Finite Group Databasebeta

← C31×#15179 #21471938

Subgroups — C31×#15179 #21471938

Order 7936.

1946 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×C22⋊Q8C211yesmaximal, characteristic
2C2×C31×#391C211yesmaximal, characteristic, complemented
3C2×C31×#391C211yesmaximal, characteristic, complemented
4C2×C31×#389C211yesmaximal, characteristic, complemented
5C2×C31×#380C211yesmaximal, characteristic
6C2×C4×C22⋊C4×C31C211yesmaximal, characteristic
7C31×#1442C212yesmaximal, complemented
8C31×#1441C212yesmaximal, complemented
9C31×#1440C212yesmaximal
10C31×#1439C212yesmaximal
11C31×C4⋊#95C211yesmaximal, characteristic, complemented
12C23×Q8×C31C2211yescharacteristic
13C24×C4×C31C2211yescharacteristic
14C2×C31×C22⋊Q8—24no—
15C2×C31×C22⋊Q8—24no—
16C2×C31×C22⋊Q8—24no—
17C22×C4⋊C4×C31C2212yes—
18C22×C4⋊C4×C31C2211yescharacteristic
19C22×C4⋊C4×C31C2212yes—
20C22×C4⋊C4×C31C2211yescharacteristic
21C22×C4⋊C4×C31C2211yescharacteristic
22C22×C22⋊C4×C31C2212yes—
23C22×C22⋊C4×C31C2211yescharacteristic
24C22×C22⋊C4×C31C2212yes—
25C22×C22⋊C4×C31C2211yescharacteristic
26C22×C42×C31C2211yescharacteristic
27C22×C42×C31C2211yescharacteristic
28C31×#391—24no—
29C31×#391—24no—
30C31×#389—24no—
31C31×#380—24no—
32C4×C22⋊C4×C31—24no—
33C2×C31×#95C2212yes—
34C2×C31×#95C2212yes—
35C2×C31×#95C2212yes—
36C2×C31×#95C2212yes—
37C2×C31×#95C2212yes—
38C2×C31×#95C2212yes—
39C2×C31×#95C2211yescharacteristic
40C2×C31×#95C2212yes—
41C2×C31×#95C2211yescharacteristic
42C2×C31×#95C2212yes—
43C25×C31C2311yescharacteristic
44C22×Q8×C31—22no—
45C22×Q8×C31—22no—
46C22×Q8×C31—22no—
47C22×Q8×C31—22no—
48C22×Q8×C31—22no—
49C22×Q8×C31—22no—
50C22×Q8×C31D414yes—
51C23×C4×C31—22no—
52C23×C4×C31—22no—
53C23×C4×C31—22no—
54C23×C4×C31—22no—
55C23×C4×C31—22no—
56C23×C4×C31—22no—
57C23×C4×C31D414yes—
58C23×C4×C31C2312yes—
59C23×C4×C31C2312yes—
60C23×C4×C31C2312yes—
61C23×C4×C31C2312yes—
62C23×C4×C31C2311yescharacteristic
63C23×C4×C31C2311yescharacteristic
64C23×C4×C31C2311yescharacteristic
65C23×C4×C31C2311yescharacteristic
66C23×C4×C31C2311yescharacteristic
67C23×C4×C31C2311yescharacteristic
68C31×C22⋊Q8—232no—
69C2×C4⋊C4×C31—24no—
70C2×C4⋊C4×C31—24no—
71C2×C4⋊C4×C31—24no—
72C2×C4⋊C4×C31—22no—
73C2×C4⋊C4×C31—22no—
74C2×C4⋊C4×C31—22no—
75C2×C4⋊C4×C31—22no—
76C2×C4⋊C4×C31—22no—
77C2×C4⋊C4×C31—24no—
78C2×C4⋊C4×C31—22no—
79C2×C4⋊C4×C31—24no—
80C2×C4⋊C4×C31—22no—
81C2×C4⋊C4×C31—42no—
82C2×C4⋊C4×C31D414yes—
83C2×C4⋊C4×C31D414yes—
84C2×C22⋊C4×C31—24no—
85C2×C22⋊C4×C31—22no—
86C2×C22⋊C4×C31—22no—
87C2×C22⋊C4×C31—22no—
88C2×C22⋊C4×C31—24no—
89C2×C22⋊C4×C31—24no—
90C2×C22⋊C4×C31—22no—
91C2×C22⋊C4×C31—22no—
92C2×C22⋊C4×C31—24no—
93C2×C22⋊C4×C31—24no—
94C2×C22⋊C4×C31—42no—
95C2×C22⋊C4×C31Q814yescomplemented
96C2×C42×C31—22no—
97C2×C42×C31—22no—
98C2×C42×C31—22no—
99C2×C42×C31—22no—
100C2×C42×C31—22no—
101C2×C42×C31—22no—
102C31×#95—22no—
103C31×#95—22no—
104C31×#95—24no—
105C31×#95—24no—
106C31×#95—24no—
107C31×#95—24no—
108C31×#95—24no—
109C31×#95—24no—
110C31×#95—24no—
111C31×#95—42no—
112C24×C31—21no—
113C24×C31—21no—
114C24×C31—21no—
115C24×C31—21no—
116C24×C31—21no—
117C24×C31—21no—
118C24×C31—21no—
119C24×C31—21no—
120C24×C31—21no—
121C24×C31—21no—
122C24×C31—21no—
123C24×C31—21no—
124C24×C31C2×D412yes—
125C24×C31C2×Q812yes—
126C24×C31#4112yes—
127C24×C31C2411yescharacteristic
128C2×Q8×C31—28no—
129C2×Q8×C31—28no—
130C2×Q8×C31—28no—
131C2×Q8×C31—44no—
132C2×Q8×C31—44no—
133C2×Q8×C31—44no—
134C2×Q8×C31—44no—
135C22×C4×C31—21no—
136C22×C4×C31—21no—
137C22×C4×C31—21no—
138C22×C4×C31—21no—
139C22×C4×C31—21no—
140C22×C4×C31—21no—
141C22×C4×C31—22no—
142C22×C4×C31—21no—
143C22×C4×C31—21no—
144C22×C4×C31—21no—
145C22×C4×C31—21no—
146C22×C4×C31—22no—
147C22×C4×C31—21no—
148C22×C4×C31—22no—
149C22×C4×C31—22no—
150C22×C4×C31—22no—
151C22×C4×C31—22no—
152C22×C4×C31—21no—
153C22×C4×C31—21no—
154C22×C4×C31—22no—
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—22no—
162C22×C4×C31—22no—
163C22×C4×C31—22no—
164C22×C4×C31—22no—
165C22×C4×C31—21no—
166C22×C4×C31—21no—
167C22×C4×C31—21no—
168C22×C4×C31—22no—
169C22×C4×C31—22no—
170C22×C4×C31—22no—
171C22×C4×C31—21no—
172C22×C4×C31—22no—
173C22×C4×C31—22no—
174C22×C4×C31—21no—
175C22×C4×C31—22no—
176C22×C4×C31—22no—
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—28no—
184C22×C4×C31—28no—
185C22×C4×C31—28no—
186C22×C4×C31—22no—
187C22×C4×C31—22no—
188C22×C4×C31—22no—
189C22×C4×C31—22no—
190C22×C4×C31—22no—
191C22×C4×C31—22no—
192C22×C4×C31—22no—
193C22×C4×C31—44no—
194C22×C4×C31—44no—
195C22×C4×C31—44no—
196C22×C4×C31—44no—
197C22×C4×C31C2×D414yes—
198C22×C4×C31C2×D414yes—
199C22×C4×C31C2×D412yes—
200C22×C4×C31C2×D414yes—
201C22×C4×C31C2×D412yes—
202C22×C4×C31C2×D412yes—
203C22×C4×C31C2×D412yes—
204C22×C4×C31C2×D412yes—
205C22×C4×C31C2×Q812yes—
206C22×C4×C31C2×Q812yes—
207C22×C4×C31#4112yes—
208C22×C4×C31#4112yes—
209C22×C4×C31#4112yes—
210C22×C4×C31#4112yes—
211C22×C4×C31#4112yes—
212C4⋊C4×C31—216no—
213C4⋊C4×C31—28no—
214C4⋊C4×C31—28no—
215C4⋊C4×C31—48no—
216C4⋊C4×C31—44no—
217C22⋊C4×C31—28no—
218C22⋊C4×C31—216no—
219C22⋊C4×C31—28no—
220C22⋊C4×C31—48no—
221C42×C31—44no—
222C42×C31—44no—
223#15179C3111yesmaximal, characteristic, direct product factor, Sylow
224C23×C31—22no—
225C23×C31—22no—
226C23×C31—22no—
227C23×C31—22no—
228C23×C31—22no—
229C23×C31—22no—
230C23×C31—22no—
231C23×C31—22no—
232C23×C31—22no—
233C23×C31—22no—
234C23×C31—22no—
235C23×C31—22no—
236C23×C31—22no—
237C23×C31—22no—
238C23×C31—22no—
239C23×C31—22no—
240C23×C31—22no—
241C23×C31—22no—
242C23×C31—41no—
243C23×C31—41no—
244C23×C31—41no—
245C23×C31—41no—
246C23×C31—41no—
247C23×C31—41no—
248C23×C31—41no—
249C23×C31—41no—
250C23×C31—41no—
251C23×C31—41no—
252C23×C31—41no—
253C23×C31—41no—
254C23×C31—41no—
255C23×C31—41no—
256C23×C31—41no—
257C23×C31—41no—
258C23×C31C22⋊Q814yes—
259C23×C31C22×D411yescharacteristic
260C23×C31C22×D411yescharacteristic
261C23×C31C22×D411yescharacteristic
262C23×C31C22×D411yescharacteristic
263C23×C31C22×Q811yescharacteristic
264C23×C31C2×#4111yescharacteristic
265C23×C31C2×#4111yescharacteristic
266C23×C31C2×#4111yescharacteristic
267C23×C31C2×#4111yescharacteristic
268C23×C31C2×#4111yescharacteristic
269C23×C31C2×#4111yescharacteristic
270C23×C31H(5,𝔽2)11yescharacteristic
271C23×C312−1+411yescharacteristic
272C23×C312−1+411yescharacteristic
273C23×C312−1+411yescharacteristic
274Q8×C31—416no—
275C2×C4×C31—24no—
276C2×C4×C31—24no—
277C2×C4×C31—22no—
278C2×C4×C31—24no—
279C2×C4×C31—22no—
280C2×C4×C31—24no—
281C2×C4×C31—22no—
282C2×C4×C31—22no—
283C2×C4×C31—22no—
284C2×C4×C31—24no—
285C2×C4×C31—22no—
286C2×C4×C31—22no—
287C2×C4×C31—24no—
288C2×C4×C31—22no—
289C2×C4×C31—24no—
290C2×C4×C31—24no—
291C2×C4×C31—24no—
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—41no—
300C2×C4×C31—41no—
301C2×C4×C31—41no—
302C2×C4×C31—41no—
303C2×C4×C31—41no—
304C2×C4×C31—41no—
305C2×C4×C31—42no—
306C2×C4×C31—42no—
307C2×C4×C31—41no—
308C2×C4×C31—42no—
309C2×C4×C31—42no—
310C2×C4×C31—41no—
311C2×C4×C31—42no—
312C2×C4×C31—42no—
313C2×C4×C31—41no—
314C2×C4×C31—41no—
315C2×C4×C31—41no—
316C2×C4×C31—42no—
317C2×C4×C31—41no—
318C2×C4×C31—42no—
319C2×C4×C31—42no—
320C2×C4×C31—41no—
321C2×C4×C31—41no—
322C2×C4×C31—41no—
323C2×C4×C31—42no—
324C2×C4×C31—41no—
325C2×C4×C31—41no—
326C2×C4×C31—42no—
327C2×C4×C31—41no—
328C2×C4×C31—42no—
329C2×C4×C31—41no—
330C2×C4×C31—41no—
331C2×C4×C31—416no—
332C2×C4×C31—42no—
333C2×C4×C31—42no—
334C2×C4×C31—42no—
335C2×C4×C31—42no—
336C2×C4×C31—42no—
337C2×C4×C31—42no—
338C2×C4×C31—42no—
339C2×C4×C31#12014yes—
340C2×C4×C31#12114yes—
341C2×C4×C31#12114yes—
342C2×C4×C31#12114yes—
343C2×C4×C31#12314yes—
344C2×C4×C31#12314yes—
345C2×C4×C31#12414yes—
346C22×C22⋊Q8C2×C3111yescharacteristic
347C2×#391C2×C3111yescharacteristic, complemented
348C2×#391C2×C3111yescharacteristic, complemented
349C2×#389C2×C3111yescharacteristic, complemented
350C2×#380C2×C3111yescharacteristic
351C2×C4×C22⋊C4C2×C3111yescharacteristic
352#1442C2×C3112yescomplemented
353#1441C2×C3112yescomplemented
354#1440C2×C3112yes—
355#1439C2×C3112yes—
356C4⋊#95C2×C3111yescharacteristic, complemented
357C22×C31—24no—
358C22×C31—24no—
359C22×C31—24no—
360C22×C31—42no—
361C22×C31—42no—
362C22×C31—42no—
363C22×C31—42no—
364C22×C31—42no—
365C22×C31—42no—
366C22×C31—42no—
367C22×C31—42no—
368C22×C31—42no—
369C22×C31—42no—
370C22×C31—42no—
371C22×C31—42no—
372C22×C31C2×#12011yescharacteristic
373C22×C31C2×#12111yescharacteristic
374C22×C31C2×#12111yescharacteristic
375C22×C31C2×#12111yescharacteristic
376C22×C31C2×C22⋊Q811yescharacteristic
377C22×C31C2×#12311yescharacteristic
378C22×C31C2×#12311yescharacteristic
379C22×C31#52511yescharacteristic
380C22×C31C2×#12411yescharacteristic
381C22×C31#52911yescharacteristic
382C22×C31#52911yescharacteristic
383C22×C31#53311yescharacteristic
384C22×C31#53311yescharacteristic
385C22×C31#53611yescharacteristic
386C22×C31#53711yescharacteristic
387C22×C31#54111yescharacteristic
388C22×C31#54111yescharacteristic
389C22×C31#54211yescharacteristic
390C22×C31#54211yescharacteristic
391C22×C31#54611yescharacteristic
392C22×C31#54611yescharacteristic
393C22×C31#54711yescharacteristic
394C22×C31#54711yescharacteristic
395C22×C31#54811yescharacteristic
396C22×C31#54811yescharacteristic
397C22×C31#54811yescharacteristic
398C22×C31#54811yescharacteristic
399C22×C31D4×Q811yescharacteristic
400C22×C31D4×Q811yescharacteristic
401C22×C31D4×Q811yescharacteristic
402C22×C31#55011yescharacteristic
403C22×C31#55211yescharacteristic
404C22×C31#55211yescharacteristic
405C22×C31#55411yescharacteristic
406C22×C31#55611yescharacteristic
407C4×C31—42no—
408C4×C31—44no—
409C4×C31—44no—
410C4×C31—42no—
411C4×C31—42no—
412C4×C31—42no—
413C4×C31—42no—
414C4×C31—44no—
415C4×C31—82no—
416C4×C31#39418yes—
417C23×Q8C22×C3111yescharacteristic
418C24×C4C22×C3111yescharacteristic
419C2×C22⋊Q8—24no—
420C2×C22⋊Q8—24no—
421C2×C22⋊Q8—24no—
422C22×C4⋊C4C22×C3112yes—
423C22×C4⋊C4C22×C3111yescharacteristic
424C22×C4⋊C4C22×C3112yes—
425C22×C4⋊C4C22×C3111yescharacteristic
426C22×C4⋊C4C22×C3111yescharacteristic
427C22×C22⋊C4C22×C3112yes—
428C22×C22⋊C4C22×C3111yescharacteristic
429C22×C22⋊C4C22×C3112yes—
430C22×C22⋊C4C22×C3111yescharacteristic
431C22×C42C22×C3111yescharacteristic
432C22×C42C22×C3111yescharacteristic
433#391—24no—
434#391—24no—
435#389—24no—
436#380—24no—
437C4×C22⋊C4—24no—
438C2×#95C22×C3112yes—
439C2×#95C22×C3112yes—
440C2×#95C22×C3112yes—
441C2×#95C22×C3112yes—
442C2×#95C22×C3112yes—
443C2×#95C22×C3112yes—
444C2×#95C22×C3111yescharacteristic
445C2×#95C22×C3112yes—
446C2×#95C22×C3111yescharacteristic
447C2×#95C22×C3112yes—
448C2×C31—44no—
449C2×C31C2×#39411yescharacteristic
450C2×C31#240711yescharacteristic
451C2×C31#240911yescharacteristic
452C2×C31#241511yescharacteristic
453C2×C31#241711yescharacteristic
454C2×C31#242111yescharacteristic
455C2×C31#242311yescharacteristic
456C2×C31#242611yescharacteristic
457C2×C31#242711yescharacteristic
458C2×C31#242911yescharacteristic
459C2×C31#242911yescharacteristic
460C2×C31#248911yescharacteristic
461C2×C31#249211yescharacteristic
462C2×C31#262511yescharacteristic
463C2×C31#285511yescharacteristic
464C25C23×C3111yescharacteristic
465C22×Q8—22no—
466C22×Q8—22no—
467C22×Q8—22no—
468C22×Q8—22no—
469C22×Q8—22no—
470C22×Q8—22no—
471C22×Q8D4×C3114yes—
472C23×C4—22no—
473C23×C4—22no—
474C23×C4—22no—
475C23×C4—22no—
476C23×C4—22no—
477C23×C4—22no—
478C23×C4D4×C3114yes—
479C23×C4C23×C3112yes—
480C23×C4C23×C3112yes—
481C23×C4C23×C3112yes—
482C23×C4C23×C3112yes—
483C23×C4C23×C3111yescharacteristic
484C23×C4C23×C3111yescharacteristic
485C23×C4C23×C3111yescharacteristic
486C23×C4C23×C3111yescharacteristic
487C23×C4C23×C3111yescharacteristic
488C23×C4C23×C3111yescharacteristic
489C22⋊Q8—232no—
490C2×C4⋊C4—24no—
491C2×C4⋊C4—24no—
492C2×C4⋊C4—24no—
493C2×C4⋊C4—22no—
494C2×C4⋊C4—22no—
495C2×C4⋊C4—22no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—24no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—24no—
501C2×C4⋊C4—22no—
502C2×C4⋊C4—42no—
503C2×C4⋊C4D4×C3114yes—
504C2×C4⋊C4D4×C3114yes—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—24no—
510C2×C22⋊C4—24no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—24no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—42no—
516C2×C22⋊C4Q8×C3114yescomplemented
517C2×C42—22no—
518C2×C42—22no—
519C2×C42—22no—
520C2×C42—22no—
521C2×C42—22no—
522C2×C42—22no—
523#95—22no—
524#95—22no—
525#95—24no—
526#95—24no—
527#95—24no—
528#95—24no—
529#95—24no—
530#95—24no—
531#95—24no—
532#95—42no—
533C31#1517911yescharacteristic, direct product factor, Sylow
534C24—21no—
535C24—21no—
536C24—21no—
537C24—21no—
538C24—21no—
539C24—21no—
540C24—21no—
541C24—21no—
542C24—21no—
543C24—21no—
544C24—21no—
545C24—21no—
546C24C2×D4×C3112yes—
547C24C2×Q8×C3112yes—
548C24#41×C3112yes—
549C24C24×C3111yescharacteristic
550C2×Q8—28no—
551C2×Q8—28no—
552C2×Q8—28no—
553C2×Q8—44no—
554C2×Q8—44no—
555C2×Q8—44no—
556C2×Q8—44no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—22no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—21no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—21no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—28no—
606C22×C4—28no—
607C22×C4—28no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—44no—
616C22×C4—44no—
617C22×C4—44no—
618C22×C4—44no—
619C22×C4C2×D4×C3114yes—
620C22×C4C2×D4×C3114yes—
621C22×C4C2×D4×C3112yes—
622C22×C4C2×D4×C3114yes—
623C22×C4C2×D4×C3112yes—
624C22×C4C2×D4×C3112yes—
625C22×C4C2×D4×C3112yes—
626C22×C4C2×D4×C3112yes—
627C22×C4C2×Q8×C3112yes—
628C22×C4C2×Q8×C3112yes—
629C22×C4#41×C3112yes—
630C22×C4#41×C3112yes—
631C22×C4#41×C3112yes—
632C22×C4#41×C3112yes—
633C22×C4#41×C3112yes—
634C4⋊C4—216no—
635C4⋊C4—28no—
636C4⋊C4—28no—
637C4⋊C4—48no—
638C4⋊C4—44no—
639C22⋊C4—28no—
640C22⋊C4—216no—
641C22⋊C4—28no—
642C22⋊C4—48no—
643C42—44no—
644C42—44no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23C31×C22⋊Q814yes—
680C23C22×D4×C3111yescharacteristic
681C23C22×D4×C3111yescharacteristic
682C23C22×D4×C3111yescharacteristic
683C23C22×D4×C3111yescharacteristic
684C23C22×Q8×C3111yescharacteristic
685C23C2×#41×C3111yescharacteristic
686C23C2×#41×C3111yescharacteristic
687C23C2×#41×C3111yescharacteristic
688C23C2×#41×C3111yescharacteristic
689C23C2×#41×C3111yescharacteristic
690C23C2×#41×C3111yescharacteristic
691C23C31×H(5,𝔽2)11yescharacteristic
692C23C31×2−1+411yescharacteristic
693C23C31×2−1+411yescharacteristic
694C23C31×2−1+411yescharacteristic
695Q8—416no—
696C2×C4—24no—
697C2×C4—24no—
698C2×C4—22no—
699C2×C4—24no—
700C2×C4—22no—
701C2×C4—24no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—24no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—24no—
709C2×C4—22no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—41no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—41no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—42no—
738C2×C4—41no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—42no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—42no—
748C2×C4—41no—
749C2×C4—42no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—416no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4C31×#12014yes—
761C2×C4C31×#12114yes—
762C2×C4C31×#12114yes—
763C2×C4C31×#12114yes—
764C2×C4C31×#12314yes—
765C2×C4C31×#12314yes—
766C2×C4C31×#12414yes—
767C22—24no—
768C22—24no—
769C22—24no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—42no—
774C22—42no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22C2×C31×#12011yescharacteristic
783C22C2×C31×#12111yescharacteristic
784C22C2×C31×#12111yescharacteristic
785C22C2×C31×#12111yescharacteristic
786C22C2×C31×C22⋊Q811yescharacteristic
787C22C2×C31×#12311yescharacteristic
788C22C2×C31×#12311yescharacteristic
789C22C31×#52511yescharacteristic
790C22C2×C31×#12411yescharacteristic
791C22C31×#52911yescharacteristic
792C22C31×#52911yescharacteristic
793C22C31×#53311yescharacteristic
794C22C31×#53311yescharacteristic
795C22C31×#53611yescharacteristic
796C22C31×#53711yescharacteristic
797C22C31×#54111yescharacteristic
798C22C31×#54111yescharacteristic
799C22C31×#54211yescharacteristic
800C22C31×#54211yescharacteristic
801C22C31×#54611yescharacteristic
802C22C31×#54611yescharacteristic
803C22C31×#54711yescharacteristic
804C22C31×#54711yescharacteristic
805C22C31×#54811yescharacteristic
806C22C31×#54811yescharacteristic
807C22C31×#54811yescharacteristic
808C22C31×#54811yescharacteristic
809C22D4×Q8×C3111yescharacteristic
810C22D4×Q8×C3111yescharacteristic
811C22D4×Q8×C3111yescharacteristic
812C22C31×#55011yescharacteristic
813C22C31×#55211yescharacteristic
814C22C31×#55211yescharacteristic
815C22C31×#55411yescharacteristic
816C22C31×#55611yescharacteristic
817C4—42no—
818C4—44no—
819C4—44no—
820C4—42no—
821C4—42no—
822C4—42no—
823C4—42no—
824C4—44no—
825C4—82no—
826C4C31×#39418yes—
827C2—44no—
828C2C2×C31×#39411yescharacteristic
829C2C31×#240711yescharacteristic
830C2C31×#240911yescharacteristic
831C2C31×#241511yescharacteristic
832C2C31×#241711yescharacteristic
833C2C31×#242111yescharacteristic
834C2C31×#242311yescharacteristic
835C2C31×#242611yescharacteristic
836C2C31×#242711yescharacteristic
837C2C31×#242911yescharacteristic
838C2C31×#242911yescharacteristic
839C2C31×#248911yescharacteristic
840C2C31×#249211yescharacteristic
841C2C31×#262511yescharacteristic
842C2C31×#285511yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutator, Frattini, cosocleC24C24×C31
prime radicalC25×C31C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#391C2semidirect
3. C2×C31×#391C2semidirect
4. C2×C31×#389C2semidirect
7. C31×#1442C2semidirect
8. C31×#1441C2semidirect
11. C31×C4⋊#95C2semidirect
95. C2×C22⋊C4×C31Q8semidirect
223. #15179C31direct (N × H)
347. C2×#391C2×C31semidirect
348. C2×#391C2×C31semidirect
349. C2×#389C2×C31semidirect
352. #1442C2×C31semidirect
353. #1441C2×C31semidirect
356. C4⋊#95C2×C31semidirect
516. C2×C22⋊C4Q8×C31semidirect
533. C31#15179direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C31×C22⋊Q82
C2×C31×#3912
C2×C31×#3892
C2×C31×#3802
C2×C4×C22⋊C4×C312
C31×#14422
C31×#14412
C31×#14402
C31×#14392
C31×C4⋊#952
#1517931