Finite Group Databasebeta

← C31×#14004 #21470763

Subgroups — C31×#14004 #21470763

Order 7936.

2106 conjugacy classes of subgroups.

The subgroup lattice has 1070 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#389C211yesmaximal, characteristic, complemented
2C2×C31×#385C211yesmaximal, characteristic
3C2×C31×#385C211yesmaximal, characteristic
4C2×C31×#385C211yesmaximal, characteristic
5C2×C31×#380C211yesmaximal, characteristic
6C2×C4×C22⋊C4×C31C211yesmaximal, characteristic
7C22×C31×#95C211yesmaximal, characteristic
8C31×#1444C211yesmaximal, characteristic, complemented
9C31×#1442C211yesmaximal, characteristic, complemented
10C31×#1441C211yesmaximal, characteristic, complemented
11C31×#1441C211yesmaximal, characteristic, complemented
12C31×#1436C211yesmaximal, characteristic, complemented
13C31×#1436C211yesmaximal, characteristic, complemented
14C31×C4⋊#95C211yesmaximal, characteristic, complemented
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
31C22×C42×C31C2211yescharacteristic
32C22×C42×C31C2211yescharacteristic
33C31×#389—24no—
34C31×#385—24no—
35C31×#385—24no—
36C31×#385C418yescomplemented
37C31×#380—24no—
38C4×C22⋊C4×C31—24no—
39C2×C31×#95—24no—
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
57C2×C31×#95C2211yescharacteristic
58C25×C31C2311yescharacteristic
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×C31C2×C414yes—
79C23×C4×C31Q814yes—
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
93C23×C4×C31C2311yescharacteristic
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—41no—
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×C31C2×C414yescomplemented
117C2×C4⋊C4×C31C2×C414yescomplemented
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×C31C2×C414yes—
126C2×C22⋊C4×C31C2×C414yes—
127C2×C22⋊C4×C31D414yes—
128C2×C22⋊C4×C31D414yes—
129C2×C22⋊C4×C31Q814yes—
130C2×C42×C31—22no—
131C2×C42×C31—22no—
132C2×C42×C31—22no—
133C2×C42×C31—22no—
134C2×C42×C31—41no—
135C2×C42×C31—41no—
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—22no—
145C31×#95—22no—
146C31×#95—22no—
147C31×#95—22no—
148C31×#95—22no—
149C31×#95—41no—
150C31×#95—41no—
151C31×#95C2×C414yescomplemented
152C31×#95C2×C414yescomplemented
153C31×#95D414yes—
154C24×C31—21no—
155C24×C31—21no—
156C24×C31—21no—
157C24×C31—21no—
158C24×C31—21no—
159C24×C31—21no—
160C24×C31—21no—
161C24×C31—21no—
162C24×C31C22×C412yes—
163C24×C31C2×D412yes—
164C24×C31C2×D412yes—
165C24×C31C2×Q812yes—
166C24×C31C2×Q812yes—
167C24×C31#4112yes—
168C24×C31#4112yes—
169C24×C31C2411yescharacteristic
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—28no—
187C22×C4×C31—28no—
188C22×C4×C31—28no—
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—28no—
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×C31C22×C412yes—
270C22×C4×C31C22×C412yes—
271C22×C4×C31C22×C412yes—
272C22×C4×C31C22×C412yes—
273C22×C4×C31C22×C412yes—
274C22×C4×C31C22×C412yes—
275C22×C4×C31C2×D412yes—
276C22×C4×C31C2×D412yes—
277C22×C4×C31C2×D412yes—
278C22×C4×C31C2×D412yes—
279C22×C4×C31C2×D412yes—
280C22×C4×C31C2×D412yes—
281C22×C4×C31C2×D412yes—
282C22×C4×C31C2×Q812yes—
283C22×C4×C31C2×Q812yes—
284C22×C4×C31C2×Q812yes—
285C22×C4×C31C2×Q812yes—
286C22×C4×C31#4112yes—
287C22×C4×C31#4112yes—
288C22×C4×C31#4112yes—
289C4⋊C4×C31—28no—
290C4⋊C4×C31—44no—
291C4⋊C4×C31—44no—
292C4⋊C4×C31—44no—
293C4⋊C4×C31—44no—
294C4⋊C4×C31—44no—
295C4⋊C4×C31—44no—
296C4⋊C4×C31—44no—
297C22⋊C4×C31—28no—
298C22⋊C4×C31—28no—
299C22⋊C4×C31—44no—
300C22⋊C4×C31C4⋊C4116yescomplemented
301C42×C31—44no—
302C42×C31—44no—
303#14004C3111yesmaximal, characteristic, direct product factor, Sylow
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—22no—
326C23×C31—22no—
327C23×C31—22no—
328C23×C31—22no—
329C23×C31—22no—
330C23×C31—22no—
331C23×C31—22no—
332C23×C31C2×C4⋊C414yes—
333C23×C31C4×D414yes—
334C23×C31C4×Q814yes—
335C23×C31#12114yes—
336C23×C31C22⋊Q814yes—
337C23×C31#12514yes—
338C23×C31C4⋊Q814yes—
339C23×C31C23×C411yescharacteristic
340C23×C31C22×D411yescharacteristic
341C23×C31C22×D411yescharacteristic
342C23×C31C22×D411yescharacteristic
343C23×C31C22×Q811yescharacteristic
344C23×C31C22×Q811yescharacteristic
345C23×C31C2×#4111yescharacteristic
346C23×C31C2×#4111yescharacteristic
347C23×C31C2×#4111yescharacteristic
348C23×C31C2×#4111yescharacteristic
349C23×C31C2×#4111yescharacteristic
350C23×C31H(5,𝔽2)11yescharacteristic
351C23×C31H(5,𝔽2)11yescharacteristic
352C23×C31H(5,𝔽2)11yescharacteristic
353C23×C312−1+411yescharacteristic
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—22no—
387C2×C4×C31—22no—
388C2×C4×C31—22no—
389C2×C4×C31—22no—
390C2×C4×C31—22no—
391C2×C4×C31—22no—
392C2×C4×C31—22no—
393C2×C4×C31—22no—
394C2×C4×C31—22no—
395C2×C4×C31—22no—
396C2×C4×C31—22no—
397C2×C4×C31—22no—
398C2×C4×C31—22no—
399C2×C4×C31—22no—
400C2×C4×C31—22no—
401C2×C4×C31—22no—
402C2×C4×C31—416no—
403C2×C4×C31—416no—
404C2×C4×C31—416no—
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×C31—41no—
448C2×C4×C31—41no—
449C2×C4×C31—41no—
450C2×C4×C31—41no—
451C2×C4×C31C2×C4⋊C414yes—
452C2×C4×C31C2×C4⋊C414yes—
453C2×C4×C31C4×D414yes—
454C2×C4×C31C22⋊Q814yes—
455C2×#389C2×C3111yescharacteristic, complemented
456C2×#385C2×C3111yescharacteristic
457C2×#385C2×C3111yescharacteristic
458C2×#385C2×C3111yescharacteristic
459C2×#380C2×C3111yescharacteristic
460C2×C4×C22⋊C4C2×C3111yescharacteristic
461C22×#95C2×C3111yescharacteristic
462#1444C2×C3111yescharacteristic, complemented
463#1442C2×C3111yescharacteristic, complemented
464#1441C2×C3111yescharacteristic, complemented
465#1441C2×C3111yescharacteristic, complemented
466#1436C2×C3111yescharacteristic, complemented
467#1436C2×C3111yescharacteristic, complemented
468C4⋊#95C2×C3111yescharacteristic, complemented
469C22⋊#95C2×C3111yescharacteristic
470C22×C31—24no—
471C22×C31—24no—
472C22×C31—24no—
473C22×C31—24no—
474C22×C31—24no—
475C22×C31—24no—
476C22×C31—24no—
477C22×C31—24no—
478C22×C31—24no—
479C22×C31—24no—
480C22×C31—24no—
481C22×C31—24no—
482C22×C31—24no—
483C22×C31—24no—
484C22×C31#38918yescomplemented
485C22×C31C22×C4⋊C411yescharacteristic
486C22×C31C2×C4×D411yescharacteristic
487C22×C31C2×C4×D411yescharacteristic
488C22×C31C2×C4×Q811yescharacteristic
489C22×C31C4×#4111yescharacteristic
490C22×C31#51811yescharacteristic
491C22×C31#52011yescharacteristic
492C22×C31C2×#12111yescharacteristic
493C22×C31C2×C22⋊Q811yescharacteristic
494C22×C31C2×C22⋊Q811yescharacteristic
495C22×C31#52511yescharacteristic
496C22×C31C2×#12511yescharacteristic
497C22×C31#52911yescharacteristic
498C22×C31C2×C4⋊Q811yescharacteristic
499C22×C31#53311yescharacteristic
500C22×C31#53811yescharacteristic
501C22×C31#53911yescharacteristic
502C22×C31#54311yescharacteristic
503C22×C31#54411yescharacteristic
504C22×C31D4211yescharacteristic
505C22×C31D4211yescharacteristic
506C22×C31#54611yescharacteristic
507C22×C31#54611yescharacteristic
508C22×C31#54611yescharacteristic
509C22×C31#54611yescharacteristic
510C22×C31#54611yescharacteristic
511C22×C31#54711yescharacteristic
512C22×C31#54711yescharacteristic
513C22×C31D4×Q811yescharacteristic
514C22×C31#55111yescharacteristic
515C22×C31#55111yescharacteristic
516C22×C31#55211yescharacteristic
517C22×C31#55411yescharacteristic
518C22×C31#55411yescharacteristic
519C22×C31#55411yescharacteristic
520C4×C31—24no—
521C4×C31—24no—
522C4×C31—24no—
523C4×C31—24no—
524C4×C31—42no—
525C4×C31—42no—
526C4×C31—42no—
527C4×C31—42no—
528C4×C31—42no—
529C4×C31—42no—
530C4×C31—42no—
531C4×C31—42no—
532C4×C31—81no—
533C4×C31—81no—
534C24×C4C22×C3111yescharacteristic
535C24×C4C22×C3111yescharacteristic
536C24×C4C22×C3111yescharacteristic
537C22×C4⋊C4C22×C3111yescharacteristic
538C22×C4⋊C4C22×C3111yescharacteristic
539C22×C4⋊C4C22×C3111yescharacteristic
540C22×C4⋊C4C22×C3111yescharacteristic
541C22×C4⋊C4C22×C3111yescharacteristic
542C22×C4⋊C4C22×C3111yescharacteristic
543C22×C4⋊C4C22×C3111yescharacteristic
544C22×C4⋊C4C22×C3111yescharacteristic
545C22×C22⋊C4C22×C3111yescharacteristic
546C22×C22⋊C4C22×C3111yescharacteristic
547C22×C22⋊C4C22×C3111yescharacteristic
548C22×C22⋊C4C22×C3111yescharacteristic
549C22×C42C22×C3111yescharacteristic
550C22×C42C22×C3111yescharacteristic
551#389—24no—
552#385—24no—
553#385—24no—
554#385C4×C3118yescomplemented
555#380—24no—
556C4×C22⋊C4—24no—
557C2×#95—24no—
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×#95C22×C3111yescharacteristic
569C2×#95C22×C3111yescharacteristic
570C2×#95C22×C3111yescharacteristic
571C2×#95C22×C3111yescharacteristic
572C2×#95C22×C3111yescharacteristic
573C2×#95C22×C3111yescharacteristic
574C2×#95C22×C3111yescharacteristic
575C2×#95C22×C3111yescharacteristic
576C2×C31—28no—
577C2×C31C2×#38911yescharacteristic
578C2×C31C4×C22⋊Q811yescharacteristic
579C2×C31#232911yescharacteristic
580C2×C31D4×C4⋊C411yescharacteristic
581C2×C31#234911yescharacteristic
582C2×C31#235811yescharacteristic
583C2×C31#235911yescharacteristic
584C2×C31#242411yescharacteristic
585C2×C31#242511yescharacteristic
586C2×C31#243711yescharacteristic
587C2×C31#243811yescharacteristic
588C2×C31#244011yescharacteristic
589C2×C31#247311yescharacteristic
590C2×C31#250511yescharacteristic
591C2×C31#254911yescharacteristic
592C25C23×C3111yescharacteristic
593C23×C4—22no—
594C23×C4—22no—
595C23×C4—22no—
596C23×C4—22no—
597C23×C4—22no—
598C23×C4—22no—
599C23×C4—22no—
600C23×C4—22no—
601C23×C4—22no—
602C23×C4—22no—
603C23×C4—22no—
604C23×C4—22no—
605C23×C4—22no—
606C23×C4—41no—
607C23×C4—41no—
608C23×C4—41no—
609C23×C4—41no—
610C23×C4—41no—
611C23×C4—41no—
612C23×C4C2×C4×C3114yes—
613C23×C4Q8×C3114yes—
614C23×C4C23×C3111yescharacteristic
615C23×C4C23×C3111yescharacteristic
616C23×C4C23×C3111yescharacteristic
617C23×C4C23×C3111yescharacteristic
618C23×C4C23×C3111yescharacteristic
619C23×C4C23×C3111yescharacteristic
620C23×C4C23×C3111yescharacteristic
621C23×C4C23×C3111yescharacteristic
622C23×C4C23×C3111yescharacteristic
623C23×C4C23×C3111yescharacteristic
624C23×C4C23×C3111yescharacteristic
625C23×C4C23×C3111yescharacteristic
626C23×C4C23×C3111yescharacteristic
627C23×C4C23×C3111yescharacteristic
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—22no—
637C2×C4⋊C4—22no—
638C2×C4⋊C4—22no—
639C2×C4⋊C4—22no—
640C2×C4⋊C4—22no—
641C2×C4⋊C4—22no—
642C2×C4⋊C4—41no—
643C2×C4⋊C4—41no—
644C2×C4⋊C4—41no—
645C2×C4⋊C4—41no—
646C2×C4⋊C4—41no—
647C2×C4⋊C4—41no—
648C2×C4⋊C4—41no—
649C2×C4⋊C4—41no—
650C2×C4⋊C4C2×C4×C3114yescomplemented
651C2×C4⋊C4C2×C4×C3114yescomplemented
652C2×C22⋊C4—22no—
653C2×C22⋊C4—22no—
654C2×C22⋊C4—22no—
655C2×C22⋊C4—22no—
656C2×C22⋊C4—22no—
657C2×C22⋊C4—22no—
658C2×C22⋊C4—22no—
659C2×C22⋊C4C2×C4×C3114yes—
660C2×C22⋊C4C2×C4×C3114yes—
661C2×C22⋊C4D4×C3114yes—
662C2×C22⋊C4D4×C3114yes—
663C2×C22⋊C4Q8×C3114yes—
664C2×C42—22no—
665C2×C42—22no—
666C2×C42—22no—
667C2×C42—22no—
668C2×C42—41no—
669C2×C42—41no—
670#95—22no—
671#95—22no—
672#95—22no—
673#95—22no—
674#95—22no—
675#95—22no—
676#95—22no—
677#95—22no—
678#95—22no—
679#95—22no—
680#95—22no—
681#95—22no—
682#95—22no—
683#95—41no—
684#95—41no—
685#95C2×C4×C3114yescomplemented
686#95C2×C4×C3114yescomplemented
687#95D4×C3114yes—
688C31#1400411yescharacteristic, direct product factor, Sylow
689C24—21no—
690C24—21no—
691C24—21no—
692C24—21no—
693C24—21no—
694C24—21no—
695C24—21no—
696C24—21no—
697C24C22×C4×C3112yes—
698C24C2×D4×C3112yes—
699C24C2×D4×C3112yes—
700C24C2×Q8×C3112yes—
701C24C2×Q8×C3112yes—
702C24#41×C3112yes—
703C24#41×C3112yes—
704C24C24×C3111yescharacteristic
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—28no—
722C22×C4—28no—
723C22×C4—28no—
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—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—28no—
773C22×C4—28no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
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×C4—44no—
799C22×C4—44no—
800C22×C4—44no—
801C22×C4—44no—
802C22×C4—44no—
803C22×C4—44no—
804C22×C4C22×C4×C3112yes—
805C22×C4C22×C4×C3112yes—
806C22×C4C22×C4×C3112yes—
807C22×C4C22×C4×C3112yes—
808C22×C4C22×C4×C3112yes—
809C22×C4C22×C4×C3112yes—
810C22×C4C2×D4×C3112yes—
811C22×C4C2×D4×C3112yes—
812C22×C4C2×D4×C3112yes—
813C22×C4C2×D4×C3112yes—
814C22×C4C2×D4×C3112yes—
815C22×C4C2×D4×C3112yes—
816C22×C4C2×D4×C3112yes—
817C22×C4C2×Q8×C3112yes—
818C22×C4C2×Q8×C3112yes—
819C22×C4C2×Q8×C3112yes—
820C22×C4C2×Q8×C3112yes—
821C22×C4#41×C3112yes—
822C22×C4#41×C3112yes—
823C22×C4#41×C3112yes—
824C4⋊C4—28no—
825C4⋊C4—44no—
826C4⋊C4—44no—
827C4⋊C4—44no—
828C4⋊C4—44no—
829C4⋊C4—44no—
830C4⋊C4—44no—
831C4⋊C4—44no—
832C22⋊C4—28no—
833C22⋊C4—28no—
834C22⋊C4—44no—
835C22⋊C4C4⋊C4×C31116yescomplemented
836C42—44no—
837C42—44no—
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—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—22no—
860C23—22no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23C2×C4⋊C4×C3114yes—
867C23C4×D4×C3114yes—
868C23C4×Q8×C3114yes—
869C23C31×#12114yes—
870C23C31×C22⋊Q814yes—
871C23C31×#12514yes—
872C23C31×C4⋊Q814yes—
873C23C23×C4×C3111yescharacteristic
874C23C22×D4×C3111yescharacteristic
875C23C22×D4×C3111yescharacteristic
876C23C22×D4×C3111yescharacteristic
877C23C22×Q8×C3111yescharacteristic
878C23C22×Q8×C3111yescharacteristic
879C23C2×#41×C3111yescharacteristic
880C23C2×#41×C3111yescharacteristic
881C23C2×#41×C3111yescharacteristic
882C23C2×#41×C3111yescharacteristic
883C23C2×#41×C3111yescharacteristic
884C23C31×H(5,𝔽2)11yescharacteristic
885C23C31×H(5,𝔽2)11yescharacteristic
886C23C31×H(5,𝔽2)11yescharacteristic
887C23C31×2−1+411yescharacteristic
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—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—416no—
937C2×C4—416no—
938C2×C4—416no—
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×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4C2×C4⋊C4×C3114yes—
986C2×C4C2×C4⋊C4×C3114yes—
987C2×C4C4×D4×C3114yes—
988C2×C4C31×C22⋊Q814yes—
989C22—24no—
990C22—24no—
991C22—24no—
992C22—24no—
993C22—24no—
994C22—24no—
995C22—24no—
996C22—24no—
997C22—24no—
998C22—24no—
999C22—24no—
1000C22—24no—
1001C22—24no—
1002C22—24no—
1003C22C31×#38918yescomplemented
1004C22C22×C4⋊C4×C3111yescharacteristic
1005C22C2×C4×D4×C3111yescharacteristic
1006C22C2×C4×D4×C3111yescharacteristic
1007C22C2×C4×Q8×C3111yescharacteristic
1008C22C4×#41×C3111yescharacteristic
1009C22C31×#51811yescharacteristic
1010C22C31×#52011yescharacteristic
1011C22C2×C31×#12111yescharacteristic
1012C22C2×C31×C22⋊Q811yescharacteristic
1013C22C2×C31×C22⋊Q811yescharacteristic
1014C22C31×#52511yescharacteristic
1015C22C2×C31×#12511yescharacteristic
1016C22C31×#52911yescharacteristic
1017C22C2×C31×C4⋊Q811yescharacteristic
1018C22C31×#53311yescharacteristic
1019C22C31×#53811yescharacteristic
1020C22C31×#53911yescharacteristic
1021C22C31×#54311yescharacteristic
1022C22C31×#54411yescharacteristic
1023C22D42×C3111yescharacteristic
1024C22D42×C3111yescharacteristic
1025C22C31×#54611yescharacteristic
1026C22C31×#54611yescharacteristic
1027C22C31×#54611yescharacteristic
1028C22C31×#54611yescharacteristic
1029C22C31×#54611yescharacteristic
1030C22C31×#54711yescharacteristic
1031C22C31×#54711yescharacteristic
1032C22D4×Q8×C3111yescharacteristic
1033C22C31×#55111yescharacteristic
1034C22C31×#55111yescharacteristic
1035C22C31×#55211yescharacteristic
1036C22C31×#55411yescharacteristic
1037C22C31×#55411yescharacteristic
1038C22C31×#55411yescharacteristic
1039C4—24no—
1040C4—24no—
1041C4—24no—
1042C4—24no—
1043C4—42no—
1044C4—42no—
1045C4—42no—
1046C4—42no—
1047C4—42no—
1048C4—42no—
1049C4—42no—
1050C4—42no—
1051C4—81no—
1052C4—81no—
1053C2—28no—
1054C2C2×C31×#38911yescharacteristic
1055C2C4×C31×C22⋊Q811yescharacteristic
1056C2C31×#232911yescharacteristic
1057C2D4×C4⋊C4×C3111yescharacteristic
1058C2C31×#234911yescharacteristic
1059C2C31×#235811yescharacteristic
1060C2C31×#235911yescharacteristic
1061C2C31×#242411yescharacteristic
1062C2C31×#242511yescharacteristic
1063C2C31×#243711yescharacteristic
1064C2C31×#243811yescharacteristic
1065C2C31×#244011yescharacteristic
1066C2C31×#247311yescharacteristic
1067C2C31×#250511yescharacteristic
1068C2C31×#254911yescharacteristic
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×#389C2semidirect
8. C31×#1444C2semidirect
9. C31×#1442C2semidirect
10. C31×#1441C2semidirect
11. C31×#1441C2semidirect
12. C31×#1436C2semidirect
13. C31×#1436C2semidirect
14. C31×C4⋊#95C2semidirect
36. C31×#385C4semidirect
116. C2×C4⋊C4×C31C2×C4semidirect
117. C2×C4⋊C4×C31C2×C4semidirect
151. C31×#95C2×C4semidirect
152. C31×#95C2×C4semidirect
300. C22⋊C4×C31C4⋊C4semidirect
303. #14004C31direct (N × H)
455. C2×#389C2×C31semidirect
462. #1444C2×C31semidirect
463. #1442C2×C31semidirect
464. #1441C2×C31semidirect
465. #1441C2×C31semidirect
466. #1436C2×C31semidirect
467. #1436C2×C31semidirect
468. C4⋊#95C2×C31semidirect
484. C22×C31#389semidirect
554. #385C4×C31semidirect
650. C2×C4⋊C4C2×C4×C31semidirect
651. C2×C4⋊C4C2×C4×C31semidirect
685. #95C2×C4×C31semidirect
686. #95C2×C4×C31semidirect
688. C31#14004direct (N × H)
835. C22⋊C4C4⋊C4×C31semidirect
1003. C22C31×#389semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#3892
C2×C31×#3852
C2×C31×#3802
C2×C4×C22⋊C4×C312
C22×C31×#952
C31×#14442
C31×#14422
C31×#14412
C31×#14362
C31×C4⋊#952
C31×C22⋊#952
#1400431