Finite Group Databasebeta

← C31×#14405 #21471164

Subgroups — C31×#14405 #21471164

Order 7936.

1750 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#389C211yesmaximal, characteristic, complemented
2C2×C31×#388C211yesmaximal, characteristic
3C2×C31×#388C211yesmaximal, characteristic
4C2×C31×#385C211yesmaximal, characteristic
5C2×C31×#385C211yesmaximal, characteristic
6C2×C31×#385C211yesmaximal, characteristic
7C2×C31×#384C211yesmaximal, characteristic, complemented
8C31×#1444C211yesmaximal, characteristic, complemented
9C31×#1444C211yesmaximal, characteristic, complemented
10C31×#1442C211yesmaximal, characteristic, complemented
11C31×#1441C211yesmaximal, characteristic, complemented
12C31×#1439C211yesmaximal, characteristic
13C31×#1439C211yesmaximal, characteristic
14C31×#1436C211yesmaximal, characteristic, complemented
15C31×#1434C211yesmaximal, characteristic, complemented
16C24×C4×C31C2211yescharacteristic
17C22×C4⋊C4×C31C2211yescharacteristic
18C22×C4⋊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×C22⋊C4×C31C2211yescharacteristic
32C22×C22⋊C4×C31C2211yescharacteristic
33C22×C42×C31C2211yescharacteristic
34C22×C42×C31C2211yescharacteristic
35C31×#389—24no—
36C31×#388—24no—
37C31×#388C418yescomplemented
38C31×#385—24no—
39C31×#385—24no—
40C31×#385—24no—
41C31×#384—24no—
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—41no—
63C23×C4×C31—41no—
64C23×C4×C31—41no—
65C23×C4×C31—41no—
66C23×C4×C31C2311yescharacteristic
67C23×C4×C31C2311yescharacteristic
68C23×C4×C31C2311yescharacteristic
69C23×C4×C31C2311yescharacteristic
70C23×C4×C31C2311yescharacteristic
71C23×C4×C31C2311yescharacteristic
72C23×C4×C31C2311yescharacteristic
73C23×C4×C31C2311yescharacteristic
74C23×C4×C31C2311yescharacteristic
75C23×C4×C31C2311yescharacteristic
76C23×C4×C31C2311yescharacteristic
77C23×C4×C31C2311yescharacteristic
78C23×C4×C31C2311yescharacteristic
79C23×C4×C31C2311yescharacteristic
80C2×C4⋊C4×C31—22no—
81C2×C4⋊C4×C31—22no—
82C2×C4⋊C4×C31—22no—
83C2×C4⋊C4×C31—22no—
84C2×C4⋊C4×C31—22no—
85C2×C4⋊C4×C31—22no—
86C2×C4⋊C4×C31—22no—
87C2×C4⋊C4×C31—22no—
88C2×C4⋊C4×C31—22no—
89C2×C4⋊C4×C31—22no—
90C2×C4⋊C4×C31—22no—
91C2×C4⋊C4×C31—22no—
92C2×C4⋊C4×C31—22no—
93C2×C4⋊C4×C31—22no—
94C2×C4⋊C4×C31—22no—
95C2×C4⋊C4×C31—22no—
96C2×C4⋊C4×C31—41no—
97C2×C4⋊C4×C31—41no—
98C2×C4⋊C4×C31—41no—
99C2×C4⋊C4×C31—41no—
100C2×C4⋊C4×C31—41no—
101C2×C4⋊C4×C31—41no—
102C2×C4⋊C4×C31—41no—
103C2×C4⋊C4×C31—41no—
104C2×C4⋊C4×C31—41no—
105C2×C4⋊C4×C31—41no—
106C2×C4⋊C4×C31—41no—
107C2×C4⋊C4×C31—41no—
108C2×C4⋊C4×C31C2×C414yescomplemented
109C2×C4⋊C4×C31D414yes—
110C2×C22⋊C4×C31—22no—
111C2×C22⋊C4×C31—22no—
112C2×C22⋊C4×C31—22no—
113C2×C22⋊C4×C31—22no—
114C2×C22⋊C4×C31—22no—
115C2×C22⋊C4×C31—22no—
116C2×C22⋊C4×C31—22no—
117C2×C22⋊C4×C31—22no—
118C2×C22⋊C4×C31—22no—
119C2×C22⋊C4×C31—41no—
120C2×C22⋊C4×C31—41no—
121C2×C22⋊C4×C31—41no—
122C2×C22⋊C4×C31—41no—
123C2×C22⋊C4×C31C2×C414yes—
124C2×C22⋊C4×C31C2×C414yes—
125C2×C22⋊C4×C31C2×C414yes—
126C2×C22⋊C4×C31D414yes—
127C2×C22⋊C4×C31Q814yes—
128C2×C42×C31—22no—
129C2×C42×C31—22no—
130C2×C42×C31—22no—
131C2×C42×C31—22no—
132C2×C42×C31—41no—
133C2×C42×C31C2×C414yescomplemented
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×#95C2×C414yescomplemented
148C31×#95C2×C414yescomplemented
149C31×#95D414yes—
150C24×C31—21no—
151C24×C31—21no—
152C24×C31—21no—
153C24×C31—21no—
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×Q812yes—
165C24×C31C2411yescharacteristic
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×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—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—44no—
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×C31C22×C412yes—
254C22×C4×C31C22×C412yes—
255C22×C4×C31C22×C412yes—
256C22×C4×C31C22×C412yes—
257C22×C4×C31C22×C412yes—
258C22×C4×C31C22×C412yes—
259C22×C4×C31C2×D412yes—
260C22×C4×C31C2×D412yes—
261C22×C4×C31C2×D412yes—
262C22×C4×C31C2×D412yes—
263C22×C4×C31C2×D412yes—
264C22×C4×C31C2×D412yes—
265C22×C4×C31C2×D412yes—
266C22×C4×C31C2×D412yes—
267C22×C4×C31C2×Q812yes—
268C22×C4×C31C2×Q812yes—
269C22×C4×C31#4112yes—
270C22×C4×C31#4112yes—
271C4⋊C4×C31—28no—
272C4⋊C4×C31—44no—
273C4⋊C4×C31—44no—
274C4⋊C4×C31—44no—
275C4⋊C4×C31—44no—
276C4⋊C4×C31—44no—
277C4⋊C4×C31—44no—
278C4⋊C4×C31—44no—
279C4⋊C4×C31—44no—
280C4⋊C4×C31—44no—
281C22⋊C4×C31—28no—
282C22⋊C4×C31—28no—
283C22⋊C4×C31—44no—
284C22⋊C4×C31—44no—
285C22⋊C4×C31—44no—
286C22⋊C4×C31C4⋊C4116yescomplemented
287C42×C31—28no—
288C42×C31—44no—
289#14405C3111yesmaximal, 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—41no—
309C23×C31—41no—
310C23×C31—41no—
311C23×C31—41no—
312C23×C31—41no—
313C23×C31—41no—
314C23×C31—41no—
315C23×C31—41no—
316C23×C31—41no—
317C23×C31—41no—
318C23×C31—41no—
319C23×C31—41no—
320C23×C31—41no—
321C23×C31—41no—
322C23×C31—41no—
323C23×C31—41no—
324C23×C31C2×C4⋊C414yes—
325C23×C31C23×C411yescharacteristic
326C23×C31C22×D411yescharacteristic
327C23×C31C22×D411yescharacteristic
328C23×C31C22×D411yescharacteristic
329C23×C31C22×Q811yescharacteristic
330C23×C31C2×#4111yescharacteristic
331C23×C31C2×#4111yescharacteristic
332C23×C31H(5,𝔽2)11yescharacteristic
333C23×C31H(5,𝔽2)11yescharacteristic
334C23×C31H(5,𝔽2)11yescharacteristic
335C23×C31H(5,𝔽2)11yescharacteristic
336C23×C312−1+411yescharacteristic
337C23×C312−1+411yescharacteristic
338C23×C312−1+411yescharacteristic
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—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—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×C31C2×C4⋊C414yes—
436C2×C4×C31C2×C4⋊C414yes—
437C2×C4×C31C4×D414yes—
438C2×C4×C31C4×D414yes—
439C2×#389C2×C3111yescharacteristic, complemented
440C2×#388C2×C3111yescharacteristic
441C2×#388C2×C3111yescharacteristic
442C2×#385C2×C3111yescharacteristic
443C2×#385C2×C3111yescharacteristic
444C2×#385C2×C3111yescharacteristic
445C2×#384C2×C3111yescharacteristic, complemented
446#1444C2×C3111yescharacteristic, complemented
447#1444C2×C3111yescharacteristic, complemented
448#1442C2×C3111yescharacteristic, complemented
449#1441C2×C3111yescharacteristic, complemented
450#1439C2×C3111yescharacteristic
451#1439C2×C3111yescharacteristic
452#1436C2×C3111yescharacteristic, complemented
453#1434C2×C3111yescharacteristic, complemented
454C22×C31—24no—
455C22×C31—24no—
456C22×C31—24no—
457C22×C31—42no—
458C22×C31—42no—
459C22×C31—42no—
460C22×C31—42no—
461C22×C31—42no—
462C22×C31—42no—
463C22×C31—42no—
464C22×C31—42no—
465C22×C31—42no—
466C22×C31—42no—
467C22×C31—42no—
468C22×C31—42no—
469C22×C31C22×C4⋊C411yescharacteristic
470C22×C31C2×C4×D411yescharacteristic
471C22×C31C2×C4×D411yescharacteristic
472C22×C31#52011yescharacteristic
473C22×C31#52011yescharacteristic
474C22×C31#52011yescharacteristic
475C22×C31#52011yescharacteristic
476C22×C31#53411yescharacteristic
477C22×C31#53511yescharacteristic
478C22×C31#53511yescharacteristic
479C22×C31#53611yescharacteristic
480C22×C31#53611yescharacteristic
481C22×C31#53611yescharacteristic
482C22×C31#53911yescharacteristic
483C22×C31#53911yescharacteristic
484C22×C31#54211yescharacteristic
485C22×C31#54211yescharacteristic
486C22×C31#54411yescharacteristic
487C22×C31#54411yescharacteristic
488C22×C31D4211yescharacteristic
489C22×C31D4211yescharacteristic
490C22×C31D4211yescharacteristic
491C22×C31#54711yescharacteristic
492C22×C31#54711yescharacteristic
493C22×C31#54711yescharacteristic
494C22×C31#54811yescharacteristic
495C22×C31D4×Q811yescharacteristic
496C22×C31D4×Q811yescharacteristic
497C22×C31#55311yescharacteristic
498C22×C31#55411yescharacteristic
499C22×C31#55411yescharacteristic
500C22×C31#56011yescharacteristic
501C22×C31#56311yescharacteristic
502C22×C31#56311yescharacteristic
503C22×C31#56311yescharacteristic
504C4×C31—24no—
505C4×C31—24no—
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—81no—
515C4×C31—81no—
516C4×C31—81no—
517C4×C31—81no—
518C24×C4C22×C3111yescharacteristic
519C22×C4⋊C4C22×C3111yescharacteristic
520C22×C4⋊C4C22×C3111yescharacteristic
521C22×C4⋊C4C22×C3111yescharacteristic
522C22×C4⋊C4C22×C3111yescharacteristic
523C22×C4⋊C4C22×C3111yescharacteristic
524C22×C4⋊C4C22×C3111yescharacteristic
525C22×C4⋊C4C22×C3111yescharacteristic
526C22×C4⋊C4C22×C3111yescharacteristic
527C22×C4⋊C4C22×C3111yescharacteristic
528C22×C4⋊C4C22×C3111yescharacteristic
529C22×C22⋊C4C22×C3111yescharacteristic
530C22×C22⋊C4C22×C3111yescharacteristic
531C22×C22⋊C4C22×C3111yescharacteristic
532C22×C22⋊C4C22×C3111yescharacteristic
533C22×C22⋊C4C22×C3111yescharacteristic
534C22×C22⋊C4C22×C3111yescharacteristic
535C22×C42C22×C3111yescharacteristic
536C22×C42C22×C3111yescharacteristic
537#389—24no—
538#388—24no—
539#388C4×C3118yescomplemented
540#385—24no—
541#385—24no—
542#385—24no—
543#384—24no—
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—44no—
561C2×C31#231711yescharacteristic
562C2×C31#232211yescharacteristic
563C2×C31#232611yescharacteristic
564C2×C31D4×C4⋊C411yescharacteristic
565C2×C31D4×C4⋊C411yescharacteristic
566C2×C31#236111yescharacteristic
567C2×C31#238311yescharacteristic
568C2×C31#266911yescharacteristic
569C2×C31#267411yescharacteristic
570C2×C31#267711yescharacteristic
571C2×C31#268011yescharacteristic
572C2×C31#271811yescharacteristic
573C2×C31#272011yescharacteristic
574C2×C31#272911yescharacteristic
575C2×C31#279011yescharacteristic
576C25C23×C3111yescharacteristic
577C23×C4—22no—
578C23×C4—22no—
579C23×C4—22no—
580C23×C4—41no—
581C23×C4—41no—
582C23×C4—41no—
583C23×C4—41no—
584C23×C4C23×C3111yescharacteristic
585C23×C4C23×C3111yescharacteristic
586C23×C4C23×C3111yescharacteristic
587C23×C4C23×C3111yescharacteristic
588C23×C4C23×C3111yescharacteristic
589C23×C4C23×C3111yescharacteristic
590C23×C4C23×C3111yescharacteristic
591C23×C4C23×C3111yescharacteristic
592C23×C4C23×C3111yescharacteristic
593C23×C4C23×C3111yescharacteristic
594C23×C4C23×C3111yescharacteristic
595C23×C4C23×C3111yescharacteristic
596C23×C4C23×C3111yescharacteristic
597C23×C4C23×C3111yescharacteristic
598C2×C4⋊C4—22no—
599C2×C4⋊C4—22no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—22no—
602C2×C4⋊C4—22no—
603C2×C4⋊C4—22no—
604C2×C4⋊C4—22no—
605C2×C4⋊C4—22no—
606C2×C4⋊C4—22no—
607C2×C4⋊C4—22no—
608C2×C4⋊C4—22no—
609C2×C4⋊C4—22no—
610C2×C4⋊C4—22no—
611C2×C4⋊C4—22no—
612C2×C4⋊C4—22no—
613C2×C4⋊C4—22no—
614C2×C4⋊C4—41no—
615C2×C4⋊C4—41no—
616C2×C4⋊C4—41no—
617C2×C4⋊C4—41no—
618C2×C4⋊C4—41no—
619C2×C4⋊C4—41no—
620C2×C4⋊C4—41no—
621C2×C4⋊C4—41no—
622C2×C4⋊C4—41no—
623C2×C4⋊C4—41no—
624C2×C4⋊C4—41no—
625C2×C4⋊C4—41no—
626C2×C4⋊C4C2×C4×C3114yescomplemented
627C2×C4⋊C4D4×C3114yes—
628C2×C22⋊C4—22no—
629C2×C22⋊C4—22no—
630C2×C22⋊C4—22no—
631C2×C22⋊C4—22no—
632C2×C22⋊C4—22no—
633C2×C22⋊C4—22no—
634C2×C22⋊C4—22no—
635C2×C22⋊C4—22no—
636C2×C22⋊C4—22no—
637C2×C22⋊C4—41no—
638C2×C22⋊C4—41no—
639C2×C22⋊C4—41no—
640C2×C22⋊C4—41no—
641C2×C22⋊C4C2×C4×C3114yes—
642C2×C22⋊C4C2×C4×C3114yes—
643C2×C22⋊C4C2×C4×C3114yes—
644C2×C22⋊C4D4×C3114yes—
645C2×C22⋊C4Q8×C3114yes—
646C2×C42—22no—
647C2×C42—22no—
648C2×C42—22no—
649C2×C42—22no—
650C2×C42—41no—
651C2×C42C2×C4×C3114yescomplemented
652#95—22no—
653#95—22no—
654#95—22no—
655#95—22no—
656#95—22no—
657#95—22no—
658#95—22no—
659#95—22no—
660#95—22no—
661#95—22no—
662#95—41no—
663#95—41no—
664#95—41no—
665#95C2×C4×C3114yescomplemented
666#95C2×C4×C3114yescomplemented
667#95D4×C3114yes—
668C31#1440511yescharacteristic, direct product factor, Sylow
669C24—21no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24—21no—
674C24—21no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—21no—
681C24C22×C4×C3112yes—
682C24C2×D4×C3112yes—
683C24C2×Q8×C3112yes—
684C24C24×C3111yescharacteristic
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×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—44no—
766C22×C4—44no—
767C22×C4—44no—
768C22×C4—44no—
769C22×C4—44no—
770C22×C4—44no—
771C22×C4—44no—
772C22×C4C22×C4×C3112yes—
773C22×C4C22×C4×C3112yes—
774C22×C4C22×C4×C3112yes—
775C22×C4C22×C4×C3112yes—
776C22×C4C22×C4×C3112yes—
777C22×C4C22×C4×C3112yes—
778C22×C4C2×D4×C3112yes—
779C22×C4C2×D4×C3112yes—
780C22×C4C2×D4×C3112yes—
781C22×C4C2×D4×C3112yes—
782C22×C4C2×D4×C3112yes—
783C22×C4C2×D4×C3112yes—
784C22×C4C2×D4×C3112yes—
785C22×C4C2×D4×C3112yes—
786C22×C4C2×Q8×C3112yes—
787C22×C4C2×Q8×C3112yes—
788C22×C4#41×C3112yes—
789C22×C4#41×C3112yes—
790C4⋊C4—28no—
791C4⋊C4—44no—
792C4⋊C4—44no—
793C4⋊C4—44no—
794C4⋊C4—44no—
795C4⋊C4—44no—
796C4⋊C4—44no—
797C4⋊C4—44no—
798C4⋊C4—44no—
799C4⋊C4—44no—
800C22⋊C4—28no—
801C22⋊C4—28no—
802C22⋊C4—44no—
803C22⋊C4—44no—
804C22⋊C4—44no—
805C22⋊C4C4⋊C4×C31116yescomplemented
806C42—28no—
807C42—44no—
808C23—22no—
809C23—22no—
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—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—41no—
842C23C2×C4⋊C4×C3114yes—
843C23C23×C4×C3111yescharacteristic
844C23C22×D4×C3111yescharacteristic
845C23C22×D4×C3111yescharacteristic
846C23C22×D4×C3111yescharacteristic
847C23C22×Q8×C3111yescharacteristic
848C23C2×#41×C3111yescharacteristic
849C23C2×#41×C3111yescharacteristic
850C23C31×H(5,𝔽2)11yescharacteristic
851C23C31×H(5,𝔽2)11yescharacteristic
852C23C31×H(5,𝔽2)11yescharacteristic
853C23C31×H(5,𝔽2)11yescharacteristic
854C23C31×2−1+411yescharacteristic
855C23C31×2−1+411yescharacteristic
856C23C31×2−1+411yescharacteristic
857C23C31×2−1+411yescharacteristic
858C2×C4—22no—
859C2×C4—22no—
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—416no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
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×C4C2×C4⋊C4×C3114yes—
954C2×C4C2×C4⋊C4×C3114yes—
955C2×C4C4×D4×C3114yes—
956C2×C4C4×D4×C3114yes—
957C22—24no—
958C22—24no—
959C22—24no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22—42no—
967C22—42no—
968C22—42no—
969C22—42no—
970C22—42no—
971C22—42no—
972C22C22×C4⋊C4×C3111yescharacteristic
973C22C2×C4×D4×C3111yescharacteristic
974C22C2×C4×D4×C3111yescharacteristic
975C22C31×#52011yescharacteristic
976C22C31×#52011yescharacteristic
977C22C31×#52011yescharacteristic
978C22C31×#52011yescharacteristic
979C22C31×#53411yescharacteristic
980C22C31×#53511yescharacteristic
981C22C31×#53511yescharacteristic
982C22C31×#53611yescharacteristic
983C22C31×#53611yescharacteristic
984C22C31×#53611yescharacteristic
985C22C31×#53911yescharacteristic
986C22C31×#53911yescharacteristic
987C22C31×#54211yescharacteristic
988C22C31×#54211yescharacteristic
989C22C31×#54411yescharacteristic
990C22C31×#54411yescharacteristic
991C22D42×C3111yescharacteristic
992C22D42×C3111yescharacteristic
993C22D42×C3111yescharacteristic
994C22C31×#54711yescharacteristic
995C22C31×#54711yescharacteristic
996C22C31×#54711yescharacteristic
997C22C31×#54811yescharacteristic
998C22D4×Q8×C3111yescharacteristic
999C22D4×Q8×C3111yescharacteristic
1000C22C31×#55311yescharacteristic
1001C22C31×#55411yescharacteristic
1002C22C31×#55411yescharacteristic
1003C22C31×#56011yescharacteristic
1004C22C31×#56311yescharacteristic
1005C22C31×#56311yescharacteristic
1006C22C31×#56311yescharacteristic
1007C4—24no—
1008C4—24no—
1009C4—24no—
1010C4—24no—
1011C4—42no—
1012C4—42no—
1013C4—42no—
1014C4—42no—
1015C4—42no—
1016C4—42no—
1017C4—81no—
1018C4—81no—
1019C4—81no—
1020C4—81no—
1021C2—44no—
1022C2C31×#231711yescharacteristic
1023C2C31×#232211yescharacteristic
1024C2C31×#232611yescharacteristic
1025C2D4×C4⋊C4×C3111yescharacteristic
1026C2D4×C4⋊C4×C3111yescharacteristic
1027C2C31×#236111yescharacteristic
1028C2C31×#238311yescharacteristic
1029C2C31×#266911yescharacteristic
1030C2C31×#267411yescharacteristic
1031C2C31×#267711yescharacteristic
1032C2C31×#268011yescharacteristic
1033C2C31×#271811yescharacteristic
1034C2C31×#272011yescharacteristic
1035C2C31×#272911yescharacteristic
1036C2C31×#279011yescharacteristic
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
7. C2×C31×#384C2semidirect
8. C31×#1444C2semidirect
9. C31×#1444C2semidirect
10. C31×#1442C2semidirect
11. C31×#1441C2semidirect
14. C31×#1436C2semidirect
15. C31×#1434C2semidirect
37. C31×#388C4semidirect
108. C2×C4⋊C4×C31C2×C4semidirect
133. C2×C42×C31C2×C4semidirect
147. C31×#95C2×C4semidirect
148. C31×#95C2×C4semidirect
286. C22⋊C4×C31C4⋊C4semidirect
289. #14405C31direct (N × H)
439. C2×#389C2×C31semidirect
445. C2×#384C2×C31semidirect
446. #1444C2×C31semidirect
447. #1444C2×C31semidirect
448. #1442C2×C31semidirect
449. #1441C2×C31semidirect
452. #1436C2×C31semidirect
453. #1434C2×C31semidirect
539. #388C4×C31semidirect
626. C2×C4⋊C4C2×C4×C31semidirect
651. C2×C42C2×C4×C31semidirect
665. #95C2×C4×C31semidirect
666. #95C2×C4×C31semidirect
668. C31#14405direct (N × H)
805. C22⋊C4C4⋊C4×C31semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#3892
C2×C31×#3882
C2×C31×#3852
C2×C31×#3842
C31×#14442
C31×#14422
C31×#14412
C31×#14392
C31×#14362
C31×#14342
#1440531