Finite Group Databasebeta

← C31×#15323 #21472082

Subgroups — C31×#15323 #21472082

Order 7936.

2258 conjugacy classes of subgroups.

The subgroup lattice has 1210 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×C31×#393C211yesmaximal, characteristic, complemented
3C2×C31×#386C211yesmaximal, characteristic
4C2×C31×#386C211yesmaximal, characteristic
5C2×C31×#385C211yesmaximal, characteristic, complemented
6C2×C31×#380C211yesmaximal, characteristic, complemented
7C31×#1446C211yesmaximal, characteristic, complemented
8C31×#1445C211yesmaximal, characteristic, complemented
9C31×#1441C211yesmaximal, characteristic, complemented
10C31×#1441C211yesmaximal, characteristic, complemented
11C31×#1439C211yesmaximal, characteristic, complemented
12C31×#1439C211yesmaximal, characteristic, complemented
13C31×#1439C211yesmaximal, characteristic, complemented
14C31×#1438C211yesmaximal, characteristic
15C31×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×Q8×C31C2211yescharacteristic
17C23×D4×C31C2211yescharacteristic
18C24×C4×C31C2211yescharacteristic
19C24×C4×C31C2211yescharacteristic
20C2×C31×C22⋊Q8—24no—
21C2×C31×C22⋊Q8—24no—
22C2×C31×C22⋊Q8—24no—
23C22×C4⋊C4×C31C2211yescharacteristic
24C22×C4⋊C4×C31C2211yescharacteristic
25C22×C4⋊C4×C31C2211yescharacteristic
26C22×C4⋊C4×C31C2211yescharacteristic
27C22×C4⋊C4×C31C2211yescharacteristic
28C22×C22⋊C4×C31C2211yescharacteristic
29C22×C22⋊C4×C31C2211yescharacteristic
30C22×C22⋊C4×C31C2211yescharacteristic
31C22×C22⋊C4×C31C2211yescharacteristic
32C22×C22⋊C4×C31C2211yescharacteristic
33C22×C22⋊C4×C31C2211yescharacteristic
34C22×C22⋊C4×C31C2211yescharacteristic
35C22×C22⋊C4×C31C2211yescharacteristic
36C22×C22⋊C4×C31C2211yescharacteristic
37C22×C22⋊C4×C31C2211yescharacteristic
38C31×#393—24no—
39C31×#386—24no—
40C31×#386—24no—
41C31×#385—24no—
42C31×#380—24no—
43C2×C31×#95C2211yescharacteristic
44C2×C31×#95C2211yescharacteristic
45C2×C31×#95C2211yescharacteristic
46C2×C31×#95C2211yescharacteristic
47C2×C31×#95C2211yescharacteristic
48C2×C31×#95C2211yescharacteristic
49C2×C31×#95C2211yescharacteristic
50C2×C31×#95C2211yescharacteristic
51C2×C31×#95C2211yescharacteristic
52C2×C31×#95C2211yescharacteristic
53C2×C31×#95C2211yescharacteristic
54C2×C31×#95C2211yescharacteristic
55C2×C31×#95C2211yescharacteristic
56C2×C31×#95C2211yescharacteristic
57C2×C31×#95C2211yescharacteristic
58C2×C31×#95C2211yescharacteristic
59C25×C31C2311yescharacteristic
60C25×C31C2311yescharacteristic
61C22×Q8×C31—22no—
62C22×Q8×C31—22no—
63C22×Q8×C31—22no—
64C22×Q8×C31—22no—
65C22×Q8×C31—22no—
66C22×Q8×C31—41no—
67C22×Q8×C31—41no—
68C22×D4×C31—22no—
69C22×D4×C31—22no—
70C22×D4×C31—22no—
71C22×D4×C31—22no—
72C22×D4×C31—41no—
73C22×D4×C31—41no—
74C22×D4×C31Q814yescomplemented
75C23×C4×C31—22no—
76C23×C4×C31—22no—
77C23×C4×C31—22no—
78C23×C4×C31—22no—
79C23×C4×C31—22no—
80C23×C4×C31—22no—
81C23×C4×C31—22no—
82C23×C4×C31—22no—
83C23×C4×C31—22no—
84C23×C4×C31—22no—
85C23×C4×C31—41no—
86C23×C4×C31—41no—
87C23×C4×C31—41no—
88C23×C4×C31—41no—
89C23×C4×C31C2311yescharacteristic
90C23×C4×C31C2311yescharacteristic
91C23×C4×C31C2311yescharacteristic
92C23×C4×C31C2311yescharacteristic
93C23×C4×C31C2311yescharacteristic
94C23×C4×C31C2311yescharacteristic
95C23×C4×C31C2311yescharacteristic
96C23×C4×C31C2311yescharacteristic
97C23×C4×C31C2311yescharacteristic
98C23×C4×C31C2311yescharacteristic
99C23×C4×C31C2311yescharacteristic
100C23×C4×C31C2311yescharacteristic
101C23×C4×C31C2311yescharacteristic
102C31×C22⋊Q8—232no—
103C2×C4⋊C4×C31—22no—
104C2×C4⋊C4×C31—22no—
105C2×C4⋊C4×C31—22no—
106C2×C4⋊C4×C31—22no—
107C2×C4⋊C4×C31—22no—
108C2×C4⋊C4×C31—22no—
109C2×C4⋊C4×C31—22no—
110C2×C4⋊C4×C31—22no—
111C2×C4⋊C4×C31—22no—
112C2×C4⋊C4×C31—22no—
113C2×C4⋊C4×C31—41no—
114C2×C4⋊C4×C31—41no—
115C2×C4⋊C4×C31—41no—
116C2×C4⋊C4×C31D414yescomplemented
117C2×C4⋊C4×C31D414yescomplemented
118C2×C22⋊C4×C31—22no—
119C2×C22⋊C4×C31—22no—
120C2×C22⋊C4×C31—22no—
121C2×C22⋊C4×C31—22no—
122C2×C22⋊C4×C31—22no—
123C2×C22⋊C4×C31—22no—
124C2×C22⋊C4×C31—22no—
125C2×C22⋊C4×C31—22no—
126C2×C22⋊C4×C31—22no—
127C2×C22⋊C4×C31—22no—
128C2×C22⋊C4×C31—22no—
129C2×C22⋊C4×C31—22no—
130C2×C22⋊C4×C31—22no—
131C2×C22⋊C4×C31—22no—
132C2×C22⋊C4×C31—22no—
133C2×C22⋊C4×C31—22no—
134C2×C22⋊C4×C31—22no—
135C2×C22⋊C4×C31—22no—
136C2×C22⋊C4×C31—22no—
137C2×C22⋊C4×C31—22no—
138C2×C22⋊C4×C31—41no—
139C2×C22⋊C4×C31—41no—
140C2×C22⋊C4×C31—41no—
141C2×C22⋊C4×C31—41no—
142C2×C22⋊C4×C31—41no—
143C2×C22⋊C4×C31—41no—
144C2×C22⋊C4×C31—41no—
145C2×C22⋊C4×C31—41no—
146C2×C22⋊C4×C31D414yes—
147C2×C22⋊C4×C31D414yes—
148C31×#95—22no—
149C31×#95—22no—
150C31×#95—22no—
151C31×#95—22no—
152C31×#95—22no—
153C31×#95—22no—
154C31×#95—22no—
155C31×#95—22no—
156C31×#95—22no—
157C31×#95—22no—
158C31×#95—22no—
159C31×#95—41no—
160C31×#95—41no—
161C31×#95—41no—
162C31×#95—41no—
163C31×#95—41no—
164C24×C31—21no—
165C24×C31—21no—
166C24×C31—21no—
167C24×C31—21no—
168C24×C31—21no—
169C24×C31—21no—
170C24×C31—21no—
171C24×C31—21no—
172C24×C31—21no—
173C24×C31—21no—
174C24×C31—21no—
175C24×C31—21no—
176C24×C31—21no—
177C24×C31—21no—
178C24×C31—21no—
179C24×C31—21no—
180C24×C31—21no—
181C24×C31—21no—
182C24×C31—21no—
183C24×C31—21no—
184C24×C31—21no—
185C24×C31—21no—
186C24×C31—21no—
187C24×C31—21no—
188C24×C31C2×D412yes—
189C24×C31C2×D412yes—
190C24×C31C2×Q812yes—
191C24×C31C2×Q812yes—
192C24×C31#4112yes—
193C24×C31#4112yes—
194C24×C31C2411yescharacteristic
195C2×Q8×C31—28no—
196C2×Q8×C31—44no—
197C2×Q8×C31—44no—
198C2×Q8×C31—44no—
199C2×Q8×C31—44no—
200C2×Q8×C31—44no—
201C2×Q8×C31—44no—
202C2×D4×C31—28no—
203C2×D4×C31—28no—
204C2×D4×C31—44no—
205C2×D4×C31—44no—
206C2×D4×C31—44no—
207C2×D4×C31—44no—
208C2×D4×C31—44no—
209C22×C4×C31—21no—
210C22×C4×C31—21no—
211C22×C4×C31—21no—
212C22×C4×C31—21no—
213C22×C4×C31—21no—
214C22×C4×C31—21no—
215C22×C4×C31—21no—
216C22×C4×C31—21no—
217C22×C4×C31—28no—
218C22×C4×C31—28no—
219C22×C4×C31—21no—
220C22×C4×C31—21no—
221C22×C4×C31—21no—
222C22×C4×C31—21no—
223C22×C4×C31—21no—
224C22×C4×C31—21no—
225C22×C4×C31—21no—
226C22×C4×C31—21no—
227C22×C4×C31—21no—
228C22×C4×C31—21no—
229C22×C4×C31—21no—
230C22×C4×C31—21no—
231C22×C4×C31—21no—
232C22×C4×C31—21no—
233C22×C4×C31—21no—
234C22×C4×C31—21no—
235C22×C4×C31—21no—
236C22×C4×C31—21no—
237C22×C4×C31—21no—
238C22×C4×C31—21no—
239C22×C4×C31—21no—
240C22×C4×C31—21no—
241C22×C4×C31—21no—
242C22×C4×C31—21no—
243C22×C4×C31—21no—
244C22×C4×C31—21no—
245C22×C4×C31—21no—
246C22×C4×C31—21no—
247C22×C4×C31—21no—
248C22×C4×C31—21no—
249C22×C4×C31—21no—
250C22×C4×C31—21no—
251C22×C4×C31—21no—
252C22×C4×C31—21no—
253C22×C4×C31—21no—
254C22×C4×C31—21no—
255C22×C4×C31—21no—
256C22×C4×C31—21no—
257C22×C4×C31—21no—
258C22×C4×C31—21no—
259C22×C4×C31—21no—
260C22×C4×C31—21no—
261C22×C4×C31—21no—
262C22×C4×C31—21no—
263C22×C4×C31—21no—
264C22×C4×C31—21no—
265C22×C4×C31—21no—
266C22×C4×C31—21no—
267C22×C4×C31—21no—
268C22×C4×C31—21no—
269C22×C4×C31—21no—
270C22×C4×C31—21no—
271C22×C4×C31—21no—
272C22×C4×C31—21no—
273C22×C4×C31—21no—
274C22×C4×C31—21no—
275C22×C4×C31—21no—
276C22×C4×C31—21no—
277C22×C4×C31—21no—
278C22×C4×C31—21no—
279C22×C4×C31—21no—
280C22×C4×C31—21no—
281C22×C4×C31—21no—
282C22×C4×C31—21no—
283C22×C4×C31—21no—
284C22×C4×C31—21no—
285C22×C4×C31—21no—
286C22×C4×C31—21no—
287C22×C4×C31—21no—
288C22×C4×C31—21no—
289C22×C4×C31—44no—
290C22×C4×C31—44no—
291C22×C4×C31—44no—
292C22×C4×C31—44no—
293C22×C4×C31—44no—
294C22×C4×C31—44no—
295C22×C4×C31—44no—
296C22×C4×C31—44no—
297C22×C4×C31—44no—
298C22×C4×C31—44no—
299C22×C4×C31—44no—
300C22×C4×C31—44no—
301C22×C4×C31C2×D412yes—
302C22×C4×C31C2×D412yes—
303C22×C4×C31C2×D412yes—
304C22×C4×C31C2×D412yes—
305C22×C4×C31C2×D412yes—
306C22×C4×C31C2×D412yes—
307C22×C4×C31C2×D412yes—
308C22×C4×C31C2×D412yes—
309C22×C4×C31C2×D412yes—
310C22×C4×C31C2×D412yes—
311C22×C4×C31C2×Q812yes—
312C22×C4×C31#4112yes—
313C22×C4×C31#4112yes—
314C4⋊C4×C31—28no—
315C4⋊C4×C31—28no—
316C4⋊C4×C31—28no—
317C4⋊C4×C31—44no—
318C4⋊C4×C31—44no—
319C22⋊C4×C31—28no—
320C22⋊C4×C31—28no—
321C22⋊C4×C31—28no—
322C22⋊C4×C31—44no—
323C22⋊C4×C31—44no—
324C22⋊C4×C31—44no—
325C22⋊C4×C31—44no—
326C22⋊C4×C31—44no—
327C22⋊C4×C31—44no—
328C22⋊C4×C31—44no—
329#15323C3111yesmaximal, characteristic, direct product factor, Sylow
330C23×C31—22no—
331C23×C31—22no—
332C23×C31—22no—
333C23×C31—22no—
334C23×C31—22no—
335C23×C31—22no—
336C23×C31—22no—
337C23×C31—22no—
338C23×C31—22no—
339C23×C31—22no—
340C23×C31—22no—
341C23×C31—22no—
342C23×C31—22no—
343C23×C31—22no—
344C23×C31—22no—
345C23×C31—22no—
346C23×C31—22no—
347C23×C31—22no—
348C23×C31—22no—
349C23×C31—22no—
350C23×C31—22no—
351C23×C31—22no—
352C23×C31—22no—
353C23×C31—22no—
354C23×C31—22no—
355C23×C31—22no—
356C23×C31—22no—
357C23×C31—22no—
358C23×C31—22no—
359C23×C31—22no—
360C23×C31—22no—
361C23×C31—22no—
362C23×C31—22no—
363C23×C31—22no—
364C23×C31—22no—
365C23×C31—22no—
366C23×C31—41no—
367C23×C31—41no—
368C23×C31—41no—
369C23×C31—41no—
370C23×C31—41no—
371C23×C31—41no—
372C23×C31—41no—
373C23×C31—41no—
374C23×C31—41no—
375C23×C31—41no—
376C23×C31—41no—
377C23×C31—41no—
378C23×C31—41no—
379C23×C31—41no—
380C23×C31—41no—
381C23×C31—41no—
382C23×C31—41no—
383C23×C31—41no—
384C23×C31—41no—
385C23×C31—41no—
386C23×C31—41no—
387C23×C31—41no—
388C23×C31—41no—
389C23×C31—41no—
390C23×C31—41no—
391C23×C31—41no—
392C23×C31—41no—
393C23×C31—41no—
394C23×C31—41no—
395C23×C31—41no—
396C23×C31—41no—
397C23×C31—41no—
398C23×C31C22⋊Q814yes—
399C23×C31C22⋊Q814yescomplemented
400C23×C31C22×D411yescharacteristic
401C23×C31C22×D411yescharacteristic
402C23×C31C22×D411yescharacteristic
403C23×C31C22×D411yescharacteristic
404C23×C31C22×Q811yescharacteristic
405C23×C31C2×#4111yescharacteristic
406C23×C31C2×#4111yescharacteristic
407C23×C31C2×#4111yescharacteristic
408C23×C31C2×#4111yescharacteristic
409C23×C31H(5,𝔽2)11yescharacteristic
410C23×C31H(5,𝔽2)11yescharacteristic
411C23×C31H(5,𝔽2)11yescharacteristic
412C23×C31H(5,𝔽2)11yescharacteristic
413C23×C312−1+411yescharacteristic
414C23×C312−1+411yescharacteristic
415Q8×C31—416no—
416D4×C31—416no—
417C2×C4×C31—22no—
418C2×C4×C31—22no—
419C2×C4×C31—22no—
420C2×C4×C31—22no—
421C2×C4×C31—22no—
422C2×C4×C31—22no—
423C2×C4×C31—22no—
424C2×C4×C31—22no—
425C2×C4×C31—22no—
426C2×C4×C31—22no—
427C2×C4×C31—22no—
428C2×C4×C31—22no—
429C2×C4×C31—22no—
430C2×C4×C31—22no—
431C2×C4×C31—22no—
432C2×C4×C31—22no—
433C2×C4×C31—22no—
434C2×C4×C31—22no—
435C2×C4×C31—22no—
436C2×C4×C31—22no—
437C2×C4×C31—22no—
438C2×C4×C31—22no—
439C2×C4×C31—22no—
440C2×C4×C31—22no—
441C2×C4×C31—22no—
442C2×C4×C31—22no—
443C2×C4×C31—22no—
444C2×C4×C31—22no—
445C2×C4×C31—22no—
446C2×C4×C31—22no—
447C2×C4×C31—22no—
448C2×C4×C31—22no—
449C2×C4×C31—22no—
450C2×C4×C31—416no—
451C2×C4×C31—416no—
452C2×C4×C31—41no—
453C2×C4×C31—41no—
454C2×C4×C31—41no—
455C2×C4×C31—41no—
456C2×C4×C31—41no—
457C2×C4×C31—41no—
458C2×C4×C31—41no—
459C2×C4×C31—41no—
460C2×C4×C31—41no—
461C2×C4×C31—41no—
462C2×C4×C31—41no—
463C2×C4×C31—41no—
464C2×C4×C31—41no—
465C2×C4×C31—41no—
466C2×C4×C31—41no—
467C2×C4×C31—41no—
468C2×C4×C31—41no—
469C2×C4×C31—41no—
470C2×C4×C31—41no—
471C2×C4×C31—41no—
472C2×C4×C31—41no—
473C2×C4×C31—41no—
474C2×C4×C31—41no—
475C2×C4×C31—41no—
476C2×C4×C31—41no—
477C2×C4×C31—41no—
478C2×C4×C31—41no—
479C2×C4×C31—41no—
480C2×C4×C31—41no—
481C2×C4×C31—41no—
482C2×C4×C31—41no—
483C2×C4×C31—41no—
484C2×C4×C31—41no—
485C2×C4×C31—41no—
486C2×C4×C31—41no—
487C2×C4×C31—41no—
488C2×C4×C31—41no—
489C2×C4×C31—41no—
490C2×C4×C31—41no—
491C2×C4×C31—41no—
492C2×C4×C31—41no—
493C2×C4×C31—41no—
494C2×C4×C31—41no—
495C2×C4×C31—41no—
496C2×C4×C31—41no—
497C2×C4×C31—41no—
498C2×C4×C31—41no—
499C2×C4×C31—41no—
500C2×C4×C31—41no—
501C2×C4×C31—41no—
502C2×C4×C31—41no—
503C2×C4×C31—41no—
504C2×C4×C31—41no—
505C2×C4×C31—41no—
506C2×C4×C31—41no—
507C2×C4×C31—41no—
508C2×C4×C31#12014yes—
509C2×C4×C31#12114yes—
510C22×C22⋊Q8C2×C3111yescharacteristic, complemented
511C2×#393C2×C3111yescharacteristic, complemented
512C2×#386C2×C3111yescharacteristic
513C2×#386C2×C3111yescharacteristic
514C2×#385C2×C3111yescharacteristic, complemented
515C2×#380C2×C3111yescharacteristic, complemented
516#1446C2×C3111yescharacteristic, complemented
517#1445C2×C3111yescharacteristic, complemented
518#1441C2×C3111yescharacteristic, complemented
519#1441C2×C3111yescharacteristic, complemented
520#1439C2×C3111yescharacteristic, complemented
521#1439C2×C3111yescharacteristic, complemented
522#1439C2×C3111yescharacteristic, complemented
523#1438C2×C3111yescharacteristic
524C22⋊#95C2×C3111yescharacteristic, complemented
525C22×C31—24no—
526C22×C31—24no—
527C22×C31—24no—
528C22×C31—24no—
529C22×C31—24no—
530C22×C31—24no—
531C22×C31—42no—
532C22×C31—42no—
533C22×C31—42no—
534C22×C31—42no—
535C22×C31—42no—
536C22×C31—42no—
537C22×C31—42no—
538C22×C31—42no—
539C22×C31—42no—
540C22×C31—42no—
541C22×C31—42no—
542C22×C31—42no—
543C22×C31—42no—
544C22×C31—42no—
545C22×C31—42no—
546C22×C31—42no—
547C22×C31—42no—
548C22×C31—42no—
549C22×C31—42no—
550C22×C31—42no—
551C22×C31—42no—
552C22×C31—42no—
553C22×C31—42no—
554C22×C31—42no—
555C22×C31C2×#12011yescharacteristic
556C22×C31C2×#12111yescharacteristic
557C22×C31C2×C22⋊Q811yescharacteristic
558C22×C31C2×C22⋊Q811yescharacteristic
559C22×C31#52511yescharacteristic
560C22×C31#52911yescharacteristic
561C22×C31#53511yescharacteristic
562C22×C31#53511yescharacteristic
563C22×C31#53611yescharacteristic
564C22×C31#53711yescharacteristic
565C22×C31#53811yescharacteristic
566C22×C31#53911yescharacteristic
567C22×C31#54211yescharacteristic
568C22×C31#54211yescharacteristic
569C22×C31#54311yescharacteristic
570C22×C31D4211yescharacteristic
571C22×C31D4211yescharacteristic
572C22×C31#54611yescharacteristic
573C22×C31#54611yescharacteristic
574C22×C31#54611yescharacteristic
575C22×C31#54611yescharacteristic
576C22×C31#54611yescharacteristic
577C22×C31#54611yescharacteristic
578C22×C31#54611yescharacteristic
579C22×C31#54711yescharacteristic
580C22×C31#54811yescharacteristic
581C22×C31#54811yescharacteristic
582C22×C31D4×Q811yescharacteristic
583C22×C31D4×Q811yescharacteristic
584C22×C31#55111yescharacteristic
585C22×C31#55211yescharacteristic
586C22×C31#55411yescharacteristic
587C22×C31#55411yescharacteristic
588C22×C31#56211yescharacteristic
589C22×C31#56211yescharacteristic
590C4×C31—24no—
591C4×C31—24no—
592C4×C31—42no—
593C4×C31—42no—
594C4×C31—42no—
595C4×C31—42no—
596C4×C31—42no—
597C4×C31—42no—
598C4×C31—42no—
599C4×C31—81no—
600C4×C31—81no—
601C4×C31—81no—
602C4×C31—81no—
603C23×Q8C22×C3111yescharacteristic
604C23×D4C22×C3111yescharacteristic
605C24×C4C22×C3111yescharacteristic
606C24×C4C22×C3111yescharacteristic
607C2×C22⋊Q8—24no—
608C2×C22⋊Q8—24no—
609C2×C22⋊Q8—24no—
610C22×C4⋊C4C22×C3111yescharacteristic
611C22×C4⋊C4C22×C3111yescharacteristic
612C22×C4⋊C4C22×C3111yescharacteristic
613C22×C4⋊C4C22×C3111yescharacteristic
614C22×C4⋊C4C22×C3111yescharacteristic
615C22×C22⋊C4C22×C3111yescharacteristic
616C22×C22⋊C4C22×C3111yescharacteristic
617C22×C22⋊C4C22×C3111yescharacteristic
618C22×C22⋊C4C22×C3111yescharacteristic
619C22×C22⋊C4C22×C3111yescharacteristic
620C22×C22⋊C4C22×C3111yescharacteristic
621C22×C22⋊C4C22×C3111yescharacteristic
622C22×C22⋊C4C22×C3111yescharacteristic
623C22×C22⋊C4C22×C3111yescharacteristic
624C22×C22⋊C4C22×C3111yescharacteristic
625#393—24no—
626#386—24no—
627#386—24no—
628#385—24no—
629#380—24no—
630C2×#95C22×C3111yescharacteristic
631C2×#95C22×C3111yescharacteristic
632C2×#95C22×C3111yescharacteristic
633C2×#95C22×C3111yescharacteristic
634C2×#95C22×C3111yescharacteristic
635C2×#95C22×C3111yescharacteristic
636C2×#95C22×C3111yescharacteristic
637C2×#95C22×C3111yescharacteristic
638C2×#95C22×C3111yescharacteristic
639C2×#95C22×C3111yescharacteristic
640C2×#95C22×C3111yescharacteristic
641C2×#95C22×C3111yescharacteristic
642C2×#95C22×C3111yescharacteristic
643C2×#95C22×C3111yescharacteristic
644C2×#95C22×C3111yescharacteristic
645C2×#95C22×C3111yescharacteristic
646C2×C31—44no—
647C2×C31—44no—
648C2×C31#240411yescharacteristic
649C2×C31#240811yescharacteristic
650C2×C31#240911yescharacteristic
651C2×C31#241711yescharacteristic
652C2×C31#242711yescharacteristic
653C2×C31#243711yescharacteristic
654C2×C31#244911yescharacteristic
655C2×C31#245011yescharacteristic
656C2×C31#247711yescharacteristic
657C2×C31#267211yescharacteristic
658C2×C31#267611yescharacteristic
659C2×C31#268711yescharacteristic
660C2×C31#269211yescharacteristic
661C2×C31#269211yescharacteristic
662C2×C31#269611yescharacteristic
663C25C23×C3111yescharacteristic
664C25C23×C3111yescharacteristic
665C22×Q8—22no—
666C22×Q8—22no—
667C22×Q8—22no—
668C22×Q8—22no—
669C22×Q8—22no—
670C22×Q8—41no—
671C22×Q8—41no—
672C22×D4—22no—
673C22×D4—22no—
674C22×D4—22no—
675C22×D4—22no—
676C22×D4—41no—
677C22×D4—41no—
678C22×D4Q8×C3114yescomplemented
679C23×C4—22no—
680C23×C4—22no—
681C23×C4—22no—
682C23×C4—22no—
683C23×C4—22no—
684C23×C4—22no—
685C23×C4—22no—
686C23×C4—22no—
687C23×C4—22no—
688C23×C4—22no—
689C23×C4—41no—
690C23×C4—41no—
691C23×C4—41no—
692C23×C4—41no—
693C23×C4C23×C3111yescharacteristic
694C23×C4C23×C3111yescharacteristic
695C23×C4C23×C3111yescharacteristic
696C23×C4C23×C3111yescharacteristic
697C23×C4C23×C3111yescharacteristic
698C23×C4C23×C3111yescharacteristic
699C23×C4C23×C3111yescharacteristic
700C23×C4C23×C3111yescharacteristic
701C23×C4C23×C3111yescharacteristic
702C23×C4C23×C3111yescharacteristic
703C23×C4C23×C3111yescharacteristic
704C23×C4C23×C3111yescharacteristic
705C23×C4C23×C3111yescharacteristic
706C22⋊Q8—232no—
707C2×C4⋊C4—22no—
708C2×C4⋊C4—22no—
709C2×C4⋊C4—22no—
710C2×C4⋊C4—22no—
711C2×C4⋊C4—22no—
712C2×C4⋊C4—22no—
713C2×C4⋊C4—22no—
714C2×C4⋊C4—22no—
715C2×C4⋊C4—22no—
716C2×C4⋊C4—22no—
717C2×C4⋊C4—41no—
718C2×C4⋊C4—41no—
719C2×C4⋊C4—41no—
720C2×C4⋊C4D4×C3114yescomplemented
721C2×C4⋊C4D4×C3114yescomplemented
722C2×C22⋊C4—22no—
723C2×C22⋊C4—22no—
724C2×C22⋊C4—22no—
725C2×C22⋊C4—22no—
726C2×C22⋊C4—22no—
727C2×C22⋊C4—22no—
728C2×C22⋊C4—22no—
729C2×C22⋊C4—22no—
730C2×C22⋊C4—22no—
731C2×C22⋊C4—22no—
732C2×C22⋊C4—22no—
733C2×C22⋊C4—22no—
734C2×C22⋊C4—22no—
735C2×C22⋊C4—22no—
736C2×C22⋊C4—22no—
737C2×C22⋊C4—22no—
738C2×C22⋊C4—22no—
739C2×C22⋊C4—22no—
740C2×C22⋊C4—22no—
741C2×C22⋊C4—22no—
742C2×C22⋊C4—41no—
743C2×C22⋊C4—41no—
744C2×C22⋊C4—41no—
745C2×C22⋊C4—41no—
746C2×C22⋊C4—41no—
747C2×C22⋊C4—41no—
748C2×C22⋊C4—41no—
749C2×C22⋊C4—41no—
750C2×C22⋊C4D4×C3114yes—
751C2×C22⋊C4D4×C3114yes—
752#95—22no—
753#95—22no—
754#95—22no—
755#95—22no—
756#95—22no—
757#95—22no—
758#95—22no—
759#95—22no—
760#95—22no—
761#95—22no—
762#95—22no—
763#95—41no—
764#95—41no—
765#95—41no—
766#95—41no—
767#95—41no—
768C31#1532311yescharacteristic, direct product factor, Sylow
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24—21no—
774C24—21no—
775C24—21no—
776C24—21no—
777C24—21no—
778C24—21no—
779C24—21no—
780C24—21no—
781C24—21no—
782C24—21no—
783C24—21no—
784C24—21no—
785C24—21no—
786C24—21no—
787C24—21no—
788C24—21no—
789C24—21no—
790C24—21no—
791C24—21no—
792C24—21no—
793C24C2×D4×C3112yes—
794C24C2×D4×C3112yes—
795C24C2×Q8×C3112yes—
796C24C2×Q8×C3112yes—
797C24#41×C3112yes—
798C24#41×C3112yes—
799C24C24×C3111yescharacteristic
800C2×Q8—28no—
801C2×Q8—44no—
802C2×Q8—44no—
803C2×Q8—44no—
804C2×Q8—44no—
805C2×Q8—44no—
806C2×Q8—44no—
807C2×D4—28no—
808C2×D4—28no—
809C2×D4—44no—
810C2×D4—44no—
811C2×D4—44no—
812C2×D4—44no—
813C2×D4—44no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—28no—
823C22×C4—28no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—44no—
895C22×C4—44no—
896C22×C4—44no—
897C22×C4—44no—
898C22×C4—44no—
899C22×C4—44no—
900C22×C4—44no—
901C22×C4—44no—
902C22×C4—44no—
903C22×C4—44no—
904C22×C4—44no—
905C22×C4—44no—
906C22×C4C2×D4×C3112yes—
907C22×C4C2×D4×C3112yes—
908C22×C4C2×D4×C3112yes—
909C22×C4C2×D4×C3112yes—
910C22×C4C2×D4×C3112yes—
911C22×C4C2×D4×C3112yes—
912C22×C4C2×D4×C3112yes—
913C22×C4C2×D4×C3112yes—
914C22×C4C2×D4×C3112yes—
915C22×C4C2×D4×C3112yes—
916C22×C4C2×Q8×C3112yes—
917C22×C4#41×C3112yes—
918C22×C4#41×C3112yes—
919C4⋊C4—28no—
920C4⋊C4—28no—
921C4⋊C4—28no—
922C4⋊C4—44no—
923C4⋊C4—44no—
924C22⋊C4—28no—
925C22⋊C4—28no—
926C22⋊C4—28no—
927C22⋊C4—44no—
928C22⋊C4—44no—
929C22⋊C4—44no—
930C22⋊C4—44no—
931C22⋊C4—44no—
932C22⋊C4—44no—
933C22⋊C4—44no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—22no—
948C23—22no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—22no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23—41no—
981C23—41no—
982C23—41no—
983C23—41no—
984C23—41no—
985C23—41no—
986C23—41no—
987C23—41no—
988C23—41no—
989C23—41no—
990C23—41no—
991C23—41no—
992C23—41no—
993C23—41no—
994C23—41no—
995C23—41no—
996C23—41no—
997C23—41no—
998C23—41no—
999C23—41no—
1000C23—41no—
1001C23—41no—
1002C23C31×C22⋊Q814yes—
1003C23C31×C22⋊Q814yescomplemented
1004C23C22×D4×C3111yescharacteristic
1005C23C22×D4×C3111yescharacteristic
1006C23C22×D4×C3111yescharacteristic
1007C23C22×D4×C3111yescharacteristic
1008C23C22×Q8×C3111yescharacteristic
1009C23C2×#41×C3111yescharacteristic
1010C23C2×#41×C3111yescharacteristic
1011C23C2×#41×C3111yescharacteristic
1012C23C2×#41×C3111yescharacteristic
1013C23C31×H(5,𝔽2)11yescharacteristic
1014C23C31×H(5,𝔽2)11yescharacteristic
1015C23C31×H(5,𝔽2)11yescharacteristic
1016C23C31×H(5,𝔽2)11yescharacteristic
1017C23C31×2−1+411yescharacteristic
1018C23C31×2−1+411yescharacteristic
1019Q8—416no—
1020D4—416no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—416no—
1055C2×C4—416no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—41no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4C31×#12014yes—
1113C2×C4C31×#12114yes—
1114C22—24no—
1115C22—24no—
1116C22—24no—
1117C22—24no—
1118C22—24no—
1119C22—24no—
1120C22—42no—
1121C22—42no—
1122C22—42no—
1123C22—42no—
1124C22—42no—
1125C22—42no—
1126C22—42no—
1127C22—42no—
1128C22—42no—
1129C22—42no—
1130C22—42no—
1131C22—42no—
1132C22—42no—
1133C22—42no—
1134C22—42no—
1135C22—42no—
1136C22—42no—
1137C22—42no—
1138C22—42no—
1139C22—42no—
1140C22—42no—
1141C22—42no—
1142C22—42no—
1143C22—42no—
1144C22C2×C31×#12011yescharacteristic
1145C22C2×C31×#12111yescharacteristic
1146C22C2×C31×C22⋊Q811yescharacteristic
1147C22C2×C31×C22⋊Q811yescharacteristic
1148C22C31×#52511yescharacteristic
1149C22C31×#52911yescharacteristic
1150C22C31×#53511yescharacteristic
1151C22C31×#53511yescharacteristic
1152C22C31×#53611yescharacteristic
1153C22C31×#53711yescharacteristic
1154C22C31×#53811yescharacteristic
1155C22C31×#53911yescharacteristic
1156C22C31×#54211yescharacteristic
1157C22C31×#54211yescharacteristic
1158C22C31×#54311yescharacteristic
1159C22D42×C3111yescharacteristic
1160C22D42×C3111yescharacteristic
1161C22C31×#54611yescharacteristic
1162C22C31×#54611yescharacteristic
1163C22C31×#54611yescharacteristic
1164C22C31×#54611yescharacteristic
1165C22C31×#54611yescharacteristic
1166C22C31×#54611yescharacteristic
1167C22C31×#54611yescharacteristic
1168C22C31×#54711yescharacteristic
1169C22C31×#54811yescharacteristic
1170C22C31×#54811yescharacteristic
1171C22D4×Q8×C3111yescharacteristic
1172C22D4×Q8×C3111yescharacteristic
1173C22C31×#55111yescharacteristic
1174C22C31×#55211yescharacteristic
1175C22C31×#55411yescharacteristic
1176C22C31×#55411yescharacteristic
1177C22C31×#56211yescharacteristic
1178C22C31×#56211yescharacteristic
1179C4—24no—
1180C4—24no—
1181C4—42no—
1182C4—42no—
1183C4—42no—
1184C4—42no—
1185C4—42no—
1186C4—42no—
1187C4—42no—
1188C4—81no—
1189C4—81no—
1190C4—81no—
1191C4—81no—
1192C2—44no—
1193C2—44no—
1194C2C31×#240411yescharacteristic
1195C2C31×#240811yescharacteristic
1196C2C31×#240911yescharacteristic
1197C2C31×#241711yescharacteristic
1198C2C31×#242711yescharacteristic
1199C2C31×#243711yescharacteristic
1200C2C31×#244911yescharacteristic
1201C2C31×#245011yescharacteristic
1202C2C31×#247711yescharacteristic
1203C2C31×#267211yescharacteristic
1204C2C31×#267611yescharacteristic
1205C2C31×#268711yescharacteristic
1206C2C31×#269211yescharacteristic
1207C2C31×#269211yescharacteristic
1208C2C31×#269611yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutator, Frattini, cosocleC24C24×C31
prime radicalC23×D4×C31C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C31×C22⋊Q8C2semidirect
2. C2×C31×#393C2semidirect
5. C2×C31×#385C2semidirect
6. C2×C31×#380C2semidirect
7. C31×#1446C2semidirect
8. C31×#1445C2semidirect
9. C31×#1441C2semidirect
10. C31×#1441C2semidirect
11. C31×#1439C2semidirect
12. C31×#1439C2semidirect
13. C31×#1439C2semidirect
15. C31×C22⋊#95C2semidirect
74. C22×D4×C31Q8semidirect
116. C2×C4⋊C4×C31D4semidirect
117. C2×C4⋊C4×C31D4semidirect
329. #15323C31direct (N × H)
399. C23×C31C22⋊Q8semidirect
510. C22×C22⋊Q8C2×C31semidirect
511. C2×#393C2×C31semidirect
514. C2×#385C2×C31semidirect
515. C2×#380C2×C31semidirect
516. #1446C2×C31semidirect
517. #1445C2×C31semidirect
518. #1441C2×C31semidirect
519. #1441C2×C31semidirect
520. #1439C2×C31semidirect
521. #1439C2×C31semidirect
522. #1439C2×C31semidirect
524. C22⋊#95C2×C31semidirect
678. C22×D4Q8×C31semidirect
720. C2×C4⋊C4D4×C31semidirect
721. C2×C4⋊C4D4×C31semidirect
768. C31#15323direct (N × H)
1003. C23C31×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×#3932
C2×C31×#3862
C2×C31×#3852
C2×C31×#3802
C31×#14462
C31×#14452
C31×#14412
C31×#14392
C31×#14382
C31×C22⋊#952
#1532331