Finite Group Databasebeta

← C31×#16524 #21473283

Subgroups — C31×#16524 #21473283

Order 7936.

1286 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#400C211yesmaximal, characteristic
2C2×C31×#395C211yesmaximal, characteristic
3C2×C31×#395C211yesmaximal, characteristic
4C2×C31×#382C211yesmaximal, characteristic
5C31×#1446C211yesmaximal, characteristic
6C31×#1445C211yesmaximal, characteristic
7C31×#1444C211yesmaximal, characteristic
8C31×#1444C211yesmaximal, characteristic
9C31×#1444C211yesmaximal, characteristic
10C31×#1442C211yesmaximal, characteristic
11C31×#1442C211yesmaximal, characteristic
12C31×#1442C211yesmaximal, characteristic
13C31×#1441C211yesmaximal, characteristic
14C31×C4⋊#95C211yesmaximal, characteristic
15C31×#1434C211yesmaximal, characteristic
16C23×Q8×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×C42×C31C2211yescharacteristic
27C31×#400—24no—
28C31×#395—24no—
29C31×#395—24no—
30C31×#382—24no—
31C2×C31×#95C2211yescharacteristic
32C2×C31×#95C2211yescharacteristic
33C2×C31×#95C2211yescharacteristic
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
55C22×Q8×C31—22no—
56C22×Q8×C31—22no—
57C22×Q8×C31—22no—
58C22×Q8×C31—41no—
59C22×Q8×C31—41no—
60C22×Q8×C31—41no—
61C22×Q8×C31—41no—
62C23×C4×C31C2311yescharacteristic
63C23×C4×C31C2311yescharacteristic
64C23×C4×C31C2311yescharacteristic
65C23×C4×C31C2311yescharacteristic
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
77C2×C4⋊C4×C31—22no—
78C2×C4⋊C4×C31—22no—
79C2×C4⋊C4×C31—22no—
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—41no—
92C2×C4⋊C4×C31—41no—
93C2×C4⋊C4×C31—41no—
94C2×C4⋊C4×C31—41no—
95C2×C4⋊C4×C31—41no—
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×C42×C31—22no—
105C2×C42×C31—22no—
106C2×C42×C31Q814yescomplemented
107C31×#95—22no—
108C31×#95—22no—
109C31×#95—22no—
110C31×#95—22no—
111C31×#95—22no—
112C31×#95—22no—
113C31×#95—22no—
114C31×#95—22no—
115C31×#95—22no—
116C31×#95—22no—
117C31×#95—22no—
118C31×#95—22no—
119C31×#95—22no—
120C31×#95—22no—
121C31×#95—41no—
122C31×#95—41no—
123C31×#95—41no—
124C31×#95—41no—
125C31×#95—41no—
126C31×#95—41no—
127C31×#95—41no—
128C31×#95D414yes—
129C31×#95D414yes—
130C31×#95Q814yescomplemented
131C24×C31C2411yescharacteristic
132C2×Q8×C31—44no—
133C2×Q8×C31—44no—
134C2×Q8×C31—44no—
135C2×Q8×C31—44no—
136C2×Q8×C31—44no—
137C2×Q8×C31—44no—
138C2×Q8×C31—44no—
139C22×C4×C31—21no—
140C22×C4×C31—21no—
141C22×C4×C31—21no—
142C22×C4×C31—21no—
143C22×C4×C31—21no—
144C22×C4×C31—21no—
145C22×C4×C31—21no—
146C22×C4×C31—21no—
147C22×C4×C31—21no—
148C22×C4×C31—21no—
149C22×C4×C31—21no—
150C22×C4×C31—21no—
151C22×C4×C31—21no—
152C22×C4×C31—21no—
153C22×C4×C31—21no—
154C22×C4×C31—21no—
155C22×C4×C31—21no—
156C22×C4×C31—21no—
157C22×C4×C31—21no—
158C22×C4×C31—21no—
159C22×C4×C31—21no—
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—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×C31C2×D412yes—
230C22×C4×C31C2×D412yes—
231C22×C4×C31C2×D412yes—
232C22×C4×C31C2×D412yes—
233C22×C4×C31C2×D412yes—
234C22×C4×C31C2×D412yes—
235C22×C4×C31C2×Q812yes—
236C22×C4×C31C2×Q812yes—
237C22×C4×C31C2×Q812yes—
238C22×C4×C31C2×Q812yes—
239C22×C4×C31C2×Q812yes—
240C22×C4×C31C2×Q812yes—
241C22×C4×C31#4112yes—
242C22×C4×C31#4112yes—
243C22×C4×C31#4112yes—
244C4⋊C4×C31—44no—
245C4⋊C4×C31—44no—
246C4⋊C4×C31—44no—
247C4⋊C4×C31—44no—
248C4⋊C4×C31—44no—
249C4⋊C4×C31—44no—
250C4⋊C4×C31—44no—
251C4⋊C4×C31—44no—
252C4⋊C4×C31—44no—
253C42×C31—28no—
254#16524C3111yesmaximal, characteristic, direct product factor, Sylow
255C23×C31C22×D411yescharacteristic
256C23×C31C22×D411yescharacteristic
257C23×C31C22×Q811yescharacteristic
258C23×C31C22×Q811yescharacteristic
259C23×C31C2×#4111yescharacteristic
260C23×C31C2×#4111yescharacteristic
261C23×C31C2×#4111yescharacteristic
262C23×C31H(5,𝔽2)11yescharacteristic
263C23×C31H(5,𝔽2)11yescharacteristic
264C23×C31H(5,𝔽2)11yescharacteristic
265C23×C31H(5,𝔽2)11yescharacteristic
266C23×C312−1+411yescharacteristic
267C23×C312−1+411yescharacteristic
268C23×C312−1+411yescharacteristic
269C23×C312−1+411yescharacteristic
270Q8×C31—416no—
271C2×C4×C31—22no—
272C2×C4×C31—22no—
273C2×C4×C31—22no—
274C2×C4×C31—22no—
275C2×C4×C31—22no—
276C2×C4×C31—22no—
277C2×C4×C31—22no—
278C2×C4×C31—22no—
279C2×C4×C31—22no—
280C2×C4×C31—22no—
281C2×C4×C31—22no—
282C2×C4×C31—22no—
283C2×C4×C31—22no—
284C2×C4×C31—22no—
285C2×C4×C31—22no—
286C2×C4×C31—22no—
287C2×C4×C31—22no—
288C2×C4×C31—22no—
289C2×C4×C31—22no—
290C2×C4×C31—22no—
291C2×C4×C31—22no—
292C2×C4×C31—22no—
293C2×C4×C31—22no—
294C2×C4×C31—22no—
295C2×C4×C31—22no—
296C2×C4×C31—22no—
297C2×C4×C31—22no—
298C2×C4×C31—22no—
299C2×C4×C31—22no—
300C2×C4×C31—22no—
301C2×C4×C31—22no—
302C2×C4×C31—22no—
303C2×C4×C31—22no—
304C2×C4×C31—22no—
305C2×C4×C31—22no—
306C2×C4×C31—22no—
307C2×C4×C31—22no—
308C2×C4×C31—22no—
309C2×C4×C31—22no—
310C2×C4×C31—41no—
311C2×C4×C31—41no—
312C2×C4×C31—41no—
313C2×C4×C31—41no—
314C2×C4×C31—41no—
315C2×C4×C31—41no—
316C2×C4×C31—41no—
317C2×C4×C31—41no—
318C2×C4×C31—41no—
319C2×C4×C31—41no—
320C2×C4×C31—41no—
321C2×C4×C31—41no—
322C2×C4×C31—41no—
323C2×C4×C31—41no—
324C2×C4×C31—41no—
325C2×C4×C31—41no—
326C2×C4×C31—41no—
327C2×C4×C31—41no—
328C2×C4×C31—41no—
329C2×C4×C31—41no—
330C2×C4×C31—41no—
331C2×C4×C31—41no—
332C2×C4×C31—41no—
333C2×C4×C31—41no—
334C2×C4×C31—41no—
335C2×C4×C31—41no—
336C2×C4×C31—41no—
337C2×C4×C31—41no—
338C2×C4×C31—41no—
339C2×C4×C31—41no—
340C2×C4×C31—41no—
341C2×C4×C31—41no—
342C2×C4×C31—41no—
343C2×C4×C31—41no—
344C2×C4×C31—41no—
345C2×C4×C31—41no—
346C2×C4×C31—41no—
347C2×C4×C31—41no—
348C2×C4×C31—41no—
349C2×C4×C31—41no—
350C2×C4×C31—41no—
351C2×C4×C31—41no—
352C2×C4×C31—41no—
353C2×C4×C31—41no—
354C2×C4×C31—41no—
355C2×C4×C31—41no—
356C2×C4×C31—41no—
357C2×C4×C31—41no—
358C2×C4×C31—41no—
359C2×C4×C31—41no—
360C2×C4×C31—41no—
361C2×C4×C31—41no—
362C2×C4×C31—41no—
363C2×C4×C31—41no—
364C2×C4×C31—41no—
365C2×C4×C31—41no—
366C2×C4×C31—41no—
367C2×C4×C31—41no—
368C2×C4×C31—41no—
369C2×C4×C31—41no—
370C2×C4×C31—41no—
371C2×C4×C31—41no—
372C2×C4×C31—41no—
373C2×C4×C31—41no—
374C2×C4×C31C22⋊Q814yes—
375C2×C4×C31C4⋊Q814yes—
376C2×#400C2×C3111yescharacteristic
377C2×#395C2×C3111yescharacteristic
378C2×#395C2×C3111yescharacteristic
379C2×#382C2×C3111yescharacteristic
380#1446C2×C3111yescharacteristic
381#1445C2×C3111yescharacteristic
382#1444C2×C3111yescharacteristic
383#1444C2×C3111yescharacteristic
384#1444C2×C3111yescharacteristic
385#1442C2×C3111yescharacteristic
386#1442C2×C3111yescharacteristic
387#1442C2×C3111yescharacteristic
388#1441C2×C3111yescharacteristic
389C4⋊#95C2×C3111yescharacteristic
390#1434C2×C3111yescharacteristic
391C22×C31C2×C22⋊Q811yescharacteristic
392C22×C31C2×C4⋊Q811yescharacteristic
393C22×C31#53311yescharacteristic
394C22×C31#53511yescharacteristic
395C22×C31#53511yescharacteristic
396C22×C31#53611yescharacteristic
397C22×C31#53611yescharacteristic
398C22×C31#53811yescharacteristic
399C22×C31#53911yescharacteristic
400C22×C31#54111yescharacteristic
401C22×C31#54211yescharacteristic
402C22×C31#54211yescharacteristic
403C22×C31#54211yescharacteristic
404C22×C31#54411yescharacteristic
405C22×C31#54411yescharacteristic
406C22×C31#54411yescharacteristic
407C22×C31#54411yescharacteristic
408C22×C31#54411yescharacteristic
409C22×C31#54411yescharacteristic
410C22×C31D4211yescharacteristic
411C22×C31#54611yescharacteristic
412C22×C31#54611yescharacteristic
413C22×C31#54711yescharacteristic
414C22×C31#54711yescharacteristic
415C22×C31#54811yescharacteristic
416C22×C31D4×Q811yescharacteristic
417C22×C31#55111yescharacteristic
418C22×C31#55211yescharacteristic
419C22×C31#55411yescharacteristic
420C22×C31#55411yescharacteristic
421C22×C31#55711yescharacteristic
422C22×C31H(3,𝔽4)11yescharacteristic
423C22×C31#56311yescharacteristic
424C22×C31#56311yescharacteristic
425C22×C31#56311yescharacteristic
426C4×C31—24no—
427C4×C31—24no—
428C4×C31—42no—
429C4×C31—42no—
430C4×C31—42no—
431C4×C31—42no—
432C4×C31—42no—
433C4×C31—42no—
434C4×C31—42no—
435C4×C31—42no—
436C4×C31—42no—
437C4×C31—81no—
438C4×C31—81no—
439C4×C31—81no—
440C4×C31—81no—
441C23×Q8C22×C3111yescharacteristic
442C22×C4⋊C4C22×C3111yescharacteristic
443C22×C4⋊C4C22×C3111yescharacteristic
444C22×C4⋊C4C22×C3111yescharacteristic
445C22×C4⋊C4C22×C3111yescharacteristic
446C22×C4⋊C4C22×C3111yescharacteristic
447C22×C4⋊C4C22×C3111yescharacteristic
448C22×C4⋊C4C22×C3111yescharacteristic
449C22×C4⋊C4C22×C3111yescharacteristic
450C22×C4⋊C4C22×C3111yescharacteristic
451C22×C42C22×C3111yescharacteristic
452#400—24no—
453#395—24no—
454#395—24no—
455#382—24no—
456C2×#95C22×C3111yescharacteristic
457C2×#95C22×C3111yescharacteristic
458C2×#95C22×C3111yescharacteristic
459C2×#95C22×C3111yescharacteristic
460C2×#95C22×C3111yescharacteristic
461C2×#95C22×C3111yescharacteristic
462C2×#95C22×C3111yescharacteristic
463C2×#95C22×C3111yescharacteristic
464C2×#95C22×C3111yescharacteristic
465C2×#95C22×C3111yescharacteristic
466C2×#95C22×C3111yescharacteristic
467C2×#95C22×C3111yescharacteristic
468C2×#95C22×C3111yescharacteristic
469C2×#95C22×C3111yescharacteristic
470C2×#95C22×C3111yescharacteristic
471C2×#95C22×C3111yescharacteristic
472C2×#95C22×C3111yescharacteristic
473C2×#95C22×C3111yescharacteristic
474C2×#95C22×C3111yescharacteristic
475C2×#95C22×C3111yescharacteristic
476C2×#95C22×C3111yescharacteristic
477C2×#95C22×C3111yescharacteristic
478C2×#95C22×C3111yescharacteristic
479C2×#95C22×C3111yescharacteristic
480C2×C31#243811yescharacteristic
481C2×C31#244011yescharacteristic
482C2×C31#255011yescharacteristic
483C2×C31#262811yescharacteristic
484C2×C31#266011yescharacteristic
485C2×C31#266611yescharacteristic
486C2×C31#267011yescharacteristic
487C2×C31#267411yescharacteristic
488C2×C31#269811yescharacteristic
489C2×C31#271311yescharacteristic
490C2×C31#272011yescharacteristic
491C2×C31#272311yescharacteristic
492C2×C31#276311yescharacteristic
493C2×C31#277411yescharacteristic
494C2×C31#284411yescharacteristic
495C22×Q8—22no—
496C22×Q8—22no—
497C22×Q8—22no—
498C22×Q8—41no—
499C22×Q8—41no—
500C22×Q8—41no—
501C22×Q8—41no—
502C23×C4C23×C3111yescharacteristic
503C23×C4C23×C3111yescharacteristic
504C23×C4C23×C3111yescharacteristic
505C23×C4C23×C3111yescharacteristic
506C23×C4C23×C3111yescharacteristic
507C23×C4C23×C3111yescharacteristic
508C23×C4C23×C3111yescharacteristic
509C23×C4C23×C3111yescharacteristic
510C23×C4C23×C3111yescharacteristic
511C23×C4C23×C3111yescharacteristic
512C23×C4C23×C3111yescharacteristic
513C23×C4C23×C3111yescharacteristic
514C23×C4C23×C3111yescharacteristic
515C23×C4C23×C3111yescharacteristic
516C23×C4C23×C3111yescharacteristic
517C2×C4⋊C4—22no—
518C2×C4⋊C4—22no—
519C2×C4⋊C4—22no—
520C2×C4⋊C4—22no—
521C2×C4⋊C4—22no—
522C2×C4⋊C4—22no—
523C2×C4⋊C4—22no—
524C2×C4⋊C4—22no—
525C2×C4⋊C4—22no—
526C2×C4⋊C4—22no—
527C2×C4⋊C4—22no—
528C2×C4⋊C4—22no—
529C2×C4⋊C4—22no—
530C2×C4⋊C4—22no—
531C2×C4⋊C4—41no—
532C2×C4⋊C4—41no—
533C2×C4⋊C4—41no—
534C2×C4⋊C4—41no—
535C2×C4⋊C4—41no—
536C2×C4⋊C4—41no—
537C2×C4⋊C4—41no—
538C2×C4⋊C4—41no—
539C2×C4⋊C4—41no—
540C2×C4⋊C4—41no—
541C2×C4⋊C4—41no—
542C2×C4⋊C4—41no—
543C2×C4⋊C4—41no—
544C2×C42—22no—
545C2×C42—22no—
546C2×C42Q8×C3114yescomplemented
547#95—22no—
548#95—22no—
549#95—22no—
550#95—22no—
551#95—22no—
552#95—22no—
553#95—22no—
554#95—22no—
555#95—22no—
556#95—22no—
557#95—22no—
558#95—22no—
559#95—22no—
560#95—22no—
561#95—41no—
562#95—41no—
563#95—41no—
564#95—41no—
565#95—41no—
566#95—41no—
567#95—41no—
568#95D4×C3114yes—
569#95D4×C3114yes—
570#95Q8×C3114yescomplemented
571C31#1652411yescharacteristic, direct product factor, Sylow
572C24C24×C3111yescharacteristic
573C2×Q8—44no—
574C2×Q8—44no—
575C2×Q8—44no—
576C2×Q8—44no—
577C2×Q8—44no—
578C2×Q8—44no—
579C2×Q8—44no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4C2×D4×C3112yes—
671C22×C4C2×D4×C3112yes—
672C22×C4C2×D4×C3112yes—
673C22×C4C2×D4×C3112yes—
674C22×C4C2×D4×C3112yes—
675C22×C4C2×D4×C3112yes—
676C22×C4C2×Q8×C3112yes—
677C22×C4C2×Q8×C3112yes—
678C22×C4C2×Q8×C3112yes—
679C22×C4C2×Q8×C3112yes—
680C22×C4C2×Q8×C3112yes—
681C22×C4C2×Q8×C3112yes—
682C22×C4#41×C3112yes—
683C22×C4#41×C3112yes—
684C22×C4#41×C3112yes—
685C4⋊C4—44no—
686C4⋊C4—44no—
687C4⋊C4—44no—
688C4⋊C4—44no—
689C4⋊C4—44no—
690C4⋊C4—44no—
691C4⋊C4—44no—
692C4⋊C4—44no—
693C4⋊C4—44no—
694C42—28no—
695C23C22×D4×C3111yescharacteristic
696C23C22×D4×C3111yescharacteristic
697C23C22×Q8×C3111yescharacteristic
698C23C22×Q8×C3111yescharacteristic
699C23C2×#41×C3111yescharacteristic
700C23C2×#41×C3111yescharacteristic
701C23C2×#41×C3111yescharacteristic
702C23C31×H(5,𝔽2)11yescharacteristic
703C23C31×H(5,𝔽2)11yescharacteristic
704C23C31×H(5,𝔽2)11yescharacteristic
705C23C31×H(5,𝔽2)11yescharacteristic
706C23C31×2−1+411yescharacteristic
707C23C31×2−1+411yescharacteristic
708C23C31×2−1+411yescharacteristic
709C23C31×2−1+411yescharacteristic
710Q8—416no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4C31×C22⋊Q814yes—
815C2×C4C31×C4⋊Q814yes—
816C22C2×C31×C22⋊Q811yescharacteristic
817C22C2×C31×C4⋊Q811yescharacteristic
818C22C31×#53311yescharacteristic
819C22C31×#53511yescharacteristic
820C22C31×#53511yescharacteristic
821C22C31×#53611yescharacteristic
822C22C31×#53611yescharacteristic
823C22C31×#53811yescharacteristic
824C22C31×#53911yescharacteristic
825C22C31×#54111yescharacteristic
826C22C31×#54211yescharacteristic
827C22C31×#54211yescharacteristic
828C22C31×#54211yescharacteristic
829C22C31×#54411yescharacteristic
830C22C31×#54411yescharacteristic
831C22C31×#54411yescharacteristic
832C22C31×#54411yescharacteristic
833C22C31×#54411yescharacteristic
834C22C31×#54411yescharacteristic
835C22D42×C3111yescharacteristic
836C22C31×#54611yescharacteristic
837C22C31×#54611yescharacteristic
838C22C31×#54711yescharacteristic
839C22C31×#54711yescharacteristic
840C22C31×#54811yescharacteristic
841C22D4×Q8×C3111yescharacteristic
842C22C31×#55111yescharacteristic
843C22C31×#55211yescharacteristic
844C22C31×#55411yescharacteristic
845C22C31×#55411yescharacteristic
846C22C31×#55711yescharacteristic
847C22C31×H(3,𝔽4)11yescharacteristic
848C22C31×#56311yescharacteristic
849C22C31×#56311yescharacteristic
850C22C31×#56311yescharacteristic
851C4—24no—
852C4—24no—
853C4—42no—
854C4—42no—
855C4—42no—
856C4—42no—
857C4—42no—
858C4—42no—
859C4—42no—
860C4—42no—
861C4—42no—
862C4—81no—
863C4—81no—
864C4—81no—
865C4—81no—
866C2C31×#243811yescharacteristic
867C2C31×#244011yescharacteristic
868C2C31×#255011yescharacteristic
869C2C31×#262811yescharacteristic
870C2C31×#266011yescharacteristic
871C2C31×#266611yescharacteristic
872C2C31×#267011yescharacteristic
873C2C31×#267411yescharacteristic
874C2C31×#269811yescharacteristic
875C2C31×#271311yescharacteristic
876C2C31×#272011yescharacteristic
877C2C31×#272311yescharacteristic
878C2C31×#276311yescharacteristic
879C2C31×#277411yescharacteristic
880C2C31×#284411yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C31C24
commutator, Frattini, cosocleC24C24×C31
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
106. C2×C42×C31Q8semidirect
130. C31×#95Q8semidirect
254. #16524C31direct (N × H)
546. C2×C42Q8×C31semidirect
570. #95Q8×C31semidirect
571. C31#16524direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4002
C2×C31×#3952
C2×C31×#3822
C31×#14462
C31×#14452
C31×#14442
C31×#14422
C31×#14412
C31×C4⋊#952
C31×#14342
#1652431