Finite Group Databasebeta

← C31×#15502 #21472261

Subgroups — C31×#15502 #21472261

Order 7936.

1738 conjugacy classes of subgroups.

The subgroup lattice has 1144 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#397C211yesmaximal, characteristic, complemented
2C2×C31×#394C211yesmaximal, characteristic
3C2×C31×#390C211yesmaximal, characteristic
4C2×C31×#386C211yesmaximal, characteristic
5C31×#1441C211yesmaximal, characteristic, complemented
6C31×#1441C211yesmaximal, characteristic, complemented
7C31×#1440C211yesmaximal, characteristic, complemented
8C31×#1440C211yesmaximal, characteristic, complemented
9C31×#1440C211yesmaximal, characteristic, complemented
10C31×#1440C211yesmaximal, characteristic, complemented
11C31×#1439C211yesmaximal, characteristic, complemented
12C31×#1436C211yesmaximal, characteristic, complemented
13C31×#1434C211yesmaximal, characteristic, complemented
14C31×C22⋊#95C211yesmaximal, characteristic, complemented
15C31×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C31C2211yescharacteristic
17C24×C4×C31C2211yescharacteristic
18C22×C4⋊C4×C31C2211yescharacteristic
19C22×C4⋊C4×C31C2211yescharacteristic
20C22×C4⋊C4×C31C2211yescharacteristic
21C22×C22⋊C4×C31C2211yescharacteristic
22C22×C22⋊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×C42×C31C2211yescharacteristic
33C31×#397—24no—
34C31×#394—24no—
35C31×#390—24no—
36C31×#386—24no—
37C2×C31×#95C2211yescharacteristic
38C2×C31×#95C2211yescharacteristic
39C2×C31×#95C2211yescharacteristic
40C2×C31×#95C2211yescharacteristic
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
55C25×C31C2311yescharacteristic
56C25×C31C2311yescharacteristic
57C22×D4×C31—22no—
58C22×D4×C31—22no—
59C22×D4×C31—22no—
60C22×D4×C31—22no—
61C22×D4×C31—41no—
62C22×D4×C31—41no—
63C22×D4×C31D414yes—
64C23×C4×C31—22no—
65C23×C4×C31—22no—
66C23×C4×C31—22no—
67C23×C4×C31—41no—
68C23×C4×C31—41no—
69C23×C4×C31—41no—
70C23×C4×C31—41no—
71C23×C4×C31C2311yescharacteristic
72C23×C4×C31C2311yescharacteristic
73C23×C4×C31C2311yescharacteristic
74C23×C4×C31C2311yescharacteristic
75C23×C4×C31C2311yescharacteristic
76C23×C4×C31C2311yescharacteristic
77C23×C4×C31C2311yescharacteristic
78C23×C4×C31C2311yescharacteristic
79C23×C4×C31C2311yescharacteristic
80C23×C4×C31C2311yescharacteristic
81C23×C4×C31C2311yescharacteristic
82C23×C4×C31C2311yescharacteristic
83C23×C4×C31C2311yescharacteristic
84C2×C4⋊C4×C31—22no—
85C2×C4⋊C4×C31—22no—
86C2×C4⋊C4×C31—22no—
87C2×C4⋊C4×C31—22no—
88C2×C4⋊C4×C31—22no—
89C2×C4⋊C4×C31—22no—
90C2×C4⋊C4×C31—41no—
91C2×C4⋊C4×C31—41no—
92C2×C4⋊C4×C31—41no—
93C2×C22⋊C4×C31—22no—
94C2×C22⋊C4×C31—22no—
95C2×C22⋊C4×C31—22no—
96C2×C22⋊C4×C31—22no—
97C2×C22⋊C4×C31—22no—
98C2×C22⋊C4×C31—22no—
99C2×C22⋊C4×C31—22no—
100C2×C22⋊C4×C31—22no—
101C2×C22⋊C4×C31—22no—
102C2×C22⋊C4×C31—22no—
103C2×C22⋊C4×C31—22no—
104C2×C22⋊C4×C31—22no—
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—41no—
114C2×C22⋊C4×C31—41no—
115C2×C22⋊C4×C31—41no—
116C2×C22⋊C4×C31—41no—
117C2×C22⋊C4×C31—41no—
118C2×C22⋊C4×C31—41no—
119C2×C22⋊C4×C31—41no—
120C2×C22⋊C4×C31—41no—
121C2×C22⋊C4×C31—41no—
122C2×C22⋊C4×C31—41no—
123C2×C22⋊C4×C31—41no—
124C2×C22⋊C4×C31—41no—
125C2×C22⋊C4×C31D414yes—
126C2×C42×C31—22no—
127C2×C42×C31—22no—
128C2×C42×C31—41no—
129C31×#95—22no—
130C31×#95—22no—
131C31×#95—22no—
132C31×#95—22no—
133C31×#95—22no—
134C31×#95—22no—
135C31×#95—22no—
136C31×#95—22no—
137C31×#95—22no—
138C31×#95—22no—
139C31×#95—41no—
140C31×#95—41no—
141C31×#95—41no—
142C31×#95—41no—
143C31×#95—41no—
144C31×#95—41no—
145C31×#95—41no—
146C31×#95—41no—
147C24×C31—21no—
148C24×C31—21no—
149C24×C31—21no—
150C24×C31—21no—
151C24×C31—21no—
152C24×C31—21no—
153C24×C31—21no—
154C24×C31—21no—
155C24×C31—21no—
156C24×C31—21no—
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×C31C2×D412yes—
174C24×C31C2×D412yes—
175C24×C31C2×D412yes—
176C24×C31#4112yes—
177C24×C31C2411yescharacteristic
178C2×D4×C31—28no—
179C2×D4×C31—28no—
180C2×D4×C31—44no—
181C2×D4×C31—44no—
182C2×D4×C31—44no—
183C2×D4×C31—44no—
184C2×D4×C31—44no—
185C22×C4×C31—21no—
186C22×C4×C31—21no—
187C22×C4×C31—21no—
188C22×C4×C31—21no—
189C22×C4×C31—21no—
190C22×C4×C31—21no—
191C22×C4×C31—21no—
192C22×C4×C31—21no—
193C22×C4×C31—21no—
194C22×C4×C31—21no—
195C22×C4×C31—21no—
196C22×C4×C31—21no—
197C22×C4×C31—21no—
198C22×C4×C31—21no—
199C22×C4×C31—21no—
200C22×C4×C31—21no—
201C22×C4×C31—21no—
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—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—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—44no—
268C22×C4×C31—44no—
269C22×C4×C31—44no—
270C22×C4×C31—44no—
271C22×C4×C31—44no—
272C22×C4×C31—44no—
273C22×C4×C31—44no—
274C22×C4×C31C2×D412yes—
275C22×C4×C31C2×D412yes—
276C22×C4×C31C2×D412yes—
277C22×C4×C31#4112yes—
278C22×C4×C31#4112yes—
279C22×C4×C31#4112yes—
280C22×C4×C31#4112yes—
281C22×C4×C31#4112yes—
282C22×C4×C31#4112yes—
283C4⋊C4×C31—44no—
284C4⋊C4×C31—44no—
285C4⋊C4×C31—44no—
286C22⋊C4×C31—44no—
287C22⋊C4×C31—44no—
288C22⋊C4×C31—44no—
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—
297C42×C31—44no—
298#15502C3111yesmaximal, characteristic, direct product factor, Sylow
299C23×C31—22no—
300C23×C31—22no—
301C23×C31—22no—
302C23×C31—22no—
303C23×C31—22no—
304C23×C31—22no—
305C23×C31—22no—
306C23×C31—22no—
307C23×C31—22no—
308C23×C31—22no—
309C23×C31—22no—
310C23×C31—22no—
311C23×C31—22no—
312C23×C31—22no—
313C23×C31—22no—
314C23×C31—22no—
315C23×C31—22no—
316C23×C31—22no—
317C23×C31—22no—
318C23×C31—22no—
319C23×C31—22no—
320C23×C31—22no—
321C23×C31—22no—
322C23×C31—22no—
323C23×C31—22no—
324C23×C31—41no—
325C23×C31—41no—
326C23×C31—41no—
327C23×C31—41no—
328C23×C31—41no—
329C23×C31—41no—
330C23×C31—41no—
331C23×C31—41no—
332C23×C31—41no—
333C23×C31—41no—
334C23×C31—41no—
335C23×C31—41no—
336C23×C31—41no—
337C23×C31—41no—
338C23×C31—41no—
339C23×C31—41no—
340C23×C31—41no—
341C23×C31—41no—
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#12114yes—
369C23×C31C22×D411yescharacteristic
370C23×C31C22×D411yescharacteristic
371C23×C31C2×#4111yescharacteristic
372C23×C31C2×#4111yescharacteristic
373C23×C31C2×#4111yescharacteristic
374C23×C31C2×#4111yescharacteristic
375C23×C31C2×#4111yescharacteristic
376C23×C31C2×#4111yescharacteristic
377C23×C31C2×#4111yescharacteristic
378C23×C31H(5,𝔽2)11yescharacteristic
379C23×C31H(5,𝔽2)11yescharacteristic
380C23×C31H(5,𝔽2)11yescharacteristic
381C23×C31H(5,𝔽2)11yescharacteristic
382C23×C31H(5,𝔽2)11yescharacteristic
383C23×C312−1+411yescharacteristic
384D4×C31—416no—
385C2×C4×C31—22no—
386C2×C4×C31—22no—
387C2×C4×C31—22no—
388C2×C4×C31—22no—
389C2×C4×C31—22no—
390C2×C4×C31—22no—
391C2×C4×C31—22no—
392C2×C4×C31—22no—
393C2×C4×C31—22no—
394C2×C4×C31—22no—
395C2×C4×C31—22no—
396C2×C4×C31—22no—
397C2×C4×C31—22no—
398C2×C4×C31—22no—
399C2×C4×C31—22no—
400C2×C4×C31—22no—
401C2×C4×C31—22no—
402C2×C4×C31—22no—
403C2×C4×C31—22no—
404C2×C4×C31—22no—
405C2×C4×C31—22no—
406C2×C4×C31—22no—
407C2×C4×C31—22no—
408C2×C4×C31—22no—
409C2×C4×C31—416no—
410C2×C4×C31—41no—
411C2×C4×C31—41no—
412C2×C4×C31—41no—
413C2×C4×C31—41no—
414C2×C4×C31—41no—
415C2×C4×C31—41no—
416C2×C4×C31—41no—
417C2×C4×C31—41no—
418C2×C4×C31—41no—
419C2×C4×C31—41no—
420C2×C4×C31—41no—
421C2×C4×C31—41no—
422C2×C4×C31—41no—
423C2×C4×C31—41no—
424C2×C4×C31—41no—
425C2×C4×C31—41no—
426C2×C4×C31—41no—
427C2×C4×C31—41no—
428C2×C4×C31—41no—
429C2×C4×C31—41no—
430C2×C4×C31—41no—
431C2×C4×C31—41no—
432C2×C4×C31—41no—
433C2×C4×C31—41no—
434C2×C4×C31—41no—
435C2×C4×C31—41no—
436C2×C4×C31—41no—
437C2×C4×C31—41no—
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#12314yes—
477C2×#397C2×C3111yescharacteristic, complemented
478C2×#394C2×C3111yescharacteristic
479C2×#390C2×C3111yescharacteristic
480C2×#386C2×C3111yescharacteristic
481#1441C2×C3111yescharacteristic, complemented
482#1441C2×C3111yescharacteristic, complemented
483#1440C2×C3111yescharacteristic, complemented
484#1440C2×C3111yescharacteristic, complemented
485#1440C2×C3111yescharacteristic, complemented
486#1440C2×C3111yescharacteristic, complemented
487#1439C2×C3111yescharacteristic, complemented
488#1436C2×C3111yescharacteristic, complemented
489#1434C2×C3111yescharacteristic, complemented
490C22⋊#95C2×C3111yescharacteristic, complemented
491C22⋊#95C2×C3111yescharacteristic, complemented
492C22×C31—24no—
493C22×C31—24no—
494C22×C31—24no—
495C22×C31—42no—
496C22×C31—42no—
497C22×C31—42no—
498C22×C31—42no—
499C22×C31—42no—
500C22×C31—42no—
501C22×C31—42no—
502C22×C31—42no—
503C22×C31—42no—
504C22×C31—42no—
505C22×C31—42no—
506C22×C31—42no—
507C22×C31—42no—
508C22×C31—42no—
509C22×C31—42no—
510C22×C31—42no—
511C22×C31—42no—
512C22×C31—42no—
513C22×C31—42no—
514C22×C31—81no—
515C22×C31—81no—
516C22×C31—81no—
517C22×C31—81no—
518C22×C31—81no—
519C22×C31—81no—
520C22×C31—81no—
521C22×C31—81no—
522C22×C31C2×#12111yescharacteristic
523C22×C31C2×#12311yescharacteristic
524C22×C31#52911yescharacteristic
525C22×C31#52911yescharacteristic
526C22×C31#52911yescharacteristic
527C22×C31#53211yescharacteristic
528C22×C31#53411yescharacteristic
529C22×C31#53411yescharacteristic
530C22×C31#53811yescharacteristic
531C22×C31#53811yescharacteristic
532C22×C31#53911yescharacteristic
533C22×C31#54011yescharacteristic
534C22×C31#54011yescharacteristic
535C22×C31#54211yescharacteristic
536C22×C31#54211yescharacteristic
537C22×C31#54611yescharacteristic
538C22×C31#54611yescharacteristic
539C22×C31#54611yescharacteristic
540C22×C31#54611yescharacteristic
541C22×C31#54611yescharacteristic
542C22×C31#54611yescharacteristic
543C22×C31#54711yescharacteristic
544C22×C31#54711yescharacteristic
545C22×C31#55111yescharacteristic
546C22×C31#55111yescharacteristic
547C22×C31#55111yescharacteristic
548C22×C31#55311yescharacteristic
549C22×C31#55311yescharacteristic
550C22×C31#55311yescharacteristic
551C22×C31#55311yescharacteristic
552C22×C31#55511yescharacteristic
553C22×C31#55611yescharacteristic
554C22×C31#55911yescharacteristic
555C22×C31#56011yescharacteristic
556C22×C31#56211yescharacteristic
557C4×C31—24no—
558C4×C31—42no—
559C4×C31—42no—
560C4×C31—42no—
561C4×C31—42no—
562C4×C31—42no—
563C4×C31—42no—
564C4×C31—81no—
565C4×C31—81no—
566C4×C31—81no—
567C4×C31—81no—
568C4×C31—81no—
569C4×C31—81no—
570C23×D4C22×C3111yescharacteristic
571C24×C4C22×C3111yescharacteristic
572C22×C4⋊C4C22×C3111yescharacteristic
573C22×C4⋊C4C22×C3111yescharacteristic
574C22×C4⋊C4C22×C3111yescharacteristic
575C22×C22⋊C4C22×C3111yescharacteristic
576C22×C22⋊C4C22×C3111yescharacteristic
577C22×C22⋊C4C22×C3111yescharacteristic
578C22×C22⋊C4C22×C3111yescharacteristic
579C22×C22⋊C4C22×C3111yescharacteristic
580C22×C22⋊C4C22×C3111yescharacteristic
581C22×C22⋊C4C22×C3111yescharacteristic
582C22×C22⋊C4C22×C3111yescharacteristic
583C22×C22⋊C4C22×C3111yescharacteristic
584C22×C22⋊C4C22×C3111yescharacteristic
585C22×C22⋊C4C22×C3111yescharacteristic
586C22×C42C22×C3111yescharacteristic
587#397—24no—
588#394—24no—
589#390—24no—
590#386—24no—
591C2×#95C22×C3111yescharacteristic
592C2×#95C22×C3111yescharacteristic
593C2×#95C22×C3111yescharacteristic
594C2×#95C22×C3111yescharacteristic
595C2×#95C22×C3111yescharacteristic
596C2×#95C22×C3111yescharacteristic
597C2×#95C22×C3111yescharacteristic
598C2×#95C22×C3111yescharacteristic
599C2×#95C22×C3111yescharacteristic
600C2×#95C22×C3111yescharacteristic
601C2×#95C22×C3111yescharacteristic
602C2×#95C22×C3111yescharacteristic
603C2×#95C22×C3111yescharacteristic
604C2×#95C22×C3111yescharacteristic
605C2×#95C22×C3111yescharacteristic
606C2×#95C22×C3111yescharacteristic
607C2×#95C22×C3111yescharacteristic
608C2×#95C22×C3111yescharacteristic
609C2×C31—44no—
610C2×C31—82no—
611C2×C31#241211yescharacteristic
612C2×C31#242011yescharacteristic
613C2×C31#242511yescharacteristic
614C2×C31#244711yescharacteristic
615C2×C31#252111yescharacteristic
616C2×C31#253111yescharacteristic
617C2×C31#254311yescharacteristic
618C2×C31#255911yescharacteristic
619C2×C31#259511yescharacteristic
620C2×C31#268611yescharacteristic
621C2×C31#269711yescharacteristic
622C2×C31#270111yescharacteristic
623C2×C31#270911yescharacteristic
624C2×C31#275711yescharacteristic
625C2×C31#278611yescharacteristic
626C25C23×C3111yescharacteristic
627C25C23×C3111yescharacteristic
628C22×D4—22no—
629C22×D4—22no—
630C22×D4—22no—
631C22×D4—22no—
632C22×D4—41no—
633C22×D4—41no—
634C22×D4D4×C3114yes—
635C23×C4—22no—
636C23×C4—22no—
637C23×C4—22no—
638C23×C4—41no—
639C23×C4—41no—
640C23×C4—41no—
641C23×C4—41no—
642C23×C4C23×C3111yescharacteristic
643C23×C4C23×C3111yescharacteristic
644C23×C4C23×C3111yescharacteristic
645C23×C4C23×C3111yescharacteristic
646C23×C4C23×C3111yescharacteristic
647C23×C4C23×C3111yescharacteristic
648C23×C4C23×C3111yescharacteristic
649C23×C4C23×C3111yescharacteristic
650C23×C4C23×C3111yescharacteristic
651C23×C4C23×C3111yescharacteristic
652C23×C4C23×C3111yescharacteristic
653C23×C4C23×C3111yescharacteristic
654C23×C4C23×C3111yescharacteristic
655C2×C4⋊C4—22no—
656C2×C4⋊C4—22no—
657C2×C4⋊C4—22no—
658C2×C4⋊C4—22no—
659C2×C4⋊C4—22no—
660C2×C4⋊C4—22no—
661C2×C4⋊C4—41no—
662C2×C4⋊C4—41no—
663C2×C4⋊C4—41no—
664C2×C22⋊C4—22no—
665C2×C22⋊C4—22no—
666C2×C22⋊C4—22no—
667C2×C22⋊C4—22no—
668C2×C22⋊C4—22no—
669C2×C22⋊C4—22no—
670C2×C22⋊C4—22no—
671C2×C22⋊C4—22no—
672C2×C22⋊C4—22no—
673C2×C22⋊C4—22no—
674C2×C22⋊C4—22no—
675C2×C22⋊C4—22no—
676C2×C22⋊C4—22no—
677C2×C22⋊C4—22no—
678C2×C22⋊C4—22no—
679C2×C22⋊C4—22no—
680C2×C22⋊C4—22no—
681C2×C22⋊C4—22no—
682C2×C22⋊C4—22no—
683C2×C22⋊C4—22no—
684C2×C22⋊C4—41no—
685C2×C22⋊C4—41no—
686C2×C22⋊C4—41no—
687C2×C22⋊C4—41no—
688C2×C22⋊C4—41no—
689C2×C22⋊C4—41no—
690C2×C22⋊C4—41no—
691C2×C22⋊C4—41no—
692C2×C22⋊C4—41no—
693C2×C22⋊C4—41no—
694C2×C22⋊C4—41no—
695C2×C22⋊C4—41no—
696C2×C22⋊C4D4×C3114yes—
697C2×C42—22no—
698C2×C42—22no—
699C2×C42—41no—
700#95—22no—
701#95—22no—
702#95—22no—
703#95—22no—
704#95—22no—
705#95—22no—
706#95—22no—
707#95—22no—
708#95—22no—
709#95—22no—
710#95—41no—
711#95—41no—
712#95—41no—
713#95—41no—
714#95—41no—
715#95—41no—
716#95—41no—
717#95—41no—
718C31#1550211yescharacteristic, direct product factor, Sylow
719C24—21no—
720C24—21no—
721C24—21no—
722C24—21no—
723C24—21no—
724C24—21no—
725C24—21no—
726C24—21no—
727C24—21no—
728C24—21no—
729C24—21no—
730C24—21no—
731C24—21no—
732C24—21no—
733C24—21no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24—21no—
743C24—21no—
744C24—21no—
745C24C2×D4×C3112yes—
746C24C2×D4×C3112yes—
747C24C2×D4×C3112yes—
748C24#41×C3112yes—
749C24C24×C3111yescharacteristic
750C2×D4—28no—
751C2×D4—28no—
752C2×D4—44no—
753C2×D4—44no—
754C2×D4—44no—
755C2×D4—44no—
756C2×D4—44no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
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—21no—
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—44no—
840C22×C4—44no—
841C22×C4—44no—
842C22×C4—44no—
843C22×C4—44no—
844C22×C4—44no—
845C22×C4—44no—
846C22×C4C2×D4×C3112yes—
847C22×C4C2×D4×C3112yes—
848C22×C4C2×D4×C3112yes—
849C22×C4#41×C3112yes—
850C22×C4#41×C3112yes—
851C22×C4#41×C3112yes—
852C22×C4#41×C3112yes—
853C22×C4#41×C3112yes—
854C22×C4#41×C3112yes—
855C4⋊C4—44no—
856C4⋊C4—44no—
857C4⋊C4—44no—
858C22⋊C4—44no—
859C22⋊C4—44no—
860C22⋊C4—44no—
861C22⋊C4—44no—
862C22⋊C4—44no—
863C22⋊C4—44no—
864C22⋊C4—44no—
865C22⋊C4—44no—
866C22⋊C4—44no—
867C22⋊C4—44no—
868C22⋊C4—44no—
869C42—44no—
870C23—22no—
871C23—22no—
872C23—22no—
873C23—22no—
874C23—22no—
875C23—22no—
876C23—22no—
877C23—22no—
878C23—22no—
879C23—22no—
880C23—22no—
881C23—22no—
882C23—22no—
883C23—22no—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—41no—
896C23—41no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23C31×#12114yes—
940C23C22×D4×C3111yescharacteristic
941C23C22×D4×C3111yescharacteristic
942C23C2×#41×C3111yescharacteristic
943C23C2×#41×C3111yescharacteristic
944C23C2×#41×C3111yescharacteristic
945C23C2×#41×C3111yescharacteristic
946C23C2×#41×C3111yescharacteristic
947C23C2×#41×C3111yescharacteristic
948C23C2×#41×C3111yescharacteristic
949C23C31×H(5,𝔽2)11yescharacteristic
950C23C31×H(5,𝔽2)11yescharacteristic
951C23C31×H(5,𝔽2)11yescharacteristic
952C23C31×H(5,𝔽2)11yescharacteristic
953C23C31×H(5,𝔽2)11yescharacteristic
954C23C31×2−1+411yescharacteristic
955D4—416no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—416no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—41no—
986C2×C4—41no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
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×C4C31×#12314yes—
1048C22—24no—
1049C22—24no—
1050C22—24no—
1051C22—42no—
1052C22—42no—
1053C22—42no—
1054C22—42no—
1055C22—42no—
1056C22—42no—
1057C22—42no—
1058C22—42no—
1059C22—42no—
1060C22—42no—
1061C22—42no—
1062C22—42no—
1063C22—42no—
1064C22—42no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—42no—
1069C22—42no—
1070C22—81no—
1071C22—81no—
1072C22—81no—
1073C22—81no—
1074C22—81no—
1075C22—81no—
1076C22—81no—
1077C22—81no—
1078C22C2×C31×#12111yescharacteristic
1079C22C2×C31×#12311yescharacteristic
1080C22C31×#52911yescharacteristic
1081C22C31×#52911yescharacteristic
1082C22C31×#52911yescharacteristic
1083C22C31×#53211yescharacteristic
1084C22C31×#53411yescharacteristic
1085C22C31×#53411yescharacteristic
1086C22C31×#53811yescharacteristic
1087C22C31×#53811yescharacteristic
1088C22C31×#53911yescharacteristic
1089C22C31×#54011yescharacteristic
1090C22C31×#54011yescharacteristic
1091C22C31×#54211yescharacteristic
1092C22C31×#54211yescharacteristic
1093C22C31×#54611yescharacteristic
1094C22C31×#54611yescharacteristic
1095C22C31×#54611yescharacteristic
1096C22C31×#54611yescharacteristic
1097C22C31×#54611yescharacteristic
1098C22C31×#54611yescharacteristic
1099C22C31×#54711yescharacteristic
1100C22C31×#54711yescharacteristic
1101C22C31×#55111yescharacteristic
1102C22C31×#55111yescharacteristic
1103C22C31×#55111yescharacteristic
1104C22C31×#55311yescharacteristic
1105C22C31×#55311yescharacteristic
1106C22C31×#55311yescharacteristic
1107C22C31×#55311yescharacteristic
1108C22C31×#55511yescharacteristic
1109C22C31×#55611yescharacteristic
1110C22C31×#55911yescharacteristic
1111C22C31×#56011yescharacteristic
1112C22C31×#56211yescharacteristic
1113C4—24no—
1114C4—42no—
1115C4—42no—
1116C4—42no—
1117C4—42no—
1118C4—42no—
1119C4—42no—
1120C4—81no—
1121C4—81no—
1122C4—81no—
1123C4—81no—
1124C4—81no—
1125C4—81no—
1126C2—44no—
1127C2—82no—
1128C2C31×#241211yescharacteristic
1129C2C31×#242011yescharacteristic
1130C2C31×#242511yescharacteristic
1131C2C31×#244711yescharacteristic
1132C2C31×#252111yescharacteristic
1133C2C31×#253111yescharacteristic
1134C2C31×#254311yescharacteristic
1135C2C31×#255911yescharacteristic
1136C2C31×#259511yescharacteristic
1137C2C31×#268611yescharacteristic
1138C2C31×#269711yescharacteristic
1139C2C31×#270111yescharacteristic
1140C2C31×#270911yescharacteristic
1141C2C31×#275711yescharacteristic
1142C2C31×#278611yescharacteristic
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×#397C2semidirect
5. C31×#1441C2semidirect
6. C31×#1441C2semidirect
7. C31×#1440C2semidirect
8. C31×#1440C2semidirect
9. C31×#1440C2semidirect
10. C31×#1440C2semidirect
11. C31×#1439C2semidirect
12. C31×#1436C2semidirect
13. C31×#1434C2semidirect
14. C31×C22⋊#95C2semidirect
15. C31×C22⋊#95C2semidirect
298. #15502C31direct (N × H)
477. C2×#397C2×C31semidirect
481. #1441C2×C31semidirect
482. #1441C2×C31semidirect
483. #1440C2×C31semidirect
484. #1440C2×C31semidirect
485. #1440C2×C31semidirect
486. #1440C2×C31semidirect
487. #1439C2×C31semidirect
488. #1436C2×C31semidirect
489. #1434C2×C31semidirect
490. C22⋊#95C2×C31semidirect
491. C22⋊#95C2×C31semidirect
718. C31#15502direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3972
C2×C31×#3942
C2×C31×#3902
C2×C31×#3862
C31×#14412
C31×#14402
C31×#14392
C31×#14362
C31×#14342
C31×C22⋊#952
#1550231