Finite Group Databasebeta

← C31×#14017 #21470776

Subgroups — C31×#14017 #21470776

Order 7936.

1810 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Q8×C31C211yesmaximal, characteristic
2C2×C31×#391C211yesmaximal, characteristic
3C2×C31×#391C211yesmaximal, characteristic
4C2×C31×#389C211yesmaximal, characteristic
5C2×C4×C4⋊C4×C31C211yesmaximal, characteristic
6C31×#1444C212yesmaximal
7C31×#1442C212yesmaximal
8C31×#1436C212yesmaximal
9C31×#1436C212yesmaximal
10C31×C4⋊#95C211yesmaximal, characteristic
11C31×C4⋊#95C211yesmaximal, characteristic
12C23×Q8×C31C2211yescharacteristic
13C2×C4×Q8×C31—24no—
14C2×C4×Q8×C31—24no—
15C2×C4×Q8×C31—24no—
16C22×C4⋊C4×C31C2212yes—
17C22×C4⋊C4×C31C2211yescharacteristic
18C22×C4⋊C4×C31C2211yescharacteristic
19C22×C4⋊C4×C31C2212yes—
20C22×C4⋊C4×C31C2211yescharacteristic
21C22×C4⋊C4×C31C2211yescharacteristic
22C22×C4⋊C4×C31C2211yescharacteristic
23C22×C42×C31C2212yes—
24C22×C42×C31C2211yescharacteristic
25C22×C42×C31C2211yescharacteristic
26C22×C42×C31C2211yescharacteristic
27C31×#391—24no—
28C31×#391C418yescomplemented
29C31×#389—24no—
30C4×C4⋊C4×C31—24no—
31C2×C31×#95C2212yes—
32C2×C31×#95C2212yes—
33C2×C31×#95C2211yescharacteristic
34C2×C31×#95C2212yes—
35C2×C31×#95C2212yes—
36C2×C31×#95C2212yes—
37C2×C31×#95C2211yescharacteristic
38C2×C31×#95C2212yes—
39C2×C31×#95C2212yes—
40C2×C31×#95C2212yes—
41C2×C31×#95C2212yes—
42C22×Q8×C31—22no—
43C22×Q8×C31—22no—
44C22×Q8×C31—22no—
45C22×Q8×C31—22no—
46C22×Q8×C31C2×C414yes—
47C22×Q8×C31D414yes—
48C22×Q8×C31Q814yes—
49C23×C4×C31C2312yes—
50C23×C4×C31C2311yescharacteristic
51C23×C4×C31C2312yes—
52C23×C4×C31C2312yes—
53C23×C4×C31C2311yescharacteristic
54C23×C4×C31C2311yescharacteristic
55C23×C4×C31C2311yescharacteristic
56C23×C4×C31C2312yes—
57C23×C4×C31C2311yescharacteristic
58C23×C4×C31C2311yescharacteristic
59C23×C4×C31C2311yescharacteristic
60C4×Q8×C31—232no—
61C2×C4⋊C4×C31—24no—
62C2×C4⋊C4×C31—24no—
63C2×C4⋊C4×C31—24no—
64C2×C4⋊C4×C31—22no—
65C2×C4⋊C4×C31—22no—
66C2×C4⋊C4×C31—22no—
67C2×C4⋊C4×C31—22no—
68C2×C4⋊C4×C31—22no—
69C2×C4⋊C4×C31—22no—
70C2×C4⋊C4×C31—22no—
71C2×C4⋊C4×C31—22no—
72C2×C4⋊C4×C31—22no—
73C2×C4⋊C4×C31—24no—
74C2×C4⋊C4×C31—22no—
75C2×C4⋊C4×C31—24no—
76C2×C4⋊C4×C31—22no—
77C2×C4⋊C4×C31—22no—
78C2×C4⋊C4×C31—42no—
79C2×C4⋊C4×C31C2×C414yes—
80C2×C4⋊C4×C31D414yes—
81C2×C4⋊C4×C31Q814yescomplemented
82C2×C42×C31—24no—
83C2×C42×C31—24no—
84C2×C42×C31—24no—
85C2×C42×C31—22no—
86C2×C42×C31—22no—
87C2×C42×C31—22no—
88C2×C42×C31—22no—
89C2×C42×C31—22no—
90C2×C42×C31—22no—
91C2×C42×C31—22no—
92C2×C42×C31C2×C414yes—
93C2×C42×C31D414yes—
94C31×#95—22no—
95C31×#95—22no—
96C31×#95—24no—
97C31×#95—24no—
98C31×#95—24no—
99C31×#95—24no—
100C31×#95—24no—
101C31×#95—42no—
102C31×#95—42no—
103C31×#95C2×C418yes—
104C31×#95C2×C418yes—
105C24×C31C2411yescharacteristic
106C2×Q8×C31—28no—
107C2×Q8×C31—28no—
108C2×Q8×C31—28no—
109C2×Q8×C31—28no—
110C2×Q8×C31—28no—
111C2×Q8×C31—28no—
112C2×Q8×C31C4⋊C4116yescomplemented
113C22×C4×C31—21no—
114C22×C4×C31—21no—
115C22×C4×C31—21no—
116C22×C4×C31—22no—
117C22×C4×C31—22no—
118C22×C4×C31—21no—
119C22×C4×C31—21no—
120C22×C4×C31—21no—
121C22×C4×C31—22no—
122C22×C4×C31—22no—
123C22×C4×C31—21no—
124C22×C4×C31—21no—
125C22×C4×C31—21no—
126C22×C4×C31—21no—
127C22×C4×C31—21no—
128C22×C4×C31—21no—
129C22×C4×C31—21no—
130C22×C4×C31—21no—
131C22×C4×C31—22no—
132C22×C4×C31—22no—
133C22×C4×C31—21no—
134C22×C4×C31—22no—
135C22×C4×C31—21no—
136C22×C4×C31—21no—
137C22×C4×C31—22no—
138C22×C4×C31—22no—
139C22×C4×C31—21no—
140C22×C4×C31—22no—
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—21no—
149C22×C4×C31—22no—
150C22×C4×C31—22no—
151C22×C4×C31—21no—
152C22×C4×C31—21no—
153C22×C4×C31—21no—
154C22×C4×C31—21no—
155C22×C4×C31—22no—
156C22×C4×C31—21no—
157C22×C4×C31—22no—
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—22no—
166C22×C4×C31—22no—
167C22×C4×C31—22no—
168C22×C4×C31C22×C412yes—
169C22×C4×C31C22×C414yes—
170C22×C4×C31C22×C414yes—
171C22×C4×C31C22×C412yes—
172C22×C4×C31C22×C412yes—
173C22×C4×C31C2×D414yes—
174C22×C4×C31C2×D412yes—
175C22×C4×C31C2×D414yes—
176C22×C4×C31C2×D412yes—
177C22×C4×C31C2×D412yes—
178C22×C4×C31C2×D412yes—
179C22×C4×C31C2×D412yes—
180C22×C4×C31C2×Q812yes—
181C22×C4×C31C2×Q814yes—
182C22×C4×C31C2×Q812yes—
183C22×C4×C31C2×Q812yes—
184C22×C4×C31C2×Q812yes—
185C22×C4×C31#4112yes—
186C22×C4×C31#4112yes—
187C22×C4×C31#4112yes—
188C22×C4×C31#4112yes—
189C22×C4×C31#4112yes—
190C4⋊C4×C31—28no—
191C4⋊C4×C31—216no—
192C4⋊C4×C31—28no—
193C4⋊C4×C31—28no—
194C4⋊C4×C31—28no—
195C4⋊C4×C31—48no—
196C4⋊C4×C31—44no—
197C42×C31—216no—
198C42×C31—28no—
199C42×C31—28no—
200C42×C31—44no—
201#14017C3111yesmaximal, characteristic, direct product factor, Sylow
202C23×C31C23×C411yescharacteristic
203C23×C31C22×D411yescharacteristic
204C23×C31C22×D411yescharacteristic
205C23×C31C22×D411yescharacteristic
206C23×C31C22×Q811yescharacteristic
207C23×C31C22×Q811yescharacteristic
208C23×C31C2×#4111yescharacteristic
209C23×C31C2×#4111yescharacteristic
210C23×C31C2×#4111yescharacteristic
211C23×C31C2×#4111yescharacteristic
212C23×C31C2×#4111yescharacteristic
213C23×C31H(5,𝔽2)11yescharacteristic
214C23×C312−1+411yescharacteristic
215C23×C312−1+411yescharacteristic
216C23×C312−1+411yescharacteristic
217Q8×C31—232no—
218C2×C4×C31—22no—
219C2×C4×C31—24no—
220C2×C4×C31—24no—
221C2×C4×C31—22no—
222C2×C4×C31—22no—
223C2×C4×C31—24no—
224C2×C4×C31—22no—
225C2×C4×C31—24no—
226C2×C4×C31—24no—
227C2×C4×C31—24no—
228C2×C4×C31—22no—
229C2×C4×C31—22no—
230C2×C4×C31—22no—
231C2×C4×C31—22no—
232C2×C4×C31—22no—
233C2×C4×C31—22no—
234C2×C4×C31—22no—
235C2×C4×C31—22no—
236C2×C4×C31—22no—
237C2×C4×C31—24no—
238C2×C4×C31—24no—
239C2×C4×C31—22no—
240C2×C4×C31—22no—
241C2×C4×C31—24no—
242C2×C4×C31—24no—
243C2×C4×C31—22no—
244C2×C4×C31—22no—
245C2×C4×C31—22no—
246C2×C4×C31—22no—
247C2×C4×C31—22no—
248C2×C4×C31—22no—
249C2×C4×C31—24no—
250C2×C4×C31—24no—
251C2×C4×C31—22no—
252C2×C4×C31—22no—
253C2×C4×C31—22no—
254C2×C4×C31—41no—
255C2×C4×C31—41no—
256C2×C4×C31—42no—
257C2×C4×C31—41no—
258C2×C4×C31—41no—
259C2×C4×C31—41no—
260C2×C4×C31—41no—
261C2×C4×C31—42no—
262C2×C4×C31—41no—
263C2×C4×C31—41no—
264C2×C4×C31—42no—
265C2×C4×C31—41no—
266C2×C4×C31—41no—
267C2×C4×C31—41no—
268C2×C4×C31—42no—
269C2×C4×C31—41no—
270C2×C4×C31—42no—
271C2×C4×C31—41no—
272C2×C4×C31—41no—
273C2×C4×C31—41no—
274C2×C4×C31—42no—
275C2×C4×C31—41no—
276C2×C4×C31—42no—
277C2×C4×C31—42no—
278C2×C4×C31—42no—
279C2×C4×C31—42no—
280C2×C4×C31—42no—
281C2×C4×C31—42no—
282C2×C4×C31—42no—
283C2×C4×C31—42no—
284C2×C4×C31—42no—
285C2×C4×C31C2×C4⋊C418yes—
286C2×C4×C31C2×C4⋊C414yes—
287C2×C4×C31C4×D414yes—
288C2×C4×C31C4×D414yes—
289C2×C4×C31C4×Q814yescomplemented
290C2×C4×C31#12014yes—
291C2×C4×C31C22⋊Q814yes—
292C2×C4×C31C22⋊Q814yes—
293C2×C4×C31C22⋊Q814yes—
294C2×C4×C31#12314yes—
295C22×C4×Q8C2×C3111yescharacteristic
296C2×#391C2×C3111yescharacteristic
297C2×#391C2×C3111yescharacteristic
298C2×#389C2×C3111yescharacteristic
299C2×C4×C4⋊C4C2×C3111yescharacteristic
300#1444C2×C3112yes—
301#1442C2×C3112yes—
302#1436C2×C3112yes—
303#1436C2×C3112yes—
304C4⋊#95C2×C3111yescharacteristic
305C4⋊#95C2×C3111yescharacteristic
306C22×C31C22×C4⋊C411yescharacteristic
307C22×C31C2×C4×D411yescharacteristic
308C22×C31C2×C4×D411yescharacteristic
309C22×C31C2×C4×Q811yescharacteristic
310C22×C31C4×#4111yescharacteristic
311C22×C31#51911yescharacteristic
312C22×C31#52011yescharacteristic
313C22×C31C2×#12011yescharacteristic
314C22×C31C2×C22⋊Q811yescharacteristic
315C22×C31C2×C22⋊Q811yescharacteristic
316C22×C31C2×C22⋊Q811yescharacteristic
317C22×C31C2×#12311yescharacteristic
318C22×C31#52511yescharacteristic
319C22×C31#52911yescharacteristic
320C22×C31#53311yescharacteristic
321C22×C31#53611yescharacteristic
322C22×C31#53711yescharacteristic
323C22×C31#54111yescharacteristic
324C22×C31#54211yescharacteristic
325C22×C31#54611yescharacteristic
326C22×C31#54711yescharacteristic
327C22×C31#54811yescharacteristic
328C22×C31#54811yescharacteristic
329C22×C31#54811yescharacteristic
330C22×C31D4×Q811yescharacteristic
331C22×C31D4×Q811yescharacteristic
332C22×C31#55011yescharacteristic
333C22×C31#55611yescharacteristic
334C22×C31#55611yescharacteristic
335C22×C31#55711yescharacteristic
336C22×C31#55711yescharacteristic
337C22×C31#55711yescharacteristic
338C22×C31#55711yescharacteristic
339C22×C31Q8211yescharacteristic
340C22×C31#55911yescharacteristic
341C4×C31—24no—
342C4×C31—28no—
343C4×C31—24no—
344C4×C31—42no—
345C4×C31—44no—
346C4×C31—42no—
347C4×C31—44no—
348C4×C31—42no—
349C4×C31—42no—
350C4×C31—82no—
351C4×C31#38518yes—
352C23×Q8C22×C3111yescharacteristic
353C2×C4×Q8—24no—
354C2×C4×Q8—24no—
355C2×C4×Q8—24no—
356C22×C4⋊C4C22×C3112yes—
357C22×C4⋊C4C22×C3111yescharacteristic
358C22×C4⋊C4C22×C3111yescharacteristic
359C22×C4⋊C4C22×C3112yes—
360C22×C4⋊C4C22×C3111yescharacteristic
361C22×C4⋊C4C22×C3111yescharacteristic
362C22×C4⋊C4C22×C3111yescharacteristic
363C22×C42C22×C3112yes—
364C22×C42C22×C3111yescharacteristic
365C22×C42C22×C3111yescharacteristic
366C22×C42C22×C3111yescharacteristic
367#391—24no—
368#391C4×C3118yescomplemented
369#389—24no—
370C4×C4⋊C4—24no—
371C2×#95C22×C3112yes—
372C2×#95C22×C3112yes—
373C2×#95C22×C3111yescharacteristic
374C2×#95C22×C3112yes—
375C2×#95C22×C3112yes—
376C2×#95C22×C3112yes—
377C2×#95C22×C3111yescharacteristic
378C2×#95C22×C3112yes—
379C2×#95C22×C3112yes—
380C2×#95C22×C3112yes—
381C2×#95C22×C3112yes—
382C2×C31C2×#38511yescharacteristic
383C2×C31C4×C22⋊Q811yescharacteristic
384C2×C31#232311yescharacteristic
385C2×C31Q8×C4⋊C411yescharacteristic
386C2×C31#235111yescharacteristic
387C2×C31#236511yescharacteristic
388C2×C31#236711yescharacteristic
389C2×C31#240711yescharacteristic
390C2×C31#240911yescharacteristic
391C2×C31#244611yescharacteristic
392C2×C31#244811yescharacteristic
393C2×C31#245111yescharacteristic
394C2×C31#245311yescharacteristic
395C2×C31#258111yescharacteristic
396C2×C31#258211yescharacteristic
397C22×Q8—22no—
398C22×Q8—22no—
399C22×Q8—22no—
400C22×Q8—22no—
401C22×Q8C2×C4×C3114yes—
402C22×Q8D4×C3114yes—
403C22×Q8Q8×C3114yes—
404C23×C4C23×C3112yes—
405C23×C4C23×C3112yes—
406C23×C4C23×C3111yescharacteristic
407C23×C4C23×C3112yes—
408C23×C4C23×C3111yescharacteristic
409C23×C4C23×C3111yescharacteristic
410C23×C4C23×C3111yescharacteristic
411C23×C4C23×C3112yes—
412C23×C4C23×C3111yescharacteristic
413C23×C4C23×C3111yescharacteristic
414C23×C4C23×C3111yescharacteristic
415C4×Q8—232no—
416C2×C4⋊C4—24no—
417C2×C4⋊C4—24no—
418C2×C4⋊C4—24no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—22no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—22no—
424C2×C4⋊C4—22no—
425C2×C4⋊C4—22no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—24no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—24no—
431C2×C4⋊C4—22no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—42no—
434C2×C4⋊C4C2×C4×C3114yes—
435C2×C4⋊C4D4×C3114yes—
436C2×C4⋊C4Q8×C3114yescomplemented
437C2×C42—24no—
438C2×C42—24no—
439C2×C42—24no—
440C2×C42—22no—
441C2×C42—22no—
442C2×C42—22no—
443C2×C42—22no—
444C2×C42—22no—
445C2×C42—22no—
446C2×C42—22no—
447C2×C42C2×C4×C3114yes—
448C2×C42D4×C3114yes—
449#95—22no—
450#95—22no—
451#95—24no—
452#95—24no—
453#95—24no—
454#95—24no—
455#95—24no—
456#95—42no—
457#95—42no—
458#95C2×C4×C3118yes—
459#95C2×C4×C3118yes—
460C31#1401711yescharacteristic, direct product factor, Sylow
461C24C24×C3111yescharacteristic
462C2×Q8—28no—
463C2×Q8—28no—
464C2×Q8—28no—
465C2×Q8—28no—
466C2×Q8—28no—
467C2×Q8—28no—
468C2×Q8C4⋊C4×C31116yescomplemented
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—21no—
490C22×C4—22no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—21no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—22no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—22no—
512C22×C4—21no—
513C22×C4—22no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4C22×C4×C3112yes—
525C22×C4C22×C4×C3114yes—
526C22×C4C22×C4×C3114yes—
527C22×C4C22×C4×C3112yes—
528C22×C4C22×C4×C3112yes—
529C22×C4C2×D4×C3114yes—
530C22×C4C2×D4×C3112yes—
531C22×C4C2×D4×C3114yes—
532C22×C4C2×D4×C3112yes—
533C22×C4C2×D4×C3112yes—
534C22×C4C2×D4×C3112yes—
535C22×C4C2×D4×C3112yes—
536C22×C4C2×Q8×C3112yes—
537C22×C4C2×Q8×C3114yes—
538C22×C4C2×Q8×C3112yes—
539C22×C4C2×Q8×C3112yes—
540C22×C4C2×Q8×C3112yes—
541C22×C4#41×C3112yes—
542C22×C4#41×C3112yes—
543C22×C4#41×C3112yes—
544C22×C4#41×C3112yes—
545C22×C4#41×C3112yes—
546C4⋊C4—28no—
547C4⋊C4—216no—
548C4⋊C4—28no—
549C4⋊C4—28no—
550C4⋊C4—28no—
551C4⋊C4—48no—
552C4⋊C4—44no—
553C42—216no—
554C42—28no—
555C42—28no—
556C42—44no—
557C23C23×C4×C3111yescharacteristic
558C23C22×D4×C3111yescharacteristic
559C23C22×D4×C3111yescharacteristic
560C23C22×D4×C3111yescharacteristic
561C23C22×Q8×C3111yescharacteristic
562C23C22×Q8×C3111yescharacteristic
563C23C2×#41×C3111yescharacteristic
564C23C2×#41×C3111yescharacteristic
565C23C2×#41×C3111yescharacteristic
566C23C2×#41×C3111yescharacteristic
567C23C2×#41×C3111yescharacteristic
568C23C31×H(5,𝔽2)11yescharacteristic
569C23C31×2−1+411yescharacteristic
570C23C31×2−1+411yescharacteristic
571C23C31×2−1+411yescharacteristic
572Q8—232no—
573C2×C4—22no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—24no—
579C2×C4—22no—
580C2×C4—24no—
581C2×C4—24no—
582C2×C4—24no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—24no—
593C2×C4—24no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—24no—
597C2×C4—24no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—24no—
605C2×C4—24no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—42no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—42no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—42no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—42no—
624C2×C4—41no—
625C2×C4—42no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—42no—
630C2×C4—41no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—42no—
640C2×C4C2×C4⋊C4×C3118yes—
641C2×C4C2×C4⋊C4×C3114yes—
642C2×C4C4×D4×C3114yes—
643C2×C4C4×D4×C3114yes—
644C2×C4C4×Q8×C3114yescomplemented
645C2×C4C31×#12014yes—
646C2×C4C31×C22⋊Q814yes—
647C2×C4C31×C22⋊Q814yes—
648C2×C4C31×C22⋊Q814yes—
649C2×C4C31×#12314yes—
650C22C22×C4⋊C4×C3111yescharacteristic
651C22C2×C4×D4×C3111yescharacteristic
652C22C2×C4×D4×C3111yescharacteristic
653C22C2×C4×Q8×C3111yescharacteristic
654C22C4×#41×C3111yescharacteristic
655C22C31×#51911yescharacteristic
656C22C31×#52011yescharacteristic
657C22C2×C31×#12011yescharacteristic
658C22C2×C31×C22⋊Q811yescharacteristic
659C22C2×C31×C22⋊Q811yescharacteristic
660C22C2×C31×C22⋊Q811yescharacteristic
661C22C2×C31×#12311yescharacteristic
662C22C31×#52511yescharacteristic
663C22C31×#52911yescharacteristic
664C22C31×#53311yescharacteristic
665C22C31×#53611yescharacteristic
666C22C31×#53711yescharacteristic
667C22C31×#54111yescharacteristic
668C22C31×#54211yescharacteristic
669C22C31×#54611yescharacteristic
670C22C31×#54711yescharacteristic
671C22C31×#54811yescharacteristic
672C22C31×#54811yescharacteristic
673C22C31×#54811yescharacteristic
674C22D4×Q8×C3111yescharacteristic
675C22D4×Q8×C3111yescharacteristic
676C22C31×#55011yescharacteristic
677C22C31×#55611yescharacteristic
678C22C31×#55611yescharacteristic
679C22C31×#55711yescharacteristic
680C22C31×#55711yescharacteristic
681C22C31×#55711yescharacteristic
682C22C31×#55711yescharacteristic
683C22Q82×C3111yescharacteristic
684C22C31×#55911yescharacteristic
685C4—24no—
686C4—28no—
687C4—24no—
688C4—42no—
689C4—44no—
690C4—42no—
691C4—44no—
692C4—42no—
693C4—42no—
694C4—82no—
695C4C31×#38518yes—
696C2C2×C31×#38511yescharacteristic
697C2C4×C31×C22⋊Q811yescharacteristic
698C2C31×#232311yescharacteristic
699C2Q8×C4⋊C4×C3111yescharacteristic
700C2C31×#235111yescharacteristic
701C2C31×#236511yescharacteristic
702C2C31×#236711yescharacteristic
703C2C31×#240711yescharacteristic
704C2C31×#240911yescharacteristic
705C2C31×#244611yescharacteristic
706C2C31×#244811yescharacteristic
707C2C31×#245111yescharacteristic
708C2C31×#245311yescharacteristic
709C2C31×#258111yescharacteristic
710C2C31×#258211yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C31C24
commutatorC23C23×C4×C31
Frattini, cosocleC24C24×C31
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
28. C31×#391C4semidirect
81. C2×C4⋊C4×C31Q8semidirect
112. C2×Q8×C31C4⋊C4semidirect
201. #14017C31direct (N × H)
289. C2×C4×C31C4×Q8semidirect
368. #391C4×C31semidirect
436. C2×C4⋊C4Q8×C31semidirect
460. C31#14017direct (N × H)
468. C2×Q8C4⋊C4×C31semidirect
644. C2×C4C4×Q8×C31semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Q8×C312
C2×C31×#3912
C2×C31×#3892
C2×C4×C4⋊C4×C312
C31×#14442
C31×#14422
C31×#14362
C31×C4⋊#952
#1401731