Finite Group Databasebeta

← C31×#22526 #21479285

Subgroups — C31×#22526 #21479285

Order 7936.

1066 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#554C211yesmaximal, characteristic
2C2×C31×#446C211yesmaximal, characteristic, complemented
3C31×#2355C211yesmaximal, characteristic, complemented
4C31×#1993C211yesmaximal, characteristic, complemented
5C31×#1992C211yesmaximal, characteristic, complemented
6C31×#1991C211yesmaximal, characteristic, complemented
7C31×#1989C211yesmaximal, characteristic, complemented
8C31×#1989C211yesmaximal, characteristic, complemented
9C31×#1988C211yesmaximal, characteristic, complemented
10C31×#1804C211yesmaximal, characteristic
11C31×#1804C211yesmaximal, characteristic
12C31×#1802C211yesmaximal, characteristic
13C31×#1762C211yesmaximal, characteristic
14C31×#1762C211yesmaximal, characteristic
15C4×C31×#102C211yesmaximal, characteristic
16C31×#554—24no—
17C31×#554C418yescomplemented
18C2×C31×C4⋊Q8C2211yescharacteristic
19C2×C31×#125C2211yescharacteristic
20C2×C31×#125C2211yescharacteristic
21C2×C31×C22⋊Q8—21no—
22C2×C31×C22⋊Q8—21no—
23C2×C31×C22⋊Q8—21no—
24C2×C4×Q8×C31C2211yescharacteristic
25C2×C4×D4×C31C2211yescharacteristic
26C2×C4×D4×C31C2211yescharacteristic
27C2×C4×D4×C31C2211yescharacteristic
28C22×C4⋊C4×C31—21no—
29C31×#446—24no—
30C2×C31×C4⋊C8C2211yescharacteristic
31C2×C31×C4⋊C8C2211yescharacteristic
32C2×C31×C4⋊C8C2211yescharacteristic
33C2×C31×#102C2211yescharacteristic
34C2×C31×#102C2211yescharacteristic
35C2×C31×#102C2211yescharacteristic
36C2×C31×#102C2211yescharacteristic
37C2×C31×#97C2211yescharacteristic
38C2×C31×#97C2211yescharacteristic
39C2×C4×C8×C31C2211yescharacteristic
40C31×#391—21no—
41C31×#387—21no—
42C31×#387—21no—
43C31×#384C2211yescharacteristic
44C31×#382C2211yescharacteristic
45C31×#382C2211yescharacteristic
46C4×C4⋊C4×C31—21no—
47C4×C4⋊C4×C31C2211yescharacteristic
48C4×C4⋊C4×C31C2211yescharacteristic
49C4×C4⋊C4×C31C2211yescharacteristic
50C31×#340C2211yescharacteristic
51C31×#340C2211yescharacteristic
52C31×#340C2211yescharacteristic
53C31×#340C2211yescharacteristic
54C31×#340C2211yescharacteristic
55C31×#340C2211yescharacteristic
56C31×#340C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#340C2211yescharacteristic
60C31×#340C2211yescharacteristic
61C31×#340C2211yescharacteristic
62C22×Q8×C31—21no—
63C22×Q8×C31D411yescharacteristic
64C22×D4×C31C2311yescharacteristic
65C23×C4×C31—21no—
66C23×C4×C31—21no—
67C23×C4×C31—21no—
68C22×C8×C31C2311yescharacteristic
69C22×C8×C31C2311yescharacteristic
70C22×C8×C31C2311yescharacteristic
71C22×C8×C31C2311yescharacteristic
72C31×C4⋊Q8—22no—
73C31×C4⋊Q8C2×C414yes—
74C31×#125—22no—
75C31×#125—22no—
76C31×#125C2×C414yes—
77C31×#125C2×C414yes—
78C31×C22⋊Q8—28no—
79C31×C22⋊Q8—28no—
80C31×C22⋊Q8—28no—
81C4×Q8×C31C2×C414yes—
82C4×Q8×C31D414yes—
83C4×D4×C31—22no—
84C4×D4×C31—22no—
85C4×D4×C31—22no—
86C4×D4×C31C2×C414yes—
87C4×D4×C31C2×C414yes—
88C4×D4×C31C2×C414yes—
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—28no—
95C2×C4⋊C4×C31—21no—
96C2×C4⋊C4×C31—21no—
97C2×C4⋊C4×C31D411yescharacteristic
98C2×C4⋊C4×C31D411yescharacteristic
99C2×C4⋊C4×C31D411yescharacteristic
100C2×C4⋊C4×C31C2311yescharacteristic
101C2×C4⋊C4×C31C2311yescharacteristic
102C2×C4⋊C4×C31C2311yescharacteristic
103C2×C4⋊C4×C31C2311yescharacteristic
104C2×C4⋊C4×C31C2311yescharacteristic
105C2×C4⋊C4×C31C2311yescharacteristic
106C2×C4⋊C4×C31C2311yescharacteristic
107C2×C22⋊C4×C31—21no—
108C2×C22⋊C4×C31—21no—
109C2×C22⋊C4×C31—21no—
110C2×C42×C31—21no—
111C2×C42×C31—21no—
112C2×C42×C31—21no—
113C2×C42×C31C2311yescharacteristic
114C2×C42×C31C2311yescharacteristic
115C2×C42×C31C2311yescharacteristic
116C31×C4⋊C8—22no—
117C31×C4⋊C8—22no—
118C31×C4⋊C8—22no—
119C31×#102—22no—
120C31×#102—22no—
121C31×#102—22no—
122C31×#102Q814yescomplemented
123C31×#97—22no—
124C31×#97—22no—
125C4×C8×C31—22no—
126C31×#95—21no—
127C31×#95—21no—
128C31×#95—21no—
129C31×#95—21no—
130C31×#95—21no—
131C31×#95—21no—
132C31×#95—21no—
133C24×C31—21no—
134C2×Q8×C31—24no—
135C2×Q8×C31—41no—
136C2×Q8×C31—41no—
137C2×Q8×C31—81no—
138C2×Q8×C31—81no—
139C2×Q8×C31C22⋊C414yes—
140C2×D4×C31—21no—
141C2×D4×C31—21no—
142C2×D4×C31—21no—
143C2×D4×C31C22×C412yes—
144C2×D4×C31C2×Q812yes—
145C2×D4×C31#4112yes—
146C22×C4×C31—21no—
147C22×C4×C31—21no—
148C22×C4×C31—21no—
149C22×C4×C31—21no—
150C22×C4×C31—24no—
151C22×C4×C31—24no—
152C22×C4×C31—24no—
153C22×C4×C31—21no—
154C22×C4×C31—21no—
155C22×C4×C31—21no—
156C22×C4×C31—42no—
157C22×C4×C31—42no—
158C22×C4×C31—81no—
159C22×C4×C31—81no—
160C22×C4×C31—81no—
161C22×C4×C31—81no—
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×C31C2411yescharacteristic
169C2×C8×C31—21no—
170C2×C8×C31—21no—
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×C31C2×Q812yes—
181C4⋊C4×C31—24no—
182C4⋊C4×C31—24no—
183C4⋊C4×C31—24no—
184C4⋊C4×C31—24no—
185C4⋊C4×C31—24no—
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—42no—
197C4⋊C4×C31—81no—
198C4⋊C4×C31C22⋊C414yes—
199C4⋊C4×C31C22⋊C414yes—
200C4⋊C4×C31C22⋊C414yes—
201C4⋊C4×C31C22×C412yes—
202C4⋊C4×C31C22×C412yes—
203C4⋊C4×C31C22×C412yes—
204C4⋊C4×C31C2×Q812yes—
205C22⋊C4×C31—24no—
206C22⋊C4×C31—24no—
207C22⋊C4×C31—24no—
208C42×C31—42no—
209C42×C31—81no—
210C42×C31—81no—
211C42×C31C22×C412yes—
212C42×C31C22×C412yes—
213C42×C31C22×C412yes—
214C42×C31C2×D412yes—
215C42×C31C2×D412yes—
216C42×C31C2×D412yes—
217#22526C3111yesmaximal, characteristic, direct product factor, Sylow
218C23×C31—22no—
219C23×C31—22no—
220C23×C31—22no—
221C23×C31—41no—
222C23×C31—41no—
223C23×C31—41no—
224C23×C31—41no—
225C23×C31C22×D411yescharacteristic
226Q8×C31—44no—
227Q8×C31—84no—
228D4×C31—22no—
229D4×C31—22no—
230D4×C31—22no—
231D4×C31C4×Q814yes—
232C2×C4×C31—21no—
233C2×C4×C31—21no—
234C2×C4×C31—21no—
235C2×C4×C31—21no—
236C2×C4×C31—21no—
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—22no—
247C2×C4×C31—22no—
248C2×C4×C31—48no—
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—84no—
267C2×C4×C31—84no—
268C2×C4×C31C2×C22⋊C412yes—
269C2×C4×C31C2×C22⋊C412yes—
270C2×C4×C31C2×C22⋊C412yes—
271C2×C4×C31C2×C22⋊C412yes—
272C2×C4×C31C2×C22⋊C412yes—
273C2×C4×C31C2×C22⋊C412yes—
274C2×C4×C31C23×C411yescharacteristic
275C2×C4×C31C22×D411yescharacteristic
276C2×C4×C31C22×Q811yescharacteristic
277C2×C4×C31C2×#4111yescharacteristic
278C2×C4×C312−1+411yescharacteristic
279C2×C4×C312−1+411yescharacteristic
280C8×C31—22no—
281C8×C31—41no—
282C8×C31—41no—
283C8×C31—41no—
284C2×#554C2×C3111yescharacteristic
285C2×#446C2×C3111yescharacteristic, complemented
286#2355C2×C3111yescharacteristic, complemented
287#1993C2×C3111yescharacteristic, complemented
288#1992C2×C3111yescharacteristic, complemented
289#1991C2×C3111yescharacteristic, complemented
290#1989C2×C3111yescharacteristic, complemented
291#1989C2×C3111yescharacteristic, complemented
292#1988C2×C3111yescharacteristic, complemented
293#1804C2×C3111yescharacteristic
294#1804C2×C3111yescharacteristic
295#1802C2×C3111yescharacteristic
296#1762C2×C3111yescharacteristic
297#1762C2×C3111yescharacteristic
298C4×#102C2×C3111yescharacteristic
299C22×C31—24no—
300C22×C31—42no—
301C22×C31—42no—
302C22×C31—42no—
303C22×C31—42no—
304C22×C31—42no—
305C22×C31—42no—
306C22×C31C22×C22⋊C411yescharacteristic
307C22×C31#54811yescharacteristic
308C22×C31D4×Q811yescharacteristic
309C22×C31#57511yescharacteristic
310C22×C31#57511yescharacteristic
311C22×C31#57611yescharacteristic
312C22×C31#57711yescharacteristic
313C4×C31—22no—
314C4×C31—22no—
315C4×C31—22no—
316C4×C31—22no—
317C4×C31—22no—
318C4×C31—22no—
319C4×C31—42no—
320C4×C31—42no—
321C4×C31—42no—
322C4×C31—42no—
323C4×C31—81no—
324C4×C31—81no—
325C4×C31—81no—
326C4×C31C2×C4×Q811yescharacteristic
327C4×C31#51911yescharacteristic
328C4×C31#54811yescharacteristic
329C4×C31D4×Q811yescharacteristic
330#554—24no—
331#554C4×C3118yescomplemented
332C2×C4⋊Q8C22×C3111yescharacteristic
333C2×#125C22×C3111yescharacteristic
334C2×#125C22×C3111yescharacteristic
335C2×C22⋊Q8—21no—
336C2×C22⋊Q8—21no—
337C2×C22⋊Q8—21no—
338C2×C4×Q8C22×C3111yescharacteristic
339C2×C4×D4C22×C3111yescharacteristic
340C2×C4×D4C22×C3111yescharacteristic
341C2×C4×D4C22×C3111yescharacteristic
342C22×C4⋊C4—21no—
343#446—24no—
344C2×C4⋊C8C22×C3111yescharacteristic
345C2×C4⋊C8C22×C3111yescharacteristic
346C2×C4⋊C8C22×C3111yescharacteristic
347C2×#102C22×C3111yescharacteristic
348C2×#102C22×C3111yescharacteristic
349C2×#102C22×C3111yescharacteristic
350C2×#102C22×C3111yescharacteristic
351C2×#97C22×C3111yescharacteristic
352C2×#97C22×C3111yescharacteristic
353C2×C4×C8C22×C3111yescharacteristic
354#391—21no—
355#387—21no—
356#387—21no—
357#384C22×C3111yescharacteristic
358#382C22×C3111yescharacteristic
359#382C22×C3111yescharacteristic
360C4×C4⋊C4—21no—
361C4×C4⋊C4C22×C3111yescharacteristic
362C4×C4⋊C4C22×C3111yescharacteristic
363C4×C4⋊C4C22×C3111yescharacteristic
364#340C22×C3111yescharacteristic
365#340C22×C3111yescharacteristic
366#340C22×C3111yescharacteristic
367#340C22×C3111yescharacteristic
368#340C22×C3111yescharacteristic
369#340C22×C3111yescharacteristic
370#340C22×C3111yescharacteristic
371#340C22×C3111yescharacteristic
372#340C22×C3111yescharacteristic
373#340C22×C3111yescharacteristic
374#340C22×C3111yescharacteristic
375#340C22×C3111yescharacteristic
376C2×C31—44no—
377C2×C31Q8×C22⋊C411yescharacteristic
378C2×C31#289611yescharacteristic
379C2×C31#289711yescharacteristic
380C2×C31#337011yescharacteristic
381C2×C31#337611yescharacteristic
382C2×C31#338811yescharacteristic
383C2×C31#338911yescharacteristic
384C22×Q8—21no—
385C22×Q8D4×C3111yescharacteristic
386C22×D4C23×C3111yescharacteristic
387C23×C4—21no—
388C23×C4—21no—
389C23×C4—21no—
390C22×C8C23×C3111yescharacteristic
391C22×C8C23×C3111yescharacteristic
392C22×C8C23×C3111yescharacteristic
393C22×C8C23×C3111yescharacteristic
394C4⋊Q8—22no—
395C4⋊Q8C2×C4×C3114yes—
396#125—22no—
397#125—22no—
398#125C2×C4×C3114yes—
399#125C2×C4×C3114yes—
400C22⋊Q8—28no—
401C22⋊Q8—28no—
402C22⋊Q8—28no—
403C4×Q8C2×C4×C3114yes—
404C4×Q8D4×C3114yes—
405C4×D4—22no—
406C4×D4—22no—
407C4×D4—22no—
408C4×D4C2×C4×C3114yes—
409C4×D4C2×C4×C3114yes—
410C4×D4C2×C4×C3114yes—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—28no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4D4×C3111yescharacteristic
420C2×C4⋊C4D4×C3111yescharacteristic
421C2×C4⋊C4D4×C3111yescharacteristic
422C2×C4⋊C4C23×C3111yescharacteristic
423C2×C4⋊C4C23×C3111yescharacteristic
424C2×C4⋊C4C23×C3111yescharacteristic
425C2×C4⋊C4C23×C3111yescharacteristic
426C2×C4⋊C4C23×C3111yescharacteristic
427C2×C4⋊C4C23×C3111yescharacteristic
428C2×C4⋊C4C23×C3111yescharacteristic
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C42—21no—
433C2×C42—21no—
434C2×C42—21no—
435C2×C42C23×C3111yescharacteristic
436C2×C42C23×C3111yescharacteristic
437C2×C42C23×C3111yescharacteristic
438C4⋊C8—22no—
439C4⋊C8—22no—
440C4⋊C8—22no—
441#102—22no—
442#102—22no—
443#102—22no—
444#102Q8×C3114yescomplemented
445#97—22no—
446#97—22no—
447C4×C8—22no—
448#95—21no—
449#95—21no—
450#95—21no—
451#95—21no—
452#95—21no—
453#95—21no—
454#95—21no—
455C31#2252611yescharacteristic, direct product factor, Sylow
456C24—21no—
457C2×Q8—24no—
458C2×Q8—41no—
459C2×Q8—41no—
460C2×Q8—81no—
461C2×Q8—81no—
462C2×Q8C22⋊C4×C3114yes—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4C22×C4×C3112yes—
467C2×D4C2×Q8×C3112yes—
468C2×D4#41×C3112yes—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—24no—
474C22×C4—24no—
475C22×C4—24no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—42no—
480C22×C4—42no—
481C22×C4—81no—
482C22×C4—81no—
483C22×C4—81no—
484C22×C4—81no—
485C22×C4C2×D4×C3111yescharacteristic
486C22×C4C2×D4×C3111yescharacteristic
487C22×C4C2×D4×C3111yescharacteristic
488C22×C4C2×D4×C3111yescharacteristic
489C22×C4C2×D4×C3111yescharacteristic
490C22×C4C2×D4×C3111yescharacteristic
491C22×C4C24×C3111yescharacteristic
492C2×C8—21no—
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—21no—
502C2×C8—21no—
503C2×C8C2×Q8×C3112yes—
504C4⋊C4—24no—
505C4⋊C4—24no—
506C4⋊C4—24no—
507C4⋊C4—24no—
508C4⋊C4—24no—
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—42no—
520C4⋊C4—81no—
521C4⋊C4C22⋊C4×C3114yes—
522C4⋊C4C22⋊C4×C3114yes—
523C4⋊C4C22⋊C4×C3114yes—
524C4⋊C4C22×C4×C3112yes—
525C4⋊C4C22×C4×C3112yes—
526C4⋊C4C22×C4×C3112yes—
527C4⋊C4C2×Q8×C3112yes—
528C22⋊C4—24no—
529C22⋊C4—24no—
530C22⋊C4—24no—
531C42—42no—
532C42—81no—
533C42—81no—
534C42C22×C4×C3112yes—
535C42C22×C4×C3112yes—
536C42C22×C4×C3112yes—
537C42C2×D4×C3112yes—
538C42C2×D4×C3112yes—
539C42C2×D4×C3112yes—
540C23—22no—
541C23—22no—
542C23—22no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23—41no—
547C23C22×D4×C3111yescharacteristic
548Q8—44no—
549Q8—84no—
550D4—22no—
551D4—22no—
552D4—22no—
553D4C4×Q8×C3114yes—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
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—48no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
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—84no—
589C2×C4—84no—
590C2×C4C2×C22⋊C4×C3112yes—
591C2×C4C2×C22⋊C4×C3112yes—
592C2×C4C2×C22⋊C4×C3112yes—
593C2×C4C2×C22⋊C4×C3112yes—
594C2×C4C2×C22⋊C4×C3112yes—
595C2×C4C2×C22⋊C4×C3112yes—
596C2×C4C23×C4×C3111yescharacteristic
597C2×C4C22×D4×C3111yescharacteristic
598C2×C4C22×Q8×C3111yescharacteristic
599C2×C4C2×#41×C3111yescharacteristic
600C2×C4C31×2−1+411yescharacteristic
601C2×C4C31×2−1+411yescharacteristic
602C8—22no—
603C8—41no—
604C8—41no—
605C8—41no—
606C22—24no—
607C22—42no—
608C22—42no—
609C22—42no—
610C22—42no—
611C22—42no—
612C22—42no—
613C22C22×C22⋊C4×C3111yescharacteristic
614C22C31×#54811yescharacteristic
615C22D4×Q8×C3111yescharacteristic
616C22C31×#57511yescharacteristic
617C22C31×#57511yescharacteristic
618C22C31×#57611yescharacteristic
619C22C31×#57711yescharacteristic
620C4—22no—
621C4—22no—
622C4—22no—
623C4—22no—
624C4—22no—
625C4—22no—
626C4—42no—
627C4—42no—
628C4—42no—
629C4—42no—
630C4—81no—
631C4—81no—
632C4—81no—
633C4C2×C4×Q8×C3111yescharacteristic
634C4C31×#51911yescharacteristic
635C4C31×#54811yescharacteristic
636C4D4×Q8×C3111yescharacteristic
637C2—44no—
638C2Q8×C22⋊C4×C3111yescharacteristic
639C2C31×#289611yescharacteristic
640C2C31×#289711yescharacteristic
641C2C31×#337011yescharacteristic
642C2C31×#337611yescharacteristic
643C2C31×#338811yescharacteristic
644C2C31×#338911yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutatorC2×C4C23×C4×C31
Frattini, cosocleC22×C4C24×C31
prime radicalC22×D4×C31C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C4×Q8×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#446C2semidirect
3. C31×#2355C2semidirect
4. C31×#1993C2semidirect
5. C31×#1992C2semidirect
6. C31×#1991C2semidirect
7. C31×#1989C2semidirect
8. C31×#1989C2semidirect
9. C31×#1988C2semidirect
17. C31×#554C4semidirect
122. C31×#102Q8semidirect
217. #22526C31direct (N × H)
285. C2×#446C2×C31semidirect
286. #2355C2×C31semidirect
287. #1993C2×C31semidirect
288. #1992C2×C31semidirect
289. #1991C2×C31semidirect
290. #1989C2×C31semidirect
291. #1989C2×C31semidirect
292. #1988C2×C31semidirect
331. #554C4×C31semidirect
444. #102Q8×C31semidirect
455. C31#22526direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5542
C2×C31×#4462
C31×#23552
C31×#19932
C31×#19922
C31×#19912
C31×#19892
C31×#19882
C31×#18042
C31×#18022
C31×#17622
C4×C31×#1022
#2252631