Finite Group Databasebeta

← C31×#18414 #21475173

Subgroups — C31×#18414 #21475173

Order 7936.

1042 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#3534C211yesmaximal, characteristic, complemented
2C31×#3194C211yesmaximal, characteristic, complemented
3C31×#3186C211yesmaximal, characteristic, complemented
4C31×#2661C211yesmaximal, characteristic, complemented
5C31×#1612C211yesmaximal, characteristic, complemented
6C31×#1610C211yesmaximal, characteristic, complemented
7C31×#1609C211yesmaximal, characteristic, complemented
8C31×#1607C211yesmaximal, characteristic, complemented
9C31×#1600C211yesmaximal, characteristic, complemented
10C31×#1598C211yesmaximal, characteristic, complemented
11C31×#1597C211yesmaximal, characteristic, complemented
12C31×#1595C211yesmaximal, characteristic, complemented
13C31×#1507C211yesmaximal, characteristic, complemented
14C31×#1501C211yesmaximal, characteristic, complemented
15C31×#1468C211yesmaximal, characteristic, complemented
16C31×#562—21no—
17C31×#560—21no—
18C31×#553—21no—
19C31×#551—21no—
20C31×#546—21no—
21C31×#546—21no—
22C31×#546—21no—
23D42×C31—21no—
24C31×#540—21no—
25C31×#539—21no—
26C31×#539C2211yescharacteristic
27C31×#538—21no—
28C31×#538C2211yescharacteristic
29C31×#537C2211yescharacteristic
30C31×#534—21no—
31C31×#534C2211yescharacteristic
32C31×#525C2211yescharacteristic
33C2×C31×#123C2211yescharacteristic
34C2×C31×#121C2211yescharacteristic
35C2×C31×#121C2211yescharacteristic, complemented
36C31×#483C2211yescharacteristic, complemented
37C31×#482—21no—
38C31×#480—21no—
39C31×#480C2211yescharacteristic
40C31×#480C2211yescharacteristic, complemented
41C31×#480C2211yescharacteristic, complemented
42C31×#469—21no—
43C31×#468—21no—
44C31×#466—21no—
45C31×#466—21no—
46C31×#450C2211yescharacteristic, complemented
47C31×#449—21no—
48C31×#447—21no—
49C31×#447C2211yescharacteristic
50C31×#447C2211yescharacteristic, complemented
51C31×#447C2211yescharacteristic, complemented
52C31×#407C2211yescharacteristic, complemented
53C2×C31×C22⋊C8C2211yescharacteristic, complemented
54C31×#398C2211yescharacteristic, complemented
55C31×#397C2211yescharacteristic, complemented
56C31×#394—21no—
57C31×#394C2211yescharacteristic, complemented
58C31×#392—21no—
59C31×#392C2211yescharacteristic, complemented
60C31×#390—21no—
61C31×#388—21no—
62C4×C22⋊C4×C31C2211yescharacteristic, complemented
63C31×#328C2211yescharacteristic, complemented
64C31×#328C2211yescharacteristic, complemented
65C31×#327C2211yescharacteristic
66C31×#327C2211yescharacteristic
67C31×#327C2211yescharacteristic, complemented
68C31×#327C2211yescharacteristic, complemented
69C31×#327C2211yescharacteristic, complemented
70C31×#327C2211yescharacteristic, complemented
71C31×#324C2211yescharacteristic, complemented
72C31×#324C2211yescharacteristic, complemented
73C31×#323C2211yescharacteristic, complemented
74C31×#323C2211yescharacteristic, complemented
75C2×#41×C31—21no—
76C2×#41×C31D411yescharacteristic, complemented
77C22×D4×C31—21no—
78C22×D4×C31—21no—
79C22×D4×C31—21no—
80C22×D4×C31—21no—
81C22×D4×C31—21no—
82C22×D4×C31D411yescharacteristic
83C22×D4×C31D411yescharacteristic, complemented
84C22×D4×C31C2311yescharacteristic
85C23×C4×C31C2311yescharacteristic
86C2×SD16×C31—21no—
87C2×D8×C31—21no—
88C2×D8×C31—21no—
89C2×D8×C31—21no—
90C2×M16×C31—21no—
91C22×C8×C31—21no—
92C31×#127—21no—
93C31×#126—21no—
94C31×#126—21no—
95C31×#126—21no—
96C31×#126—21no—
97C31×#125—21no—
98C31×#125—21no—
99C31×#124—21no—
100C31×#124—21no—
101C31×#124—21no—
102C31×#123—21no—
103C31×#123—21no—
104C31×#123—21no—
105C31×#123—21no—
106C31×#123—21no—
107C31×#123—21no—
108C31×#123—21no—
109C31×#123—21no—
110C31×#123—21no—
111C31×#123—21no—
112C31×#123—21no—
113C31×#123—21no—
114C31×#123—21no—
115C31×#123—21no—
116C31×C22⋊Q8—21no—
117C31×C22⋊Q8—21no—
118C31×C22⋊Q8—21no—
119C31×C22⋊Q8—21no—
120C31×C22⋊Q8—21no—
121C31×C22⋊Q8D411yescharacteristic, complemented
122C31×C22⋊Q8C2311yescharacteristic
123C31×#121—21no—
124C31×#121—21no—
125C31×#121—21no—
126C31×#121—21no—
127C31×#121—21no—
128C31×#121—21no—
129C31×#121—21no—
130C31×#121—21no—
131C31×#121—21no—
132C31×#121—21no—
133C31×#121—21no—
134C31×#121—21no—
135C31×#121—21no—
136C31×#121—21no—
137C31×#121—21no—
138C31×#121—21no—
139C31×#121—21no—
140C31×#121—21no—
141C31×#121—21no—
142C31×#121D411yescharacteristic, complemented
143C31×#121D411yescharacteristic, complemented
144C31×#121D411yescharacteristic, complemented
145C31×#121C2311yescharacteristic
146C31×#121C2311yescharacteristic
147C31×#121C2311yescharacteristic
148C31×#120—21no—
149C31×#120—21no—
150C31×#120—21no—
151C31×#120—21no—
152C31×#120—21no—
153C31×#120—21no—
154C31×#120—21no—
155C31×#120—21no—
156C4×D4×C31—21no—
157C4×D4×C31—21no—
158C4×D4×C31—21no—
159C4×D4×C31—21no—
160C4×D4×C31—21no—
161C4×D4×C31—21no—
162C4×D4×C31—21no—
163C4×D4×C31—21no—
164C31×#117—21no—
165C31×#117D411yescharacteristic, complemented
166C2×C4⋊C4×C31—21no—
167C2×C4⋊C4×C31D411yescharacteristic
168C2×C4⋊C4×C31D411yescharacteristic, complemented
169C2×C4⋊C4×C31C2311yescharacteristic
170C2×C4⋊C4×C31C2311yescharacteristic
171C2×C22⋊C4×C31—21no—
172C2×C22⋊C4×C31—21no—
173C2×C22⋊C4×C31—21no—
174C2×C22⋊C4×C31—21no—
175C2×C22⋊C4×C31—21no—
176C2×C22⋊C4×C31—21no—
177C2×C22⋊C4×C31—21no—
178C2×C22⋊C4×C31—21no—
179C2×C22⋊C4×C31—21no—
180C2×C22⋊C4×C31D411yescharacteristic
181C2×C22⋊C4×C31D411yescharacteristic
182C2×C22⋊C4×C31C2311yescharacteristic
183C2×C42×C31—21no—
184C31×#107—21no—
185C31×#107—21no—
186C31×#107—21no—
187C31×#106—21no—
188C31×#103—21no—
189C31×#102—21no—
190C31×#102—21no—
191C31×#102—21no—
192C31×#102—21no—
193C31×#102—21no—
194C31×#102—21no—
195C31×#102—21no—
196C31×C22⋊C8—21no—
197C31×C22⋊C8—21no—
198C31×C22⋊C8C2311yescharacteristic
199C31×C22⋊C8C2311yescharacteristic
200C31×C22⋊C8C2311yescharacteristic
201C31×C22⋊C8C2311yescharacteristic
202C31×#95—21no—
203C31×#95—21no—
204C31×#95C2311yescharacteristic
205C31×#95C2311yescharacteristic
206C24×C31—21no—
207C24×C31—21no—
208C24×C31—21no—
209C24×C31C2×D411yescharacteristic
210C24×C31C2×D411yescharacteristic
211#41×C31—81no—
212#41×C31—81no—
213#41×C31—81no—
214C2×Q8×C31—21no—
215C2×Q8×C31C2×D411yescharacteristic
216C2×D4×C31—21no—
217C2×D4×C31—21no—
218C2×D4×C31—21no—
219C2×D4×C31—21no—
220C2×D4×C31—21no—
221C2×D4×C31—21no—
222C2×D4×C31—21no—
223C2×D4×C31—21no—
224C2×D4×C31—21no—
225C2×D4×C31—21no—
226C2×D4×C31—21no—
227C2×D4×C31—21no—
228C2×D4×C31—21no—
229C2×D4×C31—21no—
230C2×D4×C31—21no—
231C2×D4×C31—21no—
232C2×D4×C31—21no—
233C2×D4×C31—21no—
234C2×D4×C31—21no—
235C2×D4×C31—42no—
236C2×D4×C31—41no—
237C2×D4×C31—41no—
238C2×D4×C31—81no—
239C2×D4×C31—81no—
240C2×D4×C31—81no—
241C2×D4×C31—81no—
242C2×D4×C31—81no—
243C2×D4×C31—81no—
244C2×D4×C31—81no—
245C2×D4×C31—81no—
246C2×D4×C31—81no—
247C2×D4×C31—81no—
248C2×D4×C31—81no—
249C2×D4×C31—82no—
250C2×D4×C31C2×D411yescharacteristic
251C2×D4×C31C2×D411yescharacteristic
252C2×D4×C31C2×D411yescharacteristic
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—81no—
264C22×C4×C31C2×D411yescharacteristic
265C22×C4×C31C2×D411yescharacteristic
266C22×C4×C31C2×D411yescharacteristic
267C22×C4×C31C2×D411yescharacteristic
268C22×C4×C31C2×D411yescharacteristic
269C22×C4×C31C2×D411yescharacteristic
270C22×C4×C31C2×D411yescharacteristic
271C22×C4×C31C2×D411yescharacteristic
272C22×C4×C31C2411yescharacteristic
273SD16×C31—81no—
274D8×C31—81no—
275D8×C31—81no—
276D8×C31—81no—
277M16×C31—81no—
278C2×C8×C31—21no—
279C2×C8×C31—21no—
280C2×C8×C31—21no—
281C2×C8×C31—21no—
282C2×C8×C31—81no—
283C4⋊C4×C31—21no—
284C4⋊C4×C31—21no—
285C4⋊C4×C31—21no—
286C4⋊C4×C31—21no—
287C4⋊C4×C31—21no—
288C4⋊C4×C31—21no—
289C4⋊C4×C31—21no—
290C4⋊C4×C31—21no—
291C4⋊C4×C31—21no—
292C4⋊C4×C31—21no—
293C4⋊C4×C31—21no—
294C4⋊C4×C31—21no—
295C4⋊C4×C31—21no—
296C4⋊C4×C31—21no—
297C4⋊C4×C31—21no—
298C4⋊C4×C31—81no—
299C4⋊C4×C31C2×D411yescharacteristic
300C4⋊C4×C31C2×D411yescharacteristic
301C4⋊C4×C31C2×D411yescharacteristic
302C4⋊C4×C31C2×D411yescharacteristic
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×C31—21no—
325C22⋊C4×C31—21no—
326C22⋊C4×C31—21no—
327C22⋊C4×C31—21no—
328C22⋊C4×C31—42no—
329C22⋊C4×C31—42no—
330C22⋊C4×C31—41no—
331C22⋊C4×C31—41no—
332C22⋊C4×C31—81no—
333C22⋊C4×C31—81no—
334C22⋊C4×C31—81no—
335C42×C31—21no—
336C42×C31—21no—
337C42×C31—21no—
338C42×C31—81no—
339#18414C3111yesmaximal, characteristic, direct product factor, Sylow
340C23×C31—21no—
341C23×C31—21no—
342C23×C31—21no—
343C23×C31—21no—
344C23×C31—21no—
345C23×C31—21no—
346C23×C31—21no—
347C23×C31—21no—
348C23×C31—41no—
349C23×C31—41no—
350C23×C31—42no—
351C23×C31—41no—
352C23×C31—41no—
353C23×C31—41no—
354C23×C31—41no—
355C23×C31—41no—
356C23×C31—41no—
357C23×C31—41no—
358C23×C31—41no—
359C23×C31—41no—
360C23×C31—81no—
361C23×C31—81no—
362C23×C31—81no—
363C23×C31—81no—
364C23×C31—81no—
365C23×C31#12011yescharacteristic
366C23×C31#12011yescharacteristic
367C23×C31C22×D411yescharacteristic
368Q8×C31—41no—
369Q8×C31—81no—
370D4×C31—41no—
371D4×C31—41no—
372D4×C31—41no—
373D4×C31—41no—
374D4×C31—41no—
375D4×C31—41no—
376D4×C31—41no—
377D4×C31—42no—
378D4×C31—42no—
379D4×C31—41no—
380D4×C31—41no—
381D4×C31—41no—
382D4×C31—41no—
383D4×C31—41no—
384D4×C31—41no—
385D4×C31—81no—
386D4×C31—81no—
387D4×C31—81no—
388D4×C31—81no—
389D4×C31—81no—
390D4×C31—81no—
391D4×C31—81no—
392D4×C31—81no—
393D4×C31—81no—
394D4×C31—81no—
395D4×C31—81no—
396D4×C31—81no—
397D4×C31—84no—
398D4×C31—82no—
399D4×C31—82no—
400C2×C4×C31—22no—
401C2×C4×C31—21no—
402C2×C4×C31—21no—
403C2×C4×C31—21no—
404C2×C4×C31—21no—
405C2×C4×C31—21no—
406C2×C4×C31—21no—
407C2×C4×C31—21no—
408C2×C4×C31—21no—
409C2×C4×C31—21no—
410C2×C4×C31—21no—
411C2×C4×C31—41no—
412C2×C4×C31—41no—
413C2×C4×C31—41no—
414C2×C4×C31—41no—
415C2×C4×C31—41no—
416C2×C4×C31—41no—
417C2×C4×C31—41no—
418C2×C4×C31—41no—
419C2×C4×C31—41no—
420C2×C4×C31—41no—
421C2×C4×C31—41no—
422C2×C4×C31—41no—
423C2×C4×C31—41no—
424C2×C4×C31—41no—
425C2×C4×C31—41no—
426C2×C4×C31—41no—
427C2×C4×C31—81no—
428C2×C4×C31—81no—
429C2×C4×C31—81no—
430C2×C4×C31—81no—
431C2×C4×C31—81no—
432C2×C4×C31—81no—
433C2×C4×C31—81no—
434C2×C4×C31#12011yescharacteristic
435C2×C4×C31#12011yescharacteristic
436C2×C4×C31C22×D411yescharacteristic
437C2×C4×C31C22×D411yescharacteristic
438C8×C31—41no—
439C8×C31—41no—
440C8×C31—41no—
441C8×C31—41no—
442#3534C2×C3111yescharacteristic, complemented
443#3194C2×C3111yescharacteristic, complemented
444#3186C2×C3111yescharacteristic, complemented
445#2661C2×C3111yescharacteristic, complemented
446#1612C2×C3111yescharacteristic, complemented
447#1610C2×C3111yescharacteristic, complemented
448#1609C2×C3111yescharacteristic, complemented
449#1607C2×C3111yescharacteristic, complemented
450#1600C2×C3111yescharacteristic, complemented
451#1598C2×C3111yescharacteristic, complemented
452#1597C2×C3111yescharacteristic, complemented
453#1595C2×C3111yescharacteristic, complemented
454#1507C2×C3111yescharacteristic, complemented
455#1501C2×C3111yescharacteristic, complemented
456#1468C2×C3111yescharacteristic, complemented
457C22×C31—21no—
458C22×C31—21no—
459C22×C31—21no—
460C22×C31—21no—
461C22×C31—21no—
462C22×C31—21no—
463C22×C31—21no—
464C22×C31—21no—
465C22×C31—41no—
466C22×C31—41no—
467C22×C31—41no—
468C22×C31—41no—
469C22×C31—41no—
470C22×C31—41no—
471C22×C31—41no—
472C22×C31—41no—
473C22×C31—41no—
474C22×C31—41no—
475C22×C31—41no—
476C22×C31—41no—
477C22×C31—81no—
478C22×C31—81no—
479C22×C31—81no—
480C22×C31—81no—
481C22×C31—81no—
482C22×C31—81no—
483C22×C31—81no—
484C22×C31—81no—
485C22×C31—81no—
486C22×C31—81no—
487C22×C31—81no—
488C22×C31—162no—
489C22×C31—162no—
490C22×C31C2×#12011yescharacteristic
491C22×C31#57611yescharacteristic
492C22×C31#57611yescharacteristic
493C4×C31—21no—
494C4×C31—21no—
495C4×C31—21no—
496C4×C31—21no—
497C4×C31—42no—
498C4×C31—41no—
499C4×C31—41no—
500C4×C31—41no—
501C4×C31—41no—
502C4×C31—41no—
503C4×C31—41no—
504C4×C31—41no—
505C4×C31—41no—
506C4×C31—81no—
507C4×C31—81no—
508#562—21no—
509#560—21no—
510#553—21no—
511#551—21no—
512#546—21no—
513#546—21no—
514#546—21no—
515D42—21no—
516#540—21no—
517#539—21no—
518#539C22×C3111yescharacteristic
519#538—21no—
520#538C22×C3111yescharacteristic
521#537C22×C3111yescharacteristic
522#534—21no—
523#534C22×C3111yescharacteristic
524#525C22×C3111yescharacteristic
525C2×#123C22×C3111yescharacteristic
526C2×#121C22×C3111yescharacteristic
527C2×#121C22×C3111yescharacteristic, complemented
528#483C22×C3111yescharacteristic, complemented
529#482—21no—
530#480—21no—
531#480C22×C3111yescharacteristic
532#480C22×C3111yescharacteristic, complemented
533#480C22×C3111yescharacteristic, complemented
534#469—21no—
535#468—21no—
536#466—21no—
537#466—21no—
538#450C22×C3111yescharacteristic, complemented
539#449—21no—
540#447—21no—
541#447C22×C3111yescharacteristic
542#447C22×C3111yescharacteristic, complemented
543#447C22×C3111yescharacteristic, complemented
544#407C22×C3111yescharacteristic, complemented
545C2×C22⋊C8C22×C3111yescharacteristic, complemented
546#398C22×C3111yescharacteristic, complemented
547#397C22×C3111yescharacteristic, complemented
548#394—21no—
549#394C22×C3111yescharacteristic, complemented
550#392—21no—
551#392C22×C3111yescharacteristic, complemented
552#390—21no—
553#388—21no—
554C4×C22⋊C4C22×C3111yescharacteristic, complemented
555#328C22×C3111yescharacteristic, complemented
556#328C22×C3111yescharacteristic, complemented
557#327C22×C3111yescharacteristic
558#327C22×C3111yescharacteristic
559#327C22×C3111yescharacteristic, complemented
560#327C22×C3111yescharacteristic, complemented
561#327C22×C3111yescharacteristic, complemented
562#327C22×C3111yescharacteristic, complemented
563#324C22×C3111yescharacteristic, complemented
564#324C22×C3111yescharacteristic, complemented
565#323C22×C3111yescharacteristic, complemented
566#323C22×C3111yescharacteristic, complemented
567C2×C31—21no—
568C2×C31—21no—
569C2×C31—41no—
570C2×C31—41no—
571C2×C31—81no—
572C2×C31—81no—
573C2×C31—81no—
574C2×C31—81no—
575C2×C31—161no—
576C2×C31#300811yescharacteristic
577C2×C31#301811yescharacteristic
578C2×C31#302611yescharacteristic
579C2×#41—21no—
580C2×#41D4×C3111yescharacteristic, complemented
581C22×D4—21no—
582C22×D4—21no—
583C22×D4—21no—
584C22×D4—21no—
585C22×D4—21no—
586C22×D4D4×C3111yescharacteristic
587C22×D4D4×C3111yescharacteristic, complemented
588C22×D4C23×C3111yescharacteristic
589C23×C4C23×C3111yescharacteristic
590C2×SD16—21no—
591C2×D8—21no—
592C2×D8—21no—
593C2×D8—21no—
594C2×M16—21no—
595C22×C8—21no—
596#127—21no—
597#126—21no—
598#126—21no—
599#126—21no—
600#126—21no—
601#125—21no—
602#125—21no—
603#124—21no—
604#124—21no—
605#124—21no—
606#123—21no—
607#123—21no—
608#123—21no—
609#123—21no—
610#123—21no—
611#123—21no—
612#123—21no—
613#123—21no—
614#123—21no—
615#123—21no—
616#123—21no—
617#123—21no—
618#123—21no—
619#123—21no—
620C22⋊Q8—21no—
621C22⋊Q8—21no—
622C22⋊Q8—21no—
623C22⋊Q8—21no—
624C22⋊Q8—21no—
625C22⋊Q8D4×C3111yescharacteristic, complemented
626C22⋊Q8C23×C3111yescharacteristic
627#121—21no—
628#121—21no—
629#121—21no—
630#121—21no—
631#121—21no—
632#121—21no—
633#121—21no—
634#121—21no—
635#121—21no—
636#121—21no—
637#121—21no—
638#121—21no—
639#121—21no—
640#121—21no—
641#121—21no—
642#121—21no—
643#121—21no—
644#121—21no—
645#121—21no—
646#121D4×C3111yescharacteristic, complemented
647#121D4×C3111yescharacteristic, complemented
648#121D4×C3111yescharacteristic, complemented
649#121C23×C3111yescharacteristic
650#121C23×C3111yescharacteristic
651#121C23×C3111yescharacteristic
652#120—21no—
653#120—21no—
654#120—21no—
655#120—21no—
656#120—21no—
657#120—21no—
658#120—21no—
659#120—21no—
660C4×D4—21no—
661C4×D4—21no—
662C4×D4—21no—
663C4×D4—21no—
664C4×D4—21no—
665C4×D4—21no—
666C4×D4—21no—
667C4×D4—21no—
668#117—21no—
669#117D4×C3111yescharacteristic, complemented
670C2×C4⋊C4—21no—
671C2×C4⋊C4D4×C3111yescharacteristic
672C2×C4⋊C4D4×C3111yescharacteristic, complemented
673C2×C4⋊C4C23×C3111yescharacteristic
674C2×C4⋊C4C23×C3111yescharacteristic
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4D4×C3111yescharacteristic
685C2×C22⋊C4D4×C3111yescharacteristic
686C2×C22⋊C4C23×C3111yescharacteristic
687C2×C42—21no—
688#107—21no—
689#107—21no—
690#107—21no—
691#106—21no—
692#103—21no—
693#102—21no—
694#102—21no—
695#102—21no—
696#102—21no—
697#102—21no—
698#102—21no—
699#102—21no—
700C22⋊C8—21no—
701C22⋊C8—21no—
702C22⋊C8C23×C3111yescharacteristic
703C22⋊C8C23×C3111yescharacteristic
704C22⋊C8C23×C3111yescharacteristic
705C22⋊C8C23×C3111yescharacteristic
706#95—21no—
707#95—21no—
708#95C23×C3111yescharacteristic
709#95C23×C3111yescharacteristic
710C31#1841411yescharacteristic, direct product factor, Sylow
711C24—21no—
712C24—21no—
713C24—21no—
714C24C2×D4×C3111yescharacteristic
715C24C2×D4×C3111yescharacteristic
716#41—81no—
717#41—81no—
718#41—81no—
719C2×Q8—21no—
720C2×Q8C2×D4×C3111yescharacteristic
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—21no—
736C2×D4—21no—
737C2×D4—21no—
738C2×D4—21no—
739C2×D4—21no—
740C2×D4—42no—
741C2×D4—41no—
742C2×D4—41no—
743C2×D4—81no—
744C2×D4—81no—
745C2×D4—81no—
746C2×D4—81no—
747C2×D4—81no—
748C2×D4—81no—
749C2×D4—81no—
750C2×D4—81no—
751C2×D4—81no—
752C2×D4—81no—
753C2×D4—81no—
754C2×D4—82no—
755C2×D4C2×D4×C3111yescharacteristic
756C2×D4C2×D4×C3111yescharacteristic
757C2×D4C2×D4×C3111yescharacteristic
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—81no—
769C22×C4C2×D4×C3111yescharacteristic
770C22×C4C2×D4×C3111yescharacteristic
771C22×C4C2×D4×C3111yescharacteristic
772C22×C4C2×D4×C3111yescharacteristic
773C22×C4C2×D4×C3111yescharacteristic
774C22×C4C2×D4×C3111yescharacteristic
775C22×C4C2×D4×C3111yescharacteristic
776C22×C4C2×D4×C3111yescharacteristic
777C22×C4C24×C3111yescharacteristic
778SD16—81no—
779D8—81no—
780D8—81no—
781D8—81no—
782M16—81no—
783C2×C8—21no—
784C2×C8—21no—
785C2×C8—21no—
786C2×C8—21no—
787C2×C8—81no—
788C4⋊C4—21no—
789C4⋊C4—21no—
790C4⋊C4—21no—
791C4⋊C4—21no—
792C4⋊C4—21no—
793C4⋊C4—21no—
794C4⋊C4—21no—
795C4⋊C4—21no—
796C4⋊C4—21no—
797C4⋊C4—21no—
798C4⋊C4—21no—
799C4⋊C4—21no—
800C4⋊C4—21no—
801C4⋊C4—21no—
802C4⋊C4—21no—
803C4⋊C4—81no—
804C4⋊C4C2×D4×C3111yescharacteristic
805C4⋊C4C2×D4×C3111yescharacteristic
806C4⋊C4C2×D4×C3111yescharacteristic
807C4⋊C4C2×D4×C3111yescharacteristic
808C22⋊C4—21no—
809C22⋊C4—21no—
810C22⋊C4—21no—
811C22⋊C4—21no—
812C22⋊C4—21no—
813C22⋊C4—21no—
814C22⋊C4—21no—
815C22⋊C4—21no—
816C22⋊C4—21no—
817C22⋊C4—21no—
818C22⋊C4—21no—
819C22⋊C4—21no—
820C22⋊C4—21no—
821C22⋊C4—21no—
822C22⋊C4—21no—
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—42no—
834C22⋊C4—42no—
835C22⋊C4—41no—
836C22⋊C4—41no—
837C22⋊C4—81no—
838C22⋊C4—81no—
839C22⋊C4—81no—
840C42—21no—
841C42—21no—
842C42—21no—
843C42—81no—
844C23—21no—
845C23—21no—
846C23—21no—
847C23—21no—
848C23—21no—
849C23—21no—
850C23—21no—
851C23—21no—
852C23—41no—
853C23—41no—
854C23—42no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—81no—
865C23—81no—
866C23—81no—
867C23—81no—
868C23—81no—
869C23C31×#12011yescharacteristic
870C23C31×#12011yescharacteristic
871C23C22×D4×C3111yescharacteristic
872Q8—41no—
873Q8—81no—
874D4—41no—
875D4—41no—
876D4—41no—
877D4—41no—
878D4—41no—
879D4—41no—
880D4—41no—
881D4—42no—
882D4—42no—
883D4—41no—
884D4—41no—
885D4—41no—
886D4—41no—
887D4—41no—
888D4—41no—
889D4—81no—
890D4—81no—
891D4—81no—
892D4—81no—
893D4—81no—
894D4—81no—
895D4—81no—
896D4—81no—
897D4—81no—
898D4—81no—
899D4—81no—
900D4—81no—
901D4—84no—
902D4—82no—
903D4—82no—
904C2×C4—22no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—21no—
913C2×C4—21no—
914C2×C4—21no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—81no—
932C2×C4—81no—
933C2×C4—81no—
934C2×C4—81no—
935C2×C4—81no—
936C2×C4—81no—
937C2×C4—81no—
938C2×C4C31×#12011yescharacteristic
939C2×C4C31×#12011yescharacteristic
940C2×C4C22×D4×C3111yescharacteristic
941C2×C4C22×D4×C3111yescharacteristic
942C8—41no—
943C8—41no—
944C8—41no—
945C8—41no—
946C22—21no—
947C22—21no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—41no—
955C22—41no—
956C22—41no—
957C22—41no—
958C22—41no—
959C22—41no—
960C22—41no—
961C22—41no—
962C22—41no—
963C22—41no—
964C22—41no—
965C22—41no—
966C22—81no—
967C22—81no—
968C22—81no—
969C22—81no—
970C22—81no—
971C22—81no—
972C22—81no—
973C22—81no—
974C22—81no—
975C22—81no—
976C22—81no—
977C22—162no—
978C22—162no—
979C22C2×C31×#12011yescharacteristic
980C22C31×#57611yescharacteristic
981C22C31×#57611yescharacteristic
982C4—21no—
983C4—21no—
984C4—21no—
985C4—21no—
986C4—42no—
987C4—41no—
988C4—41no—
989C4—41no—
990C4—41no—
991C4—41no—
992C4—41no—
993C4—41no—
994C4—41no—
995C4—81no—
996C4—81no—
997C2—21no—
998C2—21no—
999C2—41no—
1000C2—41no—
1001C2—81no—
1002C2—81no—
1003C2—81no—
1004C2—81no—
1005C2—161no—
1006C2C31×#300811yescharacteristic
1007C2C31×#301811yescharacteristic
1008C2C31×#302611yescharacteristic
subgroupG/H
center, socleC22×C31C2×#120
commutator, Frattini, cosocleC22×C4C24×C31
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C31 ◁ C23×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C31×#3534C2semidirect
2. C31×#3194C2semidirect
3. C31×#3186C2semidirect
4. C31×#2661C2semidirect
5. C31×#1612C2semidirect
6. C31×#1610C2semidirect
7. C31×#1609C2semidirect
8. C31×#1607C2semidirect
9. C31×#1600C2semidirect
10. C31×#1598C2semidirect
11. C31×#1597C2semidirect
12. C31×#1595C2semidirect
13. C31×#1507C2semidirect
14. C31×#1501C2semidirect
15. C31×#1468C2semidirect
35. C2×C31×#121C22semidirect
36. C31×#483C22semidirect
40. C31×#480C22semidirect
41. C31×#480C22semidirect
46. C31×#450C22semidirect
50. C31×#447C22semidirect
51. C31×#447C22semidirect
52. C31×#407C22semidirect
53. C2×C31×C22⋊C8C22semidirect
54. C31×#398C22semidirect
55. C31×#397C22semidirect
57. C31×#394C22semidirect
59. C31×#392C22semidirect
62. C4×C22⋊C4×C31C22semidirect
63. C31×#328C22semidirect
64. C31×#328C22semidirect
67. C31×#327C22semidirect
68. C31×#327C22semidirect
69. C31×#327C22semidirect
70. C31×#327C22semidirect
71. C31×#324C22semidirect
72. C31×#324C22semidirect
73. C31×#323C22semidirect
74. C31×#323C22semidirect
76. C2×#41×C31D4semidirect
83. C22×D4×C31D4semidirect
121. C31×C22⋊Q8D4semidirect
142. C31×#121D4semidirect
143. C31×#121D4semidirect
144. C31×#121D4semidirect
165. C31×#117D4semidirect
168. C2×C4⋊C4×C31D4semidirect
339. #18414C31direct (N × H)
442. #3534C2×C31semidirect
443. #3194C2×C31semidirect
444. #3186C2×C31semidirect
445. #2661C2×C31semidirect
446. #1612C2×C31semidirect
447. #1610C2×C31semidirect
448. #1609C2×C31semidirect
449. #1607C2×C31semidirect
450. #1600C2×C31semidirect
451. #1598C2×C31semidirect
452. #1597C2×C31semidirect
453. #1595C2×C31semidirect
454. #1507C2×C31semidirect
455. #1501C2×C31semidirect
456. #1468C2×C31semidirect
527. C2×#121C22×C31semidirect
528. #483C22×C31semidirect
532. #480C22×C31semidirect
533. #480C22×C31semidirect
538. #450C22×C31semidirect
542. #447C22×C31semidirect
543. #447C22×C31semidirect
544. #407C22×C31semidirect
545. C2×C22⋊C8C22×C31semidirect
546. #398C22×C31semidirect
547. #397C22×C31semidirect
549. #394C22×C31semidirect
551. #392C22×C31semidirect
554. C4×C22⋊C4C22×C31semidirect
555. #328C22×C31semidirect
556. #328C22×C31semidirect
559. #327C22×C31semidirect
560. #327C22×C31semidirect
561. #327C22×C31semidirect
562. #327C22×C31semidirect
563. #324C22×C31semidirect
564. #324C22×C31semidirect
565. #323C22×C31semidirect
566. #323C22×C31semidirect
580. C2×#41D4×C31semidirect
587. C22×D4D4×C31semidirect
625. C22⋊Q8D4×C31semidirect
646. #121D4×C31semidirect
647. #121D4×C31semidirect
648. #121D4×C31semidirect
669. #117D4×C31semidirect
672. C2×C4⋊C4D4×C31semidirect
710. C31#18414direct (N × H)

Maximal subgroups

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

subgroupindex
C31×#35342
C31×#31942
C31×#31862
C31×#26612
C31×#16122
C31×#16102
C31×#16092
C31×#16072
C31×#16002
C31×#15982
C31×#15972
C31×#15952
C31×#15072
C31×#15012
C31×#14682
#1841431