Finite Group Databasebeta

← C131×#18447 #45704331

Subgroups — C131×#18447 #45704331

Order 33536.

982 conjugacy classes of subgroups.

The subgroup lattice has 970 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3534×C131C211yesmaximal, characteristic
2#3193×C131C211yesmaximal, characteristic, complemented
3#3190×C131C211yesmaximal, characteristic, complemented
4#2814×C131C211yesmaximal, characteristic, complemented
5#1612×C131C211yesmaximal, characteristic, complemented
6#1610×C131C211yesmaximal, characteristic, complemented
7#1609×C131C211yesmaximal, characteristic, complemented
8#1607×C131C211yesmaximal, characteristic, complemented
9#1606×C131C211yesmaximal, characteristic, complemented
10#1604×C131C211yesmaximal, characteristic, complemented
11#1603×C131C211yesmaximal, characteristic, complemented
12#1601×C131C211yesmaximal, characteristic, complemented
13#1519×C131C211yesmaximal, characteristic, complemented
14#1513×C131C211yesmaximal, characteristic, complemented
15#1468×C131C211yesmaximal, characteristic, complemented
16#562×C131—21no—
17#560×C131—21no—
18#553×C131—21no—
19#551×C131—21no—
20#546×C131—21no—
21#546×C131—21no—
22#546×C131—21no—
23D42×C131—21no—
24#540×C131—21no—
25#539×C131—21no—
26#539×C131C2211yescharacteristic
27#538×C131—21no—
28#538×C131C2211yescharacteristic
29#537×C131C2211yescharacteristic
30#534×C131—21no—
31#534×C131C2211yescharacteristic
32#525×C131C2211yescharacteristic
33C2×#123×C131C2211yescharacteristic
34C2×C22⋊Q8×C131C2211yescharacteristic, complemented
35C2×#121×C131C2211yescharacteristic
36#485×C131—21no—
37#484×C131—21no—
38#483×C131C2211yescharacteristic, complemented
39#480×C131C2211yescharacteristic
40#480×C131C2211yescharacteristic, complemented
41#480×C131C2211yescharacteristic, complemented
42#468×C131—21no—
43#468×C131—21no—
44#467×C131—21no—
45#465×C131—21no—
46#452×C131—21no—
47#451×C131C2211yescharacteristic, complemented
48#450×C131—21no—
49#448×C131C2211yescharacteristic
50#448×C131C2211yescharacteristic, complemented
51#448×C131C2211yescharacteristic, complemented
52#407×C131C2211yescharacteristic, complemented
53C2×C22⋊C8×C131C2211yescharacteristic, complemented
54#398×C131—21no—
55#398×C131C2211yescharacteristic, complemented
56#397×C131—21no—
57#397×C131C2211yescharacteristic, complemented
58#396×C131—21no—
59#395×C131C2211yescharacteristic, complemented
60#394×C131—21no—
61#393×C131C2211yescharacteristic, complemented
62#380×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×C131D411yescharacteristic
77C22×Q8×C131C2311yescharacteristic
78C22×D4×C131—21no—
79C22×D4×C131—21no—
80C22×D4×C131—21no—
81C22×D4×C131D411yescharacteristic
82C22×D4×C131D411yescharacteristic
83C23×C4×C131C2311yescharacteristic
84C2×Q16×C131—21no—
85C2×SD16×C131—21no—
86C2×SD16×C131—21no—
87C2×SD16×C131—21no—
88C2×M16×C131—21no—
89C22×C8×C131—21no—
90#127×C131—21no—
91#126×C131—21no—
92#126×C131—21no—
93#126×C131—21no—
94#126×C131—21no—
95#125×C131—21no—
96#125×C131—21no—
97#124×C131—21no—
98#124×C131—21no—
99#124×C131—21no—
100#123×C131—21no—
101#123×C131—21no—
102#123×C131—21no—
103#123×C131—21no—
104#123×C131—21no—
105#123×C131—21no—
106#123×C131—21no—
107#123×C131—21no—
108#123×C131—21no—
109#123×C131—21no—
110#123×C131—21no—
111#123×C131—21no—
112#123×C131—21no—
113#123×C131—21no—
114C22⋊Q8×C131—21no—
115C22⋊Q8×C131—21no—
116C22⋊Q8×C131—21no—
117C22⋊Q8×C131—21no—
118C22⋊Q8×C131—21no—
119C22⋊Q8×C131—21no—
120C22⋊Q8×C131—21no—
121C22⋊Q8×C131—21no—
122C22⋊Q8×C131—21no—
123C22⋊Q8×C131D411yescharacteristic
124C22⋊Q8×C131C2311yescharacteristic
125#121×C131—21no—
126#121×C131—21no—
127#121×C131—21no—
128#121×C131—21no—
129#121×C131—21no—
130#121×C131—21no—
131#121×C131—21no—
132#121×C131—21no—
133#121×C131—21no—
134#121×C131—21no—
135#121×C131—21no—
136#121×C131—21no—
137#121×C131—21no—
138#121×C131—21no—
139#121×C131—21no—
140#121×C131D411yescharacteristic
141#121×C131D411yescharacteristic
142#121×C131D411yescharacteristic
143#121×C131C2311yescharacteristic
144#121×C131C2311yescharacteristic
145#121×C131C2311yescharacteristic
146#120×C131—21no—
147#120×C131—21no—
148#120×C131—21no—
149#120×C131—21no—
150#120×C131—21no—
151#120×C131—21no—
152#120×C131—21no—
153#120×C131—21no—
154C4×D4×C131—21no—
155C4×D4×C131—21no—
156C4×D4×C131—21no—
157C4×D4×C131—21no—
158C4×D4×C131—21no—
159C4×D4×C131—21no—
160C4×D4×C131—21no—
161C4×D4×C131—21no—
162#117×C131—21no—
163#117×C131D411yescharacteristic
164C2×C4⋊C4×C131—21no—
165C2×C4⋊C4×C131—21no—
166C2×C4⋊C4×C131—21no—
167C2×C4⋊C4×C131—21no—
168C2×C4⋊C4×C131D411yescharacteristic
169C2×C4⋊C4×C131D411yescharacteristic
170C2×C4⋊C4×C131C2311yescharacteristic
171C2×C4⋊C4×C131C2311yescharacteristic
172C2×C22⋊C4×C131—21no—
173C2×C22⋊C4×C131—21no—
174C2×C22⋊C4×C131—21no—
175C2×C22⋊C4×C131—21no—
176C2×C22⋊C4×C131—21no—
177C2×C22⋊C4×C131—21no—
178C2×C22⋊C4×C131—21no—
179C2×C22⋊C4×C131D411yescharacteristic
180C2×C22⋊C4×C131D411yescharacteristic
181C2×C22⋊C4×C131C2311yescharacteristic
182#107×C131—21no—
183#107×C131—21no—
184#107×C131—21no—
185#106×C131—21no—
186#103×C131—21no—
187#103×C131—21no—
188#103×C131—21no—
189#103×C131—21no—
190#103×C131—21no—
191#102×C131—21no—
192#102×C131—21no—
193#102×C131—21no—
194C22⋊C8×C131—21no—
195C22⋊C8×C131—21no—
196C22⋊C8×C131C2311yescharacteristic
197C22⋊C8×C131C2311yescharacteristic
198C22⋊C8×C131C2311yescharacteristic
199C22⋊C8×C131C2311yescharacteristic
200#95×C131—21no—
201#95×C131—21no—
202#95×C131—21no—
203#95×C131—21no—
204#95×C131C2311yescharacteristic
205#95×C131C2311yescharacteristic
206C24×C131—21no—
207C24×C131—21no—
208C24×C131C2×D411yescharacteristic
209C24×C131C2×D411yescharacteristic
210#41×C131—81no—
211#41×C131—81no—
212#41×C131—81no—
213C2×Q8×C131—21no—
214C2×Q8×C131—21no—
215C2×Q8×C131—21no—
216C2×Q8×C131—81no—
217C2×Q8×C131C2×D411yescharacteristic
218C2×D4×C131—21no—
219C2×D4×C131—21no—
220C2×D4×C131—21no—
221C2×D4×C131—21no—
222C2×D4×C131—21no—
223C2×D4×C131—21no—
224C2×D4×C131—21no—
225C2×D4×C131—21no—
226C2×D4×C131—21no—
227C2×D4×C131—21no—
228C2×D4×C131—21no—
229C2×D4×C131—21no—
230C2×D4×C131—21no—
231C2×D4×C131—21no—
232C2×D4×C131—21no—
233C2×D4×C131—21no—
234C2×D4×C131—21no—
235C2×D4×C131—81no—
236C2×D4×C131—81no—
237C2×D4×C131—81no—
238C2×D4×C131—81no—
239C2×D4×C131—81no—
240C2×D4×C131—81no—
241C2×D4×C131—82no—
242C2×D4×C131C2×D411yescharacteristic
243C2×D4×C131C2×D411yescharacteristic
244C2×D4×C131C2×D411yescharacteristic
245C22×C4×C131—21no—
246C22×C4×C131—21no—
247C22×C4×C131—21no—
248C22×C4×C131—21no—
249C22×C4×C131—21no—
250C22×C4×C131—21no—
251C22×C4×C131—21no—
252C22×C4×C131—21no—
253C22×C4×C131—21no—
254C22×C4×C131—21no—
255C22×C4×C131—21no—
256C22×C4×C131—81no—
257C22×C4×C131C2×D411yescharacteristic
258C22×C4×C131C2×D411yescharacteristic
259C22×C4×C131C2×D411yescharacteristic
260C22×C4×C131C2×D411yescharacteristic
261C22×C4×C131C2×D411yescharacteristic
262C22×C4×C131C2×D411yescharacteristic
263C22×C4×C131C2×D411yescharacteristic
264C22×C4×C131C2×D411yescharacteristic
265C22×C4×C131C2411yescharacteristic
266Q16×C131—81no—
267SD16×C131—81no—
268SD16×C131—81no—
269SD16×C131—81no—
270M16×C131—81no—
271C2×C8×C131—21no—
272C2×C8×C131—21no—
273C2×C8×C131—21no—
274C2×C8×C131—21no—
275C2×C8×C131—81no—
276C4⋊C4×C131—21no—
277C4⋊C4×C131—21no—
278C4⋊C4×C131—21no—
279C4⋊C4×C131—21no—
280C4⋊C4×C131—21no—
281C4⋊C4×C131—21no—
282C4⋊C4×C131—21no—
283C4⋊C4×C131—21no—
284C4⋊C4×C131—21no—
285C4⋊C4×C131—21no—
286C4⋊C4×C131—21no—
287C4⋊C4×C131—21no—
288C4⋊C4×C131—21no—
289C4⋊C4×C131—21no—
290C4⋊C4×C131—21no—
291C4⋊C4×C131—41no—
292C4⋊C4×C131—41no—
293C4⋊C4×C131—81no—
294C4⋊C4×C131—81no—
295C4⋊C4×C131—81no—
296C4⋊C4×C131C2×D411yescharacteristic
297C4⋊C4×C131C2×D411yescharacteristic
298C4⋊C4×C131C2×D411yescharacteristic
299C4⋊C4×C131C2×D411yescharacteristic
300C22⋊C4×C131—21no—
301C22⋊C4×C131—21no—
302C22⋊C4×C131—21no—
303C22⋊C4×C131—21no—
304C22⋊C4×C131—21no—
305C22⋊C4×C131—21no—
306C22⋊C4×C131—21no—
307C22⋊C4×C131—21no—
308C22⋊C4×C131—21no—
309C22⋊C4×C131—21no—
310C22⋊C4×C131—21no—
311C22⋊C4×C131—21no—
312C22⋊C4×C131—21no—
313C22⋊C4×C131—21no—
314C22⋊C4×C131—21no—
315C22⋊C4×C131—21no—
316C22⋊C4×C131—21no—
317C22⋊C4×C131—21no—
318C22⋊C4×C131—21no—
319C22⋊C4×C131—21no—
320C22⋊C4×C131—21no—
321C22⋊C4×C131—21no—
322C22⋊C4×C131—21no—
323C22⋊C4×C131—21no—
324C22⋊C4×C131—21no—
325C22⋊C4×C131—41no—
326C22⋊C4×C131—41no—
327C22⋊C4×C131—81no—
328C22⋊C4×C131—81no—
329C22⋊C4×C131—81no—
330C42×C131—21no—
331C42×C131—21no—
332C42×C131—21no—
333C23×C131—21no—
334C23×C131—21no—
335C23×C131—21no—
336C23×C131—21no—
337C23×C131—21no—
338C23×C131—21no—
339C23×C131—21no—
340C23×C131—21no—
341C23×C131—41no—
342C23×C131—41no—
343C23×C131—42no—
344C23×C131—41no—
345C23×C131—41no—
346C23×C131—81no—
347C23×C131—81no—
348C23×C131—81no—
349C23×C131—81no—
350C23×C131—81no—
351C23×C131#12011yescharacteristic
352C23×C131#12011yescharacteristic
353C23×C131C22×D411yescharacteristic
354Q8×C131—41no—
355Q8×C131—41no—
356Q8×C131—41no—
357Q8×C131—41no—
358Q8×C131—41no—
359Q8×C131—81no—
360D4×C131—41no—
361D4×C131—41no—
362D4×C131—41no—
363D4×C131—42no—
364D4×C131—42no—
365D4×C131—41no—
366D4×C131—41no—
367D4×C131—41no—
368D4×C131—41no—
369D4×C131—41no—
370D4×C131—41no—
371D4×C131—81no—
372D4×C131—81no—
373D4×C131—81no—
374D4×C131—81no—
375D4×C131—81no—
376D4×C131—81no—
377D4×C131—81no—
378D4×C131—81no—
379D4×C131—81no—
380D4×C131—81no—
381D4×C131—81no—
382D4×C131—81no—
383C2×C4×C131—21no—
384C2×C4×C131—21no—
385C2×C4×C131—21no—
386C2×C4×C131—21no—
387C2×C4×C131—21no—
388C2×C4×C131—21no—
389C2×C4×C131—21no—
390C2×C4×C131—21no—
391C2×C4×C131—21no—
392C2×C4×C131—21no—
393C2×C4×C131—41no—
394C2×C4×C131—41no—
395C2×C4×C131—41no—
396C2×C4×C131—41no—
397C2×C4×C131—41no—
398C2×C4×C131—41no—
399C2×C4×C131—41no—
400C2×C4×C131—41no—
401C2×C4×C131—41no—
402C2×C4×C131—41no—
403C2×C4×C131—41no—
404C2×C4×C131—41no—
405C2×C4×C131—41no—
406C2×C4×C131—41no—
407C2×C4×C131—41no—
408C2×C4×C131—41no—
409C2×C4×C131—41no—
410C2×C4×C131—41no—
411C2×C4×C131—41no—
412C2×C4×C131—41no—
413C2×C4×C131—81no—
414C2×C4×C131—81no—
415C2×C4×C131—81no—
416C2×C4×C131—81no—
417C2×C4×C131—81no—
418C2×C4×C131—81no—
419C2×C4×C131—81no—
420C2×C4×C131#12011yescharacteristic
421C2×C4×C131#12011yescharacteristic
422C2×C4×C131C22×D411yescharacteristic
423C2×C4×C131C22×D411yescharacteristic
424C8×C131—41no—
425C8×C131—41no—
426C8×C131—41no—
427C8×C131—41no—
428C22×C131—21no—
429C22×C131—21no—
430C22×C131—21no—
431C22×C131—21no—
432C22×C131—21no—
433C22×C131—21no—
434C22×C131—21no—
435C22×C131—21no—
436C22×C131—41no—
437C22×C131—41no—
438C22×C131—41no—
439C22×C131—41no—
440C22×C131—41no—
441C22×C131—41no—
442C22×C131—41no—
443C22×C131—41no—
444C22×C131—41no—
445C22×C131—41no—
446C22×C131—41no—
447C22×C131—41no—
448C22×C131—81no—
449C22×C131—81no—
450C22×C131—81no—
451C22×C131—81no—
452C22×C131—162no—
453C22×C131—162no—
454C22×C131C2×#12011yescharacteristic
455C22×C131#57611yescharacteristic
456C22×C131#57711yescharacteristic
457C4×C131—21no—
458C4×C131—21no—
459C4×C131—21no—
460C4×C131—21no—
461C4×C131—41no—
462C4×C131—41no—
463C4×C131—41no—
464C4×C131—41no—
465C4×C131—41no—
466C4×C131—41no—
467C4×C131—41no—
468C4×C131—41no—
469C4×C131—81no—
470C4×C131—81no—
471C4×C131—81no—
472C4×C131—81no—
473C2×C131—21no—
474C2×C131—21no—
475C2×C131—41no—
476C2×C131—41no—
477C2×C131—81no—
478C2×C131—81no—
479C2×C131—81no—
480C2×C131—81no—
481C2×C131#301211yescharacteristic
482C2×C131#302211yescharacteristic
483C2×C131#302611yescharacteristic
484#18447C13111yesmaximal, characteristic, direct product factor, Sylow
485C131#1844711yescharacteristic, direct product factor, Sylow
486#3534C2×C13111yescharacteristic
487#3193C2×C13111yescharacteristic, complemented
488#3190C2×C13111yescharacteristic, complemented
489#2814C2×C13111yescharacteristic, complemented
490#1612C2×C13111yescharacteristic, complemented
491#1610C2×C13111yescharacteristic, complemented
492#1609C2×C13111yescharacteristic, complemented
493#1607C2×C13111yescharacteristic, complemented
494#1606C2×C13111yescharacteristic, complemented
495#1604C2×C13111yescharacteristic, complemented
496#1603C2×C13111yescharacteristic, complemented
497#1601C2×C13111yescharacteristic, complemented
498#1519C2×C13111yescharacteristic, complemented
499#1513C2×C13111yescharacteristic, complemented
500#1468C2×C13111yescharacteristic, complemented
501#562—21no—
502#560—21no—
503#553—21no—
504#551—21no—
505#546—21no—
506#546—21no—
507#546—21no—
508D42—21no—
509#540—21no—
510#539—21no—
511#539C22×C13111yescharacteristic
512#538—21no—
513#538C22×C13111yescharacteristic
514#537C22×C13111yescharacteristic
515#534—21no—
516#534C22×C13111yescharacteristic
517#525C22×C13111yescharacteristic
518C2×#123C22×C13111yescharacteristic
519C2×C22⋊Q8C22×C13111yescharacteristic, complemented
520C2×#121C22×C13111yescharacteristic
521#485—21no—
522#484—21no—
523#483C22×C13111yescharacteristic, complemented
524#480C22×C13111yescharacteristic
525#480C22×C13111yescharacteristic, complemented
526#480C22×C13111yescharacteristic, complemented
527#468—21no—
528#468—21no—
529#467—21no—
530#465—21no—
531#452—21no—
532#451C22×C13111yescharacteristic, complemented
533#450—21no—
534#448C22×C13111yescharacteristic
535#448C22×C13111yescharacteristic, complemented
536#448C22×C13111yescharacteristic, complemented
537#407C22×C13111yescharacteristic, complemented
538C2×C22⋊C8C22×C13111yescharacteristic, complemented
539#398—21no—
540#398C22×C13111yescharacteristic, complemented
541#397—21no—
542#397C22×C13111yescharacteristic, complemented
543#396—21no—
544#395C22×C13111yescharacteristic, complemented
545#394—21no—
546#393C22×C13111yescharacteristic, complemented
547#380C22×C13111yescharacteristic, complemented
548#328C22×C13111yescharacteristic, complemented
549#328C22×C13111yescharacteristic, complemented
550#327C22×C13111yescharacteristic
551#327C22×C13111yescharacteristic
552#327C22×C13111yescharacteristic, complemented
553#327C22×C13111yescharacteristic, complemented
554#327C22×C13111yescharacteristic, complemented
555#327C22×C13111yescharacteristic, complemented
556#324C22×C13111yescharacteristic, complemented
557#324C22×C13111yescharacteristic, complemented
558#323C22×C13111yescharacteristic, complemented
559#323C22×C13111yescharacteristic, complemented
560C2×#41—21no—
561C2×#41D4×C13111yescharacteristic
562C22×Q8C23×C13111yescharacteristic
563C22×D4—21no—
564C22×D4—21no—
565C22×D4—21no—
566C22×D4D4×C13111yescharacteristic
567C22×D4D4×C13111yescharacteristic
568C23×C4C23×C13111yescharacteristic
569C2×Q16—21no—
570C2×SD16—21no—
571C2×SD16—21no—
572C2×SD16—21no—
573C2×M16—21no—
574C22×C8—21no—
575#127—21no—
576#126—21no—
577#126—21no—
578#126—21no—
579#126—21no—
580#125—21no—
581#125—21no—
582#124—21no—
583#124—21no—
584#124—21no—
585#123—21no—
586#123—21no—
587#123—21no—
588#123—21no—
589#123—21no—
590#123—21no—
591#123—21no—
592#123—21no—
593#123—21no—
594#123—21no—
595#123—21no—
596#123—21no—
597#123—21no—
598#123—21no—
599C22⋊Q8—21no—
600C22⋊Q8—21no—
601C22⋊Q8—21no—
602C22⋊Q8—21no—
603C22⋊Q8—21no—
604C22⋊Q8—21no—
605C22⋊Q8—21no—
606C22⋊Q8—21no—
607C22⋊Q8—21no—
608C22⋊Q8D4×C13111yescharacteristic
609C22⋊Q8C23×C13111yescharacteristic
610#121—21no—
611#121—21no—
612#121—21no—
613#121—21no—
614#121—21no—
615#121—21no—
616#121—21no—
617#121—21no—
618#121—21no—
619#121—21no—
620#121—21no—
621#121—21no—
622#121—21no—
623#121—21no—
624#121—21no—
625#121D4×C13111yescharacteristic
626#121D4×C13111yescharacteristic
627#121D4×C13111yescharacteristic
628#121C23×C13111yescharacteristic
629#121C23×C13111yescharacteristic
630#121C23×C13111yescharacteristic
631#120—21no—
632#120—21no—
633#120—21no—
634#120—21no—
635#120—21no—
636#120—21no—
637#120—21no—
638#120—21no—
639C4×D4—21no—
640C4×D4—21no—
641C4×D4—21no—
642C4×D4—21no—
643C4×D4—21no—
644C4×D4—21no—
645C4×D4—21no—
646C4×D4—21no—
647#117—21no—
648#117D4×C13111yescharacteristic
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4D4×C13111yescharacteristic
654C2×C4⋊C4D4×C13111yescharacteristic
655C2×C4⋊C4C23×C13111yescharacteristic
656C2×C4⋊C4C23×C13111yescharacteristic
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4D4×C13111yescharacteristic
665C2×C22⋊C4D4×C13111yescharacteristic
666C2×C22⋊C4C23×C13111yescharacteristic
667#107—21no—
668#107—21no—
669#107—21no—
670#106—21no—
671#103—21no—
672#103—21no—
673#103—21no—
674#103—21no—
675#103—21no—
676#102—21no—
677#102—21no—
678#102—21no—
679C22⋊C8—21no—
680C22⋊C8—21no—
681C22⋊C8C23×C13111yescharacteristic
682C22⋊C8C23×C13111yescharacteristic
683C22⋊C8C23×C13111yescharacteristic
684C22⋊C8C23×C13111yescharacteristic
685#95—21no—
686#95—21no—
687#95—21no—
688#95—21no—
689#95C23×C13111yescharacteristic
690#95C23×C13111yescharacteristic
691C24—21no—
692C24—21no—
693C24C2×D4×C13111yescharacteristic
694C24C2×D4×C13111yescharacteristic
695#41—81no—
696#41—81no—
697#41—81no—
698C2×Q8—21no—
699C2×Q8—21no—
700C2×Q8—21no—
701C2×Q8—81no—
702C2×Q8C2×D4×C13111yescharacteristic
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—21no—
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—21no—
720C2×D4—81no—
721C2×D4—81no—
722C2×D4—81no—
723C2×D4—81no—
724C2×D4—81no—
725C2×D4—81no—
726C2×D4—82no—
727C2×D4C2×D4×C13111yescharacteristic
728C2×D4C2×D4×C13111yescharacteristic
729C2×D4C2×D4×C13111yescharacteristic
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—81no—
742C22×C4C2×D4×C13111yescharacteristic
743C22×C4C2×D4×C13111yescharacteristic
744C22×C4C2×D4×C13111yescharacteristic
745C22×C4C2×D4×C13111yescharacteristic
746C22×C4C2×D4×C13111yescharacteristic
747C22×C4C2×D4×C13111yescharacteristic
748C22×C4C2×D4×C13111yescharacteristic
749C22×C4C2×D4×C13111yescharacteristic
750C22×C4C24×C13111yescharacteristic
751Q16—81no—
752SD16—81no—
753SD16—81no—
754SD16—81no—
755M16—81no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8—81no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—21no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—21no—
771C4⋊C4—21no—
772C4⋊C4—21no—
773C4⋊C4—21no—
774C4⋊C4—21no—
775C4⋊C4—21no—
776C4⋊C4—41no—
777C4⋊C4—41no—
778C4⋊C4—81no—
779C4⋊C4—81no—
780C4⋊C4—81no—
781C4⋊C4C2×D4×C13111yescharacteristic
782C4⋊C4C2×D4×C13111yescharacteristic
783C4⋊C4C2×D4×C13111yescharacteristic
784C4⋊C4C2×D4×C13111yescharacteristic
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—21no—
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—21no—
799C22⋊C4—21no—
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—41no—
811C22⋊C4—41no—
812C22⋊C4—81no—
813C22⋊C4—81no—
814C22⋊C4—81no—
815C42—21no—
816C42—21no—
817C42—21no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—21no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—41no—
827C23—41no—
828C23—42no—
829C23—41no—
830C23—41no—
831C23—81no—
832C23—81no—
833C23—81no—
834C23—81no—
835C23—81no—
836C23#120×C13111yescharacteristic
837C23#120×C13111yescharacteristic
838C23C22×D4×C13111yescharacteristic
839Q8—41no—
840Q8—41no—
841Q8—41no—
842Q8—41no—
843Q8—41no—
844Q8—81no—
845D4—41no—
846D4—41no—
847D4—41no—
848D4—42no—
849D4—42no—
850D4—41no—
851D4—41no—
852D4—41no—
853D4—41no—
854D4—41no—
855D4—41no—
856D4—81no—
857D4—81no—
858D4—81no—
859D4—81no—
860D4—81no—
861D4—81no—
862D4—81no—
863D4—81no—
864D4—81no—
865D4—81no—
866D4—81no—
867D4—81no—
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—81no—
899C2×C4—81no—
900C2×C4—81no—
901C2×C4—81no—
902C2×C4—81no—
903C2×C4—81no—
904C2×C4—81no—
905C2×C4#120×C13111yescharacteristic
906C2×C4#120×C13111yescharacteristic
907C2×C4C22×D4×C13111yescharacteristic
908C2×C4C22×D4×C13111yescharacteristic
909C8—41no—
910C8—41no—
911C8—41no—
912C8—41no—
913C22—21no—
914C22—21no—
915C22—21no—
916C22—21no—
917C22—21no—
918C22—21no—
919C22—21no—
920C22—21no—
921C22—41no—
922C22—41no—
923C22—41no—
924C22—41no—
925C22—41no—
926C22—41no—
927C22—41no—
928C22—41no—
929C22—41no—
930C22—41no—
931C22—41no—
932C22—41no—
933C22—81no—
934C22—81no—
935C22—81no—
936C22—81no—
937C22—162no—
938C22—162no—
939C22C2×#120×C13111yescharacteristic
940C22#576×C13111yescharacteristic
941C22#577×C13111yescharacteristic
942C4—21no—
943C4—21no—
944C4—21no—
945C4—21no—
946C4—41no—
947C4—41no—
948C4—41no—
949C4—41no—
950C4—41no—
951C4—41no—
952C4—41no—
953C4—41no—
954C4—81no—
955C4—81no—
956C4—81no—
957C4—81no—
958C2—21no—
959C2—21no—
960C2—41no—
961C2—41no—
962C2—81no—
963C2—81no—
964C2—81no—
965C2—81no—
966C2#3012×C13111yescharacteristic
967C2#3022×C13111yescharacteristic
968C2#3026×C13111yescharacteristic
subgroupG/H
center, socleC22×C131C2×#120
commutator, Frattini, cosocleC22×C4C24×C131
prime radical#3534×C131C2
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
2. #3193×C131C2semidirect
3. #3190×C131C2semidirect
4. #2814×C131C2semidirect
5. #1612×C131C2semidirect
6. #1610×C131C2semidirect
7. #1609×C131C2semidirect
8. #1607×C131C2semidirect
9. #1606×C131C2semidirect
10. #1604×C131C2semidirect
11. #1603×C131C2semidirect
12. #1601×C131C2semidirect
13. #1519×C131C2semidirect
14. #1513×C131C2semidirect
15. #1468×C131C2semidirect
34. C2×C22⋊Q8×C131C22semidirect
38. #483×C131C22semidirect
40. #480×C131C22semidirect
41. #480×C131C22semidirect
47. #451×C131C22semidirect
50. #448×C131C22semidirect
51. #448×C131C22semidirect
52. #407×C131C22semidirect
53. C2×C22⋊C8×C131C22semidirect
55. #398×C131C22semidirect
57. #397×C131C22semidirect
59. #395×C131C22semidirect
61. #393×C131C22semidirect
62. #380×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
484. #18447C131direct (N × H)
485. C131#18447direct (N × H)
487. #3193C2×C131semidirect
488. #3190C2×C131semidirect
489. #2814C2×C131semidirect
490. #1612C2×C131semidirect
491. #1610C2×C131semidirect
492. #1609C2×C131semidirect
493. #1607C2×C131semidirect
494. #1606C2×C131semidirect
495. #1604C2×C131semidirect
496. #1603C2×C131semidirect
497. #1601C2×C131semidirect
498. #1519C2×C131semidirect
499. #1513C2×C131semidirect
500. #1468C2×C131semidirect
519. C2×C22⋊Q8C22×C131semidirect
523. #483C22×C131semidirect
525. #480C22×C131semidirect
526. #480C22×C131semidirect
532. #451C22×C131semidirect
535. #448C22×C131semidirect
536. #448C22×C131semidirect
537. #407C22×C131semidirect
538. C2×C22⋊C8C22×C131semidirect
540. #398C22×C131semidirect
542. #397C22×C131semidirect
544. #395C22×C131semidirect
546. #393C22×C131semidirect
547. #380C22×C131semidirect
548. #328C22×C131semidirect
549. #328C22×C131semidirect
552. #327C22×C131semidirect
553. #327C22×C131semidirect
554. #327C22×C131semidirect
555. #327C22×C131semidirect
556. #324C22×C131semidirect
557. #324C22×C131semidirect
558. #323C22×C131semidirect
559. #323C22×C131semidirect

Maximal subgroups

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

subgroupindex
#3534×C1312
#3193×C1312
#3190×C1312
#2814×C1312
#1612×C1312
#1610×C1312
#1609×C1312
#1607×C1312
#1606×C1312
#1604×C1312
#1603×C1312
#1601×C1312
#1519×C1312
#1513×C1312
#1468×C1312
#18447131