Finite Group Databasebeta

← C31×#14743 #21471502

Subgroups — C31×#14743 #21471502

Order 7936.

1878 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×#399C211yesmaximal, characteristic, complemented
2C2×C31×#397C211yesmaximal, characteristic, complemented
3C2×C31×#394C211yesmaximal, characteristic
4C2×C31×#388C211yesmaximal, characteristic, complemented
5C2×C31×#386C211yesmaximal, characteristic
6C2×C4×C22⋊C4×C31C211yesmaximal, characteristic, complemented
7C31×#1442C211yesmaximal, characteristic, complemented
8C31×#1442C211yesmaximal, characteristic, complemented
9C31×#1440C211yesmaximal, characteristic, complemented
10C31×#1439C211yesmaximal, characteristic, complemented
11C31×#1438C211yesmaximal, characteristic
12C31×#1437C211yesmaximal, 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×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×C22⋊C4×C31C2211yescharacteristic
33C22×C42×C31C2211yescharacteristic
34C22×C42×C31C2211yescharacteristic
35C31×#399—24no—
36C31×#397—24no—
37C31×#394—24no—
38C31×#388—24no—
39C31×#386—24no—
40C4×C22⋊C4×C31—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—22no—
64C22×D4×C31—41no—
65C22×D4×C31—41no—
66C23×C4×C31—22no—
67C23×C4×C31—22no—
68C23×C4×C31—22no—
69C23×C4×C31—22no—
70C23×C4×C31—22no—
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—41no—
96C2×C4⋊C4×C31—41no—
97C2×C4⋊C4×C31—41no—
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—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×C31D414yes—
130C2×C22⋊C4×C31D414yes—
131C2×C42×C31—22no—
132C2×C42×C31—22no—
133C2×C42×C31—22no—
134C2×C42×C31—22no—
135C2×C42×C31—41no—
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—22no—
148C31×#95—22no—
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×C31#4112yes—
182C24×C31#4112yes—
183C24×C31C2411yescharacteristic
184C2×D4×C31—28no—
185C2×D4×C31—44no—
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—28no—
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—44no—
271C22×C4×C31—44no—
272C22×C4×C31—44no—
273C22×C4×C31—44no—
274C22×C4×C31—44no—
275C22×C4×C31—44no—
276C22×C4×C31C2×D412yes—
277C22×C4×C31C2×D412yes—
278C22×C4×C31C2×D412yes—
279C22×C4×C31C2×D412yes—
280C22×C4×C31C2×D412yes—
281C22×C4×C31C2×D412yes—
282C22×C4×C31C2×D412yes—
283C22×C4×C31#4112yes—
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—
293C22⋊C4×C31—28no—
294C22⋊C4×C31—28no—
295C22⋊C4×C31—28no—
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—
304C42×C31—44no—
305C42×C31—44no—
306#14743C3111yesmaximal, 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#12414yes—
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×C31C2×#4111yescharacteristic
387C23×C31C2×#4111yescharacteristic
388C23×C31H(5,𝔽2)11yescharacteristic
389C23×C31H(5,𝔽2)11yescharacteristic
390C23×C31H(5,𝔽2)11yescharacteristic
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—22no—
421C2×C4×C31—22no—
422C2×C4×C31—22no—
423C2×C4×C31—22no—
424C2×C4×C31—22no—
425C2×C4×C31—22no—
426C2×C4×C31—416no—
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×#399C2×C3111yescharacteristic, complemented
486C2×#397C2×C3111yescharacteristic, complemented
487C2×#394C2×C3111yescharacteristic
488C2×#388C2×C3111yescharacteristic, complemented
489C2×#386C2×C3111yescharacteristic
490C2×C4×C22⋊C4C2×C3111yescharacteristic, complemented
491#1442C2×C3111yescharacteristic, complemented
492#1442C2×C3111yescharacteristic, complemented
493#1440C2×C3111yescharacteristic, complemented
494#1439C2×C3111yescharacteristic, complemented
495#1438C2×C3111yescharacteristic
496#1437C2×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×#12311yescharacteristic
532C22×C31#52511yescharacteristic
533C22×C31#52511yescharacteristic
534C22×C31#52511yescharacteristic
535C22×C31C2×#12411yescharacteristic
536C22×C31#52911yescharacteristic
537C22×C31#52911yescharacteristic
538C22×C31#52911yescharacteristic
539C22×C31#52911yescharacteristic
540C22×C31#52911yescharacteristic
541C22×C31#53211yescharacteristic
542C22×C31#53211yescharacteristic
543C22×C31#53811yescharacteristic
544C22×C31#53811yescharacteristic
545C22×C31#53911yescharacteristic
546C22×C31#53911yescharacteristic
547C22×C31#54011yescharacteristic
548C22×C31#54211yescharacteristic
549C22×C31D4211yescharacteristic
550C22×C31D4211yescharacteristic
551C22×C31#54611yescharacteristic
552C22×C31#54611yescharacteristic
553C22×C31#54611yescharacteristic
554C22×C31#54611yescharacteristic
555C22×C31#54711yescharacteristic
556C22×C31#54711yescharacteristic
557C22×C31#54711yescharacteristic
558C22×C31#55011yescharacteristic
559C22×C31#55111yescharacteristic
560C22×C31#55111yescharacteristic
561C22×C31#55111yescharacteristic
562C22×C31#55211yescharacteristic
563C22×C31#55311yescharacteristic
564C22×C31#55911yescharacteristic
565C4×C31—24no—
566C4×C31—24no—
567C4×C31—42no—
568C4×C31—42no—
569C4×C31—42no—
570C4×C31—42no—
571C4×C31—42no—
572C4×C31—42no—
573C4×C31—42no—
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×C22⋊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×C42C22×C3111yescharacteristic
596C22×C42C22×C3111yescharacteristic
597#399—24no—
598#397—24no—
599#394—24no—
600#388—24no—
601#386—24no—
602C4×C22⋊C4—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#239511yescharacteristic
622C2×C31#241811yescharacteristic
623C2×C31#242211yescharacteristic
624C2×C31#242511yescharacteristic
625C2×C31#242811yescharacteristic
626C2×C31#245511yescharacteristic
627C2×C31#246711yescharacteristic
628C2×C31#247211yescharacteristic
629C2×C31#247911yescharacteristic
630C2×C31#248811yescharacteristic
631C2×C31#251611yescharacteristic
632C2×C31#255311yescharacteristic
633C2×C31#255711yescharacteristic
634C2×C31#264911yescharacteristic
635C2×C31#285011yescharacteristic
636C25C23×C3111yescharacteristic
637C25C23×C3111yescharacteristic
638C22×D4—22no—
639C22×D4—22no—
640C22×D4—22no—
641C22×D4—22no—
642C22×D4—22no—
643C22×D4—41no—
644C22×D4—41no—
645C23×C4—22no—
646C23×C4—22no—
647C23×C4—22no—
648C23×C4—22no—
649C23×C4—22no—
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—41no—
675C2×C4⋊C4—41no—
676C2×C4⋊C4—41no—
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—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—41no—
703C2×C22⋊C4—41no—
704C2×C22⋊C4—41no—
705C2×C22⋊C4—41no—
706C2×C22⋊C4—41no—
707C2×C22⋊C4—41no—
708C2×C22⋊C4D4×C3114yes—
709C2×C22⋊C4D4×C3114yes—
710C2×C42—22no—
711C2×C42—22no—
712C2×C42—22no—
713C2×C42—22no—
714C2×C42—41no—
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—22no—
727#95—22no—
728#95—41no—
729#95—41no—
730#95—41no—
731#95D4×C3114yescomplemented
732C31#1474311yescharacteristic, 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—
761C24#41×C3112yes—
762C24#41×C3112yes—
763C24C24×C3111yescharacteristic
764C2×D4—28no—
765C2×D4—44no—
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—28no—
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—44no—
851C22×C4—44no—
852C22×C4—44no—
853C22×C4—44no—
854C22×C4—44no—
855C22×C4—44no—
856C22×C4C2×D4×C3112yes—
857C22×C4C2×D4×C3112yes—
858C22×C4C2×D4×C3112yes—
859C22×C4C2×D4×C3112yes—
860C22×C4C2×D4×C3112yes—
861C22×C4C2×D4×C3112yes—
862C22×C4C2×D4×C3112yes—
863C22×C4#41×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—
873C22⋊C4—28no—
874C22⋊C4—28no—
875C22⋊C4—28no—
876C22⋊C4—44no—
877C22⋊C4—44no—
878C22⋊C4—44no—
879C22⋊C4—44no—
880C22⋊C4—44no—
881C22⋊C4—44no—
882C22⋊C4—44no—
883C22⋊C4—44no—
884C42—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×#12414yes—
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
965C23C2×#41×C3111yescharacteristic
966C23C2×#41×C3111yescharacteristic
967C23C31×H(5,𝔽2)11yescharacteristic
968C23C31×H(5,𝔽2)11yescharacteristic
969C23C31×H(5,𝔽2)11yescharacteristic
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—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—416no—
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×#12311yescharacteristic
1096C22C31×#52511yescharacteristic
1097C22C31×#52511yescharacteristic
1098C22C31×#52511yescharacteristic
1099C22C2×C31×#12411yescharacteristic
1100C22C31×#52911yescharacteristic
1101C22C31×#52911yescharacteristic
1102C22C31×#52911yescharacteristic
1103C22C31×#52911yescharacteristic
1104C22C31×#52911yescharacteristic
1105C22C31×#53211yescharacteristic
1106C22C31×#53211yescharacteristic
1107C22C31×#53811yescharacteristic
1108C22C31×#53811yescharacteristic
1109C22C31×#53911yescharacteristic
1110C22C31×#53911yescharacteristic
1111C22C31×#54011yescharacteristic
1112C22C31×#54211yescharacteristic
1113C22D42×C3111yescharacteristic
1114C22D42×C3111yescharacteristic
1115C22C31×#54611yescharacteristic
1116C22C31×#54611yescharacteristic
1117C22C31×#54611yescharacteristic
1118C22C31×#54611yescharacteristic
1119C22C31×#54711yescharacteristic
1120C22C31×#54711yescharacteristic
1121C22C31×#54711yescharacteristic
1122C22C31×#55011yescharacteristic
1123C22C31×#55111yescharacteristic
1124C22C31×#55111yescharacteristic
1125C22C31×#55111yescharacteristic
1126C22C31×#55211yescharacteristic
1127C22C31×#55311yescharacteristic
1128C22C31×#55911yescharacteristic
1129C4—24no—
1130C4—24no—
1131C4—42no—
1132C4—42no—
1133C4—42no—
1134C4—42no—
1135C4—42no—
1136C4—42no—
1137C4—42no—
1138C4—81no—
1139C4—81no—
1140C4—81no—
1141C4—81no—
1142C2—44no—
1143C2—82no—
1144C2C31×#239511yescharacteristic
1145C2C31×#241811yescharacteristic
1146C2C31×#242211yescharacteristic
1147C2C31×#242511yescharacteristic
1148C2C31×#242811yescharacteristic
1149C2C31×#245511yescharacteristic
1150C2C31×#246711yescharacteristic
1151C2C31×#247211yescharacteristic
1152C2C31×#247911yescharacteristic
1153C2C31×#248811yescharacteristic
1154C2C31×#251611yescharacteristic
1155C2C31×#255311yescharacteristic
1156C2C31×#255711yescharacteristic
1157C2C31×#264911yescharacteristic
1158C2C31×#285011yescharacteristic
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×#399C2semidirect
2. C2×C31×#397C2semidirect
4. C2×C31×#388C2semidirect
6. C2×C4×C22⋊C4×C31C2semidirect
7. C31×#1442C2semidirect
8. C31×#1442C2semidirect
9. C31×#1440C2semidirect
10. C31×#1439C2semidirect
12. C31×#1437C2semidirect
13. C31×#1436C2semidirect
14. C31×C4⋊#95C2semidirect
15. C31×C22⋊#95C2semidirect
152. C31×#95D4semidirect
306. #14743C31direct (N × H)
485. C2×#399C2×C31semidirect
486. C2×#397C2×C31semidirect
488. C2×#388C2×C31semidirect
490. C2×C4×C22⋊C4C2×C31semidirect
491. #1442C2×C31semidirect
492. #1442C2×C31semidirect
493. #1440C2×C31semidirect
494. #1439C2×C31semidirect
496. #1437C2×C31semidirect
497. #1436C2×C31semidirect
498. C4⋊#95C2×C31semidirect
499. C22⋊#95C2×C31semidirect
731. #95D4×C31semidirect
732. C31#14743direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3992
C2×C31×#3972
C2×C31×#3942
C2×C31×#3882
C2×C31×#3862
C2×C4×C22⋊C4×C312
C31×#14422
C31×#14402
C31×#14392
C31×#14382
C31×#14372
C31×#14362
C31×C4⋊#952
C31×C22⋊#952
#1474331