Finite Group Databasebeta

← C31×#22506 #21479265

Subgroups — C31×#22506 #21479265

Order 7936.

1148 conjugacy classes of subgroups.

The subgroup lattice has 1048 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3475C211yesmaximal, characteristic
2D4×M16×C31C211yesmaximal, characteristic, complemented
3C31×#2290C211yesmaximal, characteristic, complemented
4C31×#1995C211yesmaximal, characteristic, complemented
5C31×#1986C211yesmaximal, characteristic, complemented
6C31×#1897C211yesmaximal, characteristic, complemented
7C31×#1896C211yesmaximal, characteristic, complemented
8C31×#1871C211yesmaximal, characteristic, complemented
9C31×#1871C211yesmaximal, characteristic, complemented
10C31×#1826C211yesmaximal, characteristic, complemented
11C31×#1826C211yesmaximal, characteristic, complemented
12C31×#1806C211yesmaximal, characteristic, complemented
13C31×#1759C211yesmaximal, characteristic, complemented
14C31×#1733C211yesmaximal, characteristic, complemented
15C2×C31×#339C211yesmaximal, characteristic, complemented
16C22×M16×C31C2211yescharacteristic
17C22×M16×C31C2211yescharacteristic
18C31×#556C411yescharacteristic, complemented
19C31×#555C411yescharacteristic, complemented
20C31×#554C411yescharacteristic, complemented
21C31×#553C411yescharacteristic, complemented
22C31×#553C411yescharacteristic, complemented
23C31×#552—21no—
24C31×#552C411yescharacteristic, complemented
25C31×#552C411yescharacteristic, complemented
26C31×#551—21no—
27C31×#551—21no—
28C31×#547C411yescharacteristic, complemented
29C31×#546—21no—
30C31×#533C2211yescharacteristic
31C31×#529—21no—
32C31×#529—21no—
33C31×#529—21no—
34C31×#525C2211yescharacteristic
35C31×#525C2211yescharacteristic
36C4×#41×C31—21no—
37C4×#41×C31C2211yescharacteristic
38C2×C4×D4×C31C2211yescharacteristic
39C2×C31×#117C2211yescharacteristic
40C2×C31×#117C2211yescharacteristic
41C2×C31×#117C2211yescharacteristic
42C22×C42×C31C2211yescharacteristic
43C31×#436—21no—
44C31×#435—21no—
45C31×#435—21no—
46C8×D4×C31—21no—
47C31×#423C2211yescharacteristic
48C2×C31×#104C2211yescharacteristic
49C2×C31×#104C2211yescharacteristic
50C2×C31×#104C2211yescharacteristic
51C2×C31×#104C2211yescharacteristic
52C31×#407C2211yescharacteristic
53C31×#407C2211yescharacteristic
54C4×M16×C31C2211yescharacteristic
55C31×#388—21no—
56C31×#387—21no—
57C31×#386—21no—
58C31×#385—21no—
59C4×C4⋊C4×C31C2211yescharacteristic
60C4×C22⋊C4×C31C2211yescharacteristic
61C4×C22⋊C4×C31C2211yescharacteristic
62C31×#376C2211yescharacteristic
63C31×#339C2211yescharacteristic
64C31×#339C2211yescharacteristic
65C31×#339C2211yescharacteristic
66C31×#339C2211yescharacteristic
67C31×#339C2211yescharacteristic
68C31×#339C2211yescharacteristic
69C31×#339C2211yescharacteristic
70C31×#339C2211yescharacteristic
71C31×#339C2211yescharacteristic
72C31×#339C2211yescharacteristic
73C31×#339C2211yescharacteristic
74C31×#339C2211yescharacteristic
75C2×#41×C31—21no—
76C2×#41×C31C2311yescharacteristic
77C22×D4×C31D411yescharacteristic
78C23×C4×C31—21no—
79C23×C4×C31C2311yescharacteristic
80C23×C4×C31C2311yescharacteristic
81C2×M16×C31—21no—
82C2×M16×C31—21no—
83C2×M16×C31—22no—
84C2×M16×C31—22no—
85C2×M16×C31—41no—
86C2×M16×C31—41no—
87C2×M16×C31C2311yescharacteristic
88C2×M16×C31C2311yescharacteristic
89C2×M16×C31C2311yescharacteristic
90C2×M16×C31C2311yescharacteristic
91C22×C8×C31—21no—
92C22×C8×C31—21no—
93C31×C4⋊Q8C2×C411yescharacteristic, complemented
94C31×C4⋊Q8C2×C411yescharacteristic, complemented
95C31×#126—21no—
96C31×#126—21no—
97C31×#126—21no—
98C31×#126—21no—
99C31×#126—21no—
100C31×#126—21no—
101C31×#125—21no—
102C31×#125—21no—
103C31×#125—21no—
104C31×#125C2×C411yescharacteristic, complemented
105C31×#125C2×C411yescharacteristic, complemented
106C31×#124—21no—
107C31×#124—21no—
108C31×#124—21no—
109C31×#123—21no—
110C31×#123—21no—
111C31×#123—21no—
112C31×#123—21no—
113C31×#123—21no—
114C31×#123—21no—
115C31×#123—21no—
116C31×#123—21no—
117C31×C22⋊Q8—21no—
118C31×C22⋊Q8—21no—
119C31×C22⋊Q8—21no—
120C31×C22⋊Q8—21no—
121C31×C22⋊Q8—21no—
122C31×C22⋊Q8C2×C411yescharacteristic
123C31×C22⋊Q8C2×C411yescharacteristic
124C31×C22⋊Q8C2×C411yescharacteristic, complemented
125C31×C22⋊Q8C2×C411yescharacteristic, complemented
126C31×#121—21no—
127C31×#121—21no—
128C31×#121—21no—
129C31×#121C2×C411yescharacteristic
130C31×#121C2×C411yescharacteristic
131C31×#121C2×C411yescharacteristic, complemented
132C31×#121C2×C411yescharacteristic, complemented
133C31×#120—21no—
134C31×#120—21no—
135C4×Q8×C31—21no—
136C4×Q8×C31—21no—
137C4×Q8×C31—21no—
138C4×Q8×C31C2×C411yescharacteristic, complemented
139C4×Q8×C31C2×C411yescharacteristic, complemented
140C4×D4×C31—21no—
141C4×D4×C31—21no—
142C4×D4×C31—21no—
143C4×D4×C31—21no—
144C4×D4×C31—21no—
145C4×D4×C31—21no—
146C4×D4×C31—21no—
147C4×D4×C31—21no—
148C4×D4×C31—21no—
149C4×D4×C31C2×C411yescharacteristic
150C4×D4×C31C2×C411yescharacteristic
151C4×D4×C31C2×C411yescharacteristic
152C4×D4×C31C2×C411yescharacteristic
153C4×D4×C31C2×C411yescharacteristic, complemented
154C4×D4×C31C2×C411yescharacteristic, complemented
155C4×D4×C31D411yescharacteristic
156C4×D4×C31D411yescharacteristic
157C4×D4×C31D411yescharacteristic
158C4×D4×C31D411yescharacteristic
159C31×#117—21no—
160C31×#117—21no—
161C31×#117—21no—
162C31×#117—21no—
163C31×#117—21no—
164C31×#117—21no—
165C31×#117—21no—
166C31×#117—21no—
167C31×#117—22no—
168C31×#117—41no—
169C31×#117C2×C411yescharacteristic
170C31×#117C2×C411yescharacteristic
171C31×#117C2×C411yescharacteristic, complemented
172C31×#117C2×C411yescharacteristic, complemented
173C31×#117C2311yescharacteristic
174C31×#117C2311yescharacteristic
175C31×#117C2311yescharacteristic
176C2×C4⋊C4×C31—21no—
177C2×C4⋊C4×C31—21no—
178C2×C4⋊C4×C31C2×C411yescharacteristic
179C2×C4⋊C4×C31C2×C411yescharacteristic
180C2×C4⋊C4×C31C2×C411yescharacteristic, complemented
181C2×C4⋊C4×C31C2×C411yescharacteristic, complemented
182C2×C4⋊C4×C31D411yescharacteristic
183C2×C22⋊C4×C31—21no—
184C2×C22⋊C4×C31—21no—
185C2×C22⋊C4×C31—21no—
186C2×C22⋊C4×C31—21no—
187C2×C22⋊C4×C31—21no—
188C2×C22⋊C4×C31D411yescharacteristic
189C2×C22⋊C4×C31D411yescharacteristic
190C2×C42×C31—21no—
191C2×C42×C31—21no—
192C2×C42×C31—21no—
193C2×C42×C31—22no—
194C2×C42×C31—21no—
195C2×C42×C31—41no—
196C2×C42×C31C2311yescharacteristic
197C2×C42×C31C2311yescharacteristic
198C2×C42×C31C2311yescharacteristic
199C2×C42×C31C2311yescharacteristic
200C2×C42×C31C2311yescharacteristic
201C31×C4⋊C8—21no—
202C31×C4⋊C8—21no—
203C31×#104—22no—
204C31×#104—22no—
205C31×#104—41no—
206C31×#104—41no—
207C31×C22⋊C8—21no—
208C31×C22⋊C8—21no—
209C31×C22⋊C8—21no—
210C31×C22⋊C8—21no—
211C31×#97—21no—
212C4×C8×C31—21no—
213C31×#95—21no—
214C31×#95—21no—
215C31×#95—21no—
216C31×#95—21no—
217C31×#95—21no—
218C24×C31C2×D411yescharacteristic
219C24×C31C2×D411yescharacteristic
220#41×C31—21no—
221#41×C31—21no—
222#41×C31—21no—
223#41×C31—21no—
224#41×C31—44no—
225C2×Q8×C31—21no—
226C2×Q8×C31—21no—
227C2×Q8×C31C22×C411yescharacteristic
228C2×D4×C31—21no—
229C2×D4×C31—21no—
230C2×D4×C31—21no—
231C2×D4×C31—21no—
232C2×D4×C31—21no—
233C2×D4×C31—42no—
234C2×D4×C31C22⋊C411yescharacteristic
235C2×D4×C31C22⋊C411yescharacteristic
236C2×D4×C31C22⋊C411yescharacteristic
237C2×D4×C31C22⋊C411yescharacteristic
238C2×D4×C31C22×C411yescharacteristic
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—21no—
254C22×C4×C31—21no—
255C22×C4×C31—21no—
256C22×C4×C31—21no—
257C22×C4×C31—21no—
258C22×C4×C31—42no—
259C22×C4×C31—42no—
260C22×C4×C31—42no—
261C22×C4×C31C22×C411yescharacteristic
262C22×C4×C31C22×C411yescharacteristic
263C22×C4×C31C22×C411yescharacteristic
264C22×C4×C31C22×C411yescharacteristic
265C22×C4×C31C2×D411yescharacteristic
266C22×C4×C31C2×D411yescharacteristic
267C22×C4×C31C2×D411yescharacteristic
268C22×C4×C31C2×D411yescharacteristic
269C22×C4×C31C2×D411yescharacteristic
270C22×C4×C31C2×D411yescharacteristic
271C22×C4×C31C2×D411yescharacteristic
272C22×C4×C31C2×D411yescharacteristic
273C22×C4×C31C2411yescharacteristic
274M16×C31—21no—
275M16×C31—21no—
276M16×C31—21no—
277M16×C31—21no—
278M16×C31—21no—
279M16×C31—21no—
280M16×C31—21no—
281M16×C31—42no—
282M16×C31—42no—
283M16×C31#4112yescomplemented
284C2×C8×C31—21no—
285C2×C8×C31—21no—
286C2×C8×C31—21no—
287C2×C8×C31—21no—
288C2×C8×C31—42no—
289C2×C8×C31—42no—
290C4⋊C4×C31—21no—
291C4⋊C4×C31—21no—
292C4⋊C4×C31—21no—
293C4⋊C4×C31—21no—
294C4⋊C4×C31—21no—
295C4⋊C4×C31—21no—
296C4⋊C4×C31—21no—
297C4⋊C4×C31—21no—
298C4⋊C4×C31—21no—
299C4⋊C4×C31—21no—
300C4⋊C4×C31—21no—
301C4⋊C4×C31—21no—
302C4⋊C4×C31—21no—
303C4⋊C4×C31—21no—
304C4⋊C4×C31—21no—
305C4⋊C4×C31—21no—
306C4⋊C4×C31—42no—
307C4⋊C4×C31—42no—
308C4⋊C4×C31C22⋊C411yescharacteristic
309C4⋊C4×C31C22⋊C411yescharacteristic
310C4⋊C4×C31C22⋊C411yescharacteristic
311C4⋊C4×C31C22⋊C411yescharacteristic
312C4⋊C4×C31C22×C411yescharacteristic
313C4⋊C4×C31C22×C411yescharacteristic
314C4⋊C4×C31C22×C411yescharacteristic
315C4⋊C4×C31C22×C411yescharacteristic
316C4⋊C4×C31C22×C411yescharacteristic
317C4⋊C4×C31C22×C411yescharacteristic
318C22⋊C4×C31—21no—
319C22⋊C4×C31—21no—
320C22⋊C4×C31—21no—
321C22⋊C4×C31—21no—
322C22⋊C4×C31—21no—
323C22⋊C4×C31—21no—
324C22⋊C4×C31—21no—
325C22⋊C4×C31—21no—
326C22⋊C4×C31—21no—
327C22⋊C4×C31—21no—
328C22⋊C4×C31—21no—
329C22⋊C4×C31—21no—
330C22⋊C4×C31—21no—
331C22⋊C4×C31—21no—
332C22⋊C4×C31—21no—
333C22⋊C4×C31—21no—
334C22⋊C4×C31—21no—
335C22⋊C4×C31—42no—
336C22⋊C4×C31—42no—
337C22⋊C4×C31—42no—
338C22⋊C4×C31C22⋊C411yescharacteristic
339C22⋊C4×C31C22⋊C411yescharacteristic
340C22⋊C4×C31C22⋊C411yescharacteristic
341C22⋊C4×C31C22⋊C411yescharacteristic
342C22⋊C4×C31C22⋊C411yescharacteristic
343C22⋊C4×C31C22⋊C411yescharacteristic
344C22⋊C4×C31C22⋊C411yescharacteristic
345C22⋊C4×C31C22⋊C411yescharacteristic
346C42×C31—21no—
347C42×C31—21no—
348C42×C31—21no—
349C42×C31—21no—
350C42×C31—21no—
351C42×C31—21no—
352C42×C31—21no—
353C42×C31—21no—
354C42×C31—21no—
355C42×C31—21no—
356C42×C31—21no—
357C42×C31—21no—
358C42×C31—21no—
359C42×C31—21no—
360C42×C31—21no—
361C42×C31—21no—
362C42×C31—42no—
363C42×C31C22×C411yescharacteristic
364C42×C31C22×C411yescharacteristic
365C42×C31C2×D411yescharacteristic
366C42×C31C2×D411yescharacteristic
367C42×C31#4112yescomplemented
368#22506C3111yesmaximal, characteristic, direct product factor, Sylow
369C23×C31—21no—
370C23×C31—21no—
371C23×C31—22no—
372C23×C31—21no—
373C23×C31—21no—
374C23×C31—21no—
375C23×C31—41no—
376C23×C31—41no—
377C23×C31—41no—
378C23×C31C2×C22⋊C411yescharacteristic
379C23×C31C2×C22⋊C411yescharacteristic
380C23×C31C2×C22⋊C411yescharacteristic
381C23×C31C2×C22⋊C411yescharacteristic
382C23×C31C22×D411yescharacteristic
383Q8×C31—21no—
384Q8×C31—21no—
385Q8×C31—42no—
386Q8×C31—81no—
387D4×C31—22no—
388D4×C31—22no—
389D4×C31—21no—
390D4×C31—21no—
391D4×C31—41no—
392D4×C31—41no—
393D4×C31—42no—
394D4×C31—41no—
395D4×C31—41no—
396D4×C31—42no—
397D4×C31—81no—
398D4×C31—81no—
399C2×C4×C31—21no—
400C2×C4×C31—21no—
401C2×C4×C31—21no—
402C2×C4×C31—21no—
403C2×C4×C31—21no—
404C2×C4×C31—21no—
405C2×C4×C31—21no—
406C2×C4×C31—21no—
407C2×C4×C31—21no—
408C2×C4×C31—21no—
409C2×C4×C31—21no—
410C2×C4×C31—21no—
411C2×C4×C31—21no—
412C2×C4×C31—21no—
413C2×C4×C31—21no—
414C2×C4×C31—21no—
415C2×C4×C31—21no—
416C2×C4×C31—21no—
417C2×C4×C31—21no—
418C2×C4×C31—21no—
419C2×C4×C31—22no—
420C2×C4×C31—21no—
421C2×C4×C31—21no—
422C2×C4×C31—21no—
423C2×C4×C31—21no—
424C2×C4×C31—21no—
425C2×C4×C31—21no—
426C2×C4×C31—21no—
427C2×C4×C31—22no—
428C2×C4×C31—41no—
429C2×C4×C31—41no—
430C2×C4×C31—42no—
431C2×C4×C31—41no—
432C2×C4×C31—41no—
433C2×C4×C31—41no—
434C2×C4×C31—42no—
435C2×C4×C31—48no—
436C2×C4×C31—41no—
437C2×C4×C31—42no—
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—81no—
447C2×C4×C31—81no—
448C2×C4×C31—81no—
449C2×C4×C31C2×C22⋊C411yescharacteristic
450C2×C4×C31C2×C22⋊C411yescharacteristic
451C2×C4×C31C2×C22⋊C411yescharacteristic
452C2×C4×C31C2×C22⋊C411yescharacteristic
453C2×C4×C31C2×C22⋊C411yescharacteristic
454C2×C4×C31C2×C22⋊C411yescharacteristic
455C2×C4×C31C2×C22⋊C411yescharacteristic
456C2×C4×C31C2×C22⋊C411yescharacteristic
457C2×C4×C31C23×C411yescharacteristic
458C2×C4×C31C22×D411yescharacteristic
459C2×C4×C31C2×#4111yescharacteristic
460C2×C4×C31C2×#4111yescharacteristic
461C2×C4×C31H(5,𝔽2)11yescharacteristic
462C2×C4×C312−1+411yescharacteristic
463C8×C31—22no—
464C8×C31—41no—
465C8×C31—41no—
466C8×C31—41no—
467#3475C2×C3111yescharacteristic
468D4×M16C2×C3111yescharacteristic, complemented
469#2290C2×C3111yescharacteristic, complemented
470#1995C2×C3111yescharacteristic, complemented
471#1986C2×C3111yescharacteristic, complemented
472#1897C2×C3111yescharacteristic, complemented
473#1896C2×C3111yescharacteristic, complemented
474#1871C2×C3111yescharacteristic, complemented
475#1871C2×C3111yescharacteristic, complemented
476#1826C2×C3111yescharacteristic, complemented
477#1826C2×C3111yescharacteristic, complemented
478#1806C2×C3111yescharacteristic, complemented
479#1759C2×C3111yescharacteristic, complemented
480#1733C2×C3111yescharacteristic, complemented
481C2×#339C2×C3111yescharacteristic, complemented
482C22×C31—21no—
483C22×C31—21no—
484C22×C31—21no—
485C22×C31—21no—
486C22×C31—21no—
487C22×C31—21no—
488C22×C31—21no—
489C22×C31—21no—
490C22×C31—21no—
491C22×C31—21no—
492C22×C31—21no—
493C22×C31—21no—
494C22×C31—21no—
495C22×C31—42no—
496C22×C31—42no—
497C22×C31—41no—
498C22×C31—41no—
499C22×C31—41no—
500C22×C31—81no—
501C22×C31—81no—
502C22×C31#42112yes—
503C22×C31C22×C22⋊C411yescharacteristic
504C22×C31#54611yescharacteristic
505C22×C31#54711yescharacteristic
506C4×C31—21no—
507C4×C31—21no—
508C4×C31—21no—
509C4×C31—21no—
510C4×C31—21no—
511C4×C31—21no—
512C4×C31—21no—
513C4×C31—21no—
514C4×C31—42no—
515C4×C31—42no—
516C4×C31—41no—
517C4×C31—41no—
518C4×C31—41no—
519C4×C31—41no—
520C4×C31—41no—
521C4×C31—41no—
522C4×C31—41no—
523C4×C31—81no—
524C4×C31—81no—
525C4×C31C4×#4111yescharacteristic
526C4×C31#52011yescharacteristic
527C4×C31#54611yescharacteristic
528C4×C31#54711yescharacteristic
529C22×M16C22×C3111yescharacteristic
530C22×M16C22×C3111yescharacteristic
531#556C4×C3111yescharacteristic, complemented
532#555C4×C3111yescharacteristic, complemented
533#554C4×C3111yescharacteristic, complemented
534#553C4×C3111yescharacteristic, complemented
535#553C4×C3111yescharacteristic, complemented
536#552—21no—
537#552C4×C3111yescharacteristic, complemented
538#552C4×C3111yescharacteristic, complemented
539#551—21no—
540#551—21no—
541#547C4×C3111yescharacteristic, complemented
542#546—21no—
543#533C22×C3111yescharacteristic
544#529—21no—
545#529—21no—
546#529—21no—
547#525C22×C3111yescharacteristic
548#525C22×C3111yescharacteristic
549C4×#41—21no—
550C4×#41C22×C3111yescharacteristic
551C2×C4×D4C22×C3111yescharacteristic
552C2×#117C22×C3111yescharacteristic
553C2×#117C22×C3111yescharacteristic
554C2×#117C22×C3111yescharacteristic
555C22×C42C22×C3111yescharacteristic
556#436—21no—
557#435—21no—
558#435—21no—
559C8×D4—21no—
560#423C22×C3111yescharacteristic
561C2×#104C22×C3111yescharacteristic
562C2×#104C22×C3111yescharacteristic
563C2×#104C22×C3111yescharacteristic
564C2×#104C22×C3111yescharacteristic
565#407C22×C3111yescharacteristic
566#407C22×C3111yescharacteristic
567C4×M16C22×C3111yescharacteristic
568#388—21no—
569#387—21no—
570#386—21no—
571#385—21no—
572C4×C4⋊C4C22×C3111yescharacteristic
573C4×C22⋊C4C22×C3111yescharacteristic
574C4×C22⋊C4C22×C3111yescharacteristic
575#376C22×C3111yescharacteristic
576#339C22×C3111yescharacteristic
577#339C22×C3111yescharacteristic
578#339C22×C3111yescharacteristic
579#339C22×C3111yescharacteristic
580#339C22×C3111yescharacteristic
581#339C22×C3111yescharacteristic
582#339C22×C3111yescharacteristic
583#339C22×C3111yescharacteristic
584#339C22×C3111yescharacteristic
585#339C22×C3111yescharacteristic
586#339C22×C3111yescharacteristic
587#339C22×C3111yescharacteristic
588C2×C31—21no—
589C2×C31—21no—
590C2×C31—22no—
591C2×C31—41no—
592C2×C31—41no—
593C2×C31—41no—
594C2×C31—81no—
595C2×C31#233911yescharacteristic
596C2×C31C2×#42111yescharacteristic
597C2×C31#290111yescharacteristic
598C2×#41—21no—
599C2×#41C23×C3111yescharacteristic
600C22×D4D4×C3111yescharacteristic
601C23×C4—21no—
602C23×C4C23×C3111yescharacteristic
603C23×C4C23×C3111yescharacteristic
604C2×M16—21no—
605C2×M16—21no—
606C2×M16—22no—
607C2×M16—22no—
608C2×M16—41no—
609C2×M16—41no—
610C2×M16C23×C3111yescharacteristic
611C2×M16C23×C3111yescharacteristic
612C2×M16C23×C3111yescharacteristic
613C2×M16C23×C3111yescharacteristic
614C22×C8—21no—
615C22×C8—21no—
616C4⋊Q8C2×C4×C3111yescharacteristic, complemented
617C4⋊Q8C2×C4×C3111yescharacteristic, complemented
618#126—21no—
619#126—21no—
620#126—21no—
621#126—21no—
622#126—21no—
623#126—21no—
624#125—21no—
625#125—21no—
626#125—21no—
627#125C2×C4×C3111yescharacteristic, complemented
628#125C2×C4×C3111yescharacteristic, complemented
629#124—21no—
630#124—21no—
631#124—21no—
632#123—21no—
633#123—21no—
634#123—21no—
635#123—21no—
636#123—21no—
637#123—21no—
638#123—21no—
639#123—21no—
640C22⋊Q8—21no—
641C22⋊Q8—21no—
642C22⋊Q8—21no—
643C22⋊Q8—21no—
644C22⋊Q8—21no—
645C22⋊Q8C2×C4×C3111yescharacteristic
646C22⋊Q8C2×C4×C3111yescharacteristic
647C22⋊Q8C2×C4×C3111yescharacteristic, complemented
648C22⋊Q8C2×C4×C3111yescharacteristic, complemented
649#121—21no—
650#121—21no—
651#121—21no—
652#121C2×C4×C3111yescharacteristic
653#121C2×C4×C3111yescharacteristic
654#121C2×C4×C3111yescharacteristic, complemented
655#121C2×C4×C3111yescharacteristic, complemented
656#120—21no—
657#120—21no—
658C4×Q8—21no—
659C4×Q8—21no—
660C4×Q8—21no—
661C4×Q8C2×C4×C3111yescharacteristic, complemented
662C4×Q8C2×C4×C3111yescharacteristic, complemented
663C4×D4—21no—
664C4×D4—21no—
665C4×D4—21no—
666C4×D4—21no—
667C4×D4—21no—
668C4×D4—21no—
669C4×D4—21no—
670C4×D4—21no—
671C4×D4—21no—
672C4×D4C2×C4×C3111yescharacteristic
673C4×D4C2×C4×C3111yescharacteristic
674C4×D4C2×C4×C3111yescharacteristic
675C4×D4C2×C4×C3111yescharacteristic
676C4×D4C2×C4×C3111yescharacteristic, complemented
677C4×D4C2×C4×C3111yescharacteristic, complemented
678C4×D4D4×C3111yescharacteristic
679C4×D4D4×C3111yescharacteristic
680C4×D4D4×C3111yescharacteristic
681C4×D4D4×C3111yescharacteristic
682#117—21no—
683#117—21no—
684#117—21no—
685#117—21no—
686#117—21no—
687#117—21no—
688#117—21no—
689#117—21no—
690#117—22no—
691#117—41no—
692#117C2×C4×C3111yescharacteristic
693#117C2×C4×C3111yescharacteristic
694#117C2×C4×C3111yescharacteristic, complemented
695#117C2×C4×C3111yescharacteristic, complemented
696#117C23×C3111yescharacteristic
697#117C23×C3111yescharacteristic
698#117C23×C3111yescharacteristic
699C2×C4⋊C4—21no—
700C2×C4⋊C4—21no—
701C2×C4⋊C4C2×C4×C3111yescharacteristic
702C2×C4⋊C4C2×C4×C3111yescharacteristic
703C2×C4⋊C4C2×C4×C3111yescharacteristic, complemented
704C2×C4⋊C4C2×C4×C3111yescharacteristic, complemented
705C2×C4⋊C4D4×C3111yescharacteristic
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4D4×C3111yescharacteristic
712C2×C22⋊C4D4×C3111yescharacteristic
713C2×C42—21no—
714C2×C42—21no—
715C2×C42—21no—
716C2×C42—22no—
717C2×C42—21no—
718C2×C42—41no—
719C2×C42C23×C3111yescharacteristic
720C2×C42C23×C3111yescharacteristic
721C2×C42C23×C3111yescharacteristic
722C2×C42C23×C3111yescharacteristic
723C2×C42C23×C3111yescharacteristic
724C4⋊C8—21no—
725C4⋊C8—21no—
726#104—22no—
727#104—22no—
728#104—41no—
729#104—41no—
730C22⋊C8—21no—
731C22⋊C8—21no—
732C22⋊C8—21no—
733C22⋊C8—21no—
734#97—21no—
735C4×C8—21no—
736#95—21no—
737#95—21no—
738#95—21no—
739#95—21no—
740#95—21no—
741C31#2250611yescharacteristic, direct product factor, Sylow
742C24C2×D4×C3111yescharacteristic
743C24C2×D4×C3111yescharacteristic
744#41—21no—
745#41—21no—
746#41—21no—
747#41—21no—
748#41—44no—
749C2×Q8—21no—
750C2×Q8—21no—
751C2×Q8C22×C4×C3111yescharacteristic
752C2×D4—21no—
753C2×D4—21no—
754C2×D4—21no—
755C2×D4—21no—
756C2×D4—21no—
757C2×D4—42no—
758C2×D4C22⋊C4×C3111yescharacteristic
759C2×D4C22⋊C4×C3111yescharacteristic
760C2×D4C22⋊C4×C3111yescharacteristic
761C2×D4C22⋊C4×C3111yescharacteristic
762C2×D4C22×C4×C3111yescharacteristic
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—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—21no—
782C22×C4—42no—
783C22×C4—42no—
784C22×C4—42no—
785C22×C4C22×C4×C3111yescharacteristic
786C22×C4C22×C4×C3111yescharacteristic
787C22×C4C22×C4×C3111yescharacteristic
788C22×C4C22×C4×C3111yescharacteristic
789C22×C4C2×D4×C3111yescharacteristic
790C22×C4C2×D4×C3111yescharacteristic
791C22×C4C2×D4×C3111yescharacteristic
792C22×C4C2×D4×C3111yescharacteristic
793C22×C4C2×D4×C3111yescharacteristic
794C22×C4C2×D4×C3111yescharacteristic
795C22×C4C2×D4×C3111yescharacteristic
796C22×C4C2×D4×C3111yescharacteristic
797C22×C4C24×C3111yescharacteristic
798M16—21no—
799M16—21no—
800M16—21no—
801M16—21no—
802M16—21no—
803M16—21no—
804M16—21no—
805M16—42no—
806M16—42no—
807M16#41×C3112yescomplemented
808C2×C8—21no—
809C2×C8—21no—
810C2×C8—21no—
811C2×C8—21no—
812C2×C8—42no—
813C2×C8—42no—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—21no—
818C4⋊C4—21no—
819C4⋊C4—21no—
820C4⋊C4—21no—
821C4⋊C4—21no—
822C4⋊C4—21no—
823C4⋊C4—21no—
824C4⋊C4—21no—
825C4⋊C4—21no—
826C4⋊C4—21no—
827C4⋊C4—21no—
828C4⋊C4—21no—
829C4⋊C4—21no—
830C4⋊C4—42no—
831C4⋊C4—42no—
832C4⋊C4C22⋊C4×C3111yescharacteristic
833C4⋊C4C22⋊C4×C3111yescharacteristic
834C4⋊C4C22⋊C4×C3111yescharacteristic
835C4⋊C4C22⋊C4×C3111yescharacteristic
836C4⋊C4C22×C4×C3111yescharacteristic
837C4⋊C4C22×C4×C3111yescharacteristic
838C4⋊C4C22×C4×C3111yescharacteristic
839C4⋊C4C22×C4×C3111yescharacteristic
840C4⋊C4C22×C4×C3111yescharacteristic
841C4⋊C4C22×C4×C3111yescharacteristic
842C22⋊C4—21no—
843C22⋊C4—21no—
844C22⋊C4—21no—
845C22⋊C4—21no—
846C22⋊C4—21no—
847C22⋊C4—21no—
848C22⋊C4—21no—
849C22⋊C4—21no—
850C22⋊C4—21no—
851C22⋊C4—21no—
852C22⋊C4—21no—
853C22⋊C4—21no—
854C22⋊C4—21no—
855C22⋊C4—21no—
856C22⋊C4—21no—
857C22⋊C4—21no—
858C22⋊C4—21no—
859C22⋊C4—42no—
860C22⋊C4—42no—
861C22⋊C4—42no—
862C22⋊C4C22⋊C4×C3111yescharacteristic
863C22⋊C4C22⋊C4×C3111yescharacteristic
864C22⋊C4C22⋊C4×C3111yescharacteristic
865C22⋊C4C22⋊C4×C3111yescharacteristic
866C22⋊C4C22⋊C4×C3111yescharacteristic
867C22⋊C4C22⋊C4×C3111yescharacteristic
868C22⋊C4C22⋊C4×C3111yescharacteristic
869C22⋊C4C22⋊C4×C3111yescharacteristic
870C42—21no—
871C42—21no—
872C42—21no—
873C42—21no—
874C42—21no—
875C42—21no—
876C42—21no—
877C42—21no—
878C42—21no—
879C42—21no—
880C42—21no—
881C42—21no—
882C42—21no—
883C42—21no—
884C42—21no—
885C42—21no—
886C42—42no—
887C42C22×C4×C3111yescharacteristic
888C42C22×C4×C3111yescharacteristic
889C42C2×D4×C3111yescharacteristic
890C42C2×D4×C3111yescharacteristic
891C42#41×C3112yescomplemented
892C23—22no—
893C23—21no—
894C23—21no—
895C23—21no—
896C23—21no—
897C23—21no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23C2×C22⋊C4×C3111yescharacteristic
902C23C2×C22⋊C4×C3111yescharacteristic
903C23C2×C22⋊C4×C3111yescharacteristic
904C23C2×C22⋊C4×C3111yescharacteristic
905C23C22×D4×C3111yescharacteristic
906Q8—21no—
907Q8—21no—
908Q8—42no—
909Q8—81no—
910D4—22no—
911D4—22no—
912D4—21no—
913D4—21no—
914D4—41no—
915D4—41no—
916D4—42no—
917D4—42no—
918D4—41no—
919D4—41no—
920D4—81no—
921D4—81no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—21no—
930C2×C4—21no—
931C2×C4—21no—
932C2×C4—21no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—21no—
937C2×C4—21no—
938C2×C4—21no—
939C2×C4—21no—
940C2×C4—21no—
941C2×C4—21no—
942C2×C4—22no—
943C2×C4—21no—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—21no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—22no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—42no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—42no—
958C2×C4—48no—
959C2×C4—42no—
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—81no—
970C2×C4—81no—
971C2×C4—81no—
972C2×C4C2×C22⋊C4×C3111yescharacteristic
973C2×C4C2×C22⋊C4×C3111yescharacteristic
974C2×C4C2×C22⋊C4×C3111yescharacteristic
975C2×C4C2×C22⋊C4×C3111yescharacteristic
976C2×C4C2×C22⋊C4×C3111yescharacteristic
977C2×C4C2×C22⋊C4×C3111yescharacteristic
978C2×C4C2×C22⋊C4×C3111yescharacteristic
979C2×C4C2×C22⋊C4×C3111yescharacteristic
980C2×C4C23×C4×C3111yescharacteristic
981C2×C4C22×D4×C3111yescharacteristic
982C2×C4C2×#41×C3111yescharacteristic
983C2×C4C2×#41×C3111yescharacteristic
984C2×C4C31×H(5,𝔽2)11yescharacteristic
985C2×C4C31×2−1+411yescharacteristic
986C8—22no—
987C8—41no—
988C8—41no—
989C8—41no—
990C22—21no—
991C22—21no—
992C22—21no—
993C22—21no—
994C22—21no—
995C22—21no—
996C22—21no—
997C22—21no—
998C22—21no—
999C22—21no—
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—42no—
1004C22—42no—
1005C22—41no—
1006C22—41no—
1007C22—41no—
1008C22—81no—
1009C22—81no—
1010C22C31×#42112yes—
1011C22C22×C22⋊C4×C3111yescharacteristic
1012C22C31×#54611yescharacteristic
1013C22C31×#54711yescharacteristic
1014C4—21no—
1015C4—21no—
1016C4—21no—
1017C4—21no—
1018C4—21no—
1019C4—21no—
1020C4—21no—
1021C4—21no—
1022C4—42no—
1023C4—42no—
1024C4—41no—
1025C4—41no—
1026C4—41no—
1027C4—41no—
1028C4—41no—
1029C4—41no—
1030C4—41no—
1031C4—81no—
1032C4—81no—
1033C4C4×#41×C3111yescharacteristic
1034C4C31×#52011yescharacteristic
1035C4C31×#54611yescharacteristic
1036C4C31×#54711yescharacteristic
1037C2—21no—
1038C2—21no—
1039C2—22no—
1040C2—41no—
1041C2—41no—
1042C2—41no—
1043C2—81no—
1044C2C31×#233911yescharacteristic
1045C2C2×C31×#42111yescharacteristic
1046C2C31×#290111yescharacteristic
subgroupG/H
centerC2×C4×C31C22×D4
commutatorC2×C4C23×C4×C31
Frattini, cosocleC22×C4C24×C31
socleC22×C31C22×C22⋊C4
prime radicalC31×#3475C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C31 ◁ C2×C4×D4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. D4×M16×C31C2semidirect
3. C31×#2290C2semidirect
4. C31×#1995C2semidirect
5. C31×#1986C2semidirect
6. C31×#1897C2semidirect
7. C31×#1896C2semidirect
8. C31×#1871C2semidirect
9. C31×#1871C2semidirect
10. C31×#1826C2semidirect
11. C31×#1826C2semidirect
12. C31×#1806C2semidirect
13. C31×#1759C2semidirect
14. C31×#1733C2semidirect
15. C2×C31×#339C2semidirect
18. C31×#556C4semidirect
19. C31×#555C4semidirect
20. C31×#554C4semidirect
21. C31×#553C4semidirect
22. C31×#553C4semidirect
24. C31×#552C4semidirect
25. C31×#552C4semidirect
28. C31×#547C4semidirect
93. C31×C4⋊Q8C2×C4semidirect
94. C31×C4⋊Q8C2×C4semidirect
104. C31×#125C2×C4semidirect
105. C31×#125C2×C4semidirect
124. C31×C22⋊Q8C2×C4semidirect
125. C31×C22⋊Q8C2×C4semidirect
131. C31×#121C2×C4semidirect
132. C31×#121C2×C4semidirect
138. C4×Q8×C31C2×C4semidirect
139. C4×Q8×C31C2×C4semidirect
153. C4×D4×C31C2×C4semidirect
154. C4×D4×C31C2×C4semidirect
171. C31×#117C2×C4semidirect
172. C31×#117C2×C4semidirect
180. C2×C4⋊C4×C31C2×C4semidirect
181. C2×C4⋊C4×C31C2×C4semidirect
283. M16×C31#41semidirect
367. C42×C31#41semidirect
368. #22506C31direct (N × H)
468. D4×M16C2×C31semidirect
469. #2290C2×C31semidirect
470. #1995C2×C31semidirect
471. #1986C2×C31semidirect
472. #1897C2×C31semidirect
473. #1896C2×C31semidirect
474. #1871C2×C31semidirect
475. #1871C2×C31semidirect
476. #1826C2×C31semidirect
477. #1826C2×C31semidirect
478. #1806C2×C31semidirect
479. #1759C2×C31semidirect
480. #1733C2×C31semidirect
481. C2×#339C2×C31semidirect
531. #556C4×C31semidirect
532. #555C4×C31semidirect
533. #554C4×C31semidirect
534. #553C4×C31semidirect
535. #553C4×C31semidirect
537. #552C4×C31semidirect
538. #552C4×C31semidirect
541. #547C4×C31semidirect
616. C4⋊Q8C2×C4×C31semidirect
617. C4⋊Q8C2×C4×C31semidirect
627. #125C2×C4×C31semidirect
628. #125C2×C4×C31semidirect
647. C22⋊Q8C2×C4×C31semidirect
648. C22⋊Q8C2×C4×C31semidirect
654. #121C2×C4×C31semidirect
655. #121C2×C4×C31semidirect
661. C4×Q8C2×C4×C31semidirect
662. C4×Q8C2×C4×C31semidirect
676. C4×D4C2×C4×C31semidirect
677. C4×D4C2×C4×C31semidirect
694. #117C2×C4×C31semidirect
695. #117C2×C4×C31semidirect
703. C2×C4⋊C4C2×C4×C31semidirect
704. C2×C4⋊C4C2×C4×C31semidirect
741. C31#22506direct (N × H)
807. M16#41×C31semidirect
891. C42#41×C31semidirect

Maximal subgroups

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

subgroupindex
C31×#34752
D4×M16×C312
C31×#22902
C31×#19952
C31×#19862
C31×#18972
C31×#18962
C31×#18712
C31×#18262
C31×#18062
C31×#17592
C31×#17332
C2×C31×#3392
#2250631