Finite Group Databasebeta

← C31×#13997 #21470756

Subgroups — C31×#13997 #21470756

Order 7936.

2106 conjugacy classes of subgroups.

The subgroup lattice has 852 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×C4⋊C4×C31C211yesmaximal, characteristic, complemented
7C2×C4×C22⋊C4×C31C211yesmaximal, characteristic
8C31×#1445C212yesmaximal, complemented
9C31×#1439C212yesmaximal
10C31×#1437C212yesmaximal
11C31×C4⋊#95C212yesmaximal, complemented
12C23×Q8×C31C2211yescharacteristic
13C24×C4×C31C2211yescharacteristic
14C2×C31×C22⋊Q8—24no—
15C2×C31×C22⋊Q8—24no—
16C2×C31×C22⋊Q8C418yescomplemented
17C22×C4⋊C4×C31C2211yescharacteristic
18C22×C4⋊C4×C31C2212yes—
19C22×C4⋊C4×C31C2212yes—
20C22×C4⋊C4×C31C2211yescharacteristic
21C22×C4⋊C4×C31C2211yescharacteristic
22C22×C22⋊C4×C31C2211yescharacteristic
23C22×C22⋊C4×C31C2212yes—
24C22×C22⋊C4×C31C2212yes—
25C22×C22⋊C4×C31C2211yescharacteristic
26C22×C42×C31C2211yescharacteristic
27C22×C42×C31C2212yes—
28C22×C42×C31C2211yescharacteristic
29C31×#391—24no—
30C31×#391—24no—
31C31×#389—24no—
32C31×#380—24no—
33C4×C4⋊C4×C31—24no—
34C4×C22⋊C4×C31—24no—
35C2×C31×#95C2211yescharacteristic
36C2×C31×#95C2212yes—
37C2×C31×#95C2212yes—
38C2×C31×#95C2212yes—
39C2×C31×#95C2212yes—
40C2×C31×#95C2212yes—
41C2×C31×#95C2212yes—
42C2×C31×#95C2212yes—
43C2×C31×#95C2211yescharacteristic
44C25×C31C2311yescharacteristic
45C22×Q8×C31—22no—
46C22×Q8×C31—22no—
47C22×Q8×C31—22no—
48C22×Q8×C31—22no—
49C22×Q8×C31—22no—
50C22×Q8×C31—22no—
51C22×Q8×C31C2×C414yes—
52C23×C4×C31—22no—
53C23×C4×C31—22no—
54C23×C4×C31—22no—
55C23×C4×C31—22no—
56C23×C4×C31—22no—
57C23×C4×C31—22no—
58C23×C4×C31C2×C414yes—
59C23×C4×C31C2312yes—
60C23×C4×C31C2312yes—
61C23×C4×C31C2311yescharacteristic
62C23×C4×C31C2312yes—
63C23×C4×C31C2311yescharacteristic
64C23×C4×C31C2311yescharacteristic
65C23×C4×C31C2311yescharacteristic
66C23×C4×C31C2312yes—
67C23×C4×C31C2311yescharacteristic
68C23×C4×C31C2311yescharacteristic
69C31×C22⋊Q8—232no—
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—24no—
76C2×C4⋊C4×C31—22no—
77C2×C4⋊C4×C31—22no—
78C2×C4⋊C4×C31—24no—
79C2×C4⋊C4×C31—42no—
80C2×C4⋊C4×C31C2×C418yes—
81C2×C4⋊C4×C31C2×C414yes—
82C2×C4⋊C4×C31D414yes—
83C2×C4⋊C4×C31D414yes—
84C2×C4⋊C4×C31D414yes—
85C2×C22⋊C4×C31—22no—
86C2×C22⋊C4×C31—24no—
87C2×C22⋊C4×C31—24no—
88C2×C22⋊C4×C31—22no—
89C2×C22⋊C4×C31—22no—
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×C31C2×C418yes—
96C2×C22⋊C4×C31Q814yescomplemented
97C2×C42×C31—22no—
98C2×C42×C31—22no—
99C2×C42×C31—22no—
100C2×C42×C31—24no—
101C2×C42×C31—22no—
102C2×C42×C31—22no—
103C2×C42×C31—24no—
104C2×C42×C31—42no—
105C2×C42×C31D414yes—
106C31×#95—22no—
107C31×#95—22no—
108C31×#95—24no—
109C31×#95—24no—
110C31×#95—24no—
111C31×#95—24no—
112C31×#95—24no—
113C31×#95—24no—
114C31×#95—24no—
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×C31—21no—
125C24×C31—21no—
126C24×C31—21no—
127C24×C31C22×C412yes—
128C24×C31C2×Q812yes—
129C24×C31#4112yes—
130C24×C31C2411yescharacteristic
131C2×Q8×C31—28no—
132C2×Q8×C31—28no—
133C2×Q8×C31—28no—
134C2×Q8×C31—44no—
135C2×Q8×C31—44no—
136C2×Q8×C31—44no—
137C2×Q8×C31—44no—
138C22×C4×C31—21no—
139C22×C4×C31—22no—
140C22×C4×C31—21no—
141C22×C4×C31—22no—
142C22×C4×C31—21no—
143C22×C4×C31—22no—
144C22×C4×C31—22no—
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—22no—
153C22×C4×C31—22no—
154C22×C4×C31—21no—
155C22×C4×C31—21no—
156C22×C4×C31—22no—
157C22×C4×C31—21no—
158C22×C4×C31—22no—
159C22×C4×C31—22no—
160C22×C4×C31—21no—
161C22×C4×C31—21no—
162C22×C4×C31—21no—
163C22×C4×C31—22no—
164C22×C4×C31—21no—
165C22×C4×C31—21no—
166C22×C4×C31—21no—
167C22×C4×C31—21no—
168C22×C4×C31—22no—
169C22×C4×C31—22no—
170C22×C4×C31—21no—
171C22×C4×C31—21no—
172C22×C4×C31—22no—
173C22×C4×C31—22no—
174C22×C4×C31—22no—
175C22×C4×C31—21no—
176C22×C4×C31—21no—
177C22×C4×C31—21no—
178C22×C4×C31—22no—
179C22×C4×C31—21no—
180C22×C4×C31—21no—
181C22×C4×C31—21no—
182C22×C4×C31—28no—
183C22×C4×C31—28no—
184C22×C4×C31—28no—
185C22×C4×C31—22no—
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—44no—
193C22×C4×C31—44no—
194C22×C4×C31—44no—
195C22×C4×C31—44no—
196C22×C4×C31C22×C414yes—
197C22×C4×C31C22×C412yes—
198C22×C4×C31C22×C414yes—
199C22×C4×C31C22×C412yes—
200C22×C4×C31C2×D412yes—
201C22×C4×C31C2×D414yes—
202C22×C4×C31C2×D414yes—
203C22×C4×C31C2×D414yes—
204C22×C4×C31C2×D412yes—
205C22×C4×C31C2×D412yes—
206C22×C4×C31C2×D412yes—
207C22×C4×C31C2×D412yes—
208C22×C4×C31C2×D412yes—
209C22×C4×C31C2×Q812yes—
210C22×C4×C31C2×Q812yes—
211C22×C4×C31#4112yes—
212C22×C4×C31#4112yes—
213C22×C4×C31#4112yes—
214C22×C4×C31#4112yes—
215C4⋊C4×C31—216no—
216C4⋊C4×C31—28no—
217C4⋊C4×C31—48no—
218C4⋊C4×C31—44no—
219C4⋊C4×C31C22⋊C4116yescomplemented
220C22⋊C4×C31—28no—
221C22⋊C4×C31—216no—
222C22⋊C4×C31—28no—
223C22⋊C4×C31—48no—
224C42×C31—28no—
225C42×C31—48no—
226C42×C31—44no—
227#13997C3111yesmaximal, characteristic, direct product factor, Sylow
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—22no—
243C23×C31—22no—
244C23×C31—22no—
245C23×C31—22no—
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×C31—41no—
259C23×C31—41no—
260C23×C31—41no—
261C23×C31—41no—
262C23×C31C4×Q814yes—
263C23×C31C23×C411yescharacteristic
264C23×C31C22×D411yescharacteristic
265C23×C31C22×D411yescharacteristic
266C23×C31C22×D411yescharacteristic
267C23×C31C22×D411yescharacteristic
268C23×C31C22×Q811yescharacteristic
269C23×C31C2×#4111yescharacteristic
270C23×C31C2×#4111yescharacteristic
271C23×C31C2×#4111yescharacteristic
272C23×C31C2×#4111yescharacteristic
273C23×C31C2×#4111yescharacteristic
274C23×C31H(5,𝔽2)11yescharacteristic
275C23×C312−1+411yescharacteristic
276C23×C312−1+411yescharacteristic
277C23×C312−1+411yescharacteristic
278Q8×C31—416no—
279C2×C4×C31—24no—
280C2×C4×C31—24no—
281C2×C4×C31—22no—
282C2×C4×C31—22no—
283C2×C4×C31—22no—
284C2×C4×C31—24no—
285C2×C4×C31—24no—
286C2×C4×C31—24no—
287C2×C4×C31—24no—
288C2×C4×C31—22no—
289C2×C4×C31—22no—
290C2×C4×C31—22no—
291C2×C4×C31—24no—
292C2×C4×C31—22no—
293C2×C4×C31—22no—
294C2×C4×C31—22no—
295C2×C4×C31—24no—
296C2×C4×C31—24no—
297C2×C4×C31—22no—
298C2×C4×C31—24no—
299C2×C4×C31—22no—
300C2×C4×C31—22no—
301C2×C4×C31—22no—
302C2×C4×C31—22no—
303C2×C4×C31—24no—
304C2×C4×C31—22no—
305C2×C4×C31—24no—
306C2×C4×C31—22no—
307C2×C4×C31—22no—
308C2×C4×C31—22no—
309C2×C4×C31—41no—
310C2×C4×C31—41no—
311C2×C4×C31—42no—
312C2×C4×C31—42no—
313C2×C4×C31—41no—
314C2×C4×C31—42no—
315C2×C4×C31—42no—
316C2×C4×C31—41no—
317C2×C4×C31—41no—
318C2×C4×C31—41no—
319C2×C4×C31—42no—
320C2×C4×C31—41no—
321C2×C4×C31—41no—
322C2×C4×C31—42no—
323C2×C4×C31—42no—
324C2×C4×C31—41no—
325C2×C4×C31—41no—
326C2×C4×C31—41no—
327C2×C4×C31—41no—
328C2×C4×C31—41no—
329C2×C4×C31—42no—
330C2×C4×C31—41no—
331C2×C4×C31—41no—
332C2×C4×C31—41no—
333C2×C4×C31—416no—
334C2×C4×C31—42no—
335C2×C4×C31—42no—
336C2×C4×C31—42no—
337C2×C4×C31—42no—
338C2×C4×C31—42no—
339C2×C4×C31—42no—
340C2×C4×C31—42no—
341C2×C4×C31C2×C22⋊C418yes—
342C2×C4×C31C2×C22⋊C414yes—
343C2×C4×C31C4×D414yes—
344C2×C4×C31C4×D414yes—
345C2×C4×C31#12114yes—
346C2×C4×C31#12114yes—
347C2×C4×C31C22⋊Q814yescomplemented
348C2×C4×C31#12414yes—
349C2×C4×C31#12714yes—
350C22×C22⋊Q8C2×C3111yescharacteristic
351C2×#391C2×C3111yescharacteristic, complemented
352C2×#391C2×C3111yescharacteristic, complemented
353C2×#389C2×C3111yescharacteristic, complemented
354C2×#380C2×C3111yescharacteristic
355C2×C4×C4⋊C4C2×C3111yescharacteristic, complemented
356C2×C4×C22⋊C4C2×C3111yescharacteristic
357#1445C2×C3112yescomplemented
358#1439C2×C3112yes—
359#1437C2×C3112yes—
360C4⋊#95C2×C3112yescomplemented
361C22×C31—24no—
362C22×C31—24no—
363C22×C31—24no—
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×C31—42no—
373C22×C31—42no—
374C22×C31—42no—
375C22×C31—42no—
376C22×C31C22×C22⋊C411yescharacteristic
377C22×C31C2×C4×D411yescharacteristic
378C22×C31C2×C4×D411yescharacteristic
379C22×C31C2×C4×Q811yescharacteristic
380C22×C31C4×#4111yescharacteristic
381C22×C31#51911yescharacteristic
382C22×C31#52011yescharacteristic
383C22×C31C2×#12111yescharacteristic
384C22×C31C2×#12111yescharacteristic
385C22×C31C2×C22⋊Q811yescharacteristic
386C22×C31#52511yescharacteristic
387C22×C31C2×#12411yescharacteristic
388C22×C31#52911yescharacteristic
389C22×C31C2×#12711yescharacteristic
390C22×C31#53311yescharacteristic
391C22×C31#53611yescharacteristic
392C22×C31#53711yescharacteristic
393C22×C31#54111yescharacteristic
394C22×C31#54211yescharacteristic
395C22×C31#54611yescharacteristic
396C22×C31#54611yescharacteristic
397C22×C31#54611yescharacteristic
398C22×C31#54711yescharacteristic
399C22×C31#54711yescharacteristic
400C22×C31#54711yescharacteristic
401C22×C31#54811yescharacteristic
402C22×C31#54811yescharacteristic
403C22×C31#54811yescharacteristic
404C22×C31D4×Q811yescharacteristic
405C22×C31D4×Q811yescharacteristic
406C22×C31D4×Q811yescharacteristic
407C22×C31#55211yescharacteristic
408C22×C31#55211yescharacteristic
409C22×C31#55411yescharacteristic
410C22×C31#55611yescharacteristic
411C4×C31—28no—
412C4×C31—24no—
413C4×C31—42no—
414C4×C31—44no—
415C4×C31—42no—
416C4×C31—42no—
417C4×C31—42no—
418C4×C31—44no—
419C4×C31—82no—
420C4×C31#39018yes—
421C23×Q8C22×C3111yescharacteristic
422C24×C4C22×C3111yescharacteristic
423C2×C22⋊Q8—24no—
424C2×C22⋊Q8—24no—
425C2×C22⋊Q8C4×C3118yescomplemented
426C22×C4⋊C4C22×C3111yescharacteristic
427C22×C4⋊C4C22×C3112yes—
428C22×C4⋊C4C22×C3112yes—
429C22×C4⋊C4C22×C3111yescharacteristic
430C22×C4⋊C4C22×C3111yescharacteristic
431C22×C22⋊C4C22×C3111yescharacteristic
432C22×C22⋊C4C22×C3112yes—
433C22×C22⋊C4C22×C3112yes—
434C22×C22⋊C4C22×C3111yescharacteristic
435C22×C42C22×C3111yescharacteristic
436C22×C42C22×C3112yes—
437C22×C42C22×C3111yescharacteristic
438#391—24no—
439#391—24no—
440#389—24no—
441#380—24no—
442C4×C4⋊C4—24no—
443C4×C22⋊C4—24no—
444C2×#95C22×C3111yescharacteristic
445C2×#95C22×C3112yes—
446C2×#95C22×C3112yes—
447C2×#95C22×C3112yes—
448C2×#95C22×C3112yes—
449C2×#95C22×C3112yes—
450C2×#95C22×C3112yes—
451C2×#95C22×C3112yes—
452C2×#95C22×C3111yescharacteristic
453C2×C31—44no—
454C2×C31C2×#39011yescharacteristic
455C2×C31C4×C22⋊Q811yescharacteristic
456C2×C31#232311yescharacteristic
457C2×C31#233911yescharacteristic
458C2×C31Q8×C22⋊C411yescharacteristic
459C2×C31#236011yescharacteristic
460C2×C31#236211yescharacteristic
461C2×C31#241511yescharacteristic
462C2×C31#241711yescharacteristic
463C2×C31#242711yescharacteristic
464C2×C31#242911yescharacteristic
465C2×C31#248911yescharacteristic
466C2×C31#249211yescharacteristic
467C2×C31#254011yescharacteristic
468C2×C31#254211yescharacteristic
469C25C23×C3111yescharacteristic
470C22×Q8—22no—
471C22×Q8—22no—
472C22×Q8—22no—
473C22×Q8—22no—
474C22×Q8—22no—
475C22×Q8—22no—
476C22×Q8C2×C4×C3114yes—
477C23×C4—22no—
478C23×C4—22no—
479C23×C4—22no—
480C23×C4—22no—
481C23×C4—22no—
482C23×C4—22no—
483C23×C4C2×C4×C3114yes—
484C23×C4C23×C3112yes—
485C23×C4C23×C3112yes—
486C23×C4C23×C3111yescharacteristic
487C23×C4C23×C3112yes—
488C23×C4C23×C3111yescharacteristic
489C23×C4C23×C3111yescharacteristic
490C23×C4C23×C3111yescharacteristic
491C23×C4C23×C3112yes—
492C23×C4C23×C3111yescharacteristic
493C23×C4C23×C3111yescharacteristic
494C22⋊Q8—232no—
495C2×C4⋊C4—24no—
496C2×C4⋊C4—24no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—22no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—24no—
501C2×C4⋊C4—22no—
502C2×C4⋊C4—22no—
503C2×C4⋊C4—24no—
504C2×C4⋊C4—42no—
505C2×C4⋊C4C2×C4×C3118yes—
506C2×C4⋊C4C2×C4×C3114yes—
507C2×C4⋊C4D4×C3114yes—
508C2×C4⋊C4D4×C3114yes—
509C2×C4⋊C4D4×C3114yes—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—24no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—22no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—22no—
517C2×C22⋊C4—24no—
518C2×C22⋊C4—24no—
519C2×C22⋊C4—42no—
520C2×C22⋊C4C2×C4×C3118yes—
521C2×C22⋊C4Q8×C3114yescomplemented
522C2×C42—22no—
523C2×C42—22no—
524C2×C42—22no—
525C2×C42—24no—
526C2×C42—22no—
527C2×C42—22no—
528C2×C42—24no—
529C2×C42—42no—
530C2×C42D4×C3114yes—
531#95—22no—
532#95—22no—
533#95—24no—
534#95—24no—
535#95—24no—
536#95—24no—
537#95—24no—
538#95—24no—
539#95—24no—
540C31#1399711yescharacteristic, direct product factor, Sylow
541C24—21no—
542C24—21no—
543C24—21no—
544C24—21no—
545C24—21no—
546C24—21no—
547C24—21no—
548C24—21no—
549C24—21no—
550C24—21no—
551C24—21no—
552C24—21no—
553C24C22×C4×C3112yes—
554C24C2×Q8×C3112yes—
555C24#41×C3112yes—
556C24C24×C3111yescharacteristic
557C2×Q8—28no—
558C2×Q8—28no—
559C2×Q8—28no—
560C2×Q8—44no—
561C2×Q8—44no—
562C2×Q8—44no—
563C2×Q8—44no—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—22no—
568C22×C4—21no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—22no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—22no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—28no—
609C22×C4—28no—
610C22×C4—28no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—44no—
619C22×C4—44no—
620C22×C4—44no—
621C22×C4—44no—
622C22×C4C22×C4×C3114yes—
623C22×C4C22×C4×C3112yes—
624C22×C4C22×C4×C3114yes—
625C22×C4C22×C4×C3112yes—
626C22×C4C2×D4×C3112yes—
627C22×C4C2×D4×C3114yes—
628C22×C4C2×D4×C3114yes—
629C22×C4C2×D4×C3114yes—
630C22×C4C2×D4×C3112yes—
631C22×C4C2×D4×C3112yes—
632C22×C4C2×D4×C3112yes—
633C22×C4C2×D4×C3112yes—
634C22×C4C2×D4×C3112yes—
635C22×C4C2×Q8×C3112yes—
636C22×C4C2×Q8×C3112yes—
637C22×C4#41×C3112yes—
638C22×C4#41×C3112yes—
639C22×C4#41×C3112yes—
640C22×C4#41×C3112yes—
641C4⋊C4—216no—
642C4⋊C4—28no—
643C4⋊C4—48no—
644C4⋊C4—44no—
645C4⋊C4C22⋊C4×C31116yescomplemented
646C22⋊C4—28no—
647C22⋊C4—216no—
648C22⋊C4—28no—
649C22⋊C4—48no—
650C42—28no—
651C42—48no—
652C42—44no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23C4×Q8×C3114yes—
688C23C23×C4×C3111yescharacteristic
689C23C22×D4×C3111yescharacteristic
690C23C22×D4×C3111yescharacteristic
691C23C22×D4×C3111yescharacteristic
692C23C22×D4×C3111yescharacteristic
693C23C22×Q8×C3111yescharacteristic
694C23C2×#41×C3111yescharacteristic
695C23C2×#41×C3111yescharacteristic
696C23C2×#41×C3111yescharacteristic
697C23C2×#41×C3111yescharacteristic
698C23C2×#41×C3111yescharacteristic
699C23C31×H(5,𝔽2)11yescharacteristic
700C23C31×2−1+411yescharacteristic
701C23C31×2−1+411yescharacteristic
702C23C31×2−1+411yescharacteristic
703Q8—416no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—24no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—22no—
723C2×C4—24no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—24no—
729C2×C4—22no—
730C2×C4—24no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—42no—
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—42no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—42no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—416no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4C2×C22⋊C4×C3118yes—
767C2×C4C2×C22⋊C4×C3114yes—
768C2×C4C4×D4×C3114yes—
769C2×C4C4×D4×C3114yes—
770C2×C4C31×#12114yes—
771C2×C4C31×#12114yes—
772C2×C4C31×C22⋊Q814yescomplemented
773C2×C4C31×#12414yes—
774C2×C4C31×#12714yes—
775C22—24no—
776C22—24no—
777C22—24no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22C22×C22⋊C4×C3111yescharacteristic
791C22C2×C4×D4×C3111yescharacteristic
792C22C2×C4×D4×C3111yescharacteristic
793C22C2×C4×Q8×C3111yescharacteristic
794C22C4×#41×C3111yescharacteristic
795C22C31×#51911yescharacteristic
796C22C31×#52011yescharacteristic
797C22C2×C31×#12111yescharacteristic
798C22C2×C31×#12111yescharacteristic
799C22C2×C31×C22⋊Q811yescharacteristic
800C22C31×#52511yescharacteristic
801C22C2×C31×#12411yescharacteristic
802C22C31×#52911yescharacteristic
803C22C2×C31×#12711yescharacteristic
804C22C31×#53311yescharacteristic
805C22C31×#53611yescharacteristic
806C22C31×#53711yescharacteristic
807C22C31×#54111yescharacteristic
808C22C31×#54211yescharacteristic
809C22C31×#54611yescharacteristic
810C22C31×#54611yescharacteristic
811C22C31×#54611yescharacteristic
812C22C31×#54711yescharacteristic
813C22C31×#54711yescharacteristic
814C22C31×#54711yescharacteristic
815C22C31×#54811yescharacteristic
816C22C31×#54811yescharacteristic
817C22C31×#54811yescharacteristic
818C22D4×Q8×C3111yescharacteristic
819C22D4×Q8×C3111yescharacteristic
820C22D4×Q8×C3111yescharacteristic
821C22C31×#55211yescharacteristic
822C22C31×#55211yescharacteristic
823C22C31×#55411yescharacteristic
824C22C31×#55611yescharacteristic
825C4—28no—
826C4—24no—
827C4—42no—
828C4—44no—
829C4—42no—
830C4—42no—
831C4—42no—
832C4—44no—
833C4—82no—
834C4C31×#39018yes—
835C2—44no—
836C2C2×C31×#39011yescharacteristic
837C2C4×C31×C22⋊Q811yescharacteristic
838C2C31×#232311yescharacteristic
839C2C31×#233911yescharacteristic
840C2Q8×C22⋊C4×C3111yescharacteristic
841C2C31×#236011yescharacteristic
842C2C31×#236211yescharacteristic
843C2C31×#241511yescharacteristic
844C2C31×#241711yescharacteristic
845C2C31×#242711yescharacteristic
846C2C31×#242911yescharacteristic
847C2C31×#248911yescharacteristic
848C2C31×#249211yescharacteristic
849C2C31×#254011yescharacteristic
850C2C31×#254211yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutatorC23C23×C4×C31
Frattini, cosocleC24C24×C31
prime radicalC25×C31C23
LCSG ▷ C23 ▷ 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
6. C2×C4×C4⋊C4×C31C2semidirect
8. C31×#1445C2semidirect
11. C31×C4⋊#95C2semidirect
16. C2×C31×C22⋊Q8C4semidirect
96. C2×C22⋊C4×C31Q8semidirect
219. C4⋊C4×C31C22⋊C4semidirect
227. #13997C31direct (N × H)
347. C2×C4×C31C22⋊Q8semidirect
351. C2×#391C2×C31semidirect
352. C2×#391C2×C31semidirect
353. C2×#389C2×C31semidirect
355. C2×C4×C4⋊C4C2×C31semidirect
357. #1445C2×C31semidirect
360. C4⋊#95C2×C31semidirect
425. C2×C22⋊Q8C4×C31semidirect
521. C2×C22⋊C4Q8×C31semidirect
540. C31#13997direct (N × H)
645. C4⋊C4C22⋊C4×C31semidirect
772. C2×C4C31×C22⋊Q8semidirect

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×C4⋊C4×C312
C2×C4×C22⋊C4×C312
C31×#14452
C31×#14392
C31×#14372
C31×C4⋊#952
#1399731