Finite Group Databasebeta

← C131×#18252 #45704136

Subgroups — C131×#18252 #45704136

Order 33536.

1260 conjugacy classes of subgroups.

The subgroup lattice has 1064 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3534×C131C211yesmaximal, characteristic, complemented
2#3006×C131C211yesmaximal, characteristic, complemented
3#3002×C131C211yesmaximal, characteristic, complemented
4#2430×C131C211yesmaximal, characteristic, complemented
5#1606×C131C211yesmaximal, characteristic, complemented
6#1604×C131C211yesmaximal, characteristic, complemented
7#1603×C131C211yesmaximal, characteristic, complemented
8#1601×C131C211yesmaximal, characteristic, complemented
9#1600×C131C211yesmaximal, characteristic, complemented
10#1598×C131C211yesmaximal, characteristic, complemented
11#1597×C131C211yesmaximal, characteristic, complemented
12#1595×C131C211yesmaximal, characteristic, complemented
13#1504×C131C211yesmaximal, characteristic, complemented
14C2×#327×C131C211yesmaximal, characteristic, complemented
15#1468×C131C211yesmaximal, characteristic, complemented
16C22×#41×C131C2211yescharacteristic, complemented
17C2×AGL(1,ℤ/8)×C131—21no—
18C2×#135×C131—21no—
19#562×C131—21no—
20#560×C131—21no—
21#553×C131—21no—
22#551×C131—21no—
23#546×C131—21no—
24#546×C131—21no—
25#546×C131—21no—
26D42×C131—21no—
27#540×C131—21no—
28#539×C131—21no—
29#539×C131C2211yescharacteristic
30#538×C131—21no—
31#538×C131C2211yescharacteristic
32#537×C131C2211yescharacteristic
33#534×C131—21no—
34#534×C131C2211yescharacteristic
35#525×C131C2211yescharacteristic
36C2×#123×C131C2211yescharacteristic
37C2×#121×C131—21no—
38C2×#121×C131C2211yescharacteristic
39#452×C131—21no—
40#451×C131C2211yescharacteristic, complemented
41#450×C131C2211yescharacteristic, complemented
42#449×C131—21no—
43#449×C131—21no—
44#449×C131—21no—
45#448×C131C2211yescharacteristic
46#448×C131C2211yescharacteristic, complemented
47#448×C131C2211yescharacteristic, complemented
48#447×C131C2211yescharacteristic
49#447×C131C2211yescharacteristic, complemented
50#447×C131C2211yescharacteristic, complemented
51#417×C131—21no—
52#416×C131—21no—
53#407×C131C2211yescharacteristic, complemented
54C2×C22⋊C8×C131C2211yescharacteristic, complemented
55#395×C131C2211yescharacteristic, complemented
56#394×C131C2211yescharacteristic, complemented
57#393×C131C2211yescharacteristic, complemented
58#392×C131C2211yescharacteristic, complemented
59#386×C131—21no—
60#386×C131—21no—
61#385×C131—21no—
62C2×#95×C131C2211yescharacteristic, complemented
63#328×C131C2211yescharacteristic, complemented
64#328×C131C2211yescharacteristic, complemented
65#327×C131C2211yescharacteristic
66#327×C131C2211yescharacteristic
67#327×C131C2211yescharacteristic, complemented
68#327×C131C2211yescharacteristic, complemented
69#327×C131C2211yescharacteristic, complemented
70#327×C131C2211yescharacteristic, complemented
71#324×C131C2211yescharacteristic, complemented
72#324×C131C2211yescharacteristic, complemented
73#323×C131C2211yescharacteristic, complemented
74#323×C131C2211yescharacteristic, complemented
75C2×#41×C131—21no—
76C2×#41×C131—21no—
77C2×#41×C131—21no—
78C2×#41×C131—21no—
79C2×#41×C131—21no—
80C2×#41×C131—44no—
81C2×#41×C131D411yescharacteristic, complemented
82C22×Q8×C131C2311yescharacteristic
83C22×D4×C131—21no—
84C22×D4×C131—21no—
85C22×D4×C131—21no—
86C22×D4×C131—21no—
87C22×D4×C131—21no—
88C22×D4×C131D411yescharacteristic
89C22×D4×C131D411yescharacteristic, complemented
90C22×D4×C131C2311yescharacteristic
91C23×C4×C131—21no—
92C23×C4×C131—21no—
93C23×C4×C131C2311yescharacteristic
94AGL(1,ℤ/8)×C131—44no—
95#135×C131—44no—
96C2×Q16×C131—21no—
97C2×SD16×C131—21no—
98C2×SD16×C131—21no—
99C2×SD16×C131—21no—
100C2×SD16×C131—21no—
101C2×D8×C131—21no—
102C2×D8×C131—21no—
103C2×D8×C131—21no—
104C2×M16×C131—21no—
105C22×C8×C131—21no—
106#127×C131—21no—
107#126×C131—21no—
108#126×C131—21no—
109#126×C131—21no—
110#126×C131—21no—
111#125×C131—21no—
112#125×C131—21no—
113#124×C131—21no—
114#124×C131—21no—
115#124×C131—21no—
116#123×C131—21no—
117#123×C131—21no—
118#123×C131—21no—
119#123×C131—21no—
120#123×C131—21no—
121#123×C131—21no—
122#123×C131—21no—
123#123×C131—21no—
124#123×C131—21no—
125#123×C131—21no—
126#123×C131—21no—
127#123×C131—21no—
128#123×C131—21no—
129#123×C131—21no—
130C22⋊Q8×C131—21no—
131C22⋊Q8×C131—21no—
132C22⋊Q8×C131—21no—
133C22⋊Q8×C131—21no—
134C22⋊Q8×C131—21no—
135C22⋊Q8×C131D411yescharacteristic, complemented
136C22⋊Q8×C131C2311yescharacteristic
137#121×C131—21no—
138#121×C131—21no—
139#121×C131—21no—
140#121×C131—21no—
141#121×C131—21no—
142#121×C131—21no—
143#121×C131—21no—
144#121×C131—21no—
145#121×C131—21no—
146#121×C131—21no—
147#121×C131—21no—
148#121×C131—21no—
149#121×C131—21no—
150#121×C131—21no—
151#121×C131—21no—
152#121×C131—44no—
153#121×C131D411yescharacteristic, complemented
154#121×C131D411yescharacteristic, complemented
155#121×C131D411yescharacteristic, complemented
156#121×C131C2311yescharacteristic
157#121×C131C2311yescharacteristic
158#121×C131C2311yescharacteristic
159#120×C131—21no—
160#120×C131—21no—
161#120×C131—21no—
162#120×C131—21no—
163#120×C131—21no—
164#120×C131—21no—
165#120×C131—21no—
166#120×C131—21no—
167C4×D4×C131—21no—
168C4×D4×C131—21no—
169C4×D4×C131—21no—
170C4×D4×C131—21no—
171C4×D4×C131—21no—
172C4×D4×C131—21no—
173C4×D4×C131—21no—
174C4×D4×C131—21no—
175#117×C131—21no—
176#117×C131D411yescharacteristic, complemented
177C2×C4⋊C4×C131—21no—
178C2×C4⋊C4×C131D411yescharacteristic
179C2×C4⋊C4×C131D411yescharacteristic, complemented
180C2×C4⋊C4×C131C2311yescharacteristic
181C2×C22⋊C4×C131—21no—
182C2×C22⋊C4×C131—21no—
183C2×C22⋊C4×C131—21no—
184C2×C22⋊C4×C131—21no—
185C2×C22⋊C4×C131—21no—
186C2×C22⋊C4×C131—21no—
187C2×C22⋊C4×C131—21no—
188C2×C22⋊C4×C131D411yescharacteristic
189C2×C22⋊C4×C131D411yescharacteristic
190C2×C22⋊C4×C131C2311yescharacteristic
191#103×C131—21no—
192#103×C131—21no—
193#103×C131—21no—
194#103×C131—21no—
195#102×C131—21no—
196#102×C131—21no—
197#102×C131—21no—
198#102×C131—21no—
199C22⋊C8×C131—21no—
200C22⋊C8×C131—21no—
201C22⋊C8×C131C2311yescharacteristic
202C22⋊C8×C131C2311yescharacteristic
203C22⋊C8×C131C2311yescharacteristic
204C22⋊C8×C131C2311yescharacteristic
205#95×C131—21no—
206#95×C131—21no—
207#95×C131—21no—
208#95×C131C2311yescharacteristic
209#95×C131C2311yescharacteristic
210C24×C131—21no—
211C24×C131—21no—
212C24×C131—21no—
213C24×C131C2×D411yescharacteristic
214C24×C131C2×D411yescharacteristic
215#41×C131—24no—
216#41×C131—24no—
217#41×C131—42no—
218#41×C131—42no—
219#41×C131—42no—
220#41×C131—42no—
221#41×C131—42no—
222#41×C131—42no—
223#41×C131—42no—
224#41×C131—81no—
225#41×C131—81no—
226C2×Q8×C131—21no—
227C2×Q8×C131—21no—
228C2×Q8×C131—21no—
229C2×Q8×C131—42no—
230C2×Q8×C131C2×D411yescharacteristic
231C2×D4×C131—24no—
232C2×D4×C131—21no—
233C2×D4×C131—21no—
234C2×D4×C131—21no—
235C2×D4×C131—21no—
236C2×D4×C131—21no—
237C2×D4×C131—21no—
238C2×D4×C131—21no—
239C2×D4×C131—21no—
240C2×D4×C131—21no—
241C2×D4×C131—21no—
242C2×D4×C131—21no—
243C2×D4×C131—21no—
244C2×D4×C131—21no—
245C2×D4×C131—21no—
246C2×D4×C131—21no—
247C2×D4×C131—21no—
248C2×D4×C131—21no—
249C2×D4×C131—21no—
250C2×D4×C131—21no—
251C2×D4×C131—42no—
252C2×D4×C131—42no—
253C2×D4×C131—42no—
254C2×D4×C131—42no—
255C2×D4×C131—41no—
256C2×D4×C131—41no—
257C2×D4×C131—42no—
258C2×D4×C131—42no—
259C2×D4×C131—81no—
260C2×D4×C131—81no—
261C2×D4×C131—81no—
262C2×D4×C131—81no—
263C2×D4×C131—81no—
264C2×D4×C131—82no—
265C2×D4×C131C2×D411yescharacteristic
266C2×D4×C131C2×D411yescharacteristic
267C2×D4×C131C2×D411yescharacteristic
268C22×C4×C131—21no—
269C22×C4×C131—21no—
270C22×C4×C131—21no—
271C22×C4×C131—21no—
272C22×C4×C131—21no—
273C22×C4×C131—21no—
274C22×C4×C131—21no—
275C22×C4×C131—21no—
276C22×C4×C131—21no—
277C22×C4×C131—21no—
278C22×C4×C131—42no—
279C22×C4×C131—42no—
280C22×C4×C131—42no—
281C22×C4×C131—42no—
282C22×C4×C131—41no—
283C22×C4×C131—41no—
284C22×C4×C131—42no—
285C22×C4×C131—81no—
286C22×C4×C131C2×D411yescharacteristic
287C22×C4×C131C2×D411yescharacteristic
288C22×C4×C131C2×D411yescharacteristic
289C22×C4×C131C2×D411yescharacteristic
290C22×C4×C131C2×D411yescharacteristic
291C22×C4×C131C2×D411yescharacteristic
292C22×C4×C131C2×D411yescharacteristic
293C22×C4×C131C2×D411yescharacteristic
294C22×C4×C131C2411yescharacteristic
295Q16×C131—42no—
296SD16×C131—42no—
297SD16×C131—42no—
298SD16×C131—42no—
299SD16×C131—42no—
300D8×C131—42no—
301D8×C131—42no—
302D8×C131—42no—
303M16×C131—42no—
304C2×C8×C131—21no—
305C2×C8×C131—21no—
306C2×C8×C131—21no—
307C2×C8×C131—21no—
308C2×C8×C131—42no—
309C4⋊C4×C131—21no—
310C4⋊C4×C131—21no—
311C4⋊C4×C131—21no—
312C4⋊C4×C131—21no—
313C4⋊C4×C131—21no—
314C4⋊C4×C131—21no—
315C4⋊C4×C131—21no—
316C4⋊C4×C131—21no—
317C4⋊C4×C131—21no—
318C4⋊C4×C131—21no—
319C4⋊C4×C131—21no—
320C4⋊C4×C131—21no—
321C4⋊C4×C131—21no—
322C4⋊C4×C131—42no—
323C4⋊C4×C131C2×D411yescharacteristic
324C4⋊C4×C131C2×D411yescharacteristic
325C4⋊C4×C131C2×D411yescharacteristic
326C4⋊C4×C131C2×D411yescharacteristic
327C22⋊C4×C131—21no—
328C22⋊C4×C131—21no—
329C22⋊C4×C131—21no—
330C22⋊C4×C131—21no—
331C22⋊C4×C131—21no—
332C22⋊C4×C131—21no—
333C22⋊C4×C131—21no—
334C22⋊C4×C131—21no—
335C22⋊C4×C131—21no—
336C22⋊C4×C131—21no—
337C22⋊C4×C131—21no—
338C22⋊C4×C131—21no—
339C22⋊C4×C131—21no—
340C22⋊C4×C131—21no—
341C22⋊C4×C131—21no—
342C22⋊C4×C131—21no—
343C22⋊C4×C131—21no—
344C22⋊C4×C131—21no—
345C22⋊C4×C131—21no—
346C22⋊C4×C131—21no—
347C22⋊C4×C131—21no—
348C22⋊C4×C131—21no—
349C22⋊C4×C131—21no—
350C22⋊C4×C131—21no—
351C22⋊C4×C131—21no—
352C22⋊C4×C131—42no—
353C22⋊C4×C131—42no—
354C22⋊C4×C131—42no—
355C22⋊C4×C131—81no—
356C42×C131—21no—
357C42×C131—21no—
358C42×C131—21no—
359C23×C131—21no—
360C23×C131—21no—
361C23×C131—22no—
362C23×C131—22no—
363C23×C131—21no—
364C23×C131—21no—
365C23×C131—21no—
366C23×C131—21no—
367C23×C131—21no—
368C23×C131—21no—
369C23×C131—41no—
370C23×C131—41no—
371C23×C131—41no—
372C23×C131—41no—
373C23×C131—41no—
374C23×C131—41no—
375C23×C131—41no—
376C23×C131—41no—
377C23×C131—41no—
378C23×C131—42no—
379C23×C131—81no—
380C23×C131—81no—
381C23×C131—81no—
382C23×C131—81no—
383C23×C131—81no—
384C23×C131#12011yescharacteristic
385C23×C131#12011yescharacteristic
386C23×C131C22×D411yescharacteristic
387Q8×C131—22no—
388Q8×C131—22no—
389Q8×C131—41no—
390Q8×C131—41no—
391Q8×C131—41no—
392Q8×C131—81no—
393D4×C131—22no—
394D4×C131—22no—
395D4×C131—41no—
396D4×C131—41no—
397D4×C131—41no—
398D4×C131—41no—
399D4×C131—41no—
400D4×C131—44no—
401D4×C131—41no—
402D4×C131—41no—
403D4×C131—41no—
404D4×C131—41no—
405D4×C131—41no—
406D4×C131—41no—
407D4×C131—44no—
408D4×C131—42no—
409D4×C131—42no—
410D4×C131—81no—
411D4×C131—81no—
412D4×C131—81no—
413D4×C131—81no—
414D4×C131—81no—
415D4×C131—81no—
416D4×C131—81no—
417D4×C131—81no—
418D4×C131—81no—
419D4×C131—81no—
420D4×C131—81no—
421D4×C131—81no—
422D4×C131—84no—
423C2×C4×C131—22no—
424C2×C4×C131—22no—
425C2×C4×C131—22no—
426C2×C4×C131—22no—
427C2×C4×C131—21no—
428C2×C4×C131—21no—
429C2×C4×C131—21no—
430C2×C4×C131—21no—
431C2×C4×C131—21no—
432C2×C4×C131—21no—
433C2×C4×C131—21no—
434C2×C4×C131—21no—
435C2×C4×C131—21no—
436C2×C4×C131—21no—
437C2×C4×C131—41no—
438C2×C4×C131—41no—
439C2×C4×C131—41no—
440C2×C4×C131—41no—
441C2×C4×C131—44no—
442C2×C4×C131—44no—
443C2×C4×C131—41no—
444C2×C4×C131—41no—
445C2×C4×C131—41no—
446C2×C4×C131—41no—
447C2×C4×C131—41no—
448C2×C4×C131—41no—
449C2×C4×C131—41no—
450C2×C4×C131—41no—
451C2×C4×C131—41no—
452C2×C4×C131—81no—
453C2×C4×C131—81no—
454C2×C4×C131—81no—
455C2×C4×C131—81no—
456C2×C4×C131—81no—
457C2×C4×C131—81no—
458C2×C4×C131—81no—
459C2×C4×C131—84no—
460C2×C4×C131#12011yescharacteristic
461C2×C4×C131#12011yescharacteristic
462C2×C4×C131C22×D411yescharacteristic
463C2×C4×C131C22×D411yescharacteristic
464C8×C131—41no—
465C8×C131—41no—
466C8×C131—41no—
467C8×C131—41no—
468C22×C131—21no—
469C22×C131—21no—
470C22×C131—21no—
471C22×C131—21no—
472C22×C131—21no—
473C22×C131—21no—
474C22×C131—21no—
475C22×C131—42no—
476C22×C131—42no—
477C22×C131—42no—
478C22×C131—42no—
479C22×C131—41no—
480C22×C131—41no—
481C22×C131—41no—
482C22×C131—41no—
483C22×C131—41no—
484C22×C131—41no—
485C22×C131—41no—
486C22×C131—41no—
487C22×C131—42no—
488C22×C131—41no—
489C22×C131—41no—
490C22×C131—41no—
491C22×C131—41no—
492C22×C131—81no—
493C22×C131—81no—
494C22×C131—81no—
495C22×C131—81no—
496C22×C131—81no—
497C22×C131—81no—
498C22×C131—162no—
499C22×C131—162no—
500C22×C131B(4,𝔽2)12yes—
501C22×C131C2×#12011yescharacteristic
502C22×C131#57611yescharacteristic
503C22×C131#57711yescharacteristic
504C4×C131—21no—
505C4×C131—21no—
506C4×C131—21no—
507C4×C131—21no—
508C4×C131—42no—
509C4×C131—41no—
510C4×C131—41no—
511C4×C131—41no—
512C4×C131—41no—
513C4×C131—41no—
514C4×C131—41no—
515C4×C131—42no—
516C4×C131—41no—
517C4×C131—41no—
518C4×C131—81no—
519C2×C131—21no—
520C2×C131—21no—
521C2×C131—22no—
522C2×C131—41no—
523C2×C131—82no—
524C2×C131—81no—
525C2×C131—81no—
526C2×C131—81no—
527C2×C131—81no—
528C2×C131#301211yescharacteristic
529C2×C131#301811yescharacteristic
530C2×C131C2×B(4,𝔽2)11yescharacteristic
531#18252C13111yesmaximal, characteristic, direct product factor, Sylow
532C131#1825211yescharacteristic, direct product factor, Sylow
533#3534C2×C13111yescharacteristic, complemented
534#3006C2×C13111yescharacteristic, complemented
535#3002C2×C13111yescharacteristic, complemented
536#2430C2×C13111yescharacteristic, complemented
537#1606C2×C13111yescharacteristic, complemented
538#1604C2×C13111yescharacteristic, complemented
539#1603C2×C13111yescharacteristic, complemented
540#1601C2×C13111yescharacteristic, complemented
541#1600C2×C13111yescharacteristic, complemented
542#1598C2×C13111yescharacteristic, complemented
543#1597C2×C13111yescharacteristic, complemented
544#1595C2×C13111yescharacteristic, complemented
545#1504C2×C13111yescharacteristic, complemented
546C2×#327C2×C13111yescharacteristic, complemented
547#1468C2×C13111yescharacteristic, complemented
548C22×#41C22×C13111yescharacteristic, complemented
549C2×AGL(1,ℤ/8)—21no—
550C2×#135—21no—
551#562—21no—
552#560—21no—
553#553—21no—
554#551—21no—
555#546—21no—
556#546—21no—
557#546—21no—
558D42—21no—
559#540—21no—
560#539—21no—
561#539C22×C13111yescharacteristic
562#538—21no—
563#538C22×C13111yescharacteristic
564#537C22×C13111yescharacteristic
565#534—21no—
566#534C22×C13111yescharacteristic
567#525C22×C13111yescharacteristic
568C2×#123C22×C13111yescharacteristic
569C2×#121—21no—
570C2×#121C22×C13111yescharacteristic
571#452—21no—
572#451C22×C13111yescharacteristic, complemented
573#450C22×C13111yescharacteristic, complemented
574#449—21no—
575#449—21no—
576#449—21no—
577#448C22×C13111yescharacteristic
578#448C22×C13111yescharacteristic, complemented
579#448C22×C13111yescharacteristic, complemented
580#447C22×C13111yescharacteristic
581#447C22×C13111yescharacteristic, complemented
582#447C22×C13111yescharacteristic, complemented
583#417—21no—
584#416—21no—
585#407C22×C13111yescharacteristic, complemented
586C2×C22⋊C8C22×C13111yescharacteristic, complemented
587#395C22×C13111yescharacteristic, complemented
588#394C22×C13111yescharacteristic, complemented
589#393C22×C13111yescharacteristic, complemented
590#392C22×C13111yescharacteristic, complemented
591#386—21no—
592#386—21no—
593#385—21no—
594C2×#95C22×C13111yescharacteristic, complemented
595#328C22×C13111yescharacteristic, complemented
596#328C22×C13111yescharacteristic, complemented
597#327C22×C13111yescharacteristic
598#327C22×C13111yescharacteristic
599#327C22×C13111yescharacteristic, complemented
600#327C22×C13111yescharacteristic, complemented
601#327C22×C13111yescharacteristic, complemented
602#327C22×C13111yescharacteristic, complemented
603#324C22×C13111yescharacteristic, complemented
604#324C22×C13111yescharacteristic, complemented
605#323C22×C13111yescharacteristic, complemented
606#323C22×C13111yescharacteristic, complemented
607C2×#41—21no—
608C2×#41—21no—
609C2×#41—21no—
610C2×#41—21no—
611C2×#41—21no—
612C2×#41—44no—
613C2×#41D4×C13111yescharacteristic, complemented
614C22×Q8C23×C13111yescharacteristic
615C22×D4—21no—
616C22×D4—21no—
617C22×D4—21no—
618C22×D4—21no—
619C22×D4—21no—
620C22×D4D4×C13111yescharacteristic
621C22×D4D4×C13111yescharacteristic, complemented
622C22×D4C23×C13111yescharacteristic
623C23×C4—21no—
624C23×C4—21no—
625C23×C4C23×C13111yescharacteristic
626AGL(1,ℤ/8)—44no—
627#135—44no—
628C2×Q16—21no—
629C2×SD16—21no—
630C2×SD16—21no—
631C2×SD16—21no—
632C2×SD16—21no—
633C2×D8—21no—
634C2×D8—21no—
635C2×D8—21no—
636C2×M16—21no—
637C22×C8—21no—
638#127—21no—
639#126—21no—
640#126—21no—
641#126—21no—
642#126—21no—
643#125—21no—
644#125—21no—
645#124—21no—
646#124—21no—
647#124—21no—
648#123—21no—
649#123—21no—
650#123—21no—
651#123—21no—
652#123—21no—
653#123—21no—
654#123—21no—
655#123—21no—
656#123—21no—
657#123—21no—
658#123—21no—
659#123—21no—
660#123—21no—
661#123—21no—
662C22⋊Q8—21no—
663C22⋊Q8—21no—
664C22⋊Q8—21no—
665C22⋊Q8—21no—
666C22⋊Q8—21no—
667C22⋊Q8D4×C13111yescharacteristic, complemented
668C22⋊Q8C23×C13111yescharacteristic
669#121—21no—
670#121—21no—
671#121—21no—
672#121—21no—
673#121—21no—
674#121—21no—
675#121—21no—
676#121—21no—
677#121—21no—
678#121—21no—
679#121—21no—
680#121—21no—
681#121—21no—
682#121—21no—
683#121—21no—
684#121—44no—
685#121D4×C13111yescharacteristic, complemented
686#121D4×C13111yescharacteristic, complemented
687#121D4×C13111yescharacteristic, complemented
688#121C23×C13111yescharacteristic
689#121C23×C13111yescharacteristic
690#121C23×C13111yescharacteristic
691#120—21no—
692#120—21no—
693#120—21no—
694#120—21no—
695#120—21no—
696#120—21no—
697#120—21no—
698#120—21no—
699C4×D4—21no—
700C4×D4—21no—
701C4×D4—21no—
702C4×D4—21no—
703C4×D4—21no—
704C4×D4—21no—
705C4×D4—21no—
706C4×D4—21no—
707#117—21no—
708#117D4×C13111yescharacteristic, complemented
709C2×C4⋊C4—21no—
710C2×C4⋊C4D4×C13111yescharacteristic
711C2×C4⋊C4D4×C13111yescharacteristic, complemented
712C2×C4⋊C4C23×C13111yescharacteristic
713C2×C22⋊C4—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—21no—
719C2×C22⋊C4—21no—
720C2×C22⋊C4D4×C13111yescharacteristic
721C2×C22⋊C4D4×C13111yescharacteristic
722C2×C22⋊C4C23×C13111yescharacteristic
723#103—21no—
724#103—21no—
725#103—21no—
726#103—21no—
727#102—21no—
728#102—21no—
729#102—21no—
730#102—21no—
731C22⋊C8—21no—
732C22⋊C8—21no—
733C22⋊C8C23×C13111yescharacteristic
734C22⋊C8C23×C13111yescharacteristic
735C22⋊C8C23×C13111yescharacteristic
736C22⋊C8C23×C13111yescharacteristic
737#95—21no—
738#95—21no—
739#95—21no—
740#95C23×C13111yescharacteristic
741#95C23×C13111yescharacteristic
742C24—21no—
743C24—21no—
744C24—21no—
745C24C2×D4×C13111yescharacteristic
746C24C2×D4×C13111yescharacteristic
747#41—24no—
748#41—24no—
749#41—42no—
750#41—42no—
751#41—42no—
752#41—42no—
753#41—42no—
754#41—42no—
755#41—42no—
756#41—81no—
757#41—81no—
758C2×Q8—21no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—42no—
762C2×Q8C2×D4×C13111yescharacteristic
763C2×D4—24no—
764C2×D4—21no—
765C2×D4—21no—
766C2×D4—21no—
767C2×D4—21no—
768C2×D4—21no—
769C2×D4—21no—
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—42no—
784C2×D4—42no—
785C2×D4—42no—
786C2×D4—42no—
787C2×D4—41no—
788C2×D4—41no—
789C2×D4—42no—
790C2×D4—42no—
791C2×D4—81no—
792C2×D4—81no—
793C2×D4—81no—
794C2×D4—81no—
795C2×D4—81no—
796C2×D4—82no—
797C2×D4C2×D4×C13111yescharacteristic
798C2×D4C2×D4×C13111yescharacteristic
799C2×D4C2×D4×C13111yescharacteristic
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—42no—
811C22×C4—42no—
812C22×C4—42no—
813C22×C4—42no—
814C22×C4—41no—
815C22×C4—41no—
816C22×C4—42no—
817C22×C4—81no—
818C22×C4C2×D4×C13111yescharacteristic
819C22×C4C2×D4×C13111yescharacteristic
820C22×C4C2×D4×C13111yescharacteristic
821C22×C4C2×D4×C13111yescharacteristic
822C22×C4C2×D4×C13111yescharacteristic
823C22×C4C2×D4×C13111yescharacteristic
824C22×C4C2×D4×C13111yescharacteristic
825C22×C4C2×D4×C13111yescharacteristic
826C22×C4C24×C13111yescharacteristic
827Q16—42no—
828SD16—42no—
829SD16—42no—
830SD16—42no—
831SD16—42no—
832D8—42no—
833D8—42no—
834D8—42no—
835M16—42no—
836C2×C8—21no—
837C2×C8—21no—
838C2×C8—21no—
839C2×C8—21no—
840C2×C8—42no—
841C4⋊C4—21no—
842C4⋊C4—21no—
843C4⋊C4—21no—
844C4⋊C4—21no—
845C4⋊C4—21no—
846C4⋊C4—21no—
847C4⋊C4—21no—
848C4⋊C4—21no—
849C4⋊C4—21no—
850C4⋊C4—21no—
851C4⋊C4—21no—
852C4⋊C4—21no—
853C4⋊C4—21no—
854C4⋊C4—42no—
855C4⋊C4C2×D4×C13111yescharacteristic
856C4⋊C4C2×D4×C13111yescharacteristic
857C4⋊C4C2×D4×C13111yescharacteristic
858C4⋊C4C2×D4×C13111yescharacteristic
859C22⋊C4—21no—
860C22⋊C4—21no—
861C22⋊C4—21no—
862C22⋊C4—21no—
863C22⋊C4—21no—
864C22⋊C4—21no—
865C22⋊C4—21no—
866C22⋊C4—21no—
867C22⋊C4—21no—
868C22⋊C4—21no—
869C22⋊C4—21no—
870C22⋊C4—21no—
871C22⋊C4—21no—
872C22⋊C4—21no—
873C22⋊C4—21no—
874C22⋊C4—21no—
875C22⋊C4—21no—
876C22⋊C4—21no—
877C22⋊C4—21no—
878C22⋊C4—21no—
879C22⋊C4—21no—
880C22⋊C4—21no—
881C22⋊C4—21no—
882C22⋊C4—21no—
883C22⋊C4—21no—
884C22⋊C4—42no—
885C22⋊C4—42no—
886C22⋊C4—42no—
887C22⋊C4—81no—
888C42—21no—
889C42—21no—
890C42—21no—
891C23—22no—
892C23—21no—
893C23—21no—
894C23—22no—
895C23—21no—
896C23—21no—
897C23—21no—
898C23—21no—
899C23—21no—
900C23—21no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—42no—
911C23—81no—
912C23—81no—
913C23—81no—
914C23—81no—
915C23—81no—
916C23#120×C13111yescharacteristic
917C23#120×C13111yescharacteristic
918C23C22×D4×C13111yescharacteristic
919Q8—22no—
920Q8—22no—
921Q8—41no—
922Q8—41no—
923Q8—41no—
924Q8—81no—
925D4—22no—
926D4—22no—
927D4—41no—
928D4—41no—
929D4—41no—
930D4—41no—
931D4—41no—
932D4—44no—
933D4—44no—
934D4—42no—
935D4—42no—
936D4—41no—
937D4—41no—
938D4—41no—
939D4—41no—
940D4—41no—
941D4—41no—
942D4—81no—
943D4—81no—
944D4—81no—
945D4—81no—
946D4—81no—
947D4—81no—
948D4—81no—
949D4—81no—
950D4—81no—
951D4—81no—
952D4—81no—
953D4—81no—
954D4—84no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—44no—
974C2×C4—44no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—81no—
985C2×C4—81no—
986C2×C4—81no—
987C2×C4—81no—
988C2×C4—81no—
989C2×C4—81no—
990C2×C4—81no—
991C2×C4—84no—
992C2×C4#120×C13111yescharacteristic
993C2×C4#120×C13111yescharacteristic
994C2×C4C22×D4×C13111yescharacteristic
995C2×C4C22×D4×C13111yescharacteristic
996C8—41no—
997C8—41no—
998C8—41no—
999C8—41no—
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—21no—
1004C22—21no—
1005C22—21no—
1006C22—21no—
1007C22—42no—
1008C22—42no—
1009C22—42no—
1010C22—42no—
1011C22—41no—
1012C22—41no—
1013C22—41no—
1014C22—41no—
1015C22—41no—
1016C22—41no—
1017C22—41no—
1018C22—41no—
1019C22—42no—
1020C22—41no—
1021C22—41no—
1022C22—41no—
1023C22—41no—
1024C22—81no—
1025C22—81no—
1026C22—81no—
1027C22—81no—
1028C22—81no—
1029C22—81no—
1030C22—162no—
1031C22—162no—
1032C22B(4,𝔽2)×C13112yes—
1033C22C2×#120×C13111yescharacteristic
1034C22#576×C13111yescharacteristic
1035C22#577×C13111yescharacteristic
1036C4—21no—
1037C4—21no—
1038C4—21no—
1039C4—21no—
1040C4—42no—
1041C4—41no—
1042C4—41no—
1043C4—41no—
1044C4—41no—
1045C4—41no—
1046C4—41no—
1047C4—42no—
1048C4—41no—
1049C4—41no—
1050C4—81no—
1051C2—21no—
1052C2—21no—
1053C2—22no—
1054C2—41no—
1055C2—82no—
1056C2—81no—
1057C2—81no—
1058C2—81no—
1059C2—81no—
1060C2#3012×C13111yescharacteristic
1061C2#3018×C13111yescharacteristic
1062C2C2×B(4,𝔽2)×C13111yescharacteristic
subgroupG/H
center, socleC22×C131C2×#120
commutator, Frattini, cosocleC22×C4C24×C131
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C131 ◁ C23×C4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3534×C131C2semidirect
2. #3006×C131C2semidirect
3. #3002×C131C2semidirect
4. #2430×C131C2semidirect
5. #1606×C131C2semidirect
6. #1604×C131C2semidirect
7. #1603×C131C2semidirect
8. #1601×C131C2semidirect
9. #1600×C131C2semidirect
10. #1598×C131C2semidirect
11. #1597×C131C2semidirect
12. #1595×C131C2semidirect
13. #1504×C131C2semidirect
14. C2×#327×C131C2semidirect
15. #1468×C131C2semidirect
16. C22×#41×C131C22semidirect
40. #451×C131C22semidirect
41. #450×C131C22semidirect
46. #448×C131C22semidirect
47. #448×C131C22semidirect
49. #447×C131C22semidirect
50. #447×C131C22semidirect
53. #407×C131C22semidirect
54. C2×C22⋊C8×C131C22semidirect
55. #395×C131C22semidirect
56. #394×C131C22semidirect
57. #393×C131C22semidirect
58. #392×C131C22semidirect
62. C2×#95×C131C22semidirect
63. #328×C131C22semidirect
64. #328×C131C22semidirect
67. #327×C131C22semidirect
68. #327×C131C22semidirect
69. #327×C131C22semidirect
70. #327×C131C22semidirect
71. #324×C131C22semidirect
72. #324×C131C22semidirect
73. #323×C131C22semidirect
74. #323×C131C22semidirect
81. C2×#41×C131D4semidirect
89. C22×D4×C131D4semidirect
135. C22⋊Q8×C131D4semidirect
153. #121×C131D4semidirect
154. #121×C131D4semidirect
155. #121×C131D4semidirect
176. #117×C131D4semidirect
179. C2×C4⋊C4×C131D4semidirect
531. #18252C131direct (N × H)
532. C131#18252direct (N × H)
533. #3534C2×C131semidirect
534. #3006C2×C131semidirect
535. #3002C2×C131semidirect
536. #2430C2×C131semidirect
537. #1606C2×C131semidirect
538. #1604C2×C131semidirect
539. #1603C2×C131semidirect
540. #1601C2×C131semidirect
541. #1600C2×C131semidirect
542. #1598C2×C131semidirect
543. #1597C2×C131semidirect
544. #1595C2×C131semidirect
545. #1504C2×C131semidirect
546. C2×#327C2×C131semidirect
547. #1468C2×C131semidirect
548. C22×#41C22×C131semidirect
572. #451C22×C131semidirect
573. #450C22×C131semidirect
578. #448C22×C131semidirect
579. #448C22×C131semidirect
581. #447C22×C131semidirect
582. #447C22×C131semidirect
585. #407C22×C131semidirect
586. C2×C22⋊C8C22×C131semidirect
587. #395C22×C131semidirect
588. #394C22×C131semidirect
589. #393C22×C131semidirect
590. #392C22×C131semidirect
594. C2×#95C22×C131semidirect
595. #328C22×C131semidirect
596. #328C22×C131semidirect
599. #327C22×C131semidirect
600. #327C22×C131semidirect
601. #327C22×C131semidirect
602. #327C22×C131semidirect
603. #324C22×C131semidirect
604. #324C22×C131semidirect
605. #323C22×C131semidirect
606. #323C22×C131semidirect
613. C2×#41D4×C131semidirect
621. C22×D4D4×C131semidirect
667. C22⋊Q8D4×C131semidirect
685. #121D4×C131semidirect
686. #121D4×C131semidirect
687. #121D4×C131semidirect
708. #117D4×C131semidirect
711. C2×C4⋊C4D4×C131semidirect

Maximal subgroups

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

subgroupindex
#3534×C1312
#3006×C1312
#3002×C1312
#2430×C1312
#1606×C1312
#1604×C1312
#1603×C1312
#1601×C1312
#1600×C1312
#1598×C1312
#1597×C1312
#1595×C1312
#1504×C1312
C2×#327×C1312
#1468×C1312
#18252131