Finite Group Databasebeta

← C31×#25021 #21481780

Subgroups — C31×#25021 #21481780

Order 7936.

832 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#485C211yesmaximal, characteristic, complemented
2C2×C31×#483C211yesmaximal, characteristic, complemented
3C31×#2536C211yesmaximal, characteristic
4C31×#2352C211yesmaximal, characteristic
5C31×#2077C211yesmaximal, characteristic, complemented
6C31×#2077C211yesmaximal, characteristic, complemented
7C31×#2036C211yesmaximal, characteristic, complemented
8C31×#2036C211yesmaximal, characteristic, complemented
9C31×#1954C211yesmaximal, characteristic
10C31×#1949C211yesmaximal, characteristic, complemented
11C31×#1854C211yesmaximal, characteristic, complemented
12C31×#1852C211yesmaximal, characteristic, complemented
13C31×#1846C211yesmaximal, characteristic, complemented
14C31×#1805C211yesmaximal, characteristic, complemented
15C4×C31×#103C211yesmaximal, characteristic, complemented
16C2×C31×C22⋊Q8C2211yescharacteristic
17C2×C31×C22⋊Q8C2211yescharacteristic
18C2×C4×Q8×C31C2211yescharacteristic
19C2×C4×D4×C31C2211yescharacteristic
20C2×C31×#117C2211yescharacteristic
21C22×C4⋊C4×C31C2211yescharacteristic
22C31×#485—24no—
23C31×#483—24no—
24C2×C31×#107C2211yescharacteristic
25C2×C31×#107C2211yescharacteristic
26C2×C31×#107C2211yescharacteristic
27C2×C31×#106C2211yescharacteristic
28C2×C31×#106C2211yescharacteristic
29C2×C31×#106C2211yescharacteristic
30C2×C31×C4⋊C8C2211yescharacteristic
31C2×C31×#103C2211yescharacteristic
32C2×C31×#103C2211yescharacteristic
33C2×C31×#103C2211yescharacteristic
34C2×C31×#103C2211yescharacteristic
35C2×C31×C22⋊C8C2211yescharacteristic
36C2×C31×C22⋊C8C2211yescharacteristic
37C2×C31×C22⋊C8C2211yescharacteristic
38C2×C31×C22⋊C8C2211yescharacteristic
39C2×C4×C8×C31C2211yescharacteristic
40C31×#398—21no—
41C31×#394—21no—
42C31×#388—21no—
43C31×#388—21no—
44C31×#388—21no—
45C31×#387—21no—
46C31×#386—21no—
47C31×#382C2211yescharacteristic
48C31×#382C2211yescharacteristic
49C31×#380C2211yescharacteristic
50C31×#380C2211yescharacteristic
51C31×#380C2211yescharacteristic
52C31×#380C2211yescharacteristic
53C4×C4⋊C4×C31C2211yescharacteristic
54C4×C22⋊C4×C31—21no—
55C31×#340C2211yescharacteristic
56C31×#340C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#340C2211yescharacteristic
60C31×#340C2211yescharacteristic
61C22×Q8×C31C2311yescharacteristic
62C22×D4×C31D411yescharacteristic
63C23×C4×C31—21no—
64C23×C4×C31C2311yescharacteristic
65C23×C4×C31C2311yescharacteristic
66C22×C8×C31C2311yescharacteristic
67C22×C8×C31C2311yescharacteristic
68C22×C8×C31C2311yescharacteristic
69C22×C8×C31C2311yescharacteristic
70C31×C22⋊Q8—22no—
71C31×C22⋊Q8—22no—
72C31×C22⋊Q8—41no—
73C31×C22⋊Q8—41no—
74C4×Q8×C31—22no—
75C4×Q8×C31—22no—
76C4×D4×C31—22no—
77C4×D4×C31—22no—
78C31×#117—22no—
79C31×#117—41no—
80C2×C4⋊C4×C31—22no—
81C2×C4⋊C4×C31—21no—
82C2×C4⋊C4×C31—21no—
83C2×C4⋊C4×C31—21no—
84C2×C4⋊C4×C31—21no—
85C2×C4⋊C4×C31—41no—
86C2×C4⋊C4×C31D411yescharacteristic
87C2×C4⋊C4×C31C2311yescharacteristic
88C2×C4⋊C4×C31C2311yescharacteristic
89C2×C4⋊C4×C31C2311yescharacteristic
90C2×C4⋊C4×C31C2311yescharacteristic
91C2×C4⋊C4×C31C2311yescharacteristic
92C2×C4⋊C4×C31C2311yescharacteristic
93C2×C4⋊C4×C31C2311yescharacteristic
94C2×C22⋊C4×C31—21no—
95C2×C22⋊C4×C31—21no—
96C2×C22⋊C4×C31—21no—
97C2×C22⋊C4×C31—21no—
98C2×C22⋊C4×C31—21no—
99C2×C22⋊C4×C31—21no—
100C2×C22⋊C4×C31—21no—
101C2×C22⋊C4×C31D411yescharacteristic
102C2×C22⋊C4×C31D411yescharacteristic
103C2×C42×C31—21no—
104C2×C42×C31—21no—
105C2×C42×C31—21no—
106C2×C42×C31C2311yescharacteristic
107C31×#107—22no—
108C31×#107—41no—
109C31×#107—41no—
110C31×#106—22no—
111C31×#106—22no—
112C31×#106—22no—
113C31×C4⋊C8—22no—
114C31×#103—22no—
115C31×#103—22no—
116C31×#103—22no—
117C31×#103D414yescomplemented
118C31×C22⋊C8—22no—
119C31×C22⋊C8—22no—
120C31×C22⋊C8—22no—
121C31×C22⋊C8—22no—
122C4×C8×C31—22no—
123C31×#95—21no—
124C31×#95—21no—
125C31×#95—21no—
126C31×#95—21no—
127C31×#95—21no—
128C31×#95—21no—
129C31×#95—21no—
130C31×#95—21no—
131C31×#95—21no—
132C24×C31C2×D411yescharacteristic
133C24×C31C2×D411yescharacteristic
134C2×Q8×C31—21no—
135C2×Q8×C31—21no—
136C2×Q8×C31—21no—
137C2×Q8×C31—21no—
138C2×Q8×C31—21no—
139C2×Q8×C31C2×D412yes—
140C2×D4×C31—22no—
141C2×D4×C31—22no—
142C2×D4×C31—41no—
143C22×C4×C31—21no—
144C22×C4×C31—21no—
145C22×C4×C31—21no—
146C22×C4×C31—21no—
147C22×C4×C31—21no—
148C22×C4×C31—21no—
149C22×C4×C31—21no—
150C22×C4×C31—21no—
151C22×C4×C31—21no—
152C22×C4×C31—21no—
153C22×C4×C31—21no—
154C22×C4×C31—21no—
155C22×C4×C31—21no—
156C22×C4×C31—21no—
157C22×C4×C31—21no—
158C22×C4×C31—21no—
159C22×C4×C31—21no—
160C22×C4×C31—21no—
161C22×C4×C31—21no—
162C22×C4×C31—21no—
163C22×C4×C31—42no—
164C22×C4×C31—42no—
165C22×C4×C31—81no—
166C22×C4×C31C2×D411yescharacteristic
167C22×C4×C31C2×D411yescharacteristic
168C22×C4×C31C2×D411yescharacteristic
169C22×C4×C31C2×D411yescharacteristic
170C22×C4×C31C2411yescharacteristic
171C2×C8×C31—21no—
172C2×C8×C31—21no—
173C2×C8×C31—21no—
174C2×C8×C31—21no—
175C2×C8×C31—21no—
176C2×C8×C31—21no—
177C2×C8×C31—21no—
178C2×C8×C31—21no—
179C2×C8×C31—21no—
180C2×C8×C31—21no—
181C2×C8×C31C2×D412yes—
182C2×C8×C31#4112yes—
183C4⋊C4×C31—22no—
184C4⋊C4×C31—21no—
185C4⋊C4×C31—21no—
186C4⋊C4×C31—21no—
187C4⋊C4×C31—21no—
188C4⋊C4×C31—21no—
189C4⋊C4×C31—21no—
190C4⋊C4×C31—21no—
191C4⋊C4×C31—21no—
192C4⋊C4×C31—21no—
193C4⋊C4×C31—21no—
194C4⋊C4×C31—21no—
195C4⋊C4×C31—21no—
196C4⋊C4×C31—21no—
197C4⋊C4×C31—42no—
198C4⋊C4×C31—42no—
199C4⋊C4×C31—42no—
200C4⋊C4×C31—42no—
201C4⋊C4×C31C2×D412yes—
202C22⋊C4×C31—22no—
203C22⋊C4×C31—22no—
204C22⋊C4×C31—42no—
205C22⋊C4×C31—42no—
206C22⋊C4×C31—42no—
207C22⋊C4×C31—42no—
208C22⋊C4×C31—42no—
209C22⋊C4×C31—42no—
210C22⋊C4×C31—81no—
211C42×C31—42no—
212C42×C31—42no—
213C42×C31—81no—
214C42×C31#4112yes—
215C42×C31#4112yes—
216#25021C3111yesmaximal, characteristic, direct product factor, Sylow
217C23×C31—21no—
218C23×C31—21no—
219C23×C31—21no—
220C23×C31—21no—
221C23×C31—21no—
222C23×C31—21no—
223C23×C31—21no—
224C23×C31—21no—
225C23×C31—21no—
226C23×C31—21no—
227C23×C31—21no—
228C23×C31—21no—
229C23×C31—21no—
230C23×C31#13512yes—
231C23×C31C22×D411yescharacteristic
232Q8×C31—22no—
233Q8×C31—22no—
234Q8×C31—41no—
235Q8×C31—41no—
236D4×C31—44no—
237C2×C4×C31—21no—
238C2×C4×C31—21no—
239C2×C4×C31—21no—
240C2×C4×C31—21no—
241C2×C4×C31—21no—
242C2×C4×C31—21no—
243C2×C4×C31—21no—
244C2×C4×C31—22no—
245C2×C4×C31—22no—
246C2×C4×C31—21no—
247C2×C4×C31—21no—
248C2×C4×C31—21no—
249C2×C4×C31—41no—
250C2×C4×C31—41no—
251C2×C4×C31—41no—
252C2×C4×C31—41no—
253C2×C4×C31—41no—
254C2×C4×C31—41no—
255C2×C4×C31—41no—
256C2×C4×C31—41no—
257C2×C4×C31—41no—
258C2×C4×C31—41no—
259C2×C4×C31—41no—
260C2×C4×C31—41no—
261C2×C4×C31—41no—
262C2×C4×C31—41no—
263C2×C4×C31—41no—
264C2×C4×C31—41no—
265C2×C4×C31—41no—
266C2×C4×C31—41no—
267C2×C4×C31—41no—
268C2×C4×C31—41no—
269C2×C4×C31—41no—
270C2×C4×C31—41no—
271C2×C4×C31—41no—
272C2×C4×C31—41no—
273C2×C4×C31—41no—
274C2×C4×C31—41no—
275C2×C4×C31—41no—
276C2×C4×C31—41no—
277C2×C4×C31—41no—
278C2×C4×C31—41no—
279C2×C4×C31—84no—
280C2×C4×C31#12312yes—
281C2×C4×C31#12312yes—
282C2×C4×C31C22×D411yescharacteristic
283C2×C4×C31C2×#4111yescharacteristic
284C2×C4×C31C2×#4111yescharacteristic
285C2×C4×C31C2×#4111yescharacteristic
286C2×C4×C31H(5,𝔽2)11yescharacteristic
287C2×C4×C312−1+411yescharacteristic
288C8×C31—22no—
289C8×C31—22no—
290C8×C31—41no—
291C8×C31—41no—
292C2×#485C2×C3111yescharacteristic, complemented
293C2×#483C2×C3111yescharacteristic, complemented
294#2536C2×C3111yescharacteristic
295#2352C2×C3111yescharacteristic
296#2077C2×C3111yescharacteristic, complemented
297#2077C2×C3111yescharacteristic, complemented
298#2036C2×C3111yescharacteristic, complemented
299#2036C2×C3111yescharacteristic, complemented
300#1954C2×C3111yescharacteristic
301#1949C2×C3111yescharacteristic, complemented
302#1854C2×C3111yescharacteristic, complemented
303#1852C2×C3111yescharacteristic, complemented
304#1846C2×C3111yescharacteristic, complemented
305#1805C2×C3111yescharacteristic, complemented
306C4×#103C2×C3111yescharacteristic, complemented
307C22×C31—22no—
308C22×C31—22no—
309C22×C31—22no—
310C22×C31—41no—
311C22×C31—41no—
312C22×C31—41no—
313C22×C31—41no—
314C22×C31—41no—
315C22×C31—41no—
316C22×C31—41no—
317C22×C31—41no—
318C22×C31—41no—
319C22×C31—41no—
320C22×C31—41no—
321C22×C31C2×#12311yescharacteristic
322C22×C31D4211yescharacteristic
323C22×C31#54711yescharacteristic
324C22×C31C2×#13511yescharacteristic
325C22×C31#57511yescharacteristic
326C22×C31#57711yescharacteristic
327C22×C31#57811yescharacteristic
328C4×C31—22no—
329C4×C31—22no—
330C4×C31—41no—
331C4×C31—41no—
332C4×C31—42no—
333C4×C31—42no—
334C4×C31—81no—
335C4×C31—81no—
336C4×C31—81no—
337C4×C31—81no—
338C4×C31—81no—
339C4×C31—81no—
340C4×C31#53211yescharacteristic
341C4×C31#54211yescharacteristic
342C4×C31#54711yescharacteristic
343C4×C31#55311yescharacteristic
344C2×C22⋊Q8C22×C3111yescharacteristic
345C2×C22⋊Q8C22×C3111yescharacteristic
346C2×C4×Q8C22×C3111yescharacteristic
347C2×C4×D4C22×C3111yescharacteristic
348C2×#117C22×C3111yescharacteristic
349C22×C4⋊C4C22×C3111yescharacteristic
350#485—24no—
351#483—24no—
352C2×#107C22×C3111yescharacteristic
353C2×#107C22×C3111yescharacteristic
354C2×#107C22×C3111yescharacteristic
355C2×#106C22×C3111yescharacteristic
356C2×#106C22×C3111yescharacteristic
357C2×#106C22×C3111yescharacteristic
358C2×C4⋊C8C22×C3111yescharacteristic
359C2×#103C22×C3111yescharacteristic
360C2×#103C22×C3111yescharacteristic
361C2×#103C22×C3111yescharacteristic
362C2×#103C22×C3111yescharacteristic
363C2×C22⋊C8C22×C3111yescharacteristic
364C2×C22⋊C8C22×C3111yescharacteristic
365C2×C22⋊C8C22×C3111yescharacteristic
366C2×C22⋊C8C22×C3111yescharacteristic
367C2×C4×C8C22×C3111yescharacteristic
368#398—21no—
369#394—21no—
370#388—21no—
371#388—21no—
372#388—21no—
373#387—21no—
374#386—21no—
375#382C22×C3111yescharacteristic
376#382C22×C3111yescharacteristic
377#380C22×C3111yescharacteristic
378#380C22×C3111yescharacteristic
379#380C22×C3111yescharacteristic
380#380C22×C3111yescharacteristic
381C4×C4⋊C4C22×C3111yescharacteristic
382C4×C22⋊C4—21no—
383#340C22×C3111yescharacteristic
384#340C22×C3111yescharacteristic
385#340C22×C3111yescharacteristic
386#340C22×C3111yescharacteristic
387#340C22×C3111yescharacteristic
388#340C22×C3111yescharacteristic
389C2×C31—42no—
390C2×C31—81no—
391C2×C31#242211yescharacteristic
392C2×C31#309111yescharacteristic
393C2×C31#309711yescharacteristic
394C2×C31#327711yescharacteristic
395C2×C31#328211yescharacteristic
396C2×C31#333611yescharacteristic
397C2×C31#335111yescharacteristic
398C22×Q8C23×C3111yescharacteristic
399C22×D4D4×C3111yescharacteristic
400C23×C4—21no—
401C23×C4C23×C3111yescharacteristic
402C23×C4C23×C3111yescharacteristic
403C22×C8C23×C3111yescharacteristic
404C22×C8C23×C3111yescharacteristic
405C22×C8C23×C3111yescharacteristic
406C22×C8C23×C3111yescharacteristic
407C22⋊Q8—22no—
408C22⋊Q8—22no—
409C22⋊Q8—41no—
410C22⋊Q8—41no—
411C4×Q8—22no—
412C4×Q8—22no—
413C4×D4—22no—
414C4×D4—22no—
415#117—22no—
416#117—41no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—41no—
423C2×C4⋊C4D4×C3111yescharacteristic
424C2×C4⋊C4C23×C3111yescharacteristic
425C2×C4⋊C4C23×C3111yescharacteristic
426C2×C4⋊C4C23×C3111yescharacteristic
427C2×C4⋊C4C23×C3111yescharacteristic
428C2×C4⋊C4C23×C3111yescharacteristic
429C2×C4⋊C4C23×C3111yescharacteristic
430C2×C4⋊C4C23×C3111yescharacteristic
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4D4×C3111yescharacteristic
439C2×C22⋊C4D4×C3111yescharacteristic
440C2×C42—21no—
441C2×C42—21no—
442C2×C42—21no—
443C2×C42C23×C3111yescharacteristic
444#107—22no—
445#107—41no—
446#107—41no—
447#106—22no—
448#106—22no—
449#106—22no—
450C4⋊C8—22no—
451#103—22no—
452#103—22no—
453#103—22no—
454#103D4×C3114yescomplemented
455C22⋊C8—22no—
456C22⋊C8—22no—
457C22⋊C8—22no—
458C22⋊C8—22no—
459C4×C8—22no—
460#95—21no—
461#95—21no—
462#95—21no—
463#95—21no—
464#95—21no—
465#95—21no—
466#95—21no—
467#95—21no—
468#95—21no—
469C31#2502111yescharacteristic, direct product factor, Sylow
470C24C2×D4×C3111yescharacteristic
471C24C2×D4×C3111yescharacteristic
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8C2×D4×C3112yes—
478C2×D4—22no—
479C2×D4—22no—
480C2×D4—41no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—42no—
502C22×C4—42no—
503C22×C4—81no—
504C22×C4C2×D4×C3111yescharacteristic
505C22×C4C2×D4×C3111yescharacteristic
506C22×C4C2×D4×C3111yescharacteristic
507C22×C4C2×D4×C3111yescharacteristic
508C22×C4C24×C3111yescharacteristic
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8C2×D4×C3112yes—
520C2×C8#41×C3112yes—
521C4⋊C4—22no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—42no—
536C4⋊C4—42no—
537C4⋊C4—42no—
538C4⋊C4—42no—
539C4⋊C4C2×D4×C3112yes—
540C22⋊C4—22no—
541C22⋊C4—22no—
542C22⋊C4—42no—
543C22⋊C4—42no—
544C22⋊C4—42no—
545C22⋊C4—42no—
546C22⋊C4—42no—
547C22⋊C4—42no—
548C22⋊C4—81no—
549C42—42no—
550C42—42no—
551C42—81no—
552C42#41×C3112yes—
553C42#41×C3112yes—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23C31×#13512yes—
568C23C22×D4×C3111yescharacteristic
569Q8—22no—
570Q8—22no—
571Q8—41no—
572Q8—41no—
573D4—44no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—84no—
617C2×C4C31×#12312yes—
618C2×C4C31×#12312yes—
619C2×C4C22×D4×C3111yescharacteristic
620C2×C4C2×#41×C3111yescharacteristic
621C2×C4C2×#41×C3111yescharacteristic
622C2×C4C2×#41×C3111yescharacteristic
623C2×C4C31×H(5,𝔽2)11yescharacteristic
624C2×C4C31×2−1+411yescharacteristic
625C8—22no—
626C8—22no—
627C8—41no—
628C8—41no—
629C22—22no—
630C22—22no—
631C22—22no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22—41no—
642C22—41no—
643C22C2×C31×#12311yescharacteristic
644C22D42×C3111yescharacteristic
645C22C31×#54711yescharacteristic
646C22C2×C31×#13511yescharacteristic
647C22C31×#57511yescharacteristic
648C22C31×#57711yescharacteristic
649C22C31×#57811yescharacteristic
650C4—22no—
651C4—22no—
652C4—41no—
653C4—41no—
654C4—42no—
655C4—42no—
656C4—81no—
657C4—81no—
658C4—81no—
659C4—81no—
660C4—81no—
661C4—81no—
662C4C31×#53211yescharacteristic
663C4C31×#54211yescharacteristic
664C4C31×#54711yescharacteristic
665C4C31×#55311yescharacteristic
666C2—42no—
667C2—81no—
668C2C31×#242211yescharacteristic
669C2C31×#309111yescharacteristic
670C2C31×#309711yescharacteristic
671C2C31×#327711yescharacteristic
672C2C31×#328211yescharacteristic
673C2C31×#333611yescharacteristic
674C2C31×#335111yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC22×D4×C31D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C4×D4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#485C2semidirect
2. C2×C31×#483C2semidirect
5. C31×#2077C2semidirect
6. C31×#2077C2semidirect
7. C31×#2036C2semidirect
8. C31×#2036C2semidirect
10. C31×#1949C2semidirect
11. C31×#1854C2semidirect
12. C31×#1852C2semidirect
13. C31×#1846C2semidirect
14. C31×#1805C2semidirect
15. C4×C31×#103C2semidirect
117. C31×#103D4semidirect
216. #25021C31direct (N × H)
292. C2×#485C2×C31semidirect
293. C2×#483C2×C31semidirect
296. #2077C2×C31semidirect
297. #2077C2×C31semidirect
298. #2036C2×C31semidirect
299. #2036C2×C31semidirect
301. #1949C2×C31semidirect
302. #1854C2×C31semidirect
303. #1852C2×C31semidirect
304. #1846C2×C31semidirect
305. #1805C2×C31semidirect
306. C4×#103C2×C31semidirect
454. #103D4×C31semidirect
469. C31#25021direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4852
C2×C31×#4832
C31×#25362
C31×#23522
C31×#20772
C31×#20362
C31×#19542
C31×#19492
C31×#18542
C31×#18522
C31×#18462
C31×#18052
C4×C31×#1032
#2502131