Finite Group Databasebeta

← C31×#14045 #21470804

Subgroups — C31×#14045 #21470804

Order 7936.

1530 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#389C211yesmaximal, characteristic
2C2×C31×#389C211yesmaximal, characteristic
3C2×C31×#389C211yesmaximal, characteristic
4C2×C4×C4⋊C4×C31C211yesmaximal, characteristic
5C2×C4×C4⋊C4×C31C211yesmaximal, characteristic
6C31×#1444C212yesmaximal
7C31×#1441C212yesmaximal
8C31×#1436C212yesmaximal
9C31×C4⋊#95C211yesmaximal, characteristic
10C31×C4⋊#95C212yesmaximal
11C31×C4⋊#95C211yesmaximal, characteristic
12C22×C4⋊C4×C31C2211yescharacteristic
13C22×C4⋊C4×C31C2211yescharacteristic
14C22×C4⋊C4×C31C2212yes—
15C22×C4⋊C4×C31C2211yescharacteristic
16C22×C4⋊C4×C31C2211yescharacteristic
17C22×C4⋊C4×C31C2211yescharacteristic
18C22×C4⋊C4×C31C2212yes—
19C22×C4⋊C4×C31C2212yes—
20C22×C4⋊C4×C31C2211yescharacteristic
21C22×C42×C31C2211yescharacteristic
22C22×C42×C31C2212yes—
23C22×C42×C31C2211yescharacteristic
24C22×C42×C31C2211yescharacteristic
25C31×#389—24no—
26C31×#389—24no—
27C31×#389C418yescomplemented
28C4×C4⋊C4×C31—24no—
29C4×C4⋊C4×C31—24no—
30C2×C31×#95C2211yescharacteristic
31C2×C31×#95C2212yes—
32C2×C31×#95C2212yes—
33C2×C31×#95C2212yes—
34C2×C31×#95C2211yescharacteristic
35C2×C31×#95C2212yes—
36C2×C31×#95C2212yes—
37C2×C31×#95C2212yes—
38C2×C31×#95C2212yes—
39C2×C31×#95C2212yes—
40C23×C4×C31C2312yes—
41C23×C4×C31C2311yescharacteristic
42C23×C4×C31C2312yes—
43C23×C4×C31C2311yescharacteristic
44C23×C4×C31C2311yescharacteristic
45C23×C4×C31C2312yes—
46C23×C4×C31C2311yescharacteristic
47C23×C4×C31C2312yes—
48C23×C4×C31C2311yescharacteristic
49C23×C4×C31C2311yescharacteristic
50C23×C4×C31C2311yescharacteristic
51C2×C4⋊C4×C31—22no—
52C2×C4⋊C4×C31—22no—
53C2×C4⋊C4×C31—22no—
54C2×C4⋊C4×C31—22no—
55C2×C4⋊C4×C31—22no—
56C2×C4⋊C4×C31—22no—
57C2×C4⋊C4×C31—22no—
58C2×C4⋊C4×C31—22no—
59C2×C4⋊C4×C31—22no—
60C2×C4⋊C4×C31—24no—
61C2×C4⋊C4×C31—24no—
62C2×C4⋊C4×C31—22no—
63C2×C4⋊C4×C31—22no—
64C2×C4⋊C4×C31—24no—
65C2×C4⋊C4×C31—22no—
66C2×C4⋊C4×C31—42no—
67C2×C4⋊C4×C31—42no—
68C2×C4⋊C4×C31—42no—
69C2×C4⋊C4×C31—42no—
70C2×C4⋊C4×C31—42no—
71C2×C4⋊C4×C31C2×C414yes—
72C2×C4⋊C4×C31C2×C418yes—
73C2×C4⋊C4×C31C2×C414yes—
74C2×C4⋊C4×C31D414yes—
75C2×C4⋊C4×C31Q814yes—
76C2×C4⋊C4×C31Q814yes—
77C2×C4⋊C4×C31Q814yes—
78C2×C42×C31—22no—
79C2×C42×C31—22no—
80C2×C42×C31—22no—
81C2×C42×C31—22no—
82C2×C42×C31—24no—
83C2×C42×C31—22no—
84C2×C42×C31—22no—
85C2×C42×C31—24no—
86C2×C42×C31—22no—
87C2×C42×C31—42no—
88C2×C42×C31C2×C414yes—
89C2×C42×C31D414yes—
90C31×#95—22no—
91C31×#95—24no—
92C31×#95—22no—
93C31×#95—24no—
94C31×#95—24no—
95C31×#95—24no—
96C31×#95—42no—
97C31×#95—42no—
98C31×#95—42no—
99C31×#95C2×C418yes—
100C24×C31C2411yescharacteristic
101C22×C4×C31—21no—
102C22×C4×C31—21no—
103C22×C4×C31—21no—
104C22×C4×C31—22no—
105C22×C4×C31—21no—
106C22×C4×C31—21no—
107C22×C4×C31—21no—
108C22×C4×C31—22no—
109C22×C4×C31—21no—
110C22×C4×C31—22no—
111C22×C4×C31—22no—
112C22×C4×C31—21no—
113C22×C4×C31—21no—
114C22×C4×C31—21no—
115C22×C4×C31—21no—
116C22×C4×C31—21no—
117C22×C4×C31—22no—
118C22×C4×C31—21no—
119C22×C4×C31—22no—
120C22×C4×C31—21no—
121C22×C4×C31—22no—
122C22×C4×C31—21no—
123C22×C4×C31—21no—
124C22×C4×C31—21no—
125C22×C4×C31—21no—
126C22×C4×C31—22no—
127C22×C4×C31—22no—
128C22×C4×C31—22no—
129C22×C4×C31—21no—
130C22×C4×C31—21no—
131C22×C4×C31—21no—
132C22×C4×C31—21no—
133C22×C4×C31—21no—
134C22×C4×C31—21no—
135C22×C4×C31—21no—
136C22×C4×C31—22no—
137C22×C4×C31—22no—
138C22×C4×C31—22no—
139C22×C4×C31—22no—
140C22×C4×C31—21no—
141C22×C4×C31—21no—
142C22×C4×C31—22no—
143C22×C4×C31—21no—
144C22×C4×C31—21no—
145C22×C4×C31—21no—
146C22×C4×C31—21no—
147C22×C4×C31—22no—
148C22×C4×C31—21no—
149C22×C4×C31—22no—
150C22×C4×C31—22no—
151C22×C4×C31—22no—
152C22×C4×C31—22no—
153C22×C4×C31—22no—
154C22×C4×C31—22no—
155C22×C4×C31—22no—
156C22×C4×C31C22×C414yes—
157C22×C4×C31C22×C412yes—
158C22×C4×C31C22×C414yes—
159C22×C4×C31C22×C412yes—
160C22×C4×C31C22×C412yes—
161C22×C4×C31C2×D412yes—
162C22×C4×C31C2×D414yes—
163C22×C4×C31C2×D412yes—
164C22×C4×C31C2×D412yes—
165C22×C4×C31C2×D412yes—
166C22×C4×C31C2×Q812yes—
167C22×C4×C31C2×Q814yes—
168C22×C4×C31C2×Q814yes—
169C22×C4×C31C2×Q812yes—
170C22×C4×C31C2×Q812yes—
171C22×C4×C31C2×Q812yes—
172C22×C4×C31C2×Q812yes—
173C22×C4×C31#4112yes—
174C22×C4×C31#4112yes—
175C22×C4×C31#4112yes—
176C22×C4×C31#4112yes—
177C22×C4×C31#4112yes—
178C4⋊C4×C31—28no—
179C4⋊C4×C31—28no—
180C4⋊C4×C31—28no—
181C4⋊C4×C31—28no—
182C4⋊C4×C31—48no—
183C4⋊C4×C31—48no—
184C4⋊C4×C31—48no—
185C4⋊C4×C31—44no—
186C4⋊C4×C31C4⋊C4116yescomplemented
187C42×C31—28no—
188C42×C31—28no—
189C42×C31—48no—
190C42×C31—44no—
191#14045C3111yesmaximal, characteristic, direct product factor, Sylow
192C23×C31C23×C411yescharacteristic
193C23×C31C22×D411yescharacteristic
194C23×C31C22×D411yescharacteristic
195C23×C31C22×Q811yescharacteristic
196C23×C31C22×Q811yescharacteristic
197C23×C31C22×Q811yescharacteristic
198C23×C31C2×#4111yescharacteristic
199C23×C31C2×#4111yescharacteristic
200C23×C31C2×#4111yescharacteristic
201C23×C31C2×#4111yescharacteristic
202C23×C31C2×#4111yescharacteristic
203C23×C31H(5,𝔽2)11yescharacteristic
204C23×C31H(5,𝔽2)11yescharacteristic
205C23×C31H(5,𝔽2)11yescharacteristic
206C23×C312−1+411yescharacteristic
207C2×C4×C31—22no—
208C2×C4×C31—24no—
209C2×C4×C31—22no—
210C2×C4×C31—24no—
211C2×C4×C31—22no—
212C2×C4×C31—22no—
213C2×C4×C31—22no—
214C2×C4×C31—22no—
215C2×C4×C31—22no—
216C2×C4×C31—22no—
217C2×C4×C31—22no—
218C2×C4×C31—24no—
219C2×C4×C31—24no—
220C2×C4×C31—22no—
221C2×C4×C31—22no—
222C2×C4×C31—24no—
223C2×C4×C31—24no—
224C2×C4×C31—22no—
225C2×C4×C31—22no—
226C2×C4×C31—24no—
227C2×C4×C31—22no—
228C2×C4×C31—24no—
229C2×C4×C31—22no—
230C2×C4×C31—24no—
231C2×C4×C31—22no—
232C2×C4×C31—22no—
233C2×C4×C31—24no—
234C2×C4×C31—22no—
235C2×C4×C31—22no—
236C2×C4×C31—22no—
237C2×C4×C31—22no—
238C2×C4×C31—22no—
239C2×C4×C31—22no—
240C2×C4×C31—22no—
241C2×C4×C31—24no—
242C2×C4×C31—24no—
243C2×C4×C31—41no—
244C2×C4×C31—41no—
245C2×C4×C31—42no—
246C2×C4×C31—42no—
247C2×C4×C31—41no—
248C2×C4×C31—41no—
249C2×C4×C31—41no—
250C2×C4×C31—42no—
251C2×C4×C31—41no—
252C2×C4×C31—41no—
253C2×C4×C31—42no—
254C2×C4×C31—42no—
255C2×C4×C31—41no—
256C2×C4×C31—42no—
257C2×C4×C31—42no—
258C2×C4×C31—41no—
259C2×C4×C31—41no—
260C2×C4×C31—41no—
261C2×C4×C31—41no—
262C2×C4×C31—42no—
263C2×C4×C31—41no—
264C2×C4×C31—41no—
265C2×C4×C31—41no—
266C2×C4×C31—41no—
267C2×C4×C31—42no—
268C2×C4×C31—42no—
269C2×C4×C31—42no—
270C2×C4×C31—42no—
271C2×C4×C31—42no—
272C2×C4×C31—42no—
273C2×C4×C31—42no—
274C2×C4×C31C2×C4⋊C418yes—
275C2×C4×C31C2×C4⋊C414yes—
276C2×C4×C31C4×D414yes—
277C2×C4×C31C4×Q814yes—
278C2×C4×C31C4×Q814yes—
279C2×C4×C31#12114yes—
280C2×C4×C31C22⋊Q814yes—
281C2×C4×C31C22⋊Q814yes—
282C2×C4×C31#12514yes—
283C2×C4×C31C4⋊Q814yes—
284C2×#389C2×C3111yescharacteristic
285C2×#389C2×C3111yescharacteristic
286C2×#389C2×C3111yescharacteristic
287C2×C4×C4⋊C4C2×C3111yescharacteristic
288C2×C4×C4⋊C4C2×C3111yescharacteristic
289#1444C2×C3112yes—
290#1441C2×C3112yes—
291#1436C2×C3112yes—
292C4⋊#95C2×C3111yescharacteristic
293C4⋊#95C2×C3112yes—
294C4⋊#95C2×C3111yescharacteristic
295C22×C31C22×C4⋊C411yescharacteristic
296C22×C31C2×C4×D411yescharacteristic
297C22×C31C2×C4×Q811yescharacteristic
298C22×C31C2×C4×Q811yescharacteristic
299C22×C31C4×#4111yescharacteristic
300C22×C31#51811yescharacteristic
301C22×C31#52011yescharacteristic
302C22×C31C2×#12111yescharacteristic
303C22×C31C2×C22⋊Q811yescharacteristic
304C22×C31C2×C22⋊Q811yescharacteristic
305C22×C31#52511yescharacteristic
306C22×C31C2×#12511yescharacteristic
307C22×C31#52911yescharacteristic
308C22×C31C2×C4⋊Q811yescharacteristic
309C22×C31#53311yescharacteristic
310C22×C31#53511yescharacteristic
311C22×C31#53711yescharacteristic
312C22×C31#54011yescharacteristic
313C22×C31#54211yescharacteristic
314C22×C31#54611yescharacteristic
315C22×C31#54611yescharacteristic
316C22×C31D4×Q811yescharacteristic
317C22×C31#55011yescharacteristic
318C22×C31#55211yescharacteristic
319C22×C31#55311yescharacteristic
320C22×C31#55411yescharacteristic
321C22×C31#55411yescharacteristic
322C22×C31#55411yescharacteristic
323C22×C31#55411yescharacteristic
324C22×C31#55411yescharacteristic
325C22×C31#55511yescharacteristic
326C22×C31#55711yescharacteristic
327C22×C31#55711yescharacteristic
328C22×C31Q8211yescharacteristic
329C22×C31Q8211yescharacteristic
330C4×C31—28no—
331C4×C31—24no—
332C4×C31—24no—
333C4×C31—42no—
334C4×C31—44no—
335C4×C31—42no—
336C4×C31—42no—
337C4×C31—42no—
338C4×C31—44no—
339C4×C31—82no—
340C4×C31#38918yes—
341C22×C4⋊C4C22×C3111yescharacteristic
342C22×C4⋊C4C22×C3111yescharacteristic
343C22×C4⋊C4C22×C3112yes—
344C22×C4⋊C4C22×C3111yescharacteristic
345C22×C4⋊C4C22×C3111yescharacteristic
346C22×C4⋊C4C22×C3111yescharacteristic
347C22×C4⋊C4C22×C3112yes—
348C22×C4⋊C4C22×C3112yes—
349C22×C4⋊C4C22×C3111yescharacteristic
350C22×C42C22×C3111yescharacteristic
351C22×C42C22×C3112yes—
352C22×C42C22×C3111yescharacteristic
353C22×C42C22×C3111yescharacteristic
354#389—24no—
355#389—24no—
356#389C4×C3118yescomplemented
357C4×C4⋊C4—24no—
358C4×C4⋊C4—24no—
359C2×#95C22×C3111yescharacteristic
360C2×#95C22×C3112yes—
361C2×#95C22×C3112yes—
362C2×#95C22×C3112yes—
363C2×#95C22×C3111yescharacteristic
364C2×#95C22×C3112yes—
365C2×#95C22×C3112yes—
366C2×#95C22×C3112yes—
367C2×#95C22×C3112yes—
368C2×#95C22×C3112yes—
369C2×C31C2×#38911yescharacteristic
370C2×C31C4×C22⋊Q811yescharacteristic
371C2×C31#232411yescharacteristic
372C2×C31#234911yescharacteristic
373C2×C31Q8×C4⋊C411yescharacteristic
374C2×C31#236911yescharacteristic
375C2×C31#237011yescharacteristic
376C2×C31#241411yescharacteristic
377C2×C31#241711yescharacteristic
378C2×C31#245111yescharacteristic
379C2×C31#245411yescharacteristic
380C2×C31#250711yescharacteristic
381C2×C31#250811yescharacteristic
382C2×C31#256711yescharacteristic
383C2×C31#258411yescharacteristic
384C23×C4C23×C3112yes—
385C23×C4C23×C3112yes—
386C23×C4C23×C3111yescharacteristic
387C23×C4C23×C3111yescharacteristic
388C23×C4C23×C3111yescharacteristic
389C23×C4C23×C3112yes—
390C23×C4C23×C3111yescharacteristic
391C23×C4C23×C3112yes—
392C23×C4C23×C3111yescharacteristic
393C23×C4C23×C3111yescharacteristic
394C23×C4C23×C3111yescharacteristic
395C2×C4⋊C4—22no—
396C2×C4⋊C4—22no—
397C2×C4⋊C4—22no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—22no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—22no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—24no—
405C2×C4⋊C4—24no—
406C2×C4⋊C4—22no—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—24no—
409C2×C4⋊C4—22no—
410C2×C4⋊C4—42no—
411C2×C4⋊C4—42no—
412C2×C4⋊C4—42no—
413C2×C4⋊C4—42no—
414C2×C4⋊C4—42no—
415C2×C4⋊C4C2×C4×C3114yes—
416C2×C4⋊C4C2×C4×C3118yes—
417C2×C4⋊C4C2×C4×C3114yes—
418C2×C4⋊C4D4×C3114yes—
419C2×C4⋊C4Q8×C3114yes—
420C2×C4⋊C4Q8×C3114yes—
421C2×C4⋊C4Q8×C3114yes—
422C2×C42—22no—
423C2×C42—22no—
424C2×C42—22no—
425C2×C42—22no—
426C2×C42—24no—
427C2×C42—22no—
428C2×C42—22no—
429C2×C42—24no—
430C2×C42—22no—
431C2×C42—42no—
432C2×C42C2×C4×C3114yes—
433C2×C42D4×C3114yes—
434#95—22no—
435#95—24no—
436#95—22no—
437#95—24no—
438#95—24no—
439#95—24no—
440#95—42no—
441#95—42no—
442#95—42no—
443#95C2×C4×C3118yes—
444C31#1404511yescharacteristic, direct product factor, Sylow
445C24C24×C3111yescharacteristic
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—22no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—21no—
464C22×C4—22no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—22no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4C22×C4×C3114yes—
502C22×C4C22×C4×C3112yes—
503C22×C4C22×C4×C3114yes—
504C22×C4C22×C4×C3112yes—
505C22×C4C22×C4×C3112yes—
506C22×C4C2×D4×C3112yes—
507C22×C4C2×D4×C3114yes—
508C22×C4C2×D4×C3112yes—
509C22×C4C2×D4×C3112yes—
510C22×C4C2×D4×C3112yes—
511C22×C4C2×Q8×C3112yes—
512C22×C4C2×Q8×C3114yes—
513C22×C4C2×Q8×C3114yes—
514C22×C4C2×Q8×C3112yes—
515C22×C4C2×Q8×C3112yes—
516C22×C4C2×Q8×C3112yes—
517C22×C4C2×Q8×C3112yes—
518C22×C4#41×C3112yes—
519C22×C4#41×C3112yes—
520C22×C4#41×C3112yes—
521C22×C4#41×C3112yes—
522C22×C4#41×C3112yes—
523C4⋊C4—28no—
524C4⋊C4—28no—
525C4⋊C4—28no—
526C4⋊C4—28no—
527C4⋊C4—48no—
528C4⋊C4—48no—
529C4⋊C4—48no—
530C4⋊C4—44no—
531C4⋊C4C4⋊C4×C31116yescomplemented
532C42—28no—
533C42—28no—
534C42—48no—
535C42—44no—
536C23C23×C4×C3111yescharacteristic
537C23C22×D4×C3111yescharacteristic
538C23C22×D4×C3111yescharacteristic
539C23C22×Q8×C3111yescharacteristic
540C23C22×Q8×C3111yescharacteristic
541C23C22×Q8×C3111yescharacteristic
542C23C2×#41×C3111yescharacteristic
543C23C2×#41×C3111yescharacteristic
544C23C2×#41×C3111yescharacteristic
545C23C2×#41×C3111yescharacteristic
546C23C2×#41×C3111yescharacteristic
547C23C31×H(5,𝔽2)11yescharacteristic
548C23C31×H(5,𝔽2)11yescharacteristic
549C23C31×H(5,𝔽2)11yescharacteristic
550C23C31×2−1+411yescharacteristic
551C2×C4—22no—
552C2×C4—24no—
553C2×C4—22no—
554C2×C4—24no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—24no—
567C2×C4—24no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—24no—
571C2×C4—22no—
572C2×C4—24no—
573C2×C4—22no—
574C2×C4—24no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—24no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—24no—
586C2×C4—24no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—42no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—42no—
598C2×C4—42no—
599C2×C4—41no—
600C2×C4—42no—
601C2×C4—42no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—42no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—42no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—42no—
618C2×C4C2×C4⋊C4×C3118yes—
619C2×C4C2×C4⋊C4×C3114yes—
620C2×C4C4×D4×C3114yes—
621C2×C4C4×Q8×C3114yes—
622C2×C4C4×Q8×C3114yes—
623C2×C4C31×#12114yes—
624C2×C4C31×C22⋊Q814yes—
625C2×C4C31×C22⋊Q814yes—
626C2×C4C31×#12514yes—
627C2×C4C31×C4⋊Q814yes—
628C22C22×C4⋊C4×C3111yescharacteristic
629C22C2×C4×D4×C3111yescharacteristic
630C22C2×C4×Q8×C3111yescharacteristic
631C22C2×C4×Q8×C3111yescharacteristic
632C22C4×#41×C3111yescharacteristic
633C22C31×#51811yescharacteristic
634C22C31×#52011yescharacteristic
635C22C2×C31×#12111yescharacteristic
636C22C2×C31×C22⋊Q811yescharacteristic
637C22C2×C31×C22⋊Q811yescharacteristic
638C22C31×#52511yescharacteristic
639C22C2×C31×#12511yescharacteristic
640C22C31×#52911yescharacteristic
641C22C2×C31×C4⋊Q811yescharacteristic
642C22C31×#53311yescharacteristic
643C22C31×#53511yescharacteristic
644C22C31×#53711yescharacteristic
645C22C31×#54011yescharacteristic
646C22C31×#54211yescharacteristic
647C22C31×#54611yescharacteristic
648C22C31×#54611yescharacteristic
649C22D4×Q8×C3111yescharacteristic
650C22C31×#55011yescharacteristic
651C22C31×#55211yescharacteristic
652C22C31×#55311yescharacteristic
653C22C31×#55411yescharacteristic
654C22C31×#55411yescharacteristic
655C22C31×#55411yescharacteristic
656C22C31×#55411yescharacteristic
657C22C31×#55411yescharacteristic
658C22C31×#55511yescharacteristic
659C22C31×#55711yescharacteristic
660C22C31×#55711yescharacteristic
661C22Q82×C3111yescharacteristic
662C22Q82×C3111yescharacteristic
663C4—28no—
664C4—24no—
665C4—24no—
666C4—42no—
667C4—44no—
668C4—42no—
669C4—42no—
670C4—42no—
671C4—44no—
672C4—82no—
673C4C31×#38918yes—
674C2C2×C31×#38911yescharacteristic
675C2C4×C31×C22⋊Q811yescharacteristic
676C2C31×#232411yescharacteristic
677C2C31×#234911yescharacteristic
678C2Q8×C4⋊C4×C3111yescharacteristic
679C2C31×#236911yescharacteristic
680C2C31×#237011yescharacteristic
681C2C31×#241411yescharacteristic
682C2C31×#241711yescharacteristic
683C2C31×#245111yescharacteristic
684C2C31×#245411yescharacteristic
685C2C31×#250711yescharacteristic
686C2C31×#250811yescharacteristic
687C2C31×#256711yescharacteristic
688C2C31×#258411yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C31C24
commutatorC23C23×C4×C31
Frattini, cosocleC24C24×C31
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
27. C31×#389C4semidirect
186. C4⋊C4×C31C4⋊C4semidirect
191. #14045C31direct (N × H)
356. #389C4×C31semidirect
444. C31#14045direct (N × H)
531. C4⋊C4C4⋊C4×C31semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#3892
C2×C4×C4⋊C4×C312
C31×#14442
C31×#14412
C31×#14362
C31×C4⋊#952
#1404531