Finite Group Databasebeta

← C31×#15476 #21472235

Subgroups — C31×#15476 #21472235

Order 7936.

1938 conjugacy classes of subgroups.

The subgroup lattice has 1182 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#395C211yesmaximal, characteristic, complemented
2C2×C31×#393C211yesmaximal, characteristic, complemented
3C2×C31×#393C211yesmaximal, characteristic, complemented
4C2×C31×#390C211yesmaximal, characteristic
5C2×C31×#386C211yesmaximal, characteristic
6C2×C31×#380C211yesmaximal, characteristic, complemented
7C31×#1442C211yesmaximal, characteristic, complemented
8C31×#1439C211yesmaximal, characteristic, complemented
9C31×#1439C211yesmaximal, characteristic, complemented
10C31×#1439C211yesmaximal, characteristic, complemented
11C31×#1439C211yesmaximal, characteristic, complemented
12C31×#1438C211yesmaximal, characteristic
13C31×#1436C211yesmaximal, characteristic, complemented
14C31×#1434C211yesmaximal, characteristic, complemented
15C31×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×Q8×C31C2211yescharacteristic
17C23×D4×C31C2211yescharacteristic
18C24×C4×C31C2211yescharacteristic
19C22×C4⋊C4×C31C2211yescharacteristic
20C22×C4⋊C4×C31C2211yescharacteristic
21C22×C4⋊C4×C31C2211yescharacteristic
22C22×C4⋊C4×C31C2211yescharacteristic
23C22×C22⋊C4×C31C2211yescharacteristic
24C22×C22⋊C4×C31C2211yescharacteristic
25C22×C22⋊C4×C31C2211yescharacteristic
26C22×C22⋊C4×C31C2211yescharacteristic
27C22×C22⋊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×C42×C31C2211yescharacteristic
35C31×#395—24no—
36C31×#393—24no—
37C31×#393—24no—
38C31×#390—24no—
39C31×#386—24no—
40C31×#380—24no—
41C2×C31×#95C2211yescharacteristic
42C2×C31×#95C2211yescharacteristic
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
57C25×C31C2311yescharacteristic
58C25×C31C2311yescharacteristic
59C22×Q8×C31—22no—
60C22×Q8×C31—22no—
61C22×Q8×C31—22no—
62C22×Q8×C31—41no—
63C22×Q8×C31—41no—
64C22×Q8×C31—41no—
65C22×Q8×C31—41no—
66C22×D4×C31—22no—
67C22×D4×C31—22no—
68C22×D4×C31—22no—
69C22×D4×C31—22no—
70C22×D4×C31—41no—
71C22×D4×C31—41no—
72C22×D4×C31Q814yescomplemented
73C23×C4×C31—22no—
74C23×C4×C31—22no—
75C23×C4×C31—22no—
76C23×C4×C31—22no—
77C23×C4×C31—22no—
78C23×C4×C31—41no—
79C23×C4×C31—41no—
80C23×C4×C31C2311yescharacteristic
81C23×C4×C31C2311yescharacteristic
82C23×C4×C31C2311yescharacteristic
83C23×C4×C31C2311yescharacteristic
84C23×C4×C31C2311yescharacteristic
85C23×C4×C31C2311yescharacteristic
86C23×C4×C31C2311yescharacteristic
87C23×C4×C31C2311yescharacteristic
88C23×C4×C31C2311yescharacteristic
89C23×C4×C31C2311yescharacteristic
90C23×C4×C31C2311yescharacteristic
91C23×C4×C31C2311yescharacteristic
92C23×C4×C31C2311yescharacteristic
93C2×C4⋊C4×C31—22no—
94C2×C4⋊C4×C31—22no—
95C2×C4⋊C4×C31—22no—
96C2×C4⋊C4×C31—22no—
97C2×C4⋊C4×C31—22no—
98C2×C4⋊C4×C31—22no—
99C2×C4⋊C4×C31—22no—
100C2×C4⋊C4×C31—41no—
101C2×C4⋊C4×C31—41no—
102C2×C4⋊C4×C31—41no—
103C2×C4⋊C4×C31—41no—
104C2×C4⋊C4×C31—41no—
105C2×C22⋊C4×C31—22no—
106C2×C22⋊C4×C31—22no—
107C2×C22⋊C4×C31—22no—
108C2×C22⋊C4×C31—22no—
109C2×C22⋊C4×C31—22no—
110C2×C22⋊C4×C31—22no—
111C2×C22⋊C4×C31—22no—
112C2×C22⋊C4×C31—22no—
113C2×C22⋊C4×C31—22no—
114C2×C22⋊C4×C31—22no—
115C2×C22⋊C4×C31—22no—
116C2×C22⋊C4×C31—22no—
117C2×C22⋊C4×C31—22no—
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—41no—
124C2×C22⋊C4×C31—41no—
125C2×C22⋊C4×C31—41no—
126C2×C22⋊C4×C31—41no—
127C2×C22⋊C4×C31—41no—
128C2×C22⋊C4×C31—41no—
129C2×C22⋊C4×C31—41no—
130C2×C22⋊C4×C31—41no—
131C2×C22⋊C4×C31—41no—
132C2×C22⋊C4×C31—41no—
133C2×C22⋊C4×C31—41no—
134C2×C22⋊C4×C31—41no—
135C2×C22⋊C4×C31—41no—
136C2×C22⋊C4×C31—41no—
137C2×C22⋊C4×C31D414yes—
138C2×C42×C31—22no—
139C2×C42×C31—22no—
140C2×C42×C31—41no—
141C31×#95—22no—
142C31×#95—22no—
143C31×#95—22no—
144C31×#95—22no—
145C31×#95—22no—
146C31×#95—22no—
147C31×#95—22no—
148C31×#95—22no—
149C31×#95—22no—
150C31×#95—22no—
151C31×#95—22no—
152C31×#95—22no—
153C31×#95—41no—
154C31×#95—41no—
155C31×#95D414yes—
156C31×#95D414yescomplemented
157C24×C31—21no—
158C24×C31—21no—
159C24×C31—21no—
160C24×C31—21no—
161C24×C31—21no—
162C24×C31—21no—
163C24×C31—21no—
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×C31C2×D412yes—
184C24×C31C2×Q812yes—
185C24×C31C2×Q812yes—
186C24×C31#4112yes—
187C24×C31C2411yescharacteristic
188C2×Q8×C31—44no—
189C2×Q8×C31—44no—
190C2×Q8×C31—44no—
191C2×Q8×C31—44no—
192C2×Q8×C31—44no—
193C2×Q8×C31—44no—
194C2×Q8×C31—44no—
195C2×D4×C31—28no—
196C2×D4×C31—28no—
197C2×D4×C31—44no—
198C2×D4×C31—44no—
199C2×D4×C31—44no—
200C2×D4×C31—44no—
201C2×D4×C31—44no—
202C22×C4×C31—21no—
203C22×C4×C31—21no—
204C22×C4×C31—21no—
205C22×C4×C31—21no—
206C22×C4×C31—21no—
207C22×C4×C31—21no—
208C22×C4×C31—21no—
209C22×C4×C31—21no—
210C22×C4×C31—28no—
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—21no—
218C22×C4×C31—21no—
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—44no—
282C22×C4×C31—44no—
283C22×C4×C31—44no—
284C22×C4×C31—44no—
285C22×C4×C31—44no—
286C22×C4×C31—44no—
287C22×C4×C31C2×D412yes—
288C22×C4×C31C2×D412yes—
289C22×C4×C31C2×D412yes—
290C22×C4×C31C2×D412yes—
291C22×C4×C31C2×D412yes—
292C22×C4×C31C2×D412yes—
293C22×C4×C31C2×D412yes—
294C22×C4×C31C2×D412yes—
295C22×C4×C31C2×Q812yes—
296C22×C4×C31#4112yes—
297C22×C4×C31#4112yes—
298C22×C4×C31#4112yes—
299C22×C4×C31#4112yes—
300C4⋊C4×C31—44no—
301C4⋊C4×C31—44no—
302C4⋊C4×C31—44no—
303C4⋊C4×C31—44no—
304C22⋊C4×C31—44no—
305C22⋊C4×C31—44no—
306C22⋊C4×C31—44no—
307C22⋊C4×C31—44no—
308C22⋊C4×C31—44no—
309C22⋊C4×C31—44no—
310C22⋊C4×C31—44no—
311C22⋊C4×C31—44no—
312C22⋊C4×C31—44no—
313C22⋊C4×C31—44no—
314C22⋊C4×C31—44no—
315C42×C31—44no—
316#15476C3111yesmaximal, characteristic, direct product factor, Sylow
317C23×C31—22no—
318C23×C31—22no—
319C23×C31—22no—
320C23×C31—22no—
321C23×C31—22no—
322C23×C31—22no—
323C23×C31—22no—
324C23×C31—22no—
325C23×C31—22no—
326C23×C31—22no—
327C23×C31—22no—
328C23×C31—22no—
329C23×C31—22no—
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—41no—
343C23×C31—41no—
344C23×C31—41no—
345C23×C31—41no—
346C23×C31—41no—
347C23×C31—41no—
348C23×C31—41no—
349C23×C31—41no—
350C23×C31—41no—
351C23×C31—41no—
352C23×C31—41no—
353C23×C31—41no—
354C23×C31—41no—
355C23×C31—41no—
356C23×C31—41no—
357C23×C31—41no—
358C23×C31—41no—
359C23×C31—41no—
360C23×C31—41no—
361C23×C31—41no—
362C23×C31—41no—
363C23×C31—41no—
364C23×C31—41no—
365C23×C31—41no—
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×C31C22⋊Q814yes—
387C23×C31C22×D411yescharacteristic
388C23×C31C22×D411yescharacteristic
389C23×C31C22×D411yescharacteristic
390C23×C31C22×Q811yescharacteristic
391C23×C31C2×#4111yescharacteristic
392C23×C31C2×#4111yescharacteristic
393C23×C31C2×#4111yescharacteristic
394C23×C31C2×#4111yescharacteristic
395C23×C31C2×#4111yescharacteristic
396C23×C31H(5,𝔽2)11yescharacteristic
397C23×C31H(5,𝔽2)11yescharacteristic
398C23×C31H(5,𝔽2)11yescharacteristic
399C23×C31H(5,𝔽2)11yescharacteristic
400C23×C31H(5,𝔽2)11yescharacteristic
401C23×C312−1+411yescharacteristic
402Q8×C31—416no—
403D4×C31—416no—
404C2×C4×C31—22no—
405C2×C4×C31—22no—
406C2×C4×C31—22no—
407C2×C4×C31—22no—
408C2×C4×C31—22no—
409C2×C4×C31—22no—
410C2×C4×C31—22no—
411C2×C4×C31—22no—
412C2×C4×C31—22no—
413C2×C4×C31—22no—
414C2×C4×C31—22no—
415C2×C4×C31—22no—
416C2×C4×C31—22no—
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—416no—
438C2×C4×C31—41no—
439C2×C4×C31—41no—
440C2×C4×C31—41no—
441C2×C4×C31—41no—
442C2×C4×C31—41no—
443C2×C4×C31—41no—
444C2×C4×C31—41no—
445C2×C4×C31—41no—
446C2×C4×C31—41no—
447C2×C4×C31—41no—
448C2×C4×C31—41no—
449C2×C4×C31—41no—
450C2×C4×C31—41no—
451C2×C4×C31—41no—
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×C31C22⋊Q814yes—
495C2×C4×C31#12414yes—
496C2×#395C2×C3111yescharacteristic, complemented
497C2×#393C2×C3111yescharacteristic, complemented
498C2×#393C2×C3111yescharacteristic, complemented
499C2×#390C2×C3111yescharacteristic
500C2×#386C2×C3111yescharacteristic
501C2×#380C2×C3111yescharacteristic, complemented
502#1442C2×C3111yescharacteristic, complemented
503#1439C2×C3111yescharacteristic, complemented
504#1439C2×C3111yescharacteristic, complemented
505#1439C2×C3111yescharacteristic, complemented
506#1439C2×C3111yescharacteristic, complemented
507#1438C2×C3111yescharacteristic
508#1436C2×C3111yescharacteristic, complemented
509#1434C2×C3111yescharacteristic, complemented
510C22⋊#95C2×C3111yescharacteristic, complemented
511C22×C31—24no—
512C22×C31—24no—
513C22×C31—24no—
514C22×C31—42no—
515C22×C31—42no—
516C22×C31—42no—
517C22×C31—42no—
518C22×C31—42no—
519C22×C31—42no—
520C22×C31—42no—
521C22×C31—42no—
522C22×C31—42no—
523C22×C31—42no—
524C22×C31—42no—
525C22×C31—42no—
526C22×C31—42no—
527C22×C31—42no—
528C22×C31—42no—
529C22×C31—42no—
530C22×C31—42no—
531C22×C31—42no—
532C22×C31—42no—
533C22×C31—81no—
534C22×C31—81no—
535C22×C31—81no—
536C22×C31—81no—
537C22×C31—81no—
538C22×C31—81no—
539C22×C31—81no—
540C22×C31—81no—
541C22×C31C2×C22⋊Q811yescharacteristic
542C22×C31C2×C22⋊Q811yescharacteristic
543C22×C31#52511yescharacteristic
544C22×C31C2×#12411yescharacteristic
545C22×C31#53211yescharacteristic
546C22×C31#53211yescharacteristic
547C22×C31#53411yescharacteristic
548C22×C31#53511yescharacteristic
549C22×C31#53511yescharacteristic
550C22×C31#53811yescharacteristic
551C22×C31#53811yescharacteristic
552C22×C31#53911yescharacteristic
553C22×C31#54211yescharacteristic
554C22×C31#54211yescharacteristic
555C22×C31#54311yescharacteristic
556C22×C31D4211yescharacteristic
557C22×C31D4211yescharacteristic
558C22×C31D4211yescharacteristic
559C22×C31#54611yescharacteristic
560C22×C31#54611yescharacteristic
561C22×C31#54611yescharacteristic
562C22×C31#54711yescharacteristic
563C22×C31#54811yescharacteristic
564C22×C31D4×Q811yescharacteristic
565C22×C31#55111yescharacteristic
566C22×C31#55111yescharacteristic
567C22×C31#55111yescharacteristic
568C22×C31#55411yescharacteristic
569C22×C31#55411yescharacteristic
570C22×C31#55411yescharacteristic
571C22×C31#55511yescharacteristic
572C22×C31#55511yescharacteristic
573C22×C31#55511yescharacteristic
574C22×C31#56011yescharacteristic
575C22×C31#56211yescharacteristic
576C4×C31—24no—
577C4×C31—24no—
578C4×C31—42no—
579C4×C31—42no—
580C4×C31—42no—
581C4×C31—42no—
582C4×C31—42no—
583C4×C31—42no—
584C4×C31—42no—
585C4×C31—81no—
586C4×C31—81no—
587C4×C31—81no—
588C4×C31—81no—
589C23×Q8C22×C3111yescharacteristic
590C23×D4C22×C3111yescharacteristic
591C24×C4C22×C3111yescharacteristic
592C22×C4⋊C4C22×C3111yescharacteristic
593C22×C4⋊C4C22×C3111yescharacteristic
594C22×C4⋊C4C22×C3111yescharacteristic
595C22×C4⋊C4C22×C3111yescharacteristic
596C22×C22⋊C4C22×C3111yescharacteristic
597C22×C22⋊C4C22×C3111yescharacteristic
598C22×C22⋊C4C22×C3111yescharacteristic
599C22×C22⋊C4C22×C3111yescharacteristic
600C22×C22⋊C4C22×C3111yescharacteristic
601C22×C22⋊C4C22×C3111yescharacteristic
602C22×C22⋊C4C22×C3111yescharacteristic
603C22×C22⋊C4C22×C3111yescharacteristic
604C22×C22⋊C4C22×C3111yescharacteristic
605C22×C22⋊C4C22×C3111yescharacteristic
606C22×C22⋊C4C22×C3111yescharacteristic
607C22×C42C22×C3111yescharacteristic
608#395—24no—
609#393—24no—
610#393—24no—
611#390—24no—
612#386—24no—
613#380—24no—
614C2×#95C22×C3111yescharacteristic
615C2×#95C22×C3111yescharacteristic
616C2×#95C22×C3111yescharacteristic
617C2×#95C22×C3111yescharacteristic
618C2×#95C22×C3111yescharacteristic
619C2×#95C22×C3111yescharacteristic
620C2×#95C22×C3111yescharacteristic
621C2×#95C22×C3111yescharacteristic
622C2×#95C22×C3111yescharacteristic
623C2×#95C22×C3111yescharacteristic
624C2×#95C22×C3111yescharacteristic
625C2×#95C22×C3111yescharacteristic
626C2×#95C22×C3111yescharacteristic
627C2×#95C22×C3111yescharacteristic
628C2×#95C22×C3111yescharacteristic
629C2×#95C22×C3111yescharacteristic
630C2×C31—44no—
631C2×C31—82no—
632C2×C31#243711yescharacteristic
633C2×C31#244911yescharacteristic
634C2×C31#245211yescharacteristic
635C2×C31#247211yescharacteristic
636C2×C31#249111yescharacteristic
637C2×C31#255511yescharacteristic
638C2×C31#256311yescharacteristic
639C2×C31#256411yescharacteristic
640C2×C31#261011yescharacteristic
641C2×C31#266911yescharacteristic
642C2×C31#268611yescharacteristic
643C2×C31#269211yescharacteristic
644C2×C31#269611yescharacteristic
645C2×C31#273711yescharacteristic
646C2×C31#278411yescharacteristic
647C25C23×C3111yescharacteristic
648C25C23×C3111yescharacteristic
649C22×Q8—22no—
650C22×Q8—22no—
651C22×Q8—22no—
652C22×Q8—41no—
653C22×Q8—41no—
654C22×Q8—41no—
655C22×Q8—41no—
656C22×D4—22no—
657C22×D4—22no—
658C22×D4—22no—
659C22×D4—22no—
660C22×D4—41no—
661C22×D4—41no—
662C22×D4Q8×C3114yescomplemented
663C23×C4—22no—
664C23×C4—22no—
665C23×C4—22no—
666C23×C4—22no—
667C23×C4—22no—
668C23×C4—41no—
669C23×C4—41no—
670C23×C4C23×C3111yescharacteristic
671C23×C4C23×C3111yescharacteristic
672C23×C4C23×C3111yescharacteristic
673C23×C4C23×C3111yescharacteristic
674C23×C4C23×C3111yescharacteristic
675C23×C4C23×C3111yescharacteristic
676C23×C4C23×C3111yescharacteristic
677C23×C4C23×C3111yescharacteristic
678C23×C4C23×C3111yescharacteristic
679C23×C4C23×C3111yescharacteristic
680C23×C4C23×C3111yescharacteristic
681C23×C4C23×C3111yescharacteristic
682C23×C4C23×C3111yescharacteristic
683C2×C4⋊C4—22no—
684C2×C4⋊C4—22no—
685C2×C4⋊C4—22no—
686C2×C4⋊C4—22no—
687C2×C4⋊C4—22no—
688C2×C4⋊C4—22no—
689C2×C4⋊C4—22no—
690C2×C4⋊C4—41no—
691C2×C4⋊C4—41no—
692C2×C4⋊C4—41no—
693C2×C4⋊C4—41no—
694C2×C4⋊C4—41no—
695C2×C22⋊C4—22no—
696C2×C22⋊C4—22no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—22no—
701C2×C22⋊C4—22no—
702C2×C22⋊C4—22no—
703C2×C22⋊C4—22no—
704C2×C22⋊C4—22no—
705C2×C22⋊C4—22no—
706C2×C22⋊C4—22no—
707C2×C22⋊C4—22no—
708C2×C22⋊C4—22no—
709C2×C22⋊C4—22no—
710C2×C22⋊C4—22no—
711C2×C22⋊C4—22no—
712C2×C22⋊C4—22no—
713C2×C22⋊C4—41no—
714C2×C22⋊C4—41no—
715C2×C22⋊C4—41no—
716C2×C22⋊C4—41no—
717C2×C22⋊C4—41no—
718C2×C22⋊C4—41no—
719C2×C22⋊C4—41no—
720C2×C22⋊C4—41no—
721C2×C22⋊C4—41no—
722C2×C22⋊C4—41no—
723C2×C22⋊C4—41no—
724C2×C22⋊C4—41no—
725C2×C22⋊C4—41no—
726C2×C22⋊C4—41no—
727C2×C22⋊C4D4×C3114yes—
728C2×C42—22no—
729C2×C42—22no—
730C2×C42—41no—
731#95—22no—
732#95—22no—
733#95—22no—
734#95—22no—
735#95—22no—
736#95—22no—
737#95—22no—
738#95—22no—
739#95—22no—
740#95—22no—
741#95—22no—
742#95—22no—
743#95—41no—
744#95—41no—
745#95D4×C3114yes—
746#95D4×C3114yescomplemented
747C31#1547611yescharacteristic, direct product factor, Sylow
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24—21no—
774C24C2×D4×C3112yes—
775C24C2×Q8×C3112yes—
776C24C2×Q8×C3112yes—
777C24#41×C3112yes—
778C24C24×C3111yescharacteristic
779C2×Q8—44no—
780C2×Q8—44no—
781C2×Q8—44no—
782C2×Q8—44no—
783C2×Q8—44no—
784C2×Q8—44no—
785C2×Q8—44no—
786C2×D4—28no—
787C2×D4—28no—
788C2×D4—44no—
789C2×D4—44no—
790C2×D4—44no—
791C2×D4—44no—
792C2×D4—44no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—28no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
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—21no—
823C22×C4—21no—
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—44no—
873C22×C4—44no—
874C22×C4—44no—
875C22×C4—44no—
876C22×C4—44no—
877C22×C4—44no—
878C22×C4C2×D4×C3112yes—
879C22×C4C2×D4×C3112yes—
880C22×C4C2×D4×C3112yes—
881C22×C4C2×D4×C3112yes—
882C22×C4C2×D4×C3112yes—
883C22×C4C2×D4×C3112yes—
884C22×C4C2×D4×C3112yes—
885C22×C4C2×D4×C3112yes—
886C22×C4C2×Q8×C3112yes—
887C22×C4#41×C3112yes—
888C22×C4#41×C3112yes—
889C22×C4#41×C3112yes—
890C22×C4#41×C3112yes—
891C4⋊C4—44no—
892C4⋊C4—44no—
893C4⋊C4—44no—
894C4⋊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—
906C42—44no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23C31×C22⋊Q814yes—
977C23C22×D4×C3111yescharacteristic
978C23C22×D4×C3111yescharacteristic
979C23C22×D4×C3111yescharacteristic
980C23C22×Q8×C3111yescharacteristic
981C23C2×#41×C3111yescharacteristic
982C23C2×#41×C3111yescharacteristic
983C23C2×#41×C3111yescharacteristic
984C23C2×#41×C3111yescharacteristic
985C23C2×#41×C3111yescharacteristic
986C23C31×H(5,𝔽2)11yescharacteristic
987C23C31×H(5,𝔽2)11yescharacteristic
988C23C31×H(5,𝔽2)11yescharacteristic
989C23C31×H(5,𝔽2)11yescharacteristic
990C23C31×H(5,𝔽2)11yescharacteristic
991C23C31×2−1+411yescharacteristic
992Q8—416no—
993D4—416no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—416no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
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×C4C31×C22⋊Q814yes—
1085C2×C4C31×#12414yes—
1086C22—24no—
1087C22—24no—
1088C22—24no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—42no—
1107C22—42no—
1108C22—81no—
1109C22—81no—
1110C22—81no—
1111C22—81no—
1112C22—81no—
1113C22—81no—
1114C22—81no—
1115C22—81no—
1116C22C2×C31×C22⋊Q811yescharacteristic
1117C22C2×C31×C22⋊Q811yescharacteristic
1118C22C31×#52511yescharacteristic
1119C22C2×C31×#12411yescharacteristic
1120C22C31×#53211yescharacteristic
1121C22C31×#53211yescharacteristic
1122C22C31×#53411yescharacteristic
1123C22C31×#53511yescharacteristic
1124C22C31×#53511yescharacteristic
1125C22C31×#53811yescharacteristic
1126C22C31×#53811yescharacteristic
1127C22C31×#53911yescharacteristic
1128C22C31×#54211yescharacteristic
1129C22C31×#54211yescharacteristic
1130C22C31×#54311yescharacteristic
1131C22D42×C3111yescharacteristic
1132C22D42×C3111yescharacteristic
1133C22D42×C3111yescharacteristic
1134C22C31×#54611yescharacteristic
1135C22C31×#54611yescharacteristic
1136C22C31×#54611yescharacteristic
1137C22C31×#54711yescharacteristic
1138C22C31×#54811yescharacteristic
1139C22D4×Q8×C3111yescharacteristic
1140C22C31×#55111yescharacteristic
1141C22C31×#55111yescharacteristic
1142C22C31×#55111yescharacteristic
1143C22C31×#55411yescharacteristic
1144C22C31×#55411yescharacteristic
1145C22C31×#55411yescharacteristic
1146C22C31×#55511yescharacteristic
1147C22C31×#55511yescharacteristic
1148C22C31×#55511yescharacteristic
1149C22C31×#56011yescharacteristic
1150C22C31×#56211yescharacteristic
1151C4—24no—
1152C4—24no—
1153C4—42no—
1154C4—42no—
1155C4—42no—
1156C4—42no—
1157C4—42no—
1158C4—42no—
1159C4—42no—
1160C4—81no—
1161C4—81no—
1162C4—81no—
1163C4—81no—
1164C2—44no—
1165C2—82no—
1166C2C31×#243711yescharacteristic
1167C2C31×#244911yescharacteristic
1168C2C31×#245211yescharacteristic
1169C2C31×#247211yescharacteristic
1170C2C31×#249111yescharacteristic
1171C2C31×#255511yescharacteristic
1172C2C31×#256311yescharacteristic
1173C2C31×#256411yescharacteristic
1174C2C31×#261011yescharacteristic
1175C2C31×#266911yescharacteristic
1176C2C31×#268611yescharacteristic
1177C2C31×#269211yescharacteristic
1178C2C31×#269611yescharacteristic
1179C2C31×#273711yescharacteristic
1180C2C31×#278411yescharacteristic
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. C2×C31×#395C2semidirect
2. C2×C31×#393C2semidirect
3. C2×C31×#393C2semidirect
6. C2×C31×#380C2semidirect
7. C31×#1442C2semidirect
8. C31×#1439C2semidirect
9. C31×#1439C2semidirect
10. C31×#1439C2semidirect
11. C31×#1439C2semidirect
13. C31×#1436C2semidirect
14. C31×#1434C2semidirect
15. C31×C22⋊#95C2semidirect
72. C22×D4×C31Q8semidirect
156. C31×#95D4semidirect
316. #15476C31direct (N × H)
496. C2×#395C2×C31semidirect
497. C2×#393C2×C31semidirect
498. C2×#393C2×C31semidirect
501. C2×#380C2×C31semidirect
502. #1442C2×C31semidirect
503. #1439C2×C31semidirect
504. #1439C2×C31semidirect
505. #1439C2×C31semidirect
506. #1439C2×C31semidirect
508. #1436C2×C31semidirect
509. #1434C2×C31semidirect
510. C22⋊#95C2×C31semidirect
662. C22×D4Q8×C31semidirect
746. #95D4×C31semidirect
747. C31#15476direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3952
C2×C31×#3932
C2×C31×#3902
C2×C31×#3862
C2×C31×#3802
C31×#14422
C31×#14392
C31×#14382
C31×#14362
C31×#14342
C31×C22⋊#952
#1547631