Finite Group Databasebeta

← C31×#14760 #21471519

Subgroups — C31×#14760 #21471519

Order 7936.

2414 conjugacy classes of subgroups.

The subgroup lattice has 1336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#123C211yesmaximal, characteristic, complemented
2C2×C31×#392C211yesmaximal, characteristic
3C2×C31×#390C211yesmaximal, characteristic, complemented
4C2×C31×#388C211yesmaximal, characteristic, complemented
5C2×C31×#386C211yesmaximal, characteristic, complemented
6C2×C4×C22⋊C4×C31C211yesmaximal, characteristic, complemented
7C31×#1441C211yesmaximal, characteristic, complemented
8C31×#1440C211yesmaximal, characteristic, complemented
9C31×#1439C211yesmaximal, characteristic, complemented
10C31×#1439C211yesmaximal, characteristic, complemented
11C31×#1438C211yesmaximal, characteristic, complemented
12C31×#1438C211yesmaximal, characteristic, complemented
13C31×#1438C211yesmaximal, characteristic, complemented
14C31×#1437C211yesmaximal, characteristic, complemented
15C31×#1436C211yesmaximal, characteristic, complemented
16C23×D4×C31C2211yescharacteristic
17C23×D4×C31C2211yescharacteristic
18C23×D4×C31C2211yescharacteristic
19C24×C4×C31C2211yescharacteristic
20C2×C31×#123—24no—
21C2×C31×#123—24no—
22C2×C31×#123—24no—
23C22×C4⋊C4×C31C2211yescharacteristic
24C22×C4⋊C4×C31C2211yescharacteristic
25C22×C4⋊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×C22⋊C4×C31C2211yescharacteristic
35C22×C22⋊C4×C31C2211yescharacteristic
36C22×C22⋊C4×C31C2211yescharacteristic
37C22×C22⋊C4×C31C2211yescharacteristic
38C22×C22⋊C4×C31C2211yescharacteristic
39C22×C22⋊C4×C31C2211yescharacteristic
40C22×C42×C31C2211yescharacteristic
41C22×C42×C31C2211yescharacteristic
42C31×#392—24no—
43C31×#390—24no—
44C31×#388—24no—
45C31×#386—24no—
46C4×C22⋊C4×C31—24no—
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
57C2×C31×#95C2211yescharacteristic
58C2×C31×#95C2211yescharacteristic
59C25×C31C2311yescharacteristic
60C25×C31C2311yescharacteristic
61C25×C31C2311yescharacteristic
62C22×D4×C31—22no—
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—22no—
76C22×D4×C31—22no—
77C22×D4×C31—41no—
78C22×D4×C31—41no—
79C22×D4×C31—41no—
80C22×D4×C31—41no—
81C22×D4×C31—41no—
82C22×D4×C31—41no—
83C23×C4×C31—22no—
84C23×C4×C31—22no—
85C23×C4×C31—22no—
86C23×C4×C31—22no—
87C23×C4×C31—41no—
88C23×C4×C31—41no—
89C23×C4×C31D414yescomplemented
90C23×C4×C31C2311yescharacteristic
91C23×C4×C31C2311yescharacteristic
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
102C31×#123—232no—
103C2×C4⋊C4×C31—22no—
104C2×C4⋊C4×C31—22no—
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—41no—
111C2×C4⋊C4×C31D414yescomplemented
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—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—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×C31D414yes—
153C2×C22⋊C4×C31D414yescomplemented
154C2×C42×C31—22no—
155C2×C42×C31—22no—
156C2×C42×C31—22no—
157C2×C42×C31—22no—
158C2×C42×C31—41no—
159C2×C42×C31—41no—
160C31×#95—22no—
161C31×#95—22no—
162C31×#95—22no—
163C31×#95—22no—
164C31×#95—22no—
165C31×#95—22no—
166C31×#95—22no—
167C31×#95—22no—
168C31×#95—22no—
169C31×#95—41no—
170C31×#95—41no—
171C31×#95—41no—
172C24×C31—21no—
173C24×C31—21no—
174C24×C31—21no—
175C24×C31—21no—
176C24×C31—21no—
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×C31C2×D412yes—
213C24×C31C2×D412yes—
214C24×C31C2×D412yes—
215C24×C31#4112yes—
216C24×C31#4112yes—
217C24×C31C2411yescharacteristic
218C2×D4×C31—28no—
219C2×D4×C31—28no—
220C2×D4×C31—28no—
221C2×D4×C31—44no—
222C2×D4×C31—44no—
223C2×D4×C31—44no—
224C2×D4×C31—44no—
225C2×D4×C31—44no—
226C2×D4×C31—44no—
227C2×D4×C31—44no—
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—
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—28no—
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—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—28no—
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—44no—
312C22×C4×C31—44no—
313C22×C4×C31—44no—
314C22×C4×C31—44no—
315C22×C4×C31—44no—
316C22×C4×C31C2×D412yes—
317C22×C4×C31C2×D412yes—
318C22×C4×C31C2×D412yes—
319C22×C4×C31C2×D412yes—
320C22×C4×C31C2×D412yes—
321C22×C4×C31C2×D412yes—
322C22×C4×C31C2×D412yes—
323C22×C4×C31C2×D412yes—
324C22×C4×C31C2×D412yes—
325C22×C4×C31#4112yes—
326C22×C4×C31#4112yes—
327C22×C4×C31#4112yes—
328C22×C4×C31#4112yes—
329C22×C4×C31#4112yes—
330C4⋊C4×C31—28no—
331C4⋊C4×C31—28no—
332C4⋊C4×C31—44no—
333C22⋊C4×C31—28no—
334C22⋊C4×C31—28no—
335C22⋊C4×C31—28no—
336C22⋊C4×C31—28no—
337C22⋊C4×C31—28no—
338C22⋊C4×C31—28no—
339C22⋊C4×C31—44no—
340C22⋊C4×C31—44no—
341C22⋊C4×C31—44no—
342C22⋊C4×C31—44no—
343C22⋊C4×C31—44no—
344C22⋊C4×C31—44no—
345C22⋊C4×C31—44no—
346C22⋊C4×C31—44no—
347C42×C31—44no—
348C42×C31—44no—
349#14760C3111yesmaximal, characteristic, direct product factor, Sylow
350C23×C31—22no—
351C23×C31—22no—
352C23×C31—22no—
353C23×C31—22no—
354C23×C31—22no—
355C23×C31—22no—
356C23×C31—22no—
357C23×C31—22no—
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—41no—
383C23×C31—41no—
384C23×C31—41no—
385C23×C31—41no—
386C23×C31—41no—
387C23×C31—41no—
388C23×C31—41no—
389C23×C31—41no—
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#12114yes—
455C23×C31C22×D411yescharacteristic
456C23×C31C22×D411yescharacteristic
457C23×C31C22×D411yescharacteristic
458C23×C31C22×D411yescharacteristic
459C23×C31C2×#4111yescharacteristic
460C23×C31C2×#4111yescharacteristic
461C23×C31C2×#4111yescharacteristic
462C23×C31C2×#4111yescharacteristic
463C23×C31C2×#4111yescharacteristic
464C23×C31C2×#4111yescharacteristic
465C23×C31C2×#4111yescharacteristic
466C23×C31H(5,𝔽2)11yescharacteristic
467C23×C31H(5,𝔽2)11yescharacteristic
468C23×C31H(5,𝔽2)11yescharacteristic
469C23×C31H(5,𝔽2)11yescharacteristic
470D4×C31—416no—
471D4×C31—416no—
472D4×C31—416no—
473C2×C4×C31—22no—
474C2×C4×C31—22no—
475C2×C4×C31—22no—
476C2×C4×C31—22no—
477C2×C4×C31—22no—
478C2×C4×C31—22no—
479C2×C4×C31—22no—
480C2×C4×C31—22no—
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—416no—
510C2×C4×C31—41no—
511C2×C4×C31—41no—
512C2×C4×C31—41no—
513C2×C4×C31—41no—
514C2×C4×C31—41no—
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#12014yes—
557C2×C4×C31#12314yescomplemented
558C22×#123C2×C3111yescharacteristic, complemented
559C2×#392C2×C3111yescharacteristic
560C2×#390C2×C3111yescharacteristic, complemented
561C2×#388C2×C3111yescharacteristic, complemented
562C2×#386C2×C3111yescharacteristic, complemented
563C2×C4×C22⋊C4C2×C3111yescharacteristic, complemented
564#1441C2×C3111yescharacteristic, complemented
565#1440C2×C3111yescharacteristic, complemented
566#1439C2×C3111yescharacteristic, complemented
567#1439C2×C3111yescharacteristic, complemented
568#1438C2×C3111yescharacteristic, complemented
569#1438C2×C3111yescharacteristic, complemented
570#1438C2×C3111yescharacteristic, complemented
571#1437C2×C3111yescharacteristic, complemented
572#1436C2×C3111yescharacteristic, complemented
573C22×C31—24no—
574C22×C31—24no—
575C22×C31—24no—
576C22×C31—42no—
577C22×C31—42no—
578C22×C31—42no—
579C22×C31—42no—
580C22×C31—42no—
581C22×C31—42no—
582C22×C31—42no—
583C22×C31—42no—
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—81no—
603C22×C31—81no—
604C22×C31—81no—
605C22×C31—81no—
606C22×C31—81no—
607C22×C31—81no—
608C22×C31—81no—
609C22×C31—81no—
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×C31C2×#12011yescharacteristic
619C22×C31C2×#12111yescharacteristic
620C22×C31C2×#12311yescharacteristic
621C22×C31#52511yescharacteristic
622C22×C31#52511yescharacteristic
623C22×C31#52511yescharacteristic
624C22×C31#52511yescharacteristic
625C22×C31#52911yescharacteristic
626C22×C31#52911yescharacteristic
627C22×C31#53211yescharacteristic
628C22×C31#53211yescharacteristic
629C22×C31#53211yescharacteristic
630C22×C31#53211yescharacteristic
631C22×C31#53411yescharacteristic
632C22×C31#53511yescharacteristic
633C22×C31#53811yescharacteristic
634C22×C31#53811yescharacteristic
635C22×C31#54011yescharacteristic
636C22×C31#54011yescharacteristic
637C22×C31D4211yescharacteristic
638C22×C31D4211yescharacteristic
639C22×C31#54611yescharacteristic
640C22×C31#54611yescharacteristic
641C22×C31#54611yescharacteristic
642C22×C31#54611yescharacteristic
643C22×C31#54611yescharacteristic
644C22×C31#54611yescharacteristic
645C22×C31#55011yescharacteristic
646C22×C31#55011yescharacteristic
647C22×C31#55111yescharacteristic
648C22×C31#55111yescharacteristic
649C22×C31#55111yescharacteristic
650C22×C31#55311yescharacteristic
651C22×C31#55311yescharacteristic
652C22×C31#55911yescharacteristic
653C4×C31—24no—
654C4×C31—24no—
655C4×C31—42no—
656C4×C31—42no—
657C4×C31—42no—
658C4×C31—42no—
659C4×C31—42no—
660C4×C31—42no—
661C4×C31—42no—
662C4×C31—42no—
663C4×C31—81no—
664C4×C31—81no—
665C23×D4C22×C3111yescharacteristic
666C23×D4C22×C3111yescharacteristic
667C23×D4C22×C3111yescharacteristic
668C24×C4C22×C3111yescharacteristic
669C2×#123—24no—
670C2×#123—24no—
671C2×#123—24no—
672C22×C4⋊C4C22×C3111yescharacteristic
673C22×C4⋊C4C22×C3111yescharacteristic
674C22×C4⋊C4C22×C3111yescharacteristic
675C22×C22⋊C4C22×C3111yescharacteristic
676C22×C22⋊C4C22×C3111yescharacteristic
677C22×C22⋊C4C22×C3111yescharacteristic
678C22×C22⋊C4C22×C3111yescharacteristic
679C22×C22⋊C4C22×C3111yescharacteristic
680C22×C22⋊C4C22×C3111yescharacteristic
681C22×C22⋊C4C22×C3111yescharacteristic
682C22×C22⋊C4C22×C3111yescharacteristic
683C22×C22⋊C4C22×C3111yescharacteristic
684C22×C22⋊C4C22×C3111yescharacteristic
685C22×C22⋊C4C22×C3111yescharacteristic
686C22×C22⋊C4C22×C3111yescharacteristic
687C22×C22⋊C4C22×C3111yescharacteristic
688C22×C22⋊C4C22×C3111yescharacteristic
689C22×C42C22×C3111yescharacteristic
690C22×C42C22×C3111yescharacteristic
691#392—24no—
692#390—24no—
693#388—24no—
694#386—24no—
695C4×C22⋊C4—24no—
696C2×#95C22×C3111yescharacteristic
697C2×#95C22×C3111yescharacteristic
698C2×#95C22×C3111yescharacteristic
699C2×#95C22×C3111yescharacteristic
700C2×#95C22×C3111yescharacteristic
701C2×#95C22×C3111yescharacteristic
702C2×#95C22×C3111yescharacteristic
703C2×#95C22×C3111yescharacteristic
704C2×#95C22×C3111yescharacteristic
705C2×#95C22×C3111yescharacteristic
706C2×#95C22×C3111yescharacteristic
707C2×#95C22×C3111yescharacteristic
708C2×C31—44no—
709C2×C31—82no—
710C2×C31—82no—
711C2×C31#238811yescharacteristic
712C2×C31#241011yescharacteristic
713C2×C31#241111yescharacteristic
714C2×C31#241811yescharacteristic
715C2×C31#243111yescharacteristic
716C2×C31#244511yescharacteristic
717C2×C31#245611yescharacteristic
718C2×C31#245711yescharacteristic
719C2×C31#246411yescharacteristic
720C2×C31#247111yescharacteristic
721C2×C31#255411yescharacteristic
722C2×C31#255711yescharacteristic
723C2×C31#260211yescharacteristic
724C2×C31#266111yescharacteristic
725C2×C31#285411yescharacteristic
726C25C23×C3111yescharacteristic
727C25C23×C3111yescharacteristic
728C25C23×C3111yescharacteristic
729C22×D4—22no—
730C22×D4—22no—
731C22×D4—22no—
732C22×D4—22no—
733C22×D4—22no—
734C22×D4—22no—
735C22×D4—22no—
736C22×D4—22no—
737C22×D4—22no—
738C22×D4—22no—
739C22×D4—22no—
740C22×D4—22no—
741C22×D4—22no—
742C22×D4—22no—
743C22×D4—22no—
744C22×D4—41no—
745C22×D4—41no—
746C22×D4—41no—
747C22×D4—41no—
748C22×D4—41no—
749C22×D4—41no—
750C23×C4—22no—
751C23×C4—22no—
752C23×C4—22no—
753C23×C4—22no—
754C23×C4—41no—
755C23×C4—41no—
756C23×C4D4×C3114yescomplemented
757C23×C4C23×C3111yescharacteristic
758C23×C4C23×C3111yescharacteristic
759C23×C4C23×C3111yescharacteristic
760C23×C4C23×C3111yescharacteristic
761C23×C4C23×C3111yescharacteristic
762C23×C4C23×C3111yescharacteristic
763C23×C4C23×C3111yescharacteristic
764C23×C4C23×C3111yescharacteristic
765C23×C4C23×C3111yescharacteristic
766C23×C4C23×C3111yescharacteristic
767C23×C4C23×C3111yescharacteristic
768C23×C4C23×C3111yescharacteristic
769#123—232no—
770C2×C4⋊C4—22no—
771C2×C4⋊C4—22no—
772C2×C4⋊C4—22no—
773C2×C4⋊C4—22no—
774C2×C4⋊C4—22no—
775C2×C4⋊C4—22no—
776C2×C4⋊C4—22no—
777C2×C4⋊C4—41no—
778C2×C4⋊C4D4×C3114yescomplemented
779C2×C22⋊C4—22no—
780C2×C22⋊C4—22no—
781C2×C22⋊C4—22no—
782C2×C22⋊C4—22no—
783C2×C22⋊C4—22no—
784C2×C22⋊C4—22no—
785C2×C22⋊C4—22no—
786C2×C22⋊C4—22no—
787C2×C22⋊C4—22no—
788C2×C22⋊C4—22no—
789C2×C22⋊C4—22no—
790C2×C22⋊C4—22no—
791C2×C22⋊C4—22no—
792C2×C22⋊C4—22no—
793C2×C22⋊C4—22no—
794C2×C22⋊C4—22no—
795C2×C22⋊C4—22no—
796C2×C22⋊C4—22no—
797C2×C22⋊C4—22no—
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—41no—
810C2×C22⋊C4—41no—
811C2×C22⋊C4—41no—
812C2×C22⋊C4—41no—
813C2×C22⋊C4—41no—
814C2×C22⋊C4—41no—
815C2×C22⋊C4—41no—
816C2×C22⋊C4—41no—
817C2×C22⋊C4—41no—
818C2×C22⋊C4—41no—
819C2×C22⋊C4D4×C3114yes—
820C2×C22⋊C4D4×C3114yescomplemented
821C2×C42—22no—
822C2×C42—22no—
823C2×C42—22no—
824C2×C42—22no—
825C2×C42—41no—
826C2×C42—41no—
827#95—22no—
828#95—22no—
829#95—22no—
830#95—22no—
831#95—22no—
832#95—22no—
833#95—22no—
834#95—22no—
835#95—22no—
836#95—41no—
837#95—41no—
838#95—41no—
839C31#1476011yescharacteristic, direct product factor, Sylow
840C24—21no—
841C24—21no—
842C24—21no—
843C24—21no—
844C24—21no—
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—21no—
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—
880C24C2×D4×C3112yes—
881C24C2×D4×C3112yes—
882C24C2×D4×C3112yes—
883C24#41×C3112yes—
884C24#41×C3112yes—
885C24C24×C3111yescharacteristic
886C2×D4—28no—
887C2×D4—28no—
888C2×D4—28no—
889C2×D4—44no—
890C2×D4—44no—
891C2×D4—44no—
892C2×D4—44no—
893C2×D4—44no—
894C2×D4—44no—
895C2×D4—44no—
896C2×D4—44no—
897C2×D4—44no—
898C2×D4—44no—
899C2×D4—44no—
900C2×D4—44no—
901C2×D4—44no—
902C2×D4—44no—
903C2×D4—44no—
904C2×D4—44no—
905C2×D4—44no—
906C2×D4—44no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—28no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
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—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—28no—
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—44no—
980C22×C4—44no—
981C22×C4—44no—
982C22×C4—44no—
983C22×C4—44no—
984C22×C4C2×D4×C3112yes—
985C22×C4C2×D4×C3112yes—
986C22×C4C2×D4×C3112yes—
987C22×C4C2×D4×C3112yes—
988C22×C4C2×D4×C3112yes—
989C22×C4C2×D4×C3112yes—
990C22×C4C2×D4×C3112yes—
991C22×C4C2×D4×C3112yes—
992C22×C4C2×D4×C3112yes—
993C22×C4#41×C3112yes—
994C22×C4#41×C3112yes—
995C22×C4#41×C3112yes—
996C22×C4#41×C3112yes—
997C22×C4#41×C3112yes—
998C4⋊C4—28no—
999C4⋊C4—28no—
1000C4⋊C4—44no—
1001C22⋊C4—28no—
1002C22⋊C4—28no—
1003C22⋊C4—28no—
1004C22⋊C4—28no—
1005C22⋊C4—28no—
1006C22⋊C4—28no—
1007C22⋊C4—44no—
1008C22⋊C4—44no—
1009C22⋊C4—44no—
1010C22⋊C4—44no—
1011C22⋊C4—44no—
1012C22⋊C4—44no—
1013C22⋊C4—44no—
1014C22⋊C4—44no—
1015C42—44no—
1016C42—44no—
1017C23—22no—
1018C23—22no—
1019C23—22no—
1020C23—22no—
1021C23—22no—
1022C23—22no—
1023C23—22no—
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
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—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
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—
1121C23C31×#12114yes—
1122C23C22×D4×C3111yescharacteristic
1123C23C22×D4×C3111yescharacteristic
1124C23C22×D4×C3111yescharacteristic
1125C23C22×D4×C3111yescharacteristic
1126C23C2×#41×C3111yescharacteristic
1127C23C2×#41×C3111yescharacteristic
1128C23C2×#41×C3111yescharacteristic
1129C23C2×#41×C3111yescharacteristic
1130C23C2×#41×C3111yescharacteristic
1131C23C2×#41×C3111yescharacteristic
1132C23C2×#41×C3111yescharacteristic
1133C23C31×H(5,𝔽2)11yescharacteristic
1134C23C31×H(5,𝔽2)11yescharacteristic
1135C23C31×H(5,𝔽2)11yescharacteristic
1136C23C31×H(5,𝔽2)11yescharacteristic
1137D4—416no—
1138D4—416no—
1139D4—416no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
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—416no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
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×C4C31×#12014yes—
1224C2×C4C31×#12314yescomplemented
1225C22—24no—
1226C22—24no—
1227C22—24no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—42no—
1235C22—42no—
1236C22—42no—
1237C22—42no—
1238C22—42no—
1239C22—42no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—42no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—42no—
1249C22—42no—
1250C22—42no—
1251C22—42no—
1252C22—42no—
1253C22—42no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22—81no—
1259C22—81no—
1260C22—81no—
1261C22—81no—
1262C22—81no—
1263C22—81no—
1264C22—81no—
1265C22—81no—
1266C22—81no—
1267C22—81no—
1268C22—81no—
1269C22—81no—
1270C22C2×C31×#12011yescharacteristic
1271C22C2×C31×#12111yescharacteristic
1272C22C2×C31×#12311yescharacteristic
1273C22C31×#52511yescharacteristic
1274C22C31×#52511yescharacteristic
1275C22C31×#52511yescharacteristic
1276C22C31×#52511yescharacteristic
1277C22C31×#52911yescharacteristic
1278C22C31×#52911yescharacteristic
1279C22C31×#53211yescharacteristic
1280C22C31×#53211yescharacteristic
1281C22C31×#53211yescharacteristic
1282C22C31×#53211yescharacteristic
1283C22C31×#53411yescharacteristic
1284C22C31×#53511yescharacteristic
1285C22C31×#53811yescharacteristic
1286C22C31×#53811yescharacteristic
1287C22C31×#54011yescharacteristic
1288C22C31×#54011yescharacteristic
1289C22D42×C3111yescharacteristic
1290C22D42×C3111yescharacteristic
1291C22C31×#54611yescharacteristic
1292C22C31×#54611yescharacteristic
1293C22C31×#54611yescharacteristic
1294C22C31×#54611yescharacteristic
1295C22C31×#54611yescharacteristic
1296C22C31×#54611yescharacteristic
1297C22C31×#55011yescharacteristic
1298C22C31×#55011yescharacteristic
1299C22C31×#55111yescharacteristic
1300C22C31×#55111yescharacteristic
1301C22C31×#55111yescharacteristic
1302C22C31×#55311yescharacteristic
1303C22C31×#55311yescharacteristic
1304C22C31×#55911yescharacteristic
1305C4—24no—
1306C4—24no—
1307C4—42no—
1308C4—42no—
1309C4—42no—
1310C4—42no—
1311C4—42no—
1312C4—42no—
1313C4—42no—
1314C4—42no—
1315C4—81no—
1316C4—81no—
1317C2—44no—
1318C2—82no—
1319C2—82no—
1320C2C31×#238811yescharacteristic
1321C2C31×#241011yescharacteristic
1322C2C31×#241111yescharacteristic
1323C2C31×#241811yescharacteristic
1324C2C31×#243111yescharacteristic
1325C2C31×#244511yescharacteristic
1326C2C31×#245611yescharacteristic
1327C2C31×#245711yescharacteristic
1328C2C31×#246411yescharacteristic
1329C2C31×#247111yescharacteristic
1330C2C31×#255411yescharacteristic
1331C2C31×#255711yescharacteristic
1332C2C31×#260211yescharacteristic
1333C2C31×#266111yescharacteristic
1334C2C31×#285411yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutator, Frattini, cosocleC24C24×C31
prime radicalC2×C31×#392C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C31×#123C2semidirect
3. C2×C31×#390C2semidirect
4. C2×C31×#388C2semidirect
5. C2×C31×#386C2semidirect
6. C2×C4×C22⋊C4×C31C2semidirect
7. C31×#1441C2semidirect
8. C31×#1440C2semidirect
9. C31×#1439C2semidirect
10. C31×#1439C2semidirect
11. C31×#1438C2semidirect
12. C31×#1438C2semidirect
13. C31×#1438C2semidirect
14. C31×#1437C2semidirect
15. C31×#1436C2semidirect
89. C23×C4×C31D4semidirect
111. C2×C4⋊C4×C31D4semidirect
153. C2×C22⋊C4×C31D4semidirect
349. #14760C31direct (N × H)
557. C2×C4×C31#123semidirect
558. C22×#123C2×C31semidirect
560. C2×#390C2×C31semidirect
561. C2×#388C2×C31semidirect
562. C2×#386C2×C31semidirect
563. C2×C4×C22⋊C4C2×C31semidirect
564. #1441C2×C31semidirect
565. #1440C2×C31semidirect
566. #1439C2×C31semidirect
567. #1439C2×C31semidirect
568. #1438C2×C31semidirect
569. #1438C2×C31semidirect
570. #1438C2×C31semidirect
571. #1437C2×C31semidirect
572. #1436C2×C31semidirect
756. C23×C4D4×C31semidirect
778. C2×C4⋊C4D4×C31semidirect
820. C2×C22⋊C4D4×C31semidirect
839. C31#14760direct (N × H)
1224. C2×C4C31×#123semidirect

Maximal subgroups

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

subgroupindex
C22×C31×#1232
C2×C31×#3922
C2×C31×#3902
C2×C31×#3882
C2×C31×#3862
C2×C4×C22⋊C4×C312
C31×#14412
C31×#14402
C31×#14392
C31×#14382
C31×#14372
C31×#14362
#1476031