Finite Group Databasebeta

← C31×#24397 #21481156

Subgroups — C31×#24397 #21481156

Order 7936.

1508 conjugacy classes of subgroups.

The subgroup lattice has 954 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#537C211yesmaximal, characteristic, complemented
2C2×C31×#469C211yesmaximal, characteristic, complemented
3C2×C31×#465C211yesmaximal, characteristic, complemented
4C2×C31×#449C211yesmaximal, characteristic, complemented
5C2×C31×#408C211yesmaximal, characteristic, complemented
6C31×#2615C211yesmaximal, characteristic, complemented
7C31×#2035C211yesmaximal, characteristic, complemented
8C31×#2034C211yesmaximal, characteristic, complemented
9C31×#2000C211yesmaximal, characteristic, complemented
10C31×#1999C211yesmaximal, characteristic, complemented
11C31×#1894C211yesmaximal, characteristic, complemented
12C31×#1893C211yesmaximal, characteristic, complemented
13C31×#1874C211yesmaximal, characteristic, complemented
14C31×#1853C211yesmaximal, characteristic, complemented
15C31×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C31C2211yescharacteristic
17C22×#41×C31C2211yescharacteristic
18C22×SD16×C31C2211yescharacteristic
19C22×D8×C31C2211yescharacteristic
20C22×M16×C31C2211yescharacteristic
21C23×C8×C31C2211yescharacteristic
22C31×#537—24no—
23C31×#537—24no—
24C2×C31×C22⋊Q8—21no—
25C2×C31×C22⋊Q8C2211yescharacteristic
26C2×C31×C22⋊Q8C2211yescharacteristic
27C2×C31×#121—21no—
28C2×C31×#121—21no—
29C2×C31×#121—21no—
30C2×C31×#121C2211yescharacteristic
31C2×C31×#121C2211yescharacteristic
32C2×C31×#121C2211yescharacteristic
33C2×C31×#121C2211yescharacteristic
34C2×C31×#121C2211yescharacteristic
35C22×C4⋊C4×C31C2211yescharacteristic
36C31×#469—24no—
37C31×#465—24no—
38C31×#449—24no—
39C2×C31×#106C2211yescharacteristic
40C2×C31×#106C2211yescharacteristic
41C2×C31×#103C2211yescharacteristic
42C2×C31×#103C2211yescharacteristic
43C2×C31×#103C2211yescharacteristic
44C2×C31×#102C2211yescharacteristic
45C2×C31×#102C2211yescharacteristic
46C2×C31×#102C2211yescharacteristic
47C2×C31×#102C2211yescharacteristic
48C2×C31×#102C2211yescharacteristic
49C31×#408—24no—
50C2×C31×C22⋊C8C2211yescharacteristic
51C2×C31×C22⋊C8C2211yescharacteristic
52C2×C31×C22⋊C8C2211yescharacteristic
53C2×C31×C22⋊C8C2211yescharacteristic
54C31×#393—21no—
55C31×#392—21no—
56C31×#392—21no—
57C31×#392—21no—
58C31×#380C2211yescharacteristic
59C31×#380C2211yescharacteristic
60C31×#380C2211yescharacteristic
61C31×#340C2211yescharacteristic
62C31×#340C2211yescharacteristic
63C31×#340C2211yescharacteristic
64C31×#340C2211yescharacteristic
65C2×#41×C31—22no—
66C2×#41×C31—22no—
67C2×#41×C31—22no—
68C2×#41×C31—22no—
69C2×#41×C31—22no—
70C2×#41×C31—22no—
71C2×#41×C31—22no—
72C2×#41×C31—22no—
73C2×#41×C31—41no—
74C2×#41×C31—41no—
75C2×#41×C31—41no—
76C2×#41×C31—41no—
77C22×Q8×C31D411yescharacteristic
78C22×Q8×C31C2311yescharacteristic
79C22×D4×C31—21no—
80C22×D4×C31—21no—
81C22×D4×C31—21no—
82C22×D4×C31—21no—
83C22×D4×C31—21no—
84C22×D4×C31—21no—
85C22×D4×C31D411yescharacteristic
86C22×D4×C31D411yescharacteristic
87C22×D4×C31D411yescharacteristic
88C22×D4×C31C2311yescharacteristic
89C22×D4×C31C2311yescharacteristic
90C23×C4×C31—21no—
91C23×C4×C31—21no—
92C23×C4×C31C2311yescharacteristic
93C23×C4×C31C2311yescharacteristic
94C23×C4×C31C2311yescharacteristic
95C2×SD16×C31—22no—
96C2×SD16×C31—22no—
97C2×SD16×C31—41no—
98C2×D8×C31—22no—
99C2×D8×C31—22no—
100C2×D8×C31—41no—
101C2×M16×C31—22no—
102C2×M16×C31—22no—
103C2×M16×C31—41no—
104C22×C8×C31—22no—
105C22×C8×C31—22no—
106C22×C8×C31—41no—
107C22×C8×C31C2311yescharacteristic
108C22×C8×C31C2311yescharacteristic
109C22×C8×C31C2311yescharacteristic
110C22×C8×C31C2311yescharacteristic
111C31×C22⋊Q8—28no—
112C31×C22⋊Q8—22no—
113C31×C22⋊Q8—22no—
114C31×C22⋊Q8—22no—
115C31×C22⋊Q8D414yescomplemented
116C31×#121—28no—
117C31×#121—28no—
118C31×#121—28no—
119C31×#121—22no—
120C31×#121—22no—
121C31×#121—22no—
122C31×#121—22no—
123C31×#121—22no—
124C31×#121—22no—
125C31×#121—22no—
126C31×#121—41no—
127C31×#121—41no—
128C31×#121D414yescomplemented
129C2×C4⋊C4×C31—21no—
130C2×C4⋊C4×C31—21no—
131C2×C4⋊C4×C31—21no—
132C2×C4⋊C4×C31—22no—
133C2×C4⋊C4×C31—22no—
134C2×C4⋊C4×C31C2311yescharacteristic
135C2×C4⋊C4×C31C2311yescharacteristic
136C2×C4⋊C4×C31C2311yescharacteristic
137C2×C4⋊C4×C31C2311yescharacteristic
138C2×C4⋊C4×C31C2311yescharacteristic
139C2×C22⋊C4×C31—21no—
140C2×C22⋊C4×C31—21no—
141C2×C22⋊C4×C31—21no—
142C2×C22⋊C4×C31—21no—
143C2×C22⋊C4×C31—21no—
144C2×C22⋊C4×C31—21no—
145C2×C22⋊C4×C31—21no—
146C2×C22⋊C4×C31—21no—
147C2×C22⋊C4×C31—21no—
148C2×C22⋊C4×C31—21no—
149C31×#106—22no—
150C31×#106—22no—
151C31×#103—22no—
152C31×#103—22no—
153C31×#103—41no—
154C31×#102—22no—
155C31×#102—22no—
156C31×#102—22no—
157C31×#102—22no—
158C31×#102—41no—
159C31×C22⋊C8—22no—
160C31×C22⋊C8—22no—
161C31×C22⋊C8—22no—
162C31×C22⋊C8D414yescomplemented
163C31×#95—21no—
164C31×#95—21no—
165C31×#95—21no—
166C24×C31—21no—
167C24×C31—21no—
168C24×C31C2×D411yescharacteristic
169C24×C31C2×D411yescharacteristic
170C24×C31C2×D411yescharacteristic
171#41×C31—44no—
172#41×C31—44no—
173#41×C31—44no—
174#41×C31—44no—
175#41×C31—44no—
176#41×C31—44no—
177#41×C31—44no—
178#41×C31—44no—
179C2×Q8×C31—22no—
180C2×Q8×C31—22no—
181C2×Q8×C31—21no—
182C2×Q8×C31—21no—
183C2×Q8×C31—21no—
184C2×Q8×C31—21no—
185C2×Q8×C31—21no—
186C2×Q8×C31—41no—
187C2×Q8×C31C2×D412yes—
188C2×D4×C31—24no—
189C2×D4×C31—22no—
190C2×D4×C31—22no—
191C2×D4×C31—22no—
192C2×D4×C31—22no—
193C2×D4×C31—24no—
194C2×D4×C31—24no—
195C2×D4×C31—22no—
196C2×D4×C31—22no—
197C2×D4×C31—21no—
198C2×D4×C31—21no—
199C2×D4×C31—21no—
200C2×D4×C31—21no—
201C2×D4×C31—21no—
202C2×D4×C31—21no—
203C2×D4×C31—21no—
204C2×D4×C31—21no—
205C2×D4×C31—21no—
206C2×D4×C31—21no—
207C2×D4×C31—21no—
208C2×D4×C31—41no—
209C2×D4×C31—41no—
210C2×D4×C31—41no—
211C2×D4×C31—42no—
212C2×D4×C31—42no—
213C2×D4×C31—42no—
214C2×D4×C31—42no—
215C2×D4×C31—42no—
216C2×D4×C31—81no—
217C2×D4×C31—81no—
218C2×D4×C31—81no—
219C2×D4×C31—81no—
220C2×D4×C31—81no—
221C2×D4×C31—81no—
222C2×D4×C31—81no—
223C2×D4×C31—81no—
224C2×D4×C31—81no—
225C2×D4×C31—81no—
226C2×D4×C31C2×D412yes—
227C22×C4×C31—21no—
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—24no—
236C22×C4×C31—21no—
237C22×C4×C31—21no—
238C22×C4×C31—21no—
239C22×C4×C31—24no—
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—42no—
250C22×C4×C31—42no—
251C22×C4×C31—81no—
252C22×C4×C31—81no—
253C22×C4×C31C2×D411yescharacteristic
254C22×C4×C31C2×D411yescharacteristic
255C22×C4×C31C2×D412yes—
256C22×C4×C31C2×D412yes—
257C22×C4×C31C2×D411yescharacteristic
258C22×C4×C31C2×D412yes—
259C22×C4×C31#4112yes—
260C22×C4×C31C2411yescharacteristic
261SD16×C31—44no—
262D8×C31—44no—
263M16×C31—44no—
264C2×C8×C31—21no—
265C2×C8×C31—21no—
266C2×C8×C31—21no—
267C2×C8×C31—21no—
268C2×C8×C31—21no—
269C2×C8×C31—21no—
270C2×C8×C31—21no—
271C2×C8×C31—21no—
272C2×C8×C31—21no—
273C2×C8×C31—21no—
274C2×C8×C31—44no—
275C2×C8×C31C2×D412yes—
276C2×C8×C31C2×D412yes—
277C4⋊C4×C31—24no—
278C4⋊C4×C31—24no—
279C4⋊C4×C31—24no—
280C4⋊C4×C31—21no—
281C4⋊C4×C31—21no—
282C4⋊C4×C31—21no—
283C4⋊C4×C31—21no—
284C4⋊C4×C31—21no—
285C4⋊C4×C31—21no—
286C4⋊C4×C31—21no—
287C4⋊C4×C31—21no—
288C4⋊C4×C31C2×D412yes—
289C4⋊C4×C31C2×D412yes—
290C22⋊C4×C31—24no—
291C22⋊C4×C31—24no—
292C22⋊C4×C31—24no—
293C22⋊C4×C31—24no—
294C22⋊C4×C31—42no—
295C22⋊C4×C31—42no—
296C22⋊C4×C31—42no—
297C22⋊C4×C31—81no—
298C22⋊C4×C31—81no—
299C22⋊C4×C31—81no—
300#24397C3111yesmaximal, characteristic, direct product factor, Sylow
301C23×C31—21no—
302C23×C31—21no—
303C23×C31—21no—
304C23×C31—21no—
305C23×C31—21no—
306C23×C31—21no—
307C23×C31—21no—
308C23×C31—21no—
309C23×C31—21no—
310C23×C31—21no—
311C23×C31—21no—
312C23×C31—21no—
313C23×C31—21no—
314C23×C31—22no—
315C23×C31—21no—
316C23×C31—21no—
317C23×C31—21no—
318C23×C31—21no—
319C23×C31—21no—
320C23×C31—21no—
321C23×C31—41no—
322C23×C31—41no—
323C23×C31—41no—
324C23×C31—41no—
325C23×C31—41no—
326C23×C31—41no—
327C23×C31—41no—
328C23×C31—41no—
329C23×C31—41no—
330C23×C31—41no—
331C23×C31—41no—
332C23×C31—41no—
333C23×C31—41no—
334C23×C31#12012yes—
335C23×C31#12112yes—
336C23×C31C22×D411yescharacteristic
337Q8×C31—22no—
338Q8×C31—22no—
339Q8×C31—44no—
340Q8×C31—41no—
341Q8×C31—41no—
342D4×C31—22no—
343D4×C31—22no—
344D4×C31—44no—
345D4×C31—44no—
346D4×C31—44no—
347D4×C31—48no—
348D4×C31—41no—
349D4×C31—41no—
350D4×C31—41no—
351D4×C31—41no—
352D4×C31—41no—
353D4×C31—41no—
354D4×C31—84no—
355D4×C31—84no—
356D4×C31—84no—
357D4×C31—84no—
358D4×C31—84no—
359C2×C4×C31—21no—
360C2×C4×C31—21no—
361C2×C4×C31—21no—
362C2×C4×C31—21no—
363C2×C4×C31—22no—
364C2×C4×C31—22no—
365C2×C4×C31—22no—
366C2×C4×C31—22no—
367C2×C4×C31—22no—
368C2×C4×C31—22no—
369C2×C4×C31—22no—
370C2×C4×C31—22no—
371C2×C4×C31—22no—
372C2×C4×C31—22no—
373C2×C4×C31—22no—
374C2×C4×C31—21no—
375C2×C4×C31—21no—
376C2×C4×C31—21no—
377C2×C4×C31—48no—
378C2×C4×C31—41no—
379C2×C4×C31—41no—
380C2×C4×C31—41no—
381C2×C4×C31—41no—
382C2×C4×C31—41no—
383C2×C4×C31—41no—
384C2×C4×C31—41no—
385C2×C4×C31—41no—
386C2×C4×C31—41no—
387C2×C4×C31—41no—
388C2×C4×C31—41no—
389C2×C4×C31—41no—
390C2×C4×C31—41no—
391C2×C4×C31—41no—
392C2×C4×C31—41no—
393C2×C4×C31—41no—
394C2×C4×C31—41no—
395C2×C4×C31—41no—
396C2×C4×C31—41no—
397C2×C4×C31—84no—
398C2×C4×C31#12012yes—
399C2×C4×C31#12112yes—
400C2×C4×C31C22×D411yescharacteristic
401C2×C4×C31C22×D411yescharacteristic
402C2×C4×C31C22×D411yescharacteristic
403C2×C4×C31C2×#4111yescharacteristic
404C2×C4×C31H(5,𝔽2)11yescharacteristic
405C2×C4×C31H(5,𝔽2)11yescharacteristic
406C8×C31—22no—
407C8×C31—22no—
408C8×C31—41no—
409C8×C31—41no—
410C2×#537C2×C3111yescharacteristic, complemented
411C2×#469C2×C3111yescharacteristic, complemented
412C2×#465C2×C3111yescharacteristic, complemented
413C2×#449C2×C3111yescharacteristic, complemented
414C2×#408C2×C3111yescharacteristic, complemented
415#2615C2×C3111yescharacteristic, complemented
416#2035C2×C3111yescharacteristic, complemented
417#2034C2×C3111yescharacteristic, complemented
418#2000C2×C3111yescharacteristic, complemented
419#1999C2×C3111yescharacteristic, complemented
420#1894C2×C3111yescharacteristic, complemented
421#1893C2×C3111yescharacteristic, complemented
422#1874C2×C3111yescharacteristic, complemented
423#1853C2×C3111yescharacteristic, complemented
424#1788C2×C3111yescharacteristic, complemented
425C22×C31—22no—
426C22×C31—22no—
427C22×C31—22no—
428C22×C31—22no—
429C22×C31—22no—
430C22×C31—22no—
431C22×C31—41no—
432C22×C31—41no—
433C22×C31—41no—
434C22×C31—41no—
435C22×C31—41no—
436C22×C31—41no—
437C22×C31—41no—
438C22×C31—41no—
439C22×C31—42no—
440C22×C31—41no—
441C22×C31—41no—
442C22×C31—41no—
443C22×C31—41no—
444C22×C31—42no—
445C22×C31—41no—
446C22×C31—42no—
447C22×C31—41no—
448C22×C31—41no—
449C22×C31—81no—
450C22×C31—81no—
451C22×C31—81no—
452C22×C31—81no—
453C22×C31—81no—
454C22×C31—81no—
455C22×C31—81no—
456C22×C31—81no—
457C22×C31—81no—
458C22×C31—81no—
459C22×C31—81no—
460C22×C31C2×#12011yescharacteristic
461C22×C31C2×#12111yescharacteristic
462C22×C31#53411yescharacteristic
463C22×C31#57611yescharacteristic
464C22×C31#57711yescharacteristic
465C22×C31#57711yescharacteristic
466C22×C31#57711yescharacteristic
467C4×C31—22no—
468C4×C31—22no—
469C4×C31—41no—
470C4×C31—42no—
471C4×C31—42no—
472C4×C31—42no—
473C4×C31—81no—
474C4×C31—81no—
475C4×C31—81no—
476C4×C31D4211yescharacteristic
477C4×C31D4211yescharacteristic
478C4×C31#54611yescharacteristic
479C4×C31#54611yescharacteristic
480C22×#41C22×C3111yescharacteristic
481C22×#41C22×C3111yescharacteristic
482C22×SD16C22×C3111yescharacteristic
483C22×D8C22×C3111yescharacteristic
484C22×M16C22×C3111yescharacteristic
485C23×C8C22×C3111yescharacteristic
486#537—24no—
487#537—24no—
488C2×C22⋊Q8—21no—
489C2×C22⋊Q8C22×C3111yescharacteristic
490C2×C22⋊Q8C22×C3111yescharacteristic
491C2×#121—21no—
492C2×#121—21no—
493C2×#121—21no—
494C2×#121C22×C3111yescharacteristic
495C2×#121C22×C3111yescharacteristic
496C2×#121C22×C3111yescharacteristic
497C2×#121C22×C3111yescharacteristic
498C2×#121C22×C3111yescharacteristic
499C22×C4⋊C4C22×C3111yescharacteristic
500#469—24no—
501#465—24no—
502#449—24no—
503C2×#106C22×C3111yescharacteristic
504C2×#106C22×C3111yescharacteristic
505C2×#103C22×C3111yescharacteristic
506C2×#103C22×C3111yescharacteristic
507C2×#103C22×C3111yescharacteristic
508C2×#102C22×C3111yescharacteristic
509C2×#102C22×C3111yescharacteristic
510C2×#102C22×C3111yescharacteristic
511C2×#102C22×C3111yescharacteristic
512C2×#102C22×C3111yescharacteristic
513#408—24no—
514C2×C22⋊C8C22×C3111yescharacteristic
515C2×C22⋊C8C22×C3111yescharacteristic
516C2×C22⋊C8C22×C3111yescharacteristic
517C2×C22⋊C8C22×C3111yescharacteristic
518#393—21no—
519#392—21no—
520#392—21no—
521#392—21no—
522#380C22×C3111yescharacteristic
523#380C22×C3111yescharacteristic
524#380C22×C3111yescharacteristic
525#340C22×C3111yescharacteristic
526#340C22×C3111yescharacteristic
527#340C22×C3111yescharacteristic
528#340C22×C3111yescharacteristic
529C2×C31—42no—
530C2×C31—42no—
531C2×C31—81no—
532C2×C31—82no—
533C2×C31—161no—
534C2×C31#241011yescharacteristic
535C2×C31#301011yescharacteristic
536C2×C31#301211yescharacteristic
537C2×C31#306011yescharacteristic
538C2×C31#306211yescharacteristic
539C2×C31#319811yescharacteristic
540C2×C31#320411yescharacteristic
541C2×#41—22no—
542C2×#41—22no—
543C2×#41—22no—
544C2×#41—22no—
545C2×#41—22no—
546C2×#41—22no—
547C2×#41—22no—
548C2×#41—22no—
549C2×#41—41no—
550C2×#41—41no—
551C2×#41—41no—
552C2×#41—41no—
553C22×Q8D4×C3111yescharacteristic
554C22×Q8C23×C3111yescharacteristic
555C22×D4—21no—
556C22×D4—21no—
557C22×D4—21no—
558C22×D4—21no—
559C22×D4—21no—
560C22×D4—21no—
561C22×D4D4×C3111yescharacteristic
562C22×D4D4×C3111yescharacteristic
563C22×D4D4×C3111yescharacteristic
564C22×D4C23×C3111yescharacteristic
565C22×D4C23×C3111yescharacteristic
566C23×C4—21no—
567C23×C4—21no—
568C23×C4C23×C3111yescharacteristic
569C23×C4C23×C3111yescharacteristic
570C23×C4C23×C3111yescharacteristic
571C2×SD16—22no—
572C2×SD16—22no—
573C2×SD16—41no—
574C2×D8—22no—
575C2×D8—22no—
576C2×D8—41no—
577C2×M16—22no—
578C2×M16—22no—
579C2×M16—41no—
580C22×C8—22no—
581C22×C8—22no—
582C22×C8—41no—
583C22×C8C23×C3111yescharacteristic
584C22×C8C23×C3111yescharacteristic
585C22×C8C23×C3111yescharacteristic
586C22×C8C23×C3111yescharacteristic
587C22⋊Q8—28no—
588C22⋊Q8—22no—
589C22⋊Q8—22no—
590C22⋊Q8—22no—
591C22⋊Q8D4×C3114yescomplemented
592#121—28no—
593#121—28no—
594#121—28no—
595#121—22no—
596#121—22no—
597#121—22no—
598#121—22no—
599#121—22no—
600#121—22no—
601#121—22no—
602#121—41no—
603#121—41no—
604#121D4×C3114yescomplemented
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—22no—
609C2×C4⋊C4—22no—
610C2×C4⋊C4C23×C3111yescharacteristic
611C2×C4⋊C4C23×C3111yescharacteristic
612C2×C4⋊C4C23×C3111yescharacteristic
613C2×C4⋊C4C23×C3111yescharacteristic
614C2×C4⋊C4C23×C3111yescharacteristic
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625#106—22no—
626#106—22no—
627#103—22no—
628#103—22no—
629#103—41no—
630#102—22no—
631#102—22no—
632#102—22no—
633#102—22no—
634#102—41no—
635C22⋊C8—22no—
636C22⋊C8—22no—
637C22⋊C8—22no—
638C22⋊C8D4×C3114yescomplemented
639#95—21no—
640#95—21no—
641#95—21no—
642C31#2439711yescharacteristic, direct product factor, Sylow
643C24—21no—
644C24—21no—
645C24C2×D4×C3111yescharacteristic
646C24C2×D4×C3111yescharacteristic
647C24C2×D4×C3111yescharacteristic
648#41—44no—
649#41—44no—
650#41—44no—
651#41—44no—
652#41—44no—
653#41—44no—
654#41—44no—
655#41—44no—
656C2×Q8—22no—
657C2×Q8—22no—
658C2×Q8—21no—
659C2×Q8—21no—
660C2×Q8—21no—
661C2×Q8—21no—
662C2×Q8—21no—
663C2×Q8—41no—
664C2×Q8C2×D4×C3112yes—
665C2×D4—24no—
666C2×D4—22no—
667C2×D4—22no—
668C2×D4—22no—
669C2×D4—22no—
670C2×D4—24no—
671C2×D4—24no—
672C2×D4—22no—
673C2×D4—22no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—41no—
686C2×D4—41no—
687C2×D4—41no—
688C2×D4—42no—
689C2×D4—42no—
690C2×D4—42no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—81no—
694C2×D4—81no—
695C2×D4—81no—
696C2×D4—81no—
697C2×D4—81no—
698C2×D4—81no—
699C2×D4—81no—
700C2×D4—81no—
701C2×D4—81no—
702C2×D4—81no—
703C2×D4C2×D4×C3112yes—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—24no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—24no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—42no—
727C22×C4—42no—
728C22×C4—81no—
729C22×C4—81no—
730C22×C4C2×D4×C3111yescharacteristic
731C22×C4C2×D4×C3111yescharacteristic
732C22×C4C2×D4×C3112yes—
733C22×C4C2×D4×C3112yes—
734C22×C4C2×D4×C3111yescharacteristic
735C22×C4C2×D4×C3112yes—
736C22×C4#41×C3112yes—
737C22×C4C24×C3111yescharacteristic
738SD16—44no—
739D8—44no—
740M16—44no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—44no—
752C2×C8C2×D4×C3112yes—
753C2×C8C2×D4×C3112yes—
754C4⋊C4—24no—
755C4⋊C4—24no—
756C4⋊C4—24no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4C2×D4×C3112yes—
766C4⋊C4C2×D4×C3112yes—
767C22⋊C4—24no—
768C22⋊C4—24no—
769C22⋊C4—24no—
770C22⋊C4—24no—
771C22⋊C4—42no—
772C22⋊C4—42no—
773C22⋊C4—42no—
774C22⋊C4—81no—
775C22⋊C4—81no—
776C22⋊C4—81no—
777C23—21no—
778C23—21no—
779C23—21no—
780C23—21no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—21no—
789C23—21no—
790C23—22no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—21no—
796C23—21no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23C31×#12012yes—
811C23C31×#12112yes—
812C23C22×D4×C3111yescharacteristic
813Q8—22no—
814Q8—22no—
815Q8—44no—
816Q8—41no—
817Q8—41no—
818D4—22no—
819D4—22no—
820D4—44no—
821D4—44no—
822D4—44no—
823D4—48no—
824D4—41no—
825D4—41no—
826D4—41no—
827D4—41no—
828D4—41no—
829D4—41no—
830D4—84no—
831D4—84no—
832D4—84no—
833D4—84no—
834D4—84no—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—48no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—84no—
874C2×C4C31×#12012yes—
875C2×C4C31×#12112yes—
876C2×C4C22×D4×C3111yescharacteristic
877C2×C4C22×D4×C3111yescharacteristic
878C2×C4C22×D4×C3111yescharacteristic
879C2×C4C2×#41×C3111yescharacteristic
880C2×C4C31×H(5,𝔽2)11yescharacteristic
881C2×C4C31×H(5,𝔽2)11yescharacteristic
882C8—22no—
883C8—22no—
884C8—41no—
885C8—41no—
886C22—22no—
887C22—22no—
888C22—22no—
889C22—22no—
890C22—22no—
891C22—22no—
892C22—41no—
893C22—41no—
894C22—41no—
895C22—41no—
896C22—41no—
897C22—41no—
898C22—41no—
899C22—41no—
900C22—42no—
901C22—41no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—42no—
906C22—41no—
907C22—42no—
908C22—41no—
909C22—41no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22C2×C31×#12011yescharacteristic
922C22C2×C31×#12111yescharacteristic
923C22C31×#53411yescharacteristic
924C22C31×#57611yescharacteristic
925C22C31×#57711yescharacteristic
926C22C31×#57711yescharacteristic
927C22C31×#57711yescharacteristic
928C4—22no—
929C4—22no—
930C4—41no—
931C4—42no—
932C4—42no—
933C4—42no—
934C4—81no—
935C4—81no—
936C4—81no—
937C4D42×C3111yescharacteristic
938C4D42×C3111yescharacteristic
939C4C31×#54611yescharacteristic
940C4C31×#54611yescharacteristic
941C2—42no—
942C2—42no—
943C2—81no—
944C2—82no—
945C2—161no—
946C2C31×#241011yescharacteristic
947C2C31×#301011yescharacteristic
948C2C31×#301211yescharacteristic
949C2C31×#306011yescharacteristic
950C2C31×#306211yescharacteristic
951C2C31×#319811yescharacteristic
952C2C31×#320411yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C22×#41×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#537C2semidirect
2. C2×C31×#469C2semidirect
3. C2×C31×#465C2semidirect
4. C2×C31×#449C2semidirect
5. C2×C31×#408C2semidirect
6. C31×#2615C2semidirect
7. C31×#2035C2semidirect
8. C31×#2034C2semidirect
9. C31×#2000C2semidirect
10. C31×#1999C2semidirect
11. C31×#1894C2semidirect
12. C31×#1893C2semidirect
13. C31×#1874C2semidirect
14. C31×#1853C2semidirect
15. C31×#1788C2semidirect
115. C31×C22⋊Q8D4semidirect
128. C31×#121D4semidirect
162. C31×C22⋊C8D4semidirect
300. #24397C31direct (N × H)
410. C2×#537C2×C31semidirect
411. C2×#469C2×C31semidirect
412. C2×#465C2×C31semidirect
413. C2×#449C2×C31semidirect
414. C2×#408C2×C31semidirect
415. #2615C2×C31semidirect
416. #2035C2×C31semidirect
417. #2034C2×C31semidirect
418. #2000C2×C31semidirect
419. #1999C2×C31semidirect
420. #1894C2×C31semidirect
421. #1893C2×C31semidirect
422. #1874C2×C31semidirect
423. #1853C2×C31semidirect
424. #1788C2×C31semidirect
591. C22⋊Q8D4×C31semidirect
604. #121D4×C31semidirect
638. C22⋊C8D4×C31semidirect
642. C31#24397direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5372
C2×C31×#4692
C2×C31×#4652
C2×C31×#4492
C2×C31×#4082
C31×#26152
C31×#20352
C31×#20342
C31×#20002
C31×#19992
C31×#18942
C31×#18932
C31×#18742
C31×#18532
C31×#17882
#2439731