Finite Group Databasebeta

← C31×#18251 #21475010

Subgroups — C31×#18251 #21475010

Order 7936.

876 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3564C211yesmaximal, characteristic
2C31×#3113C211yesmaximal, characteristic, complemented
3C31×#3108C211yesmaximal, characteristic, complemented
4C31×#2637C211yesmaximal, characteristic, complemented
5C31×#1612C211yesmaximal, characteristic
6C31×#1611C211yesmaximal, characteristic, complemented
7C31×#1609C211yesmaximal, characteristic, complemented
8C31×#1608C211yesmaximal, characteristic, complemented
9C31×#1606C211yesmaximal, characteristic
10C31×#1605C211yesmaximal, characteristic, complemented
11C31×#1603C211yesmaximal, characteristic, complemented
12C31×#1602C211yesmaximal, characteristic, complemented
13C31×#1518C211yesmaximal, characteristic, complemented
14C31×#1512C211yesmaximal, characteristic, complemented
15C31×#1473C211yesmaximal, characteristic, complemented
16C31×#563—21no—
17C31×#563—21no—
18C31×#556—21no—
19C31×#554—21no—
20C31×#552—21no—
21C31×#552—21no—
22C31×#551—21no—
23C31×#551—21no—
24C31×#544C2211yescharacteristic
25C31×#543C2211yescharacteristic
26C31×#542—21no—
27C31×#541—21no—
28C31×#541—21no—
29C31×#539—21no—
30C31×#539C2211yescharacteristic
31C31×#538C2211yescharacteristic
32C31×#533C2211yescharacteristic
33C31×#529C2211yescharacteristic
34C2×C31×#126C2211yescharacteristic
35C2×C4×Q8×C31C2211yescharacteristic
36C31×#483C2211yescharacteristic
37C31×#483C2211yescharacteristic
38C31×#483C2211yescharacteristic
39C31×#480C2211yescharacteristic
40C31×#479—21no—
41C31×#475—21no—
42C31×#464—21no—
43C31×#462—21no—
44C31×#451C2211yescharacteristic
45C31×#451C2211yescharacteristic
46C31×#451C2211yescharacteristic
47C31×#448C2211yescharacteristic
48C31×#441—21no—
49C31×#441—21no—
50C4×Q16×C31—21no—
51C4×SD16×C31—21no—
52C31×#432C2211yescharacteristic
53C31×#431C2211yescharacteristic
54C31×#398—21no—
55C31×#398C2211yescharacteristic
56C31×#397C2211yescharacteristic
57C31×#396—21no—
58C31×#395C2211yescharacteristic
59C31×#393C2211yescharacteristic
60C31×#388—21no—
61C31×#387—21no—
62C31×#382C2211yescharacteristic
63C31×#328C2211yescharacteristic
64C31×#328C2211yescharacteristic
65C31×#328C2211yescharacteristic
66C31×#328C2211yescharacteristic
67C31×#328C2211yescharacteristic
68C31×#328C2211yescharacteristic
69C31×#327C2211yescharacteristic
70C31×#327C2211yescharacteristic
71C31×#324C2211yescharacteristic
72C31×#324C2211yescharacteristic
73C31×#323C2211yescharacteristic
74C31×#323C2211yescharacteristic
75C22×Q8×C31C2311yescharacteristic
76C2×Q16×C31—21no—
77C2×Q16×C31—21no—
78C2×Q16×C31—21no—
79C2×SD16×C31—21no—
80C31×C4⋊Q8—21no—
81C31×C4⋊Q8—21no—
82C31×C4⋊Q8—21no—
83C31×C4⋊Q8D411yescharacteristic
84C31×C4⋊Q8D411yescharacteristic
85C31×#126—21no—
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×#126—21no—
96C31×#126—21no—
97C31×#126—21no—
98C31×#125—21no—
99C31×#125—21no—
100C31×#125—21no—
101C31×#125—21no—
102C31×#125—21no—
103C31×#125—21no—
104C31×#125—21no—
105C31×#125—21no—
106C31×#125—21no—
107C31×#125D411yescharacteristic
108C31×#124—21no—
109C31×#124—21no—
110C31×#124—21no—
111C31×#124D411yescharacteristic
112C31×#123—21no—
113C31×#123—21no—
114C31×#123—21no—
115C31×#123—21no—
116C31×#123—21no—
117C31×#123—21no—
118C31×#123—21no—
119C31×#123—21no—
120C31×C22⋊Q8—21no—
121C31×C22⋊Q8—21no—
122C31×C22⋊Q8—21no—
123C31×C22⋊Q8—21no—
124C31×C22⋊Q8—21no—
125C31×C22⋊Q8—21no—
126C31×C22⋊Q8—21no—
127C31×C22⋊Q8—21no—
128C31×C22⋊Q8—21no—
129C31×C22⋊Q8—21no—
130C31×C22⋊Q8—21no—
131C31×C22⋊Q8—21no—
132C31×C22⋊Q8—21no—
133C31×C22⋊Q8—21no—
134C31×C22⋊Q8C2311yescharacteristic
135C31×C22⋊Q8C2311yescharacteristic
136C31×C22⋊Q8C2311yescharacteristic
137C31×#121—21no—
138C31×#121C2311yescharacteristic
139C31×#120—21no—
140C4×Q8×C31—21no—
141C4×Q8×C31—21no—
142C4×Q8×C31—21no—
143C4×Q8×C31—21no—
144C4×Q8×C31—21no—
145C4×Q8×C31—21no—
146C4×Q8×C31—21no—
147C4×Q8×C31D411yescharacteristic
148C4×Q8×C31D411yescharacteristic
149C4×Q8×C31D411yescharacteristic
150C4×D4×C31—21no—
151C4×D4×C31—21no—
152C4×D4×C31—21no—
153C4×D4×C31—21no—
154C4×D4×C31—21no—
155C4×D4×C31D411yescharacteristic
156C31×#117—21no—
157C31×#117—21no—
158C31×#117—21no—
159C31×#117—21no—
160C31×#117—21no—
161C31×#117—21no—
162C2×C4⋊C4×C31—21no—
163C2×C4⋊C4×C31—21no—
164C2×C4⋊C4×C31—21no—
165C2×C4⋊C4×C31—21no—
166C2×C4⋊C4×C31—21no—
167C2×C4⋊C4×C31D411yescharacteristic
168C2×C4⋊C4×C31D411yescharacteristic
169C2×C4⋊C4×C31C2311yescharacteristic
170C2×C4⋊C4×C31C2311yescharacteristic
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×#106—21no—
181C31×#106—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×#103—21no—
191C31×#103—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×C31C2×D411yescharacteristic
207C2×Q8×C31—21no—
208C2×Q8×C31—21no—
209C2×Q8×C31—21no—
210C2×Q8×C31—21no—
211C2×Q8×C31—21no—
212C2×Q8×C31—42no—
213C2×Q8×C31C2×D411yescharacteristic
214C2×Q8×C31C2×D411yescharacteristic
215C2×Q8×C31C2×D411yescharacteristic
216C2×D4×C31—21no—
217C2×D4×C31—21no—
218C2×D4×C31—21no—
219C2×D4×C31C2×D411yescharacteristic
220C22×C4×C31—21no—
221C22×C4×C31—21no—
222C22×C4×C31—21no—
223C22×C4×C31—21no—
224C22×C4×C31—21no—
225C22×C4×C31—21no—
226C22×C4×C31—21no—
227C22×C4×C31—21no—
228C22×C4×C31—21no—
229C22×C4×C31C2×D411yescharacteristic
230C22×C4×C31C2×D411yescharacteristic
231C22×C4×C31C2×D411yescharacteristic
232C22×C4×C31C2×D411yescharacteristic
233C22×C4×C31C2×D411yescharacteristic
234C22×C4×C31C2411yescharacteristic
235Q16×C31—42no—
236Q16×C31—42no—
237Q16×C31—42no—
238SD16×C31—42no—
239C2×C8×C31—21no—
240C2×C8×C31—21no—
241C2×C8×C31—21no—
242C2×C8×C31—21no—
243C4⋊C4×C31—21no—
244C4⋊C4×C31—21no—
245C4⋊C4×C31—21no—
246C4⋊C4×C31—21no—
247C4⋊C4×C31—21no—
248C4⋊C4×C31—21no—
249C4⋊C4×C31—21no—
250C4⋊C4×C31—21no—
251C4⋊C4×C31—21no—
252C4⋊C4×C31—21no—
253C4⋊C4×C31—21no—
254C4⋊C4×C31—21no—
255C4⋊C4×C31—21no—
256C4⋊C4×C31—21no—
257C4⋊C4×C31—21no—
258C4⋊C4×C31—21no—
259C4⋊C4×C31—21no—
260C4⋊C4×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—42no—
275C4⋊C4×C31—41no—
276C4⋊C4×C31—41no—
277C4⋊C4×C31—81no—
278C4⋊C4×C31—81no—
279C4⋊C4×C31C2×D411yescharacteristic
280C4⋊C4×C31C2×D411yescharacteristic
281C4⋊C4×C31C2×D411yescharacteristic
282C4⋊C4×C31C2×D411yescharacteristic
283C22⋊C4×C31—21no—
284C22⋊C4×C31—21no—
285C22⋊C4×C31—21no—
286C22⋊C4×C31—21no—
287C22⋊C4×C31—21no—
288C22⋊C4×C31—21no—
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—42no—
305C22⋊C4×C31—81no—
306C42×C31—21no—
307C42×C31—21no—
308C42×C31—21no—
309C42×C31—21no—
310C42×C31—21no—
311C42×C31—21no—
312C42×C31—21no—
313C42×C31—41no—
314C42×C31—41no—
315C42×C31C2×D411yescharacteristic
316C42×C31C2×D411yescharacteristic
317C42×C31C2×D411yescharacteristic
318C42×C31C2×D411yescharacteristic
319#18251C3111yesmaximal, characteristic, direct product factor, Sylow
320C23×C31—21no—
321C23×C31—21no—
322C23×C31—21no—
323C23×C31—21no—
324C23×C31—41no—
325C23×C31—41no—
326C23×C31C22×D411yescharacteristic
327Q8×C31—22no—
328Q8×C31—22no—
329Q8×C31—41no—
330Q8×C31—41no—
331Q8×C31—41no—
332Q8×C31—41no—
333Q8×C31—41no—
334Q8×C31—81no—
335Q8×C31—81no—
336Q8×C31—81no—
337D4×C31—41no—
338D4×C31—41no—
339D4×C31—41no—
340D4×C31—81no—
341D4×C31—81no—
342C2×C4×C31—21no—
343C2×C4×C31—21no—
344C2×C4×C31—22no—
345C2×C4×C31—21no—
346C2×C4×C31—21no—
347C2×C4×C31—21no—
348C2×C4×C31—21no—
349C2×C4×C31—21no—
350C2×C4×C31—21no—
351C2×C4×C31—21no—
352C2×C4×C31—21no—
353C2×C4×C31—21no—
354C2×C4×C31—21no—
355C2×C4×C31—21no—
356C2×C4×C31—21no—
357C2×C4×C31—41no—
358C2×C4×C31—41no—
359C2×C4×C31—41no—
360C2×C4×C31—41no—
361C2×C4×C31—41no—
362C2×C4×C31—41no—
363C2×C4×C31—41no—
364C2×C4×C31—41no—
365C2×C4×C31—41no—
366C2×C4×C31—41no—
367C2×C4×C31—41no—
368C2×C4×C31—41no—
369C2×C4×C31—41no—
370C2×C4×C31—41no—
371C2×C4×C31—41no—
372C2×C4×C31—81no—
373C2×C4×C31—81no—
374C2×C4×C31—81no—
375C2×C4×C31—81no—
376C2×C4×C31—81no—
377C2×C4×C31#12011yescharacteristic
378C2×C4×C31#12011yescharacteristic
379C2×C4×C31#12011yescharacteristic
380C2×C4×C31#12011yescharacteristic
381C2×C4×C31C22×D411yescharacteristic
382C2×C4×C31C22×D411yescharacteristic
383C8×C31—41no—
384C8×C31—41no—
385C8×C31—41no—
386C8×C31—41no—
387#3564C2×C3111yescharacteristic
388#3113C2×C3111yescharacteristic, complemented
389#3108C2×C3111yescharacteristic, complemented
390#2637C2×C3111yescharacteristic, complemented
391#1612C2×C3111yescharacteristic
392#1611C2×C3111yescharacteristic, complemented
393#1609C2×C3111yescharacteristic, complemented
394#1608C2×C3111yescharacteristic, complemented
395#1606C2×C3111yescharacteristic
396#1605C2×C3111yescharacteristic, complemented
397#1603C2×C3111yescharacteristic, complemented
398#1602C2×C3111yescharacteristic, complemented
399#1518C2×C3111yescharacteristic, complemented
400#1512C2×C3111yescharacteristic, complemented
401#1473C2×C3111yescharacteristic, complemented
402C22×C31—21no—
403C22×C31—21no—
404C22×C31—41no—
405C22×C31—41no—
406C22×C31—41no—
407C22×C31—41no—
408C22×C31—41no—
409C22×C31—41no—
410C22×C31—81no—
411C22×C31—81no—
412C22×C31C2×#12011yescharacteristic
413C22×C31#57711yescharacteristic
414C22×C31#57811yescharacteristic
415C4×C31—21no—
416C4×C31—21no—
417C4×C31—21no—
418C4×C31—21no—
419C4×C31—21no—
420C4×C31—21no—
421C4×C31—41no—
422C4×C31—41no—
423C4×C31—41no—
424C4×C31—41no—
425C4×C31—41no—
426C4×C31—41no—
427C4×C31—42no—
428C4×C31—41no—
429C4×C31—41no—
430C4×C31—41no—
431C4×C31—41no—
432C4×C31—81no—
433C4×C31—81no—
434C4×C31—81no—
435#563—21no—
436#563—21no—
437#556—21no—
438#554—21no—
439#552—21no—
440#552—21no—
441#551—21no—
442#551—21no—
443#544C22×C3111yescharacteristic
444#543C22×C3111yescharacteristic
445#542—21no—
446#541—21no—
447#541—21no—
448#539—21no—
449#539C22×C3111yescharacteristic
450#538C22×C3111yescharacteristic
451#533C22×C3111yescharacteristic
452#529C22×C3111yescharacteristic
453C2×#126C22×C3111yescharacteristic
454C2×C4×Q8C22×C3111yescharacteristic
455#483C22×C3111yescharacteristic
456#483C22×C3111yescharacteristic
457#483C22×C3111yescharacteristic
458#480C22×C3111yescharacteristic
459#479—21no—
460#475—21no—
461#464—21no—
462#462—21no—
463#451C22×C3111yescharacteristic
464#451C22×C3111yescharacteristic
465#451C22×C3111yescharacteristic
466#448C22×C3111yescharacteristic
467#441—21no—
468#441—21no—
469C4×Q16—21no—
470C4×SD16—21no—
471#432C22×C3111yescharacteristic
472#431C22×C3111yescharacteristic
473#398—21no—
474#398C22×C3111yescharacteristic
475#397C22×C3111yescharacteristic
476#396—21no—
477#395C22×C3111yescharacteristic
478#393C22×C3111yescharacteristic
479#388—21no—
480#387—21no—
481#382C22×C3111yescharacteristic
482#328C22×C3111yescharacteristic
483#328C22×C3111yescharacteristic
484#328C22×C3111yescharacteristic
485#328C22×C3111yescharacteristic
486#328C22×C3111yescharacteristic
487#328C22×C3111yescharacteristic
488#327C22×C3111yescharacteristic
489#327C22×C3111yescharacteristic
490#324C22×C3111yescharacteristic
491#324C22×C3111yescharacteristic
492#323C22×C3111yescharacteristic
493#323C22×C3111yescharacteristic
494C2×C31—21no—
495C2×C31—21no—
496C2×C31—81no—
497C2×C31—81no—
498C2×C31#301311yescharacteristic
499C2×C31#302211yescharacteristic
500C2×C31#302511yescharacteristic
501C22×Q8C23×C3111yescharacteristic
502C2×Q16—21no—
503C2×Q16—21no—
504C2×Q16—21no—
505C2×SD16—21no—
506C4⋊Q8—21no—
507C4⋊Q8—21no—
508C4⋊Q8—21no—
509C4⋊Q8D4×C3111yescharacteristic
510C4⋊Q8D4×C3111yescharacteristic
511#126—21no—
512#126—21no—
513#126—21no—
514#126—21no—
515#126—21no—
516#126—21no—
517#126—21no—
518#126—21no—
519#126—21no—
520#126—21no—
521#126—21no—
522#126—21no—
523#126—21no—
524#125—21no—
525#125—21no—
526#125—21no—
527#125—21no—
528#125—21no—
529#125—21no—
530#125—21no—
531#125—21no—
532#125—21no—
533#125D4×C3111yescharacteristic
534#124—21no—
535#124—21no—
536#124—21no—
537#124D4×C3111yescharacteristic
538#123—21no—
539#123—21no—
540#123—21no—
541#123—21no—
542#123—21no—
543#123—21no—
544#123—21no—
545#123—21no—
546C22⋊Q8—21no—
547C22⋊Q8—21no—
548C22⋊Q8—21no—
549C22⋊Q8—21no—
550C22⋊Q8—21no—
551C22⋊Q8—21no—
552C22⋊Q8—21no—
553C22⋊Q8—21no—
554C22⋊Q8—21no—
555C22⋊Q8—21no—
556C22⋊Q8—21no—
557C22⋊Q8—21no—
558C22⋊Q8—21no—
559C22⋊Q8—21no—
560C22⋊Q8C23×C3111yescharacteristic
561C22⋊Q8C23×C3111yescharacteristic
562C22⋊Q8C23×C3111yescharacteristic
563#121—21no—
564#121C23×C3111yescharacteristic
565#120—21no—
566C4×Q8—21no—
567C4×Q8—21no—
568C4×Q8—21no—
569C4×Q8—21no—
570C4×Q8—21no—
571C4×Q8—21no—
572C4×Q8—21no—
573C4×Q8D4×C3111yescharacteristic
574C4×Q8D4×C3111yescharacteristic
575C4×Q8D4×C3111yescharacteristic
576C4×D4—21no—
577C4×D4—21no—
578C4×D4—21no—
579C4×D4—21no—
580C4×D4—21no—
581C4×D4D4×C3111yescharacteristic
582#117—21no—
583#117—21no—
584#117—21no—
585#117—21no—
586#117—21no—
587#117—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4D4×C3111yescharacteristic
594C2×C4⋊C4D4×C3111yescharacteristic
595C2×C4⋊C4C23×C3111yescharacteristic
596C2×C4⋊C4C23×C3111yescharacteristic
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4D4×C3111yescharacteristic
601C2×C22⋊C4D4×C3111yescharacteristic
602C2×C22⋊C4C23×C3111yescharacteristic
603C2×C42—21no—
604C2×C42C23×C3111yescharacteristic
605#107—21no—
606#106—21no—
607#106—21no—
608#106—21no—
609C4⋊C8—21no—
610C4⋊C8—21no—
611#103—21no—
612#103—21no—
613#103—21no—
614#103—21no—
615#103—21no—
616#103—21no—
617#103—21no—
618#102—21no—
619C22⋊C8C23×C3111yescharacteristic
620C22⋊C8C23×C3111yescharacteristic
621C22⋊C8C23×C3111yescharacteristic
622C22⋊C8C23×C3111yescharacteristic
623#97—21no—
624C4×C8—21no—
625#95—21no—
626#95—21no—
627#95—21no—
628#95—21no—
629#95—21no—
630#95C23×C3111yescharacteristic
631#95C23×C3111yescharacteristic
632C31#1825111yescharacteristic, direct product factor, Sylow
633C24C2×D4×C3111yescharacteristic
634C2×Q8—21no—
635C2×Q8—21no—
636C2×Q8—21no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—42no—
640C2×Q8C2×D4×C3111yescharacteristic
641C2×Q8C2×D4×C3111yescharacteristic
642C2×Q8C2×D4×C3111yescharacteristic
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4C2×D4×C3111yescharacteristic
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4C2×D4×C3111yescharacteristic
657C22×C4C2×D4×C3111yescharacteristic
658C22×C4C2×D4×C3111yescharacteristic
659C22×C4C2×D4×C3111yescharacteristic
660C22×C4C2×D4×C3111yescharacteristic
661C22×C4C24×C3111yescharacteristic
662Q16—42no—
663Q16—42no—
664Q16—42no—
665SD16—42no—
666C2×C8—21no—
667C2×C8—21no—
668C2×C8—21no—
669C2×C8—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—42no—
702C4⋊C4—41no—
703C4⋊C4—41no—
704C4⋊C4—81no—
705C4⋊C4—81no—
706C4⋊C4C2×D4×C3111yescharacteristic
707C4⋊C4C2×D4×C3111yescharacteristic
708C4⋊C4C2×D4×C3111yescharacteristic
709C4⋊C4C2×D4×C3111yescharacteristic
710C22⋊C4—21no—
711C22⋊C4—21no—
712C22⋊C4—21no—
713C22⋊C4—21no—
714C22⋊C4—21no—
715C22⋊C4—21no—
716C22⋊C4—21no—
717C22⋊C4—21no—
718C22⋊C4—21no—
719C22⋊C4—21no—
720C22⋊C4—21no—
721C22⋊C4—21no—
722C22⋊C4—21no—
723C22⋊C4—21no—
724C22⋊C4—21no—
725C22⋊C4—21no—
726C22⋊C4—21no—
727C22⋊C4—21no—
728C22⋊C4—21no—
729C22⋊C4—21no—
730C22⋊C4—21no—
731C22⋊C4—42no—
732C22⋊C4—81no—
733C42—21no—
734C42—21no—
735C42—21no—
736C42—21no—
737C42—21no—
738C42—21no—
739C42—21no—
740C42—41no—
741C42—41no—
742C42C2×D4×C3111yescharacteristic
743C42C2×D4×C3111yescharacteristic
744C42C2×D4×C3111yescharacteristic
745C42C2×D4×C3111yescharacteristic
746C23—21no—
747C23—21no—
748C23—21no—
749C23—21no—
750C23—41no—
751C23—41no—
752C23C22×D4×C3111yescharacteristic
753Q8—22no—
754Q8—22no—
755Q8—41no—
756Q8—41no—
757Q8—41no—
758Q8—41no—
759Q8—41no—
760Q8—81no—
761Q8—81no—
762Q8—81no—
763D4—41no—
764D4—41no—
765D4—41no—
766D4—81no—
767D4—81no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—22no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—81no—
799C2×C4—81no—
800C2×C4—81no—
801C2×C4—81no—
802C2×C4—81no—
803C2×C4C31×#12011yescharacteristic
804C2×C4C31×#12011yescharacteristic
805C2×C4C31×#12011yescharacteristic
806C2×C4C31×#12011yescharacteristic
807C2×C4C22×D4×C3111yescharacteristic
808C2×C4C22×D4×C3111yescharacteristic
809C8—41no—
810C8—41no—
811C8—41no—
812C8—41no—
813C22—21no—
814C22—21no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22—81no—
822C22—81no—
823C22C2×C31×#12011yescharacteristic
824C22C31×#57711yescharacteristic
825C22C31×#57811yescharacteristic
826C4—21no—
827C4—21no—
828C4—21no—
829C4—21no—
830C4—21no—
831C4—21no—
832C4—41no—
833C4—41no—
834C4—41no—
835C4—41no—
836C4—41no—
837C4—41no—
838C4—42no—
839C4—41no—
840C4—41no—
841C4—41no—
842C4—41no—
843C4—81no—
844C4—81no—
845C4—81no—
846C2—21no—
847C2—21no—
848C2—81no—
849C2—81no—
850C2C31×#301311yescharacteristic
851C2C31×#302211yescharacteristic
852C2C31×#302511yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC31×#538C22
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×#3113C2semidirect
3. C31×#3108C2semidirect
4. C31×#2637C2semidirect
6. C31×#1611C2semidirect
7. C31×#1609C2semidirect
8. C31×#1608C2semidirect
10. C31×#1605C2semidirect
11. C31×#1603C2semidirect
12. C31×#1602C2semidirect
13. C31×#1518C2semidirect
14. C31×#1512C2semidirect
15. C31×#1473C2semidirect
319. #18251C31direct (N × H)
388. #3113C2×C31semidirect
389. #3108C2×C31semidirect
390. #2637C2×C31semidirect
392. #1611C2×C31semidirect
393. #1609C2×C31semidirect
394. #1608C2×C31semidirect
396. #1605C2×C31semidirect
397. #1603C2×C31semidirect
398. #1602C2×C31semidirect
399. #1518C2×C31semidirect
400. #1512C2×C31semidirect
401. #1473C2×C31semidirect
632. C31#18251direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35642
C31×#31132
C31×#31082
C31×#26372
C31×#16122
C31×#16112
C31×#16092
C31×#16082
C31×#16062
C31×#16052
C31×#16032
C31×#16022
C31×#15182
C31×#15122
C31×#14732
#1825131