Finite Group Databasebeta

← C31×#18249 #21475008

Subgroups — C31×#18249 #21475008

Order 7936.

936 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3560C211yesmaximal, characteristic
2C31×#3112C211yesmaximal, characteristic, complemented
3C31×#3108C211yesmaximal, characteristic, complemented
4C31×#2637C211yesmaximal, characteristic, complemented
5C31×#1612C211yesmaximal, characteristic, complemented
6C31×#1610C211yesmaximal, characteristic, complemented
7C31×#1609C211yesmaximal, characteristic, complemented
8C31×#1607C211yesmaximal, characteristic, complemented
9C31×#1606C211yesmaximal, characteristic, complemented
10C31×#1604C211yesmaximal, characteristic, complemented
11C31×#1603C211yesmaximal, characteristic, complemented
12C31×#1601C211yesmaximal, characteristic, complemented
13C31×#1517C211yesmaximal, characteristic, complemented
14C31×#1512C211yesmaximal, characteristic, complemented
15C31×#1473C211yesmaximal, characteristic, complemented
16C31×#563—21no—
17C31×#560—21no—
18C31×#553—21no—
19C31×#553—21no—
20C31×#551—21no—
21C31×#547—21no—
22C31×#546—21no—
23C31×#546—21no—
24C31×#542—21no—
25C31×#539—21no—
26C31×#539C2211yescharacteristic
27C31×#538—21no—
28C31×#538—21no—
29C31×#538C2211yescharacteristic
30C31×#537C2211yescharacteristic
31C31×#534C2211yescharacteristic
32C31×#532C2211yescharacteristic
33C31×#529C2211yescharacteristic
34C2×C31×#126C2211yescharacteristic
35C2×C4×Q8×C31C2211yescharacteristic, complemented
36C31×#483C2211yescharacteristic, complemented
37C31×#480C2211yescharacteristic
38C31×#480C2211yescharacteristic
39C31×#480C2211yescharacteristic, complemented
40C31×#479—21no—
41C31×#477—21no—
42C31×#464—21no—
43C31×#460—21no—
44C31×#451C2211yescharacteristic, complemented
45C31×#448C2211yescharacteristic
46C31×#448C2211yescharacteristic
47C31×#448C2211yescharacteristic, complemented
48C31×#440—21no—
49C31×#440—21no—
50C4×Q16×C31—21no—
51C4×SD16×C31—21no—
52C31×#432C2211yescharacteristic, complemented
53C31×#431C2211yescharacteristic, complemented
54C31×#398—21no—
55C31×#398C2211yescharacteristic, complemented
56C31×#397C2211yescharacteristic
57C31×#396—21no—
58C31×#395C2211yescharacteristic, complemented
59C31×#393C2211yescharacteristic
60C31×#388—21no—
61C31×#387—21no—
62C31×#382C2211yescharacteristic, complemented
63C31×#328C2211yescharacteristic, complemented
64C31×#328C2211yescharacteristic, complemented
65C31×#327C2211yescharacteristic
66C31×#327C2211yescharacteristic
67C31×#327C2211yescharacteristic
68C31×#327C2211yescharacteristic
69C31×#327C2211yescharacteristic, complemented
70C31×#327C2211yescharacteristic, complemented
71C31×#324C2211yescharacteristic, complemented
72C31×#324C2211yescharacteristic, complemented
73C31×#323C2211yescharacteristic
74C31×#323C2211yescharacteristic
75C2×#41×C31—21no—
76C2×#41×C31—21no—
77C22×Q8×C31C2311yescharacteristic
78C22×D4×C31—21no—
79C2×Q16×C31—21no—
80C2×SD16×C31—21no—
81C2×SD16×C31—21no—
82C2×SD16×C31—21no—
83C31×C4⋊Q8—21no—
84C31×C4⋊Q8D411yescharacteristic
85C31×#127D411yescharacteristic
86C31×#126—21no—
87C31×#126—21no—
88C31×#126—21no—
89C31×#126—21no—
90C31×#126—21no—
91C31×#126—21no—
92C31×#126—21no—
93C31×#126—21no—
94C31×#126—21no—
95C31×#125—21no—
96C31×#125—21no—
97C31×#125D411yescharacteristic
98C31×#124—21no—
99C31×#124—21no—
100C31×#124—21no—
101C31×#124—21no—
102C31×#124D411yescharacteristic
103C31×#123—21no—
104C31×#123—21no—
105C31×#123—21no—
106C31×#123—21no—
107C31×#123—21no—
108C31×#123—21no—
109C31×#123—21no—
110C31×#123—21no—
111C31×#123—21no—
112C31×#123—21no—
113C31×#123—21no—
114C31×#123—21no—
115C31×C22⋊Q8—21no—
116C31×C22⋊Q8—21no—
117C31×C22⋊Q8—21no—
118C31×C22⋊Q8—21no—
119C31×C22⋊Q8—21no—
120C31×C22⋊Q8—21no—
121C31×C22⋊Q8—21no—
122C31×C22⋊Q8C2311yescharacteristic
123C31×#121—21no—
124C31×#121—21no—
125C31×#121—21no—
126C31×#121—21no—
127C31×#121—21no—
128C31×#121—21no—
129C31×#121—21no—
130C31×#121—21no—
131C31×#121—21no—
132C31×#121—21no—
133C31×#121—21no—
134C31×#121—21no—
135C31×#121C2311yescharacteristic
136C31×#121C2311yescharacteristic
137C31×#121C2311yescharacteristic
138C31×#120—21no—
139C31×#120—21no—
140C31×#120—21no—
141C31×#120—21no—
142C31×#120—21no—
143C4×Q8×C31—21no—
144C4×Q8×C31—21no—
145C4×Q8×C31—21no—
146C4×Q8×C31—21no—
147C4×Q8×C31D411yescharacteristic
148C4×D4×C31—21no—
149C4×D4×C31—21no—
150C4×D4×C31—21no—
151C4×D4×C31—21no—
152C4×D4×C31—21no—
153C4×D4×C31—21no—
154C4×D4×C31—21no—
155C4×D4×C31—21no—
156C4×D4×C31D411yescharacteristic
157C4×D4×C31D411yescharacteristic
158C4×D4×C31D411yescharacteristic
159C31×#117—21no—
160C31×#117—21no—
161C2×C4⋊C4×C31—21no—
162C2×C4⋊C4×C31—21no—
163C2×C4⋊C4×C31—21no—
164C2×C4⋊C4×C31—21no—
165C2×C4⋊C4×C31—21no—
166C2×C4⋊C4×C31D411yescharacteristic
167C2×C4⋊C4×C31D411yescharacteristic
168C2×C4⋊C4×C31C2311yescharacteristic
169C2×C4⋊C4×C31C2311yescharacteristic
170C2×C22⋊C4×C31—21no—
171C2×C22⋊C4×C31—21no—
172C2×C22⋊C4×C31—21no—
173C2×C22⋊C4×C31—21no—
174C2×C22⋊C4×C31D411yescharacteristic
175C2×C22⋊C4×C31D411yescharacteristic
176C2×C22⋊C4×C31C2311yescharacteristic
177C2×C42×C31—21no—
178C2×C42×C31C2311yescharacteristic
179C31×#107—21no—
180C31×#107—21no—
181C31×#107—21no—
182C31×#106—21no—
183C31×C4⋊C8—21no—
184C31×C4⋊C8—21no—
185C31×#103—21no—
186C31×#103—21no—
187C31×#103—21no—
188C31×#103—21no—
189C31×#103—21no—
190C31×#102—21no—
191C31×#102—21no—
192C31×#102—21no—
193C31×C22⋊C8C2311yescharacteristic
194C31×C22⋊C8C2311yescharacteristic
195C31×C22⋊C8C2311yescharacteristic
196C31×C22⋊C8C2311yescharacteristic
197C31×#97—21no—
198C4×C8×C31—21no—
199C31×#95—21no—
200C31×#95—21no—
201C31×#95—21no—
202C31×#95—21no—
203C31×#95—21no—
204C31×#95C2311yescharacteristic
205C31×#95C2311yescharacteristic
206C24×C31—21no—
207C24×C31C2×D411yescharacteristic
208#41×C31—81no—
209#41×C31—81no—
210#41×C31—81no—
211#41×C31—81no—
212C2×Q8×C31—21no—
213C2×Q8×C31—21no—
214C2×Q8×C31—21no—
215C2×Q8×C31—21no—
216C2×Q8×C31—42no—
217C2×Q8×C31C2×D411yescharacteristic
218C2×D4×C31—21no—
219C2×D4×C31—21no—
220C2×D4×C31—21no—
221C2×D4×C31—21no—
222C2×D4×C31—21no—
223C2×D4×C31—21no—
224C2×D4×C31—21no—
225C2×D4×C31—21no—
226C2×D4×C31—21no—
227C2×D4×C31—21no—
228C2×D4×C31—21no—
229C2×D4×C31—21no—
230C2×D4×C31—81no—
231C2×D4×C31—81no—
232C2×D4×C31C2×D411yescharacteristic
233C2×D4×C31C2×D411yescharacteristic
234C2×D4×C31C2×D411yescharacteristic
235C22×C4×C31—21no—
236C22×C4×C31—21no—
237C22×C4×C31—21no—
238C22×C4×C31—21no—
239C22×C4×C31—21no—
240C22×C4×C31—21no—
241C22×C4×C31—21no—
242C22×C4×C31—21no—
243C22×C4×C31—21no—
244C22×C4×C31—21no—
245C22×C4×C31—21no—
246C22×C4×C31—21no—
247C22×C4×C31C2×D411yescharacteristic
248C22×C4×C31C2×D411yescharacteristic
249C22×C4×C31C2×D411yescharacteristic
250C22×C4×C31C2×D411yescharacteristic
251C22×C4×C31C2×D411yescharacteristic
252C22×C4×C31C2411yescharacteristic
253Q16×C31—42no—
254SD16×C31—42no—
255SD16×C31—42no—
256SD16×C31—42no—
257C2×C8×C31—21no—
258C2×C8×C31—21no—
259C2×C8×C31—21no—
260C2×C8×C31—21no—
261C4⋊C4×C31—21no—
262C4⋊C4×C31—21no—
263C4⋊C4×C31—21no—
264C4⋊C4×C31—21no—
265C4⋊C4×C31—21no—
266C4⋊C4×C31—21no—
267C4⋊C4×C31—21no—
268C4⋊C4×C31—21no—
269C4⋊C4×C31—21no—
270C4⋊C4×C31—21no—
271C4⋊C4×C31—21no—
272C4⋊C4×C31—21no—
273C4⋊C4×C31—21no—
274C4⋊C4×C31—21no—
275C4⋊C4×C31—21no—
276C4⋊C4×C31—21no—
277C4⋊C4×C31—21no—
278C4⋊C4×C31—21no—
279C4⋊C4×C31—21no—
280C4⋊C4×C31—42no—
281C4⋊C4×C31—41no—
282C4⋊C4×C31—41no—
283C4⋊C4×C31—81no—
284C4⋊C4×C31—81no—
285C4⋊C4×C31C2×D411yescharacteristic
286C4⋊C4×C31C2×D411yescharacteristic
287C4⋊C4×C31C2×D411yescharacteristic
288C4⋊C4×C31C2×D411yescharacteristic
289C22⋊C4×C31—21no—
290C22⋊C4×C31—21no—
291C22⋊C4×C31—21no—
292C22⋊C4×C31—21no—
293C22⋊C4×C31—21no—
294C22⋊C4×C31—21no—
295C22⋊C4×C31—21no—
296C22⋊C4×C31—21no—
297C22⋊C4×C31—21no—
298C22⋊C4×C31—21no—
299C22⋊C4×C31—21no—
300C22⋊C4×C31—21no—
301C22⋊C4×C31—21no—
302C22⋊C4×C31—21no—
303C22⋊C4×C31—21no—
304C22⋊C4×C31—21no—
305C22⋊C4×C31—21no—
306C22⋊C4×C31—21no—
307C22⋊C4×C31—21no—
308C22⋊C4×C31—21no—
309C22⋊C4×C31—21no—
310C22⋊C4×C31—21no—
311C22⋊C4×C31—21no—
312C22⋊C4×C31—21no—
313C22⋊C4×C31—21no—
314C22⋊C4×C31—42no—
315C22⋊C4×C31—81no—
316C42×C31—21no—
317C42×C31—21no—
318C42×C31—21no—
319C42×C31—41no—
320C42×C31—41no—
321C42×C31C2×D411yescharacteristic
322C42×C31C2×D411yescharacteristic
323C42×C31C2×D411yescharacteristic
324C42×C31C2×D411yescharacteristic
325#18249C3111yesmaximal, characteristic, direct product factor, Sylow
326C23×C31—21no—
327C23×C31—21no—
328C23×C31—21no—
329C23×C31—21no—
330C23×C31—21no—
331C23×C31—21no—
332C23×C31—41no—
333C23×C31—41no—
334C23×C31—81no—
335C23×C31—81no—
336C23×C31—81no—
337C23×C31C22×D411yescharacteristic
338Q8×C31—22no—
339Q8×C31—22no—
340Q8×C31—41no—
341Q8×C31—41no—
342Q8×C31—41no—
343Q8×C31—81no—
344Q8×C31—81no—
345D4×C31—41no—
346D4×C31—41no—
347D4×C31—41no—
348D4×C31—41no—
349D4×C31—41no—
350D4×C31—41no—
351D4×C31—41no—
352D4×C31—41no—
353D4×C31—41no—
354D4×C31—81no—
355D4×C31—81no—
356D4×C31—81no—
357D4×C31—81no—
358D4×C31—81no—
359D4×C31—81no—
360D4×C31—81no—
361D4×C31—81no—
362D4×C31—81no—
363C2×C4×C31—21no—
364C2×C4×C31—21no—
365C2×C4×C31—22no—
366C2×C4×C31—21no—
367C2×C4×C31—21no—
368C2×C4×C31—21no—
369C2×C4×C31—21no—
370C2×C4×C31—21no—
371C2×C4×C31—21no—
372C2×C4×C31—21no—
373C2×C4×C31—21no—
374C2×C4×C31—21no—
375C2×C4×C31—21no—
376C2×C4×C31—41no—
377C2×C4×C31—41no—
378C2×C4×C31—41no—
379C2×C4×C31—41no—
380C2×C4×C31—41no—
381C2×C4×C31—41no—
382C2×C4×C31—41no—
383C2×C4×C31—41no—
384C2×C4×C31—41no—
385C2×C4×C31—41no—
386C2×C4×C31—41no—
387C2×C4×C31—41no—
388C2×C4×C31—41no—
389C2×C4×C31—41no—
390C2×C4×C31—41no—
391C2×C4×C31—81no—
392C2×C4×C31—81no—
393C2×C4×C31—81no—
394C2×C4×C31—81no—
395C2×C4×C31—81no—
396C2×C4×C31—81no—
397C2×C4×C31—81no—
398C2×C4×C31—81no—
399C2×C4×C31#12011yescharacteristic
400C2×C4×C31#12011yescharacteristic
401C2×C4×C31#12011yescharacteristic
402C2×C4×C31#12011yescharacteristic
403C2×C4×C31C22×D411yescharacteristic
404C2×C4×C31C22×D411yescharacteristic
405C8×C31—41no—
406C8×C31—41no—
407C8×C31—41no—
408C8×C31—41no—
409#3560C2×C3111yescharacteristic
410#3112C2×C3111yescharacteristic, complemented
411#3108C2×C3111yescharacteristic, complemented
412#2637C2×C3111yescharacteristic, complemented
413#1612C2×C3111yescharacteristic, complemented
414#1610C2×C3111yescharacteristic, complemented
415#1609C2×C3111yescharacteristic, complemented
416#1607C2×C3111yescharacteristic, complemented
417#1606C2×C3111yescharacteristic, complemented
418#1604C2×C3111yescharacteristic, complemented
419#1603C2×C3111yescharacteristic, complemented
420#1601C2×C3111yescharacteristic, complemented
421#1517C2×C3111yescharacteristic, complemented
422#1512C2×C3111yescharacteristic, complemented
423#1473C2×C3111yescharacteristic, complemented
424C22×C31—21no—
425C22×C31—21no—
426C22×C31—41no—
427C22×C31—41no—
428C22×C31—41no—
429C22×C31—41no—
430C22×C31—41no—
431C22×C31—41no—
432C22×C31—41no—
433C22×C31—41no—
434C22×C31—41no—
435C22×C31—41no—
436C22×C31—41no—
437C22×C31—41no—
438C22×C31—81no—
439C22×C31—81no—
440C22×C31—162no—
441C22×C31C2×#12011yescharacteristic
442C22×C31#57611yescharacteristic
443C22×C31#57711yescharacteristic
444C4×C31—21no—
445C4×C31—21no—
446C4×C31—21no—
447C4×C31—21no—
448C4×C31—21no—
449C4×C31—21no—
450C4×C31—41no—
451C4×C31—41no—
452C4×C31—41no—
453C4×C31—41no—
454C4×C31—41no—
455C4×C31—41no—
456C4×C31—42no—
457C4×C31—41no—
458C4×C31—41no—
459C4×C31—81no—
460C4×C31—81no—
461C4×C31—81no—
462#563—21no—
463#560—21no—
464#553—21no—
465#553—21no—
466#551—21no—
467#547—21no—
468#546—21no—
469#546—21no—
470#542—21no—
471#539—21no—
472#539C22×C3111yescharacteristic
473#538—21no—
474#538—21no—
475#538C22×C3111yescharacteristic
476#537C22×C3111yescharacteristic
477#534C22×C3111yescharacteristic
478#532C22×C3111yescharacteristic
479#529C22×C3111yescharacteristic
480C2×#126C22×C3111yescharacteristic
481C2×C4×Q8C22×C3111yescharacteristic, complemented
482#483C22×C3111yescharacteristic, complemented
483#480C22×C3111yescharacteristic
484#480C22×C3111yescharacteristic
485#480C22×C3111yescharacteristic, complemented
486#479—21no—
487#477—21no—
488#464—21no—
489#460—21no—
490#451C22×C3111yescharacteristic, complemented
491#448C22×C3111yescharacteristic
492#448C22×C3111yescharacteristic
493#448C22×C3111yescharacteristic, complemented
494#440—21no—
495#440—21no—
496C4×Q16—21no—
497C4×SD16—21no—
498#432C22×C3111yescharacteristic, complemented
499#431C22×C3111yescharacteristic, complemented
500#398—21no—
501#398C22×C3111yescharacteristic, complemented
502#397C22×C3111yescharacteristic
503#396—21no—
504#395C22×C3111yescharacteristic, complemented
505#393C22×C3111yescharacteristic
506#388—21no—
507#387—21no—
508#382C22×C3111yescharacteristic, complemented
509#328C22×C3111yescharacteristic, complemented
510#328C22×C3111yescharacteristic, complemented
511#327C22×C3111yescharacteristic
512#327C22×C3111yescharacteristic
513#327C22×C3111yescharacteristic
514#327C22×C3111yescharacteristic
515#327C22×C3111yescharacteristic, complemented
516#327C22×C3111yescharacteristic, complemented
517#324C22×C3111yescharacteristic, complemented
518#324C22×C3111yescharacteristic, complemented
519#323C22×C3111yescharacteristic
520#323C22×C3111yescharacteristic
521C2×C31—21no—
522C2×C31—21no—
523C2×C31—81no—
524C2×C31—81no—
525C2×C31—81no—
526C2×C31—81no—
527C2×C31#301211yescharacteristic
528C2×C31#302211yescharacteristic
529C2×C31#302511yescharacteristic
530C2×#41—21no—
531C2×#41—21no—
532C22×Q8C23×C3111yescharacteristic
533C22×D4—21no—
534C2×Q16—21no—
535C2×SD16—21no—
536C2×SD16—21no—
537C2×SD16—21no—
538C4⋊Q8—21no—
539C4⋊Q8D4×C3111yescharacteristic
540#127D4×C3111yescharacteristic
541#126—21no—
542#126—21no—
543#126—21no—
544#126—21no—
545#126—21no—
546#126—21no—
547#126—21no—
548#126—21no—
549#126—21no—
550#125—21no—
551#125—21no—
552#125D4×C3111yescharacteristic
553#124—21no—
554#124—21no—
555#124—21no—
556#124—21no—
557#124D4×C3111yescharacteristic
558#123—21no—
559#123—21no—
560#123—21no—
561#123—21no—
562#123—21no—
563#123—21no—
564#123—21no—
565#123—21no—
566#123—21no—
567#123—21no—
568#123—21no—
569#123—21no—
570C22⋊Q8—21no—
571C22⋊Q8—21no—
572C22⋊Q8—21no—
573C22⋊Q8—21no—
574C22⋊Q8—21no—
575C22⋊Q8—21no—
576C22⋊Q8—21no—
577C22⋊Q8C23×C3111yescharacteristic
578#121—21no—
579#121—21no—
580#121—21no—
581#121—21no—
582#121—21no—
583#121—21no—
584#121—21no—
585#121—21no—
586#121—21no—
587#121—21no—
588#121—21no—
589#121—21no—
590#121C23×C3111yescharacteristic
591#121C23×C3111yescharacteristic
592#121C23×C3111yescharacteristic
593#120—21no—
594#120—21no—
595#120—21no—
596#120—21no—
597#120—21no—
598C4×Q8—21no—
599C4×Q8—21no—
600C4×Q8—21no—
601C4×Q8—21no—
602C4×Q8D4×C3111yescharacteristic
603C4×D4—21no—
604C4×D4—21no—
605C4×D4—21no—
606C4×D4—21no—
607C4×D4—21no—
608C4×D4—21no—
609C4×D4—21no—
610C4×D4—21no—
611C4×D4D4×C3111yescharacteristic
612C4×D4D4×C3111yescharacteristic
613C4×D4D4×C3111yescharacteristic
614#117—21no—
615#117—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4D4×C3111yescharacteristic
622C2×C4⋊C4D4×C3111yescharacteristic
623C2×C4⋊C4C23×C3111yescharacteristic
624C2×C4⋊C4C23×C3111yescharacteristic
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4D4×C3111yescharacteristic
630C2×C22⋊C4D4×C3111yescharacteristic
631C2×C22⋊C4C23×C3111yescharacteristic
632C2×C42—21no—
633C2×C42C23×C3111yescharacteristic
634#107—21no—
635#107—21no—
636#107—21no—
637#106—21no—
638C4⋊C8—21no—
639C4⋊C8—21no—
640#103—21no—
641#103—21no—
642#103—21no—
643#103—21no—
644#103—21no—
645#102—21no—
646#102—21no—
647#102—21no—
648C22⋊C8C23×C3111yescharacteristic
649C22⋊C8C23×C3111yescharacteristic
650C22⋊C8C23×C3111yescharacteristic
651C22⋊C8C23×C3111yescharacteristic
652#97—21no—
653C4×C8—21no—
654#95—21no—
655#95—21no—
656#95—21no—
657#95—21no—
658#95—21no—
659#95C23×C3111yescharacteristic
660#95C23×C3111yescharacteristic
661C31#1824911yescharacteristic, direct product factor, Sylow
662C24—21no—
663C24C2×D4×C3111yescharacteristic
664#41—81no—
665#41—81no—
666#41—81no—
667#41—81no—
668C2×Q8—21no—
669C2×Q8—21no—
670C2×Q8—21no—
671C2×Q8—21no—
672C2×Q8—42no—
673C2×Q8C2×D4×C3111yescharacteristic
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—81no—
687C2×D4—81no—
688C2×D4C2×D4×C3111yescharacteristic
689C2×D4C2×D4×C3111yescharacteristic
690C2×D4C2×D4×C3111yescharacteristic
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4C2×D4×C3111yescharacteristic
704C22×C4C2×D4×C3111yescharacteristic
705C22×C4C2×D4×C3111yescharacteristic
706C22×C4C2×D4×C3111yescharacteristic
707C22×C4C2×D4×C3111yescharacteristic
708C22×C4C24×C3111yescharacteristic
709Q16—42no—
710SD16—42no—
711SD16—42no—
712SD16—42no—
713C2×C8—21no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4—42no—
737C4⋊C4—41no—
738C4⋊C4—41no—
739C4⋊C4—81no—
740C4⋊C4—81no—
741C4⋊C4C2×D4×C3111yescharacteristic
742C4⋊C4C2×D4×C3111yescharacteristic
743C4⋊C4C2×D4×C3111yescharacteristic
744C4⋊C4C2×D4×C3111yescharacteristic
745C22⋊C4—21no—
746C22⋊C4—21no—
747C22⋊C4—21no—
748C22⋊C4—21no—
749C22⋊C4—21no—
750C22⋊C4—21no—
751C22⋊C4—21no—
752C22⋊C4—21no—
753C22⋊C4—21no—
754C22⋊C4—21no—
755C22⋊C4—21no—
756C22⋊C4—21no—
757C22⋊C4—21no—
758C22⋊C4—21no—
759C22⋊C4—21no—
760C22⋊C4—21no—
761C22⋊C4—21no—
762C22⋊C4—21no—
763C22⋊C4—21no—
764C22⋊C4—21no—
765C22⋊C4—21no—
766C22⋊C4—21no—
767C22⋊C4—21no—
768C22⋊C4—21no—
769C22⋊C4—21no—
770C22⋊C4—42no—
771C22⋊C4—81no—
772C42—21no—
773C42—21no—
774C42—21no—
775C42—41no—
776C42—41no—
777C42C2×D4×C3111yescharacteristic
778C42C2×D4×C3111yescharacteristic
779C42C2×D4×C3111yescharacteristic
780C42C2×D4×C3111yescharacteristic
781C23—21no—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—41no—
788C23—41no—
789C23—81no—
790C23—81no—
791C23—81no—
792C23C22×D4×C3111yescharacteristic
793Q8—22no—
794Q8—22no—
795Q8—41no—
796Q8—41no—
797Q8—41no—
798Q8—81no—
799Q8—81no—
800D4—41no—
801D4—41no—
802D4—41no—
803D4—41no—
804D4—41no—
805D4—41no—
806D4—41no—
807D4—41no—
808D4—41no—
809D4—81no—
810D4—81no—
811D4—81no—
812D4—81no—
813D4—81no—
814D4—81no—
815D4—81no—
816D4—81no—
817D4—81no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—22no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—81no—
847C2×C4—81no—
848C2×C4—81no—
849C2×C4—81no—
850C2×C4—81no—
851C2×C4—81no—
852C2×C4—81no—
853C2×C4—81no—
854C2×C4C31×#12011yescharacteristic
855C2×C4C31×#12011yescharacteristic
856C2×C4C31×#12011yescharacteristic
857C2×C4C31×#12011yescharacteristic
858C2×C4C22×D4×C3111yescharacteristic
859C2×C4C22×D4×C3111yescharacteristic
860C8—41no—
861C8—41no—
862C8—41no—
863C8—41no—
864C22—21no—
865C22—21no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—41no—
871C22—41no—
872C22—41no—
873C22—41no—
874C22—41no—
875C22—41no—
876C22—41no—
877C22—41no—
878C22—81no—
879C22—81no—
880C22—162no—
881C22C2×C31×#12011yescharacteristic
882C22C31×#57611yescharacteristic
883C22C31×#57711yescharacteristic
884C4—21no—
885C4—21no—
886C4—21no—
887C4—21no—
888C4—21no—
889C4—21no—
890C4—41no—
891C4—41no—
892C4—41no—
893C4—41no—
894C4—41no—
895C4—41no—
896C4—42no—
897C4—41no—
898C4—41no—
899C4—81no—
900C4—81no—
901C4—81no—
902C2—21no—
903C2—21no—
904C2—81no—
905C2—81no—
906C2—81no—
907C2—81no—
908C2C31×#301211yescharacteristic
909C2C31×#302211yescharacteristic
910C2C31×#302511yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC31×#3560C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C2×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#3112C2semidirect
3. C31×#3108C2semidirect
4. C31×#2637C2semidirect
5. C31×#1612C2semidirect
6. C31×#1610C2semidirect
7. C31×#1609C2semidirect
8. C31×#1607C2semidirect
9. C31×#1606C2semidirect
10. C31×#1604C2semidirect
11. C31×#1603C2semidirect
12. C31×#1601C2semidirect
13. C31×#1517C2semidirect
14. C31×#1512C2semidirect
15. C31×#1473C2semidirect
35. C2×C4×Q8×C31C22semidirect
36. C31×#483C22semidirect
39. C31×#480C22semidirect
44. C31×#451C22semidirect
47. C31×#448C22semidirect
52. C31×#432C22semidirect
53. C31×#431C22semidirect
55. C31×#398C22semidirect
58. C31×#395C22semidirect
62. C31×#382C22semidirect
63. C31×#328C22semidirect
64. C31×#328C22semidirect
69. C31×#327C22semidirect
70. C31×#327C22semidirect
71. C31×#324C22semidirect
72. C31×#324C22semidirect
325. #18249C31direct (N × H)
410. #3112C2×C31semidirect
411. #3108C2×C31semidirect
412. #2637C2×C31semidirect
413. #1612C2×C31semidirect
414. #1610C2×C31semidirect
415. #1609C2×C31semidirect
416. #1607C2×C31semidirect
417. #1606C2×C31semidirect
418. #1604C2×C31semidirect
419. #1603C2×C31semidirect
420. #1601C2×C31semidirect
421. #1517C2×C31semidirect
422. #1512C2×C31semidirect
423. #1473C2×C31semidirect
481. C2×C4×Q8C22×C31semidirect
482. #483C22×C31semidirect
485. #480C22×C31semidirect
490. #451C22×C31semidirect
493. #448C22×C31semidirect
498. #432C22×C31semidirect
499. #431C22×C31semidirect
501. #398C22×C31semidirect
504. #395C22×C31semidirect
508. #382C22×C31semidirect
509. #328C22×C31semidirect
510. #328C22×C31semidirect
515. #327C22×C31semidirect
516. #327C22×C31semidirect
517. #324C22×C31semidirect
518. #324C22×C31semidirect
661. C31#18249direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35602
C31×#31122
C31×#31082
C31×#26372
C31×#16122
C31×#16102
C31×#16092
C31×#16072
C31×#16062
C31×#16042
C31×#16032
C31×#16012
C31×#15172
C31×#15122
C31×#14732
#1824931