Finite Group Databasebeta

← C31×#15316 #21472075

Subgroups — C31×#15316 #21472075

Order 7936.

2442 conjugacy classes of subgroups.

The subgroup lattice has 1352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#121C211yesmaximal, characteristic
2C2×C31×#396C211yesmaximal, characteristic, complemented
3C2×C31×#394C211yesmaximal, characteristic, complemented
4C2×C31×#394C211yesmaximal, characteristic, complemented
5C2×C31×#394C211yesmaximal, characteristic, complemented
6C2×C31×#390C211yesmaximal, characteristic, complemented
7C2×C31×#389C211yesmaximal, characteristic, complemented
8C2×C31×#385C211yesmaximal, characteristic, complemented
9C31×#1441C211yesmaximal, characteristic, complemented
10C31×#1439C211yesmaximal, characteristic, complemented
11C31×#1439C211yesmaximal, characteristic, complemented
12C31×#1438C211yesmaximal, characteristic, complemented
13C31×#1438C211yesmaximal, characteristic, complemented
14C31×#1437C211yesmaximal, characteristic, complemented
15C31×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C31C2211yescharacteristic
17C23×D4×C31C2211yescharacteristic
18C23×D4×C31C2211yescharacteristic
19C24×C4×C31C2211yescharacteristic
20C2×C31×#121—24no—
21C2×C31×#121—24no—
22C2×C31×#121—24no—
23C22×C4⋊C4×C31C2211yescharacteristic
24C22×C4⋊C4×C31C2211yescharacteristic
25C22×C4⋊C4×C31C2211yescharacteristic
26C22×C4⋊C4×C31C2211yescharacteristic
27C22×C4⋊C4×C31C2211yescharacteristic
28C22×C4⋊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×C22⋊C4×C31C2211yescharacteristic
42C22×C22⋊C4×C31C2211yescharacteristic
43C22×C42×C31C2211yescharacteristic
44C31×#396—24no—
45C31×#394—24no—
46C31×#394—24no—
47C31×#394—24no—
48C31×#390—24no—
49C31×#389—24no—
50C31×#385—24no—
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
60C2×C31×#95C2211yescharacteristic
61C25×C31C2311yescharacteristic
62C25×C31C2311yescharacteristic
63C25×C31C2311yescharacteristic
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—22no—
76C22×D4×C31—22no—
77C22×D4×C31—22no—
78C22×D4×C31—41no—
79C22×D4×C31—41no—
80C22×D4×C31—41no—
81C22×D4×C31—41no—
82C22×D4×C31—41no—
83C22×D4×C31—41no—
84C22×D4×C31D414yes—
85C23×C4×C31—22no—
86C23×C4×C31—22no—
87C23×C4×C31—22no—
88C23×C4×C31—22no—
89C23×C4×C31—22no—
90C23×C4×C31—41no—
91C23×C4×C31—41no—
92C23×C4×C31C2311yescharacteristic
93C23×C4×C31C2311yescharacteristic
94C23×C4×C31C2311yescharacteristic
95C23×C4×C31C2311yescharacteristic
96C23×C4×C31C2311yescharacteristic
97C23×C4×C31C2311yescharacteristic
98C23×C4×C31C2311yescharacteristic
99C23×C4×C31C2311yescharacteristic
100C23×C4×C31C2311yescharacteristic
101C23×C4×C31C2311yescharacteristic
102C23×C4×C31C2311yescharacteristic
103C23×C4×C31C2311yescharacteristic
104C31×#121—232no—
105C2×C4⋊C4×C31—22no—
106C2×C4⋊C4×C31—22no—
107C2×C4⋊C4×C31—22no—
108C2×C4⋊C4×C31—22no—
109C2×C4⋊C4×C31—22no—
110C2×C4⋊C4×C31—22no—
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—41no—
119C2×C4⋊C4×C31—41no—
120C2×C4⋊C4×C31—41no—
121C2×C4⋊C4×C31D414yes—
122C2×C4⋊C4×C31D414yescomplemented
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—22no—
140C2×C22⋊C4×C31—22no—
141C2×C22⋊C4×C31—22no—
142C2×C22⋊C4×C31—22no—
143C2×C22⋊C4×C31—22no—
144C2×C22⋊C4×C31—22no—
145C2×C22⋊C4×C31—22no—
146C2×C22⋊C4×C31—22no—
147C2×C22⋊C4×C31—22no—
148C2×C22⋊C4×C31—22no—
149C2×C22⋊C4×C31—22no—
150C2×C22⋊C4×C31—22no—
151C2×C22⋊C4×C31—22no—
152C2×C22⋊C4×C31—22no—
153C2×C22⋊C4×C31—41no—
154C2×C22⋊C4×C31—41no—
155C2×C22⋊C4×C31—41no—
156C2×C22⋊C4×C31—41no—
157C2×C22⋊C4×C31—41no—
158C2×C22⋊C4×C31—41no—
159C2×C22⋊C4×C31—41no—
160C2×C22⋊C4×C31—41no—
161C2×C22⋊C4×C31—41no—
162C2×C22⋊C4×C31—41no—
163C2×C22⋊C4×C31D414yes—
164C2×C22⋊C4×C31D414yescomplemented
165C2×C42×C31—22no—
166C2×C42×C31—22no—
167C2×C42×C31—41no—
168C31×#95—22no—
169C31×#95—22no—
170C31×#95—22no—
171C31×#95—22no—
172C31×#95—22no—
173C31×#95—22no—
174C31×#95—22no—
175C31×#95—22no—
176C31×#95—41no—
177C31×#95—41no—
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×C31—21no—
216C24×C31—21no—
217C24×C31—21no—
218C24×C31C2×D412yes—
219C24×C31C2×D412yes—
220C24×C31C2×D412yes—
221C24×C31C2×D412yes—
222C24×C31#4112yes—
223C24×C31C2411yescharacteristic
224C2×D4×C31—28no—
225C2×D4×C31—28no—
226C2×D4×C31—28no—
227C2×D4×C31—28no—
228C2×D4×C31—44no—
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—
244C2×D4×C31—44no—
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—28no—
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—21no—
287C22×C4×C31—21no—
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×C31C2×D412yes—
323C22×C4×C31C2×D412yes—
324C22×C4×C31C2×D412yes—
325C22×C4×C31C2×D412yes—
326C22×C4×C31C2×D412yes—
327C22×C4×C31C2×D412yes—
328C22×C4×C31C2×D412yes—
329C22×C4×C31C2×D412yes—
330C22×C4×C31C2×D412yes—
331C22×C4×C31C2×D412yes—
332C22×C4×C31C2×D412yes—
333C22×C4×C31#4112yes—
334C22×C4×C31#4112yes—
335C22×C4×C31#4112yes—
336C4⋊C4×C31—28no—
337C4⋊C4×C31—28no—
338C4⋊C4×C31—44no—
339C4⋊C4×C31—44no—
340C4⋊C4×C31—44no—
341C4⋊C4×C31—44no—
342C22⋊C4×C31—28no—
343C22⋊C4×C31—28no—
344C22⋊C4×C31—28no—
345C22⋊C4×C31—44no—
346C22⋊C4×C31—44no—
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—
356C42×C31—44no—
357#15316C3111yesmaximal, characteristic, direct product factor, Sylow
358C23×C31—22no—
359C23×C31—22no—
360C23×C31—22no—
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—41no—
391C23×C31—41no—
392C23×C31—41no—
393C23×C31—41no—
394C23×C31—41no—
395C23×C31—41no—
396C23×C31—41no—
397C23×C31—41no—
398C23×C31—41no—
399C23×C31—41no—
400C23×C31—41no—
401C23×C31—41no—
402C23×C31—41no—
403C23×C31—41no—
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#12114yes—
463C23×C31C22×D411yescharacteristic
464C23×C31C22×D411yescharacteristic
465C23×C31C22×D411yescharacteristic
466C23×C31C22×D411yescharacteristic
467C23×C31C22×D411yescharacteristic
468C23×C31C2×#4111yescharacteristic
469C23×C31C2×#4111yescharacteristic
470C23×C31C2×#4111yescharacteristic
471C23×C31C2×#4111yescharacteristic
472C23×C31H(5,𝔽2)11yescharacteristic
473C23×C31H(5,𝔽2)11yescharacteristic
474C23×C31H(5,𝔽2)11yescharacteristic
475C23×C31H(5,𝔽2)11yescharacteristic
476C23×C312−1+411yescharacteristic
477C23×C312−1+411yescharacteristic
478D4×C31—416no—
479D4×C31—416no—
480D4×C31—416no—
481C2×C4×C31—22no—
482C2×C4×C31—22no—
483C2×C4×C31—22no—
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—416no—
515C2×C4×C31—41no—
516C2×C4×C31—41no—
517C2×C4×C31—41no—
518C2×C4×C31—41no—
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#12014yes—
564C2×C4×C31#12114yes—
565C2×C4×C31#12114yescomplemented
566C22×#121C2×C3111yescharacteristic
567C2×#396C2×C3111yescharacteristic, complemented
568C2×#394C2×C3111yescharacteristic, complemented
569C2×#394C2×C3111yescharacteristic, complemented
570C2×#394C2×C3111yescharacteristic, complemented
571C2×#390C2×C3111yescharacteristic, complemented
572C2×#389C2×C3111yescharacteristic, complemented
573C2×#385C2×C3111yescharacteristic, complemented
574#1441C2×C3111yescharacteristic, complemented
575#1439C2×C3111yescharacteristic, complemented
576#1439C2×C3111yescharacteristic, complemented
577#1438C2×C3111yescharacteristic, complemented
578#1438C2×C3111yescharacteristic, complemented
579#1437C2×C3111yescharacteristic, complemented
580C22⋊#95C2×C3111yescharacteristic, complemented
581C22×C31—24no—
582C22×C31—24no—
583C22×C31—24no—
584C22×C31—42no—
585C22×C31—42no—
586C22×C31—42no—
587C22×C31—42no—
588C22×C31—42no—
589C22×C31—42no—
590C22×C31—42no—
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—81no—
611C22×C31—81no—
612C22×C31—81no—
613C22×C31—81no—
614C22×C31—81no—
615C22×C31—81no—
616C22×C31—81no—
617C22×C31—81no—
618C22×C31—81no—
619C22×C31—81no—
620C22×C31—81no—
621C22×C31—81no—
622C22×C31—81no—
623C22×C31—81no—
624C22×C31—81no—
625C22×C31—81no—
626C22×C31C2×#12011yescharacteristic
627C22×C31C2×#12111yescharacteristic
628C22×C31C2×#12111yescharacteristic
629C22×C31C2×#12111yescharacteristic
630C22×C31#52911yescharacteristic
631C22×C31#53211yescharacteristic
632C22×C31#53411yescharacteristic
633C22×C31#53511yescharacteristic
634C22×C31#53611yescharacteristic
635C22×C31#53711yescharacteristic
636C22×C31#53711yescharacteristic
637C22×C31#53811yescharacteristic
638C22×C31#53911yescharacteristic
639C22×C31#54011yescharacteristic
640C22×C31#54211yescharacteristic
641C22×C31D4211yescharacteristic
642C22×C31D4211yescharacteristic
643C22×C31D4211yescharacteristic
644C22×C31D4211yescharacteristic
645C22×C31#54611yescharacteristic
646C22×C31#54611yescharacteristic
647C22×C31#54611yescharacteristic
648C22×C31#54611yescharacteristic
649C22×C31#54611yescharacteristic
650C22×C31#54711yescharacteristic
651C22×C31#54711yescharacteristic
652C22×C31#54711yescharacteristic
653C22×C31#54811yescharacteristic
654C22×C31#54811yescharacteristic
655C22×C31#54811yescharacteristic
656C22×C31#55011yescharacteristic
657C22×C31#55311yescharacteristic
658C22×C31#55311yescharacteristic
659C22×C31#56211yescharacteristic
660C22×C31#56211yescharacteristic
661C4×C31—24no—
662C4×C31—24no—
663C4×C31—24no—
664C4×C31—42no—
665C4×C31—42no—
666C4×C31—42no—
667C4×C31—42no—
668C4×C31—42no—
669C4×C31—81no—
670C4×C31—81no—
671C4×C31—81no—
672C4×C31—81no—
673C23×D4C22×C3111yescharacteristic
674C23×D4C22×C3111yescharacteristic
675C23×D4C22×C3111yescharacteristic
676C24×C4C22×C3111yescharacteristic
677C2×#121—24no—
678C2×#121—24no—
679C2×#121—24no—
680C22×C4⋊C4C22×C3111yescharacteristic
681C22×C4⋊C4C22×C3111yescharacteristic
682C22×C4⋊C4C22×C3111yescharacteristic
683C22×C4⋊C4C22×C3111yescharacteristic
684C22×C4⋊C4C22×C3111yescharacteristic
685C22×C4⋊C4C22×C3111yescharacteristic
686C22×C22⋊C4C22×C3111yescharacteristic
687C22×C22⋊C4C22×C3111yescharacteristic
688C22×C22⋊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×C42C22×C3111yescharacteristic
701#396—24no—
702#394—24no—
703#394—24no—
704#394—24no—
705#390—24no—
706#389—24no—
707#385—24no—
708C2×#95C22×C3111yescharacteristic
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×C31—44no—
719C2×C31—82no—
720C2×C31—82no—
721C2×C31#240811yescharacteristic
722C2×C31#241011yescharacteristic
723C2×C31#241611yescharacteristic
724C2×C31#241611yescharacteristic
725C2×C31#242511yescharacteristic
726C2×C31#242611yescharacteristic
727C2×C31#242811yescharacteristic
728C2×C31#243211yescharacteristic
729C2×C31#255911yescharacteristic
730C2×C31#267211yescharacteristic
731C2×C31#267611yescharacteristic
732C2×C31#268111yescharacteristic
733C2×C31#268211yescharacteristic
734C2×C31#270111yescharacteristic
735C2×C31#271111yescharacteristic
736C25C23×C3111yescharacteristic
737C25C23×C3111yescharacteristic
738C25C23×C3111yescharacteristic
739C22×D4—22no—
740C22×D4—22no—
741C22×D4—22no—
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—41no—
754C22×D4—41no—
755C22×D4—41no—
756C22×D4—41no—
757C22×D4—41no—
758C22×D4—41no—
759C22×D4D4×C3114yes—
760C23×C4—22no—
761C23×C4—22no—
762C23×C4—22no—
763C23×C4—22no—
764C23×C4—22no—
765C23×C4—41no—
766C23×C4—41no—
767C23×C4C23×C3111yescharacteristic
768C23×C4C23×C3111yescharacteristic
769C23×C4C23×C3111yescharacteristic
770C23×C4C23×C3111yescharacteristic
771C23×C4C23×C3111yescharacteristic
772C23×C4C23×C3111yescharacteristic
773C23×C4C23×C3111yescharacteristic
774C23×C4C23×C3111yescharacteristic
775C23×C4C23×C3111yescharacteristic
776C23×C4C23×C3111yescharacteristic
777C23×C4C23×C3111yescharacteristic
778C23×C4C23×C3111yescharacteristic
779#121—232no—
780C2×C4⋊C4—22no—
781C2×C4⋊C4—22no—
782C2×C4⋊C4—22no—
783C2×C4⋊C4—22no—
784C2×C4⋊C4—22no—
785C2×C4⋊C4—22no—
786C2×C4⋊C4—22no—
787C2×C4⋊C4—22no—
788C2×C4⋊C4—22no—
789C2×C4⋊C4—22no—
790C2×C4⋊C4—22no—
791C2×C4⋊C4—22no—
792C2×C4⋊C4—22no—
793C2×C4⋊C4—41no—
794C2×C4⋊C4—41no—
795C2×C4⋊C4—41no—
796C2×C4⋊C4D4×C3114yes—
797C2×C4⋊C4D4×C3114yescomplemented
798C2×C22⋊C4—22no—
799C2×C22⋊C4—22no—
800C2×C22⋊C4—22no—
801C2×C22⋊C4—22no—
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—22no—
819C2×C22⋊C4—22no—
820C2×C22⋊C4—22no—
821C2×C22⋊C4—22no—
822C2×C22⋊C4—22no—
823C2×C22⋊C4—22no—
824C2×C22⋊C4—22no—
825C2×C22⋊C4—22no—
826C2×C22⋊C4—22no—
827C2×C22⋊C4—22no—
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⋊C4—41no—
837C2×C22⋊C4—41no—
838C2×C22⋊C4D4×C3114yes—
839C2×C22⋊C4D4×C3114yescomplemented
840C2×C42—22no—
841C2×C42—22no—
842C2×C42—41no—
843#95—22no—
844#95—22no—
845#95—22no—
846#95—22no—
847#95—22no—
848#95—22no—
849#95—22no—
850#95—22no—
851#95—41no—
852#95—41no—
853C31#1531611yescharacteristic, direct product factor, Sylow
854C24—21no—
855C24—21no—
856C24—21no—
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—
894C24C2×D4×C3112yes—
895C24C2×D4×C3112yes—
896C24C2×D4×C3112yes—
897C24C2×D4×C3112yes—
898C24#41×C3112yes—
899C24C24×C3111yescharacteristic
900C2×D4—28no—
901C2×D4—28no—
902C2×D4—28no—
903C2×D4—28no—
904C2×D4—44no—
905C2×D4—44no—
906C2×D4—44no—
907C2×D4—44no—
908C2×D4—44no—
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—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
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—28no—
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—21no—
967C22×C4—21no—
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—44no—
993C22×C4—44no—
994C22×C4—44no—
995C22×C4—44no—
996C22×C4—44no—
997C22×C4—44no—
998C22×C4C2×D4×C3112yes—
999C22×C4C2×D4×C3112yes—
1000C22×C4C2×D4×C3112yes—
1001C22×C4C2×D4×C3112yes—
1002C22×C4C2×D4×C3112yes—
1003C22×C4C2×D4×C3112yes—
1004C22×C4C2×D4×C3112yes—
1005C22×C4C2×D4×C3112yes—
1006C22×C4C2×D4×C3112yes—
1007C22×C4C2×D4×C3112yes—
1008C22×C4C2×D4×C3112yes—
1009C22×C4#41×C3112yes—
1010C22×C4#41×C3112yes—
1011C22×C4#41×C3112yes—
1012C4⋊C4—28no—
1013C4⋊C4—28no—
1014C4⋊C4—44no—
1015C4⋊C4—44no—
1016C4⋊C4—44no—
1017C4⋊C4—44no—
1018C22⋊C4—28no—
1019C22⋊C4—28no—
1020C22⋊C4—28no—
1021C22⋊C4—44no—
1022C22⋊C4—44no—
1023C22⋊C4—44no—
1024C22⋊C4—44no—
1025C22⋊C4—44no—
1026C22⋊C4—44no—
1027C22⋊C4—44no—
1028C22⋊C4—44no—
1029C22⋊C4—44no—
1030C22⋊C4—44no—
1031C22⋊C4—44no—
1032C42—44no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
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—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
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—
1137C23C31×#12114yes—
1138C23C22×D4×C3111yescharacteristic
1139C23C22×D4×C3111yescharacteristic
1140C23C22×D4×C3111yescharacteristic
1141C23C22×D4×C3111yescharacteristic
1142C23C22×D4×C3111yescharacteristic
1143C23C2×#41×C3111yescharacteristic
1144C23C2×#41×C3111yescharacteristic
1145C23C2×#41×C3111yescharacteristic
1146C23C2×#41×C3111yescharacteristic
1147C23C31×H(5,𝔽2)11yescharacteristic
1148C23C31×H(5,𝔽2)11yescharacteristic
1149C23C31×H(5,𝔽2)11yescharacteristic
1150C23C31×H(5,𝔽2)11yescharacteristic
1151C23C31×2−1+411yescharacteristic
1152C23C31×2−1+411yescharacteristic
1153D4—416no—
1154D4—416no—
1155D4—416no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
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—416no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
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×C4C31×#12014yes—
1239C2×C4C31×#12114yes—
1240C2×C4C31×#12114yescomplemented
1241C22—24no—
1242C22—24no—
1243C22—24no—
1244C22—42no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—42no—
1249C22—42no—
1250C22—42no—
1251C22—42no—
1252C22—42no—
1253C22—42no—
1254C22—42no—
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—81no—
1271C22—81no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22—81no—
1281C22—81no—
1282C22—81no—
1283C22—81no—
1284C22—81no—
1285C22—81no—
1286C22C2×C31×#12011yescharacteristic
1287C22C2×C31×#12111yescharacteristic
1288C22C2×C31×#12111yescharacteristic
1289C22C2×C31×#12111yescharacteristic
1290C22C31×#52911yescharacteristic
1291C22C31×#53211yescharacteristic
1292C22C31×#53411yescharacteristic
1293C22C31×#53511yescharacteristic
1294C22C31×#53611yescharacteristic
1295C22C31×#53711yescharacteristic
1296C22C31×#53711yescharacteristic
1297C22C31×#53811yescharacteristic
1298C22C31×#53911yescharacteristic
1299C22C31×#54011yescharacteristic
1300C22C31×#54211yescharacteristic
1301C22D42×C3111yescharacteristic
1302C22D42×C3111yescharacteristic
1303C22D42×C3111yescharacteristic
1304C22D42×C3111yescharacteristic
1305C22C31×#54611yescharacteristic
1306C22C31×#54611yescharacteristic
1307C22C31×#54611yescharacteristic
1308C22C31×#54611yescharacteristic
1309C22C31×#54611yescharacteristic
1310C22C31×#54711yescharacteristic
1311C22C31×#54711yescharacteristic
1312C22C31×#54711yescharacteristic
1313C22C31×#54811yescharacteristic
1314C22C31×#54811yescharacteristic
1315C22C31×#54811yescharacteristic
1316C22C31×#55011yescharacteristic
1317C22C31×#55311yescharacteristic
1318C22C31×#55311yescharacteristic
1319C22C31×#56211yescharacteristic
1320C22C31×#56211yescharacteristic
1321C4—24no—
1322C4—24no—
1323C4—24no—
1324C4—42no—
1325C4—42no—
1326C4—42no—
1327C4—42no—
1328C4—42no—
1329C4—81no—
1330C4—81no—
1331C4—81no—
1332C4—81no—
1333C2—44no—
1334C2—82no—
1335C2—82no—
1336C2C31×#240811yescharacteristic
1337C2C31×#241011yescharacteristic
1338C2C31×#241611yescharacteristic
1339C2C31×#241611yescharacteristic
1340C2C31×#242511yescharacteristic
1341C2C31×#242611yescharacteristic
1342C2C31×#242811yescharacteristic
1343C2C31×#243211yescharacteristic
1344C2C31×#255911yescharacteristic
1345C2C31×#267211yescharacteristic
1346C2C31×#267611yescharacteristic
1347C2C31×#268111yescharacteristic
1348C2C31×#268211yescharacteristic
1349C2C31×#270111yescharacteristic
1350C2C31×#271111yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutator, Frattini, cosocleC24C24×C31
prime radicalC22×C31×#121C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#396C2semidirect
3. C2×C31×#394C2semidirect
4. C2×C31×#394C2semidirect
5. C2×C31×#394C2semidirect
6. C2×C31×#390C2semidirect
7. C2×C31×#389C2semidirect
8. C2×C31×#385C2semidirect
9. C31×#1441C2semidirect
10. C31×#1439C2semidirect
11. C31×#1439C2semidirect
12. C31×#1438C2semidirect
13. C31×#1438C2semidirect
14. C31×#1437C2semidirect
15. C31×C22⋊#95C2semidirect
122. C2×C4⋊C4×C31D4semidirect
164. C2×C22⋊C4×C31D4semidirect
357. #15316C31direct (N × H)
565. C2×C4×C31#121semidirect
567. C2×#396C2×C31semidirect
568. C2×#394C2×C31semidirect
569. C2×#394C2×C31semidirect
570. C2×#394C2×C31semidirect
571. C2×#390C2×C31semidirect
572. C2×#389C2×C31semidirect
573. C2×#385C2×C31semidirect
574. #1441C2×C31semidirect
575. #1439C2×C31semidirect
576. #1439C2×C31semidirect
577. #1438C2×C31semidirect
578. #1438C2×C31semidirect
579. #1437C2×C31semidirect
580. C22⋊#95C2×C31semidirect
797. C2×C4⋊C4D4×C31semidirect
839. C2×C22⋊C4D4×C31semidirect
853. C31#15316direct (N × H)
1240. C2×C4C31×#121semidirect

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×#3962
C2×C31×#3942
C2×C31×#3902
C2×C31×#3892
C2×C31×#3852
C31×#14412
C31×#14392
C31×#14382
C31×#14372
C31×C22⋊#952
#1531631