Finite Group Databasebeta

← C31×#26952 #21483711

Subgroups — C31×#26952 #21483711

Order 7936.

836 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#485C211yesmaximal, characteristic
2C2×C31×#462C211yesmaximal, characteristic, complemented
3C31×#2429C211yesmaximal, characteristic
4C31×#2362C211yesmaximal, characteristic
5C31×#2088C211yesmaximal, characteristic, complemented
6C31×#2043C211yesmaximal, characteristic, complemented
7C31×#2001C211yesmaximal, characteristic
8C31×#2001C211yesmaximal, characteristic
9C31×#1971C211yesmaximal, characteristic, complemented
10C31×#1928C211yesmaximal, characteristic, complemented
11C31×#1924C211yesmaximal, characteristic
12C31×#1878C211yesmaximal, characteristic, complemented
13C31×#1873C211yesmaximal, characteristic
14C31×#1863C211yesmaximal, characteristic, complemented
15C31×#1763C211yesmaximal, characteristic, complemented
16C22×Q16×C31C2211yescharacteristic
17C22×Q16×C31C2211yescharacteristic
18C2×C31×C4⋊Q8C2211yescharacteristic
19C2×C31×C22⋊Q8C2211yescharacteristic
20C2×C31×C22⋊Q8C2211yescharacteristic
21C2×C31×C22⋊Q8C2211yescharacteristic
22C2×C4×Q8×C31C2211yescharacteristic
23C2×C4×Q8×C31C2211yescharacteristic
24C2×C31×#117C2211yescharacteristic
25C31×#485—24no—
26C31×#462—24no—
27C2×C31×#107C2211yescharacteristic
28C2×C31×#106C2211yescharacteristic
29C2×C31×C4⋊C8C2211yescharacteristic
30C2×C31×#103C2211yescharacteristic
31C2×C31×#103C2211yescharacteristic
32C2×C31×#103C2211yescharacteristic
33C2×C31×#103C2211yescharacteristic
34C2×C31×#103C2211yescharacteristic
35C2×C31×#103C2211yescharacteristic
36C2×C31×#103C2211yescharacteristic
37C2×C31×#103C2211yescharacteristic
38C2×C31×C22⋊C8C2211yescharacteristic
39C2×C31×C22⋊C8C2211yescharacteristic
40C2×C31×#97C2211yescharacteristic
41C31×#398—21no—
42C31×#396—21no—
43C31×#391C2211yescharacteristic
44C31×#391C2211yescharacteristic
45C31×#389—21no—
46C31×#389C2211yescharacteristic
47C31×#389C2211yescharacteristic
48C31×#388—21no—
49C31×#388—21no—
50C31×#388—21no—
51C31×#387—21no—
52C4×C4⋊C4×C31—21no—
53C4×C4⋊C4×C31C2211yescharacteristic
54C4×C22⋊C4×C31C2211yescharacteristic
55C31×#340C2211yescharacteristic
56C31×#340C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#336C2211yescharacteristic
60C31×#336C2211yescharacteristic
61C22×Q8×C31C2311yescharacteristic
62C22×Q8×C31C2311yescharacteristic
63C22×Q8×C31C2311yescharacteristic
64C23×C4×C31C2311yescharacteristic
65C2×Q16×C31—22no—
66C2×Q16×C31—22no—
67C2×Q16×C31—22no—
68C2×Q16×C31—22no—
69C2×Q16×C31—41no—
70C2×Q16×C31—41no—
71C22×C8×C31C2311yescharacteristic
72C22×C8×C31C2311yescharacteristic
73C22×C8×C31C2311yescharacteristic
74C22×C8×C31C2311yescharacteristic
75C31×C4⋊Q8—22no—
76C31×C4⋊Q8—41no—
77C31×C22⋊Q8—22no—
78C31×C22⋊Q8—22no—
79C31×C22⋊Q8—22no—
80C31×C22⋊Q8—22no—
81C31×C22⋊Q8—41no—
82C31×C22⋊Q8—41no—
83C4×Q8×C31—22no—
84C4×Q8×C31—22no—
85C4×Q8×C31—41no—
86C4×Q8×C31—41no—
87C31×#117—22no—
88C31×#117—41no—
89C2×C4⋊C4×C31—21no—
90C2×C4⋊C4×C31—21no—
91C2×C4⋊C4×C31—21no—
92C2×C4⋊C4×C31—21no—
93C2×C4⋊C4×C31—21no—
94C2×C4⋊C4×C31—21no—
95C2×C4⋊C4×C31—21no—
96C2×C4⋊C4×C31—21no—
97C2×C4⋊C4×C31—21no—
98C2×C4⋊C4×C31C2311yescharacteristic
99C2×C4⋊C4×C31C2311yescharacteristic
100C2×C4⋊C4×C31C2311yescharacteristic
101C2×C4⋊C4×C31C2311yescharacteristic
102C2×C4⋊C4×C31C2311yescharacteristic
103C2×C22⋊C4×C31—21no—
104C2×C22⋊C4×C31—21no—
105C2×C22⋊C4×C31—21no—
106C2×C22⋊C4×C31—21no—
107C2×C22⋊C4×C31D411yescharacteristic
108C2×C22⋊C4×C31D411yescharacteristic
109C2×C42×C31—21no—
110C2×C42×C31—21no—
111C2×C42×C31—21no—
112C2×C42×C31—21no—
113C2×C42×C31C2311yescharacteristic
114C2×C42×C31C2311yescharacteristic
115C31×#107—22no—
116C31×#106—22no—
117C31×C4⋊C8—22no—
118C31×#103—22no—
119C31×#103—22no—
120C31×#103—22no—
121C31×#103—22no—
122C31×#103—22no—
123C31×#103—41no—
124C31×#103—41no—
125C31×#103D414yes—
126C31×C22⋊C8—22no—
127C31×C22⋊C8—41no—
128C31×#97—41no—
129C31×#95—21no—
130C31×#95—21no—
131C31×#95—21no—
132C31×#95—21no—
133C31×#95—21no—
134C31×#95—21no—
135C31×#95—21no—
136C31×#95D411yescharacteristic
137C31×#95D411yescharacteristic
138C24×C31C2×D411yescharacteristic
139C2×Q8×C31—21no—
140C2×Q8×C31—21no—
141C2×Q8×C31—21no—
142C2×Q8×C31—21no—
143C2×Q8×C31—21no—
144C2×Q8×C31—21no—
145C2×Q8×C31—21no—
146C2×Q8×C31—21no—
147C2×Q8×C31—21no—
148C2×Q8×C31—21no—
149C2×Q8×C31—21no—
150C2×Q8×C31—21no—
151C2×Q8×C31—21no—
152C2×Q8×C31—21no—
153C2×Q8×C31—21no—
154C2×Q8×C31—21no—
155C2×Q8×C31C2×D412yes—
156C2×Q8×C31#4112yes—
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—21no—
164C22×C4×C31—21no—
165C22×C4×C31—21no—
166C22×C4×C31—21no—
167C22×C4×C31—21no—
168C22×C4×C31—21no—
169C22×C4×C31—21no—
170C22×C4×C31—21no—
171C22×C4×C31C2×D411yescharacteristic
172C22×C4×C31C2×D411yescharacteristic
173C22×C4×C31C2×D411yescharacteristic
174C22×C4×C31C2×D411yescharacteristic
175C22×C4×C31C2×D411yescharacteristic
176C22×C4×C31C2411yescharacteristic
177Q16×C31—44no—
178Q16×C31—44no—
179C2×C8×C31—21no—
180C2×C8×C31—21no—
181C2×C8×C31—21no—
182C2×C8×C31—21no—
183C2×C8×C31—21no—
184C2×C8×C31—21no—
185C2×C8×C31—21no—
186C2×C8×C31—21no—
187C2×C8×C31—21no—
188C2×C8×C31—21no—
189C2×C8×C31—21no—
190C2×C8×C31C2×D412yes—
191C4⋊C4×C31—24no—
192C4⋊C4×C31—21no—
193C4⋊C4×C31—21no—
194C4⋊C4×C31—21no—
195C4⋊C4×C31—21no—
196C4⋊C4×C31—21no—
197C4⋊C4×C31—21no—
198C4⋊C4×C31—21no—
199C4⋊C4×C31—42no—
200C4⋊C4×C31—42no—
201C4⋊C4×C31—42no—
202C4⋊C4×C31—42no—
203C4⋊C4×C31—42no—
204C4⋊C4×C31—42no—
205C4⋊C4×C31—42no—
206C4⋊C4×C31—42no—
207C4⋊C4×C31C2×D412yes—
208C4⋊C4×C31#4112yes—
209C4⋊C4×C31#4112yes—
210C22⋊C4×C31—24no—
211C22⋊C4×C31—22no—
212C22⋊C4×C31—41no—
213C22⋊C4×C31—42no—
214C22⋊C4×C31—42no—
215C22⋊C4×C31—42no—
216C42×C31—21no—
217C42×C31—21no—
218C42×C31—21no—
219C42×C31—21no—
220C42×C31—42no—
221C42×C31—42no—
222C42×C31—42no—
223C42×C31—42no—
224#26952C3111yesmaximal, characteristic, direct product factor, Sylow
225C23×C31—21no—
226C23×C31—21no—
227C23×C31—21no—
228C23×C31—21no—
229C23×C31—21no—
230C23×C31—21no—
231C23×C31—21no—
232C23×C31C22×D411yescharacteristic
233Q8×C31—22no—
234Q8×C31—22no—
235Q8×C31—22no—
236Q8×C31—22no—
237Q8×C31—41no—
238Q8×C31—41no—
239Q8×C31—41no—
240Q8×C31—41no—
241Q8×C31—41no—
242Q8×C31—41no—
243Q8×C31—41no—
244Q8×C31—41no—
245C2×C4×C31—21no—
246C2×C4×C31—21no—
247C2×C4×C31—22no—
248C2×C4×C31—22no—
249C2×C4×C31—21no—
250C2×C4×C31—21no—
251C2×C4×C31—22no—
252C2×C4×C31—21no—
253C2×C4×C31—22no—
254C2×C4×C31—21no—
255C2×C4×C31—21no—
256C2×C4×C31—22no—
257C2×C4×C31—21no—
258C2×C4×C31—21no—
259C2×C4×C31—21no—
260C2×C4×C31—21no—
261C2×C4×C31—21no—
262C2×C4×C31—21no—
263C2×C4×C31—21no—
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—41no—
280C2×C4×C31—41no—
281C2×C4×C31—41no—
282C2×C4×C31—41no—
283C2×C4×C31—41no—
284C2×C4×C31—41no—
285C2×C4×C31—41no—
286C2×C4×C31—41no—
287C2×C4×C31#13712yes—
288C2×C4×C31C22×D411yescharacteristic
289C2×C4×C31C2×#4111yescharacteristic
290C2×C4×C31C2×#4111yescharacteristic
291C2×C4×C31C2×#4111yescharacteristic
292C2×C4×C31H(5,𝔽2)11yescharacteristic
293C2×C4×C31H(5,𝔽2)11yescharacteristic
294C8×C31—22no—
295C8×C31—41no—
296C8×C31—41no—
297C8×C31—41no—
298C2×#485C2×C3111yescharacteristic
299C2×#462C2×C3111yescharacteristic, complemented
300#2429C2×C3111yescharacteristic
301#2362C2×C3111yescharacteristic
302#2088C2×C3111yescharacteristic, complemented
303#2043C2×C3111yescharacteristic, complemented
304#2001C2×C3111yescharacteristic
305#2001C2×C3111yescharacteristic
306#1971C2×C3111yescharacteristic, complemented
307#1928C2×C3111yescharacteristic, complemented
308#1924C2×C3111yescharacteristic
309#1878C2×C3111yescharacteristic, complemented
310#1873C2×C3111yescharacteristic
311#1863C2×C3111yescharacteristic, complemented
312#1763C2×C3111yescharacteristic, complemented
313C22×C31—41no—
314C22×C31—41no—
315C22×C31—41no—
316C22×C31—41no—
317C22×C31—41no—
318C22×C31—41no—
319C22×C31—41no—
320C22×C31#52511yescharacteristic
321C22×C31D4211yescharacteristic
322C22×C31#54611yescharacteristic
323C22×C31C2×#13711yescharacteristic
324C22×C31#57511yescharacteristic
325C22×C31#57811yescharacteristic
326C22×C31#57811yescharacteristic
327C4×C31—22no—
328C4×C31—41no—
329C4×C31—42no—
330C4×C31—41no—
331C4×C31—42no—
332C4×C31—42no—
333C4×C31—41no—
334C4×C31—42no—
335C4×C31—41no—
336C4×C31—42no—
337C4×C31—81no—
338C4×C31—81no—
339C4×C31—81no—
340C4×C31#53211yescharacteristic
341C4×C31#54011yescharacteristic
342C4×C31#54611yescharacteristic
343C4×C31#55311yescharacteristic
344C22×Q16C22×C3111yescharacteristic
345C22×Q16C22×C3111yescharacteristic
346C2×C4⋊Q8C22×C3111yescharacteristic
347C2×C22⋊Q8C22×C3111yescharacteristic
348C2×C22⋊Q8C22×C3111yescharacteristic
349C2×C22⋊Q8C22×C3111yescharacteristic
350C2×C4×Q8C22×C3111yescharacteristic
351C2×C4×Q8C22×C3111yescharacteristic
352C2×#117C22×C3111yescharacteristic
353#485—24no—
354#462—24no—
355C2×#107C22×C3111yescharacteristic
356C2×#106C22×C3111yescharacteristic
357C2×C4⋊C8C22×C3111yescharacteristic
358C2×#103C22×C3111yescharacteristic
359C2×#103C22×C3111yescharacteristic
360C2×#103C22×C3111yescharacteristic
361C2×#103C22×C3111yescharacteristic
362C2×#103C22×C3111yescharacteristic
363C2×#103C22×C3111yescharacteristic
364C2×#103C22×C3111yescharacteristic
365C2×#103C22×C3111yescharacteristic
366C2×C22⋊C8C22×C3111yescharacteristic
367C2×C22⋊C8C22×C3111yescharacteristic
368C2×#97C22×C3111yescharacteristic
369#398—21no—
370#396—21no—
371#391C22×C3111yescharacteristic
372#391C22×C3111yescharacteristic
373#389—21no—
374#389C22×C3111yescharacteristic
375#389C22×C3111yescharacteristic
376#388—21no—
377#388—21no—
378#388—21no—
379#387—21no—
380C4×C4⋊C4—21no—
381C4×C4⋊C4C22×C3111yescharacteristic
382C4×C22⋊C4C22×C3111yescharacteristic
383#340C22×C3111yescharacteristic
384#340C22×C3111yescharacteristic
385#340C22×C3111yescharacteristic
386#340C22×C3111yescharacteristic
387#336C22×C3111yescharacteristic
388#336C22×C3111yescharacteristic
389C2×C31—81no—
390C2×C31#246411yescharacteristic
391C2×C31#311611yescharacteristic
392C2×C31#312711yescharacteristic
393C2×C31#326911yescharacteristic
394C2×C31#327011yescharacteristic
395C2×C31#331511yescharacteristic
396C2×C31#332811yescharacteristic
397C22×Q8C23×C3111yescharacteristic
398C22×Q8C23×C3111yescharacteristic
399C22×Q8C23×C3111yescharacteristic
400C23×C4C23×C3111yescharacteristic
401C2×Q16—22no—
402C2×Q16—22no—
403C2×Q16—22no—
404C2×Q16—22no—
405C2×Q16—41no—
406C2×Q16—41no—
407C22×C8C23×C3111yescharacteristic
408C22×C8C23×C3111yescharacteristic
409C22×C8C23×C3111yescharacteristic
410C22×C8C23×C3111yescharacteristic
411C4⋊Q8—22no—
412C4⋊Q8—41no—
413C22⋊Q8—22no—
414C22⋊Q8—22no—
415C22⋊Q8—22no—
416C22⋊Q8—22no—
417C22⋊Q8—41no—
418C22⋊Q8—41no—
419C4×Q8—22no—
420C4×Q8—22no—
421C4×Q8—41no—
422C4×Q8—41no—
423#117—22no—
424#117—41no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4C23×C3111yescharacteristic
435C2×C4⋊C4C23×C3111yescharacteristic
436C2×C4⋊C4C23×C3111yescharacteristic
437C2×C4⋊C4C23×C3111yescharacteristic
438C2×C4⋊C4C23×C3111yescharacteristic
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4D4×C3111yescharacteristic
444C2×C22⋊C4D4×C3111yescharacteristic
445C2×C42—21no—
446C2×C42—21no—
447C2×C42—21no—
448C2×C42—21no—
449C2×C42C23×C3111yescharacteristic
450C2×C42C23×C3111yescharacteristic
451#107—22no—
452#106—22no—
453C4⋊C8—22no—
454#103—22no—
455#103—22no—
456#103—22no—
457#103—22no—
458#103—22no—
459#103—41no—
460#103—41no—
461#103D4×C3114yes—
462C22⋊C8—22no—
463C22⋊C8—41no—
464#97—41no—
465#95—21no—
466#95—21no—
467#95—21no—
468#95—21no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95D4×C3111yescharacteristic
473#95D4×C3111yescharacteristic
474C31#2695211yescharacteristic, direct product factor, Sylow
475C24C2×D4×C3111yescharacteristic
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8C2×D4×C3112yes—
493C2×Q8#41×C3112yes—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4C2×D4×C3111yescharacteristic
509C22×C4C2×D4×C3111yescharacteristic
510C22×C4C2×D4×C3111yescharacteristic
511C22×C4C2×D4×C3111yescharacteristic
512C22×C4C2×D4×C3111yescharacteristic
513C22×C4C24×C3111yescharacteristic
514Q16—44no—
515Q16—44no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8C2×D4×C3112yes—
528C4⋊C4—24no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—42no—
537C4⋊C4—42no—
538C4⋊C4—42no—
539C4⋊C4—42no—
540C4⋊C4—42no—
541C4⋊C4—42no—
542C4⋊C4—42no—
543C4⋊C4—42no—
544C4⋊C4C2×D4×C3112yes—
545C4⋊C4#41×C3112yes—
546C4⋊C4#41×C3112yes—
547C22⋊C4—24no—
548C22⋊C4—22no—
549C22⋊C4—41no—
550C22⋊C4—42no—
551C22⋊C4—42no—
552C22⋊C4—42no—
553C42—21no—
554C42—21no—
555C42—21no—
556C42—21no—
557C42—42no—
558C42—42no—
559C42—42no—
560C42—42no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23C22×D4×C3111yescharacteristic
569Q8—22no—
570Q8—22no—
571Q8—22no—
572Q8—22no—
573Q8—41no—
574Q8—41no—
575Q8—41no—
576Q8—41no—
577Q8—41no—
578Q8—41no—
579Q8—41no—
580Q8—41no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—22no—
588C2×C4—21no—
589C2×C4—22no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—22no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
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—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4C31×#13712yes—
624C2×C4C22×D4×C3111yescharacteristic
625C2×C4C2×#41×C3111yescharacteristic
626C2×C4C2×#41×C3111yescharacteristic
627C2×C4C2×#41×C3111yescharacteristic
628C2×C4C31×H(5,𝔽2)11yescharacteristic
629C2×C4C31×H(5,𝔽2)11yescharacteristic
630C8—22no—
631C8—41no—
632C8—41no—
633C8—41no—
634C22—41no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22C31×#52511yescharacteristic
642C22D42×C3111yescharacteristic
643C22C31×#54611yescharacteristic
644C22C2×C31×#13711yescharacteristic
645C22C31×#57511yescharacteristic
646C22C31×#57811yescharacteristic
647C22C31×#57811yescharacteristic
648C4—22no—
649C4—42no—
650C4—41no—
651C4—42no—
652C4—42no—
653C4—41no—
654C4—42no—
655C4—41no—
656C4—42no—
657C4—41no—
658C4—81no—
659C4—81no—
660C4—81no—
661C4C31×#53211yescharacteristic
662C4C31×#54011yescharacteristic
663C4C31×#54611yescharacteristic
664C4C31×#55311yescharacteristic
665C2—81no—
666C2C31×#246411yescharacteristic
667C2C31×#311611yescharacteristic
668C2C31×#312711yescharacteristic
669C2C31×#326911yescharacteristic
670C2C31×#327011yescharacteristic
671C2C31×#331511yescharacteristic
672C2C31×#332811yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC24×C31C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C4×C22⋊C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#462C2semidirect
5. C31×#2088C2semidirect
6. C31×#2043C2semidirect
9. C31×#1971C2semidirect
10. C31×#1928C2semidirect
12. C31×#1878C2semidirect
14. C31×#1863C2semidirect
15. C31×#1763C2semidirect
224. #26952C31direct (N × H)
299. C2×#462C2×C31semidirect
302. #2088C2×C31semidirect
303. #2043C2×C31semidirect
306. #1971C2×C31semidirect
307. #1928C2×C31semidirect
309. #1878C2×C31semidirect
311. #1863C2×C31semidirect
312. #1763C2×C31semidirect
474. C31#26952direct (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×#4622
C31×#24292
C31×#23622
C31×#20882
C31×#20432
C31×#20012
C31×#19712
C31×#19282
C31×#19242
C31×#18782
C31×#18732
C31×#18632
C31×#17632
#2695231