Finite Group Databasebeta

← C31×#14736 #21471495

Subgroups — C31×#14736 #21471495

Order 7936.

1938 conjugacy classes of subgroups.

The subgroup lattice has 1056 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#398C211yesmaximal, characteristic, complemented
2C2×C31×#385C211yesmaximal, characteristic
3C2×C31×#385C211yesmaximal, characteristic
4C2×C31×#385C211yesmaximal, characteristic
5C2×C31×#380C211yesmaximal, characteristic
6C22×C31×#95C211yesmaximal, characteristic
7C31×#1445C211yesmaximal, characteristic, complemented
8C31×#1444C211yesmaximal, characteristic, complemented
9C31×#1442C211yesmaximal, characteristic, complemented
10C31×#1442C211yesmaximal, characteristic, complemented
11C31×#1441C211yesmaximal, characteristic, complemented
12C31×#1441C211yesmaximal, characteristic, complemented
13C31×#1441C211yesmaximal, characteristic, complemented
14C31×C22⋊#95C211yesmaximal, characteristic
15C31×C22⋊#95C211yesmaximal, characteristic
16C24×C4×C31C2211yescharacteristic
17C24×C4×C31C2211yescharacteristic
18C24×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×C22⋊C4×C31C2211yescharacteristic
28C22×C22⋊C4×C31C2211yescharacteristic
29C22×C22⋊C4×C31C2211yescharacteristic
30C22×C22⋊C4×C31C2211yescharacteristic
31C31×#398—24no—
32C31×#385—24no—
33C31×#385—24no—
34C31×#385—24no—
35C31×#380—24no—
36C2×C31×#95—24no—
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
55C2×C31×#95C2211yescharacteristic
56C2×C31×#95C2211yescharacteristic
57C25×C31C2311yescharacteristic
58C23×C4×C31—22no—
59C23×C4×C31—22no—
60C23×C4×C31—22no—
61C23×C4×C31—22no—
62C23×C4×C31—22no—
63C23×C4×C31—22no—
64C23×C4×C31—22no—
65C23×C4×C31—22no—
66C23×C4×C31—22no—
67C23×C4×C31—22no—
68C23×C4×C31—22no—
69C23×C4×C31—22no—
70C23×C4×C31—22no—
71C23×C4×C31—22no—
72C23×C4×C31—41no—
73C23×C4×C31—41no—
74C23×C4×C31—41no—
75C23×C4×C31—41no—
76C23×C4×C31—41no—
77C23×C4×C31—41no—
78C23×C4×C31Q814yes—
79C23×C4×C31C2311yescharacteristic
80C23×C4×C31C2311yescharacteristic
81C23×C4×C31C2311yescharacteristic
82C23×C4×C31C2311yescharacteristic
83C23×C4×C31C2311yescharacteristic
84C23×C4×C31C2311yescharacteristic
85C23×C4×C31C2311yescharacteristic
86C23×C4×C31C2311yescharacteristic
87C23×C4×C31C2311yescharacteristic
88C23×C4×C31C2311yescharacteristic
89C23×C4×C31C2311yescharacteristic
90C23×C4×C31C2311yescharacteristic
91C23×C4×C31C2311yescharacteristic
92C23×C4×C31C2311yescharacteristic
93C2×C4⋊C4×C31—22no—
94C2×C4⋊C4×C31—22no—
95C2×C4⋊C4×C31—22no—
96C2×C4⋊C4×C31—22no—
97C2×C4⋊C4×C31—22no—
98C2×C4⋊C4×C31—22no—
99C2×C4⋊C4×C31—22no—
100C2×C4⋊C4×C31—22no—
101C2×C4⋊C4×C31—22no—
102C2×C4⋊C4×C31—22no—
103C2×C4⋊C4×C31—22no—
104C2×C4⋊C4×C31—22no—
105C2×C4⋊C4×C31—22no—
106C2×C4⋊C4×C31—22no—
107C2×C4⋊C4×C31—22no—
108C2×C4⋊C4×C31—22no—
109C2×C4⋊C4×C31—41no—
110C2×C4⋊C4×C31—41no—
111C2×C4⋊C4×C31—41no—
112C2×C4⋊C4×C31—41no—
113C2×C4⋊C4×C31—41no—
114C2×C4⋊C4×C31—41no—
115C2×C4⋊C4×C31—41no—
116C2×C4⋊C4×C31—41no—
117C2×C22⋊C4×C31—22no—
118C2×C22⋊C4×C31—22no—
119C2×C22⋊C4×C31—22no—
120C2×C22⋊C4×C31—22no—
121C2×C22⋊C4×C31—22no—
122C2×C22⋊C4×C31—22no—
123C2×C22⋊C4×C31—22no—
124C2×C22⋊C4×C31—22no—
125C2×C22⋊C4×C31—22no—
126C2×C22⋊C4×C31D414yes—
127C2×C22⋊C4×C31D414yes—
128C2×C22⋊C4×C31Q814yes—
129C31×#95—22no—
130C31×#95—22no—
131C31×#95—22no—
132C31×#95—22no—
133C31×#95—22no—
134C31×#95—22no—
135C31×#95—22no—
136C31×#95—22no—
137C31×#95—22no—
138C31×#95—22no—
139C31×#95—22no—
140C31×#95—22no—
141C31×#95—22no—
142C31×#95—22no—
143C31×#95—22no—
144C31×#95—41no—
145C31×#95—41no—
146C31×#95—41no—
147C31×#95—41no—
148C31×#95D414yes—
149C24×C31—21no—
150C24×C31—21no—
151C24×C31—21no—
152C24×C31—21no—
153C24×C31—21no—
154C24×C31—21no—
155C24×C31—21no—
156C24×C31—21no—
157C24×C31C2×D412yes—
158C24×C31C2×D412yes—
159C24×C31C2×Q812yes—
160C24×C31C2×Q812yes—
161C24×C31#4112yes—
162C24×C31#4112yes—
163C24×C31#4112yes—
164C24×C31C2411yescharacteristic
165C22×C4×C31—21no—
166C22×C4×C31—21no—
167C22×C4×C31—21no—
168C22×C4×C31—21no—
169C22×C4×C31—28no—
170C22×C4×C31—28no—
171C22×C4×C31—28no—
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×C31—21no—
232C22×C4×C31—21no—
233C22×C4×C31—21no—
234C22×C4×C31—21no—
235C22×C4×C31—21no—
236C22×C4×C31—21no—
237C22×C4×C31—21no—
238C22×C4×C31—28no—
239C22×C4×C31—21no—
240C22×C4×C31—21no—
241C22×C4×C31—21no—
242C22×C4×C31—21no—
243C22×C4×C31—21no—
244C22×C4×C31—21no—
245C22×C4×C31—21no—
246C22×C4×C31—21no—
247C22×C4×C31—21no—
248C22×C4×C31—21no—
249C22×C4×C31—21no—
250C22×C4×C31—21no—
251C22×C4×C31—21no—
252C22×C4×C31—21no—
253C22×C4×C31—44no—
254C22×C4×C31—44no—
255C22×C4×C31—44no—
256C22×C4×C31—44no—
257C22×C4×C31—44no—
258C22×C4×C31—44no—
259C22×C4×C31—44no—
260C22×C4×C31—44no—
261C22×C4×C31—44no—
262C22×C4×C31—44no—
263C22×C4×C31—44no—
264C22×C4×C31—44no—
265C22×C4×C31—44no—
266C22×C4×C31—44no—
267C22×C4×C31—44no—
268C22×C4×C31—44no—
269C22×C4×C31—44no—
270C22×C4×C31C2×D412yes—
271C22×C4×C31C2×D412yes—
272C22×C4×C31C2×D412yes—
273C22×C4×C31C2×D412yes—
274C22×C4×C31C2×D412yes—
275C22×C4×C31C2×D412yes—
276C22×C4×C31C2×D412yes—
277C22×C4×C31C2×Q812yes—
278C22×C4×C31C2×Q812yes—
279C22×C4×C31C2×Q812yes—
280C22×C4×C31C2×Q812yes—
281C22×C4×C31#4112yes—
282C22×C4×C31#4112yes—
283C22×C4×C31#4112yes—
284C4⋊C4×C31—44no—
285C4⋊C4×C31—44no—
286C4⋊C4×C31—44no—
287C4⋊C4×C31—44no—
288C4⋊C4×C31—44no—
289C4⋊C4×C31—44no—
290C4⋊C4×C31—44no—
291C4⋊C4×C31—44no—
292C22⋊C4×C31—28no—
293C22⋊C4×C31—28no—
294C22⋊C4×C31—28no—
295C22⋊C4×C31—44no—
296#14736C3111yesmaximal, characteristic, direct product factor, Sylow
297C23×C31—22no—
298C23×C31—22no—
299C23×C31—22no—
300C23×C31—22no—
301C23×C31—22no—
302C23×C31—22no—
303C23×C31—22no—
304C23×C31—22no—
305C23×C31—22no—
306C23×C31—22no—
307C23×C31—22no—
308C23×C31—22no—
309C23×C31—22no—
310C23×C31—22no—
311C23×C31—22no—
312C23×C31—22no—
313C23×C31—22no—
314C23×C31—22no—
315C23×C31—22no—
316C23×C31—22no—
317C23×C31—22no—
318C23×C31—22no—
319C23×C31—22no—
320C23×C31—22no—
321C23×C31—22no—
322C23×C31—22no—
323C23×C31—22no—
324C23×C31—22no—
325C23×C31#12114yes—
326C23×C31C22⋊Q814yes—
327C23×C31C22⋊Q814yes—
328C23×C31#12314yes—
329C23×C31#12514yes—
330C23×C31#12514yes—
331C23×C31C4⋊Q814yes—
332C23×C31C22×D411yescharacteristic
333C23×C31C22×D411yescharacteristic
334C23×C31C22×D411yescharacteristic
335C23×C31C22×Q811yescharacteristic
336C23×C31C22×Q811yescharacteristic
337C23×C31C2×#4111yescharacteristic
338C23×C31C2×#4111yescharacteristic
339C23×C31C2×#4111yescharacteristic
340C23×C31C2×#4111yescharacteristic
341C23×C31C2×#4111yescharacteristic
342C23×C31C2×#4111yescharacteristic
343C23×C31H(5,𝔽2)11yescharacteristic
344C23×C31H(5,𝔽2)11yescharacteristic
345C23×C31H(5,𝔽2)11yescharacteristic
346C23×C312−1+411yescharacteristic
347C2×C4×C31—22no—
348C2×C4×C31—22no—
349C2×C4×C31—22no—
350C2×C4×C31—22no—
351C2×C4×C31—22no—
352C2×C4×C31—22no—
353C2×C4×C31—22no—
354C2×C4×C31—22no—
355C2×C4×C31—22no—
356C2×C4×C31—22no—
357C2×C4×C31—22no—
358C2×C4×C31—22no—
359C2×C4×C31—22no—
360C2×C4×C31—22no—
361C2×C4×C31—22no—
362C2×C4×C31—22no—
363C2×C4×C31—22no—
364C2×C4×C31—22no—
365C2×C4×C31—22no—
366C2×C4×C31—22no—
367C2×C4×C31—22no—
368C2×C4×C31—22no—
369C2×C4×C31—22no—
370C2×C4×C31—22no—
371C2×C4×C31—22no—
372C2×C4×C31—22no—
373C2×C4×C31—22no—
374C2×C4×C31—22no—
375C2×C4×C31—22no—
376C2×C4×C31—22no—
377C2×C4×C31—22no—
378C2×C4×C31—22no—
379C2×C4×C31—22no—
380C2×C4×C31—22no—
381C2×C4×C31—22no—
382C2×C4×C31—22no—
383C2×C4×C31—22no—
384C2×C4×C31—22no—
385C2×C4×C31—22no—
386C2×C4×C31—416no—
387C2×C4×C31—416no—
388C2×C4×C31—416no—
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—41no—
404C2×C4×C31—41no—
405C2×C4×C31—41no—
406C2×C4×C31—41no—
407C2×C4×C31—41no—
408C2×C4×C31—41no—
409C2×C4×C31—41no—
410C2×C4×C31—41no—
411C2×C4×C31—41no—
412C2×C4×C31—41no—
413C2×C4×C31—41no—
414C2×C4×C31—41no—
415C2×C4×C31—41no—
416C2×C4×C31—41no—
417C2×C4×C31—41no—
418C2×C4×C31—41no—
419C2×C4×C31—41no—
420C2×C4×C31—41no—
421C2×C4×C31—41no—
422C2×C4×C31—41no—
423C2×C4×C31—41no—
424C2×C4×C31—41no—
425C2×C4×C31—41no—
426C2×C4×C31—41no—
427C2×C4×C31—41no—
428C2×C4×C31—41no—
429C2×C4×C31—41no—
430C2×C4×C31—41no—
431C2×C4×C31—41no—
432C2×C4×C31—41no—
433C2×C4×C31—41no—
434C2×C4×C31—41no—
435C2×C4×C31—41no—
436C2×C4×C31—41no—
437C2×C4×C31—41no—
438C2×C4×C31—41no—
439C2×C4×C31—41no—
440C2×C4×C31—41no—
441C2×C4×C31—41no—
442C2×C4×C31—41no—
443C2×C4×C31—41no—
444C2×C4×C31—41no—
445C2×C4×C31—41no—
446C2×C4×C31—41no—
447C2×C4×C31C22⋊Q814yes—
448C2×#398C2×C3111yescharacteristic, complemented
449C2×#385C2×C3111yescharacteristic
450C2×#385C2×C3111yescharacteristic
451C2×#385C2×C3111yescharacteristic
452C2×#380C2×C3111yescharacteristic
453C22×#95C2×C3111yescharacteristic
454#1445C2×C3111yescharacteristic, complemented
455#1444C2×C3111yescharacteristic, complemented
456#1442C2×C3111yescharacteristic, complemented
457#1442C2×C3111yescharacteristic, complemented
458#1441C2×C3111yescharacteristic, complemented
459#1441C2×C3111yescharacteristic, complemented
460#1441C2×C3111yescharacteristic, complemented
461C22⋊#95C2×C3111yescharacteristic
462C22⋊#95C2×C3111yescharacteristic
463C22×C31—24no—
464C22×C31—24no—
465C22×C31—24no—
466C22×C31—24no—
467C22×C31—24no—
468C22×C31—24no—
469C22×C31—24no—
470C22×C31—24no—
471C22×C31—24no—
472C22×C31—24no—
473C22×C31—24no—
474C22×C31—24no—
475C22×C31—24no—
476C22×C31—24no—
477C22×C31#39818yescomplemented
478C22×C31C2×#12111yescharacteristic
479C22×C31C2×C22⋊Q811yescharacteristic
480C22×C31C2×C22⋊Q811yescharacteristic
481C22×C31C2×C22⋊Q811yescharacteristic
482C22×C31C2×#12311yescharacteristic
483C22×C31#52511yescharacteristic
484C22×C31#52511yescharacteristic
485C22×C31C2×#12511yescharacteristic
486C22×C31C2×#12511yescharacteristic
487C22×C31#52911yescharacteristic
488C22×C31#52911yescharacteristic
489C22×C31C2×C4⋊Q811yescharacteristic
490C22×C31#53311yescharacteristic
491C22×C31#53811yescharacteristic
492C22×C31#53811yescharacteristic
493C22×C31#53911yescharacteristic
494C22×C31#53911yescharacteristic
495C22×C31#54311yescharacteristic
496C22×C31#54411yescharacteristic
497C22×C31D4211yescharacteristic
498C22×C31D4211yescharacteristic
499C22×C31#54611yescharacteristic
500C22×C31#54611yescharacteristic
501C22×C31#54611yescharacteristic
502C22×C31#54611yescharacteristic
503C22×C31#54611yescharacteristic
504C22×C31#54711yescharacteristic
505C22×C31#54711yescharacteristic
506C22×C31D4×Q811yescharacteristic
507C22×C31#55111yescharacteristic
508C22×C31#55111yescharacteristic
509C22×C31#55211yescharacteristic
510C22×C31#55411yescharacteristic
511C22×C31#55411yescharacteristic
512C22×C31#55411yescharacteristic
513C4×C31—24no—
514C4×C31—42no—
515C4×C31—42no—
516C4×C31—42no—
517C4×C31—42no—
518C4×C31—42no—
519C4×C31—42no—
520C4×C31—42no—
521C4×C31—42no—
522C4×C31—42no—
523C4×C31—42no—
524C4×C31—42no—
525C4×C31—81no—
526C4×C31—81no—
527C24×C4C22×C3111yescharacteristic
528C24×C4C22×C3111yescharacteristic
529C24×C4C22×C3111yescharacteristic
530C22×C4⋊C4C22×C3111yescharacteristic
531C22×C4⋊C4C22×C3111yescharacteristic
532C22×C4⋊C4C22×C3111yescharacteristic
533C22×C4⋊C4C22×C3111yescharacteristic
534C22×C4⋊C4C22×C3111yescharacteristic
535C22×C4⋊C4C22×C3111yescharacteristic
536C22×C4⋊C4C22×C3111yescharacteristic
537C22×C4⋊C4C22×C3111yescharacteristic
538C22×C22⋊C4C22×C3111yescharacteristic
539C22×C22⋊C4C22×C3111yescharacteristic
540C22×C22⋊C4C22×C3111yescharacteristic
541C22×C22⋊C4C22×C3111yescharacteristic
542#398—24no—
543#385—24no—
544#385—24no—
545#385—24no—
546#380—24no—
547C2×#95—24no—
548C2×#95C22×C3111yescharacteristic
549C2×#95C22×C3111yescharacteristic
550C2×#95C22×C3111yescharacteristic
551C2×#95C22×C3111yescharacteristic
552C2×#95C22×C3111yescharacteristic
553C2×#95C22×C3111yescharacteristic
554C2×#95C22×C3111yescharacteristic
555C2×#95C22×C3111yescharacteristic
556C2×#95C22×C3111yescharacteristic
557C2×#95C22×C3111yescharacteristic
558C2×#95C22×C3111yescharacteristic
559C2×#95C22×C3111yescharacteristic
560C2×#95C22×C3111yescharacteristic
561C2×#95C22×C3111yescharacteristic
562C2×#95C22×C3111yescharacteristic
563C2×#95C22×C3111yescharacteristic
564C2×#95C22×C3111yescharacteristic
565C2×#95C22×C3111yescharacteristic
566C2×#95C22×C3111yescharacteristic
567C2×#95C22×C3111yescharacteristic
568C2×C31—28no—
569C2×C31C2×#39811yescharacteristic
570C2×C31#241811yescharacteristic
571C2×C31#241911yescharacteristic
572C2×C31#242411yescharacteristic
573C2×C31#242511yescharacteristic
574C2×C31#243711yescharacteristic
575C2×C31#243811yescharacteristic
576C2×C31#244011yescharacteristic
577C2×C31#244911yescharacteristic
578C2×C31#245011yescharacteristic
579C2×C31#247311yescharacteristic
580C2×C31#250511yescharacteristic
581C2×C31#254911yescharacteristic
582C2×C31#264611yescharacteristic
583C2×C31#285111yescharacteristic
584C25C23×C3111yescharacteristic
585C23×C4—22no—
586C23×C4—22no—
587C23×C4—22no—
588C23×C4—22no—
589C23×C4—22no—
590C23×C4—22no—
591C23×C4—22no—
592C23×C4—22no—
593C23×C4—22no—
594C23×C4—22no—
595C23×C4—22no—
596C23×C4—22no—
597C23×C4—22no—
598C23×C4—22no—
599C23×C4—41no—
600C23×C4—41no—
601C23×C4—41no—
602C23×C4—41no—
603C23×C4—41no—
604C23×C4—41no—
605C23×C4Q8×C3114yes—
606C23×C4C23×C3111yescharacteristic
607C23×C4C23×C3111yescharacteristic
608C23×C4C23×C3111yescharacteristic
609C23×C4C23×C3111yescharacteristic
610C23×C4C23×C3111yescharacteristic
611C23×C4C23×C3111yescharacteristic
612C23×C4C23×C3111yescharacteristic
613C23×C4C23×C3111yescharacteristic
614C23×C4C23×C3111yescharacteristic
615C23×C4C23×C3111yescharacteristic
616C23×C4C23×C3111yescharacteristic
617C23×C4C23×C3111yescharacteristic
618C23×C4C23×C3111yescharacteristic
619C23×C4C23×C3111yescharacteristic
620C2×C4⋊C4—22no—
621C2×C4⋊C4—22no—
622C2×C4⋊C4—22no—
623C2×C4⋊C4—22no—
624C2×C4⋊C4—22no—
625C2×C4⋊C4—22no—
626C2×C4⋊C4—22no—
627C2×C4⋊C4—22no—
628C2×C4⋊C4—22no—
629C2×C4⋊C4—22no—
630C2×C4⋊C4—22no—
631C2×C4⋊C4—22no—
632C2×C4⋊C4—22no—
633C2×C4⋊C4—22no—
634C2×C4⋊C4—22no—
635C2×C4⋊C4—22no—
636C2×C4⋊C4—41no—
637C2×C4⋊C4—41no—
638C2×C4⋊C4—41no—
639C2×C4⋊C4—41no—
640C2×C4⋊C4—41no—
641C2×C4⋊C4—41no—
642C2×C4⋊C4—41no—
643C2×C4⋊C4—41no—
644C2×C22⋊C4—22no—
645C2×C22⋊C4—22no—
646C2×C22⋊C4—22no—
647C2×C22⋊C4—22no—
648C2×C22⋊C4—22no—
649C2×C22⋊C4—22no—
650C2×C22⋊C4—22no—
651C2×C22⋊C4—22no—
652C2×C22⋊C4—22no—
653C2×C22⋊C4D4×C3114yes—
654C2×C22⋊C4D4×C3114yes—
655C2×C22⋊C4Q8×C3114yes—
656#95—22no—
657#95—22no—
658#95—22no—
659#95—22no—
660#95—22no—
661#95—22no—
662#95—22no—
663#95—22no—
664#95—22no—
665#95—22no—
666#95—22no—
667#95—22no—
668#95—22no—
669#95—22no—
670#95—22no—
671#95—41no—
672#95—41no—
673#95—41no—
674#95—41no—
675#95D4×C3114yes—
676C31#1473611yescharacteristic, direct product factor, Sylow
677C24—21no—
678C24—21no—
679C24—21no—
680C24—21no—
681C24—21no—
682C24—21no—
683C24—21no—
684C24—21no—
685C24C2×D4×C3112yes—
686C24C2×D4×C3112yes—
687C24C2×Q8×C3112yes—
688C24C2×Q8×C3112yes—
689C24#41×C3112yes—
690C24#41×C3112yes—
691C24#41×C3112yes—
692C24C24×C3111yescharacteristic
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—28no—
698C22×C4—28no—
699C22×C4—28no—
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×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—28no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—44no—
782C22×C4—44no—
783C22×C4—44no—
784C22×C4—44no—
785C22×C4—44no—
786C22×C4—44no—
787C22×C4—44no—
788C22×C4—44no—
789C22×C4—44no—
790C22×C4—44no—
791C22×C4—44no—
792C22×C4—44no—
793C22×C4—44no—
794C22×C4—44no—
795C22×C4—44no—
796C22×C4—44no—
797C22×C4—44no—
798C22×C4C2×D4×C3112yes—
799C22×C4C2×D4×C3112yes—
800C22×C4C2×D4×C3112yes—
801C22×C4C2×D4×C3112yes—
802C22×C4C2×D4×C3112yes—
803C22×C4C2×D4×C3112yes—
804C22×C4C2×D4×C3112yes—
805C22×C4C2×Q8×C3112yes—
806C22×C4C2×Q8×C3112yes—
807C22×C4C2×Q8×C3112yes—
808C22×C4C2×Q8×C3112yes—
809C22×C4#41×C3112yes—
810C22×C4#41×C3112yes—
811C22×C4#41×C3112yes—
812C4⋊C4—44no—
813C4⋊C4—44no—
814C4⋊C4—44no—
815C4⋊C4—44no—
816C4⋊C4—44no—
817C4⋊C4—44no—
818C4⋊C4—44no—
819C4⋊C4—44no—
820C22⋊C4—28no—
821C22⋊C4—28no—
822C22⋊C4—28no—
823C22⋊C4—44no—
824C23—22no—
825C23—22no—
826C23—22no—
827C23—22no—
828C23—22no—
829C23—22no—
830C23—22no—
831C23—22no—
832C23—22no—
833C23—22no—
834C23—22no—
835C23—22no—
836C23—22no—
837C23—22no—
838C23—22no—
839C23—22no—
840C23—22no—
841C23—22no—
842C23—22no—
843C23—22no—
844C23—22no—
845C23—22no—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—22no—
850C23—22no—
851C23—22no—
852C23C31×#12114yes—
853C23C31×C22⋊Q814yes—
854C23C31×C22⋊Q814yes—
855C23C31×#12314yes—
856C23C31×#12514yes—
857C23C31×#12514yes—
858C23C31×C4⋊Q814yes—
859C23C22×D4×C3111yescharacteristic
860C23C22×D4×C3111yescharacteristic
861C23C22×D4×C3111yescharacteristic
862C23C22×Q8×C3111yescharacteristic
863C23C22×Q8×C3111yescharacteristic
864C23C2×#41×C3111yescharacteristic
865C23C2×#41×C3111yescharacteristic
866C23C2×#41×C3111yescharacteristic
867C23C2×#41×C3111yescharacteristic
868C23C2×#41×C3111yescharacteristic
869C23C2×#41×C3111yescharacteristic
870C23C31×H(5,𝔽2)11yescharacteristic
871C23C31×H(5,𝔽2)11yescharacteristic
872C23C31×H(5,𝔽2)11yescharacteristic
873C23C31×2−1+411yescharacteristic
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—416no—
914C2×C4—416no—
915C2×C4—416no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4C31×C22⋊Q814yes—
975C22—24no—
976C22—24no—
977C22—24no—
978C22—24no—
979C22—24no—
980C22—24no—
981C22—24no—
982C22—24no—
983C22—24no—
984C22—24no—
985C22—24no—
986C22—24no—
987C22—24no—
988C22—24no—
989C22C31×#39818yescomplemented
990C22C2×C31×#12111yescharacteristic
991C22C2×C31×C22⋊Q811yescharacteristic
992C22C2×C31×C22⋊Q811yescharacteristic
993C22C2×C31×C22⋊Q811yescharacteristic
994C22C2×C31×#12311yescharacteristic
995C22C31×#52511yescharacteristic
996C22C31×#52511yescharacteristic
997C22C2×C31×#12511yescharacteristic
998C22C2×C31×#12511yescharacteristic
999C22C31×#52911yescharacteristic
1000C22C31×#52911yescharacteristic
1001C22C2×C31×C4⋊Q811yescharacteristic
1002C22C31×#53311yescharacteristic
1003C22C31×#53811yescharacteristic
1004C22C31×#53811yescharacteristic
1005C22C31×#53911yescharacteristic
1006C22C31×#53911yescharacteristic
1007C22C31×#54311yescharacteristic
1008C22C31×#54411yescharacteristic
1009C22D42×C3111yescharacteristic
1010C22D42×C3111yescharacteristic
1011C22C31×#54611yescharacteristic
1012C22C31×#54611yescharacteristic
1013C22C31×#54611yescharacteristic
1014C22C31×#54611yescharacteristic
1015C22C31×#54611yescharacteristic
1016C22C31×#54711yescharacteristic
1017C22C31×#54711yescharacteristic
1018C22D4×Q8×C3111yescharacteristic
1019C22C31×#55111yescharacteristic
1020C22C31×#55111yescharacteristic
1021C22C31×#55211yescharacteristic
1022C22C31×#55411yescharacteristic
1023C22C31×#55411yescharacteristic
1024C22C31×#55411yescharacteristic
1025C4—24no—
1026C4—42no—
1027C4—42no—
1028C4—42no—
1029C4—42no—
1030C4—42no—
1031C4—42no—
1032C4—42no—
1033C4—42no—
1034C4—42no—
1035C4—42no—
1036C4—42no—
1037C4—81no—
1038C4—81no—
1039C2—28no—
1040C2C2×C31×#39811yescharacteristic
1041C2C31×#241811yescharacteristic
1042C2C31×#241911yescharacteristic
1043C2C31×#242411yescharacteristic
1044C2C31×#242511yescharacteristic
1045C2C31×#243711yescharacteristic
1046C2C31×#243811yescharacteristic
1047C2C31×#244011yescharacteristic
1048C2C31×#244911yescharacteristic
1049C2C31×#245011yescharacteristic
1050C2C31×#247311yescharacteristic
1051C2C31×#250511yescharacteristic
1052C2C31×#254911yescharacteristic
1053C2C31×#264611yescharacteristic
1054C2C31×#285111yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutator, Frattini, cosocleC24C24×C31
prime radicalC25×C31C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#398C2semidirect
7. C31×#1445C2semidirect
8. C31×#1444C2semidirect
9. C31×#1442C2semidirect
10. C31×#1442C2semidirect
11. C31×#1441C2semidirect
12. C31×#1441C2semidirect
13. C31×#1441C2semidirect
296. #14736C31direct (N × H)
448. C2×#398C2×C31semidirect
454. #1445C2×C31semidirect
455. #1444C2×C31semidirect
456. #1442C2×C31semidirect
457. #1442C2×C31semidirect
458. #1441C2×C31semidirect
459. #1441C2×C31semidirect
460. #1441C2×C31semidirect
477. C22×C31#398semidirect
676. C31#14736direct (N × H)
989. C22C31×#398semidirect

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×#3852
C2×C31×#3802
C22×C31×#952
C31×#14452
C31×#14442
C31×#14422
C31×#14412
C31×C22⋊#952
#1473631