Finite Group Databasebeta

← C31×#16827 #21473586

Subgroups — C31×#16827 #21473586

Order 7936.

1322 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#398C211yesmaximal, characteristic
2C2×C31×#398C211yesmaximal, characteristic
3C2×C31×#395C211yesmaximal, characteristic
4C2×C31×#395C211yesmaximal, characteristic
5C31×#1446C211yesmaximal, characteristic
6C31×#1444C211yesmaximal, characteristic
7C31×#1444C211yesmaximal, characteristic
8C31×#1442C211yesmaximal, characteristic
9C31×#1441C211yesmaximal, characteristic
10C31×#1441C211yesmaximal, characteristic
11C31×#1441C211yesmaximal, characteristic
12C31×#1441C211yesmaximal, characteristic
13C31×C4⋊#95C211yesmaximal, characteristic
14C31×C4⋊#95C211yesmaximal, characteristic
15C31×#1434C211yesmaximal, characteristic
16C23×Q8×C31C2211yescharacteristic
17C22×C4⋊C4×C31C2211yescharacteristic
18C22×C4⋊C4×C31C2211yescharacteristic
19C22×C4⋊C4×C31C2211yescharacteristic
20C22×C4⋊C4×C31C2211yescharacteristic
21C22×C4⋊C4×C31C2211yescharacteristic
22C22×C4⋊C4×C31C2211yescharacteristic
23C22×C4⋊C4×C31C2211yescharacteristic
24C22×C4⋊C4×C31C2211yescharacteristic
25C22×C4⋊C4×C31C2211yescharacteristic
26C22×C4⋊C4×C31C2211yescharacteristic
27C22×C4⋊C4×C31C2211yescharacteristic
28C22×C42×C31C2211yescharacteristic
29C31×#398—24no—
30C31×#398—24no—
31C31×#395—24no—
32C31×#395—24no—
33C2×C31×#95C2211yescharacteristic
34C2×C31×#95C2211yescharacteristic
35C2×C31×#95C2211yescharacteristic
36C2×C31×#95C2211yescharacteristic
37C2×C31×#95C2211yescharacteristic
38C2×C31×#95C2211yescharacteristic
39C2×C31×#95C2211yescharacteristic
40C2×C31×#95C2211yescharacteristic
41C2×C31×#95C2211yescharacteristic
42C2×C31×#95C2211yescharacteristic
43C2×C31×#95C2211yescharacteristic
44C2×C31×#95C2211yescharacteristic
45C2×C31×#95C2211yescharacteristic
46C2×C31×#95C2211yescharacteristic
47C2×C31×#95C2211yescharacteristic
48C2×C31×#95C2211yescharacteristic
49C2×C31×#95C2211yescharacteristic
50C2×C31×#95C2211yescharacteristic
51C2×C31×#95C2211yescharacteristic
52C2×C31×#95C2211yescharacteristic
53C2×C31×#95C2211yescharacteristic
54C2×C31×#95C2211yescharacteristic
55C22×Q8×C31—22no—
56C22×Q8×C31—22no—
57C22×Q8×C31—22no—
58C22×Q8×C31—41no—
59C22×Q8×C31—41no—
60C22×Q8×C31—41no—
61C22×Q8×C31—41no—
62C23×C4×C31C2311yescharacteristic
63C23×C4×C31C2311yescharacteristic
64C23×C4×C31C2311yescharacteristic
65C23×C4×C31C2311yescharacteristic
66C23×C4×C31C2311yescharacteristic
67C23×C4×C31C2311yescharacteristic
68C23×C4×C31C2311yescharacteristic
69C23×C4×C31C2311yescharacteristic
70C23×C4×C31C2311yescharacteristic
71C23×C4×C31C2311yescharacteristic
72C23×C4×C31C2311yescharacteristic
73C23×C4×C31C2311yescharacteristic
74C23×C4×C31C2311yescharacteristic
75C23×C4×C31C2311yescharacteristic
76C23×C4×C31C2311yescharacteristic
77C2×C4⋊C4×C31—22no—
78C2×C4⋊C4×C31—22no—
79C2×C4⋊C4×C31—22no—
80C2×C4⋊C4×C31—22no—
81C2×C4⋊C4×C31—22no—
82C2×C4⋊C4×C31—22no—
83C2×C4⋊C4×C31—22no—
84C2×C4⋊C4×C31—22no—
85C2×C4⋊C4×C31—22no—
86C2×C4⋊C4×C31—22no—
87C2×C4⋊C4×C31—22no—
88C2×C4⋊C4×C31—22no—
89C2×C4⋊C4×C31—22no—
90C2×C4⋊C4×C31—22no—
91C2×C4⋊C4×C31—22no—
92C2×C4⋊C4×C31—22no—
93C2×C4⋊C4×C31—41no—
94C2×C4⋊C4×C31—41no—
95C2×C4⋊C4×C31—41no—
96C2×C4⋊C4×C31—41no—
97C2×C4⋊C4×C31—41no—
98C2×C4⋊C4×C31—41no—
99C2×C4⋊C4×C31—41no—
100C2×C4⋊C4×C31—41no—
101C2×C4⋊C4×C31—41no—
102C2×C4⋊C4×C31—41no—
103C2×C4⋊C4×C31—41no—
104C2×C4⋊C4×C31—41no—
105C2×C4⋊C4×C31—41no—
106C2×C4⋊C4×C31—41no—
107C2×C4⋊C4×C31—41no—
108C2×C4⋊C4×C31D414yes—
109C2×C4⋊C4×C31Q814yescomplemented
110C2×C42×C31—41no—
111C2×C42×C31—41no—
112C2×C42×C31Q814yescomplemented
113C31×#95—22no—
114C31×#95—22no—
115C31×#95—22no—
116C31×#95—22no—
117C31×#95—22no—
118C31×#95—22no—
119C31×#95—22no—
120C31×#95—22no—
121C31×#95—22no—
122C31×#95—22no—
123C31×#95—22no—
124C31×#95—41no—
125C31×#95—41no—
126C31×#95—41no—
127C31×#95—41no—
128C31×#95—41no—
129C31×#95—41no—
130C31×#95—41no—
131C31×#95—41no—
132C31×#95—41no—
133C31×#95D414yes—
134C31×#95Q814yescomplemented
135C24×C31C2411yescharacteristic
136C2×Q8×C31—44no—
137C2×Q8×C31—44no—
138C2×Q8×C31—44no—
139C2×Q8×C31—44no—
140C2×Q8×C31—44no—
141C2×Q8×C31—44no—
142C2×Q8×C31—44no—
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—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×C31—21no—
172C22×C4×C31—21no—
173C22×C4×C31—21no—
174C22×C4×C31—21no—
175C22×C4×C31—21no—
176C22×C4×C31—21no—
177C22×C4×C31—21no—
178C22×C4×C31—21no—
179C22×C4×C31—21no—
180C22×C4×C31—21no—
181C22×C4×C31—21no—
182C22×C4×C31—21no—
183C22×C4×C31—21no—
184C22×C4×C31—21no—
185C22×C4×C31—21no—
186C22×C4×C31—21no—
187C22×C4×C31—21no—
188C22×C4×C31—21no—
189C22×C4×C31—21no—
190C22×C4×C31—21no—
191C22×C4×C31—21no—
192C22×C4×C31—21no—
193C22×C4×C31—21no—
194C22×C4×C31—21no—
195C22×C4×C31—21no—
196C22×C4×C31—21no—
197C22×C4×C31—21no—
198C22×C4×C31—21no—
199C22×C4×C31—21no—
200C22×C4×C31—21no—
201C22×C4×C31—21no—
202C22×C4×C31—21no—
203C22×C4×C31—21no—
204C22×C4×C31—21no—
205C22×C4×C31—21no—
206C22×C4×C31—21no—
207C22×C4×C31—21no—
208C22×C4×C31—21no—
209C22×C4×C31—21no—
210C22×C4×C31—21no—
211C22×C4×C31—21no—
212C22×C4×C31—21no—
213C22×C4×C31—21no—
214C22×C4×C31—21no—
215C22×C4×C31—21no—
216C22×C4×C31—21no—
217C22×C4×C31—21no—
218C22×C4×C31—21no—
219C22×C4×C31—21no—
220C22×C4×C31—21no—
221C22×C4×C31—21no—
222C22×C4×C31—21no—
223C22×C4×C31—21no—
224C22×C4×C31—21no—
225C22×C4×C31—21no—
226C22×C4×C31—21no—
227C22×C4×C31—21no—
228C22×C4×C31—21no—
229C22×C4×C31—21no—
230C22×C4×C31—21no—
231C22×C4×C31C2×D412yes—
232C22×C4×C31C2×D412yes—
233C22×C4×C31C2×D412yes—
234C22×C4×C31C2×D412yes—
235C22×C4×C31C2×D412yes—
236C22×C4×C31C2×D412yes—
237C22×C4×C31C2×Q812yes—
238C22×C4×C31C2×Q812yes—
239C22×C4×C31C2×Q812yes—
240C22×C4×C31C2×Q812yes—
241C22×C4×C31C2×Q812yes—
242C22×C4×C31C2×Q812yes—
243C22×C4×C31C2×Q812yes—
244C22×C4×C31C2×Q812yes—
245C22×C4×C31C2×Q812yes—
246C22×C4×C31#4112yes—
247C22×C4×C31#4112yes—
248C4⋊C4×C31—44no—
249C4⋊C4×C31—44no—
250C4⋊C4×C31—44no—
251C4⋊C4×C31—44no—
252C4⋊C4×C31—44no—
253C4⋊C4×C31—44no—
254C4⋊C4×C31—44no—
255C4⋊C4×C31—44no—
256C4⋊C4×C31—44no—
257C4⋊C4×C31—44no—
258C4⋊C4×C31—44no—
259C42×C31—44no—
260#16827C3111yesmaximal, characteristic, direct product factor, Sylow
261C23×C31C22×D411yescharacteristic
262C23×C31C22×D411yescharacteristic
263C23×C31C22×Q811yescharacteristic
264C23×C31C22×Q811yescharacteristic
265C23×C31C22×Q811yescharacteristic
266C23×C31C2×#4111yescharacteristic
267C23×C31C2×#4111yescharacteristic
268C23×C31H(5,𝔽2)11yescharacteristic
269C23×C31H(5,𝔽2)11yescharacteristic
270C23×C31H(5,𝔽2)11yescharacteristic
271C23×C31H(5,𝔽2)11yescharacteristic
272C23×C31H(5,𝔽2)11yescharacteristic
273C23×C312−1+411yescharacteristic
274C23×C312−1+411yescharacteristic
275C23×C312−1+411yescharacteristic
276Q8×C31—416no—
277C2×C4×C31—22no—
278C2×C4×C31—22no—
279C2×C4×C31—22no—
280C2×C4×C31—22no—
281C2×C4×C31—22no—
282C2×C4×C31—22no—
283C2×C4×C31—22no—
284C2×C4×C31—22no—
285C2×C4×C31—22no—
286C2×C4×C31—22no—
287C2×C4×C31—22no—
288C2×C4×C31—22no—
289C2×C4×C31—22no—
290C2×C4×C31—22no—
291C2×C4×C31—22no—
292C2×C4×C31—22no—
293C2×C4×C31—22no—
294C2×C4×C31—22no—
295C2×C4×C31—22no—
296C2×C4×C31—22no—
297C2×C4×C31—22no—
298C2×C4×C31—22no—
299C2×C4×C31—22no—
300C2×C4×C31—22no—
301C2×C4×C31—22no—
302C2×C4×C31—22no—
303C2×C4×C31—22no—
304C2×C4×C31—22no—
305C2×C4×C31—22no—
306C2×C4×C31—22no—
307C2×C4×C31—22no—
308C2×C4×C31—22no—
309C2×C4×C31—22no—
310C2×C4×C31—22no—
311C2×C4×C31—22no—
312C2×C4×C31—22no—
313C2×C4×C31—22no—
314C2×C4×C31—22no—
315C2×C4×C31—22no—
316C2×C4×C31—22no—
317C2×C4×C31—22no—
318C2×C4×C31—22no—
319C2×C4×C31—22no—
320C2×C4×C31—22no—
321C2×C4×C31—22no—
322C2×C4×C31—41no—
323C2×C4×C31—41no—
324C2×C4×C31—41no—
325C2×C4×C31—41no—
326C2×C4×C31—41no—
327C2×C4×C31—41no—
328C2×C4×C31—41no—
329C2×C4×C31—41no—
330C2×C4×C31—41no—
331C2×C4×C31—41no—
332C2×C4×C31—41no—
333C2×C4×C31—41no—
334C2×C4×C31—41no—
335C2×C4×C31—41no—
336C2×C4×C31—41no—
337C2×C4×C31—41no—
338C2×C4×C31—41no—
339C2×C4×C31—41no—
340C2×C4×C31—41no—
341C2×C4×C31—41no—
342C2×C4×C31—41no—
343C2×C4×C31—41no—
344C2×C4×C31—41no—
345C2×C4×C31—41no—
346C2×C4×C31—41no—
347C2×C4×C31—41no—
348C2×C4×C31—41no—
349C2×C4×C31—41no—
350C2×C4×C31—41no—
351C2×C4×C31—41no—
352C2×C4×C31—41no—
353C2×C4×C31—41no—
354C2×C4×C31—41no—
355C2×C4×C31—41no—
356C2×C4×C31—41no—
357C2×C4×C31—41no—
358C2×C4×C31—41no—
359C2×C4×C31—41no—
360C2×C4×C31—41no—
361C2×C4×C31—41no—
362C2×C4×C31—41no—
363C2×C4×C31—41no—
364C2×C4×C31—41no—
365C2×C4×C31—41no—
366C2×C4×C31—41no—
367C2×C4×C31—41no—
368C2×C4×C31—41no—
369C2×C4×C31—41no—
370C2×C4×C31—41no—
371C2×C4×C31—41no—
372C2×C4×C31—41no—
373C2×C4×C31—41no—
374C2×C4×C31—41no—
375C2×C4×C31—41no—
376C2×C4×C31—41no—
377C2×C4×C31—41no—
378C2×C4×C31—41no—
379C2×C4×C31—41no—
380C2×C4×C31C4⋊Q814yes—
381C2×C4×C31C4⋊Q814yes—
382C2×#398C2×C3111yescharacteristic
383C2×#398C2×C3111yescharacteristic
384C2×#395C2×C3111yescharacteristic
385C2×#395C2×C3111yescharacteristic
386#1446C2×C3111yescharacteristic
387#1444C2×C3111yescharacteristic
388#1444C2×C3111yescharacteristic
389#1442C2×C3111yescharacteristic
390#1441C2×C3111yescharacteristic
391#1441C2×C3111yescharacteristic
392#1441C2×C3111yescharacteristic
393#1441C2×C3111yescharacteristic
394C4⋊#95C2×C3111yescharacteristic
395C4⋊#95C2×C3111yescharacteristic
396#1434C2×C3111yescharacteristic
397C22×C31C2×C4⋊Q811yescharacteristic
398C22×C31C2×C4⋊Q811yescharacteristic
399C22×C31#53311yescharacteristic
400C22×C31#53411yescharacteristic
401C22×C31#53511yescharacteristic
402C22×C31#53611yescharacteristic
403C22×C31#53711yescharacteristic
404C22×C31#53811yescharacteristic
405C22×C31#53911yescharacteristic
406C22×C31#54111yescharacteristic
407C22×C31#54211yescharacteristic
408C22×C31#54311yescharacteristic
409C22×C31#54311yescharacteristic
410C22×C31#54411yescharacteristic
411C22×C31#54411yescharacteristic
412C22×C31#54411yescharacteristic
413C22×C31#54411yescharacteristic
414C22×C31#54411yescharacteristic
415C22×C31#54411yescharacteristic
416C22×C31D4211yescharacteristic
417C22×C31#54611yescharacteristic
418C22×C31#54611yescharacteristic
419C22×C31#54611yescharacteristic
420C22×C31#54811yescharacteristic
421C22×C31D4×Q811yescharacteristic
422C22×C31D4×Q811yescharacteristic
423C22×C31#55411yescharacteristic
424C22×C31#55411yescharacteristic
425C22×C31#55411yescharacteristic
426C22×C31#55711yescharacteristic
427C22×C31Q8211yescharacteristic
428C22×C31#56011yescharacteristic
429C22×C31#56211yescharacteristic
430C22×C31#56211yescharacteristic
431C22×C31#56311yescharacteristic
432C4×C31—24no—
433C4×C31—24no—
434C4×C31—42no—
435C4×C31—42no—
436C4×C31—42no—
437C4×C31—42no—
438C4×C31—42no—
439C4×C31—42no—
440C4×C31—42no—
441C4×C31—42no—
442C4×C31—42no—
443C4×C31—42no—
444C4×C31—42no—
445C4×C31—81no—
446C4×C31—81no—
447C23×Q8C22×C3111yescharacteristic
448C22×C4⋊C4C22×C3111yescharacteristic
449C22×C4⋊C4C22×C3111yescharacteristic
450C22×C4⋊C4C22×C3111yescharacteristic
451C22×C4⋊C4C22×C3111yescharacteristic
452C22×C4⋊C4C22×C3111yescharacteristic
453C22×C4⋊C4C22×C3111yescharacteristic
454C22×C4⋊C4C22×C3111yescharacteristic
455C22×C4⋊C4C22×C3111yescharacteristic
456C22×C4⋊C4C22×C3111yescharacteristic
457C22×C4⋊C4C22×C3111yescharacteristic
458C22×C4⋊C4C22×C3111yescharacteristic
459C22×C42C22×C3111yescharacteristic
460#398—24no—
461#398—24no—
462#395—24no—
463#395—24no—
464C2×#95C22×C3111yescharacteristic
465C2×#95C22×C3111yescharacteristic
466C2×#95C22×C3111yescharacteristic
467C2×#95C22×C3111yescharacteristic
468C2×#95C22×C3111yescharacteristic
469C2×#95C22×C3111yescharacteristic
470C2×#95C22×C3111yescharacteristic
471C2×#95C22×C3111yescharacteristic
472C2×#95C22×C3111yescharacteristic
473C2×#95C22×C3111yescharacteristic
474C2×#95C22×C3111yescharacteristic
475C2×#95C22×C3111yescharacteristic
476C2×#95C22×C3111yescharacteristic
477C2×#95C22×C3111yescharacteristic
478C2×#95C22×C3111yescharacteristic
479C2×#95C22×C3111yescharacteristic
480C2×#95C22×C3111yescharacteristic
481C2×#95C22×C3111yescharacteristic
482C2×#95C22×C3111yescharacteristic
483C2×#95C22×C3111yescharacteristic
484C2×#95C22×C3111yescharacteristic
485C2×#95C22×C3111yescharacteristic
486C2×C31#254911yescharacteristic
487C2×C31#255011yescharacteristic
488C2×C31#255111yescharacteristic
489C2×C31#265911yescharacteristic
490C2×C31#266011yescharacteristic
491C2×C31#266611yescharacteristic
492C2×C31#267811yescharacteristic
493C2×C31#268111yescharacteristic
494C2×C31#269211yescharacteristic
495C2×C31#270411yescharacteristic
496C2×C31#271311yescharacteristic
497C2×C31#272911yescharacteristic
498C2×C31#279211yescharacteristic
499C2×C31#280611yescharacteristic
500C2×C31#284111yescharacteristic
501C22×Q8—22no—
502C22×Q8—22no—
503C22×Q8—22no—
504C22×Q8—41no—
505C22×Q8—41no—
506C22×Q8—41no—
507C22×Q8—41no—
508C23×C4C23×C3111yescharacteristic
509C23×C4C23×C3111yescharacteristic
510C23×C4C23×C3111yescharacteristic
511C23×C4C23×C3111yescharacteristic
512C23×C4C23×C3111yescharacteristic
513C23×C4C23×C3111yescharacteristic
514C23×C4C23×C3111yescharacteristic
515C23×C4C23×C3111yescharacteristic
516C23×C4C23×C3111yescharacteristic
517C23×C4C23×C3111yescharacteristic
518C23×C4C23×C3111yescharacteristic
519C23×C4C23×C3111yescharacteristic
520C23×C4C23×C3111yescharacteristic
521C23×C4C23×C3111yescharacteristic
522C23×C4C23×C3111yescharacteristic
523C2×C4⋊C4—22no—
524C2×C4⋊C4—22no—
525C2×C4⋊C4—22no—
526C2×C4⋊C4—22no—
527C2×C4⋊C4—22no—
528C2×C4⋊C4—22no—
529C2×C4⋊C4—22no—
530C2×C4⋊C4—22no—
531C2×C4⋊C4—22no—
532C2×C4⋊C4—22no—
533C2×C4⋊C4—22no—
534C2×C4⋊C4—22no—
535C2×C4⋊C4—22no—
536C2×C4⋊C4—22no—
537C2×C4⋊C4—22no—
538C2×C4⋊C4—22no—
539C2×C4⋊C4—41no—
540C2×C4⋊C4—41no—
541C2×C4⋊C4—41no—
542C2×C4⋊C4—41no—
543C2×C4⋊C4—41no—
544C2×C4⋊C4—41no—
545C2×C4⋊C4—41no—
546C2×C4⋊C4—41no—
547C2×C4⋊C4—41no—
548C2×C4⋊C4—41no—
549C2×C4⋊C4—41no—
550C2×C4⋊C4—41no—
551C2×C4⋊C4—41no—
552C2×C4⋊C4—41no—
553C2×C4⋊C4—41no—
554C2×C4⋊C4D4×C3114yes—
555C2×C4⋊C4Q8×C3114yescomplemented
556C2×C42—41no—
557C2×C42—41no—
558C2×C42Q8×C3114yescomplemented
559#95—22no—
560#95—22no—
561#95—22no—
562#95—22no—
563#95—22no—
564#95—22no—
565#95—22no—
566#95—22no—
567#95—22no—
568#95—22no—
569#95—22no—
570#95—41no—
571#95—41no—
572#95—41no—
573#95—41no—
574#95—41no—
575#95—41no—
576#95—41no—
577#95—41no—
578#95—41no—
579#95D4×C3114yes—
580#95Q8×C3114yescomplemented
581C31#1682711yescharacteristic, direct product factor, Sylow
582C24C24×C3111yescharacteristic
583C2×Q8—44no—
584C2×Q8—44no—
585C2×Q8—44no—
586C2×Q8—44no—
587C2×Q8—44no—
588C2×Q8—44no—
589C2×Q8—44no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4C2×D4×C3112yes—
679C22×C4C2×D4×C3112yes—
680C22×C4C2×D4×C3112yes—
681C22×C4C2×D4×C3112yes—
682C22×C4C2×D4×C3112yes—
683C22×C4C2×D4×C3112yes—
684C22×C4C2×Q8×C3112yes—
685C22×C4C2×Q8×C3112yes—
686C22×C4C2×Q8×C3112yes—
687C22×C4C2×Q8×C3112yes—
688C22×C4C2×Q8×C3112yes—
689C22×C4C2×Q8×C3112yes—
690C22×C4C2×Q8×C3112yes—
691C22×C4C2×Q8×C3112yes—
692C22×C4C2×Q8×C3112yes—
693C22×C4#41×C3112yes—
694C22×C4#41×C3112yes—
695C4⋊C4—44no—
696C4⋊C4—44no—
697C4⋊C4—44no—
698C4⋊C4—44no—
699C4⋊C4—44no—
700C4⋊C4—44no—
701C4⋊C4—44no—
702C4⋊C4—44no—
703C4⋊C4—44no—
704C4⋊C4—44no—
705C4⋊C4—44no—
706C42—44no—
707C23C22×D4×C3111yescharacteristic
708C23C22×D4×C3111yescharacteristic
709C23C22×Q8×C3111yescharacteristic
710C23C22×Q8×C3111yescharacteristic
711C23C22×Q8×C3111yescharacteristic
712C23C2×#41×C3111yescharacteristic
713C23C2×#41×C3111yescharacteristic
714C23C31×H(5,𝔽2)11yescharacteristic
715C23C31×H(5,𝔽2)11yescharacteristic
716C23C31×H(5,𝔽2)11yescharacteristic
717C23C31×H(5,𝔽2)11yescharacteristic
718C23C31×H(5,𝔽2)11yescharacteristic
719C23C31×2−1+411yescharacteristic
720C23C31×2−1+411yescharacteristic
721C23C31×2−1+411yescharacteristic
722Q8—416no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4C31×C4⋊Q814yes—
827C2×C4C31×C4⋊Q814yes—
828C22C2×C31×C4⋊Q811yescharacteristic
829C22C2×C31×C4⋊Q811yescharacteristic
830C22C31×#53311yescharacteristic
831C22C31×#53411yescharacteristic
832C22C31×#53511yescharacteristic
833C22C31×#53611yescharacteristic
834C22C31×#53711yescharacteristic
835C22C31×#53811yescharacteristic
836C22C31×#53911yescharacteristic
837C22C31×#54111yescharacteristic
838C22C31×#54211yescharacteristic
839C22C31×#54311yescharacteristic
840C22C31×#54311yescharacteristic
841C22C31×#54411yescharacteristic
842C22C31×#54411yescharacteristic
843C22C31×#54411yescharacteristic
844C22C31×#54411yescharacteristic
845C22C31×#54411yescharacteristic
846C22C31×#54411yescharacteristic
847C22D42×C3111yescharacteristic
848C22C31×#54611yescharacteristic
849C22C31×#54611yescharacteristic
850C22C31×#54611yescharacteristic
851C22C31×#54811yescharacteristic
852C22D4×Q8×C3111yescharacteristic
853C22D4×Q8×C3111yescharacteristic
854C22C31×#55411yescharacteristic
855C22C31×#55411yescharacteristic
856C22C31×#55411yescharacteristic
857C22C31×#55711yescharacteristic
858C22Q82×C3111yescharacteristic
859C22C31×#56011yescharacteristic
860C22C31×#56211yescharacteristic
861C22C31×#56211yescharacteristic
862C22C31×#56311yescharacteristic
863C4—24no—
864C4—24no—
865C4—42no—
866C4—42no—
867C4—42no—
868C4—42no—
869C4—42no—
870C4—42no—
871C4—42no—
872C4—42no—
873C4—42no—
874C4—42no—
875C4—42no—
876C4—81no—
877C4—81no—
878C2C31×#254911yescharacteristic
879C2C31×#255011yescharacteristic
880C2C31×#255111yescharacteristic
881C2C31×#265911yescharacteristic
882C2C31×#266011yescharacteristic
883C2C31×#266611yescharacteristic
884C2C31×#267811yescharacteristic
885C2C31×#268111yescharacteristic
886C2C31×#269211yescharacteristic
887C2C31×#270411yescharacteristic
888C2C31×#271311yescharacteristic
889C2C31×#272911yescharacteristic
890C2C31×#279211yescharacteristic
891C2C31×#280611yescharacteristic
892C2C31×#284111yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C31C24
commutator, Frattini, cosocleC24C24×C31
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
109. C2×C4⋊C4×C31Q8semidirect
112. C2×C42×C31Q8semidirect
134. C31×#95Q8semidirect
260. #16827C31direct (N × H)
555. C2×C4⋊C4Q8×C31semidirect
558. C2×C42Q8×C31semidirect
580. #95Q8×C31semidirect
581. C31#16827direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3982
C2×C31×#3952
C31×#14462
C31×#14442
C31×#14422
C31×#14412
C31×C4⋊#952
C31×#14342
#1682731