Finite Group Databasebeta

← C31×#15497 #21472256

Subgroups — C31×#15497 #21472256

Order 7936.

1830 conjugacy classes of subgroups.

The subgroup lattice has 1160 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#397C211yesmaximal, characteristic, complemented
2C2×C31×#397C211yesmaximal, characteristic, complemented
3C2×C31×#394C211yesmaximal, characteristic
4C2×C31×#390C211yesmaximal, characteristic
5C2×C31×#386C211yesmaximal, characteristic
6C2×C31×#385C211yesmaximal, characteristic, complemented
7C31×#1441C211yesmaximal, characteristic, complemented
8C31×#1441C211yesmaximal, characteristic, complemented
9C31×#1440C211yesmaximal, characteristic, complemented
10C31×#1440C211yesmaximal, characteristic, complemented
11C31×#1439C211yesmaximal, characteristic, complemented
12C31×#1439C211yesmaximal, characteristic, complemented
13C31×#1436C211yesmaximal, characteristic, complemented
14C31×C4⋊#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×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×#397—24no—
36C31×#397—24no—
37C31×#394—24no—
38C31×#390—24no—
39C31×#386—24no—
40C31×#385—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×D4×C31—22no—
60C22×D4×C31—22no—
61C22×D4×C31—22no—
62C22×D4×C31—22no—
63C22×D4×C31—41no—
64C22×D4×C31—41no—
65C22×D4×C31D414yes—
66C23×C4×C31—22no—
67C23×C4×C31—22no—
68C23×C4×C31—22no—
69C23×C4×C31—41no—
70C23×C4×C31—41no—
71C23×C4×C31—41no—
72C23×C4×C31—41no—
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
84C23×C4×C31C2311yescharacteristic
85C23×C4×C31C2311yescharacteristic
86C2×C4⋊C4×C31—22no—
87C2×C4⋊C4×C31—22no—
88C2×C4⋊C4×C31—22no—
89C2×C4⋊C4×C31—22no—
90C2×C4⋊C4×C31—22no—
91C2×C4⋊C4×C31—22no—
92C2×C4⋊C4×C31—22no—
93C2×C4⋊C4×C31—22no—
94C2×C4⋊C4×C31—22no—
95C2×C4⋊C4×C31—22no—
96C2×C4⋊C4×C31—22no—
97C2×C4⋊C4×C31—41no—
98C2×C4⋊C4×C31—41no—
99C2×C4⋊C4×C31—41no—
100C2×C4⋊C4×C31—41no—
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—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—22no—
124C2×C22⋊C4×C31—22no—
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×C31D414yes—
134C2×C42×C31—22no—
135C2×C42×C31—22no—
136C2×C42×C31—41no—
137C31×#95—22no—
138C31×#95—22no—
139C31×#95—22no—
140C31×#95—22no—
141C31×#95—22no—
142C31×#95—22no—
143C31×#95—22no—
144C31×#95—22no—
145C31×#95—22no—
146C31×#95—22no—
147C31×#95—41no—
148C31×#95—41no—
149C31×#95—41no—
150C31×#95—41no—
151C31×#95—41no—
152C31×#95D414yescomplemented
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×C31—21no—
174C24×C31—21no—
175C24×C31—21no—
176C24×C31—21no—
177C24×C31—21no—
178C24×C31—21no—
179C24×C31C2×D412yes—
180C24×C31C2×D412yes—
181C24×C31C2×D412yes—
182C24×C31#4112yes—
183C24×C31C2411yescharacteristic
184C2×D4×C31—28no—
185C2×D4×C31—28no—
186C2×D4×C31—44no—
187C2×D4×C31—44no—
188C2×D4×C31—44no—
189C2×D4×C31—44no—
190C2×D4×C31—44no—
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—21no—
268C22×C4×C31—21no—
269C22×C4×C31—21no—
270C22×C4×C31—21no—
271C22×C4×C31—44no—
272C22×C4×C31—44no—
273C22×C4×C31—44no—
274C22×C4×C31—44no—
275C22×C4×C31—44no—
276C22×C4×C31—44no—
277C22×C4×C31—44no—
278C22×C4×C31C2×D412yes—
279C22×C4×C31C2×D412yes—
280C22×C4×C31C2×D412yes—
281C22×C4×C31C2×D412yes—
282C22×C4×C31C2×D412yes—
283C22×C4×C31C2×D412yes—
284C22×C4×C31#4112yes—
285C22×C4×C31#4112yes—
286C22×C4×C31#4112yes—
287C22×C4×C31#4112yes—
288C22×C4×C31#4112yes—
289C4⋊C4×C31—44no—
290C4⋊C4×C31—44no—
291C4⋊C4×C31—44no—
292C4⋊C4×C31—44no—
293C4⋊C4×C31—44no—
294C22⋊C4×C31—28no—
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×C31—44no—
302C22⋊C4×C31—44no—
303C22⋊C4×C31—44no—
304C22⋊C4×C31—44no—
305C42×C31—44no—
306#15497C3111yesmaximal, characteristic, direct product factor, Sylow
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—22no—
325C23×C31—22no—
326C23×C31—22no—
327C23×C31—22no—
328C23×C31—22no—
329C23×C31—22no—
330C23×C31—22no—
331C23×C31—22no—
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—41no—
369C23×C31—41no—
370C23×C31—41no—
371C23×C31—41no—
372C23×C31—41no—
373C23×C31—41no—
374C23×C31—41no—
375C23×C31—41no—
376C23×C31#12114yes—
377C23×C31C22×D411yescharacteristic
378C23×C31C22×D411yescharacteristic
379C23×C31C22×D411yescharacteristic
380C23×C31C2×#4111yescharacteristic
381C23×C31C2×#4111yescharacteristic
382C23×C31C2×#4111yescharacteristic
383C23×C31C2×#4111yescharacteristic
384C23×C31C2×#4111yescharacteristic
385C23×C31C2×#4111yescharacteristic
386C23×C31H(5,𝔽2)11yescharacteristic
387C23×C31H(5,𝔽2)11yescharacteristic
388C23×C31H(5,𝔽2)11yescharacteristic
389C23×C31H(5,𝔽2)11yescharacteristic
390C23×C312−1+411yescharacteristic
391C23×C312−1+411yescharacteristic
392D4×C31—416no—
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—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—416no—
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—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#12114yes—
484C2×C4×C31#12314yes—
485C2×#397C2×C3111yescharacteristic, complemented
486C2×#397C2×C3111yescharacteristic, complemented
487C2×#394C2×C3111yescharacteristic
488C2×#390C2×C3111yescharacteristic
489C2×#386C2×C3111yescharacteristic
490C2×#385C2×C3111yescharacteristic, complemented
491#1441C2×C3111yescharacteristic, complemented
492#1441C2×C3111yescharacteristic, complemented
493#1440C2×C3111yescharacteristic, complemented
494#1440C2×C3111yescharacteristic, complemented
495#1439C2×C3111yescharacteristic, complemented
496#1439C2×C3111yescharacteristic, complemented
497#1436C2×C3111yescharacteristic, complemented
498C4⋊#95C2×C3111yescharacteristic, complemented
499C22⋊#95C2×C3111yescharacteristic, complemented
500C22×C31—24no—
501C22×C31—24no—
502C22×C31—24no—
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—42no—
515C22×C31—42no—
516C22×C31—42no—
517C22×C31—42no—
518C22×C31—42no—
519C22×C31—42no—
520C22×C31—42no—
521C22×C31—42no—
522C22×C31—81no—
523C22×C31—81no—
524C22×C31—81no—
525C22×C31—81no—
526C22×C31—81no—
527C22×C31—81no—
528C22×C31—81no—
529C22×C31—81no—
530C22×C31C2×#12111yescharacteristic
531C22×C31C2×#12111yescharacteristic
532C22×C31C2×#12311yescharacteristic
533C22×C31#52911yescharacteristic
534C22×C31#52911yescharacteristic
535C22×C31#53211yescharacteristic
536C22×C31#53411yescharacteristic
537C22×C31#53511yescharacteristic
538C22×C31#53711yescharacteristic
539C22×C31#53811yescharacteristic
540C22×C31#53911yescharacteristic
541C22×C31#53911yescharacteristic
542C22×C31#53911yescharacteristic
543C22×C31#54211yescharacteristic
544C22×C31#54211yescharacteristic
545C22×C31D4211yescharacteristic
546C22×C31#54611yescharacteristic
547C22×C31#54611yescharacteristic
548C22×C31#54611yescharacteristic
549C22×C31#54611yescharacteristic
550C22×C31#54611yescharacteristic
551C22×C31#54711yescharacteristic
552C22×C31#54711yescharacteristic
553C22×C31#54711yescharacteristic
554C22×C31#54711yescharacteristic
555C22×C31#54811yescharacteristic
556C22×C31#55111yescharacteristic
557C22×C31#55111yescharacteristic
558C22×C31#55311yescharacteristic
559C22×C31#55311yescharacteristic
560C22×C31#55611yescharacteristic
561C22×C31#55911yescharacteristic
562C22×C31#55911yescharacteristic
563C22×C31#56011yescharacteristic
564C22×C31#56311yescharacteristic
565C4×C31—24no—
566C4×C31—24no—
567C4×C31—42no—
568C4×C31—42no—
569C4×C31—42no—
570C4×C31—42no—
571C4×C31—42no—
572C4×C31—81no—
573C4×C31—81no—
574C4×C31—81no—
575C4×C31—81no—
576C4×C31—81no—
577C4×C31—81no—
578C23×D4C22×C3111yescharacteristic
579C24×C4C22×C3111yescharacteristic
580C22×C4⋊C4C22×C3111yescharacteristic
581C22×C4⋊C4C22×C3111yescharacteristic
582C22×C4⋊C4C22×C3111yescharacteristic
583C22×C4⋊C4C22×C3111yescharacteristic
584C22×C4⋊C4C22×C3111yescharacteristic
585C22×C22⋊C4C22×C3111yescharacteristic
586C22×C22⋊C4C22×C3111yescharacteristic
587C22×C22⋊C4C22×C3111yescharacteristic
588C22×C22⋊C4C22×C3111yescharacteristic
589C22×C22⋊C4C22×C3111yescharacteristic
590C22×C22⋊C4C22×C3111yescharacteristic
591C22×C22⋊C4C22×C3111yescharacteristic
592C22×C22⋊C4C22×C3111yescharacteristic
593C22×C22⋊C4C22×C3111yescharacteristic
594C22×C22⋊C4C22×C3111yescharacteristic
595C22×C22⋊C4C22×C3111yescharacteristic
596C22×C42C22×C3111yescharacteristic
597#397—24no—
598#397—24no—
599#394—24no—
600#390—24no—
601#386—24no—
602#385—24no—
603C2×#95C22×C3111yescharacteristic
604C2×#95C22×C3111yescharacteristic
605C2×#95C22×C3111yescharacteristic
606C2×#95C22×C3111yescharacteristic
607C2×#95C22×C3111yescharacteristic
608C2×#95C22×C3111yescharacteristic
609C2×#95C22×C3111yescharacteristic
610C2×#95C22×C3111yescharacteristic
611C2×#95C22×C3111yescharacteristic
612C2×#95C22×C3111yescharacteristic
613C2×#95C22×C3111yescharacteristic
614C2×#95C22×C3111yescharacteristic
615C2×#95C22×C3111yescharacteristic
616C2×#95C22×C3111yescharacteristic
617C2×#95C22×C3111yescharacteristic
618C2×#95C22×C3111yescharacteristic
619C2×C31—44no—
620C2×C31—82no—
621C2×C31#241211yescharacteristic
622C2×C31#241611yescharacteristic
623C2×C31#242211yescharacteristic
624C2×C31#242511yescharacteristic
625C2×C31#242511yescharacteristic
626C2×C31#244711yescharacteristic
627C2×C31#254411yescharacteristic
628C2×C31#256011yescharacteristic
629C2×C31#259711yescharacteristic
630C2×C31#267811yescharacteristic
631C2×C31#269111yescharacteristic
632C2×C31#271511yescharacteristic
633C2×C31#272311yescharacteristic
634C2×C31#272411yescharacteristic
635C2×C31#279611yescharacteristic
636C25C23×C3111yescharacteristic
637C25C23×C3111yescharacteristic
638C22×D4—22no—
639C22×D4—22no—
640C22×D4—22no—
641C22×D4—22no—
642C22×D4—41no—
643C22×D4—41no—
644C22×D4D4×C3114yes—
645C23×C4—22no—
646C23×C4—22no—
647C23×C4—22no—
648C23×C4—41no—
649C23×C4—41no—
650C23×C4—41no—
651C23×C4—41no—
652C23×C4C23×C3111yescharacteristic
653C23×C4C23×C3111yescharacteristic
654C23×C4C23×C3111yescharacteristic
655C23×C4C23×C3111yescharacteristic
656C23×C4C23×C3111yescharacteristic
657C23×C4C23×C3111yescharacteristic
658C23×C4C23×C3111yescharacteristic
659C23×C4C23×C3111yescharacteristic
660C23×C4C23×C3111yescharacteristic
661C23×C4C23×C3111yescharacteristic
662C23×C4C23×C3111yescharacteristic
663C23×C4C23×C3111yescharacteristic
664C23×C4C23×C3111yescharacteristic
665C2×C4⋊C4—22no—
666C2×C4⋊C4—22no—
667C2×C4⋊C4—22no—
668C2×C4⋊C4—22no—
669C2×C4⋊C4—22no—
670C2×C4⋊C4—22no—
671C2×C4⋊C4—22no—
672C2×C4⋊C4—22no—
673C2×C4⋊C4—22no—
674C2×C4⋊C4—22no—
675C2×C4⋊C4—22no—
676C2×C4⋊C4—41no—
677C2×C4⋊C4—41no—
678C2×C4⋊C4—41no—
679C2×C4⋊C4—41no—
680C2×C22⋊C4—22no—
681C2×C22⋊C4—22no—
682C2×C22⋊C4—22no—
683C2×C22⋊C4—22no—
684C2×C22⋊C4—22no—
685C2×C22⋊C4—22no—
686C2×C22⋊C4—22no—
687C2×C22⋊C4—22no—
688C2×C22⋊C4—22no—
689C2×C22⋊C4—22no—
690C2×C22⋊C4—22no—
691C2×C22⋊C4—22no—
692C2×C22⋊C4—22no—
693C2×C22⋊C4—22no—
694C2×C22⋊C4—22no—
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—41no—
705C2×C22⋊C4—41no—
706C2×C22⋊C4—41no—
707C2×C22⋊C4—41no—
708C2×C22⋊C4—41no—
709C2×C22⋊C4—41no—
710C2×C22⋊C4—41no—
711C2×C22⋊C4—41no—
712C2×C22⋊C4D4×C3114yes—
713C2×C42—22no—
714C2×C42—22no—
715C2×C42—41no—
716#95—22no—
717#95—22no—
718#95—22no—
719#95—22no—
720#95—22no—
721#95—22no—
722#95—22no—
723#95—22no—
724#95—22no—
725#95—22no—
726#95—41no—
727#95—41no—
728#95—41no—
729#95—41no—
730#95—41no—
731#95D4×C3114yescomplemented
732C31#1549711yescharacteristic, direct product factor, Sylow
733C24—21no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24—21no—
743C24—21no—
744C24—21no—
745C24—21no—
746C24—21no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24C2×D4×C3112yes—
760C24C2×D4×C3112yes—
761C24C2×D4×C3112yes—
762C24#41×C3112yes—
763C24C24×C3111yescharacteristic
764C2×D4—28no—
765C2×D4—28no—
766C2×D4—44no—
767C2×D4—44no—
768C2×D4—44no—
769C2×D4—44no—
770C2×D4—44no—
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—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—44no—
852C22×C4—44no—
853C22×C4—44no—
854C22×C4—44no—
855C22×C4—44no—
856C22×C4—44no—
857C22×C4—44no—
858C22×C4C2×D4×C3112yes—
859C22×C4C2×D4×C3112yes—
860C22×C4C2×D4×C3112yes—
861C22×C4C2×D4×C3112yes—
862C22×C4C2×D4×C3112yes—
863C22×C4C2×D4×C3112yes—
864C22×C4#41×C3112yes—
865C22×C4#41×C3112yes—
866C22×C4#41×C3112yes—
867C22×C4#41×C3112yes—
868C22×C4#41×C3112yes—
869C4⋊C4—44no—
870C4⋊C4—44no—
871C4⋊C4—44no—
872C4⋊C4—44no—
873C4⋊C4—44no—
874C22⋊C4—28no—
875C22⋊C4—44no—
876C22⋊C4—44no—
877C22⋊C4—44no—
878C22⋊C4—44no—
879C22⋊C4—44no—
880C22⋊C4—44no—
881C22⋊C4—44no—
882C22⋊C4—44no—
883C22⋊C4—44no—
884C22⋊C4—44no—
885C42—44no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
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—
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—
955C23C31×#12114yes—
956C23C22×D4×C3111yescharacteristic
957C23C22×D4×C3111yescharacteristic
958C23C22×D4×C3111yescharacteristic
959C23C2×#41×C3111yescharacteristic
960C23C2×#41×C3111yescharacteristic
961C23C2×#41×C3111yescharacteristic
962C23C2×#41×C3111yescharacteristic
963C23C2×#41×C3111yescharacteristic
964C23C2×#41×C3111yescharacteristic
965C23C31×H(5,𝔽2)11yescharacteristic
966C23C31×H(5,𝔽2)11yescharacteristic
967C23C31×H(5,𝔽2)11yescharacteristic
968C23C31×H(5,𝔽2)11yescharacteristic
969C23C31×2−1+411yescharacteristic
970C23C31×2−1+411yescharacteristic
971D4—416no—
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—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—416no—
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×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×C4C31×#12114yes—
1063C2×C4C31×#12314yes—
1064C22—24no—
1065C22—24no—
1066C22—24no—
1067C22—42no—
1068C22—42no—
1069C22—42no—
1070C22—42no—
1071C22—42no—
1072C22—42no—
1073C22—42no—
1074C22—42no—
1075C22—42no—
1076C22—42no—
1077C22—42no—
1078C22—42no—
1079C22—42no—
1080C22—42no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—81no—
1087C22—81no—
1088C22—81no—
1089C22—81no—
1090C22—81no—
1091C22—81no—
1092C22—81no—
1093C22—81no—
1094C22C2×C31×#12111yescharacteristic
1095C22C2×C31×#12111yescharacteristic
1096C22C2×C31×#12311yescharacteristic
1097C22C31×#52911yescharacteristic
1098C22C31×#52911yescharacteristic
1099C22C31×#53211yescharacteristic
1100C22C31×#53411yescharacteristic
1101C22C31×#53511yescharacteristic
1102C22C31×#53711yescharacteristic
1103C22C31×#53811yescharacteristic
1104C22C31×#53911yescharacteristic
1105C22C31×#53911yescharacteristic
1106C22C31×#53911yescharacteristic
1107C22C31×#54211yescharacteristic
1108C22C31×#54211yescharacteristic
1109C22D42×C3111yescharacteristic
1110C22C31×#54611yescharacteristic
1111C22C31×#54611yescharacteristic
1112C22C31×#54611yescharacteristic
1113C22C31×#54611yescharacteristic
1114C22C31×#54611yescharacteristic
1115C22C31×#54711yescharacteristic
1116C22C31×#54711yescharacteristic
1117C22C31×#54711yescharacteristic
1118C22C31×#54711yescharacteristic
1119C22C31×#54811yescharacteristic
1120C22C31×#55111yescharacteristic
1121C22C31×#55111yescharacteristic
1122C22C31×#55311yescharacteristic
1123C22C31×#55311yescharacteristic
1124C22C31×#55611yescharacteristic
1125C22C31×#55911yescharacteristic
1126C22C31×#55911yescharacteristic
1127C22C31×#56011yescharacteristic
1128C22C31×#56311yescharacteristic
1129C4—24no—
1130C4—24no—
1131C4—42no—
1132C4—42no—
1133C4—42no—
1134C4—42no—
1135C4—42no—
1136C4—81no—
1137C4—81no—
1138C4—81no—
1139C4—81no—
1140C4—81no—
1141C4—81no—
1142C2—44no—
1143C2—82no—
1144C2C31×#241211yescharacteristic
1145C2C31×#241611yescharacteristic
1146C2C31×#242211yescharacteristic
1147C2C31×#242511yescharacteristic
1148C2C31×#242511yescharacteristic
1149C2C31×#244711yescharacteristic
1150C2C31×#254411yescharacteristic
1151C2C31×#256011yescharacteristic
1152C2C31×#259711yescharacteristic
1153C2C31×#267811yescharacteristic
1154C2C31×#269111yescharacteristic
1155C2C31×#271511yescharacteristic
1156C2C31×#272311yescharacteristic
1157C2C31×#272411yescharacteristic
1158C2C31×#279611yescharacteristic
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
2. C2×C31×#397C2semidirect
6. C2×C31×#385C2semidirect
7. C31×#1441C2semidirect
8. C31×#1441C2semidirect
9. C31×#1440C2semidirect
10. C31×#1440C2semidirect
11. C31×#1439C2semidirect
12. C31×#1439C2semidirect
13. C31×#1436C2semidirect
14. C31×C4⋊#95C2semidirect
15. C31×C22⋊#95C2semidirect
152. C31×#95D4semidirect
306. #15497C31direct (N × H)
485. C2×#397C2×C31semidirect
486. C2×#397C2×C31semidirect
490. C2×#385C2×C31semidirect
491. #1441C2×C31semidirect
492. #1441C2×C31semidirect
493. #1440C2×C31semidirect
494. #1440C2×C31semidirect
495. #1439C2×C31semidirect
496. #1439C2×C31semidirect
497. #1436C2×C31semidirect
498. C4⋊#95C2×C31semidirect
499. C22⋊#95C2×C31semidirect
731. #95D4×C31semidirect
732. C31#15497direct (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
C2×C31×#3852
C31×#14412
C31×#14402
C31×#14392
C31×#14362
C31×C4⋊#952
C31×C22⋊#952
#1549731