Finite Group Databasebeta

← C31×#24309 #21481068

Subgroups — C31×#24309 #21481068

Order 7936.

1068 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#544C211yesmaximal, characteristic, complemented
2C2×C31×#478C211yesmaximal, characteristic, complemented
3C2×C31×#476C211yesmaximal, characteristic, complemented
4C31×#2324C211yesmaximal, characteristic
5C31×#2059C211yesmaximal, characteristic, complemented
6C31×#2058C211yesmaximal, characteristic, complemented
7C31×#2025C211yesmaximal, characteristic, complemented
8C31×#2023C211yesmaximal, characteristic, complemented
9C31×#1989C211yesmaximal, characteristic, complemented
10C31×#1988C211yesmaximal, characteristic, complemented
11C31×#1875C211yesmaximal, characteristic
12C31×#1874C211yesmaximal, characteristic
13C31×#1854C211yesmaximal, characteristic, complemented
14C31×#1853C211yesmaximal, characteristic, complemented
15C31×#1798C211yesmaximal, characteristic, complemented
16C31×#544—24no—
17C31×#544—24no—
18C2×C31×C4⋊Q8—21no—
19C2×C31×C4⋊Q8C2211yescharacteristic
20C2×C31×C4⋊Q8C2211yescharacteristic
21C2×C31×#125—21no—
22C2×C31×#125C2211yescharacteristic
23C2×C31×#125C2211yescharacteristic
24C2×C31×C22⋊Q8—21no—
25C2×C31×C22⋊Q8—21no—
26C2×C31×#121C2211yescharacteristic
27C2×C4×D4×C31C2211yescharacteristic
28C2×C31×#117C2211yescharacteristic
29C2×C31×#117C2211yescharacteristic
30C22×C4⋊C4×C31C2211yescharacteristic
31C31×#478—24no—
32C31×#476—24no—
33C2×C31×#107C2211yescharacteristic
34C2×C31×#106C2211yescharacteristic
35C2×C31×#106C2211yescharacteristic
36C2×C31×#106C2211yescharacteristic
37C2×C31×C4⋊C8C2211yescharacteristic
38C2×C31×C4⋊C8C2211yescharacteristic
39C2×C31×#102C2211yescharacteristic
40C2×C31×#102C2211yescharacteristic
41C2×C31×#102C2211yescharacteristic
42C2×C31×#102C2211yescharacteristic
43C2×C31×C22⋊C8C2211yescharacteristic
44C2×C31×C22⋊C8C2211yescharacteristic
45C31×#390—21no—
46C31×#390C2211yescharacteristic
47C31×#389C2211yescharacteristic
48C31×#388—21no—
49C31×#386—21no—
50C31×#385—21no—
51C31×#380C2211yescharacteristic
52C4×C4⋊C4×C31C2211yescharacteristic
53C31×#340C2211yescharacteristic
54C31×#340C2211yescharacteristic
55C31×#340C2211yescharacteristic
56C31×#340C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#340C2211yescharacteristic
60C31×#340C2211yescharacteristic
61C31×#336C2211yescharacteristic
62C31×#336C2211yescharacteristic
63C22×Q8×C31—21no—
64C22×Q8×C31—21no—
65C22×D4×C31—21no—
66C22×D4×C31C2311yescharacteristic
67C23×C4×C31—21no—
68C23×C4×C31—21no—
69C23×C4×C31C2311yescharacteristic
70C22×C8×C31C2311yescharacteristic
71C22×C8×C31C2311yescharacteristic
72C22×C8×C31C2311yescharacteristic
73C22×C8×C31C2311yescharacteristic
74C31×C4⋊Q8—28no—
75C31×C4⋊Q8—22no—
76C31×C4⋊Q8—22no—
77C31×C4⋊Q8—22no—
78C31×C4⋊Q8D414yescomplemented
79C31×#125—28no—
80C31×#125—22no—
81C31×#125—22no—
82C31×#125—22no—
83C31×#125D414yescomplemented
84C31×C22⋊Q8—28no—
85C31×C22⋊Q8—28no—
86C31×#121—22no—
87C31×#121Q814yescomplemented
88C4×D4×C31—22no—
89C4×D4×C31—22no—
90C31×#117—22no—
91C31×#117—22no—
92C31×#117—22no—
93C31×#117—22no—
94C2×C4⋊C4×C31—21no—
95C2×C4⋊C4×C31—21no—
96C2×C4⋊C4×C31—21no—
97C2×C4⋊C4×C31—21no—
98C2×C4⋊C4×C31—21no—
99C2×C4⋊C4×C31—21no—
100C2×C4⋊C4×C31—21no—
101C2×C4⋊C4×C31—22no—
102C2×C4⋊C4×C31—22no—
103C2×C4⋊C4×C31—21no—
104C2×C4⋊C4×C31D411yescharacteristic
105C2×C4⋊C4×C31D411yescharacteristic
106C2×C4⋊C4×C31C2311yescharacteristic
107C2×C4⋊C4×C31C2311yescharacteristic
108C2×C4⋊C4×C31C2311yescharacteristic
109C2×C4⋊C4×C31C2311yescharacteristic
110C2×C4⋊C4×C31C2311yescharacteristic
111C2×C4⋊C4×C31C2311yescharacteristic
112C2×C4⋊C4×C31C2311yescharacteristic
113C2×C22⋊C4×C31—21no—
114C2×C22⋊C4×C31—21no—
115C2×C22⋊C4×C31—21no—
116C2×C22⋊C4×C31—21no—
117C2×C22⋊C4×C31—21no—
118C2×C22⋊C4×C31—21no—
119C2×C22⋊C4×C31D411yescharacteristic
120C2×C22⋊C4×C31D411yescharacteristic
121C2×C42×C31—21no—
122C2×C42×C31—21no—
123C2×C42×C31C2311yescharacteristic
124C2×C42×C31C2311yescharacteristic
125C31×#107—22no—
126C31×#106—22no—
127C31×#106—22no—
128C31×#106—22no—
129C31×C4⋊C8—22no—
130C31×C4⋊C8—22no—
131C31×#102—22no—
132C31×#102—22no—
133C31×#102—22no—
134C31×#102—22no—
135C31×C22⋊C8—22no—
136C31×C22⋊C8—22no—
137C31×#95—21no—
138C31×#95—21no—
139C31×#95—21no—
140C24×C31—21no—
141C24×C31C2×D411yescharacteristic
142C2×Q8×C31—24no—
143C2×Q8×C31—24no—
144C2×Q8×C31—81no—
145C2×Q8×C31—81no—
146C2×Q8×C31—81no—
147C2×Q8×C31—81no—
148C2×D4×C31—24no—
149C2×D4×C31—21no—
150C2×D4×C31—21no—
151C2×D4×C31—21no—
152C2×D4×C31—21no—
153C2×D4×C31—21no—
154C2×D4×C31—81no—
155C2×D4×C31—81no—
156C2×D4×C31C2×Q812yes—
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—24no—
167C22×C4×C31—21no—
168C22×C4×C31—21no—
169C22×C4×C31—42no—
170C22×C4×C31—81no—
171C22×C4×C31—81no—
172C22×C4×C31—81no—
173C22×C4×C31—81no—
174C22×C4×C31C2×D411yescharacteristic
175C22×C4×C31C2×D411yescharacteristic
176C22×C4×C31C2×D411yescharacteristic
177C22×C4×C31C2×D411yescharacteristic
178C22×C4×C31C2×D411yescharacteristic
179C22×C4×C31C2×Q812yes—
180C22×C4×C31#4112yes—
181C22×C4×C31C2411yescharacteristic
182C2×C8×C31—21no—
183C2×C8×C31—21no—
184C2×C8×C31—21no—
185C2×C8×C31—21no—
186C2×C8×C31—21no—
187C2×C8×C31—21no—
188C2×C8×C31—21no—
189C2×C8×C31—21no—
190C2×C8×C31—21no—
191C2×C8×C31—21no—
192C2×C8×C31—21no—
193C2×C8×C31—21no—
194C4⋊C4×C31—24no—
195C4⋊C4×C31—24no—
196C4⋊C4×C31—24no—
197C4⋊C4×C31—24no—
198C4⋊C4×C31—24no—
199C4⋊C4×C31—24no—
200C4⋊C4×C31—24no—
201C4⋊C4×C31—22no—
202C4⋊C4×C31—22no—
203C4⋊C4×C31—21no—
204C4⋊C4×C31—21no—
205C4⋊C4×C31—21no—
206C4⋊C4×C31—21no—
207C4⋊C4×C31—21no—
208C4⋊C4×C31—21no—
209C4⋊C4×C31—21no—
210C4⋊C4×C31—21no—
211C4⋊C4×C31—21no—
212C4⋊C4×C31—81no—
213C4⋊C4×C31C2×D412yes—
214C4⋊C4×C31C2×D412yes—
215C4⋊C4×C31C2×D412yes—
216C4⋊C4×C31C2×D412yes—
217C4⋊C4×C31C2×Q812yes—
218C22⋊C4×C31—24no—
219C22⋊C4×C31—22no—
220C22⋊C4×C31—22no—
221C22⋊C4×C31—24no—
222C22⋊C4×C31—42no—
223C22⋊C4×C31—81no—
224C22⋊C4×C31—81no—
225C22⋊C4×C31—81no—
226C42×C31—24no—
227C42×C31—21no—
228C42×C31—21no—
229C42×C31—81no—
230C42×C31C2×D412yes—
231C42×C31C2×D412yes—
232#24309C3111yesmaximal, characteristic, direct product factor, Sylow
233C23×C31—21no—
234C23×C31—21no—
235C23×C31—21no—
236C23×C31—21no—
237C23×C31—21no—
238C23×C31—21no—
239C23×C31—22no—
240C23×C31—41no—
241C23×C31—41no—
242C23×C31—41no—
243C23×C31—41no—
244C23×C31—41no—
245C23×C31—41no—
246C23×C31C22⋊Q812yes—
247C23×C31C22×D411yescharacteristic
248Q8×C31—84no—
249Q8×C31—84no—
250D4×C31—22no—
251D4×C31—22no—
252D4×C31—41no—
253D4×C31—41no—
254D4×C31—84no—
255C2×C4×C31—21no—
256C2×C4×C31—21no—
257C2×C4×C31—21no—
258C2×C4×C31—21no—
259C2×C4×C31—21no—
260C2×C4×C31—21no—
261C2×C4×C31—22no—
262C2×C4×C31—22no—
263C2×C4×C31—22no—
264C2×C4×C31—22no—
265C2×C4×C31—21no—
266C2×C4×C31—22no—
267C2×C4×C31—21no—
268C2×C4×C31—22no—
269C2×C4×C31—22no—
270C2×C4×C31—22no—
271C2×C4×C31—22no—
272C2×C4×C31—21no—
273C2×C4×C31—21no—
274C2×C4×C31—21no—
275C2×C4×C31—21no—
276C2×C4×C31—41no—
277C2×C4×C31—41no—
278C2×C4×C31—41no—
279C2×C4×C31—41no—
280C2×C4×C31—41no—
281C2×C4×C31—41no—
282C2×C4×C31—41no—
283C2×C4×C31—41no—
284C2×C4×C31—41no—
285C2×C4×C31—41no—
286C2×C4×C31—41no—
287C2×C4×C31—41no—
288C2×C4×C31—41no—
289C2×C4×C31—41no—
290C2×C4×C31—41no—
291C2×C4×C31—41no—
292C2×C4×C31—84no—
293C2×C4×C31—84no—
294C2×C4×C31#12012yes—
295C2×C4×C31#12012yes—
296C2×C4×C31C22⋊Q812yes—
297C2×C4×C31C22×D411yescharacteristic
298C2×C4×C31C22×D411yescharacteristic
299C2×C4×C31C22×Q811yescharacteristic
300C2×C4×C31C2×#4111yescharacteristic
301C2×C4×C312−1+411yescharacteristic
302C2×C4×C312−1+411yescharacteristic
303C8×C31—41no—
304C8×C31—41no—
305C8×C31—41no—
306C8×C31—41no—
307C2×#544C2×C3111yescharacteristic, complemented
308C2×#478C2×C3111yescharacteristic, complemented
309C2×#476C2×C3111yescharacteristic, complemented
310#2324C2×C3111yescharacteristic
311#2059C2×C3111yescharacteristic, complemented
312#2058C2×C3111yescharacteristic, complemented
313#2025C2×C3111yescharacteristic, complemented
314#2023C2×C3111yescharacteristic, complemented
315#1989C2×C3111yescharacteristic, complemented
316#1988C2×C3111yescharacteristic, complemented
317#1875C2×C3111yescharacteristic
318#1874C2×C3111yescharacteristic
319#1854C2×C3111yescharacteristic, complemented
320#1853C2×C3111yescharacteristic, complemented
321#1798C2×C3111yescharacteristic, complemented
322C22×C31—22no—
323C22×C31—22no—
324C22×C31—22no—
325C22×C31—41no—
326C22×C31—41no—
327C22×C31—41no—
328C22×C31—41no—
329C22×C31—42no—
330C22×C31—42no—
331C22×C31—42no—
332C22×C31—81no—
333C22×C31—81no—
334C22×C31—81no—
335C22×C31—81no—
336C22×C31C2×#12011yescharacteristic
337C22×C31C2×C22⋊Q811yescharacteristic
338C22×C31#53611yescharacteristic
339C22×C31#57611yescharacteristic
340C22×C31#57711yescharacteristic
341C22×C31#57711yescharacteristic
342C22×C31#57711yescharacteristic
343C4×C31—22no—
344C4×C31—22no—
345C4×C31—22no—
346C4×C31—42no—
347C4×C31—41no—
348C4×C31—42no—
349C4×C31—41no—
350C4×C31—42no—
351C4×C31—42no—
352C4×C31—42no—
353C4×C31—81no—
354C4×C31—81no—
355C4×C31#54811yescharacteristic
356C4×C31#54811yescharacteristic
357C4×C31D4×Q811yescharacteristic
358C4×C31D4×Q811yescharacteristic
359#544—24no—
360#544—24no—
361C2×C4⋊Q8—21no—
362C2×C4⋊Q8C22×C3111yescharacteristic
363C2×C4⋊Q8C22×C3111yescharacteristic
364C2×#125—21no—
365C2×#125C22×C3111yescharacteristic
366C2×#125C22×C3111yescharacteristic
367C2×C22⋊Q8—21no—
368C2×C22⋊Q8—21no—
369C2×#121C22×C3111yescharacteristic
370C2×C4×D4C22×C3111yescharacteristic
371C2×#117C22×C3111yescharacteristic
372C2×#117C22×C3111yescharacteristic
373C22×C4⋊C4C22×C3111yescharacteristic
374#478—24no—
375#476—24no—
376C2×#107C22×C3111yescharacteristic
377C2×#106C22×C3111yescharacteristic
378C2×#106C22×C3111yescharacteristic
379C2×#106C22×C3111yescharacteristic
380C2×C4⋊C8C22×C3111yescharacteristic
381C2×C4⋊C8C22×C3111yescharacteristic
382C2×#102C22×C3111yescharacteristic
383C2×#102C22×C3111yescharacteristic
384C2×#102C22×C3111yescharacteristic
385C2×#102C22×C3111yescharacteristic
386C2×C22⋊C8C22×C3111yescharacteristic
387C2×C22⋊C8C22×C3111yescharacteristic
388#390—21no—
389#390C22×C3111yescharacteristic
390#389C22×C3111yescharacteristic
391#388—21no—
392#386—21no—
393#385—21no—
394#380C22×C3111yescharacteristic
395C4×C4⋊C4C22×C3111yescharacteristic
396#340C22×C3111yescharacteristic
397#340C22×C3111yescharacteristic
398#340C22×C3111yescharacteristic
399#340C22×C3111yescharacteristic
400#340C22×C3111yescharacteristic
401#340C22×C3111yescharacteristic
402#340C22×C3111yescharacteristic
403#340C22×C3111yescharacteristic
404#336C22×C3111yescharacteristic
405#336C22×C3111yescharacteristic
406C2×C31—42no—
407C2×C31—82no—
408C2×C31#240911yescharacteristic
409C2×C31#301011yescharacteristic
410C2×C31#301211yescharacteristic
411C2×C31#308111yescharacteristic
412C2×C31#308411yescharacteristic
413C2×C31#324111yescharacteristic
414C2×C31#324411yescharacteristic
415C22×Q8—21no—
416C22×Q8—21no—
417C22×D4—21no—
418C22×D4C23×C3111yescharacteristic
419C23×C4—21no—
420C23×C4—21no—
421C23×C4C23×C3111yescharacteristic
422C22×C8C23×C3111yescharacteristic
423C22×C8C23×C3111yescharacteristic
424C22×C8C23×C3111yescharacteristic
425C22×C8C23×C3111yescharacteristic
426C4⋊Q8—28no—
427C4⋊Q8—22no—
428C4⋊Q8—22no—
429C4⋊Q8—22no—
430C4⋊Q8D4×C3114yescomplemented
431#125—28no—
432#125—22no—
433#125—22no—
434#125—22no—
435#125D4×C3114yescomplemented
436C22⋊Q8—28no—
437C22⋊Q8—28no—
438#121—22no—
439#121Q8×C3114yescomplemented
440C4×D4—22no—
441C4×D4—22no—
442#117—22no—
443#117—22no—
444#117—22no—
445#117—22no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—21no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4D4×C3111yescharacteristic
457C2×C4⋊C4D4×C3111yescharacteristic
458C2×C4⋊C4C23×C3111yescharacteristic
459C2×C4⋊C4C23×C3111yescharacteristic
460C2×C4⋊C4C23×C3111yescharacteristic
461C2×C4⋊C4C23×C3111yescharacteristic
462C2×C4⋊C4C23×C3111yescharacteristic
463C2×C4⋊C4C23×C3111yescharacteristic
464C2×C4⋊C4C23×C3111yescharacteristic
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4D4×C3111yescharacteristic
472C2×C22⋊C4D4×C3111yescharacteristic
473C2×C42—21no—
474C2×C42—21no—
475C2×C42C23×C3111yescharacteristic
476C2×C42C23×C3111yescharacteristic
477#107—22no—
478#106—22no—
479#106—22no—
480#106—22no—
481C4⋊C8—22no—
482C4⋊C8—22no—
483#102—22no—
484#102—22no—
485#102—22no—
486#102—22no—
487C22⋊C8—22no—
488C22⋊C8—22no—
489#95—21no—
490#95—21no—
491#95—21no—
492C31#2430911yescharacteristic, direct product factor, Sylow
493C24—21no—
494C24C2×D4×C3111yescharacteristic
495C2×Q8—24no—
496C2×Q8—24no—
497C2×Q8—81no—
498C2×Q8—81no—
499C2×Q8—81no—
500C2×Q8—81no—
501C2×D4—24no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—81no—
508C2×D4—81no—
509C2×D4C2×Q8×C3112yes—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—24no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—42no—
523C22×C4—81no—
524C22×C4—81no—
525C22×C4—81no—
526C22×C4—81no—
527C22×C4C2×D4×C3111yescharacteristic
528C22×C4C2×D4×C3111yescharacteristic
529C22×C4C2×D4×C3111yescharacteristic
530C22×C4C2×D4×C3111yescharacteristic
531C22×C4C2×D4×C3111yescharacteristic
532C22×C4C2×Q8×C3112yes—
533C22×C4#41×C3112yes—
534C22×C4C24×C3111yescharacteristic
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C4⋊C4—24no—
548C4⋊C4—24no—
549C4⋊C4—24no—
550C4⋊C4—24no—
551C4⋊C4—24no—
552C4⋊C4—24no—
553C4⋊C4—24no—
554C4⋊C4—22no—
555C4⋊C4—22no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—81no—
566C4⋊C4C2×D4×C3112yes—
567C4⋊C4C2×D4×C3112yes—
568C4⋊C4C2×D4×C3112yes—
569C4⋊C4C2×D4×C3112yes—
570C4⋊C4C2×Q8×C3112yes—
571C22⋊C4—24no—
572C22⋊C4—22no—
573C22⋊C4—22no—
574C22⋊C4—24no—
575C22⋊C4—42no—
576C22⋊C4—81no—
577C22⋊C4—81no—
578C22⋊C4—81no—
579C42—24no—
580C42—21no—
581C42—21no—
582C42—81no—
583C42C2×D4×C3112yes—
584C42C2×D4×C3112yes—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—22no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23C31×C22⋊Q812yes—
599C23C22×D4×C3111yescharacteristic
600Q8—84no—
601Q8—84no—
602D4—22no—
603D4—22no—
604D4—41no—
605D4—41no—
606D4—84no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—21no—
618C2×C4—22no—
619C2×C4—21no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—84no—
645C2×C4—84no—
646C2×C4C31×#12012yes—
647C2×C4C31×#12012yes—
648C2×C4C31×C22⋊Q812yes—
649C2×C4C22×D4×C3111yescharacteristic
650C2×C4C22×D4×C3111yescharacteristic
651C2×C4C22×Q8×C3111yescharacteristic
652C2×C4C2×#41×C3111yescharacteristic
653C2×C4C31×2−1+411yescharacteristic
654C2×C4C31×2−1+411yescharacteristic
655C8—41no—
656C8—41no—
657C8—41no—
658C8—41no—
659C22—22no—
660C22—22no—
661C22—22no—
662C22—41no—
663C22—41no—
664C22—41no—
665C22—41no—
666C22—42no—
667C22—42no—
668C22—42no—
669C22—81no—
670C22—81no—
671C22—81no—
672C22—81no—
673C22C2×C31×#12011yescharacteristic
674C22C2×C31×C22⋊Q811yescharacteristic
675C22C31×#53611yescharacteristic
676C22C31×#57611yescharacteristic
677C22C31×#57711yescharacteristic
678C22C31×#57711yescharacteristic
679C22C31×#57711yescharacteristic
680C4—22no—
681C4—22no—
682C4—22no—
683C4—42no—
684C4—41no—
685C4—42no—
686C4—41no—
687C4—42no—
688C4—42no—
689C4—42no—
690C4—81no—
691C4—81no—
692C4C31×#54811yescharacteristic
693C4C31×#54811yescharacteristic
694C4D4×Q8×C3111yescharacteristic
695C4D4×Q8×C3111yescharacteristic
696C2—42no—
697C2—82no—
698C2C31×#240911yescharacteristic
699C2C31×#301011yescharacteristic
700C2C31×#301211yescharacteristic
701C2C31×#308111yescharacteristic
702C2C31×#308411yescharacteristic
703C2C31×#324111yescharacteristic
704C2C31×#324411yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C31×#117 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#544C2semidirect
2. C2×C31×#478C2semidirect
3. C2×C31×#476C2semidirect
5. C31×#2059C2semidirect
6. C31×#2058C2semidirect
7. C31×#2025C2semidirect
8. C31×#2023C2semidirect
9. C31×#1989C2semidirect
10. C31×#1988C2semidirect
13. C31×#1854C2semidirect
14. C31×#1853C2semidirect
15. C31×#1798C2semidirect
78. C31×C4⋊Q8D4semidirect
83. C31×#125D4semidirect
87. C31×#121Q8semidirect
232. #24309C31direct (N × H)
307. C2×#544C2×C31semidirect
308. C2×#478C2×C31semidirect
309. C2×#476C2×C31semidirect
311. #2059C2×C31semidirect
312. #2058C2×C31semidirect
313. #2025C2×C31semidirect
314. #2023C2×C31semidirect
315. #1989C2×C31semidirect
316. #1988C2×C31semidirect
319. #1854C2×C31semidirect
320. #1853C2×C31semidirect
321. #1798C2×C31semidirect
430. C4⋊Q8D4×C31semidirect
435. #125D4×C31semidirect
439. #121Q8×C31semidirect
492. C31#24309direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5442
C2×C31×#4782
C2×C31×#4762
C31×#23242
C31×#20592
C31×#20582
C31×#20252
C31×#20232
C31×#19892
C31×#19882
C31×#18752
C31×#18742
C31×#18542
C31×#18532
C31×#17982
#2430931