Finite Group Databasebeta

← C31×#22712 #21479471

Subgroups — C31×#22712 #21479471

Order 7936.

898 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#435C211yesmaximal, characteristic
2C31×#2354C211yesmaximal, characteristic
3C31×#2352C211yesmaximal, characteristic
4C31×#1949C211yesmaximal, characteristic, complemented
5C31×#1947C211yesmaximal, characteristic, complemented
6C31×#1854C211yesmaximal, characteristic, complemented
7C31×#1854C211yesmaximal, characteristic, complemented
8C31×#1854C211yesmaximal, characteristic, complemented
9C31×#1852C211yesmaximal, characteristic, complemented
10C31×#1836C211yesmaximal, characteristic, complemented
11C31×#1809C211yesmaximal, characteristic, complemented
12C31×#1808C211yesmaximal, characteristic, complemented
13C31×#1776C211yesmaximal, characteristic, complemented
14C31×#1736C211yesmaximal, characteristic, complemented
15C31×#1735C211yesmaximal, characteristic, complemented
16C22×M16×C31C2211yescharacteristic
17C23×C8×C31C2211yescharacteristic
18C2×C4×D4×C31C2211yescharacteristic
19C2×C31×#117C2211yescharacteristic
20C2×C31×#117C2211yescharacteristic
21C2×C31×#117C2211yescharacteristic
22C22×C4⋊C4×C31C2211yescharacteristic
23C31×#435C418yescomplemented
24C2×C31×#107C2211yescharacteristic
25C2×C31×#107C2211yescharacteristic
26C2×C31×#107C2211yescharacteristic
27C2×C31×#107C2211yescharacteristic
28C2×C31×#106C2211yescharacteristic
29C2×C31×#106C2211yescharacteristic
30C2×C31×C4⋊C8C2211yescharacteristic
31C2×C31×C22⋊C8C2211yescharacteristic
32C2×C31×C22⋊C8C2211yescharacteristic
33C2×C31×#97C2211yescharacteristic
34C31×#390—21no—
35C31×#388—21no—
36C31×#388—21no—
37C31×#388—21no—
38C31×#387—21no—
39C31×#386—21no—
40C31×#384C2211yescharacteristic
41C31×#382C2211yescharacteristic
42C31×#380C2211yescharacteristic
43C31×#380C2211yescharacteristic
44C31×#380C2211yescharacteristic
45C31×#380C2211yescharacteristic
46C4×C4⋊C4×C31—21no—
47C4×C4⋊C4×C31C2211yescharacteristic
48C4×C4⋊C4×C31C2211yescharacteristic
49C4×C22⋊C4×C31—21no—
50C31×#340C2211yescharacteristic
51C31×#340C2211yescharacteristic
52C31×#340C2211yescharacteristic
53C31×#340C2211yescharacteristic
54C31×#340C2211yescharacteristic
55C31×#340C2211yescharacteristic
56C31×#340C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#340C2211yescharacteristic
60C22×D4×C31D411yescharacteristic
61C23×C4×C31—21no—
62C23×C4×C31C2311yescharacteristic
63C23×C4×C31C2311yescharacteristic
64C2×M16×C31—41no—
65C2×M16×C31—41no—
66C2×M16×C31C2×C414yes—
67C22×C8×C31—41no—
68C22×C8×C31—41no—
69C22×C8×C31C2×C414yescomplemented
70C22×C8×C31C2311yescharacteristic
71C22×C8×C31C2311yescharacteristic
72C22×C8×C31C2311yescharacteristic
73C22×C8×C31C2311yescharacteristic
74C4×D4×C31C2×C414yes—
75C4×D4×C31Q814yes—
76C31×#117—22no—
77C31×#117—22no—
78C31×#117—22no—
79C31×#117—41no—
80C31×#117—41no—
81C31×#117—41no—
82C2×C4⋊C4×C31—22no—
83C2×C4⋊C4×C31—21no—
84C2×C4⋊C4×C31—21no—
85C2×C4⋊C4×C31—21no—
86C2×C4⋊C4×C31—41no—
87C2×C4⋊C4×C31D411yescharacteristic
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×C4⋊C4×C31C2311yescharacteristic
95C2×C4⋊C4×C31C2311yescharacteristic
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×C31—21no—
102C2×C22⋊C4×C31—21no—
103C2×C22⋊C4×C31D411yescharacteristic
104C2×C22⋊C4×C31D411yescharacteristic
105C2×C42×C31—21no—
106C2×C42×C31—21no—
107C2×C42×C31—21no—
108C2×C42×C31—21no—
109C2×C42×C31—21no—
110C2×C42×C31C2311yescharacteristic
111C31×#107—22no—
112C31×#107—41no—
113C31×#107—41no—
114C31×#107—41no—
115C31×#106—22no—
116C31×#106—41no—
117C31×C4⋊C8C2×C414yescomplemented
118C31×C22⋊C8C2×C414yes—
119C31×C22⋊C8C2×C414yescomplemented
120C31×#97C2×C414yescomplemented
121C31×#95—21no—
122C31×#95—21no—
123C31×#95—21no—
124C31×#95—21no—
125C31×#95—21no—
126C31×#95—21no—
127C31×#95—21no—
128C31×#95—21no—
129C24×C31C2×D411yescharacteristic
130C24×C31C2×D411yescharacteristic
131C2×D4×C31—41no—
132C2×D4×C31—41no—
133C2×D4×C31C4⋊C414yes—
134C22×C4×C31—21no—
135C22×C4×C31—21no—
136C22×C4×C31—21no—
137C22×C4×C31—21no—
138C22×C4×C31—21no—
139C22×C4×C31—21no—
140C22×C4×C31—21no—
141C22×C4×C31—21no—
142C22×C4×C31—21no—
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—42no—
151C22×C4×C31—42no—
152C22×C4×C31—81no—
153C22×C4×C31C22×C412yes—
154C22×C4×C31C22×C412yes—
155C22×C4×C31C2×D411yescharacteristic
156C22×C4×C31C2×D411yescharacteristic
157C22×C4×C31C2×D411yescharacteristic
158C22×C4×C31C2×D411yescharacteristic
159C22×C4×C31C2×Q812yes—
160C22×C4×C31C2×Q812yes—
161C22×C4×C31C2411yescharacteristic
162M16×C31—44no—
163C2×C8×C31—21no—
164C2×C8×C31—21no—
165C2×C8×C31—21no—
166C2×C8×C31—21no—
167C2×C8×C31—21no—
168C2×C8×C31—21no—
169C2×C8×C31—21no—
170C2×C8×C31—21no—
171C2×C8×C31—44no—
172C2×C8×C31C22×C412yes—
173C2×C8×C31C22×C412yes—
174C2×C8×C31C22×C412yes—
175C2×C8×C31C22×C412yes—
176C4⋊C4×C31—21no—
177C4⋊C4×C31—21no—
178C4⋊C4×C31—21no—
179C4⋊C4×C31—21no—
180C4⋊C4×C31—21no—
181C4⋊C4×C31—21no—
182C4⋊C4×C31—21no—
183C4⋊C4×C31—21no—
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—42no—
191C4⋊C4×C31—42no—
192C4⋊C4×C31—81no—
193C4⋊C4×C31C4⋊C414yes—
194C4⋊C4×C31#4112yes—
195C4⋊C4×C31#4112yes—
196C22⋊C4×C31—42no—
197C22⋊C4×C31—42no—
198C22⋊C4×C31—42no—
199C22⋊C4×C31—42no—
200C22⋊C4×C31—81no—
201C22⋊C4×C31—81no—
202C22⋊C4×C31—81no—
203C22⋊C4×C31C4⋊C414yes—
204C22⋊C4×C31C4⋊C414yes—
205C42×C31—42no—
206C42×C31—42no—
207C42×C31—42no—
208C42×C31—42no—
209C42×C31—81no—
210C42×C31C22×C412yes—
211C42×C31C2×Q812yes—
212#22712C3111yesmaximal, characteristic, direct product factor, Sylow
213C23×C31—21no—
214C23×C31—21no—
215C23×C31—21no—
216C23×C31—21no—
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×C31C2×C4⋊C412yes—
226C23×C31C2×C4⋊C412yes—
227C23×C31C22×D411yescharacteristic
228D4×C31—44no—
229C2×C4×C31—21no—
230C2×C4×C31—21no—
231C2×C4×C31—21no—
232C2×C4×C31—21no—
233C2×C4×C31—21no—
234C2×C4×C31—21no—
235C2×C4×C31—21no—
236C2×C4×C31—21no—
237C2×C4×C31—22no—
238C2×C4×C31—22no—
239C2×C4×C31—22no—
240C2×C4×C31—22no—
241C2×C4×C31—22no—
242C2×C4×C31—22no—
243C2×C4×C31—22no—
244C2×C4×C31—22no—
245C2×C4×C31—22no—
246C2×C4×C31—22no—
247C2×C4×C31—41no—
248C2×C4×C31—41no—
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—84no—
270C2×C4×C31C2×C4⋊C412yes—
271C2×C4×C31C2×C4⋊C412yes—
272C2×C4×C31C2×C4⋊C412yes—
273C2×C4×C31C2×C4⋊C412yes—
274C2×C4×C31C23×C411yescharacteristic
275C2×C4×C31C22×Q811yescharacteristic
276C2×C4×C31C2×#4111yescharacteristic
277C2×C4×C31C2×#4111yescharacteristic
278C2×C4×C31H(5,𝔽2)11yescharacteristic
279C2×C4×C31H(5,𝔽2)11yescharacteristic
280C8×C31—22no—
281C8×C31—22no—
282C8×C31—22no—
283C8×C31—22no—
284C2×#435C2×C3111yescharacteristic
285#2354C2×C3111yescharacteristic
286#2352C2×C3111yescharacteristic
287#1949C2×C3111yescharacteristic, complemented
288#1947C2×C3111yescharacteristic, complemented
289#1854C2×C3111yescharacteristic, complemented
290#1854C2×C3111yescharacteristic, complemented
291#1854C2×C3111yescharacteristic, complemented
292#1852C2×C3111yescharacteristic, complemented
293#1836C2×C3111yescharacteristic, complemented
294#1809C2×C3111yescharacteristic, complemented
295#1808C2×C3111yescharacteristic, complemented
296#1776C2×C3111yescharacteristic, complemented
297#1736C2×C3111yescharacteristic, complemented
298#1735C2×C3111yescharacteristic, complemented
299C22×C31—22no—
300C22×C31—22no—
301C22×C31—22no—
302C22×C31—22no—
303C22×C31—22no—
304C22×C31—22no—
305C22×C31—41no—
306C22×C31—41no—
307C22×C31—41no—
308C22×C31—41no—
309C22×C31—41no—
310C22×C31—41no—
311C22×C31—41no—
312C22×C31—41no—
313C22×C31C22×C4⋊C411yescharacteristic
314C22×C31#54611yescharacteristic
315C22×C31#54611yescharacteristic
316C22×C31#57511yescharacteristic
317C22×C31#57511yescharacteristic
318C22×C31#57611yescharacteristic
319C22×C31#57811yescharacteristic
320C4×C31—22no—
321C4×C31—22no—
322C4×C31—22no—
323C4×C31—22no—
324C4×C31—42no—
325C4×C31—42no—
326C4×C31—81no—
327C4×C31—81no—
328C4×C31—81no—
329C4×C31—81no—
330C4×C31—81no—
331C4×C31—81no—
332C4×C31C4×#4111yescharacteristic
333C4×C31#51811yescharacteristic
334C4×C31#55411yescharacteristic
335C4×C31#55411yescharacteristic
336C22×M16C22×C3111yescharacteristic
337C23×C8C22×C3111yescharacteristic
338C2×C4×D4C22×C3111yescharacteristic
339C2×#117C22×C3111yescharacteristic
340C2×#117C22×C3111yescharacteristic
341C2×#117C22×C3111yescharacteristic
342C22×C4⋊C4C22×C3111yescharacteristic
343#435C4×C3118yescomplemented
344C2×#107C22×C3111yescharacteristic
345C2×#107C22×C3111yescharacteristic
346C2×#107C22×C3111yescharacteristic
347C2×#107C22×C3111yescharacteristic
348C2×#106C22×C3111yescharacteristic
349C2×#106C22×C3111yescharacteristic
350C2×C4⋊C8C22×C3111yescharacteristic
351C2×C22⋊C8C22×C3111yescharacteristic
352C2×C22⋊C8C22×C3111yescharacteristic
353C2×#97C22×C3111yescharacteristic
354#390—21no—
355#388—21no—
356#388—21no—
357#388—21no—
358#387—21no—
359#386—21no—
360#384C22×C3111yescharacteristic
361#382C22×C3111yescharacteristic
362#380C22×C3111yescharacteristic
363#380C22×C3111yescharacteristic
364#380C22×C3111yescharacteristic
365#380C22×C3111yescharacteristic
366C4×C4⋊C4—21no—
367C4×C4⋊C4C22×C3111yescharacteristic
368C4×C4⋊C4C22×C3111yescharacteristic
369C4×C22⋊C4—21no—
370#340C22×C3111yescharacteristic
371#340C22×C3111yescharacteristic
372#340C22×C3111yescharacteristic
373#340C22×C3111yescharacteristic
374#340C22×C3111yescharacteristic
375#340C22×C3111yescharacteristic
376#340C22×C3111yescharacteristic
377#340C22×C3111yescharacteristic
378#340C22×C3111yescharacteristic
379#340C22×C3111yescharacteristic
380C2×C31—42no—
381C2×C31—42no—
382C2×C31#234911yescharacteristic
383C2×C31#291111yescharacteristic
384C2×C31#291311yescharacteristic
385C2×C31#330911yescharacteristic
386C2×C31#331311yescharacteristic
387C2×C31#331511yescharacteristic
388C2×C31#331911yescharacteristic
389C22×D4D4×C3111yescharacteristic
390C23×C4—21no—
391C23×C4C23×C3111yescharacteristic
392C23×C4C23×C3111yescharacteristic
393C2×M16—41no—
394C2×M16—41no—
395C2×M16C2×C4×C3114yes—
396C22×C8—41no—
397C22×C8—41no—
398C22×C8C2×C4×C3114yescomplemented
399C22×C8C23×C3111yescharacteristic
400C22×C8C23×C3111yescharacteristic
401C22×C8C23×C3111yescharacteristic
402C22×C8C23×C3111yescharacteristic
403C4×D4C2×C4×C3114yes—
404C4×D4Q8×C3114yes—
405#117—22no—
406#117—22no—
407#117—22no—
408#117—41no—
409#117—41no—
410#117—41no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—41no—
416C2×C4⋊C4D4×C3111yescharacteristic
417C2×C4⋊C4C23×C3111yescharacteristic
418C2×C4⋊C4C23×C3111yescharacteristic
419C2×C4⋊C4C23×C3111yescharacteristic
420C2×C4⋊C4C23×C3111yescharacteristic
421C2×C4⋊C4C23×C3111yescharacteristic
422C2×C4⋊C4C23×C3111yescharacteristic
423C2×C4⋊C4C23×C3111yescharacteristic
424C2×C4⋊C4C23×C3111yescharacteristic
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—21no—
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4D4×C3111yescharacteristic
433C2×C22⋊C4D4×C3111yescharacteristic
434C2×C42—21no—
435C2×C42—21no—
436C2×C42—21no—
437C2×C42—21no—
438C2×C42—21no—
439C2×C42C23×C3111yescharacteristic
440#107—22no—
441#107—41no—
442#107—41no—
443#107—41no—
444#106—22no—
445#106—41no—
446C4⋊C8C2×C4×C3114yescomplemented
447C22⋊C8C2×C4×C3114yes—
448C22⋊C8C2×C4×C3114yescomplemented
449#97C2×C4×C3114yescomplemented
450#95—21no—
451#95—21no—
452#95—21no—
453#95—21no—
454#95—21no—
455#95—21no—
456#95—21no—
457#95—21no—
458C31#2271211yescharacteristic, direct product factor, Sylow
459C24C2×D4×C3111yescharacteristic
460C24C2×D4×C3111yescharacteristic
461C2×D4—41no—
462C2×D4—41no—
463C2×D4C4⋊C4×C3114yes—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—42no—
481C22×C4—42no—
482C22×C4—81no—
483C22×C4C22×C4×C3112yes—
484C22×C4C22×C4×C3112yes—
485C22×C4C2×D4×C3111yescharacteristic
486C22×C4C2×D4×C3111yescharacteristic
487C22×C4C2×D4×C3111yescharacteristic
488C22×C4C2×D4×C3111yescharacteristic
489C22×C4C2×Q8×C3112yes—
490C22×C4C2×Q8×C3112yes—
491C22×C4C24×C3111yescharacteristic
492M16—44no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—44no—
502C2×C8C22×C4×C3112yes—
503C2×C8C22×C4×C3112yes—
504C2×C8C22×C4×C3112yes—
505C2×C8C22×C4×C3112yes—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—42no—
521C4⋊C4—42no—
522C4⋊C4—81no—
523C4⋊C4C4⋊C4×C3114yes—
524C4⋊C4#41×C3112yes—
525C4⋊C4#41×C3112yes—
526C22⋊C4—42no—
527C22⋊C4—42no—
528C22⋊C4—42no—
529C22⋊C4—42no—
530C22⋊C4—81no—
531C22⋊C4—81no—
532C22⋊C4—81no—
533C22⋊C4C4⋊C4×C3114yes—
534C22⋊C4C4⋊C4×C3114yes—
535C42—42no—
536C42—42no—
537C42—42no—
538C42—42no—
539C42—81no—
540C42C22×C4×C3112yes—
541C42C2×Q8×C3112yes—
542C23—21no—
543C23—21no—
544C23—21no—
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23—21no—
554C23C2×C4⋊C4×C3112yes—
555C23C2×C4⋊C4×C3112yes—
556C23C22×D4×C3111yescharacteristic
557D4—44no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
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—84no—
599C2×C4C2×C4⋊C4×C3112yes—
600C2×C4C2×C4⋊C4×C3112yes—
601C2×C4C2×C4⋊C4×C3112yes—
602C2×C4C2×C4⋊C4×C3112yes—
603C2×C4C23×C4×C3111yescharacteristic
604C2×C4C22×Q8×C3111yescharacteristic
605C2×C4C2×#41×C3111yescharacteristic
606C2×C4C2×#41×C3111yescharacteristic
607C2×C4C31×H(5,𝔽2)11yescharacteristic
608C2×C4C31×H(5,𝔽2)11yescharacteristic
609C8—22no—
610C8—22no—
611C8—22no—
612C8—22no—
613C22—22no—
614C22—22no—
615C22—22no—
616C22—22no—
617C22—22no—
618C22—22no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22—41no—
624C22—41no—
625C22—41no—
626C22—41no—
627C22C22×C4⋊C4×C3111yescharacteristic
628C22C31×#54611yescharacteristic
629C22C31×#54611yescharacteristic
630C22C31×#57511yescharacteristic
631C22C31×#57511yescharacteristic
632C22C31×#57611yescharacteristic
633C22C31×#57811yescharacteristic
634C4—22no—
635C4—22no—
636C4—22no—
637C4—22no—
638C4—42no—
639C4—42no—
640C4—81no—
641C4—81no—
642C4—81no—
643C4—81no—
644C4—81no—
645C4—81no—
646C4C4×#41×C3111yescharacteristic
647C4C31×#51811yescharacteristic
648C4C31×#55411yescharacteristic
649C4C31×#55411yescharacteristic
650C2—42no—
651C2—42no—
652C2C31×#234911yescharacteristic
653C2C31×#291111yescharacteristic
654C2C31×#291311yescharacteristic
655C2C31×#330911yescharacteristic
656C2C31×#331311yescharacteristic
657C2C31×#331511yescharacteristic
658C2C31×#331911yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutatorC2×C4C23×C4×C31
Frattini, cosocleC22×C4C24×C31
prime radicalC22×D4×C31D4
LCSG ▷ C2×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
4. C31×#1949C2semidirect
5. C31×#1947C2semidirect
6. C31×#1854C2semidirect
7. C31×#1854C2semidirect
8. C31×#1854C2semidirect
9. C31×#1852C2semidirect
10. C31×#1836C2semidirect
11. C31×#1809C2semidirect
12. C31×#1808C2semidirect
13. C31×#1776C2semidirect
14. C31×#1736C2semidirect
15. C31×#1735C2semidirect
23. C31×#435C4semidirect
69. C22×C8×C31C2×C4semidirect
117. C31×C4⋊C8C2×C4semidirect
119. C31×C22⋊C8C2×C4semidirect
120. C31×#97C2×C4semidirect
212. #22712C31direct (N × H)
287. #1949C2×C31semidirect
288. #1947C2×C31semidirect
289. #1854C2×C31semidirect
290. #1854C2×C31semidirect
291. #1854C2×C31semidirect
292. #1852C2×C31semidirect
293. #1836C2×C31semidirect
294. #1809C2×C31semidirect
295. #1808C2×C31semidirect
296. #1776C2×C31semidirect
297. #1736C2×C31semidirect
298. #1735C2×C31semidirect
343. #435C4×C31semidirect
398. C22×C8C2×C4×C31semidirect
446. C4⋊C8C2×C4×C31semidirect
448. C22⋊C8C2×C4×C31semidirect
449. #97C2×C4×C31semidirect
458. C31#22712direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4352
C31×#23542
C31×#23522
C31×#19492
C31×#19472
C31×#18542
C31×#18522
C31×#18362
C31×#18092
C31×#18082
C31×#17762
C31×#17362
C31×#17352
#2271231