Finite Group Databasebeta

← C31×#14361 #21471120

Subgroups — C31×#14361 #21471120

Order 7936.

2594 conjugacy classes of subgroups.

The subgroup lattice has 1360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#121C211yesmaximal, characteristic
2C2×C31×#390C211yesmaximal, characteristic, complemented
3C2×C31×#388C211yesmaximal, characteristic, complemented
4C2×C31×#386C211yesmaximal, characteristic, complemented
5C2×C31×#386C211yesmaximal, characteristic, complemented
6C2×C31×#385C211yesmaximal, characteristic, complemented
7C2×C31×#380C211yesmaximal, characteristic, complemented
8C31×#1441C211yesmaximal, characteristic, complemented
9C31×#1439C211yesmaximal, characteristic, complemented
10C31×#1439C211yesmaximal, characteristic, complemented
11C31×#1438C211yesmaximal, characteristic, complemented
12C31×#1438C211yesmaximal, characteristic, complemented
13C31×#1438C211yesmaximal, characteristic, complemented
14C31×#1436C211yesmaximal, characteristic, complemented
15C31×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C31C2211yescharacteristic
17C23×D4×C31C2211yescharacteristic
18C23×D4×C31C2211yescharacteristic
19C24×C4×C31C2211yescharacteristic
20C24×C4×C31C2211yescharacteristic
21C2×C31×#121—24no—
22C2×C31×#121—24no—
23C2×C31×#121C418yescomplemented
24C22×C4⋊C4×C31C2211yescharacteristic
25C22×C4⋊C4×C31C2211yescharacteristic
26C22×C4⋊C4×C31C2211yescharacteristic
27C22×C4⋊C4×C31C2211yescharacteristic
28C22×C22⋊C4×C31C2211yescharacteristic
29C22×C22⋊C4×C31C2211yescharacteristic
30C22×C22⋊C4×C31C2211yescharacteristic
31C22×C22⋊C4×C31C2211yescharacteristic
32C22×C22⋊C4×C31C2211yescharacteristic
33C22×C22⋊C4×C31C2211yescharacteristic
34C22×C22⋊C4×C31C2211yescharacteristic
35C22×C22⋊C4×C31C2211yescharacteristic
36C22×C22⋊C4×C31C2211yescharacteristic
37C22×C22⋊C4×C31C2211yescharacteristic
38C22×C22⋊C4×C31C2211yescharacteristic
39C22×C22⋊C4×C31C2211yescharacteristic
40C22×C22⋊C4×C31C2211yescharacteristic
41C22×C42×C31C2211yescharacteristic
42C31×#390—24no—
43C31×#388—24no—
44C31×#386—24no—
45C31×#386—24no—
46C31×#385—24no—
47C31×#380—24no—
48C2×C31×#95C2211yescharacteristic
49C2×C31×#95C2211yescharacteristic
50C2×C31×#95C2211yescharacteristic
51C2×C31×#95C2211yescharacteristic
52C2×C31×#95C2211yescharacteristic
53C2×C31×#95C2211yescharacteristic
54C2×C31×#95C2211yescharacteristic
55C2×C31×#95C2211yescharacteristic
56C2×C31×#95C2211yescharacteristic
57C2×C31×#95C2211yescharacteristic
58C2×C31×#95C2211yescharacteristic
59C2×C31×#95C2211yescharacteristic
60C25×C31C2311yescharacteristic
61C25×C31C2311yescharacteristic
62C25×C31C2311yescharacteristic
63C22×D4×C31—22no—
64C22×D4×C31—22no—
65C22×D4×C31—22no—
66C22×D4×C31—22no—
67C22×D4×C31—22no—
68C22×D4×C31—22no—
69C22×D4×C31—22no—
70C22×D4×C31—22no—
71C22×D4×C31—22no—
72C22×D4×C31—22no—
73C22×D4×C31—22no—
74C22×D4×C31—22no—
75C22×D4×C31—41no—
76C22×D4×C31—41no—
77C22×D4×C31—41no—
78C22×D4×C31—41no—
79C22×D4×C31—41no—
80C22×D4×C31—41no—
81C22×D4×C31C2×C414yes—
82C22×D4×C31C2×C414yes—
83C22×D4×C31C2×C414yescomplemented
84C23×C4×C31—22no—
85C23×C4×C31—22no—
86C23×C4×C31—22no—
87C23×C4×C31—22no—
88C23×C4×C31—22no—
89C23×C4×C31—22no—
90C23×C4×C31—22no—
91C23×C4×C31—41no—
92C23×C4×C31—41no—
93C23×C4×C31—41no—
94C23×C4×C31—41no—
95C23×C4×C31—41no—
96C23×C4×C31—41no—
97C23×C4×C31C2×C414yescomplemented
98C23×C4×C31C2311yescharacteristic
99C23×C4×C31C2311yescharacteristic
100C23×C4×C31C2311yescharacteristic
101C23×C4×C31C2311yescharacteristic
102C23×C4×C31C2311yescharacteristic
103C23×C4×C31C2311yescharacteristic
104C23×C4×C31C2311yescharacteristic
105C23×C4×C31C2311yescharacteristic
106C23×C4×C31C2311yescharacteristic
107C23×C4×C31C2311yescharacteristic
108C23×C4×C31C2311yescharacteristic
109C23×C4×C31C2311yescharacteristic
110C31×#121—232no—
111C2×C4⋊C4×C31—22no—
112C2×C4⋊C4×C31—22no—
113C2×C4⋊C4×C31—22no—
114C2×C4⋊C4×C31—22no—
115C2×C4⋊C4×C31—22no—
116C2×C4⋊C4×C31—22no—
117C2×C4⋊C4×C31—22no—
118C2×C4⋊C4×C31—22no—
119C2×C4⋊C4×C31—41no—
120C2×C4⋊C4×C31—41no—
121C2×C4⋊C4×C31—41no—
122C2×C4⋊C4×C31C2×C414yescomplemented
123C2×C22⋊C4×C31—22no—
124C2×C22⋊C4×C31—22no—
125C2×C22⋊C4×C31—22no—
126C2×C22⋊C4×C31—22no—
127C2×C22⋊C4×C31—22no—
128C2×C22⋊C4×C31—22no—
129C2×C22⋊C4×C31—22no—
130C2×C22⋊C4×C31—22no—
131C2×C22⋊C4×C31—22no—
132C2×C22⋊C4×C31—22no—
133C2×C22⋊C4×C31—22no—
134C2×C22⋊C4×C31—22no—
135C2×C22⋊C4×C31—22no—
136C2×C22⋊C4×C31—22no—
137C2×C22⋊C4×C31—22no—
138C2×C22⋊C4×C31—22no—
139C2×C22⋊C4×C31—41no—
140C2×C22⋊C4×C31—41no—
141C2×C22⋊C4×C31—41no—
142C2×C22⋊C4×C31—41no—
143C2×C22⋊C4×C31—41no—
144C2×C22⋊C4×C31—41no—
145C2×C22⋊C4×C31—41no—
146C2×C22⋊C4×C31—41no—
147C2×C22⋊C4×C31—41no—
148C2×C22⋊C4×C31—41no—
149C2×C22⋊C4×C31—41no—
150C2×C22⋊C4×C31—41no—
151C2×C22⋊C4×C31—41no—
152C2×C22⋊C4×C31—41no—
153C2×C22⋊C4×C31—41no—
154C2×C22⋊C4×C31—41no—
155C2×C22⋊C4×C31—41no—
156C2×C22⋊C4×C31—41no—
157C2×C22⋊C4×C31C2×C414yes—
158C2×C22⋊C4×C31C2×C414yescomplemented
159C2×C22⋊C4×C31D414yes—
160C2×C22⋊C4×C31D414yes—
161C2×C22⋊C4×C31D414yescomplemented
162C2×C42×C31—22no—
163C2×C42×C31—22no—
164C2×C42×C31—41no—
165C31×#95—22no—
166C31×#95—22no—
167C31×#95—22no—
168C31×#95—22no—
169C31×#95—22no—
170C31×#95—22no—
171C31×#95—22no—
172C31×#95—22no—
173C31×#95—22no—
174C31×#95—41no—
175C31×#95—41no—
176C31×#95D414yescomplemented
177C24×C31—21no—
178C24×C31—21no—
179C24×C31—21no—
180C24×C31—21no—
181C24×C31—21no—
182C24×C31—21no—
183C24×C31—21no—
184C24×C31—21no—
185C24×C31—21no—
186C24×C31—21no—
187C24×C31—21no—
188C24×C31—21no—
189C24×C31—21no—
190C24×C31—21no—
191C24×C31—21no—
192C24×C31—21no—
193C24×C31—21no—
194C24×C31—21no—
195C24×C31—21no—
196C24×C31—21no—
197C24×C31—21no—
198C24×C31—21no—
199C24×C31—21no—
200C24×C31—21no—
201C24×C31—21no—
202C24×C31—21no—
203C24×C31—21no—
204C24×C31—21no—
205C24×C31—21no—
206C24×C31—21no—
207C24×C31—21no—
208C24×C31—21no—
209C24×C31—21no—
210C24×C31—21no—
211C24×C31—21no—
212C24×C31—21no—
213C24×C31—21no—
214C24×C31—21no—
215C24×C31C22×C412yes—
216C24×C31C22×C412yes—
217C24×C31C22×C412yes—
218C24×C31C2×D412yes—
219C24×C31C2×D412yes—
220C24×C31C2×D412yes—
221C24×C31#4112yes—
222C24×C31C2411yescharacteristic
223C2×D4×C31—28no—
224C2×D4×C31—28no—
225C2×D4×C31—28no—
226C2×D4×C31—28no—
227C2×D4×C31—28no—
228C2×D4×C31—28no—
229C2×D4×C31—44no—
230C2×D4×C31—44no—
231C2×D4×C31—44no—
232C2×D4×C31—44no—
233C2×D4×C31—44no—
234C2×D4×C31—44no—
235C2×D4×C31—44no—
236C2×D4×C31—44no—
237C2×D4×C31—44no—
238C2×D4×C31—44no—
239C2×D4×C31—44no—
240C2×D4×C31—44no—
241C2×D4×C31—44no—
242C2×D4×C31—44no—
243C2×D4×C31—44no—
244C22×C4×C31—21no—
245C22×C4×C31—21no—
246C22×C4×C31—21no—
247C22×C4×C31—21no—
248C22×C4×C31—21no—
249C22×C4×C31—21no—
250C22×C4×C31—21no—
251C22×C4×C31—21no—
252C22×C4×C31—21no—
253C22×C4×C31—21no—
254C22×C4×C31—21no—
255C22×C4×C31—21no—
256C22×C4×C31—21no—
257C22×C4×C31—21no—
258C22×C4×C31—21no—
259C22×C4×C31—21no—
260C22×C4×C31—21no—
261C22×C4×C31—21no—
262C22×C4×C31—21no—
263C22×C4×C31—21no—
264C22×C4×C31—21no—
265C22×C4×C31—21no—
266C22×C4×C31—21no—
267C22×C4×C31—21no—
268C22×C4×C31—21no—
269C22×C4×C31—21no—
270C22×C4×C31—21no—
271C22×C4×C31—21no—
272C22×C4×C31—21no—
273C22×C4×C31—21no—
274C22×C4×C31—21no—
275C22×C4×C31—21no—
276C22×C4×C31—21no—
277C22×C4×C31—21no—
278C22×C4×C31—21no—
279C22×C4×C31—21no—
280C22×C4×C31—21no—
281C22×C4×C31—21no—
282C22×C4×C31—21no—
283C22×C4×C31—21no—
284C22×C4×C31—21no—
285C22×C4×C31—21no—
286C22×C4×C31—28no—
287C22×C4×C31—28no—
288C22×C4×C31—21no—
289C22×C4×C31—21no—
290C22×C4×C31—21no—
291C22×C4×C31—21no—
292C22×C4×C31—21no—
293C22×C4×C31—21no—
294C22×C4×C31—21no—
295C22×C4×C31—21no—
296C22×C4×C31—21no—
297C22×C4×C31—21no—
298C22×C4×C31—21no—
299C22×C4×C31—21no—
300C22×C4×C31—21no—
301C22×C4×C31—21no—
302C22×C4×C31—21no—
303C22×C4×C31—21no—
304C22×C4×C31—21no—
305C22×C4×C31—21no—
306C22×C4×C31—21no—
307C22×C4×C31—21no—
308C22×C4×C31—21no—
309C22×C4×C31—21no—
310C22×C4×C31—21no—
311C22×C4×C31—21no—
312C22×C4×C31—21no—
313C22×C4×C31—21no—
314C22×C4×C31—21no—
315C22×C4×C31—21no—
316C22×C4×C31—44no—
317C22×C4×C31—44no—
318C22×C4×C31—44no—
319C22×C4×C31—44no—
320C22×C4×C31—44no—
321C22×C4×C31—44no—
322C22×C4×C31—44no—
323C22×C4×C31—44no—
324C22×C4×C31—44no—
325C22×C4×C31—44no—
326C22×C4×C31—44no—
327C22×C4×C31—44no—
328C22×C4×C31C22×C412yes—
329C22×C4×C31C22×C412yes—
330C22×C4×C31C22×C412yes—
331C22×C4×C31C22×C412yes—
332C22×C4×C31C2×D412yes—
333C22×C4×C31C2×D412yes—
334C22×C4×C31C2×D412yes—
335C22×C4×C31C2×D412yes—
336C22×C4×C31C2×D412yes—
337C22×C4×C31C2×D412yes—
338C22×C4×C31C2×D412yes—
339C22×C4×C31C2×D412yes—
340C22×C4×C31C2×D412yes—
341C22×C4×C31#4112yes—
342C4⋊C4×C31—28no—
343C4⋊C4×C31—44no—
344C4⋊C4×C31—44no—
345C4⋊C4×C31—44no—
346C22⋊C4×C31—28no—
347C22⋊C4×C31—44no—
348C22⋊C4×C31—44no—
349C22⋊C4×C31—44no—
350C22⋊C4×C31—44no—
351C22⋊C4×C31—44no—
352C22⋊C4×C31—44no—
353C22⋊C4×C31—44no—
354C22⋊C4×C31—44no—
355C22⋊C4×C31—44no—
356C22⋊C4×C31—44no—
357C22⋊C4×C31—44no—
358C22⋊C4×C31C22⋊C4116yescomplemented
359C42×C31—44no—
360#14361C3111yesmaximal, characteristic, direct product factor, Sylow
361C23×C31—22no—
362C23×C31—22no—
363C23×C31—22no—
364C23×C31—22no—
365C23×C31—22no—
366C23×C31—22no—
367C23×C31—22no—
368C23×C31—22no—
369C23×C31—22no—
370C23×C31—22no—
371C23×C31—22no—
372C23×C31—22no—
373C23×C31—22no—
374C23×C31—22no—
375C23×C31—22no—
376C23×C31—22no—
377C23×C31—22no—
378C23×C31—22no—
379C23×C31—22no—
380C23×C31—22no—
381C23×C31—22no—
382C23×C31—22no—
383C23×C31—22no—
384C23×C31—22no—
385C23×C31—22no—
386C23×C31—22no—
387C23×C31—22no—
388C23×C31—22no—
389C23×C31—22no—
390C23×C31—22no—
391C23×C31—22no—
392C23×C31—22no—
393C23×C31—22no—
394C23×C31—22no—
395C23×C31—22no—
396C23×C31—22no—
397C23×C31—22no—
398C23×C31—22no—
399C23×C31—22no—
400C23×C31—22no—
401C23×C31—22no—
402C23×C31—22no—
403C23×C31—22no—
404C23×C31—41no—
405C23×C31—41no—
406C23×C31—41no—
407C23×C31—41no—
408C23×C31—41no—
409C23×C31—41no—
410C23×C31—41no—
411C23×C31—41no—
412C23×C31—41no—
413C23×C31—41no—
414C23×C31—41no—
415C23×C31—41no—
416C23×C31—41no—
417C23×C31—41no—
418C23×C31—41no—
419C23×C31—41no—
420C23×C31—41no—
421C23×C31—41no—
422C23×C31—41no—
423C23×C31—41no—
424C23×C31—41no—
425C23×C31—41no—
426C23×C31—41no—
427C23×C31—41no—
428C23×C31—41no—
429C23×C31—41no—
430C23×C31—41no—
431C23×C31—41no—
432C23×C31—41no—
433C23×C31—41no—
434C23×C31—41no—
435C23×C31—41no—
436C23×C31—41no—
437C23×C31—41no—
438C23×C31—41no—
439C23×C31—41no—
440C23×C31—41no—
441C23×C31—41no—
442C23×C31—41no—
443C23×C31—41no—
444C23×C31—41no—
445C23×C31—41no—
446C23×C31—41no—
447C23×C31—41no—
448C23×C31—41no—
449C23×C31—41no—
450C23×C31—41no—
451C23×C31—41no—
452C23×C31—41no—
453C23×C31—41no—
454C23×C31—41no—
455C23×C31—41no—
456C23×C31—41no—
457C23×C31—41no—
458C23×C31—41no—
459C23×C31—41no—
460C23×C31—41no—
461C23×C31—41no—
462C23×C31—41no—
463C23×C31—41no—
464C23×C31C2×C22⋊C414yes—
465C23×C31C4×D414yes—
466C23×C31C23×C411yescharacteristic
467C23×C31C22×D411yescharacteristic
468C23×C31C22×D411yescharacteristic
469C23×C31C22×D411yescharacteristic
470C23×C31C22×D411yescharacteristic
471C23×C31C2×#4111yescharacteristic
472C23×C31C2×#4111yescharacteristic
473C23×C31H(5,𝔽2)11yescharacteristic
474C23×C31H(5,𝔽2)11yescharacteristic
475C23×C31H(5,𝔽2)11yescharacteristic
476C23×C31H(5,𝔽2)11yescharacteristic
477C23×C31H(5,𝔽2)11yescharacteristic
478C23×C31H(5,𝔽2)11yescharacteristic
479C23×C312−1+411yescharacteristic
480C23×C312−1+411yescharacteristic
481D4×C31—416no—
482D4×C31—416no—
483D4×C31—416no—
484C2×C4×C31—22no—
485C2×C4×C31—22no—
486C2×C4×C31—22no—
487C2×C4×C31—22no—
488C2×C4×C31—22no—
489C2×C4×C31—22no—
490C2×C4×C31—22no—
491C2×C4×C31—22no—
492C2×C4×C31—22no—
493C2×C4×C31—22no—
494C2×C4×C31—22no—
495C2×C4×C31—22no—
496C2×C4×C31—22no—
497C2×C4×C31—22no—
498C2×C4×C31—22no—
499C2×C4×C31—22no—
500C2×C4×C31—22no—
501C2×C4×C31—22no—
502C2×C4×C31—22no—
503C2×C4×C31—22no—
504C2×C4×C31—22no—
505C2×C4×C31—22no—
506C2×C4×C31—22no—
507C2×C4×C31—22no—
508C2×C4×C31—22no—
509C2×C4×C31—22no—
510C2×C4×C31—22no—
511C2×C4×C31—22no—
512C2×C4×C31—22no—
513C2×C4×C31—22no—
514C2×C4×C31—22no—
515C2×C4×C31—22no—
516C2×C4×C31—22no—
517C2×C4×C31—416no—
518C2×C4×C31—416no—
519C2×C4×C31—41no—
520C2×C4×C31—41no—
521C2×C4×C31—41no—
522C2×C4×C31—41no—
523C2×C4×C31—41no—
524C2×C4×C31—41no—
525C2×C4×C31—41no—
526C2×C4×C31—41no—
527C2×C4×C31—41no—
528C2×C4×C31—41no—
529C2×C4×C31—41no—
530C2×C4×C31—41no—
531C2×C4×C31—41no—
532C2×C4×C31—41no—
533C2×C4×C31—41no—
534C2×C4×C31—41no—
535C2×C4×C31—41no—
536C2×C4×C31—41no—
537C2×C4×C31—41no—
538C2×C4×C31—41no—
539C2×C4×C31—41no—
540C2×C4×C31—41no—
541C2×C4×C31—41no—
542C2×C4×C31—41no—
543C2×C4×C31—41no—
544C2×C4×C31—41no—
545C2×C4×C31—41no—
546C2×C4×C31—41no—
547C2×C4×C31—41no—
548C2×C4×C31—41no—
549C2×C4×C31—41no—
550C2×C4×C31—41no—
551C2×C4×C31—41no—
552C2×C4×C31—41no—
553C2×C4×C31—41no—
554C2×C4×C31—41no—
555C2×C4×C31—41no—
556C2×C4×C31—41no—
557C2×C4×C31—41no—
558C2×C4×C31—41no—
559C2×C4×C31—41no—
560C2×C4×C31—41no—
561C2×C4×C31—41no—
562C2×C4×C31—41no—
563C2×C4×C31—41no—
564C2×C4×C31—41no—
565C2×C4×C31—41no—
566C2×C4×C31—41no—
567C2×C4×C31C2×C22⋊C414yes—
568C2×C4×C31C2×C22⋊C414yes—
569C2×C4×C31C4×D414yes—
570C22×#121C2×C3111yescharacteristic
571C2×#390C2×C3111yescharacteristic, complemented
572C2×#388C2×C3111yescharacteristic, complemented
573C2×#386C2×C3111yescharacteristic, complemented
574C2×#386C2×C3111yescharacteristic, complemented
575C2×#385C2×C3111yescharacteristic, complemented
576C2×#380C2×C3111yescharacteristic, complemented
577#1441C2×C3111yescharacteristic, complemented
578#1439C2×C3111yescharacteristic, complemented
579#1439C2×C3111yescharacteristic, complemented
580#1438C2×C3111yescharacteristic, complemented
581#1438C2×C3111yescharacteristic, complemented
582#1438C2×C3111yescharacteristic, complemented
583#1436C2×C3111yescharacteristic, complemented
584C22⋊#95C2×C3111yescharacteristic, complemented
585C22×C31—24no—
586C22×C31—24no—
587C22×C31—24no—
588C22×C31—24no—
589C22×C31—24no—
590C22×C31—24no—
591C22×C31—42no—
592C22×C31—42no—
593C22×C31—42no—
594C22×C31—42no—
595C22×C31—42no—
596C22×C31—42no—
597C22×C31—42no—
598C22×C31—42no—
599C22×C31—42no—
600C22×C31—42no—
601C22×C31—42no—
602C22×C31—42no—
603C22×C31—42no—
604C22×C31—42no—
605C22×C31—42no—
606C22×C31—42no—
607C22×C31—42no—
608C22×C31—42no—
609C22×C31—42no—
610C22×C31—42no—
611C22×C31—42no—
612C22×C31—42no—
613C22×C31—42no—
614C22×C31—42no—
615C22×C31—42no—
616C22×C31—42no—
617C22×C31—42no—
618C22×C31—42no—
619C22×C31—42no—
620C22×C31—42no—
621C22×C31—42no—
622C22×C31—81no—
623C22×C31—81no—
624C22×C31—81no—
625C22×C31—81no—
626C22×C31—81no—
627C22×C31—81no—
628C22×C31—81no—
629C22×C31—81no—
630C22×C31C22×C22⋊C411yescharacteristic
631C22×C31C2×C4×D411yescharacteristic
632C22×C31C2×C4×D411yescharacteristic
633C22×C31#51811yescharacteristic
634C22×C31#51811yescharacteristic
635C22×C31#52011yescharacteristic
636C22×C31#52011yescharacteristic
637C22×C31#53411yescharacteristic
638C22×C31#53511yescharacteristic
639C22×C31#53511yescharacteristic
640C22×C31#53611yescharacteristic
641C22×C31#53711yescharacteristic
642C22×C31#53711yescharacteristic
643C22×C31#53711yescharacteristic
644C22×C31#53711yescharacteristic
645C22×C31#53811yescharacteristic
646C22×C31#53911yescharacteristic
647C22×C31#54011yescharacteristic
648C22×C31#54211yescharacteristic
649C22×C31D4211yescharacteristic
650C22×C31D4211yescharacteristic
651C22×C31D4211yescharacteristic
652C22×C31D4211yescharacteristic
653C22×C31D4211yescharacteristic
654C22×C31#54611yescharacteristic
655C22×C31#54611yescharacteristic
656C22×C31#54611yescharacteristic
657C22×C31#54611yescharacteristic
658C22×C31#54711yescharacteristic
659C22×C31#54811yescharacteristic
660C22×C31#55311yescharacteristic
661C22×C31#56011yescharacteristic
662C22×C31#56011yescharacteristic
663C22×C31#56211yescharacteristic
664C22×C31#56211yescharacteristic
665C4×C31—24no—
666C4×C31—24no—
667C4×C31—24no—
668C4×C31—42no—
669C4×C31—42no—
670C4×C31—42no—
671C4×C31—42no—
672C4×C31—42no—
673C4×C31—81no—
674C4×C31—81no—
675C4×C31—81no—
676C4×C31—81no—
677C23×D4C22×C3111yescharacteristic
678C23×D4C22×C3111yescharacteristic
679C23×D4C22×C3111yescharacteristic
680C24×C4C22×C3111yescharacteristic
681C24×C4C22×C3111yescharacteristic
682C2×#121—24no—
683C2×#121—24no—
684C2×#121C4×C3118yescomplemented
685C22×C4⋊C4C22×C3111yescharacteristic
686C22×C4⋊C4C22×C3111yescharacteristic
687C22×C4⋊C4C22×C3111yescharacteristic
688C22×C4⋊C4C22×C3111yescharacteristic
689C22×C22⋊C4C22×C3111yescharacteristic
690C22×C22⋊C4C22×C3111yescharacteristic
691C22×C22⋊C4C22×C3111yescharacteristic
692C22×C22⋊C4C22×C3111yescharacteristic
693C22×C22⋊C4C22×C3111yescharacteristic
694C22×C22⋊C4C22×C3111yescharacteristic
695C22×C22⋊C4C22×C3111yescharacteristic
696C22×C22⋊C4C22×C3111yescharacteristic
697C22×C22⋊C4C22×C3111yescharacteristic
698C22×C22⋊C4C22×C3111yescharacteristic
699C22×C22⋊C4C22×C3111yescharacteristic
700C22×C22⋊C4C22×C3111yescharacteristic
701C22×C22⋊C4C22×C3111yescharacteristic
702C22×C42C22×C3111yescharacteristic
703#390—24no—
704#388—24no—
705#386—24no—
706#386—24no—
707#385—24no—
708#380—24no—
709C2×#95C22×C3111yescharacteristic
710C2×#95C22×C3111yescharacteristic
711C2×#95C22×C3111yescharacteristic
712C2×#95C22×C3111yescharacteristic
713C2×#95C22×C3111yescharacteristic
714C2×#95C22×C3111yescharacteristic
715C2×#95C22×C3111yescharacteristic
716C2×#95C22×C3111yescharacteristic
717C2×#95C22×C3111yescharacteristic
718C2×#95C22×C3111yescharacteristic
719C2×#95C22×C3111yescharacteristic
720C2×#95C22×C3111yescharacteristic
721C2×C31—44no—
722C2×C31—44no—
723C2×C31—82no—
724C2×C31#231111yescharacteristic
725C2×C31#232411yescharacteristic
726C2×C31#232511yescharacteristic
727C2×C31D4×C22⋊C411yescharacteristic
728C2×C31D4×C22⋊C411yescharacteristic
729C2×C31#236111yescharacteristic
730C2×C31#237711yescharacteristic
731C2×C31#266911yescharacteristic
732C2×C31#267111yescharacteristic
733C2×C31#267211yescharacteristic
734C2×C31#267511yescharacteristic
735C2×C31#267611yescharacteristic
736C2×C31#268111yescharacteristic
737C2×C31#269111yescharacteristic
738C2×C31#270311yescharacteristic
739C25C23×C3111yescharacteristic
740C25C23×C3111yescharacteristic
741C25C23×C3111yescharacteristic
742C22×D4—22no—
743C22×D4—22no—
744C22×D4—22no—
745C22×D4—22no—
746C22×D4—22no—
747C22×D4—22no—
748C22×D4—22no—
749C22×D4—22no—
750C22×D4—22no—
751C22×D4—22no—
752C22×D4—22no—
753C22×D4—22no—
754C22×D4—41no—
755C22×D4—41no—
756C22×D4—41no—
757C22×D4—41no—
758C22×D4—41no—
759C22×D4—41no—
760C22×D4C2×C4×C3114yes—
761C22×D4C2×C4×C3114yes—
762C22×D4C2×C4×C3114yescomplemented
763C23×C4—22no—
764C23×C4—22no—
765C23×C4—22no—
766C23×C4—22no—
767C23×C4—22no—
768C23×C4—22no—
769C23×C4—22no—
770C23×C4—41no—
771C23×C4—41no—
772C23×C4—41no—
773C23×C4—41no—
774C23×C4—41no—
775C23×C4—41no—
776C23×C4C2×C4×C3114yescomplemented
777C23×C4C23×C3111yescharacteristic
778C23×C4C23×C3111yescharacteristic
779C23×C4C23×C3111yescharacteristic
780C23×C4C23×C3111yescharacteristic
781C23×C4C23×C3111yescharacteristic
782C23×C4C23×C3111yescharacteristic
783C23×C4C23×C3111yescharacteristic
784C23×C4C23×C3111yescharacteristic
785C23×C4C23×C3111yescharacteristic
786C23×C4C23×C3111yescharacteristic
787C23×C4C23×C3111yescharacteristic
788C23×C4C23×C3111yescharacteristic
789#121—232no—
790C2×C4⋊C4—22no—
791C2×C4⋊C4—22no—
792C2×C4⋊C4—22no—
793C2×C4⋊C4—22no—
794C2×C4⋊C4—22no—
795C2×C4⋊C4—22no—
796C2×C4⋊C4—22no—
797C2×C4⋊C4—22no—
798C2×C4⋊C4—41no—
799C2×C4⋊C4—41no—
800C2×C4⋊C4—41no—
801C2×C4⋊C4C2×C4×C3114yescomplemented
802C2×C22⋊C4—22no—
803C2×C22⋊C4—22no—
804C2×C22⋊C4—22no—
805C2×C22⋊C4—22no—
806C2×C22⋊C4—22no—
807C2×C22⋊C4—22no—
808C2×C22⋊C4—22no—
809C2×C22⋊C4—22no—
810C2×C22⋊C4—22no—
811C2×C22⋊C4—22no—
812C2×C22⋊C4—22no—
813C2×C22⋊C4—22no—
814C2×C22⋊C4—22no—
815C2×C22⋊C4—22no—
816C2×C22⋊C4—22no—
817C2×C22⋊C4—22no—
818C2×C22⋊C4—41no—
819C2×C22⋊C4—41no—
820C2×C22⋊C4—41no—
821C2×C22⋊C4—41no—
822C2×C22⋊C4—41no—
823C2×C22⋊C4—41no—
824C2×C22⋊C4—41no—
825C2×C22⋊C4—41no—
826C2×C22⋊C4—41no—
827C2×C22⋊C4—41no—
828C2×C22⋊C4—41no—
829C2×C22⋊C4—41no—
830C2×C22⋊C4—41no—
831C2×C22⋊C4—41no—
832C2×C22⋊C4—41no—
833C2×C22⋊C4—41no—
834C2×C22⋊C4—41no—
835C2×C22⋊C4—41no—
836C2×C22⋊C4C2×C4×C3114yes—
837C2×C22⋊C4C2×C4×C3114yescomplemented
838C2×C22⋊C4D4×C3114yes—
839C2×C22⋊C4D4×C3114yes—
840C2×C22⋊C4D4×C3114yescomplemented
841C2×C42—22no—
842C2×C42—22no—
843C2×C42—41no—
844#95—22no—
845#95—22no—
846#95—22no—
847#95—22no—
848#95—22no—
849#95—22no—
850#95—22no—
851#95—22no—
852#95—22no—
853#95—41no—
854#95—41no—
855#95D4×C3114yescomplemented
856C31#1436111yescharacteristic, direct product factor, Sylow
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24—21no—
862C24—21no—
863C24—21no—
864C24—21no—
865C24—21no—
866C24—21no—
867C24—21no—
868C24—21no—
869C24—21no—
870C24—21no—
871C24—21no—
872C24—21no—
873C24—21no—
874C24—21no—
875C24—21no—
876C24—21no—
877C24—21no—
878C24—21no—
879C24—21no—
880C24—21no—
881C24—21no—
882C24—21no—
883C24—21no—
884C24—21no—
885C24—21no—
886C24—21no—
887C24—21no—
888C24—21no—
889C24—21no—
890C24—21no—
891C24—21no—
892C24—21no—
893C24—21no—
894C24—21no—
895C24C22×C4×C3112yes—
896C24C22×C4×C3112yes—
897C24C22×C4×C3112yes—
898C24C2×D4×C3112yes—
899C24C2×D4×C3112yes—
900C24C2×D4×C3112yes—
901C24#41×C3112yes—
902C24C24×C3111yescharacteristic
903C2×D4—28no—
904C2×D4—28no—
905C2×D4—28no—
906C2×D4—28no—
907C2×D4—28no—
908C2×D4—28no—
909C2×D4—44no—
910C2×D4—44no—
911C2×D4—44no—
912C2×D4—44no—
913C2×D4—44no—
914C2×D4—44no—
915C2×D4—44no—
916C2×D4—44no—
917C2×D4—44no—
918C2×D4—44no—
919C2×D4—44no—
920C2×D4—44no—
921C2×D4—44no—
922C2×D4—44no—
923C2×D4—44no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—28no—
967C22×C4—28no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—21no—
975C22×C4—21no—
976C22×C4—21no—
977C22×C4—21no—
978C22×C4—21no—
979C22×C4—21no—
980C22×C4—21no—
981C22×C4—21no—
982C22×C4—21no—
983C22×C4—21no—
984C22×C4—21no—
985C22×C4—21no—
986C22×C4—21no—
987C22×C4—21no—
988C22×C4—21no—
989C22×C4—21no—
990C22×C4—21no—
991C22×C4—21no—
992C22×C4—21no—
993C22×C4—21no—
994C22×C4—21no—
995C22×C4—21no—
996C22×C4—44no—
997C22×C4—44no—
998C22×C4—44no—
999C22×C4—44no—
1000C22×C4—44no—
1001C22×C4—44no—
1002C22×C4—44no—
1003C22×C4—44no—
1004C22×C4—44no—
1005C22×C4—44no—
1006C22×C4—44no—
1007C22×C4—44no—
1008C22×C4C22×C4×C3112yes—
1009C22×C4C22×C4×C3112yes—
1010C22×C4C22×C4×C3112yes—
1011C22×C4C22×C4×C3112yes—
1012C22×C4C2×D4×C3112yes—
1013C22×C4C2×D4×C3112yes—
1014C22×C4C2×D4×C3112yes—
1015C22×C4C2×D4×C3112yes—
1016C22×C4C2×D4×C3112yes—
1017C22×C4C2×D4×C3112yes—
1018C22×C4C2×D4×C3112yes—
1019C22×C4C2×D4×C3112yes—
1020C22×C4C2×D4×C3112yes—
1021C22×C4#41×C3112yes—
1022C4⋊C4—28no—
1023C4⋊C4—44no—
1024C4⋊C4—44no—
1025C4⋊C4—44no—
1026C22⋊C4—28no—
1027C22⋊C4—44no—
1028C22⋊C4—44no—
1029C22⋊C4—44no—
1030C22⋊C4—44no—
1031C22⋊C4—44no—
1032C22⋊C4—44no—
1033C22⋊C4—44no—
1034C22⋊C4—44no—
1035C22⋊C4—44no—
1036C22⋊C4—44no—
1037C22⋊C4—44no—
1038C22⋊C4C22⋊C4×C31116yescomplemented
1039C42—44no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—22no—
1051C23—22no—
1052C23—22no—
1053C23—22no—
1054C23—22no—
1055C23—22no—
1056C23—22no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—22no—
1065C23—22no—
1066C23—22no—
1067C23—22no—
1068C23—22no—
1069C23—22no—
1070C23—22no—
1071C23—22no—
1072C23—22no—
1073C23—22no—
1074C23—22no—
1075C23—22no—
1076C23—22no—
1077C23—22no—
1078C23—22no—
1079C23—22no—
1080C23—22no—
1081C23—22no—
1082C23—22no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23C2×C22⋊C4×C3114yes—
1144C23C4×D4×C3114yes—
1145C23C23×C4×C3111yescharacteristic
1146C23C22×D4×C3111yescharacteristic
1147C23C22×D4×C3111yescharacteristic
1148C23C22×D4×C3111yescharacteristic
1149C23C22×D4×C3111yescharacteristic
1150C23C2×#41×C3111yescharacteristic
1151C23C2×#41×C3111yescharacteristic
1152C23C31×H(5,𝔽2)11yescharacteristic
1153C23C31×H(5,𝔽2)11yescharacteristic
1154C23C31×H(5,𝔽2)11yescharacteristic
1155C23C31×H(5,𝔽2)11yescharacteristic
1156C23C31×H(5,𝔽2)11yescharacteristic
1157C23C31×H(5,𝔽2)11yescharacteristic
1158C23C31×2−1+411yescharacteristic
1159C23C31×2−1+411yescharacteristic
1160D4—416no—
1161D4—416no—
1162D4—416no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—22no—
1177C2×C4—22no—
1178C2×C4—22no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—22no—
1183C2×C4—22no—
1184C2×C4—22no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—22no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—22no—
1195C2×C4—22no—
1196C2×C4—416no—
1197C2×C4—416no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—41no—
1246C2×C4C2×C22⋊C4×C3114yes—
1247C2×C4C2×C22⋊C4×C3114yes—
1248C2×C4C4×D4×C3114yes—
1249C22—24no—
1250C22—24no—
1251C22—24no—
1252C22—24no—
1253C22—24no—
1254C22—24no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—42no—
1271C22—42no—
1272C22—42no—
1273C22—42no—
1274C22—42no—
1275C22—42no—
1276C22—42no—
1277C22—42no—
1278C22—42no—
1279C22—42no—
1280C22—42no—
1281C22—42no—
1282C22—42no—
1283C22—42no—
1284C22—42no—
1285C22—42no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22—81no—
1292C22—81no—
1293C22—81no—
1294C22C22×C22⋊C4×C3111yescharacteristic
1295C22C2×C4×D4×C3111yescharacteristic
1296C22C2×C4×D4×C3111yescharacteristic
1297C22C31×#51811yescharacteristic
1298C22C31×#51811yescharacteristic
1299C22C31×#52011yescharacteristic
1300C22C31×#52011yescharacteristic
1301C22C31×#53411yescharacteristic
1302C22C31×#53511yescharacteristic
1303C22C31×#53511yescharacteristic
1304C22C31×#53611yescharacteristic
1305C22C31×#53711yescharacteristic
1306C22C31×#53711yescharacteristic
1307C22C31×#53711yescharacteristic
1308C22C31×#53711yescharacteristic
1309C22C31×#53811yescharacteristic
1310C22C31×#53911yescharacteristic
1311C22C31×#54011yescharacteristic
1312C22C31×#54211yescharacteristic
1313C22D42×C3111yescharacteristic
1314C22D42×C3111yescharacteristic
1315C22D42×C3111yescharacteristic
1316C22D42×C3111yescharacteristic
1317C22D42×C3111yescharacteristic
1318C22C31×#54611yescharacteristic
1319C22C31×#54611yescharacteristic
1320C22C31×#54611yescharacteristic
1321C22C31×#54611yescharacteristic
1322C22C31×#54711yescharacteristic
1323C22C31×#54811yescharacteristic
1324C22C31×#55311yescharacteristic
1325C22C31×#56011yescharacteristic
1326C22C31×#56011yescharacteristic
1327C22C31×#56211yescharacteristic
1328C22C31×#56211yescharacteristic
1329C4—24no—
1330C4—24no—
1331C4—24no—
1332C4—42no—
1333C4—42no—
1334C4—42no—
1335C4—42no—
1336C4—42no—
1337C4—81no—
1338C4—81no—
1339C4—81no—
1340C4—81no—
1341C2—44no—
1342C2—44no—
1343C2—82no—
1344C2C31×#231111yescharacteristic
1345C2C31×#232411yescharacteristic
1346C2C31×#232511yescharacteristic
1347C2D4×C22⋊C4×C3111yescharacteristic
1348C2D4×C22⋊C4×C3111yescharacteristic
1349C2C31×#236111yescharacteristic
1350C2C31×#237711yescharacteristic
1351C2C31×#266911yescharacteristic
1352C2C31×#267111yescharacteristic
1353C2C31×#267211yescharacteristic
1354C2C31×#267511yescharacteristic
1355C2C31×#267611yescharacteristic
1356C2C31×#268111yescharacteristic
1357C2C31×#269111yescharacteristic
1358C2C31×#270311yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutatorC23C23×C4×C31
Frattini, cosocleC24C24×C31
prime radicalC22×C31×#121C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#390C2semidirect
3. C2×C31×#388C2semidirect
4. C2×C31×#386C2semidirect
5. C2×C31×#386C2semidirect
6. C2×C31×#385C2semidirect
7. C2×C31×#380C2semidirect
8. C31×#1441C2semidirect
9. C31×#1439C2semidirect
10. C31×#1439C2semidirect
11. C31×#1438C2semidirect
12. C31×#1438C2semidirect
13. C31×#1438C2semidirect
14. C31×#1436C2semidirect
15. C31×C22⋊#95C2semidirect
23. C2×C31×#121C4semidirect
83. C22×D4×C31C2×C4semidirect
97. C23×C4×C31C2×C4semidirect
122. C2×C4⋊C4×C31C2×C4semidirect
158. C2×C22⋊C4×C31C2×C4semidirect
161. C2×C22⋊C4×C31D4semidirect
176. C31×#95D4semidirect
358. C22⋊C4×C31C22⋊C4semidirect
360. #14361C31direct (N × H)
571. C2×#390C2×C31semidirect
572. C2×#388C2×C31semidirect
573. C2×#386C2×C31semidirect
574. C2×#386C2×C31semidirect
575. C2×#385C2×C31semidirect
576. C2×#380C2×C31semidirect
577. #1441C2×C31semidirect
578. #1439C2×C31semidirect
579. #1439C2×C31semidirect
580. #1438C2×C31semidirect
581. #1438C2×C31semidirect
582. #1438C2×C31semidirect
583. #1436C2×C31semidirect
584. C22⋊#95C2×C31semidirect
684. C2×#121C4×C31semidirect
762. C22×D4C2×C4×C31semidirect
776. C23×C4C2×C4×C31semidirect
801. C2×C4⋊C4C2×C4×C31semidirect
837. C2×C22⋊C4C2×C4×C31semidirect
840. C2×C22⋊C4D4×C31semidirect
855. #95D4×C31semidirect
856. C31#14361direct (N × H)
1038. C22⋊C4C22⋊C4×C31semidirect

Maximal subgroups

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

subgroupindex
C22×C31×#1212
C2×C31×#3902
C2×C31×#3882
C2×C31×#3862
C2×C31×#3852
C2×C31×#3802
C31×#14412
C31×#14392
C31×#14382
C31×#14362
C31×C22⋊#952
#1436131