊Q8×C131—22no—
100C22⋊Q8×C131D414yescomplemented
101#121×C131—22no—
102#121×C131—22no—
103C4×Q8×C131—22no—
104C4×Q8×C131—41no—
105#117×C131—22no—
106#117×C131—41no—
107C2×C4⋊C4×C131—21no—
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×C131D411yescharacteristic
122C2×C22⋊C4×C131D411yescharacteristic
123C2×C42×C131—21no—
124C2×C42×C131—21no—
125C2×C42×C131—21no—
126C2×C42×C131C2311yescharacteristic
127C2×C42×C131C2311yescharacteristic
128#106×C131—22no—
129C4⋊C8×C131—22no—
130C4⋊C8×C131—41no—
131#103×C131—22no—
132#103×C131—22no—
133#103×C131—22no—
134#103×C131D414yescomplemented
135#102×C131—22no—
136#102×C131—22no—
137#102×C131—22no—
138#102×C131—22no—
139#102×C131—22no—
140#102×C131—41no—
141C22⋊C8×C131—22no—
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—28no—
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×C131C2×D412yes—
168C2×Q8×C131C2×D412yes—
169C2×D4×C131—21no—
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—21no—
179C2×D4×C131—21no—
180C2×D4×C131—42no—
181C2×D4×C131—42no—
182C2×D4×C131—42no—
183C2×D4×C131—42no—
184C2×D4×C131—42no—
185C2×D4×C131—42no—
186C2×D4×C131—42no—
187C2×D4×C131—42no—
188C2×D4×C131—81no—
189C2×D4×C131—81no—
190C2×D4×C131—81no—
191C2×D4×C131—81no—
192C2×D4×C131#4112yes—
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—21no—
201C22×C4×C131—21no—
202C22×C4×C131—21no—
203C22×C4×C131—42no—
204C22×C4×C131—42no—
205C22×C4×C131—42no—
206C22×C4×C131C2×D411yescharacteristic
207C22×C4×C131C2×D411yescharacteristic
208C22×C4×C131C2×D411yescharacteristic
209C22×C4×C131C2×D411yescharacteristic
210C22×C4×C131C2×D412yes—
211C22×C4×C131C2×D411yescharacteristic
212C22×C4×C131#4112yes—
213C22×C4×C131C2411yescharacteristic
214Q16×C131—44no—
215SD16×C131—44no—
216SD16×C131—44no—
217C2×C8×C131—21no—
218C2×C8×C131—21no—
219C2×C8×C131—21no—
220C2×C8×C131—21no—
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—44no—
229C2×C8×C131C2×D412yes—
230C4⋊C4×C131—24no—
231C4⋊C4×C131—21no—
232C4⋊C4×C131—21no—
233C4⋊C4×C131—21no—
234C4⋊C4×C131—21no—
235C4⋊C4×C131—21no—
236C4⋊C4×C131—21no—
237C4⋊C4×C131—42no—
238C4⋊C4×C131—42no—
239C4⋊C4×C131C2×D412yes—
240C4⋊C4×C131C2×D412yes—
241C22⋊C4×C131—24no—
242C22⋊C4×C131—22no—
243C22⋊C4×C131—41no—
244C22⋊C4×C131—42no—
245C22⋊C4×C131—42no—
246C22⋊C4×C131—42no—
247C22⋊C4×C131—42no—
248C22⋊C4×C131—81no—
249C22⋊C4×C131—81no—
250C42×C131—21no—
251C42×C131—21no—
252C42×C131—21no—
253C42×C131—21no—
254C42×C131—42no—
255C42×C131—42no—
256C42×C131—42no—
257C23×C131—21no—
258C23×C131—21no—
259C23×C131—21no—
260C23×C131—21no—
261C23×C131—21no—
262C23×C131—21no—
263C23×C131—22no—
264C23×C131—41no—
265C23×C131—41no—
266C23×C131—41no—
267C23×C131—41no—
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#12112yes—
278C23×C131C22×D411yescharacteristic
279Q8×C131—22no—
280Q8×C131—22no—
281Q8×C131—22no—
282Q8×C131—22no—
283Q8×C131—41no—
284Q8×C131—41no—
285Q8×C131—41no—
286Q8×C131—41no—
287D4×C131—22no—
288D4×C131—22no—
289D4×C131—48no—
290D4×C131—41no—
291D4×C131—41no—
292D4×C131—41no—
293D4×C131—41no—
294D4×C131—41no—
295D4×C131—41no—
296D4×C131—84no—
297D4×C131—84no—
298D4×C131—84no—
299C2×C4×C131—21no—
300C2×C4×C131—21no—
301C2×C4×C131—21no—
302C2×C4×C131—21no—
303C2×C4×C131—22no—
304C2×C4×C131—22no—
305C2×C4×C131—22no—
306C2×C4×C131—22no—
307C2×C4×C131—22no—
308C2×C4×C131—22no—
309C2×C4×C131—21no—
310C2×C4×C131—21no—
311C2×C4×C131—22no—
312C2×C4×C131—22no—
313C2×C4×C131—21no—
314C2×C4×C131—21no—
315C2×C4×C131—21no—
316C2×C4×C131—21no—
317C2×C4×C131—21no—
318C2×C4×C131—21no—
319C2×C4×C131—21no—
320C2×C4×C131—48no—
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—41no—
335C2×C4×C131#12112yes—
336C2×C4×C131#13512yes—
337C2×C4×C131C22×D411yescharacteristic
338C2×C4×C131C22×D411yescharacteristic
339C2×C4×C131C2×#4111yescharacteristic
340C2×C4×C131C2×#4111yescharacteristic
341C2×C4×C131H(5,𝔽2)11yescharacteristic
342C2×C4×C131H(5,𝔽2)11yescharacteristic
343C8×C131—22no—
344C8×C131—41no—
345C8×C131—41no—
346C8×C131—41no—
347C22×C131—22no—
348C22×C131—22no—
349C22×C131—22no—
350C22×C131—41no—
351C22×C131—41no—
352C22×C131—41no—
353C22×C131—41no—
354C22×C131—42no—
355C22×C131—42no—
356C22×C131—42no—
357C22×C131—81no—
358C22×C131—81no—
359C22×C131—81no—
360C22×C131—81no—
361C22×C131—81no—
362C22×C131—81no—
363C22×C131—81no—
364C22×C131—81no—
365C22×C131—81no—
366C22×C131—81no—
367C22×C131—81no—
368C22×C131C2×#12111yescharacteristic
369C22×C131D4211yescharacteristic
370C22×C131#54611yescharacteristic
371C22×C131C2×#13511yescharacteristic
372C22×C131#57511yescharacteristic
373C22×C131#57711yescharacteristic
374C22×C131#57711yescharacteristic
375C4×C131—22no—
376C4×C131—22no—
377C4×C131—42no—
378C4×C131—42no—
379C4×C131—41no—
380C4×C131—41no—
381C4×C131—42no—
382C4×C131—42no—
383C4×C131—41no—
384C4×C131—81no—
385C4×C131—81no—
386C4×C131#52511yescharacteristic
387C4×C131#53811yescharacteristic
388C4×C131D4211yescharacteristic
389C4×C131#54611yescharacteristic
390C2×C131—42no—
391C2×C131—82no—
392C2×C131—161no—
393C2×C131#242411yescharacteristic
394C2×C131#303511yescharacteristic
395C2×C131#304311yescharacteristic
396C2×C131#327111yescharacteristic
397C2×C131#328411yescharacteristic
398C2×C131#329611yescharacteristic
399C2×C131#331111yescharacteristic
400#25091C13111yesmaximal, characteristic, direct product factor, Sylow
401C131#2509111yescharacteristic, direct product factor, Sylow
402C2×#465C2×C13111yescharacteristic, complemented
403C2×#464C2×C13111yescharacteristic, complemented
404C2×#452C2×C13111yescharacteristic, complemented
405C2×#416C2×C13111yescharacteristic, complemented
406#2431C2×C13111yescharacteristic
407#2362C2×C13111yescharacteristic, complemented
408#2065C2×C13111yescharacteristic, complemented
409#2056C2×C13111yescharacteristic, complemented
410#2042C2×C13111yescharacteristic, complemented
411#2014C2×C13111yescharacteristic, complemented
412#1982C2×C13111yescharacteristic, complemented
413#1927C2×C13111yescharacteristic, complemented
414#1880C2×C13111yescharacteristic, complemented
415#1875C2×C13111yescharacteristic, complemented
416#1850C2×C13111yescharacteristic, complemented
417C22×#41C22×C13111yescharacteristic
418C22×Q16C22×C13111yescharacteristic
419C22×SD16C22×C13111yescharacteristic
420C22×SD16C22×C13111yescharacteristic
421C23×C8C22×C13111yescharacteristic
422C2×#127C22×C13111yescharacteristic
423C2×#124C22×C13111yescharacteristic
424C2×C22⋊Q8C22×C13111yescharacteristic
425C2×#121C22×C13111yescharacteristic
426C2×C4×Q8C22×C13111yescharacteristic
427C2×#117C22×C13111yescharacteristic
428#465—24no—
429#464—24no—
430#452—24no—
431C2×#106C22×C13111yescharacteristic
432C2×C4⋊C8C22×C13111yescharacteristic
433C2×C4⋊C8C22×C13111yescharacteristic
434#416—24no—
435C2×#103C22×C13111yescharacteristic
436C2×#103C22×C13111yescharacteristic
437C2×#103C22×C13111yescharacteristic
438C2×#103C22×C13111yescharacteristic
439C2×#102C22×C13111yescharacteristic
440C2×#102C22×C13111yescharacteristic
441C2×#102C22×C13111yescharacteristic
442C2×#102C22×C13111yescharacteristic
443C2×#102C22×C13111yescharacteristic
444C2×#102C22×C13111yescharacteristic
445C2×C22⋊C8C22×C13111yescharacteristic
446#392—21no—
447#392—21no—
448#391C22×C13111yescharacteristic
449#391C22×C13111yescharacteristic
450#390C22×C13111yescharacteristic
451#389C22×C13111yescharacteristic
452#388—21no—
453#388—21no—
454#387—21no—
455#386—21no—
456#386—21no—
457C4×C4⋊C4—21no—
458C4×C4⋊C4C22×C13111yescharacteristic
459C4×C22⋊C4C22×C13111yescharacteristic
460#340C22×C13111yescharacteristic
461#340C22×C13111yescharacteristic
462#336C22×C13111yescharacteristic
463#336C22×C13111yescharacteristic
464C2×#41—22no—
465C2×#41—22no—
466C2×#41—22no—
467C2×#41—22no—
468C2×#41—41no—
469C2×#41—41no—
470C22×Q8C23×C13111yescharacteristic
471C22×Q8C23×C13111yescharacteristic
472C22×D4—21no—
473C22×D4—21no—
474C22×D4—21no—
475C22×D4—21no—
476C22×D4C23×C13111yescharacteristic
477C22×D4C23×C13111yescharacteristic
478C23×C4—21no—
479C23×C4C23×C13111yescharacteristic
480C2×Q16—22no—
481C2×Q16—22no—
482C2×Q16—41no—
483C2×SD16—22no—
484C2×SD16—22no—
485C2×SD16—22no—
486C2×SD16—22no—
487C2×SD16—41no—
488C2×SD16—41no—
489C22×C8—22no—
490C22×C8—22no—
491C22×C8—41no—
492C22×C8C23×C13111yescharacteristic
493C22×C8C23×C13111yescharacteristic
494C22×C8C23×C13111yescharacteristic
495C22×C8C23×C13111yescharacteristic
496#127—22no—
497#127—41no—
498#124—22no—
499#124—41no—
500C22⋊Q8—22no—
501C22⋊Q8D4×C13114yescomplemented
502#121—22no—
503#121—22no—
504C4×Q8—22no—
505C4×Q8—41no—
506#117—22no—
507#117—41no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4C23×C13111yescharacteristic
512C2×C4⋊C4C23×C13111yescharacteristic
513C2×C4⋊C4C23×C13111yescharacteristic
514C2×C4⋊C4C23×C13111yescharacteristic
515C2×C22⋊C4—21no—
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⋊C4D4×C13111yescharacteristic
523C2×C22⋊C4D4×C13111yescharacteristic
524C2×C42—21no—
525C2×C42—21no—
526C2×C42—21no—
527C2×C42C23×C13111yescharacteristic
528C2×C42C23×C13111yescharacteristic
529#106—22no—
530C4⋊C8—22no—
531C4⋊C8—41no—
532#103—22no—
533#103—22no—
534#103—22no—
535#103D4×C13114yescomplemented
536#102—22no—
537#102—22no—
538#102—22no—
539#102—22no—
540#102—22no—
541#102—41no—
542C22⋊C8—22no—
543#95—21no—
544#95—21no—
545#95—21no—
546#95—21no—
547#95—21no—
548#95—21no—
549#95D4×C13111yescharacteristic
550#95D4×C13111yescharacteristic
551C24—21no—
552C24—21no—
553C24C2×D4×C13111yescharacteristic
554#41—28no—
555#41—44no—
556#41—44no—
557#41—44no—
558C2×Q8—21no—
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×Q8C2×D4×C13112yes—
569C2×Q8C2×D4×C13112yes—
570C2×D4—21no—
571C2×D4—21no—
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—21no—
581C2×D4—42no—
582C2×D4—42no—
583C2×D4—42no—
584C2×D4—42no—
585C2×D4—42no—
586C2×D4—42no—
587C2×D4—42no—
588C2×D4—42no—
589C2×D4—81no—
590C2×D4—81no—
591C2×D4—81no—
592C2×D4—81no—
593C2×D4#41×C13112yes—
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—21no—
603C22×C4—21no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4—42no—
607C22×C4C2×D4×C13111yescharacteristic
608C22×C4C2×D4×C13111yescharacteristic
609C22×C4C2×D4×C13111yescharacteristic
610C22×C4C2×D4×C13111yescharacteristic
611C22×C4C2×D4×C13112yes—
612C22×C4C2×D4×C13111yescharacteristic
613C22×C4#41×C13112yes—
614C22×C4C24×C13111yescharacteristic
615Q16—44no—
616SD16—44no—
617SD16—44no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—44no—
630C2×C8C2×D4×C13112yes—
631C4⋊C4—24no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—42no—
639C4⋊C4—42no—
640C4⋊C4C2×D4×C13112yes—
641C4⋊C4C2×D4×C13112yes—
642C22⋊C4—24no—
643C22⋊C4—22no—
644C22⋊C4—41no—
645C22⋊C4—42no—
646C22⋊C4—42no—
647C22⋊C4—42no—
648C22⋊C4—42no—
649C22⋊C4—81no—
650C22⋊C4—81no—
651C42—21no—
652C42—21no—
653C42—21no—
654C42—21no—
655C42—42no—
656C42—42no—
657C42—42no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—22no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23#121×C13112yes—
679C23C22×D4×C13111yescharacteristic
680Q8—22no—
681Q8—22no—
682Q8—22no—
683Q8—22no—
684Q8—41no—
685Q8—41no—
686Q8—41no—
687Q8—41no—
688D4—22no—
689D4—22no—
690D4—48no—
691D4—41no—
692D4—41no—
693D4—41no—
694D4—41no—
695D4—41no—
696D4—41no—
697D4—84no—
698D4—84no—
699D4—84no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—48no—
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#121×C13112yes—
737C2×C4#135×C13112yes—
738C2×C4C22×D4×C13111yescharacteristic
739C2×C4C22×D4×C13111yescharacteristic
740C2×C4C2×#41×C13111yescharacteristic
741C2×C4C2×#41×C13111yescharacteristic
742C2×C4H(5,𝔽2)×C13111yescharacteristic
743C2×C4H(5,𝔽2)×C13111yescharacteristic
744C8—22no—
745C8—41no—
746C8—41no—
747C8—41no—
748C22—22no—
749C22—22no—
750C22—22no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22—81no—
768C22—81no—
769C22C2×#121×C13111yescharacteristic
770C22D42×C13111yescharacteristic
771C22#546×C13111yescharacteristic
772C22C2×#135×C13111yescharacteristic
773C22#575×C13111yescharacteristic
774C22#577×C13111yescharacteristic
775C22#577×C13111yescharacteristic
776C4—22no—
777C4—22no—
778C4—41no—
779C4—41no—
780C4—42no—
781C4—42no—
782C4—41no—
783C4—42no—
784C4—42no—
785C4—81no—
786C4—81no—
787C4#525×C13111yescharacteristic
788C4#538×C13111yescharacteristic
789C4D42×C13111yescharacteristic
790C4#546×C13111yescharacteristic
791C2—42no—
792C2—82no—
793C2—161no—
794C2#2424×C13111yescharacteristic
795C2#3035×C13111yescharacteristic
796C2#3043×C13111yescharacteristic
797C2#3271×C13111yescharacteristic
798C2#3284×C13111yescharacteristic
799C2#3296×C13111yescharacteristic
800C2#3311×C13111yescharacteristic
subgroupG/H
center, socleC23×C131C22×D4
commutator, Frattini, cosocleC22×C4C24×C131
prime radical#2431×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×#465×C131C2semidirect
2. C2×#464×C131C2semidirect
3. C2×#452×C131C2semidirect
4. C2×#416×C131C2semidirect
6. #2362×C131C2semidirect
7. #2065×C131C2semidirect
8. #2056×C131C2semidirect
9. #2042×C131C2semidirect
10. #2014×C131C2semidirect
11. #1982×C131C2semidirect
12. #1927×C131C2semidirect
13. #1880×C131C2semidirect
14. #1875×C131C2semidirect
15. #1850×C131C2semidirect
100. C22⋊Q8×C131D4semidirect
134. #103×C131D4semidirect
400. #25091C131direct (N × H)
401. C131#25091direct (N × H)
402. C2×#465C2×C131semidirect
403. C2×#464C2×C131semidirect
404. C2×#452C2×C131semidirect
405. C2×#416C2×C131semidirect
407. #2362C2×C131semidirect
408. #2065C2×C131semidirect
409. #2056C2×C131semidirect
410. #2042C2×C131semidirect
411. #2014C2×C131semidirect
412. #1982C2×C131semidirect
413. #1927C2×C131semidirect
414. #1880C2×C131semidirect
415. #1875C2×C131semidirect
416. #1850C2×C131semidirect
501. C22⋊Q8D4×C131semidirect
535. #103D4×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#465×C1312
C2×#464×C1312
C2×#452×C1312
C2×#416×C1312
#2431×C1312
#2362×C1312
#2065×C1312
#2056×C1312
#2042×C1312
#2014×C1312
#1982×C1312
#1927×C1312
#1880×C1312
#1875×C1312
#1850×C1312
#25091131