Finite Group Databasebeta

← C31×#15325 #21472084

Subgroups — C31×#15325 #21472084

Order 7936.

2226 conjugacy classes of subgroups.

The subgroup lattice has 1216 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×C31×#399C211yesmaximal, characteristic, complemented
3C2×C31×#396C211yesmaximal, characteristic, complemented
4C2×C31×#395C211yesmaximal, characteristic, complemented
5C2×C31×#393C211yesmaximal, characteristic, complemented
6C2×C31×#390C211yesmaximal, characteristic
7C2×C31×#386C211yesmaximal, characteristic
8C2×C31×#385C211yesmaximal, characteristic, complemented
9C31×#1444C211yesmaximal, characteristic, complemented
10C31×#1439C211yesmaximal, characteristic, complemented
11C31×#1439C211yesmaximal, characteristic, complemented
12C31×#1439C211yesmaximal, characteristic, complemented
13C31×#1438C211yesmaximal, characteristic
14C31×#1436C211yesmaximal, characteristic, complemented
15C31×C4⋊#95C211yesmaximal, characteristic, complemented
16C23×Q8×C31C2211yescharacteristic
17C23×D4×C31C2211yescharacteristic
18C24×C4×C31C2211yescharacteristic
19C2×C31×C22⋊Q8—24no—
20C2×C31×C22⋊Q8—24no—
21C2×C31×C22⋊Q8—24no—
22C22×C4⋊C4×C31C2211yescharacteristic
23C22×C4⋊C4×C31C2211yescharacteristic
24C22×C4⋊C4×C31C2211yescharacteristic
25C22×C4⋊C4×C31C2211yescharacteristic
26C22×C4⋊C4×C31C2211yescharacteristic
27C22×C4⋊C4×C31C2211yescharacteristic
28C22×C4⋊C4×C31C2211yescharacteristic
29C22×C4⋊C4×C31C2211yescharacteristic
30C22×C22⋊C4×C31C2211yescharacteristic
31C22×C22⋊C4×C31C2211yescharacteristic
32C22×C22⋊C4×C31C2211yescharacteristic
33C22×C22⋊C4×C31C2211yescharacteristic
34C22×C22⋊C4×C31C2211yescharacteristic
35C22×C22⋊C4×C31C2211yescharacteristic
36C22×C22⋊C4×C31C2211yescharacteristic
37C22×C22⋊C4×C31C2211yescharacteristic
38C22×C22⋊C4×C31C2211yescharacteristic
39C22×C22⋊C4×C31C2211yescharacteristic
40C22×C22⋊C4×C31C2211yescharacteristic
41C22×C42×C31C2211yescharacteristic
42C31×#399—24no—
43C31×#396—24no—
44C31×#395—24no—
45C31×#393—24no—
46C31×#390—24no—
47C31×#386—24no—
48C31×#385—24no—
49C2×C31×#95C2211yescharacteristic
50C2×C31×#95C2211yescharacteristic
51C2×C31×#95C2211yescharacteristic
52C2×C31×#95C2211yescharacteristic
53C2×C31×#95C2211yescharacteristic
54C2×C31×#95C2211yescharacteristic
55C2×C31×#95C2211yescharacteristic
56C2×C31×#95C2211yescharacteristic
57C2×C31×#95C2211yescharacteristic
58C2×C31×#95C2211yescharacteristic
59C2×C31×#95C2211yescharacteristic
60C2×C31×#95C2211yescharacteristic
61C25×C31C2311yescharacteristic
62C25×C31C2311yescharacteristic
63C22×Q8×C31—22no—
64C22×Q8×C31—22no—
65C22×Q8×C31—22no—
66C22×Q8×C31—22no—
67C22×Q8×C31—22no—
68C22×Q8×C31—41no—
69C22×Q8×C31—41no—
70C22×D4×C31—22no—
71C22×D4×C31—22no—
72C22×D4×C31—22no—
73C22×D4×C31—22no—
74C22×D4×C31—41no—
75C22×D4×C31—41no—
76C22×D4×C31Q814yescomplemented
77C23×C4×C31—22no—
78C23×C4×C31—22no—
79C23×C4×C31—22no—
80C23×C4×C31—22no—
81C23×C4×C31—22no—
82C23×C4×C31—41no—
83C23×C4×C31—41no—
84C23×C4×C31C2311yescharacteristic
85C23×C4×C31C2311yescharacteristic
86C23×C4×C31C2311yescharacteristic
87C23×C4×C31C2311yescharacteristic
88C23×C4×C31C2311yescharacteristic
89C23×C4×C31C2311yescharacteristic
90C23×C4×C31C2311yescharacteristic
91C23×C4×C31C2311yescharacteristic
92C23×C4×C31C2311yescharacteristic
93C23×C4×C31C2311yescharacteristic
94C23×C4×C31C2311yescharacteristic
95C23×C4×C31C2311yescharacteristic
96C23×C4×C31C2311yescharacteristic
97C31×C22⋊Q8—232no—
98C2×C4⋊C4×C31—22no—
99C2×C4⋊C4×C31—22no—
100C2×C4⋊C4×C31—22no—
101C2×C4⋊C4×C31—22no—
102C2×C4⋊C4×C31—22no—
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—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—41no—
117C2×C4⋊C4×C31—41no—
118C2×C4⋊C4×C31—41no—
119C2×C4⋊C4×C31—41no—
120C2×C4⋊C4×C31D414yescomplemented
121C2×C4⋊C4×C31D414yescomplemented
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—22no—
146C2×C22⋊C4×C31—22no—
147C2×C22⋊C4×C31—22no—
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×C31D414yes—
155C2×C42×C31—22no—
156C2×C42×C31—22no—
157C2×C42×C31—41no—
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—22no—
167C31×#95—41no—
168C31×#95D414yes—
169C31×#95D414yescomplemented
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×C31C2×D412yes—
197C24×C31C2×Q812yes—
198C24×C31C2×Q812yes—
199C24×C31#4112yes—
200C24×C31C2411yescharacteristic
201C2×Q8×C31—28no—
202C2×Q8×C31—44no—
203C2×Q8×C31—44no—
204C2×Q8×C31—44no—
205C2×Q8×C31—44no—
206C2×Q8×C31—44no—
207C2×Q8×C31—44no—
208C2×D4×C31—28no—
209C2×D4×C31—28no—
210C2×D4×C31—44no—
211C2×D4×C31—44no—
212C2×D4×C31—44no—
213C2×D4×C31—44no—
214C2×D4×C31—44no—
215C22×C4×C31—21no—
216C22×C4×C31—21no—
217C22×C4×C31—21no—
218C22×C4×C31—21no—
219C22×C4×C31—21no—
220C22×C4×C31—21no—
221C22×C4×C31—21no—
222C22×C4×C31—21no—
223C22×C4×C31—21no—
224C22×C4×C31—21no—
225C22×C4×C31—21no—
226C22×C4×C31—21no—
227C22×C4×C31—28no—
228C22×C4×C31—21no—
229C22×C4×C31—21no—
230C22×C4×C31—21no—
231C22×C4×C31—21no—
232C22×C4×C31—21no—
233C22×C4×C31—21no—
234C22×C4×C31—21no—
235C22×C4×C31—21no—
236C22×C4×C31—21no—
237C22×C4×C31—21no—
238C22×C4×C31—21no—
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—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—44no—
291C22×C4×C31—44no—
292C22×C4×C31—44no—
293C22×C4×C31—44no—
294C22×C4×C31—44no—
295C22×C4×C31—44no—
296C22×C4×C31C2×D412yes—
297C22×C4×C31C2×D412yes—
298C22×C4×C31C2×D412yes—
299C22×C4×C31C2×D412yes—
300C22×C4×C31C2×D412yes—
301C22×C4×C31C2×D412yes—
302C22×C4×C31C2×D412yes—
303C22×C4×C31C2×D412yes—
304C22×C4×C31C2×D412yes—
305C22×C4×C31C2×D412yes—
306C22×C4×C31C2×D412yes—
307C22×C4×C31C2×D412yes—
308C22×C4×C31C2×D412yes—
309C22×C4×C31C2×D412yes—
310C22×C4×C31C2×Q812yes—
311C22×C4×C31#4112yes—
312C22×C4×C31#4112yes—
313C4⋊C4×C31—28no—
314C4⋊C4×C31—28no—
315C4⋊C4×C31—28no—
316C4⋊C4×C31—44no—
317C4⋊C4×C31—44no—
318C4⋊C4×C31—44no—
319C4⋊C4×C31—44no—
320C4⋊C4×C31—44no—
321C22⋊C4×C31—28no—
322C22⋊C4×C31—28no—
323C22⋊C4×C31—28no—
324C22⋊C4×C31—44no—
325C22⋊C4×C31—44no—
326C22⋊C4×C31—44no—
327C22⋊C4×C31—44no—
328C22⋊C4×C31—44no—
329C22⋊C4×C31—44no—
330C22⋊C4×C31—44no—
331C22⋊C4×C31—44no—
332C42×C31—44no—
333#15325C3111yesmaximal, characteristic, direct product factor, Sylow
334C23×C31—22no—
335C23×C31—22no—
336C23×C31—22no—
337C23×C31—22no—
338C23×C31—22no—
339C23×C31—22no—
340C23×C31—22no—
341C23×C31—22no—
342C23×C31—22no—
343C23×C31—22no—
344C23×C31—22no—
345C23×C31—22no—
346C23×C31—22no—
347C23×C31—22no—
348C23×C31—22no—
349C23×C31—22no—
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—41no—
360C23×C31—41no—
361C23×C31—41no—
362C23×C31—41no—
363C23×C31—41no—
364C23×C31—41no—
365C23×C31—41no—
366C23×C31—41no—
367C23×C31—41no—
368C23×C31—41no—
369C23×C31—41no—
370C23×C31—41no—
371C23×C31—41no—
372C23×C31—41no—
373C23×C31—41no—
374C23×C31—41no—
375C23×C31—41no—
376C23×C31—41no—
377C23×C31—41no—
378C23×C31—41no—
379C23×C31—41no—
380C23×C31—41no—
381C23×C31—41no—
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×C31C22⋊Q814yes—
404C23×C31C22×D411yescharacteristic
405C23×C31C22×D411yescharacteristic
406C23×C31C22×D411yescharacteristic
407C23×C31C22×D411yescharacteristic
408C23×C31C22×D411yescharacteristic
409C23×C31C22×Q811yescharacteristic
410C23×C31C2×#4111yescharacteristic
411C23×C31C2×#4111yescharacteristic
412C23×C31C2×#4111yescharacteristic
413C23×C31H(5,𝔽2)11yescharacteristic
414C23×C31H(5,𝔽2)11yescharacteristic
415C23×C31H(5,𝔽2)11yescharacteristic
416C23×C312−1+411yescharacteristic
417C23×C312−1+411yescharacteristic
418C23×C312−1+411yescharacteristic
419Q8×C31—416no—
420D4×C31—416no—
421C2×C4×C31—22no—
422C2×C4×C31—22no—
423C2×C4×C31—22no—
424C2×C4×C31—22no—
425C2×C4×C31—22no—
426C2×C4×C31—22no—
427C2×C4×C31—22no—
428C2×C4×C31—22no—
429C2×C4×C31—22no—
430C2×C4×C31—22no—
431C2×C4×C31—22no—
432C2×C4×C31—22no—
433C2×C4×C31—22no—
434C2×C4×C31—22no—
435C2×C4×C31—22no—
436C2×C4×C31—22no—
437C2×C4×C31—22no—
438C2×C4×C31—22no—
439C2×C4×C31—22no—
440C2×C4×C31—22no—
441C2×C4×C31—22no—
442C2×C4×C31—22no—
443C2×C4×C31—22no—
444C2×C4×C31—22no—
445C2×C4×C31—22no—
446C2×C4×C31—22no—
447C2×C4×C31—22no—
448C2×C4×C31—22no—
449C2×C4×C31—22no—
450C2×C4×C31—22no—
451C2×C4×C31—22no—
452C2×C4×C31—22no—
453C2×C4×C31—22no—
454C2×C4×C31—22no—
455C2×C4×C31—22no—
456C2×C4×C31—22no—
457C2×C4×C31—22no—
458C2×C4×C31—22no—
459C2×C4×C31—22no—
460C2×C4×C31—22no—
461C2×C4×C31—22no—
462C2×C4×C31—22no—
463C2×C4×C31—416no—
464C2×C4×C31—41no—
465C2×C4×C31—41no—
466C2×C4×C31—41no—
467C2×C4×C31—41no—
468C2×C4×C31—41no—
469C2×C4×C31—41no—
470C2×C4×C31—41no—
471C2×C4×C31—41no—
472C2×C4×C31—41no—
473C2×C4×C31—41no—
474C2×C4×C31—41no—
475C2×C4×C31—41no—
476C2×C4×C31—41no—
477C2×C4×C31—41no—
478C2×C4×C31—41no—
479C2×C4×C31—41no—
480C2×C4×C31—41no—
481C2×C4×C31—41no—
482C2×C4×C31—41no—
483C2×C4×C31—41no—
484C2×C4×C31—41no—
485C2×C4×C31—41no—
486C2×C4×C31—41no—
487C2×C4×C31—41no—
488C2×C4×C31—41no—
489C2×C4×C31—41no—
490C2×C4×C31—41no—
491C2×C4×C31—41no—
492C2×C4×C31—41no—
493C2×C4×C31—41no—
494C2×C4×C31—41no—
495C2×C4×C31—41no—
496C2×C4×C31—41no—
497C2×C4×C31—41no—
498C2×C4×C31—41no—
499C2×C4×C31—41no—
500C2×C4×C31—41no—
501C2×C4×C31—41no—
502C2×C4×C31—41no—
503C2×C4×C31—41no—
504C2×C4×C31—41no—
505C2×C4×C31—41no—
506C2×C4×C31—41no—
507C2×C4×C31—41no—
508C2×C4×C31—41no—
509C2×C4×C31—41no—
510C2×C4×C31#12014yes—
511C2×C4×C31C22⋊Q814yescomplemented
512C2×C4×C31#12714yes—
513C22×C22⋊Q8C2×C3111yescharacteristic, complemented
514C2×#399C2×C3111yescharacteristic, complemented
515C2×#396C2×C3111yescharacteristic, complemented
516C2×#395C2×C3111yescharacteristic, complemented
517C2×#393C2×C3111yescharacteristic, complemented
518C2×#390C2×C3111yescharacteristic
519C2×#386C2×C3111yescharacteristic
520C2×#385C2×C3111yescharacteristic, complemented
521#1444C2×C3111yescharacteristic, complemented
522#1439C2×C3111yescharacteristic, complemented
523#1439C2×C3111yescharacteristic, complemented
524#1439C2×C3111yescharacteristic, complemented
525#1438C2×C3111yescharacteristic
526#1436C2×C3111yescharacteristic, complemented
527C4⋊#95C2×C3111yescharacteristic, complemented
528C22×C31—24no—
529C22×C31—24no—
530C22×C31—24no—
531C22×C31—42no—
532C22×C31—42no—
533C22×C31—42no—
534C22×C31—42no—
535C22×C31—42no—
536C22×C31—42no—
537C22×C31—42no—
538C22×C31—42no—
539C22×C31—42no—
540C22×C31—42no—
541C22×C31—42no—
542C22×C31—42no—
543C22×C31—42no—
544C22×C31—42no—
545C22×C31—42no—
546C22×C31—42no—
547C22×C31—42no—
548C22×C31—42no—
549C22×C31—42no—
550C22×C31—81no—
551C22×C31—81no—
552C22×C31—81no—
553C22×C31—81no—
554C22×C31—81no—
555C22×C31—81no—
556C22×C31—81no—
557C22×C31—81no—
558C22×C31C2×#12011yescharacteristic
559C22×C31C2×C22⋊Q811yescharacteristic
560C22×C31C2×C22⋊Q811yescharacteristic
561C22×C31#52511yescharacteristic
562C22×C31C2×#12711yescharacteristic
563C22×C31#53211yescharacteristic
564C22×C31#53511yescharacteristic
565C22×C31#53611yescharacteristic
566C22×C31#53611yescharacteristic
567C22×C31#53711yescharacteristic
568C22×C31#53711yescharacteristic
569C22×C31#53911yescharacteristic
570C22×C31#54211yescharacteristic
571C22×C31#54211yescharacteristic
572C22×C31#54311yescharacteristic
573C22×C31D4211yescharacteristic
574C22×C31D4211yescharacteristic
575C22×C31D4211yescharacteristic
576C22×C31D4211yescharacteristic
577C22×C31#54611yescharacteristic
578C22×C31#54611yescharacteristic
579C22×C31#54611yescharacteristic
580C22×C31#54711yescharacteristic
581C22×C31#54711yescharacteristic
582C22×C31#54711yescharacteristic
583C22×C31#54811yescharacteristic
584C22×C31#54811yescharacteristic
585C22×C31#54811yescharacteristic
586C22×C31D4×Q811yescharacteristic
587C22×C31D4×Q811yescharacteristic
588C22×C31D4×Q811yescharacteristic
589C22×C31#55111yescharacteristic
590C22×C31#55411yescharacteristic
591C22×C31#56211yescharacteristic
592C22×C31#56311yescharacteristic
593C4×C31—24no—
594C4×C31—24no—
595C4×C31—24no—
596C4×C31—42no—
597C4×C31—42no—
598C4×C31—42no—
599C4×C31—42no—
600C4×C31—42no—
601C4×C31—42no—
602C4×C31—42no—
603C4×C31—42no—
604C4×C31—81no—
605C4×C31—81no—
606C23×Q8C22×C3111yescharacteristic
607C23×D4C22×C3111yescharacteristic
608C24×C4C22×C3111yescharacteristic
609C2×C22⋊Q8—24no—
610C2×C22⋊Q8—24no—
611C2×C22⋊Q8—24no—
612C22×C4⋊C4C22×C3111yescharacteristic
613C22×C4⋊C4C22×C3111yescharacteristic
614C22×C4⋊C4C22×C3111yescharacteristic
615C22×C4⋊C4C22×C3111yescharacteristic
616C22×C4⋊C4C22×C3111yescharacteristic
617C22×C4⋊C4C22×C3111yescharacteristic
618C22×C4⋊C4C22×C3111yescharacteristic
619C22×C4⋊C4C22×C3111yescharacteristic
620C22×C22⋊C4C22×C3111yescharacteristic
621C22×C22⋊C4C22×C3111yescharacteristic
622C22×C22⋊C4C22×C3111yescharacteristic
623C22×C22⋊C4C22×C3111yescharacteristic
624C22×C22⋊C4C22×C3111yescharacteristic
625C22×C22⋊C4C22×C3111yescharacteristic
626C22×C22⋊C4C22×C3111yescharacteristic
627C22×C22⋊C4C22×C3111yescharacteristic
628C22×C22⋊C4C22×C3111yescharacteristic
629C22×C22⋊C4C22×C3111yescharacteristic
630C22×C22⋊C4C22×C3111yescharacteristic
631C22×C42C22×C3111yescharacteristic
632#399—24no—
633#396—24no—
634#395—24no—
635#393—24no—
636#390—24no—
637#386—24no—
638#385—24no—
639C2×#95C22×C3111yescharacteristic
640C2×#95C22×C3111yescharacteristic
641C2×#95C22×C3111yescharacteristic
642C2×#95C22×C3111yescharacteristic
643C2×#95C22×C3111yescharacteristic
644C2×#95C22×C3111yescharacteristic
645C2×#95C22×C3111yescharacteristic
646C2×#95C22×C3111yescharacteristic
647C2×#95C22×C3111yescharacteristic
648C2×#95C22×C3111yescharacteristic
649C2×#95C22×C3111yescharacteristic
650C2×#95C22×C3111yescharacteristic
651C2×C31—44no—
652C2×C31—82no—
653C2×C31#240911yescharacteristic
654C2×C31#243011yescharacteristic
655C2×C31#243311yescharacteristic
656C2×C31#243711yescharacteristic
657C2×C31#244911yescharacteristic
658C2×C31#245211yescharacteristic
659C2×C31#246111yescharacteristic
660C2×C31#254011yescharacteristic
661C2×C31#254211yescharacteristic
662C2×C31#267211yescharacteristic
663C2×C31#267411yescharacteristic
664C2×C31#268111yescharacteristic
665C2×C31#268311yescharacteristic
666C2×C31#269211yescharacteristic
667C2×C31#272311yescharacteristic
668C25C23×C3111yescharacteristic
669C25C23×C3111yescharacteristic
670C22×Q8—22no—
671C22×Q8—22no—
672C22×Q8—22no—
673C22×Q8—22no—
674C22×Q8—22no—
675C22×Q8—41no—
676C22×Q8—41no—
677C22×D4—22no—
678C22×D4—22no—
679C22×D4—22no—
680C22×D4—22no—
681C22×D4—41no—
682C22×D4—41no—
683C22×D4Q8×C3114yescomplemented
684C23×C4—22no—
685C23×C4—22no—
686C23×C4—22no—
687C23×C4—22no—
688C23×C4—22no—
689C23×C4—41no—
690C23×C4—41no—
691C23×C4C23×C3111yescharacteristic
692C23×C4C23×C3111yescharacteristic
693C23×C4C23×C3111yescharacteristic
694C23×C4C23×C3111yescharacteristic
695C23×C4C23×C3111yescharacteristic
696C23×C4C23×C3111yescharacteristic
697C23×C4C23×C3111yescharacteristic
698C23×C4C23×C3111yescharacteristic
699C23×C4C23×C3111yescharacteristic
700C23×C4C23×C3111yescharacteristic
701C23×C4C23×C3111yescharacteristic
702C23×C4C23×C3111yescharacteristic
703C23×C4C23×C3111yescharacteristic
704C22⋊Q8—232no—
705C2×C4⋊C4—22no—
706C2×C4⋊C4—22no—
707C2×C4⋊C4—22no—
708C2×C4⋊C4—22no—
709C2×C4⋊C4—22no—
710C2×C4⋊C4—22no—
711C2×C4⋊C4—22no—
712C2×C4⋊C4—22no—
713C2×C4⋊C4—22no—
714C2×C4⋊C4—22no—
715C2×C4⋊C4—22no—
716C2×C4⋊C4—22no—
717C2×C4⋊C4—22no—
718C2×C4⋊C4—22no—
719C2×C4⋊C4—22no—
720C2×C4⋊C4—22no—
721C2×C4⋊C4—22no—
722C2×C4⋊C4—22no—
723C2×C4⋊C4—41no—
724C2×C4⋊C4—41no—
725C2×C4⋊C4—41no—
726C2×C4⋊C4—41no—
727C2×C4⋊C4D4×C3114yescomplemented
728C2×C4⋊C4D4×C3114yescomplemented
729C2×C22⋊C4—22no—
730C2×C22⋊C4—22no—
731C2×C22⋊C4—22no—
732C2×C22⋊C4—22no—
733C2×C22⋊C4—22no—
734C2×C22⋊C4—22no—
735C2×C22⋊C4—22no—
736C2×C22⋊C4—22no—
737C2×C22⋊C4—22no—
738C2×C22⋊C4—22no—
739C2×C22⋊C4—22no—
740C2×C22⋊C4—22no—
741C2×C22⋊C4—22no—
742C2×C22⋊C4—22no—
743C2×C22⋊C4—22no—
744C2×C22⋊C4—22no—
745C2×C22⋊C4—22no—
746C2×C22⋊C4—22no—
747C2×C22⋊C4—22no—
748C2×C22⋊C4—22no—
749C2×C22⋊C4—22no—
750C2×C22⋊C4—22no—
751C2×C22⋊C4—22no—
752C2×C22⋊C4—22no—
753C2×C22⋊C4—22no—
754C2×C22⋊C4—22no—
755C2×C22⋊C4—41no—
756C2×C22⋊C4—41no—
757C2×C22⋊C4—41no—
758C2×C22⋊C4—41no—
759C2×C22⋊C4—41no—
760C2×C22⋊C4—41no—
761C2×C22⋊C4D4×C3114yes—
762C2×C42—22no—
763C2×C42—22no—
764C2×C42—41no—
765#95—22no—
766#95—22no—
767#95—22no—
768#95—22no—
769#95—22no—
770#95—22no—
771#95—22no—
772#95—22no—
773#95—22no—
774#95—41no—
775#95D4×C3114yes—
776#95D4×C3114yescomplemented
777C31#1532511yescharacteristic, direct product factor, Sylow
778C24—21no—
779C24—21no—
780C24—21no—
781C24—21no—
782C24—21no—
783C24—21no—
784C24—21no—
785C24—21no—
786C24—21no—
787C24—21no—
788C24—21no—
789C24—21no—
790C24—21no—
791C24—21no—
792C24—21no—
793C24—21no—
794C24—21no—
795C24—21no—
796C24—21no—
797C24—21no—
798C24—21no—
799C24—21no—
800C24—21no—
801C24—21no—
802C24—21no—
803C24—21no—
804C24C2×D4×C3112yes—
805C24C2×Q8×C3112yes—
806C24C2×Q8×C3112yes—
807C24#41×C3112yes—
808C24C24×C3111yescharacteristic
809C2×Q8—28no—
810C2×Q8—44no—
811C2×Q8—44no—
812C2×Q8—44no—
813C2×Q8—44no—
814C2×Q8—44no—
815C2×Q8—44no—
816C2×D4—28no—
817C2×D4—28no—
818C2×D4—44no—
819C2×D4—44no—
820C2×D4—44no—
821C2×D4—44no—
822C2×D4—44no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—28no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—44no—
899C22×C4—44no—
900C22×C4—44no—
901C22×C4—44no—
902C22×C4—44no—
903C22×C4—44no—
904C22×C4C2×D4×C3112yes—
905C22×C4C2×D4×C3112yes—
906C22×C4C2×D4×C3112yes—
907C22×C4C2×D4×C3112yes—
908C22×C4C2×D4×C3112yes—
909C22×C4C2×D4×C3112yes—
910C22×C4C2×D4×C3112yes—
911C22×C4C2×D4×C3112yes—
912C22×C4C2×D4×C3112yes—
913C22×C4C2×D4×C3112yes—
914C22×C4C2×D4×C3112yes—
915C22×C4C2×D4×C3112yes—
916C22×C4C2×D4×C3112yes—
917C22×C4C2×D4×C3112yes—
918C22×C4C2×Q8×C3112yes—
919C22×C4#41×C3112yes—
920C22×C4#41×C3112yes—
921C4⋊C4—28no—
922C4⋊C4—28no—
923C4⋊C4—28no—
924C4⋊C4—44no—
925C4⋊C4—44no—
926C4⋊C4—44no—
927C4⋊C4—44no—
928C4⋊C4—44no—
929C22⋊C4—28no—
930C22⋊C4—28no—
931C22⋊C4—28no—
932C22⋊C4—44no—
933C22⋊C4—44no—
934C22⋊C4—44no—
935C22⋊C4—44no—
936C22⋊C4—44no—
937C22⋊C4—44no—
938C22⋊C4—44no—
939C22⋊C4—44no—
940C42—44no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—22no—
948C23—22no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—22no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23—41no—
981C23—41no—
982C23—41no—
983C23—41no—
984C23—41no—
985C23—41no—
986C23—41no—
987C23—41no—
988C23—41no—
989C23—41no—
990C23—41no—
991C23—41no—
992C23—41no—
993C23—41no—
994C23—41no—
995C23—41no—
996C23—41no—
997C23—41no—
998C23—41no—
999C23—41no—
1000C23—41no—
1001C23—41no—
1002C23—41no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23C31×C22⋊Q814yes—
1011C23C22×D4×C3111yescharacteristic
1012C23C22×D4×C3111yescharacteristic
1013C23C22×D4×C3111yescharacteristic
1014C23C22×D4×C3111yescharacteristic
1015C23C22×D4×C3111yescharacteristic
1016C23C22×Q8×C3111yescharacteristic
1017C23C2×#41×C3111yescharacteristic
1018C23C2×#41×C3111yescharacteristic
1019C23C2×#41×C3111yescharacteristic
1020C23C31×H(5,𝔽2)11yescharacteristic
1021C23C31×H(5,𝔽2)11yescharacteristic
1022C23C31×H(5,𝔽2)11yescharacteristic
1023C23C31×2−1+411yescharacteristic
1024C23C31×2−1+411yescharacteristic
1025C23C31×2−1+411yescharacteristic
1026Q8—416no—
1027D4—416no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—416no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—41no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4C31×#12014yes—
1118C2×C4C31×C22⋊Q814yescomplemented
1119C2×C4C31×#12714yes—
1120C22—24no—
1121C22—24no—
1122C22—24no—
1123C22—42no—
1124C22—42no—
1125C22—42no—
1126C22—42no—
1127C22—42no—
1128C22—42no—
1129C22—42no—
1130C22—42no—
1131C22—42no—
1132C22—42no—
1133C22—42no—
1134C22—42no—
1135C22—42no—
1136C22—42no—
1137C22—42no—
1138C22—42no—
1139C22—42no—
1140C22—42no—
1141C22—42no—
1142C22—81no—
1143C22—81no—
1144C22—81no—
1145C22—81no—
1146C22—81no—
1147C22—81no—
1148C22—81no—
1149C22—81no—
1150C22C2×C31×#12011yescharacteristic
1151C22C2×C31×C22⋊Q811yescharacteristic
1152C22C2×C31×C22⋊Q811yescharacteristic
1153C22C31×#52511yescharacteristic
1154C22C2×C31×#12711yescharacteristic
1155C22C31×#53211yescharacteristic
1156C22C31×#53511yescharacteristic
1157C22C31×#53611yescharacteristic
1158C22C31×#53611yescharacteristic
1159C22C31×#53711yescharacteristic
1160C22C31×#53711yescharacteristic
1161C22C31×#53911yescharacteristic
1162C22C31×#54211yescharacteristic
1163C22C31×#54211yescharacteristic
1164C22C31×#54311yescharacteristic
1165C22D42×C3111yescharacteristic
1166C22D42×C3111yescharacteristic
1167C22D42×C3111yescharacteristic
1168C22D42×C3111yescharacteristic
1169C22C31×#54611yescharacteristic
1170C22C31×#54611yescharacteristic
1171C22C31×#54611yescharacteristic
1172C22C31×#54711yescharacteristic
1173C22C31×#54711yescharacteristic
1174C22C31×#54711yescharacteristic
1175C22C31×#54811yescharacteristic
1176C22C31×#54811yescharacteristic
1177C22C31×#54811yescharacteristic
1178C22D4×Q8×C3111yescharacteristic
1179C22D4×Q8×C3111yescharacteristic
1180C22D4×Q8×C3111yescharacteristic
1181C22C31×#55111yescharacteristic
1182C22C31×#55411yescharacteristic
1183C22C31×#56211yescharacteristic
1184C22C31×#56311yescharacteristic
1185C4—24no—
1186C4—24no—
1187C4—24no—
1188C4—42no—
1189C4—42no—
1190C4—42no—
1191C4—42no—
1192C4—42no—
1193C4—42no—
1194C4—42no—
1195C4—42no—
1196C4—81no—
1197C4—81no—
1198C2—44no—
1199C2—82no—
1200C2C31×#240911yescharacteristic
1201C2C31×#243011yescharacteristic
1202C2C31×#243311yescharacteristic
1203C2C31×#243711yescharacteristic
1204C2C31×#244911yescharacteristic
1205C2C31×#245211yescharacteristic
1206C2C31×#246111yescharacteristic
1207C2C31×#254011yescharacteristic
1208C2C31×#254211yescharacteristic
1209C2C31×#267211yescharacteristic
1210C2C31×#267411yescharacteristic
1211C2C31×#268111yescharacteristic
1212C2C31×#268311yescharacteristic
1213C2C31×#269211yescharacteristic
1214C2C31×#272311yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutator, Frattini, cosocleC24C24×C31
prime radicalC23×D4×C31C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C31×C22⋊Q8C2semidirect
2. C2×C31×#399C2semidirect
3. C2×C31×#396C2semidirect
4. C2×C31×#395C2semidirect
5. C2×C31×#393C2semidirect
8. C2×C31×#385C2semidirect
9. C31×#1444C2semidirect
10. C31×#1439C2semidirect
11. C31×#1439C2semidirect
12. C31×#1439C2semidirect
14. C31×#1436C2semidirect
15. C31×C4⋊#95C2semidirect
76. C22×D4×C31Q8semidirect
120. C2×C4⋊C4×C31D4semidirect
121. C2×C4⋊C4×C31D4semidirect
169. C31×#95D4semidirect
333. #15325C31direct (N × H)
511. C2×C4×C31C22⋊Q8semidirect
513. C22×C22⋊Q8C2×C31semidirect
514. C2×#399C2×C31semidirect
515. C2×#396C2×C31semidirect
516. C2×#395C2×C31semidirect
517. C2×#393C2×C31semidirect
520. C2×#385C2×C31semidirect
521. #1444C2×C31semidirect
522. #1439C2×C31semidirect
523. #1439C2×C31semidirect
524. #1439C2×C31semidirect
526. #1436C2×C31semidirect
527. C4⋊#95C2×C31semidirect
683. C22×D4Q8×C31semidirect
727. C2×C4⋊C4D4×C31semidirect
728. C2×C4⋊C4D4×C31semidirect
776. #95D4×C31semidirect
777. C31#15325direct (N × H)
1118. C2×C4C31×C22⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C22×C31×C22⋊Q82
C2×C31×#3992
C2×C31×#3962
C2×C31×#3952
C2×C31×#3932
C2×C31×#3902
C2×C31×#3862
C2×C31×#3852
C31×#14442
C31×#14392
C31×#14382
C31×#14362
C31×C4⋊#952
#1532531