Finite Group Databasebeta

← C31×#22429 #21479188

Subgroups — C31×#22429 #21479188

Order 7936.

1466 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#548C211yesmaximal, characteristic
2C2×C31×#436C211yesmaximal, characteristic, complemented
3C2×C31×#417C211yesmaximal, characteristic, complemented
4C2×C31×#419C211yesmaximal, characteristic, complemented
5C31×#2352C211yesmaximal, characteristic, complemented
6C31×#1983C211yesmaximal, characteristic, complemented
7C31×#1958C211yesmaximal, characteristic, complemented
8C31×#1895C211yesmaximal, characteristic, complemented
9C31×#1894C211yesmaximal, characteristic, complemented
10C31×#1875C211yesmaximal, characteristic, complemented
11C31×#1872C211yesmaximal, characteristic, complemented
12C31×#1805C211yesmaximal, characteristic, complemented
13C31×#1788C211yesmaximal, characteristic, complemented
14C31×#1787C211yesmaximal, characteristic, complemented
15C4×C31×#103C211yesmaximal, characteristic, complemented
16C22×#41×C31C2211yescharacteristic
17C23×Q8×C31C2211yescharacteristic
18C22×M16×C31C2211yescharacteristic
19C22×M16×C31C2211yescharacteristic
20C31×#548—24no—
21C31×#548C418yescomplemented
22C2×C31×#124—21no—
23C2×C31×#124C2211yescharacteristic
24C2×C31×C22⋊Q8—21no—
25C2×C31×C22⋊Q8C2211yescharacteristic
26C2×C31×#121—21no—
27C2×C31×#121C2211yescharacteristic
28C2×C4×Q8×C31C2211yescharacteristic
29C2×C4×D4×C31—21no—
30C2×C4×D4×C31C2211yescharacteristic
31C2×C31×#117C2211yescharacteristic
32C22×C4⋊C4×C31C2211yescharacteristic
33C31×#436—24no—
34C2×C31×C4⋊C8C2211yescharacteristic
35C31×#419—24no—
36C31×#417—24no—
37C2×C31×#103C2211yescharacteristic
38C2×C31×#103C2211yescharacteristic
39C2×C31×#103C2211yescharacteristic
40C2×C31×#103C2211yescharacteristic
41C2×C31×#103C2211yescharacteristic
42C2×C31×#103C2211yescharacteristic
43C2×C31×#103C2211yescharacteristic
44C2×C31×#103C2211yescharacteristic
45C2×C31×#102C2211yescharacteristic
46C2×C31×#102C2211yescharacteristic
47C2×C31×#102C2211yescharacteristic
48C2×C31×#102C2211yescharacteristic
49C2×C31×C22⋊C8C2211yescharacteristic
50C2×C31×C22⋊C8C2211yescharacteristic
51C2×C4×C8×C31C2211yescharacteristic
52C31×#388—21no—
53C31×#387—21no—
54C31×#386—21no—
55C31×#382C2211yescharacteristic
56C31×#380C2211yescharacteristic
57C31×#380C2211yescharacteristic
58C4×C4⋊C4×C31C2211yescharacteristic
59C4×C22⋊C4×C31—21no—
60C31×#340C2211yescharacteristic
61C31×#340C2211yescharacteristic
62C31×#340C2211yescharacteristic
63C31×#340C2211yescharacteristic
64C2×#41×C31—22no—
65C2×#41×C31—22no—
66C2×#41×C31—22no—
67C2×#41×C31—41no—
68C2×#41×C31—41no—
69C2×#41×C31C2×C414yes—
70C22×Q8×C31—21no—
71C22×Q8×C31—22no—
72C22×Q8×C31—22no—
73C22×Q8×C31—22no—
74C22×Q8×C31—41no—
75C22×Q8×C31—41no—
76C22×Q8×C31C2×C414yescomplemented
77C22×Q8×C31C2311yescharacteristic
78C22×Q8×C31C2311yescharacteristic
79C22×D4×C31—21no—
80C22×D4×C31—21no—
81C22×D4×C31D411yescharacteristic
82C22×D4×C31C2311yescharacteristic
83C23×C4×C31—21no—
84C23×C4×C31—21no—
85C23×C4×C31—21no—
86C23×C4×C31C2311yescharacteristic
87C23×C4×C31C2311yescharacteristic
88C2×M16×C31—22no—
89C2×M16×C31—22no—
90C2×M16×C31—22no—
91C2×M16×C31—22no—
92C2×M16×C31—41no—
93C2×M16×C31—41no—
94C22×C8×C31C2311yescharacteristic
95C22×C8×C31C2311yescharacteristic
96C22×C8×C31C2311yescharacteristic
97C22×C8×C31C2311yescharacteristic
98C31×#124—28no—
99C31×#124—22no—
100C31×#124C2×C414yescomplemented
101C31×C22⋊Q8—22no—
102C31×C22⋊Q8—28no—
103C31×C22⋊Q8C2×C414yes—
104C31×#121—28no—
105C31×#121—22no—
106C31×#121C2×C414yescomplemented
107C4×Q8×C31—22no—
108C4×Q8×C31C2×C414yescomplemented
109C4×D4×C31—28no—
110C4×D4×C31C2×C414yes—
111C4×D4×C31D414yes—
112C31×#117—22no—
113C31×#117—41no—
114C2×C4⋊C4×C31—21no—
115C2×C4⋊C4×C31—21no—
116C2×C4⋊C4×C31—22no—
117C2×C4⋊C4×C31—21no—
118C2×C4⋊C4×C31—41no—
119C2×C4⋊C4×C31D411yescharacteristic
120C2×C4⋊C4×C31C2311yescharacteristic
121C2×C4⋊C4×C31C2311yescharacteristic
122C2×C4⋊C4×C31C2311yescharacteristic
123C2×C4⋊C4×C31C2311yescharacteristic
124C2×C4⋊C4×C31C2311yescharacteristic
125C2×C22⋊C4×C31—21no—
126C2×C22⋊C4×C31—21no—
127C2×C22⋊C4×C31—21no—
128C2×C22⋊C4×C31—21no—
129C2×C22⋊C4×C31—21no—
130C2×C22⋊C4×C31—21no—
131C2×C22⋊C4×C31—21no—
132C2×C22⋊C4×C31D411yescharacteristic
133C2×C22⋊C4×C31D411yescharacteristic
134C2×C42×C31—21no—
135C2×C42×C31—21no—
136C2×C42×C31—21no—
137C2×C42×C31C2311yescharacteristic
138C31×C4⋊C8—22no—
139C31×#103—22no—
140C31×#103—22no—
141C31×#103—22no—
142C31×#103—22no—
143C31×#103—22no—
144C31×#103—41no—
145C31×#103—41no—
146C31×#103D414yescomplemented
147C31×#102—22no—
148C31×#102—22no—
149C31×#102—41no—
150C31×#102—41no—
151C31×C22⋊C8—22no—
152C31×C22⋊C8—22no—
153C4×C8×C31—22no—
154C31×#95—21no—
155C31×#95—21no—
156C31×#95—21no—
157C31×#95—21no—
158C31×#95—21no—
159C24×C31—21no—
160C24×C31C2×D411yescharacteristic
161C24×C31C2×D411yescharacteristic
162#41×C31—28no—
163#41×C31—44no—
164#41×C31—44no—
165#41×C31—44no—
166C2×Q8×C31—24no—
167C2×Q8×C31—21no—
168C2×Q8×C31—21no—
169C2×Q8×C31—21no—
170C2×Q8×C31—21no—
171C2×Q8×C31—28no—
172C2×Q8×C31—21no—
173C2×Q8×C31—21no—
174C2×Q8×C31—21no—
175C2×Q8×C31—21no—
176C2×Q8×C31—42no—
177C2×Q8×C31—42no—
178C2×Q8×C31—44no—
179C2×Q8×C31—44no—
180C2×Q8×C31—44no—
181C2×Q8×C31C22×C412yes—
182C2×Q8×C31C22×C412yes—
183C2×Q8×C31C2×D412yes—
184C2×Q8×C31#4112yes—
185C2×D4×C31—24no—
186C2×D4×C31—24no—
187C2×D4×C31—21no—
188C2×D4×C31—21no—
189C2×D4×C31—21no—
190C2×D4×C31—21no—
191C2×D4×C31—21no—
192C2×D4×C31—41no—
193C2×D4×C31—41no—
194C2×D4×C31—42no—
195C2×D4×C31—42no—
196C2×D4×C31—42no—
197C2×D4×C31—42no—
198C2×D4×C31C22⋊C414yes—
199C2×D4×C31C22×C412yes—
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—24no—
210C22×C4×C31—21no—
211C22×C4×C31—21no—
212C22×C4×C31—21no—
213C22×C4×C31—24no—
214C22×C4×C31—21no—
215C22×C4×C31—21no—
216C22×C4×C31—21no—
217C22×C4×C31—42no—
218C22×C4×C31—42no—
219C22×C4×C31—42no—
220C22×C4×C31—42no—
221C22×C4×C31—42no—
222C22×C4×C31—42no—
223C22×C4×C31—81no—
224C22×C4×C31C22×C412yes—
225C22×C4×C31C22×C412yes—
226C22×C4×C31C2×D411yescharacteristic
227C22×C4×C31C2×D411yescharacteristic
228C22×C4×C31C2×D411yescharacteristic
229C22×C4×C31C2×D411yescharacteristic
230C22×C4×C31C2×D412yes—
231C22×C4×C31C2×D412yes—
232C22×C4×C31C2411yescharacteristic
233M16×C31—44no—
234M16×C31—44no—
235C2×C8×C31—21no—
236C2×C8×C31—21no—
237C2×C8×C31—21no—
238C2×C8×C31—21no—
239C2×C8×C31—21no—
240C2×C8×C31—21no—
241C2×C8×C31—21no—
242C2×C8×C31—21no—
243C2×C8×C31—21no—
244C2×C8×C31—21no—
245C2×C8×C31—21no—
246C2×C8×C31C2×D412yes—
247C4⋊C4×C31—24no—
248C4⋊C4×C31—24no—
249C4⋊C4×C31—21no—
250C4⋊C4×C31—21no—
251C4⋊C4×C31—21no—
252C4⋊C4×C31—21no—
253C4⋊C4×C31—21no—
254C4⋊C4×C31—21no—
255C4⋊C4×C31—21no—
256C4⋊C4×C31—21no—
257C4⋊C4×C31—42no—
258C4⋊C4×C31C22⋊C414yes—
259C4⋊C4×C31C22×C412yes—
260C4⋊C4×C31C2×D412yes—
261C22⋊C4×C31—24no—
262C22⋊C4×C31—24no—
263C22⋊C4×C31—24no—
264C22⋊C4×C31—24no—
265C22⋊C4×C31—42no—
266C22⋊C4×C31—42no—
267C22⋊C4×C31—81no—
268C22⋊C4×C31C22⋊C414yes—
269C22⋊C4×C31C22⋊C414yes—
270C42×C31—24no—
271C42×C31—42no—
272C42×C31—81no—
273C42×C31C22×C412yes—
274C42×C31C2×D412yes—
275#22429C3111yesmaximal, characteristic, direct product factor, Sylow
276C23×C31—21no—
277C23×C31—21no—
278C23×C31—21no—
279C23×C31—21no—
280C23×C31—21no—
281C23×C31—21no—
282C23×C31—21no—
283C23×C31—21no—
284C23×C31—21no—
285C23×C31—21no—
286C23×C31—21no—
287C23×C31—21no—
288C23×C31—22no—
289C23×C31—41no—
290C23×C31—41no—
291C23×C31—41no—
292C23×C31—41no—
293C23×C31—41no—
294C23×C31—41no—
295C23×C31C2×C22⋊C412yes—
296C23×C31C2×C22⋊C412yes—
297C23×C31C22×D411yescharacteristic
298Q8×C31—22no—
299Q8×C31—22no—
300Q8×C31—22no—
301Q8×C31—22no—
302Q8×C31—22no—
303Q8×C31—48no—
304Q8×C31—41no—
305Q8×C31—41no—
306Q8×C31C4×D414yes—
307D4×C31—22no—
308D4×C31—22no—
309D4×C31—44no—
310D4×C31—48no—
311D4×C31—48no—
312D4×C31—41no—
313D4×C31—41no—
314C2×C4×C31—22no—
315C2×C4×C31—21no—
316C2×C4×C31—21no—
317C2×C4×C31—22no—
318C2×C4×C31—21no—
319C2×C4×C31—21no—
320C2×C4×C31—22no—
321C2×C4×C31—21no—
322C2×C4×C31—21no—
323C2×C4×C31—21no—
324C2×C4×C31—21no—
325C2×C4×C31—22no—
326C2×C4×C31—22no—
327C2×C4×C31—22no—
328C2×C4×C31—22no—
329C2×C4×C31—22no—
330C2×C4×C31—22no—
331C2×C4×C31—22no—
332C2×C4×C31—22no—
333C2×C4×C31—22no—
334C2×C4×C31—22no—
335C2×C4×C31—22no—
336C2×C4×C31—48no—
337C2×C4×C31—48no—
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—84no—
354C2×C4×C31C2×C22⋊C412yes—
355C2×C4×C31C2×C22⋊C412yes—
356C2×C4×C31C2×C22⋊C412yes—
357C2×C4×C31C2×C22⋊C412yes—
358C2×C4×C31C23×C411yescharacteristic
359C2×C4×C31C22×D411yescharacteristic
360C2×C4×C31C22×D411yescharacteristic
361C2×C4×C31C2×#4111yescharacteristic
362C2×C4×C31H(5,𝔽2)11yescharacteristic
363C2×C4×C31H(5,𝔽2)11yescharacteristic
364C8×C31—22no—
365C8×C31—41no—
366C8×C31—41no—
367C8×C31—41no—
368C2×#548C2×C3111yescharacteristic
369C2×#436C2×C3111yescharacteristic, complemented
370C2×#417C2×C3111yescharacteristic, complemented
371C2×#419C2×C3111yescharacteristic, complemented
372#2352C2×C3111yescharacteristic, complemented
373#1983C2×C3111yescharacteristic, complemented
374#1958C2×C3111yescharacteristic, complemented
375#1895C2×C3111yescharacteristic, complemented
376#1894C2×C3111yescharacteristic, complemented
377#1875C2×C3111yescharacteristic, complemented
378#1872C2×C3111yescharacteristic, complemented
379#1805C2×C3111yescharacteristic, complemented
380#1788C2×C3111yescharacteristic, complemented
381#1787C2×C3111yescharacteristic, complemented
382C4×#103C2×C3111yescharacteristic, complemented
383C22×C31—22no—
384C22×C31—22no—
385C22×C31—22no—
386C22×C31—22no—
387C22×C31—22no—
388C22×C31—22no—
389C22×C31—41no—
390C22×C31—41no—
391C22×C31—41no—
392C22×C31—41no—
393C22×C31—41no—
394C22×C31—41no—
395C22×C31—41no—
396C22×C31—41no—
397C22×C31—42no—
398C22×C31—42no—
399C22×C31—42no—
400C22×C31—81no—
401C22×C31—81no—
402C22×C31—81no—
403C22×C31—81no—
404C22×C31C22×C22⋊C411yescharacteristic
405C22×C31D4211yescharacteristic
406C22×C31#54611yescharacteristic
407C22×C31#57511yescharacteristic
408C22×C31#57511yescharacteristic
409C22×C31#57711yescharacteristic
410C22×C31#57811yescharacteristic
411C4×C31—22no—
412C4×C31—22no—
413C4×C31—24no—
414C4×C31—22no—
415C4×C31—22no—
416C4×C31—42no—
417C4×C31—42no—
418C4×C31—42no—
419C4×C31—81no—
420C4×C31—81no—
421C4×C31—81no—
422C4×C31C2×C4×D411yescharacteristic
423C4×C31#51811yescharacteristic
424C4×C31D4211yescharacteristic
425C4×C31#54611yescharacteristic
426C22×#41C22×C3111yescharacteristic
427C23×Q8C22×C3111yescharacteristic
428C22×M16C22×C3111yescharacteristic
429C22×M16C22×C3111yescharacteristic
430#548—24no—
431#548C4×C3118yescomplemented
432C2×#124—21no—
433C2×#124C22×C3111yescharacteristic
434C2×C22⋊Q8—21no—
435C2×C22⋊Q8C22×C3111yescharacteristic
436C2×#121—21no—
437C2×#121C22×C3111yescharacteristic
438C2×C4×Q8C22×C3111yescharacteristic
439C2×C4×D4—21no—
440C2×C4×D4C22×C3111yescharacteristic
441C2×#117C22×C3111yescharacteristic
442C22×C4⋊C4C22×C3111yescharacteristic
443#436—24no—
444C2×C4⋊C8C22×C3111yescharacteristic
445#419—24no—
446#417—24no—
447C2×#103C22×C3111yescharacteristic
448C2×#103C22×C3111yescharacteristic
449C2×#103C22×C3111yescharacteristic
450C2×#103C22×C3111yescharacteristic
451C2×#103C22×C3111yescharacteristic
452C2×#103C22×C3111yescharacteristic
453C2×#103C22×C3111yescharacteristic
454C2×#103C22×C3111yescharacteristic
455C2×#102C22×C3111yescharacteristic
456C2×#102C22×C3111yescharacteristic
457C2×#102C22×C3111yescharacteristic
458C2×#102C22×C3111yescharacteristic
459C2×C22⋊C8C22×C3111yescharacteristic
460C2×C22⋊C8C22×C3111yescharacteristic
461C2×C4×C8C22×C3111yescharacteristic
462#388—21no—
463#387—21no—
464#386—21no—
465#382C22×C3111yescharacteristic
466#380C22×C3111yescharacteristic
467#380C22×C3111yescharacteristic
468C4×C4⋊C4C22×C3111yescharacteristic
469C4×C22⋊C4—21no—
470#340C22×C3111yescharacteristic
471#340C22×C3111yescharacteristic
472#340C22×C3111yescharacteristic
473#340C22×C3111yescharacteristic
474C2×C31—42no—
475C2×C31—42no—
476C2×C31—82no—
477C2×C31D4×C22⋊C411yescharacteristic
478C2×C31#289611yescharacteristic
479C2×C31#289811yescharacteristic
480C2×C31#327511yescharacteristic
481C2×C31#327711yescharacteristic
482C2×C31#332611yescharacteristic
483C2×C31#332711yescharacteristic
484C2×#41—22no—
485C2×#41—22no—
486C2×#41—22no—
487C2×#41—41no—
488C2×#41—41no—
489C2×#41C2×C4×C3114yes—
490C22×Q8—21no—
491C22×Q8—22no—
492C22×Q8—22no—
493C22×Q8—22no—
494C22×Q8—41no—
495C22×Q8—41no—
496C22×Q8C2×C4×C3114yescomplemented
497C22×Q8C23×C3111yescharacteristic
498C22×Q8C23×C3111yescharacteristic
499C22×D4—21no—
500C22×D4—21no—
501C22×D4D4×C3111yescharacteristic
502C22×D4C23×C3111yescharacteristic
503C23×C4—21no—
504C23×C4—21no—
505C23×C4—21no—
506C23×C4C23×C3111yescharacteristic
507C23×C4C23×C3111yescharacteristic
508C2×M16—22no—
509C2×M16—22no—
510C2×M16—22no—
511C2×M16—22no—
512C2×M16—41no—
513C2×M16—41no—
514C22×C8C23×C3111yescharacteristic
515C22×C8C23×C3111yescharacteristic
516C22×C8C23×C3111yescharacteristic
517C22×C8C23×C3111yescharacteristic
518#124—28no—
519#124—22no—
520#124C2×C4×C3114yescomplemented
521C22⋊Q8—22no—
522C22⋊Q8—28no—
523C22⋊Q8C2×C4×C3114yes—
524#121—28no—
525#121—22no—
526#121C2×C4×C3114yescomplemented
527C4×Q8—22no—
528C4×Q8C2×C4×C3114yescomplemented
529C4×D4—28no—
530C4×D4C2×C4×C3114yes—
531C4×D4D4×C3114yes—
532#117—22no—
533#117—41no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—22no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—41no—
539C2×C4⋊C4D4×C3111yescharacteristic
540C2×C4⋊C4C23×C3111yescharacteristic
541C2×C4⋊C4C23×C3111yescharacteristic
542C2×C4⋊C4C23×C3111yescharacteristic
543C2×C4⋊C4C23×C3111yescharacteristic
544C2×C4⋊C4C23×C3111yescharacteristic
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4D4×C3111yescharacteristic
553C2×C22⋊C4D4×C3111yescharacteristic
554C2×C42—21no—
555C2×C42—21no—
556C2×C42—21no—
557C2×C42C23×C3111yescharacteristic
558C4⋊C8—22no—
559#103—22no—
560#103—22no—
561#103—22no—
562#103—22no—
563#103—22no—
564#103—41no—
565#103—41no—
566#103D4×C3114yescomplemented
567#102—22no—
568#102—22no—
569#102—41no—
570#102—41no—
571C22⋊C8—22no—
572C22⋊C8—22no—
573C4×C8—22no—
574#95—21no—
575#95—21no—
576#95—21no—
577#95—21no—
578#95—21no—
579C31#2242911yescharacteristic, direct product factor, Sylow
580C24—21no—
581C24C2×D4×C3111yescharacteristic
582C24C2×D4×C3111yescharacteristic
583#41—28no—
584#41—44no—
585#41—44no—
586#41—44no—
587C2×Q8—24no—
588C2×Q8—21no—
589C2×Q8—21no—
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—28no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—42no—
598C2×Q8—42no—
599C2×Q8—44no—
600C2×Q8—44no—
601C2×Q8—44no—
602C2×Q8C22×C4×C3112yes—
603C2×Q8C22×C4×C3112yes—
604C2×Q8C2×D4×C3112yes—
605C2×Q8#41×C3112yes—
606C2×D4—24no—
607C2×D4—24no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—21no—
612C2×D4—21no—
613C2×D4—41no—
614C2×D4—41no—
615C2×D4—42no—
616C2×D4—42no—
617C2×D4—42no—
618C2×D4—42no—
619C2×D4C22⋊C4×C3114yes—
620C2×D4C22×C4×C3112yes—
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—24no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—24no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—42no—
639C22×C4—42no—
640C22×C4—42no—
641C22×C4—42no—
642C22×C4—42no—
643C22×C4—42no—
644C22×C4—81no—
645C22×C4C22×C4×C3112yes—
646C22×C4C22×C4×C3112yes—
647C22×C4C2×D4×C3111yescharacteristic
648C22×C4C2×D4×C3111yescharacteristic
649C22×C4C2×D4×C3111yescharacteristic
650C22×C4C2×D4×C3111yescharacteristic
651C22×C4C2×D4×C3112yes—
652C22×C4C2×D4×C3112yes—
653C22×C4C24×C3111yescharacteristic
654M16—44no—
655M16—44no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—21no—
666C2×C8—21no—
667C2×C8C2×D4×C3112yes—
668C4⋊C4—24no—
669C4⋊C4—24no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—42no—
679C4⋊C4C22⋊C4×C3114yes—
680C4⋊C4C22×C4×C3112yes—
681C4⋊C4C2×D4×C3112yes—
682C22⋊C4—24no—
683C22⋊C4—24no—
684C22⋊C4—24no—
685C22⋊C4—24no—
686C22⋊C4—42no—
687C22⋊C4—42no—
688C22⋊C4—81no—
689C22⋊C4C22⋊C4×C3114yes—
690C22⋊C4C22⋊C4×C3114yes—
691C42—24no—
692C42—42no—
693C42—81no—
694C42C22×C4×C3112yes—
695C42C2×D4×C3112yes—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—22no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23C2×C22⋊C4×C3112yes—
716C23C2×C22⋊C4×C3112yes—
717C23C22×D4×C3111yescharacteristic
718Q8—22no—
719Q8—22no—
720Q8—22no—
721Q8—22no—
722Q8—22no—
723Q8—48no—
724Q8—41no—
725Q8—41no—
726Q8C4×D4×C3114yes—
727D4—22no—
728D4—22no—
729D4—44no—
730D4—48no—
731D4—48no—
732D4—41no—
733D4—41no—
734C2×C4—22no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—22no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—22no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—48no—
757C2×C4—48no—
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—84no—
774C2×C4C2×C22⋊C4×C3112yes—
775C2×C4C2×C22⋊C4×C3112yes—
776C2×C4C2×C22⋊C4×C3112yes—
777C2×C4C2×C22⋊C4×C3112yes—
778C2×C4C23×C4×C3111yescharacteristic
779C2×C4C22×D4×C3111yescharacteristic
780C2×C4C22×D4×C3111yescharacteristic
781C2×C4C2×#41×C3111yescharacteristic
782C2×C4C31×H(5,𝔽2)11yescharacteristic
783C2×C4C31×H(5,𝔽2)11yescharacteristic
784C8—22no—
785C8—41no—
786C8—41no—
787C8—41no—
788C22—22no—
789C22—22no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—42no—
803C22—42no—
804C22—42no—
805C22—81no—
806C22—81no—
807C22—81no—
808C22—81no—
809C22C22×C22⋊C4×C3111yescharacteristic
810C22D42×C3111yescharacteristic
811C22C31×#54611yescharacteristic
812C22C31×#57511yescharacteristic
813C22C31×#57511yescharacteristic
814C22C31×#57711yescharacteristic
815C22C31×#57811yescharacteristic
816C4—22no—
817C4—22no—
818C4—24no—
819C4—22no—
820C4—22no—
821C4—42no—
822C4—42no—
823C4—42no—
824C4—81no—
825C4—81no—
826C4—81no—
827C4C2×C4×D4×C3111yescharacteristic
828C4C31×#51811yescharacteristic
829C4D42×C3111yescharacteristic
830C4C31×#54611yescharacteristic
831C2—42no—
832C2—42no—
833C2—82no—
834C2D4×C22⋊C4×C3111yescharacteristic
835C2C31×#289611yescharacteristic
836C2C31×#289811yescharacteristic
837C2C31×#327511yescharacteristic
838C2C31×#327711yescharacteristic
839C2C31×#332611yescharacteristic
840C2C31×#332711yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutatorC2×C4C23×C4×C31
Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#548C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C4×D4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#436C2semidirect
3. C2×C31×#417C2semidirect
4. C2×C31×#419C2semidirect
5. C31×#2352C2semidirect
6. C31×#1983C2semidirect
7. C31×#1958C2semidirect
8. C31×#1895C2semidirect
9. C31×#1894C2semidirect
10. C31×#1875C2semidirect
11. C31×#1872C2semidirect
12. C31×#1805C2semidirect
13. C31×#1788C2semidirect
14. C31×#1787C2semidirect
15. C4×C31×#103C2semidirect
21. C31×#548C4semidirect
76. C22×Q8×C31C2×C4semidirect
100. C31×#124C2×C4semidirect
106. C31×#121C2×C4semidirect
108. C4×Q8×C31C2×C4semidirect
146. C31×#103D4semidirect
275. #22429C31direct (N × H)
369. C2×#436C2×C31semidirect
370. C2×#417C2×C31semidirect
371. C2×#419C2×C31semidirect
372. #2352C2×C31semidirect
373. #1983C2×C31semidirect
374. #1958C2×C31semidirect
375. #1895C2×C31semidirect
376. #1894C2×C31semidirect
377. #1875C2×C31semidirect
378. #1872C2×C31semidirect
379. #1805C2×C31semidirect
380. #1788C2×C31semidirect
381. #1787C2×C31semidirect
382. C4×#103C2×C31semidirect
431. #548C4×C31semidirect
496. C22×Q8C2×C4×C31semidirect
520. #124C2×C4×C31semidirect
526. #121C2×C4×C31semidirect
528. C4×Q8C2×C4×C31semidirect
566. #103D4×C31semidirect
579. C31#22429direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5482
C2×C31×#4362
C2×C31×#4172
C2×C31×#4192
C31×#23522
C31×#19832
C31×#19582
C31×#18952
C31×#18942
C31×#18752
C31×#18722
C31×#18052
C31×#17882
C31×#17872
C4×C31×#1032
#2242931