Finite Group Databasebeta

← C31×#15297 #21472056

Subgroups — C31×#15297 #21472056

Order 7936.

2826 conjugacy classes of subgroups.

The subgroup lattice has 1366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#397C211yesmaximal, characteristic, complemented
2C2×C31×#396C211yesmaximal, characteristic, complemented
3C2×C31×#388C211yesmaximal, characteristic, complemented
4C2×C31×#379C211yesmaximal, characteristic
5C2×C31×#379C211yesmaximal, characteristic
6C2×C31×#379C211yesmaximal, characteristic
7C31×#1440C211yesmaximal, characteristic, complemented
8C31×#1440C211yesmaximal, characteristic, complemented
9C31×#1440C211yesmaximal, characteristic, complemented
10C31×#1439C211yesmaximal, characteristic, complemented
11C31×#1439C211yesmaximal, characteristic, complemented
12C31×#1439C211yesmaximal, characteristic, complemented
13C31×#1439C211yesmaximal, characteristic, complemented
14C31×#1437C211yesmaximal, characteristic, complemented
15C31×#1437C211yesmaximal, characteristic, complemented
16C26×C31C2211yescharacteristic
17C22×C4⋊C4×C31C2211yescharacteristic, complemented
18C22×C4⋊C4×C31C2211yescharacteristic, complemented
19C22×C4⋊C4×C31C2211yescharacteristic, complemented
20C22×C22⋊C4×C31C2211yescharacteristic
21C22×C22⋊C4×C31C2211yescharacteristic
22C22×C22⋊C4×C31C2211yescharacteristic
23C22×C22⋊C4×C31C2211yescharacteristic
24C22×C22⋊C4×C31C2211yescharacteristic
25C22×C22⋊C4×C31C2211yescharacteristic
26C22×C22⋊C4×C31C2211yescharacteristic
27C22×C22⋊C4×C31C2211yescharacteristic
28C22×C22⋊C4×C31C2211yescharacteristic
29C22×C22⋊C4×C31C2211yescharacteristic
30C22×C22⋊C4×C31C2211yescharacteristic
31C22×C22⋊C4×C31C2211yescharacteristic
32C22×C22⋊C4×C31C2211yescharacteristic
33C22×C22⋊C4×C31C2211yescharacteristic
34C22×C22⋊C4×C31C2211yescharacteristic
35C22×C22⋊C4×C31C2211yescharacteristic
36C22×C22⋊C4×C31C2211yescharacteristic
37C22×C22⋊C4×C31C2211yescharacteristic
38C22×C42×C31C2211yescharacteristic, complemented
39C31×#397—24no—
40C31×#396—24no—
41C31×#388—24no—
42C31×#379—24no—
43C31×#379—24no—
44C31×#379—24no—
45C2×C31×#95C2211yescharacteristic, complemented
46C2×C31×#95C2211yescharacteristic, complemented
47C2×C31×#95C2211yescharacteristic, complemented
48C2×C31×#95C2211yescharacteristic, complemented
49C2×C31×#95C2211yescharacteristic, complemented
50C2×C31×#95C2211yescharacteristic, complemented
51C2×C31×#95C2211yescharacteristic, complemented
52C2×C31×#95C2211yescharacteristic, complemented
53C2×C31×#95C2211yescharacteristic, complemented
54C2×C31×#95C2211yescharacteristic, complemented
55C2×C31×#95C2211yescharacteristic, complemented
56C2×C31×#95C2211yescharacteristic, complemented
57C25×C31—22no—
58C25×C31—22no—
59C25×C31—22no—
60C25×C31—22no—
61C25×C31—22no—
62C25×C31—22no—
63C25×C31—22no—
64C25×C31—22no—
65C25×C31—22no—
66C25×C31—41no—
67C25×C31—41no—
68C25×C31—41no—
69C25×C31—41no—
70C25×C31—41no—
71C25×C31—41no—
72C25×C31C2311yescharacteristic
73C25×C31C2311yescharacteristic
74C25×C31C2311yescharacteristic
75C23×C4×C31C2311yescharacteristic
76C23×C4×C31C2311yescharacteristic
77C23×C4×C31C2311yescharacteristic
78C23×C4×C31C2311yescharacteristic
79C23×C4×C31C2311yescharacteristic
80C23×C4×C31C2311yescharacteristic
81C23×C4×C31C2311yescharacteristic
82C23×C4×C31C2311yescharacteristic
83C23×C4×C31C2311yescharacteristic
84C23×C4×C31C2311yescharacteristic
85C23×C4×C31C2311yescharacteristic
86C23×C4×C31C2311yescharacteristic
87C2×C4⋊C4×C31—22no—
88C2×C4⋊C4×C31—22no—
89C2×C4⋊C4×C31—22no—
90C2×C4⋊C4×C31—22no—
91C2×C4⋊C4×C31—22no—
92C2×C4⋊C4×C31—41no—
93C2×C4⋊C4×C31—41no—
94C2×C4⋊C4×C31—41no—
95C2×C4⋊C4×C31—41no—
96C2×C22⋊C4×C31—22no—
97C2×C22⋊C4×C31—22no—
98C2×C22⋊C4×C31—22no—
99C2×C22⋊C4×C31—22no—
100C2×C22⋊C4×C31—22no—
101C2×C22⋊C4×C31—22no—
102C2×C22⋊C4×C31—22no—
103C2×C22⋊C4×C31—22no—
104C2×C22⋊C4×C31—22no—
105C2×C22⋊C4×C31—22no—
106C2×C22⋊C4×C31—22no—
107C2×C22⋊C4×C31—22no—
108C2×C22⋊C4×C31—22no—
109C2×C22⋊C4×C31—22no—
110C2×C22⋊C4×C31—22no—
111C2×C22⋊C4×C31—22no—
112C2×C22⋊C4×C31—22no—
113C2×C22⋊C4×C31—22no—
114C2×C22⋊C4×C31—22no—
115C2×C22⋊C4×C31—22no—
116C2×C22⋊C4×C31—22no—
117C2×C22⋊C4×C31—22no—
118C2×C22⋊C4×C31—22no—
119C2×C22⋊C4×C31—22no—
120C2×C22⋊C4×C31—22no—
121C2×C22⋊C4×C31—22no—
122C2×C22⋊C4×C31—22no—
123C2×C22⋊C4×C31—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—41no—
130C2×C22⋊C4×C31—41no—
131C2×C22⋊C4×C31—41no—
132C2×C22⋊C4×C31—41no—
133C2×C22⋊C4×C31—41no—
134C2×C22⋊C4×C31—41no—
135C2×C22⋊C4×C31—41no—
136C2×C22⋊C4×C31—41no—
137C2×C22⋊C4×C31—41no—
138C2×C22⋊C4×C31—41no—
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×C31D414yes—
148C2×C22⋊C4×C31D414yes—
149C2×C22⋊C4×C31D414yes—
150C2×C42×C31—22no—
151C2×C42×C31—41no—
152C2×C42×C31—41no—
153C31×#95—22no—
154C31×#95—22no—
155C31×#95—22no—
156C31×#95—22no—
157C31×#95—22no—
158C31×#95—22no—
159C31×#95—41no—
160C31×#95—41no—
161C31×#95—41no—
162C31×#95—41no—
163C31×#95—41no—
164C31×#95—41no—
165C24×C31—21no—
166C24×C31—21no—
167C24×C31—21no—
168C24×C31—21no—
169C24×C31—21no—
170C24×C31—21no—
171C24×C31—21no—
172C24×C31—21no—
173C24×C31—21no—
174C24×C31—21no—
175C24×C31—21no—
176C24×C31—21no—
177C24×C31—21no—
178C24×C31—21no—
179C24×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—28no—
202C24×C31—28no—
203C24×C31—28no—
204C24×C31—44no—
205C24×C31—44no—
206C24×C31—44no—
207C24×C31—44no—
208C24×C31—44no—
209C24×C31—44no—
210C24×C31—44no—
211C24×C31—44no—
212C24×C31—44no—
213C24×C31—44no—
214C24×C31—44no—
215C24×C31—44no—
216C24×C31—44no—
217C24×C31—44no—
218C24×C31—44no—
219C24×C31—44no—
220C24×C31—44no—
221C24×C31—44no—
222C24×C31—44no—
223C24×C31—44no—
224C24×C31—44no—
225C24×C31—44no—
226C24×C31—44no—
227C24×C31—44no—
228C24×C31—44no—
229C24×C31—44no—
230C24×C31—44no—
231C24×C31—44no—
232C24×C31—44no—
233C24×C31—44no—
234C24×C31—44no—
235C24×C31—44no—
236C24×C31C2×D412yes—
237C24×C31C2×D412yes—
238C24×C31C2×D412yes—
239C24×C31#4112yes—
240C24×C31#4112yes—
241C24×C31#4112yes—
242C24×C31#4112yes—
243C24×C31#4112yes—
244C24×C31#4112yes—
245C24×C31C2411yescharacteristic
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—21no—
315C22×C4×C31—21no—
316C22×C4×C31—21no—
317C22×C4×C31—21no—
318C22×C4×C31—21no—
319C22×C4×C31—21no—
320C22×C4×C31—21no—
321C22×C4×C31—21no—
322C22×C4×C31—21no—
323C22×C4×C31—21no—
324C22×C4×C31C2×D412yes—
325C22×C4×C31C2×D412yes—
326C22×C4×C31C2×D412yes—
327C22×C4×C31C2×D412yes—
328C22×C4×C31C2×D412yes—
329C22×C4×C31C2×D412yes—
330C4⋊C4×C31—44no—
331C4⋊C4×C31—44no—
332C4⋊C4×C31—44no—
333C22⋊C4×C31—28no—
334C22⋊C4×C31—44no—
335C22⋊C4×C31—44no—
336C22⋊C4×C31—44no—
337C22⋊C4×C31—44no—
338C22⋊C4×C31—44no—
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—
347C22⋊C4×C31—44no—
348C22⋊C4×C31—44no—
349C22⋊C4×C31—44no—
350C22⋊C4×C31—44no—
351C42×C31—44no—
352#15297C3111yesmaximal, characteristic, direct product factor, Sylow
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—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—22no—
405C23×C31—22no—
406C23×C31—22no—
407C23×C31—416no—
408C23×C31—416no—
409C23×C31—416no—
410C23×C31—416no—
411C23×C31—416no—
412C23×C31—416no—
413C23×C31—416no—
414C23×C31—416no—
415C23×C31—416no—
416C23×C31—416no—
417C23×C31—416no—
418C23×C31—416no—
419C23×C31—416no—
420C23×C31—416no—
421C23×C31—416no—
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×C31—41no—
465C23×C31—41no—
466C23×C31—41no—
467C23×C31—41no—
468C23×C31—41no—
469C23×C31—41no—
470C23×C31#12114yes—
471C23×C31#12414yes—
472C23×C31#12614yes—
473C23×C31C22×D411yescharacteristic
474C23×C31C22×D411yescharacteristic
475C23×C31C22×D411yescharacteristic
476C23×C31C2×#4111yescharacteristic
477C23×C31C2×#4111yescharacteristic
478C23×C31C2×#4111yescharacteristic
479C23×C31C2×#4111yescharacteristic
480C23×C31C2×#4111yescharacteristic
481C23×C31C2×#4111yescharacteristic
482C23×C31H(5,𝔽2)11yescharacteristic
483C23×C31H(5,𝔽2)11yescharacteristic
484C23×C31H(5,𝔽2)11yescharacteristic
485C23×C31H(5,𝔽2)11yescharacteristic
486C23×C31H(5,𝔽2)11yescharacteristic
487C23×C31H(5,𝔽2)11yescharacteristic
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—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—41no—
563C2×C4×C31—41no—
564C2×C4×C31—41no—
565C2×C4×C31—41no—
566C2×C4×C31—41no—
567C2×C4×C31—41no—
568C2×C4×C31—41no—
569C2×C4×C31—41no—
570C2×C4×C31—41no—
571C2×C4×C31—41no—
572C2×#397C2×C3111yescharacteristic, complemented
573C2×#396C2×C3111yescharacteristic, complemented
574C2×#388C2×C3111yescharacteristic, complemented
575C2×#379C2×C3111yescharacteristic
576C2×#379C2×C3111yescharacteristic
577C2×#379C2×C3111yescharacteristic
578#1440C2×C3111yescharacteristic, complemented
579#1440C2×C3111yescharacteristic, complemented
580#1440C2×C3111yescharacteristic, complemented
581#1439C2×C3111yescharacteristic, complemented
582#1439C2×C3111yescharacteristic, complemented
583#1439C2×C3111yescharacteristic, complemented
584#1439C2×C3111yescharacteristic, complemented
585#1437C2×C3111yescharacteristic, complemented
586#1437C2×C3111yescharacteristic, complemented
587C22×C31—24no—
588C22×C31—24no—
589C22×C31—24no—
590C22×C31—24no—
591C22×C31—24no—
592C22×C31—24no—
593C22×C31—24no—
594C22×C31—24no—
595C22×C31—24no—
596C22×C31—464no—
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—42no—
623C22×C31—42no—
624C22×C31—42no—
625C22×C31—42no—
626C22×C31—42no—
627C22×C31—42no—
628C22×C31—42no—
629C22×C31—42no—
630C22×C31—42no—
631C22×C31—42no—
632C22×C31—42no—
633C22×C31C2×#12111yescharacteristic
634C22×C31#52511yescharacteristic
635C22×C31#52511yescharacteristic
636C22×C31#52511yescharacteristic
637C22×C31C2×#12411yescharacteristic
638C22×C31C2×#12611yescharacteristic
639C22×C31#53411yescharacteristic
640C22×C31#53411yescharacteristic
641C22×C31#53511yescharacteristic
642C22×C31#53811yescharacteristic
643C22×C31#53811yescharacteristic
644C22×C31#53811yescharacteristic
645C22×C31#53811yescharacteristic
646C22×C31#53811yescharacteristic
647C22×C31#53811yescharacteristic
648C22×C31D4211yescharacteristic
649C22×C31D4211yescharacteristic
650C22×C31#54611yescharacteristic
651C22×C31#54611yescharacteristic
652C22×C31#54611yescharacteristic
653C22×C31#54611yescharacteristic
654C22×C31#54611yescharacteristic
655C22×C31#54611yescharacteristic
656C22×C31#54611yescharacteristic
657C22×C31#54611yescharacteristic
658C22×C31#55111yescharacteristic
659C22×C31#55111yescharacteristic
660C22×C31#55111yescharacteristic
661C22×C31#55111yescharacteristic
662C22×C31#55111yescharacteristic
663C22×C31#55111yescharacteristic
664C22×C31#55111yescharacteristic
665C22×C31#55111yescharacteristic
666C22×C31#56011yescharacteristic
667C22×C31#56011yescharacteristic
668C4×C31—42no—
669C4×C31—42no—
670C4×C31—42no—
671C4×C31—42no—
672C4×C31—42no—
673C4×C31—42no—
674C4×C31—81no—
675C4×C31—81no—
676C4×C31—81no—
677C4×C31—81no—
678C4×C31—81no—
679C4×C31—81no—
680C26C22×C3111yescharacteristic
681C22×C4⋊C4C22×C3111yescharacteristic, complemented
682C22×C4⋊C4C22×C3111yescharacteristic, complemented
683C22×C4⋊C4C22×C3111yescharacteristic, complemented
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
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, complemented
703#397—24no—
704#396—24no—
705#388—24no—
706#379—24no—
707#379—24no—
708#379—24no—
709C2×#95C22×C3111yescharacteristic, complemented
710C2×#95C22×C3111yescharacteristic, complemented
711C2×#95C22×C3111yescharacteristic, complemented
712C2×#95C22×C3111yescharacteristic, complemented
713C2×#95C22×C3111yescharacteristic, complemented
714C2×#95C22×C3111yescharacteristic, complemented
715C2×#95C22×C3111yescharacteristic, complemented
716C2×#95C22×C3111yescharacteristic, complemented
717C2×#95C22×C3111yescharacteristic, complemented
718C2×#95C22×C3111yescharacteristic, complemented
719C2×#95C22×C3111yescharacteristic, complemented
720C2×#95C22×C3111yescharacteristic, complemented
721C2×C31—44no—
722C2×C31—44no—
723C2×C31—44no—
724C2×C31#241111yescharacteristic
725C2×C31#242411yescharacteristic
726C2×C31#247211yescharacteristic
727C2×C31#247211yescharacteristic
728C2×C31#248011yescharacteristic
729C2×C31#248011yescharacteristic
730C2×C31#248011yescharacteristic
731C2×C31#253411yescharacteristic
732C2×C31#256111yescharacteristic
733C2×C31#266811yescharacteristic
734C2×C31#267811yescharacteristic
735C2×C31#268511yescharacteristic
736C2×C31#269711yescharacteristic
737C2×C31#273511yescharacteristic
738C2×C31#273511yescharacteristic
739C25—22no—
740C25—22no—
741C25—22no—
742C25—22no—
743C25—22no—
744C25—22no—
745C25—22no—
746C25—22no—
747C25—22no—
748C25—41no—
749C25—41no—
750C25—41no—
751C25—41no—
752C25—41no—
753C25—41no—
754C25C23×C3111yescharacteristic
755C25C23×C3111yescharacteristic
756C25C23×C3111yescharacteristic
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
769C2×C4⋊C4—22no—
770C2×C4⋊C4—22no—
771C2×C4⋊C4—22no—
772C2×C4⋊C4—22no—
773C2×C4⋊C4—22no—
774C2×C4⋊C4—41no—
775C2×C4⋊C4—41no—
776C2×C4⋊C4—41no—
777C2×C4⋊C4—41no—
778C2×C22⋊C4—22no—
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—22no—
810C2×C22⋊C4—22no—
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⋊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—
830C2×C22⋊C4D4×C3114yes—
831C2×C22⋊C4D4×C3114yes—
832C2×C42—22no—
833C2×C42—41no—
834C2×C42—41no—
835#95—22no—
836#95—22no—
837#95—22no—
838#95—22no—
839#95—22no—
840#95—22no—
841#95—41no—
842#95—41no—
843#95—41no—
844#95—41no—
845#95—41no—
846#95—41no—
847C31#1529711yescharacteristic, direct product factor, Sylow
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—
883C24—21no—
884C24—28no—
885C24—28no—
886C24—28no—
887C24—44no—
888C24—44no—
889C24—44no—
890C24—44no—
891C24—44no—
892C24—44no—
893C24—44no—
894C24—44no—
895C24—44no—
896C24—44no—
897C24—44no—
898C24—44no—
899C24—44no—
900C24—44no—
901C24—44no—
902C24—44no—
903C24—44no—
904C24—44no—
905C24—44no—
906C24—44no—
907C24—44no—
908C24—44no—
909C24—44no—
910C24—44no—
911C24—44no—
912C24—44no—
913C24—44no—
914C24—44no—
915C24—44no—
916C24—44no—
917C24—44no—
918C24—44no—
919C24C2×D4×C3112yes—
920C24C2×D4×C3112yes—
921C24C2×D4×C3112yes—
922C24#41×C3112yes—
923C24#41×C3112yes—
924C24#41×C3112yes—
925C24#41×C3112yes—
926C24#41×C3112yes—
927C24#41×C3112yes—
928C24C24×C3111yescharacteristic
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—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—21no—
997C22×C4—21no—
998C22×C4—21no—
999C22×C4—21no—
1000C22×C4—21no—
1001C22×C4—21no—
1002C22×C4—21no—
1003C22×C4—21no—
1004C22×C4—21no—
1005C22×C4—21no—
1006C22×C4—21no—
1007C22×C4C2×D4×C3112yes—
1008C22×C4C2×D4×C3112yes—
1009C22×C4C2×D4×C3112yes—
1010C22×C4C2×D4×C3112yes—
1011C22×C4C2×D4×C3112yes—
1012C22×C4C2×D4×C3112yes—
1013C4⋊C4—44no—
1014C4⋊C4—44no—
1015C4⋊C4—44no—
1016C22⋊C4—28no—
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—
1026C22⋊C4—44no—
1027C22⋊C4—44no—
1028C22⋊C4—44no—
1029C22⋊C4—44no—
1030C22⋊C4—44no—
1031C22⋊C4—44no—
1032C22⋊C4—44no—
1033C22⋊C4—44no—
1034C42—44no—
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—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—22no—
1084C23—22no—
1085C23—22no—
1086C23—22no—
1087C23—22no—
1088C23—22no—
1089C23—416no—
1090C23—416no—
1091C23—416no—
1092C23—416no—
1093C23—416no—
1094C23—416no—
1095C23—416no—
1096C23—416no—
1097C23—416no—
1098C23—416no—
1099C23—416no—
1100C23—416no—
1101C23—416no—
1102C23—416no—
1103C23—416no—
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—
1143C23—41no—
1144C23—41no—
1145C23—41no—
1146C23—41no—
1147C23—41no—
1148C23—41no—
1149C23—41no—
1150C23—41no—
1151C23—41no—
1152C23C31×#12114yes—
1153C23C31×#12414yes—
1154C23C31×#12614yes—
1155C23C22×D4×C3111yescharacteristic
1156C23C22×D4×C3111yescharacteristic
1157C23C22×D4×C3111yescharacteristic
1158C23C2×#41×C3111yescharacteristic
1159C23C2×#41×C3111yescharacteristic
1160C23C2×#41×C3111yescharacteristic
1161C23C2×#41×C3111yescharacteristic
1162C23C2×#41×C3111yescharacteristic
1163C23C2×#41×C3111yescharacteristic
1164C23C31×H(5,𝔽2)11yescharacteristic
1165C23C31×H(5,𝔽2)11yescharacteristic
1166C23C31×H(5,𝔽2)11yescharacteristic
1167C23C31×H(5,𝔽2)11yescharacteristic
1168C23C31×H(5,𝔽2)11yescharacteristic
1169C23C31×H(5,𝔽2)11yescharacteristic
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—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×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×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C22—24no—
1255C22—24no—
1256C22—24no—
1257C22—24no—
1258C22—24no—
1259C22—24no—
1260C22—24no—
1261C22—24no—
1262C22—24no—
1263C22—464no—
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—42no—
1287C22—42no—
1288C22—42no—
1289C22—42no—
1290C22—42no—
1291C22—42no—
1292C22—42no—
1293C22—42no—
1294C22—42no—
1295C22—42no—
1296C22—42no—
1297C22—42no—
1298C22—42no—
1299C22—42no—
1300C22C2×C31×#12111yescharacteristic
1301C22C31×#52511yescharacteristic
1302C22C31×#52511yescharacteristic
1303C22C31×#52511yescharacteristic
1304C22C2×C31×#12411yescharacteristic
1305C22C2×C31×#12611yescharacteristic
1306C22C31×#53411yescharacteristic
1307C22C31×#53411yescharacteristic
1308C22C31×#53511yescharacteristic
1309C22C31×#53811yescharacteristic
1310C22C31×#53811yescharacteristic
1311C22C31×#53811yescharacteristic
1312C22C31×#53811yescharacteristic
1313C22C31×#53811yescharacteristic
1314C22C31×#53811yescharacteristic
1315C22D42×C3111yescharacteristic
1316C22D42×C3111yescharacteristic
1317C22C31×#54611yescharacteristic
1318C22C31×#54611yescharacteristic
1319C22C31×#54611yescharacteristic
1320C22C31×#54611yescharacteristic
1321C22C31×#54611yescharacteristic
1322C22C31×#54611yescharacteristic
1323C22C31×#54611yescharacteristic
1324C22C31×#54611yescharacteristic
1325C22C31×#55111yescharacteristic
1326C22C31×#55111yescharacteristic
1327C22C31×#55111yescharacteristic
1328C22C31×#55111yescharacteristic
1329C22C31×#55111yescharacteristic
1330C22C31×#55111yescharacteristic
1331C22C31×#55111yescharacteristic
1332C22C31×#55111yescharacteristic
1333C22C31×#56011yescharacteristic
1334C22C31×#56011yescharacteristic
1335C4—42no—
1336C4—42no—
1337C4—42no—
1338C4—42no—
1339C4—42no—
1340C4—42no—
1341C4—81no—
1342C4—81no—
1343C4—81no—
1344C4—81no—
1345C4—81no—
1346C4—81no—
1347C2—44no—
1348C2—44no—
1349C2—44no—
1350C2C31×#241111yescharacteristic
1351C2C31×#242411yescharacteristic
1352C2C31×#247211yescharacteristic
1353C2C31×#247211yescharacteristic
1354C2C31×#248011yescharacteristic
1355C2C31×#248011yescharacteristic
1356C2C31×#248011yescharacteristic
1357C2C31×#253411yescharacteristic
1358C2C31×#256111yescharacteristic
1359C2C31×#266811yescharacteristic
1360C2C31×#267811yescharacteristic
1361C2C31×#268511yescharacteristic
1362C2C31×#269711yescharacteristic
1363C2C31×#273511yescharacteristic
1364C2C31×#273511yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutator, Frattini, cosocleC24C24×C31
prime radicalC26×C31C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#397C2semidirect
2. C2×C31×#396C2semidirect
3. C2×C31×#388C2semidirect
7. C31×#1440C2semidirect
8. C31×#1440C2semidirect
9. C31×#1440C2semidirect
10. C31×#1439C2semidirect
11. C31×#1439C2semidirect
12. C31×#1439C2semidirect
13. C31×#1439C2semidirect
14. C31×#1437C2semidirect
15. C31×#1437C2semidirect
17. C22×C4⋊C4×C31C22semidirect
18. C22×C4⋊C4×C31C22semidirect
19. C22×C4⋊C4×C31C22semidirect
38. C22×C42×C31C22semidirect
45. C2×C31×#95C22semidirect
46. C2×C31×#95C22semidirect
47. C2×C31×#95C22semidirect
48. C2×C31×#95C22semidirect
49. C2×C31×#95C22semidirect
50. C2×C31×#95C22semidirect
51. C2×C31×#95C22semidirect
52. C2×C31×#95C22semidirect
53. C2×C31×#95C22semidirect
54. C2×C31×#95C22semidirect
55. C2×C31×#95C22semidirect
56. C2×C31×#95C22semidirect
352. #15297C31direct (N × H)
572. C2×#397C2×C31semidirect
573. C2×#396C2×C31semidirect
574. C2×#388C2×C31semidirect
578. #1440C2×C31semidirect
579. #1440C2×C31semidirect
580. #1440C2×C31semidirect
581. #1439C2×C31semidirect
582. #1439C2×C31semidirect
583. #1439C2×C31semidirect
584. #1439C2×C31semidirect
585. #1437C2×C31semidirect
586. #1437C2×C31semidirect
681. C22×C4⋊C4C22×C31semidirect
682. C22×C4⋊C4C22×C31semidirect
683. C22×C4⋊C4C22×C31semidirect
702. C22×C42C22×C31semidirect
709. C2×#95C22×C31semidirect
710. C2×#95C22×C31semidirect
711. C2×#95C22×C31semidirect
712. C2×#95C22×C31semidirect
713. C2×#95C22×C31semidirect
714. C2×#95C22×C31semidirect
715. C2×#95C22×C31semidirect
716. C2×#95C22×C31semidirect
717. C2×#95C22×C31semidirect
718. C2×#95C22×C31semidirect
719. C2×#95C22×C31semidirect
720. C2×#95C22×C31semidirect
847. C31#15297direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#3972
C2×C31×#3962
C2×C31×#3882
C2×C31×#3792
C31×#14402
C31×#14392
C31×#14372
#1529731