Finite Group Databasebeta

← C31×#14504 #21471263

Subgroups — C31×#14504 #21471263

Order 7936.

1298 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#388C211yesmaximal, characteristic
2C31×#1445C211yesmaximal, characteristic, complemented
3C31×#1443C211yesmaximal, characteristic, complemented
4C31×#1440C211yesmaximal, characteristic
5C31×#1440C211yesmaximal, characteristic
6C31×#1439C211yesmaximal, characteristic
7C31×#1439C211yesmaximal, characteristic
8C31×#1437C211yesmaximal, characteristic
9C31×#1437C211yesmaximal, characteristic
10C31×#1436C211yesmaximal, characteristic, complemented
11C31×#1436C211yesmaximal, characteristic, complemented
12C31×#1436C211yesmaximal, characteristic, complemented
13C31×C4⋊#95C211yesmaximal, characteristic, complemented
14C31×#1434C211yesmaximal, characteristic, complemented
15C31×#1434C211yesmaximal, characteristic, complemented
16C22×C4⋊C4×C31C2211yescharacteristic
17C22×C4⋊C4×C31C2211yescharacteristic
18C22×C4⋊C4×C31C2211yescharacteristic
19C22×C22⋊C4×C31C2211yescharacteristic
20C22×C22⋊C4×C31C2211yescharacteristic
21C22×C22⋊C4×C31C2211yescharacteristic
22C22×C22⋊C4×C31C2211yescharacteristic
23C22×C22⋊C4×C31C2211yescharacteristic
24C22×C22⋊C4×C31C2211yescharacteristic
25C22×C22⋊C4×C31C2211yescharacteristic
26C22×C42×C31C2211yescharacteristic
27C22×C42×C31C2211yescharacteristic
28C22×C42×C31C2211yescharacteristic
29C31×#388C418yescomplemented
30C2×C31×#95C2211yescharacteristic
31C2×C31×#95C2211yescharacteristic
32C2×C31×#95C2211yescharacteristic
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
52C25×C31C2311yescharacteristic
53C23×C4×C31C2311yescharacteristic
54C23×C4×C31C2311yescharacteristic
55C23×C4×C31C2311yescharacteristic
56C23×C4×C31C2311yescharacteristic
57C23×C4×C31C2311yescharacteristic
58C23×C4×C31C2311yescharacteristic
59C23×C4×C31C2311yescharacteristic
60C23×C4×C31C2311yescharacteristic
61C23×C4×C31C2311yescharacteristic
62C23×C4×C31C2311yescharacteristic
63C23×C4×C31C2311yescharacteristic
64C23×C4×C31C2311yescharacteristic
65C23×C4×C31C2311yescharacteristic
66C23×C4×C31C2311yescharacteristic
67C2×C4⋊C4×C31—22no—
68C2×C4⋊C4×C31—22no—
69C2×C4⋊C4×C31—22no—
70C2×C4⋊C4×C31—22no—
71C2×C4⋊C4×C31—41no—
72C2×C4⋊C4×C31—41no—
73C2×C4⋊C4×C31—41no—
74C2×C4⋊C4×C31—41no—
75C2×C4⋊C4×C31C2×C414yes—
76C2×C22⋊C4×C31—22no—
77C2×C22⋊C4×C31—22no—
78C2×C22⋊C4×C31—22no—
79C2×C22⋊C4×C31—22no—
80C2×C22⋊C4×C31—22no—
81C2×C22⋊C4×C31—22no—
82C2×C22⋊C4×C31—41no—
83C2×C22⋊C4×C31—41no—
84C2×C22⋊C4×C31—41no—
85C2×C22⋊C4×C31—41no—
86C2×C22⋊C4×C31—41no—
87C2×C22⋊C4×C31—41no—
88C2×C22⋊C4×C31—41no—
89C2×C22⋊C4×C31—41no—
90C2×C22⋊C4×C31—41no—
91C2×C22⋊C4×C31—41no—
92C2×C22⋊C4×C31—41no—
93C2×C22⋊C4×C31—41no—
94C2×C22⋊C4×C31C2×C414yes—
95C2×C22⋊C4×C31C2×C414yes—
96C2×C22⋊C4×C31C2×C414yes—
97C2×C42×C31—22no—
98C2×C42×C31—41no—
99C2×C42×C31—41no—
100C2×C42×C31—41no—
101C2×C42×C31—41no—
102C2×C42×C31—41no—
103C2×C42×C31—41no—
104C2×C42×C31—41no—
105C2×C42×C31C2×C414yes—
106C31×#95—22no—
107C31×#95—22no—
108C31×#95—22no—
109C31×#95—22no—
110C31×#95—22no—
111C31×#95—22no—
112C31×#95—22no—
113C31×#95—41no—
114C31×#95—41no—
115C31×#95—41no—
116C31×#95—41no—
117C31×#95—41no—
118C31×#95—41no—
119C31×#95—41no—
120C31×#95—41no—
121C31×#95—41no—
122C31×#95—41no—
123C31×#95—41no—
124C31×#95—41no—
125C31×#95—41no—
126C31×#95C2×C414yes—
127C31×#95C2×C414yes—
128C24×C31—21no—
129C24×C31—21no—
130C24×C31—21no—
131C24×C31—21no—
132C24×C31—21no—
133C24×C31—21no—
134C24×C31—21no—
135C24×C31—21no—
136C24×C31—21no—
137C24×C31—21no—
138C24×C31—21no—
139C24×C31—21no—
140C24×C31—21no—
141C24×C31—21no—
142C24×C31C22×C412yes—
143C24×C31C2411yescharacteristic
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×C31C22×C412yes—
231C22×C4×C31C22×C412yes—
232C22×C4×C31C22×C412yes—
233C22×C4×C31C22×C412yes—
234C22×C4×C31C22×C412yes—
235C22×C4×C31C22×C412yes—
236C22×C4×C31#4112yes—
237C22×C4×C31#4112yes—
238C22×C4×C31#4112yes—
239C22×C4×C31#4112yes—
240C22×C4×C31#4112yes—
241C22×C4×C31#4112yes—
242C4⋊C4×C31—44no—
243C4⋊C4×C31—44no—
244C4⋊C4×C31—44no—
245C22⋊C4×C31—28no—
246C22⋊C4×C31—44no—
247C22⋊C4×C31—44no—
248C22⋊C4×C31—44no—
249C22⋊C4×C31—44no—
250C22⋊C4×C31—44no—
251C22⋊C4×C31—44no—
252C42×C31—44no—
253C42×C31—44no—
254C42×C31—44no—
255#14504C3111yesmaximal, characteristic, direct product factor, Sylow
256C23×C31—22no—
257C23×C31—22no—
258C23×C31—22no—
259C23×C31—22no—
260C23×C31—22no—
261C23×C31—22no—
262C23×C31—22no—
263C23×C31—41no—
264C23×C31—41no—
265C23×C31—41no—
266C23×C31—41no—
267C23×C31—41no—
268C23×C31—41no—
269C23×C31—41no—
270C23×C31—41no—
271C23×C31—41no—
272C23×C31—41no—
273C23×C31—41no—
274C23×C31—41no—
275C23×C31—41no—
276C23×C31—41no—
277C23×C31—41no—
278C23×C31—41no—
279C23×C31—41no—
280C23×C31—41no—
281C23×C31—41no—
282C23×C31—41no—
283C23×C31—41no—
284C23×C31—41no—
285C23×C31—41no—
286C23×C31—41no—
287C23×C31—41no—
288C23×C31—41no—
289C23×C31—41no—
290C23×C31—41no—
291C23×C31C23×C411yescharacteristic
292C23×C31C2×#4111yescharacteristic
293C23×C31C2×#4111yescharacteristic
294C23×C31C2×#4111yescharacteristic
295C23×C31C2×#4111yescharacteristic
296C23×C31C2×#4111yescharacteristic
297C23×C31C2×#4111yescharacteristic
298C23×C31H(5,𝔽2)11yescharacteristic
299C23×C31H(5,𝔽2)11yescharacteristic
300C23×C31H(5,𝔽2)11yescharacteristic
301C23×C31H(5,𝔽2)11yescharacteristic
302C23×C31H(5,𝔽2)11yescharacteristic
303C23×C31H(5,𝔽2)11yescharacteristic
304C23×C312−1+411yescharacteristic
305C23×C312−1+411yescharacteristic
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—22no—
323C2×C4×C31—22no—
324C2×C4×C31—22no—
325C2×C4×C31—22no—
326C2×C4×C31—22no—
327C2×C4×C31—22no—
328C2×C4×C31—22no—
329C2×C4×C31—22no—
330C2×C4×C31—22no—
331C2×C4×C31—22no—
332C2×C4×C31—22no—
333C2×C4×C31—22no—
334C2×C4×C31—22no—
335C2×C4×C31—22no—
336C2×C4×C31—22no—
337C2×C4×C31—22no—
338C2×C4×C31—22no—
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×C31—41no—
381C2×C4×C31—41no—
382C2×C4×C31—41no—
383C2×C4×C31—41no—
384C2×C4×C31—41no—
385C2×C4×C31—41no—
386C2×C4×C31—41no—
387C2×C4×C31—41no—
388C2×C4×C31—41no—
389C2×C4×C31—41no—
390C2×C4×C31—41no—
391C2×C4×C31—41no—
392C2×C4×C31—41no—
393C2×C4×C31—41no—
394C2×C4×C31—41no—
395C2×C4×C31—41no—
396C2×C4×C31—41no—
397C2×C4×C31—41no—
398C2×C4×C31—41no—
399C2×C4×C31—41no—
400C2×C4×C31—41no—
401C2×C4×C31—41no—
402C2×C4×C31—41no—
403C2×C4×C31#11714yes—
404C2×#388C2×C3111yescharacteristic
405#1445C2×C3111yescharacteristic, complemented
406#1443C2×C3111yescharacteristic, complemented
407#1440C2×C3111yescharacteristic
408#1440C2×C3111yescharacteristic
409#1439C2×C3111yescharacteristic
410#1439C2×C3111yescharacteristic
411#1437C2×C3111yescharacteristic
412#1437C2×C3111yescharacteristic
413#1436C2×C3111yescharacteristic, complemented
414#1436C2×C3111yescharacteristic, complemented
415#1436C2×C3111yescharacteristic, complemented
416C4⋊#95C2×C3111yescharacteristic, complemented
417#1434C2×C3111yescharacteristic, complemented
418#1434C2×C3111yescharacteristic, complemented
419C22×C31—42no—
420C22×C31—42no—
421C22×C31—42no—
422C22×C31—42no—
423C22×C31—42no—
424C22×C31—42no—
425C22×C31—42no—
426C22×C31—81no—
427C22×C31—81no—
428C22×C31—81no—
429C22×C31—81no—
430C22×C31—81no—
431C22×C31—81no—
432C22×C31—81no—
433C22×C31—81no—
434C22×C31C2×#11711yescharacteristic
435C22×C31C4×#4111yescharacteristic
436C22×C31C4×#4111yescharacteristic
437C22×C31#51811yescharacteristic
438C22×C31#51811yescharacteristic
439C22×C31#52011yescharacteristic
440C22×C31#52011yescharacteristic
441C22×C31#53811yescharacteristic
442C22×C31#53811yescharacteristic
443C22×C31#53811yescharacteristic
444C22×C31#53911yescharacteristic
445C22×C31#54011yescharacteristic
446C22×C31#54011yescharacteristic
447C22×C31#54111yescharacteristic
448C22×C31#54211yescharacteristic
449C22×C31#54211yescharacteristic
450C22×C31#54211yescharacteristic
451C22×C31#54211yescharacteristic
452C22×C31#54211yescharacteristic
453C22×C31#55111yescharacteristic
454C22×C31#55111yescharacteristic
455C22×C31#55111yescharacteristic
456C22×C31#55211yescharacteristic
457C22×C31#55311yescharacteristic
458C22×C31#55311yescharacteristic
459C22×C31#55311yescharacteristic
460C22×C31#55311yescharacteristic
461C22×C31#55311yescharacteristic
462C22×C31#55611yescharacteristic
463C22×C31#55911yescharacteristic
464C22×C31#55911yescharacteristic
465C22×C31#56011yescharacteristic
466C22×C31#56011yescharacteristic
467C22×C31#56211yescharacteristic
468C22×C31#56211yescharacteristic
469C4×C31—24no—
470C4×C31—42no—
471C4×C31—42no—
472C4×C31—42no—
473C4×C31—42no—
474C4×C31—42no—
475C4×C31—42no—
476C4×C31—42no—
477C4×C31—42no—
478C4×C31—42no—
479C4×C31—81no—
480C4×C31—81no—
481C4×C31—81no—
482C4×C31—81no—
483C22×C4⋊C4C22×C3111yescharacteristic
484C22×C4⋊C4C22×C3111yescharacteristic
485C22×C4⋊C4C22×C3111yescharacteristic
486C22×C22⋊C4C22×C3111yescharacteristic
487C22×C22⋊C4C22×C3111yescharacteristic
488C22×C22⋊C4C22×C3111yescharacteristic
489C22×C22⋊C4C22×C3111yescharacteristic
490C22×C22⋊C4C22×C3111yescharacteristic
491C22×C22⋊C4C22×C3111yescharacteristic
492C22×C22⋊C4C22×C3111yescharacteristic
493C22×C42C22×C3111yescharacteristic
494C22×C42C22×C3111yescharacteristic
495C22×C42C22×C3111yescharacteristic
496#388C4×C3118yescomplemented
497C2×#95C22×C3111yescharacteristic
498C2×#95C22×C3111yescharacteristic
499C2×#95C22×C3111yescharacteristic
500C2×#95C22×C3111yescharacteristic
501C2×#95C22×C3111yescharacteristic
502C2×#95C22×C3111yescharacteristic
503C2×#95C22×C3111yescharacteristic
504C2×#95C22×C3111yescharacteristic
505C2×#95C22×C3111yescharacteristic
506C2×#95C22×C3111yescharacteristic
507C2×#95C22×C3111yescharacteristic
508C2×#95C22×C3111yescharacteristic
509C2×#95C22×C3111yescharacteristic
510C2×#95C22×C3111yescharacteristic
511C2×#95C22×C3111yescharacteristic
512C2×#95C22×C3111yescharacteristic
513C2×#95C22×C3111yescharacteristic
514C2×#95C22×C3111yescharacteristic
515C2×#95C22×C3111yescharacteristic
516C2×#95C22×C3111yescharacteristic
517C2×#95C22×C3111yescharacteristic
518C2×#95C22×C3111yescharacteristic
519C2×C31—82no—
520C2×C31#231411yescharacteristic
521C2×C31#233511yescharacteristic
522C2×C31#233711yescharacteristic
523C2×C31#235311yescharacteristic
524C2×C31#235711yescharacteristic
525C2×C31#237311yescharacteristic
526C2×C31#237711yescharacteristic
527C2×C31#275211yescharacteristic
528C2×C31#275411yescharacteristic
529C2×C31#275711yescharacteristic
530C2×C31#277911yescharacteristic
531C2×C31#279711yescharacteristic
532C2×C31#279811yescharacteristic
533C2×C31#280011yescharacteristic
534C2×C31#280111yescharacteristic
535C25C23×C3111yescharacteristic
536C23×C4C23×C3111yescharacteristic
537C23×C4C23×C3111yescharacteristic
538C23×C4C23×C3111yescharacteristic
539C23×C4C23×C3111yescharacteristic
540C23×C4C23×C3111yescharacteristic
541C23×C4C23×C3111yescharacteristic
542C23×C4C23×C3111yescharacteristic
543C23×C4C23×C3111yescharacteristic
544C23×C4C23×C3111yescharacteristic
545C23×C4C23×C3111yescharacteristic
546C23×C4C23×C3111yescharacteristic
547C23×C4C23×C3111yescharacteristic
548C23×C4C23×C3111yescharacteristic
549C23×C4C23×C3111yescharacteristic
550C2×C4⋊C4—22no—
551C2×C4⋊C4—22no—
552C2×C4⋊C4—22no—
553C2×C4⋊C4—22no—
554C2×C4⋊C4—41no—
555C2×C4⋊C4—41no—
556C2×C4⋊C4—41no—
557C2×C4⋊C4—41no—
558C2×C4⋊C4C2×C4×C3114yes—
559C2×C22⋊C4—22no—
560C2×C22⋊C4—22no—
561C2×C22⋊C4—22no—
562C2×C22⋊C4—22no—
563C2×C22⋊C4—22no—
564C2×C22⋊C4—22no—
565C2×C22⋊C4—41no—
566C2×C22⋊C4—41no—
567C2×C22⋊C4—41no—
568C2×C22⋊C4—41no—
569C2×C22⋊C4—41no—
570C2×C22⋊C4—41no—
571C2×C22⋊C4—41no—
572C2×C22⋊C4—41no—
573C2×C22⋊C4—41no—
574C2×C22⋊C4—41no—
575C2×C22⋊C4—41no—
576C2×C22⋊C4—41no—
577C2×C22⋊C4C2×C4×C3114yes—
578C2×C22⋊C4C2×C4×C3114yes—
579C2×C22⋊C4C2×C4×C3114yes—
580C2×C42—22no—
581C2×C42—41no—
582C2×C42—41no—
583C2×C42—41no—
584C2×C42—41no—
585C2×C42—41no—
586C2×C42—41no—
587C2×C42—41no—
588C2×C42C2×C4×C3114yes—
589#95—22no—
590#95—22no—
591#95—22no—
592#95—22no—
593#95—22no—
594#95—22no—
595#95—22no—
596#95—41no—
597#95—41no—
598#95—41no—
599#95—41no—
600#95—41no—
601#95—41no—
602#95—41no—
603#95—41no—
604#95—41no—
605#95—41no—
606#95—41no—
607#95—41no—
608#95—41no—
609#95C2×C4×C3114yes—
610#95C2×C4×C3114yes—
611C31#1450411yescharacteristic, direct product factor, Sylow
612C24—21no—
613C24—21no—
614C24—21no—
615C24—21no—
616C24—21no—
617C24—21no—
618C24—21no—
619C24—21no—
620C24—21no—
621C24—21no—
622C24—21no—
623C24—21no—
624C24—21no—
625C24—21no—
626C24C22×C4×C3112yes—
627C24C24×C3111yescharacteristic
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×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4C22×C4×C3112yes—
715C22×C4C22×C4×C3112yes—
716C22×C4C22×C4×C3112yes—
717C22×C4C22×C4×C3112yes—
718C22×C4C22×C4×C3112yes—
719C22×C4C22×C4×C3112yes—
720C22×C4#41×C3112yes—
721C22×C4#41×C3112yes—
722C22×C4#41×C3112yes—
723C22×C4#41×C3112yes—
724C22×C4#41×C3112yes—
725C22×C4#41×C3112yes—
726C4⋊C4—44no—
727C4⋊C4—44no—
728C4⋊C4—44no—
729C22⋊C4—28no—
730C22⋊C4—44no—
731C22⋊C4—44no—
732C22⋊C4—44no—
733C22⋊C4—44no—
734C22⋊C4—44no—
735C22⋊C4—44no—
736C42—44no—
737C42—44no—
738C42—44no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23C23×C4×C3111yescharacteristic
775C23C2×#41×C3111yescharacteristic
776C23C2×#41×C3111yescharacteristic
777C23C2×#41×C3111yescharacteristic
778C23C2×#41×C3111yescharacteristic
779C23C2×#41×C3111yescharacteristic
780C23C2×#41×C3111yescharacteristic
781C23C31×H(5,𝔽2)11yescharacteristic
782C23C31×H(5,𝔽2)11yescharacteristic
783C23C31×H(5,𝔽2)11yescharacteristic
784C23C31×H(5,𝔽2)11yescharacteristic
785C23C31×H(5,𝔽2)11yescharacteristic
786C23C31×H(5,𝔽2)11yescharacteristic
787C23C31×2−1+411yescharacteristic
788C23C31×2−1+411yescharacteristic
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4C31×#11714yes—
887C22—42no—
888C22—42no—
889C22—42no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—42no—
894C22—81no—
895C22—81no—
896C22—81no—
897C22—81no—
898C22—81no—
899C22—81no—
900C22—81no—
901C22—81no—
902C22C2×C31×#11711yescharacteristic
903C22C4×#41×C3111yescharacteristic
904C22C4×#41×C3111yescharacteristic
905C22C31×#51811yescharacteristic
906C22C31×#51811yescharacteristic
907C22C31×#52011yescharacteristic
908C22C31×#52011yescharacteristic
909C22C31×#53811yescharacteristic
910C22C31×#53811yescharacteristic
911C22C31×#53811yescharacteristic
912C22C31×#53911yescharacteristic
913C22C31×#54011yescharacteristic
914C22C31×#54011yescharacteristic
915C22C31×#54111yescharacteristic
916C22C31×#54211yescharacteristic
917C22C31×#54211yescharacteristic
918C22C31×#54211yescharacteristic
919C22C31×#54211yescharacteristic
920C22C31×#54211yescharacteristic
921C22C31×#55111yescharacteristic
922C22C31×#55111yescharacteristic
923C22C31×#55111yescharacteristic
924C22C31×#55211yescharacteristic
925C22C31×#55311yescharacteristic
926C22C31×#55311yescharacteristic
927C22C31×#55311yescharacteristic
928C22C31×#55311yescharacteristic
929C22C31×#55311yescharacteristic
930C22C31×#55611yescharacteristic
931C22C31×#55911yescharacteristic
932C22C31×#55911yescharacteristic
933C22C31×#56011yescharacteristic
934C22C31×#56011yescharacteristic
935C22C31×#56211yescharacteristic
936C22C31×#56211yescharacteristic
937C4—24no—
938C4—42no—
939C4—42no—
940C4—42no—
941C4—42no—
942C4—42no—
943C4—42no—
944C4—42no—
945C4—42no—
946C4—42no—
947C4—81no—
948C4—81no—
949C4—81no—
950C4—81no—
951C2—82no—
952C2C31×#231411yescharacteristic
953C2C31×#233511yescharacteristic
954C2C31×#233711yescharacteristic
955C2C31×#235311yescharacteristic
956C2C31×#235711yescharacteristic
957C2C31×#237311yescharacteristic
958C2C31×#237711yescharacteristic
959C2C31×#275211yescharacteristic
960C2C31×#275411yescharacteristic
961C2C31×#275711yescharacteristic
962C2C31×#277911yescharacteristic
963C2C31×#279711yescharacteristic
964C2C31×#279811yescharacteristic
965C2C31×#280011yescharacteristic
966C2C31×#280111yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutatorC23C23×C4×C31
Frattini, cosocleC24C24×C31
prime radicalC25×C31C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#1445C2semidirect
3. C31×#1443C2semidirect
10. C31×#1436C2semidirect
11. C31×#1436C2semidirect
12. C31×#1436C2semidirect
13. C31×C4⋊#95C2semidirect
14. C31×#1434C2semidirect
15. C31×#1434C2semidirect
29. C31×#388C4semidirect
255. #14504C31direct (N × H)
405. #1445C2×C31semidirect
406. #1443C2×C31semidirect
413. #1436C2×C31semidirect
414. #1436C2×C31semidirect
415. #1436C2×C31semidirect
416. C4⋊#95C2×C31semidirect
417. #1434C2×C31semidirect
418. #1434C2×C31semidirect
496. #388C4×C31semidirect
611. C31#14504direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3882
C31×#14452
C31×#14432
C31×#14402
C31×#14392
C31×#14372
C31×#14362
C31×C4⋊#952
C31×#14342
#1450431