Finite Group Databasebeta

← C31×#13980 #21470739

Subgroups — C31×#13980 #21470739

Order 7936.

1962 conjugacy classes of subgroups.

The subgroup lattice has 1042 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#387C211yesmaximal, characteristic, complemented
2C2×C31×#385C211yesmaximal, characteristic
3C2×C31×#380C211yesmaximal, characteristic
4C2×C4×C22⋊C4×C31C211yesmaximal, characteristic
5C22×C31×#95C211yesmaximal, characteristic
6C31×#1445C211yesmaximal, characteristic, complemented
7C31×#1443C211yesmaximal, characteristic, complemented
8C31×#1442C211yesmaximal, characteristic, complemented
9C31×#1441C211yesmaximal, characteristic, complemented
10C31×#1436C211yesmaximal, characteristic, complemented
11C31×#1436C211yesmaximal, characteristic, complemented
12C31×#1434C211yesmaximal, characteristic, complemented
13C31×C22⋊#95C211yesmaximal, characteristic
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×C22⋊C4×C31C2211yescharacteristic
24C22×C22⋊C4×C31C2211yescharacteristic
25C22×C22⋊C4×C31C2211yescharacteristic
26C22×C22⋊C4×C31C2211yescharacteristic
27C22×C42×C31C2211yescharacteristic
28C22×C42×C31C2211yescharacteristic
29C31×#387—24no—
30C31×#385C418yescomplemented
31C31×#380—24no—
32C4×C22⋊C4×C31—24no—
33C2×C31×#95—24no—
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
55C2×C31×#95C2211yescharacteristic
56C25×C31C2311yescharacteristic
57C23×C4×C31—22no—
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—41no—
71C23×C4×C31—41no—
72C23×C4×C31—41no—
73C23×C4×C31—41no—
74C23×C4×C31—41no—
75C23×C4×C31—41no—
76C23×C4×C31C2×C414yes—
77C23×C4×C31Q814yes—
78C23×C4×C31C2311yescharacteristic
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
92C2×C4⋊C4×C31—22no—
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—41no—
99C2×C4⋊C4×C31—41no—
100C2×C4⋊C4×C31—41no—
101C2×C4⋊C4×C31—41no—
102C2×C4⋊C4×C31C2×C414yescomplemented
103C2×C4⋊C4×C31C2×C414yescomplemented
104C2×C22⋊C4×C31—22no—
105C2×C22⋊C4×C31—22no—
106C2×C22⋊C4×C31—22no—
107C2×C22⋊C4×C31—22no—
108C2×C22⋊C4×C31—22no—
109C2×C22⋊C4×C31—22no—
110C2×C22⋊C4×C31—22no—
111C2×C22⋊C4×C31—22no—
112C2×C22⋊C4×C31—22no—
113C2×C22⋊C4×C31C2×C414yes—
114C2×C22⋊C4×C31C2×C414yes—
115C2×C22⋊C4×C31D414yes—
116C2×C42×C31—22no—
117C2×C42×C31—22no—
118C2×C42×C31—22no—
119C2×C42×C31—22no—
120C2×C42×C31—41no—
121C2×C42×C31—41no—
122C31×#95—22no—
123C31×#95—22no—
124C31×#95—22no—
125C31×#95—22no—
126C31×#95—22no—
127C31×#95—22no—
128C31×#95—22no—
129C31×#95—22no—
130C31×#95—22no—
131C31×#95—22no—
132C31×#95—22no—
133C31×#95—22no—
134C31×#95—22no—
135C31×#95—41no—
136C31×#95—41no—
137C31×#95—41no—
138C31×#95—41no—
139C31×#95—41no—
140C31×#95—41no—
141C31×#95C2×C414yescomplemented
142C31×#95C2×C414yescomplemented
143C31×#95D414yes—
144C24×C31—21no—
145C24×C31—21no—
146C24×C31—21no—
147C24×C31—21no—
148C24×C31—21no—
149C24×C31—21no—
150C24×C31—21no—
151C24×C31—21no—
152C24×C31C22×C412yes—
153C24×C31C2×D412yes—
154C24×C31C2×Q812yes—
155C24×C31#4112yes—
156C24×C31#4112yes—
157C24×C31#4112yes—
158C24×C31#4112yes—
159C24×C31C2411yescharacteristic
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—28no—
169C22×C4×C31—28no—
170C22×C4×C31—28no—
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×C31—28no—
232C22×C4×C31—28no—
233C22×C4×C31—21no—
234C22×C4×C31—21no—
235C22×C4×C31—21no—
236C22×C4×C31—21no—
237C22×C4×C31—21no—
238C22×C4×C31—21no—
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—44no—
248C22×C4×C31—44no—
249C22×C4×C31—44no—
250C22×C4×C31—44no—
251C22×C4×C31—44no—
252C22×C4×C31—44no—
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×C31C22×C412yes—
264C22×C4×C31C22×C412yes—
265C22×C4×C31C22×C412yes—
266C22×C4×C31C22×C412yes—
267C22×C4×C31C22×C412yes—
268C22×C4×C31C22×C412yes—
269C22×C4×C31C2×D412yes—
270C22×C4×C31C2×D412yes—
271C22×C4×C31C2×D412yes—
272C22×C4×C31C2×D412yes—
273C22×C4×C31C2×D412yes—
274C22×C4×C31C2×Q812yes—
275C22×C4×C31C2×Q812yes—
276C22×C4×C31#4112yes—
277C22×C4×C31#4112yes—
278C22×C4×C31#4112yes—
279C4⋊C4×C31—28no—
280C4⋊C4×C31—44no—
281C4⋊C4×C31—44no—
282C4⋊C4×C31—44no—
283C22⋊C4×C31—28no—
284C22⋊C4×C31—28no—
285C22⋊C4×C31—28no—
286C22⋊C4×C31—44no—
287C42×C31—44no—
288C42×C31—44no—
289#13980C3111yesmaximal, characteristic, direct product factor, Sylow
290C23×C31—22no—
291C23×C31—22no—
292C23×C31—22no—
293C23×C31—22no—
294C23×C31—22no—
295C23×C31—22no—
296C23×C31—22no—
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#11714yes—
319C23×C31C4×D414yes—
320C23×C31C4×Q814yes—
321C23×C31C22⋊Q814yes—
322C23×C31#12314yes—
323C23×C31#12514yes—
324C23×C31#12614yes—
325C23×C31C23×C411yescharacteristic
326C23×C31C22×D411yescharacteristic
327C23×C31C22×D411yescharacteristic
328C23×C31C22×Q811yescharacteristic
329C23×C31C2×#4111yescharacteristic
330C23×C31C2×#4111yescharacteristic
331C23×C31C2×#4111yescharacteristic
332C23×C31C2×#4111yescharacteristic
333C23×C31C2×#4111yescharacteristic
334C23×C31C2×#4111yescharacteristic
335C23×C31C2×#4111yescharacteristic
336C23×C31H(5,𝔽2)11yescharacteristic
337C23×C31H(5,𝔽2)11yescharacteristic
338C23×C31H(5,𝔽2)11yescharacteristic
339C23×C312−1+411yescharacteristic
340C2×C4×C31—22no—
341C2×C4×C31—22no—
342C2×C4×C31—22no—
343C2×C4×C31—22no—
344C2×C4×C31—22no—
345C2×C4×C31—22no—
346C2×C4×C31—22no—
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—416no—
383C2×C4×C31—416no—
384C2×C4×C31—416no—
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—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×C31C4×D414yes—
440C2×C4×C31C22⋊Q814yes—
441C2×#387C2×C3111yescharacteristic, complemented
442C2×#385C2×C3111yescharacteristic
443C2×#380C2×C3111yescharacteristic
444C2×C4×C22⋊C4C2×C3111yescharacteristic
445C22×#95C2×C3111yescharacteristic
446#1445C2×C3111yescharacteristic, complemented
447#1443C2×C3111yescharacteristic, complemented
448#1442C2×C3111yescharacteristic, complemented
449#1441C2×C3111yescharacteristic, complemented
450#1436C2×C3111yescharacteristic, complemented
451#1436C2×C3111yescharacteristic, complemented
452#1434C2×C3111yescharacteristic, complemented
453C22⋊#95C2×C3111yescharacteristic
454C22⋊#95C2×C3111yescharacteristic
455C22⋊#95C2×C3111yescharacteristic
456C22×C31—24no—
457C22×C31—24no—
458C22×C31—24no—
459C22×C31—24no—
460C22×C31—24no—
461C22×C31—24no—
462C22×C31—24no—
463C22×C31—24no—
464C22×C31—24no—
465C22×C31—24no—
466C22×C31—24no—
467C22×C31—24no—
468C22×C31—24no—
469C22×C31—24no—
470C22×C31#38718yescomplemented
471C22×C31C2×#11711yescharacteristic
472C22×C31C2×C4×D411yescharacteristic
473C22×C31C2×C4×D411yescharacteristic
474C22×C31C2×C4×Q811yescharacteristic
475C22×C31C4×#4111yescharacteristic
476C22×C31#51811yescharacteristic
477C22×C31#52011yescharacteristic
478C22×C31C2×C22⋊Q811yescharacteristic
479C22×C31C2×C22⋊Q811yescharacteristic
480C22×C31C2×#12311yescharacteristic
481C22×C31#52511yescharacteristic
482C22×C31C2×#12511yescharacteristic
483C22×C31C2×#12611yescharacteristic
484C22×C31#52911yescharacteristic
485C22×C31#53311yescharacteristic
486C22×C31#53811yescharacteristic
487C22×C31#53911yescharacteristic
488C22×C31#54311yescharacteristic
489C22×C31#54411yescharacteristic
490C22×C31D4211yescharacteristic
491C22×C31#54611yescharacteristic
492C22×C31#54611yescharacteristic
493C22×C31#54611yescharacteristic
494C22×C31#54611yescharacteristic
495C22×C31#54711yescharacteristic
496C22×C31#54811yescharacteristic
497C22×C31#55111yescharacteristic
498C22×C31#55111yescharacteristic
499C22×C31#55111yescharacteristic
500C22×C31#55111yescharacteristic
501C22×C31#55211yescharacteristic
502C22×C31#55211yescharacteristic
503C22×C31#55311yescharacteristic
504C22×C31#55311yescharacteristic
505C22×C31#55311yescharacteristic
506C4×C31—24no—
507C4×C31—24no—
508C4×C31—42no—
509C4×C31—42no—
510C4×C31—42no—
511C4×C31—42no—
512C4×C31—42no—
513C4×C31—42no—
514C4×C31—42no—
515C4×C31—42no—
516C4×C31—42no—
517C4×C31—42no—
518C4×C31—81no—
519C4×C31—81no—
520C24×C4C22×C3111yescharacteristic
521C24×C4C22×C3111yescharacteristic
522C24×C4C22×C3111yescharacteristic
523C22×C4⋊C4C22×C3111yescharacteristic
524C22×C4⋊C4C22×C3111yescharacteristic
525C22×C4⋊C4C22×C3111yescharacteristic
526C22×C4⋊C4C22×C3111yescharacteristic
527C22×C22⋊C4C22×C3111yescharacteristic
528C22×C22⋊C4C22×C3111yescharacteristic
529C22×C22⋊C4C22×C3111yescharacteristic
530C22×C22⋊C4C22×C3111yescharacteristic
531C22×C42C22×C3111yescharacteristic
532C22×C42C22×C3111yescharacteristic
533#387—24no—
534#385C4×C3118yescomplemented
535#380—24no—
536C4×C22⋊C4—24no—
537C2×#95—24no—
538C2×#95C22×C3111yescharacteristic
539C2×#95C22×C3111yescharacteristic
540C2×#95C22×C3111yescharacteristic
541C2×#95C22×C3111yescharacteristic
542C2×#95C22×C3111yescharacteristic
543C2×#95C22×C3111yescharacteristic
544C2×#95C22×C3111yescharacteristic
545C2×#95C22×C3111yescharacteristic
546C2×#95C22×C3111yescharacteristic
547C2×#95C22×C3111yescharacteristic
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×C31—28no—
561C2×C31C2×#38711yescharacteristic
562C2×C31C4×C22⋊Q811yescharacteristic
563C2×C31#232911yescharacteristic
564C2×C31#235211yescharacteristic
565C2×C31#235311yescharacteristic
566C2×C31#235811yescharacteristic
567C2×C31#235911yescharacteristic
568C2×C31#243711yescharacteristic
569C2×C31#243811yescharacteristic
570C2×C31#244211yescharacteristic
571C2×C31#244311yescharacteristic
572C2×C31#244411yescharacteristic
573C2×C31#248011yescharacteristic
574C2×C31#249311yescharacteristic
575C2×C31#256911yescharacteristic
576C25C23×C3111yescharacteristic
577C23×C4—22no—
578C23×C4—22no—
579C23×C4—22no—
580C23×C4—22no—
581C23×C4—22no—
582C23×C4—22no—
583C23×C4—22no—
584C23×C4—22no—
585C23×C4—22no—
586C23×C4—22no—
587C23×C4—22no—
588C23×C4—22no—
589C23×C4—22no—
590C23×C4—41no—
591C23×C4—41no—
592C23×C4—41no—
593C23×C4—41no—
594C23×C4—41no—
595C23×C4—41no—
596C23×C4C2×C4×C3114yes—
597C23×C4Q8×C3114yes—
598C23×C4C23×C3111yescharacteristic
599C23×C4C23×C3111yescharacteristic
600C23×C4C23×C3111yescharacteristic
601C23×C4C23×C3111yescharacteristic
602C23×C4C23×C3111yescharacteristic
603C23×C4C23×C3111yescharacteristic
604C23×C4C23×C3111yescharacteristic
605C23×C4C23×C3111yescharacteristic
606C23×C4C23×C3111yescharacteristic
607C23×C4C23×C3111yescharacteristic
608C23×C4C23×C3111yescharacteristic
609C23×C4C23×C3111yescharacteristic
610C23×C4C23×C3111yescharacteristic
611C23×C4C23×C3111yescharacteristic
612C2×C4⋊C4—22no—
613C2×C4⋊C4—22no—
614C2×C4⋊C4—22no—
615C2×C4⋊C4—22no—
616C2×C4⋊C4—22no—
617C2×C4⋊C4—22no—
618C2×C4⋊C4—41no—
619C2×C4⋊C4—41no—
620C2×C4⋊C4—41no—
621C2×C4⋊C4—41no—
622C2×C4⋊C4C2×C4×C3114yescomplemented
623C2×C4⋊C4C2×C4×C3114yescomplemented
624C2×C22⋊C4—22no—
625C2×C22⋊C4—22no—
626C2×C22⋊C4—22no—
627C2×C22⋊C4—22no—
628C2×C22⋊C4—22no—
629C2×C22⋊C4—22no—
630C2×C22⋊C4—22no—
631C2×C22⋊C4—22no—
632C2×C22⋊C4—22no—
633C2×C22⋊C4C2×C4×C3114yes—
634C2×C22⋊C4C2×C4×C3114yes—
635C2×C22⋊C4D4×C3114yes—
636C2×C42—22no—
637C2×C42—22no—
638C2×C42—22no—
639C2×C42—22no—
640C2×C42—41no—
641C2×C42—41no—
642#95—22no—
643#95—22no—
644#95—22no—
645#95—22no—
646#95—22no—
647#95—22no—
648#95—22no—
649#95—22no—
650#95—22no—
651#95—22no—
652#95—22no—
653#95—22no—
654#95—22no—
655#95—41no—
656#95—41no—
657#95—41no—
658#95—41no—
659#95—41no—
660#95—41no—
661#95C2×C4×C3114yescomplemented
662#95C2×C4×C3114yescomplemented
663#95D4×C3114yes—
664C31#1398011yescharacteristic, direct product factor, Sylow
665C24—21no—
666C24—21no—
667C24—21no—
668C24—21no—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24C22×C4×C3112yes—
674C24C2×D4×C3112yes—
675C24C2×Q8×C3112yes—
676C24#41×C3112yes—
677C24#41×C3112yes—
678C24#41×C3112yes—
679C24#41×C3112yes—
680C24C24×C3111yescharacteristic
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—28no—
690C22×C4—28no—
691C22×C4—28no—
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×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—28no—
753C22×C4—28no—
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—21no—
767C22×C4—21no—
768C22×C4—44no—
769C22×C4—44no—
770C22×C4—44no—
771C22×C4—44no—
772C22×C4—44no—
773C22×C4—44no—
774C22×C4—44no—
775C22×C4—44no—
776C22×C4—44no—
777C22×C4—44no—
778C22×C4—44no—
779C22×C4—44no—
780C22×C4—44no—
781C22×C4—44no—
782C22×C4—44no—
783C22×C4—44no—
784C22×C4C22×C4×C3112yes—
785C22×C4C22×C4×C3112yes—
786C22×C4C22×C4×C3112yes—
787C22×C4C22×C4×C3112yes—
788C22×C4C22×C4×C3112yes—
789C22×C4C22×C4×C3112yes—
790C22×C4C2×D4×C3112yes—
791C22×C4C2×D4×C3112yes—
792C22×C4C2×D4×C3112yes—
793C22×C4C2×D4×C3112yes—
794C22×C4C2×D4×C3112yes—
795C22×C4C2×Q8×C3112yes—
796C22×C4C2×Q8×C3112yes—
797C22×C4#41×C3112yes—
798C22×C4#41×C3112yes—
799C22×C4#41×C3112yes—
800C4⋊C4—28no—
801C4⋊C4—44no—
802C4⋊C4—44no—
803C4⋊C4—44no—
804C22⋊C4—28no—
805C22⋊C4—28no—
806C22⋊C4—28no—
807C22⋊C4—44no—
808C42—44no—
809C42—44no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
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—
838C23C31×#11714yes—
839C23C4×D4×C3114yes—
840C23C4×Q8×C3114yes—
841C23C31×C22⋊Q814yes—
842C23C31×#12314yes—
843C23C31×#12514yes—
844C23C31×#12614yes—
845C23C23×C4×C3111yescharacteristic
846C23C22×D4×C3111yescharacteristic
847C23C22×D4×C3111yescharacteristic
848C23C22×Q8×C3111yescharacteristic
849C23C2×#41×C3111yescharacteristic
850C23C2×#41×C3111yescharacteristic
851C23C2×#41×C3111yescharacteristic
852C23C2×#41×C3111yescharacteristic
853C23C2×#41×C3111yescharacteristic
854C23C2×#41×C3111yescharacteristic
855C23C2×#41×C3111yescharacteristic
856C23C31×H(5,𝔽2)11yescharacteristic
857C23C31×H(5,𝔽2)11yescharacteristic
858C23C31×H(5,𝔽2)11yescharacteristic
859C23C31×2−1+411yescharacteristic
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
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—416no—
903C2×C4—416no—
904C2×C4—416no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
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×C4C4×D4×C3114yes—
960C2×C4C31×C22⋊Q814yes—
961C22—24no—
962C22—24no—
963C22—24no—
964C22—24no—
965C22—24no—
966C22—24no—
967C22—24no—
968C22—24no—
969C22—24no—
970C22—24no—
971C22—24no—
972C22—24no—
973C22—24no—
974C22—24no—
975C22C31×#38718yescomplemented
976C22C2×C31×#11711yescharacteristic
977C22C2×C4×D4×C3111yescharacteristic
978C22C2×C4×D4×C3111yescharacteristic
979C22C2×C4×Q8×C3111yescharacteristic
980C22C4×#41×C3111yescharacteristic
981C22C31×#51811yescharacteristic
982C22C31×#52011yescharacteristic
983C22C2×C31×C22⋊Q811yescharacteristic
984C22C2×C31×C22⋊Q811yescharacteristic
985C22C2×C31×#12311yescharacteristic
986C22C31×#52511yescharacteristic
987C22C2×C31×#12511yescharacteristic
988C22C2×C31×#12611yescharacteristic
989C22C31×#52911yescharacteristic
990C22C31×#53311yescharacteristic
991C22C31×#53811yescharacteristic
992C22C31×#53911yescharacteristic
993C22C31×#54311yescharacteristic
994C22C31×#54411yescharacteristic
995C22D42×C3111yescharacteristic
996C22C31×#54611yescharacteristic
997C22C31×#54611yescharacteristic
998C22C31×#54611yescharacteristic
999C22C31×#54611yescharacteristic
1000C22C31×#54711yescharacteristic
1001C22C31×#54811yescharacteristic
1002C22C31×#55111yescharacteristic
1003C22C31×#55111yescharacteristic
1004C22C31×#55111yescharacteristic
1005C22C31×#55111yescharacteristic
1006C22C31×#55211yescharacteristic
1007C22C31×#55211yescharacteristic
1008C22C31×#55311yescharacteristic
1009C22C31×#55311yescharacteristic
1010C22C31×#55311yescharacteristic
1011C4—24no—
1012C4—24no—
1013C4—42no—
1014C4—42no—
1015C4—42no—
1016C4—42no—
1017C4—42no—
1018C4—42no—
1019C4—42no—
1020C4—42no—
1021C4—42no—
1022C4—42no—
1023C4—81no—
1024C4—81no—
1025C2—28no—
1026C2C2×C31×#38711yescharacteristic
1027C2C4×C31×C22⋊Q811yescharacteristic
1028C2C31×#232911yescharacteristic
1029C2C31×#235211yescharacteristic
1030C2C31×#235311yescharacteristic
1031C2C31×#235811yescharacteristic
1032C2C31×#235911yescharacteristic
1033C2C31×#243711yescharacteristic
1034C2C31×#243811yescharacteristic
1035C2C31×#244211yescharacteristic
1036C2C31×#244311yescharacteristic
1037C2C31×#244411yescharacteristic
1038C2C31×#248011yescharacteristic
1039C2C31×#249311yescharacteristic
1040C2C31×#256911yescharacteristic
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
1. C2×C31×#387C2semidirect
6. C31×#1445C2semidirect
7. C31×#1443C2semidirect
8. C31×#1442C2semidirect
9. C31×#1441C2semidirect
10. C31×#1436C2semidirect
11. C31×#1436C2semidirect
12. C31×#1434C2semidirect
30. C31×#385C4semidirect
102. C2×C4⋊C4×C31C2×C4semidirect
103. C2×C4⋊C4×C31C2×C4semidirect
141. C31×#95C2×C4semidirect
142. C31×#95C2×C4semidirect
289. #13980C31direct (N × H)
441. C2×#387C2×C31semidirect
446. #1445C2×C31semidirect
447. #1443C2×C31semidirect
448. #1442C2×C31semidirect
449. #1441C2×C31semidirect
450. #1436C2×C31semidirect
451. #1436C2×C31semidirect
452. #1434C2×C31semidirect
470. C22×C31#387semidirect
534. #385C4×C31semidirect
622. C2×C4⋊C4C2×C4×C31semidirect
623. C2×C4⋊C4C2×C4×C31semidirect
661. #95C2×C4×C31semidirect
662. #95C2×C4×C31semidirect
664. C31#13980direct (N × H)
975. C22C31×#387semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#3872
C2×C31×#3852
C2×C31×#3802
C2×C4×C22⋊C4×C312
C22×C31×#952
C31×#14452
C31×#14432
C31×#14422
C31×#14412
C31×#14362
C31×#14342
C31×C22⋊#952
#1398031