Finite Group Databasebeta

← C31×#15277 #21472036

Subgroups — C31×#15277 #21472036

Order 7936.

2466 conjugacy classes of subgroups.

The subgroup lattice has 1346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#121C211yesmaximal, characteristic
2C2×C31×#397C211yesmaximal, characteristic, complemented
3C2×C31×#394C211yesmaximal, characteristic, complemented
4C2×C31×#386C211yesmaximal, characteristic, complemented
5C2×C31×#386C211yesmaximal, characteristic, complemented
6C2×C31×#385C211yesmaximal, characteristic, complemented
7C31×#1442C211yesmaximal, characteristic, complemented
8C31×#1441C211yesmaximal, characteristic, complemented
9C31×#1440C211yesmaximal, characteristic, complemented
10C31×#1439C211yesmaximal, characteristic, complemented
11C31×#1438C211yesmaximal, characteristic, complemented
12C31×#1438C211yesmaximal, characteristic, complemented
13C31×#1438C211yesmaximal, characteristic, complemented
14C31×C22⋊#95C211yesmaximal, 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×#121—24no—
24C22×C4⋊C4×C31C2211yescharacteristic
25C22×C4⋊C4×C31C2211yescharacteristic
26C22×C4⋊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
40C31×#397—24no—
41C31×#394—24no—
42C31×#386—24no—
43C31×#386—24no—
44C31×#385—24no—
45C2×C31×#95C2211yescharacteristic
46C2×C31×#95C2211yescharacteristic
47C2×C31×#95C2211yescharacteristic
48C2×C31×#95C2211yescharacteristic
49C2×C31×#95C2211yescharacteristic
50C2×C31×#95C2211yescharacteristic
51C2×C31×#95C2211yescharacteristic
52C2×C31×#95C2211yescharacteristic
53C2×C31×#95C2211yescharacteristic
54C2×C31×#95C2211yescharacteristic
55C2×C31×#95C2211yescharacteristic
56C2×C31×#95C2211yescharacteristic
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—41no—
76C22×D4×C31—41no—
77C22×D4×C31—41no—
78C22×D4×C31—41no—
79C22×D4×C31—41no—
80C22×D4×C31—41no—
81C22×D4×C31D414yes—
82C22×D4×C31D414yes—
83C23×C4×C31—22no—
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×C31C2311yescharacteristic
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
109C31×#121—232no—
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×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—22no—
143C2×C22⋊C4×C31—22no—
144C2×C22⋊C4×C31—22no—
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×C31D414yes—
158C31×#95—22no—
159C31×#95—22no—
160C31×#95—22no—
161C31×#95—22no—
162C31×#95—22no—
163C31×#95—22no—
164C31×#95—22no—
165C31×#95—22no—
166C31×#95—41no—
167C31×#95—41no—
168C31×#95—41no—
169C31×#95—41no—
170C31×#95—41no—
171C31×#95D414yescomplemented
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×C31C2×D412yes—
211C24×C31C2×D412yes—
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—28no—
222C2×D4×C31—28no—
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—28no—
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—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—44no—
315C22×C4×C31—44no—
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×C31C2×D412yes—
328C22×C4×C31C2×D412yes—
329C22×C4×C31C2×D412yes—
330C22×C4×C31C2×D412yes—
331C22×C4×C31C2×D412yes—
332C22×C4×C31C2×D412yes—
333C22×C4×C31C2×D412yes—
334C22×C4×C31#4112yes—
335C22×C4×C31#4112yes—
336C22×C4×C31#4112yes—
337C4⋊C4×C31—28no—
338C4⋊C4×C31—44no—
339C4⋊C4×C31—44no—
340C22⋊C4×C31—28no—
341C22⋊C4×C31—28no—
342C22⋊C4×C31—28no—
343C22⋊C4×C31—44no—
344C22⋊C4×C31—44no—
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—
353#15277C3111yesmaximal, characteristic, direct product factor, Sylow
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—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—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#12014yes—
458C23×C31#12314yes—
459C23×C31C22×D411yescharacteristic
460C23×C31C22×D411yescharacteristic
461C23×C31C22×D411yescharacteristic
462C23×C31C22×D411yescharacteristic
463C23×C31C2×#4111yescharacteristic
464C23×C31C2×#4111yescharacteristic
465C23×C31C2×#4111yescharacteristic
466C23×C31C2×#4111yescharacteristic
467C23×C31C2×#4111yescharacteristic
468C23×C31H(5,𝔽2)11yescharacteristic
469C23×C31H(5,𝔽2)11yescharacteristic
470C23×C31H(5,𝔽2)11yescharacteristic
471C23×C31H(5,𝔽2)11yescharacteristic
472C23×C31H(5,𝔽2)11yescharacteristic
473C23×C312−1+411yescharacteristic
474D4×C31—416no—
475D4×C31—416no—
476D4×C31—416no—
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—416no—
505C2×C4×C31—416no—
506C2×C4×C31—41no—
507C2×C4×C31—41no—
508C2×C4×C31—41no—
509C2×C4×C31—41no—
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—41no—
557C2×C4×C31—41no—
558C2×C4×C31—41no—
559C2×C4×C31—41no—
560C2×C4×C31—41no—
561C2×C4×C31—41no—
562C2×C4×C31#12114yes—
563C22×#121C2×C3111yescharacteristic
564C2×#397C2×C3111yescharacteristic, complemented
565C2×#394C2×C3111yescharacteristic, complemented
566C2×#386C2×C3111yescharacteristic, complemented
567C2×#386C2×C3111yescharacteristic, complemented
568C2×#385C2×C3111yescharacteristic, complemented
569#1442C2×C3111yescharacteristic, complemented
570#1441C2×C3111yescharacteristic, complemented
571#1440C2×C3111yescharacteristic, complemented
572#1439C2×C3111yescharacteristic, complemented
573#1438C2×C3111yescharacteristic, complemented
574#1438C2×C3111yescharacteristic, complemented
575#1438C2×C3111yescharacteristic, complemented
576C22⋊#95C2×C3111yescharacteristic, complemented
577C22⋊#95C2×C3111yescharacteristic, complemented
578C22×C31—24no—
579C22×C31—24no—
580C22×C31—24no—
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—42no—
611C22×C31—42no—
612C22×C31—42no—
613C22×C31—42no—
614C22×C31—42no—
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×C31C2×#12011yescharacteristic
624C22×C31C2×#12111yescharacteristic
625C22×C31C2×#12311yescharacteristic
626C22×C31#52511yescharacteristic
627C22×C31#52911yescharacteristic
628C22×C31#53211yescharacteristic
629C22×C31#53411yescharacteristic
630C22×C31#53411yescharacteristic
631C22×C31#53511yescharacteristic
632C22×C31#53711yescharacteristic
633C22×C31#53811yescharacteristic
634C22×C31#53811yescharacteristic
635C22×C31#53911yescharacteristic
636C22×C31#54011yescharacteristic
637C22×C31#54211yescharacteristic
638C22×C31D4211yescharacteristic
639C22×C31D4211yescharacteristic
640C22×C31#54611yescharacteristic
641C22×C31#54611yescharacteristic
642C22×C31#54611yescharacteristic
643C22×C31#54611yescharacteristic
644C22×C31#54611yescharacteristic
645C22×C31#54611yescharacteristic
646C22×C31#54611yescharacteristic
647C22×C31#54611yescharacteristic
648C22×C31#54611yescharacteristic
649C22×C31#54711yescharacteristic
650C22×C31#54711yescharacteristic
651C22×C31#54811yescharacteristic
652C22×C31#55311yescharacteristic
653C22×C31#55311yescharacteristic
654C22×C31#55311yescharacteristic
655C22×C31#55311yescharacteristic
656C22×C31#56011yescharacteristic
657C22×C31#56211yescharacteristic
658C4×C31—24no—
659C4×C31—42no—
660C4×C31—42no—
661C4×C31—42no—
662C4×C31—42no—
663C4×C31—42no—
664C4×C31—42no—
665C4×C31—42no—
666C4×C31—81no—
667C4×C31—81no—
668C4×C31—81no—
669C4×C31—81no—
670C23×D4C22×C3111yescharacteristic
671C23×D4C22×C3111yescharacteristic
672C23×D4C22×C3111yescharacteristic
673C24×C4C22×C3111yescharacteristic
674C24×C4C22×C3111yescharacteristic
675C2×#121—24no—
676C2×#121—24no—
677C2×#121—24no—
678C22×C4⋊C4C22×C3111yescharacteristic
679C22×C4⋊C4C22×C3111yescharacteristic
680C22×C4⋊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×C22⋊C4C22×C3111yescharacteristic
690C22×C22⋊C4C22×C3111yescharacteristic
691C22×C22⋊C4C22×C3111yescharacteristic
692C22×C22⋊C4C22×C3111yescharacteristic
693C22×C22⋊C4C22×C3111yescharacteristic
694#397—24no—
695#394—24no—
696#386—24no—
697#386—24no—
698#385—24no—
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×#95C22×C3111yescharacteristic
709C2×#95C22×C3111yescharacteristic
710C2×#95C22×C3111yescharacteristic
711C2×#95C22×C3111yescharacteristic
712C2×#95C22×C3111yescharacteristic
713C2×C31—44no—
714C2×C31—44no—
715C2×C31—82no—
716C2×C31#240511yescharacteristic
717C2×C31#241011yescharacteristic
718C2×C31#242711yescharacteristic
719C2×C31#243011yescharacteristic
720C2×C31#244311yescharacteristic
721C2×C31#244411yescharacteristic
722C2×C31#246411yescharacteristic
723C2×C31#253511yescharacteristic
724C2×C31#255911yescharacteristic
725C2×C31#267611yescharacteristic
726C2×C31#267811yescharacteristic
727C2×C31#268811yescharacteristic
728C2×C31#269111yescharacteristic
729C2×C31#270111yescharacteristic
730C2×C31#270811yescharacteristic
731C25C23×C3111yescharacteristic
732C25C23×C3111yescharacteristic
733C25C23×C3111yescharacteristic
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—22no—
745C22×D4—22no—
746C22×D4—22no—
747C22×D4—41no—
748C22×D4—41no—
749C22×D4—41no—
750C22×D4—41no—
751C22×D4—41no—
752C22×D4—41no—
753C22×D4D4×C3114yes—
754C22×D4D4×C3114yes—
755C23×C4—22no—
756C23×C4—22no—
757C23×C4—22no—
758C23×C4—22no—
759C23×C4—22no—
760C23×C4—22no—
761C23×C4—22no—
762C23×C4—22no—
763C23×C4—41no—
764C23×C4—41no—
765C23×C4—41no—
766C23×C4—41no—
767C23×C4—41no—
768C23×C4—41no—
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
779C23×C4C23×C3111yescharacteristic
780C23×C4C23×C3111yescharacteristic
781#121—232no—
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—41no—
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—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—41no—
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⋊C4D4×C3114yes—
830#95—22no—
831#95—22no—
832#95—22no—
833#95—22no—
834#95—22no—
835#95—22no—
836#95—22no—
837#95—22no—
838#95—41no—
839#95—41no—
840#95—41no—
841#95—41no—
842#95—41no—
843#95D4×C3114yescomplemented
844C31#1527711yescharacteristic, direct product factor, Sylow
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—
880C24—21no—
881C24—21no—
882C24—21no—
883C24C2×D4×C3112yes—
884C24C2×D4×C3112yes—
885C24C2×D4×C3112yes—
886C24C2×D4×C3112yes—
887C24C2×D4×C3112yes—
888C24#41×C3112yes—
889C24#41×C3112yes—
890C24C24×C3111yescharacteristic
891C2×D4—28no—
892C2×D4—28no—
893C2×D4—28no—
894C2×D4—28no—
895C2×D4—28no—
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—
907C2×D4—44no—
908C2×D4—44no—
909C2×D4—44no—
910C2×D4—44no—
911C2×D4—44no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—28no—
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—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—44no—
988C22×C4—44no—
989C22×C4—44no—
990C22×C4—44no—
991C22×C4—44no—
992C22×C4—44no—
993C22×C4—44no—
994C22×C4—44no—
995C22×C4—44no—
996C22×C4—44no—
997C22×C4—44no—
998C22×C4—44no—
999C22×C4—44no—
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×C4#41×C3112yes—
1008C22×C4#41×C3112yes—
1009C22×C4#41×C3112yes—
1010C4⋊C4—28no—
1011C4⋊C4—44no—
1012C4⋊C4—44no—
1013C22⋊C4—28no—
1014C22⋊C4—28no—
1015C22⋊C4—28no—
1016C22⋊C4—44no—
1017C22⋊C4—44no—
1018C22⋊C4—44no—
1019C22⋊C4—44no—
1020C22⋊C4—44no—
1021C22⋊C4—44no—
1022C22⋊C4—44no—
1023C22⋊C4—44no—
1024C22⋊C4—44no—
1025C22⋊C4—44no—
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—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—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—
1129C23C31×#12014yes—
1130C23C31×#12314yes—
1131C23C22×D4×C3111yescharacteristic
1132C23C22×D4×C3111yescharacteristic
1133C23C22×D4×C3111yescharacteristic
1134C23C22×D4×C3111yescharacteristic
1135C23C2×#41×C3111yescharacteristic
1136C23C2×#41×C3111yescharacteristic
1137C23C2×#41×C3111yescharacteristic
1138C23C2×#41×C3111yescharacteristic
1139C23C2×#41×C3111yescharacteristic
1140C23C31×H(5,𝔽2)11yescharacteristic
1141C23C31×H(5,𝔽2)11yescharacteristic
1142C23C31×H(5,𝔽2)11yescharacteristic
1143C23C31×H(5,𝔽2)11yescharacteristic
1144C23C31×H(5,𝔽2)11yescharacteristic
1145C23C31×2−1+411yescharacteristic
1146D4—416no—
1147D4—416no—
1148D4—416no—
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—416no—
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×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×C4C31×#12114yes—
1235C22—24no—
1236C22—24no—
1237C22—24no—
1238C22—24no—
1239C22—24no—
1240C22—24no—
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—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—42no—
1271C22—42no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22C2×C31×#12011yescharacteristic
1281C22C2×C31×#12111yescharacteristic
1282C22C2×C31×#12311yescharacteristic
1283C22C31×#52511yescharacteristic
1284C22C31×#52911yescharacteristic
1285C22C31×#53211yescharacteristic
1286C22C31×#53411yescharacteristic
1287C22C31×#53411yescharacteristic
1288C22C31×#53511yescharacteristic
1289C22C31×#53711yescharacteristic
1290C22C31×#53811yescharacteristic
1291C22C31×#53811yescharacteristic
1292C22C31×#53911yescharacteristic
1293C22C31×#54011yescharacteristic
1294C22C31×#54211yescharacteristic
1295C22D42×C3111yescharacteristic
1296C22D42×C3111yescharacteristic
1297C22C31×#54611yescharacteristic
1298C22C31×#54611yescharacteristic
1299C22C31×#54611yescharacteristic
1300C22C31×#54611yescharacteristic
1301C22C31×#54611yescharacteristic
1302C22C31×#54611yescharacteristic
1303C22C31×#54611yescharacteristic
1304C22C31×#54611yescharacteristic
1305C22C31×#54611yescharacteristic
1306C22C31×#54711yescharacteristic
1307C22C31×#54711yescharacteristic
1308C22C31×#54811yescharacteristic
1309C22C31×#55311yescharacteristic
1310C22C31×#55311yescharacteristic
1311C22C31×#55311yescharacteristic
1312C22C31×#55311yescharacteristic
1313C22C31×#56011yescharacteristic
1314C22C31×#56211yescharacteristic
1315C4—24no—
1316C4—42no—
1317C4—42no—
1318C4—42no—
1319C4—42no—
1320C4—42no—
1321C4—42no—
1322C4—42no—
1323C4—81no—
1324C4—81no—
1325C4—81no—
1326C4—81no—
1327C2—44no—
1328C2—44no—
1329C2—82no—
1330C2C31×#240511yescharacteristic
1331C2C31×#241011yescharacteristic
1332C2C31×#242711yescharacteristic
1333C2C31×#243011yescharacteristic
1334C2C31×#244311yescharacteristic
1335C2C31×#244411yescharacteristic
1336C2C31×#246411yescharacteristic
1337C2C31×#253511yescharacteristic
1338C2C31×#255911yescharacteristic
1339C2C31×#267611yescharacteristic
1340C2C31×#267811yescharacteristic
1341C2C31×#268811yescharacteristic
1342C2C31×#269111yescharacteristic
1343C2C31×#270111yescharacteristic
1344C2C31×#270811yescharacteristic
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×#397C2semidirect
3. C2×C31×#394C2semidirect
4. C2×C31×#386C2semidirect
5. C2×C31×#386C2semidirect
6. C2×C31×#385C2semidirect
7. C31×#1442C2semidirect
8. C31×#1441C2semidirect
9. C31×#1440C2semidirect
10. C31×#1439C2semidirect
11. C31×#1438C2semidirect
12. C31×#1438C2semidirect
13. C31×#1438C2semidirect
14. C31×C22⋊#95C2semidirect
15. C31×C22⋊#95C2semidirect
171. C31×#95D4semidirect
353. #15277C31direct (N × H)
564. C2×#397C2×C31semidirect
565. C2×#394C2×C31semidirect
566. C2×#386C2×C31semidirect
567. C2×#386C2×C31semidirect
568. C2×#385C2×C31semidirect
569. #1442C2×C31semidirect
570. #1441C2×C31semidirect
571. #1440C2×C31semidirect
572. #1439C2×C31semidirect
573. #1438C2×C31semidirect
574. #1438C2×C31semidirect
575. #1438C2×C31semidirect
576. C22⋊#95C2×C31semidirect
577. C22⋊#95C2×C31semidirect
843. #95D4×C31semidirect
844. C31#15277direct (N × H)

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×#3972
C2×C31×#3942
C2×C31×#3862
C2×C31×#3852
C31×#14422
C31×#14412
C31×#14402
C31×#14392
C31×#14382
C31×C22⋊#952
#1527731