Finite Group Databasebeta

← C31×#21875 #21478634

Subgroups — C31×#21875 #21478634

Order 7936.

1158 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#529C211yesmaximal, characteristic
2C31×#2285C211yesmaximal, characteristic, complemented
3C31×#2283C211yesmaximal, characteristic, complemented
4C31×#1996C212yesmaximal, complemented
5C31×#1964C212yesmaximal
6C31×#1899C214yesmaximal, complemented
7C31×#1799C214yesmaximal, complemented
8C31×#529—21no—
9C31×#529—21no—
10C31×#529—21no—
11C31×#529—21no—
12C31×#529—21no—
13C31×#529—21no—
14C31×#529—21no—
15C31×#529—21no—
16C2×C31×#126C412yescomplemented
17C2×C31×#125C411yescharacteristic, complemented
18C2×C31×#124C411yescharacteristic, complemented
19C2×C31×#123C2212yes—
20C2×C31×C22⋊Q8C2211yescharacteristic
21C2×C31×#121C2211yescharacteristic
22C2×C4×Q8×C31C411yescharacteristic, complemented
23C2×C4×D4×C31C411yescharacteristic, complemented
24C2×C4×D4×C31C2212yes—
25C2×C31×#117C412yescomplemented
26C2×C31×#117C2212yes—
27C22×C42×C31C2211yescharacteristic
28C2×C31×#99C2218yes—
29C31×#384—21no—
30C31×#383—21no—
31C31×#382—21no—
32C31×#382—21no—
33C31×#381C2212yes—
34C31×#380C2212yes—
35C31×#380C2212yes—
36C31×#380C2212yes—
37C4×C4⋊C4×C31—21no—
38C4×C4⋊C4×C31—21no—
39C4×C4⋊C4×C31—21no—
40C4×C22⋊C4×C31C2212yes—
41C31×#376—21no—
42C31×#342C2218yes—
43C22×Q8×C31C2×C411yescharacteristic
44C22×D4×C31C2×C411yescharacteristic
45C22×D4×C31C2312yes—
46C23×C4×C31C2×C412yes—
47C23×C4×C31C2311yescharacteristic
48C23×C4×C31C2311yescharacteristic
49C23×C4×C31C2311yescharacteristic
50C31×#126—22no—
51C31×#126—22no—
52C31×#126—22no—
53C31×#126—22no—
54C31×#125—21no—
55C31×#125—21no—
56C31×#125—21no—
57C31×#125—21no—
58C31×#124—21no—
59C31×#124—21no—
60C31×#124—21no—
61C31×#124—21no—
62C31×#123—22no—
63C31×#123—22no—
64C31×#123—22no—
65C31×#123—22no—
66C31×C22⋊Q8—21no—
67C31×C22⋊Q8—21no—
68C31×C22⋊Q8—21no—
69C31×C22⋊Q8—21no—
70C31×#121—21no—
71C31×#121—21no—
72C31×#121—21no—
73C31×#121—21no—
74C4×Q8×C31—21no—
75C4×Q8×C31—21no—
76C4×Q8×C31—21no—
77C4×Q8×C31—21no—
78C4×D4×C31—22no—
79C4×D4×C31—22no—
80C4×D4×C31—22no—
81C4×D4×C31—22no—
82C4×D4×C31—21no—
83C4×D4×C31—21no—
84C4×D4×C31—21no—
85C4×D4×C31—21no—
86C31×#117—22no—
87C31×#117—22no—
88C31×#117—22no—
89C31×#117—22no—
90C31×#117—44no—
91C2×C4⋊C4×C31—22no—
92C2×C4⋊C4×C31—22no—
93C2×C4⋊C4×C31—22no—
94C2×C4⋊C4×C31—22no—
95C2×C4⋊C4×C31C2×C412yes—
96C2×C4⋊C4×C31C2×C412yes—
97C2×C4⋊C4×C31C2×C411yescharacteristic
98C2×C4⋊C4×C31C2×C412yes—
99C2×C4⋊C4×C31C2×C411yescharacteristic
100C2×C4⋊C4×C31C2×C412yes—
101C2×C22⋊C4×C31C2×C412yes—
102C2×C22⋊C4×C31C2×C412yes—
103C2×C22⋊C4×C31C2×C412yes—
104C2×C22⋊C4×C31C2×C412yes—
105C2×C22⋊C4×C31C2314yes—
106C2×C22⋊C4×C31C2314yes—
107C2×C22⋊C4×C31C2312yes—
108C2×C42×C31—22no—
109C2×C42×C31—22no—
110C2×C42×C31C2×C412yes—
111C2×C42×C31C2×C411yescharacteristic
112C2×C42×C31C2×C411yescharacteristic
113C2×C42×C31C2×C411yescharacteristic
114C2×C42×C31C2×C411yescharacteristic
115C2×C42×C31D411yescharacteristic
116C2×C42×C31D411yescharacteristic
117C2×C42×C31D411yescharacteristic
118C2×C42×C31D411yescharacteristic
119C2×C42×C31D411yescharacteristic
120C2×C42×C31D411yescharacteristic
121C2×C42×C31D411yescharacteristic
122C2×C42×C31D411yescharacteristic
123C31×#99—48no—
124C31×#95—22no—
125C31×#95—22no—
126C31×#95—22no—
127C31×#95—22no—
128C31×#95—22no—
129C31×#95—22no—
130C24×C31C22×C412yes—
131C24×C31C2411yescharacteristic
132C2×Q8×C31—21no—
133C2×Q8×C31—21no—
134C2×Q8×C31—42no—
135C2×D4×C31—22no—
136C2×D4×C31—22no—
137C2×D4×C31—24no—
138C2×D4×C31—24no—
139C2×D4×C31—21no—
140C2×D4×C31—21no—
141C2×D4×C31—42no—
142C22×C4×C31—22no—
143C22×C4×C31—22no—
144C22×C4×C31—22no—
145C22×C4×C31—22no—
146C22×C4×C31—24no—
147C22×C4×C31—24no—
148C22×C4×C31—42no—
149C22×C4×C31—42no—
150C22×C4×C31—44no—
151C22×C4×C31C22×C412yes—
152C22×C4×C31C22×C411yescharacteristic
153C22×C4×C31C22×C411yescharacteristic
154C22×C4×C31C22×C411yescharacteristic
155C22×C4×C31C22×C411yescharacteristic
156C22×C4×C31C22×C412yes—
157C22×C4×C31C22×C412yes—
158C22×C4×C31C22×C411yescharacteristic
159C22×C4×C31C22×C411yescharacteristic
160C22×C4×C31C2×D411yescharacteristic
161C22×C4×C31C2×D411yescharacteristic
162C22×C4×C31C2×D411yescharacteristic
163C22×C4×C31C2×D411yescharacteristic
164C22×C4×C31C2×D411yescharacteristic
165C22×C4×C31C2×D411yescharacteristic
166C22×C4×C31C2×D411yescharacteristic
167C22×C4×C31C2×D411yescharacteristic
168C22×C4×C31C2×D411yescharacteristic
169C22×C4×C31C2×D411yescharacteristic
170C22×C4×C31C2×D411yescharacteristic
171C22×C4×C31C2×D411yescharacteristic
172C4⋊C4×C31—22no—
173C4⋊C4×C31—22no—
174C4⋊C4×C31—22no—
175C4⋊C4×C31—22no—
176C4⋊C4×C31—21no—
177C4⋊C4×C31—21no—
178C4⋊C4×C31—22no—
179C4⋊C4×C31—22no—
180C4⋊C4×C31—21no—
181C4⋊C4×C31—21no—
182C4⋊C4×C31—22no—
183C4⋊C4×C31—22no—
184C4⋊C4×C31—44no—
185C4⋊C4×C31—44no—
186C4⋊C4×C31—44no—
187C4⋊C4×C31—44no—
188C22⋊C4×C31—22no—
189C22⋊C4×C31—22no—
190C22⋊C4×C31—22no—
191C22⋊C4×C31—22no—
192C22⋊C4×C31—22no—
193C22⋊C4×C31—22no—
194C22⋊C4×C31—22no—
195C22⋊C4×C31—22no—
196C22⋊C4×C31—22no—
197C22⋊C4×C31—22no—
198C22⋊C4×C31—24no—
199C22⋊C4×C31—28no—
200C22⋊C4×C31—24no—
201C42×C31—22no—
202C42×C31—22no—
203C42×C31—44no—
204C42×C31—44no—
205C42×C31C22⋊C411yescharacteristic
206C42×C31C22⋊C411yescharacteristic
207C42×C31C22⋊C411yescharacteristic
208C42×C31C22⋊C411yescharacteristic
209C42×C31C22⋊C411yescharacteristic
210C42×C31C22⋊C411yescharacteristic
211C42×C31C22⋊C411yescharacteristic
212C42×C31C22⋊C411yescharacteristic
213C42×C31C22⋊C411yescharacteristic
214C42×C31C22⋊C411yescharacteristic
215C42×C31C22⋊C411yescharacteristic
216C42×C31C22⋊C411yescharacteristic
217C42×C31C22⋊C411yescharacteristic
218C42×C31C22⋊C411yescharacteristic
219C42×C31C22⋊C411yescharacteristic
220C42×C31C22⋊C411yescharacteristic
221#21875C3111yesmaximal, characteristic, direct product factor, Sylow
222C23×C31—22no—
223C23×C31—24no—
224C23×C31—41no—
225C23×C31—41no—
226C23×C31—42no—
227C23×C31—42no—
228C23×C31C23×C411yescharacteristic
229C23×C31C22×D411yescharacteristic
230C23×C31C22×D411yescharacteristic
231C23×C31H(5,𝔽2)12yes—
232C23×C312−1+412yes—
233Q8×C31—42no—
234Q8×C31—42no—
235D4×C31—42no—
236D4×C31—42no—
237D4×C31—42no—
238D4×C31—44no—
239D4×C31—42no—
240C2×C4×C31—22no—
241C2×C4×C31—22no—
242C2×C4×C31—21no—
243C2×C4×C31—21no—
244C2×C4×C31—21no—
245C2×C4×C31—21no—
246C2×C4×C31—22no—
247C2×C4×C31—22no—
248C2×C4×C31—22no—
249C2×C4×C31—22no—
250C2×C4×C31—22no—
251C2×C4×C31—22no—
252C2×C4×C31—22no—
253C2×C4×C31—22no—
254C2×C4×C31—22no—
255C2×C4×C31—22no—
256C2×C4×C31—22no—
257C2×C4×C31—24no—
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—44no—
265C2×C4×C31—44no—
266C2×C4×C31—42no—
267C2×C4×C31—42no—
268C2×C4×C31—44no—
269C2×C4×C31—44no—
270C2×C4×C31—44no—
271C2×C4×C31—44no—
272C2×C4×C31—44no—
273C2×C4×C31—44no—
274C2×C4×C31C2×C22⋊C411yescharacteristic
275C2×C4×C31C2×C22⋊C411yescharacteristic
276C2×C4×C31C2×C22⋊C411yescharacteristic
277C2×C4×C31C2×C22⋊C411yescharacteristic
278C2×C4×C31C2×C22⋊C411yescharacteristic
279C2×C4×C31C2×C22⋊C411yescharacteristic
280C2×C4×C31C2×C22⋊C411yescharacteristic
281C2×C4×C31C2×C22⋊C411yescharacteristic
282C2×C4×C31C2×C22⋊C411yescharacteristic
283C2×C4×C31C2×C22⋊C411yescharacteristic
284C2×C4×C31C2×C22⋊C411yescharacteristic
285C2×C4×C31C2×C22⋊C411yescharacteristic
286C2×#529C2×C3111yescharacteristic
287#2285C2×C3111yescharacteristic, complemented
288#2283C2×C3111yescharacteristic, complemented
289#1996C2×C3112yescomplemented
290#1964C2×C3112yes—
291#1899C2×C3114yescomplemented
292#1799C2×C3114yescomplemented
293C22×C31—21no—
294C22×C31—21no—
295C22×C31—21no—
296C22×C31—21no—
297C22×C31—21no—
298C22×C31—21no—
299C22×C31—42no—
300C22×C31—42no—
301C22×C31—42no—
302C22×C31—42no—
303C22×C31—42no—
304C22×C31—84no—
305C22×C31C22×C22⋊C411yescharacteristic
306C22×C31#52012yes—
307C22×C31#53511yescharacteristic
308C22×C31#53611yescharacteristic
309C22×C31#53712yes—
310C4×C31—21no—
311C4×C31—21no—
312C4×C31—21no—
313C4×C31—21no—
314C4×C31—21no—
315C4×C31—21no—
316C4×C31—21no—
317C4×C31—21no—
318C4×C31—21no—
319C4×C31—21no—
320C4×C31—42no—
321C4×C31—42no—
322C4×C31—42no—
323C4×C31—84no—
324C4×C31—84no—
325C4×C31#41012yes—
326C4×C31#41012yes—
327#529—21no—
328#529—21no—
329#529—21no—
330#529—21no—
331#529—21no—
332#529—21no—
333#529—21no—
334#529—21no—
335C2×#126C4×C3112yescomplemented
336C2×#125C4×C3111yescharacteristic, complemented
337C2×#124C4×C3111yescharacteristic, complemented
338C2×#123C22×C3112yes—
339C2×C22⋊Q8C22×C3111yescharacteristic
340C2×#121C22×C3111yescharacteristic
341C2×C4×Q8C4×C3111yescharacteristic, complemented
342C2×C4×D4C4×C3111yescharacteristic, complemented
343C2×C4×D4C22×C3112yes—
344C2×#117C4×C3112yescomplemented
345C2×#117C22×C3112yes—
346C22×C42C22×C3111yescharacteristic
347C2×#99C22×C3118yes—
348#384—21no—
349#383—21no—
350#382—21no—
351#382—21no—
352#381C22×C3112yes—
353#380C22×C3112yes—
354#380C22×C3112yes—
355#380C22×C3112yes—
356C4×C4⋊C4—21no—
357C4×C4⋊C4—21no—
358C4×C4⋊C4—21no—
359C4×C22⋊C4C22×C3112yes—
360#376—21no—
361#342C22×C3118yes—
362C2×C31—21no—
363C2×C31—22no—
364C2×C31—22no—
365C2×C31—21no—
366C2×C31—82no—
367C2×C31#231111yescharacteristic
368C2×C31C2×#41011yescharacteristic
369C2×C31C2×#41011yescharacteristic
370C22×Q8C2×C4×C3111yescharacteristic
371C22×D4C2×C4×C3111yescharacteristic
372C22×D4C23×C3112yes—
373C23×C4C2×C4×C3112yes—
374C23×C4C23×C3111yescharacteristic
375C23×C4C23×C3111yescharacteristic
376C23×C4C23×C3111yescharacteristic
377#126—22no—
378#126—22no—
379#126—22no—
380#126—22no—
381#125—21no—
382#125—21no—
383#125—21no—
384#125—21no—
385#124—21no—
386#124—21no—
387#124—21no—
388#124—21no—
389#123—22no—
390#123—22no—
391#123—22no—
392#123—22no—
393C22⋊Q8—21no—
394C22⋊Q8—21no—
395C22⋊Q8—21no—
396C22⋊Q8—21no—
397#121—21no—
398#121—21no—
399#121—21no—
400#121—21no—
401C4×Q8—21no—
402C4×Q8—21no—
403C4×Q8—21no—
404C4×Q8—21no—
405C4×D4—22no—
406C4×D4—22no—
407C4×D4—22no—
408C4×D4—22no—
409C4×D4—21no—
410C4×D4—21no—
411C4×D4—21no—
412C4×D4—21no—
413#117—22no—
414#117—22no—
415#117—22no—
416#117—22no—
417#117—44no—
418C2×C4⋊C4—22no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4C2×C4×C3112yes—
423C2×C4⋊C4C2×C4×C3112yes—
424C2×C4⋊C4C2×C4×C3111yescharacteristic
425C2×C4⋊C4C2×C4×C3112yes—
426C2×C4⋊C4C2×C4×C3111yescharacteristic
427C2×C4⋊C4C2×C4×C3112yes—
428C2×C22⋊C4C2×C4×C3112yes—
429C2×C22⋊C4C2×C4×C3112yes—
430C2×C22⋊C4C2×C4×C3112yes—
431C2×C22⋊C4C2×C4×C3112yes—
432C2×C22⋊C4C23×C3114yes—
433C2×C22⋊C4C23×C3114yes—
434C2×C22⋊C4C23×C3112yes—
435C2×C42—22no—
436C2×C42—22no—
437C2×C42C2×C4×C3112yes—
438C2×C42C2×C4×C3111yescharacteristic
439C2×C42C2×C4×C3111yescharacteristic
440C2×C42C2×C4×C3111yescharacteristic
441C2×C42C2×C4×C3111yescharacteristic
442C2×C42D4×C3111yescharacteristic
443C2×C42D4×C3111yescharacteristic
444C2×C42D4×C3111yescharacteristic
445C2×C42D4×C3111yescharacteristic
446C2×C42D4×C3111yescharacteristic
447C2×C42D4×C3111yescharacteristic
448C2×C42D4×C3111yescharacteristic
449C2×C42D4×C3111yescharacteristic
450#99—48no—
451#95—22no—
452#95—22no—
453#95—22no—
454#95—22no—
455#95—22no—
456#95—22no—
457C31#2187511yescharacteristic, direct product factor, Sylow
458C24C22×C4×C3112yes—
459C24C24×C3111yescharacteristic
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—42no—
463C2×D4—22no—
464C2×D4—22no—
465C2×D4—24no—
466C2×D4—24no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—42no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—24no—
475C22×C4—24no—
476C22×C4—42no—
477C22×C4—42no—
478C22×C4—44no—
479C22×C4C22×C4×C3112yes—
480C22×C4C22×C4×C3111yescharacteristic
481C22×C4C22×C4×C3111yescharacteristic
482C22×C4C22×C4×C3111yescharacteristic
483C22×C4C22×C4×C3111yescharacteristic
484C22×C4C22×C4×C3112yes—
485C22×C4C22×C4×C3112yes—
486C22×C4C22×C4×C3111yescharacteristic
487C22×C4C22×C4×C3111yescharacteristic
488C22×C4C2×D4×C3111yescharacteristic
489C22×C4C2×D4×C3111yescharacteristic
490C22×C4C2×D4×C3111yescharacteristic
491C22×C4C2×D4×C3111yescharacteristic
492C22×C4C2×D4×C3111yescharacteristic
493C22×C4C2×D4×C3111yescharacteristic
494C22×C4C2×D4×C3111yescharacteristic
495C22×C4C2×D4×C3111yescharacteristic
496C22×C4C2×D4×C3111yescharacteristic
497C22×C4C2×D4×C3111yescharacteristic
498C22×C4C2×D4×C3111yescharacteristic
499C22×C4C2×D4×C3111yescharacteristic
500C4⋊C4—22no—
501C4⋊C4—22no—
502C4⋊C4—22no—
503C4⋊C4—22no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—22no—
507C4⋊C4—22no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—22no—
511C4⋊C4—22no—
512C4⋊C4—44no—
513C4⋊C4—44no—
514C4⋊C4—44no—
515C4⋊C4—44no—
516C22⋊C4—22no—
517C22⋊C4—22no—
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—22no—
523C22⋊C4—22no—
524C22⋊C4—22no—
525C22⋊C4—22no—
526C22⋊C4—24no—
527C22⋊C4—28no—
528C22⋊C4—24no—
529C42—22no—
530C42—22no—
531C42—44no—
532C42—44no—
533C42C22⋊C4×C3111yescharacteristic
534C42C22⋊C4×C3111yescharacteristic
535C42C22⋊C4×C3111yescharacteristic
536C42C22⋊C4×C3111yescharacteristic
537C42C22⋊C4×C3111yescharacteristic
538C42C22⋊C4×C3111yescharacteristic
539C42C22⋊C4×C3111yescharacteristic
540C42C22⋊C4×C3111yescharacteristic
541C42C22⋊C4×C3111yescharacteristic
542C42C22⋊C4×C3111yescharacteristic
543C42C22⋊C4×C3111yescharacteristic
544C42C22⋊C4×C3111yescharacteristic
545C42C22⋊C4×C3111yescharacteristic
546C42C22⋊C4×C3111yescharacteristic
547C42C22⋊C4×C3111yescharacteristic
548C42C22⋊C4×C3111yescharacteristic
549C23—22no—
550C23—24no—
551C23—41no—
552C23—41no—
553C23—42no—
554C23—42no—
555C23C23×C4×C3111yescharacteristic
556C23C22×D4×C3111yescharacteristic
557C23C22×D4×C3111yescharacteristic
558C23C31×H(5,𝔽2)12yes—
559C23C31×2−1+412yes—
560Q8—42no—
561Q8—42no—
562D4—42no—
563D4—42no—
564D4—42no—
565D4—44no—
566D4—42no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—24no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—44no—
592C2×C4—44no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—44no—
596C2×C4—44no—
597C2×C4—44no—
598C2×C4—44no—
599C2×C4—44no—
600C2×C4—44no—
601C2×C4C2×C22⋊C4×C3111yescharacteristic
602C2×C4C2×C22⋊C4×C3111yescharacteristic
603C2×C4C2×C22⋊C4×C3111yescharacteristic
604C2×C4C2×C22⋊C4×C3111yescharacteristic
605C2×C4C2×C22⋊C4×C3111yescharacteristic
606C2×C4C2×C22⋊C4×C3111yescharacteristic
607C2×C4C2×C22⋊C4×C3111yescharacteristic
608C2×C4C2×C22⋊C4×C3111yescharacteristic
609C2×C4C2×C22⋊C4×C3111yescharacteristic
610C2×C4C2×C22⋊C4×C3111yescharacteristic
611C2×C4C2×C22⋊C4×C3111yescharacteristic
612C2×C4C2×C22⋊C4×C3111yescharacteristic
613C22—21no—
614C22—21no—
615C22—21no—
616C22—21no—
617C22—21no—
618C22—21no—
619C22—42no—
620C22—42no—
621C22—42no—
622C22—42no—
623C22—42no—
624C22—84no—
625C22C22×C22⋊C4×C3111yescharacteristic
626C22C31×#52012yes—
627C22C31×#53511yescharacteristic
628C22C31×#53611yescharacteristic
629C22C31×#53712yes—
630C4—21no—
631C4—21no—
632C4—21no—
633C4—21no—
634C4—21no—
635C4—21no—
636C4—21no—
637C4—21no—
638C4—21no—
639C4—21no—
640C4—42no—
641C4—42no—
642C4—42no—
643C4—84no—
644C4—84no—
645C4C31×#41012yes—
646C4C31×#41012yes—
647C2—21no—
648C2—22no—
649C2—22no—
650C2—21no—
651C2—82no—
652C2C31×#231111yescharacteristic
653C2C2×C31×#41011yescharacteristic
654C2C2×C31×#41011yescharacteristic
subgroupG/H
center, socleC22×C31C22×C22⋊C4
commutatorC23C23×C4×C31
Frattini, cosocleC24C24×C31
prime radicalC2×C31×#121C22
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C22×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#2285C2semidirect
3. C31×#2283C2semidirect
4. C31×#1996C2semidirect
6. C31×#1899C2semidirect
7. C31×#1799C2semidirect
16. C2×C31×#126C4semidirect
17. C2×C31×#125C4semidirect
18. C2×C31×#124C4semidirect
22. C2×C4×Q8×C31C4semidirect
23. C2×C4×D4×C31C4semidirect
25. C2×C31×#117C4semidirect
221. #21875C31direct (N × H)
287. #2285C2×C31semidirect
288. #2283C2×C31semidirect
289. #1996C2×C31semidirect
291. #1899C2×C31semidirect
292. #1799C2×C31semidirect
335. C2×#126C4×C31semidirect
336. C2×#125C4×C31semidirect
337. C2×#124C4×C31semidirect
341. C2×C4×Q8C4×C31semidirect
342. C2×C4×D4C4×C31semidirect
344. C2×#117C4×C31semidirect
457. C31#21875direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5292
C31×#22852
C31×#22832
C31×#19962
C31×#19642
C31×#18992
C31×#17992
#2187531