Finite Group Databasebeta

← C31×#24388 #21481147

Subgroups — C31×#24388 #21481147

Order 7936.

1646 conjugacy classes of subgroups.

The subgroup lattice has 972 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#525C211yesmaximal, characteristic, complemented
2C2×C31×#469C211yesmaximal, characteristic, complemented
3C2×C31×#468C211yesmaximal, characteristic, complemented
4C2×C31×#449C211yesmaximal, characteristic, complemented
5C2×C31×#407C211yesmaximal, characteristic, complemented
6C31×#2847C211yesmaximal, characteristic, complemented
7C31×#2035C211yesmaximal, characteristic, complemented
8C31×#2033C211yesmaximal, characteristic, complemented
9C31×#2000C211yesmaximal, characteristic, complemented
10C31×#1999C211yesmaximal, characteristic, complemented
11C31×#1895C211yesmaximal, characteristic, complemented
12C31×#1894C211yesmaximal, characteristic, complemented
13C31×#1875C211yesmaximal, characteristic, complemented
14C31×#1854C211yesmaximal, characteristic, complemented
15C31×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C31C2211yescharacteristic
17C24×C4×C31C2211yescharacteristic
18C22×SD16×C31C2211yescharacteristic, complemented
19C22×D8×C31C2211yescharacteristic, complemented
20C22×M16×C31C2211yescharacteristic
21C22×M16×C31C2211yescharacteristic
22C31×#525—24no—
23C31×#525—24no—
24C2×C31×#123—21no—
25C2×C31×C22⋊Q8C2211yescharacteristic
26C2×C31×C22⋊Q8C2211yescharacteristic
27C2×C31×#121C2211yescharacteristic
28C2×C31×#121C2211yescharacteristic
29C2×C31×#121C2211yescharacteristic
30C2×C31×#121C2211yescharacteristic
31C2×C31×#121C2211yescharacteristic
32C2×C31×#120—21no—
33C2×C31×#120—21no—
34C2×C4×D4×C31—21no—
35C2×C4×D4×C31—21no—
36C2×C31×#117C2211yescharacteristic
37C31×#469—24no—
38C31×#468—24no—
39C31×#449—24no—
40C2×C31×#107C2211yescharacteristic, complemented
41C2×C31×#106C2211yescharacteristic, complemented
42C2×C31×#103C2211yescharacteristic, complemented
43C2×C31×#103C2211yescharacteristic, complemented
44C2×C31×#103C2211yescharacteristic, complemented
45C2×C31×#102C2211yescharacteristic, complemented
46C2×C31×#102C2211yescharacteristic, complemented
47C2×C31×#102C2211yescharacteristic, complemented
48C2×C31×#102C2211yescharacteristic, complemented
49C2×C31×#102C2211yescharacteristic, complemented
50C31×#407—24no—
51C2×C31×C22⋊C8C2211yescharacteristic
52C2×C31×C22⋊C8C2211yescharacteristic
53C2×C31×C22⋊C8C2211yescharacteristic
54C2×C31×C22⋊C8C2211yescharacteristic
55C31×#386—21no—
56C31×#386—21no—
57C31×#386—21no—
58C31×#380C2211yescharacteristic
59C31×#380C2211yescharacteristic
60C31×#380C2211yescharacteristic
61C31×#340C2211yescharacteristic, complemented
62C31×#340C2211yescharacteristic, complemented
63C31×#340C2211yescharacteristic, complemented
64C31×#340C2211yescharacteristic, complemented
65C25×C31D411yescharacteristic
66C2×#41×C31—22no—
67C2×#41×C31—22no—
68C2×#41×C31—22no—
69C2×#41×C31—22no—
70C2×#41×C31—41no—
71C2×#41×C31—41no—
72C22×Q8×C31C2311yescharacteristic
73C22×D4×C31—21no—
74C22×D4×C31—21no—
75C22×D4×C31—21no—
76C22×D4×C31—21no—
77C22×D4×C31—21no—
78C22×D4×C31—21no—
79C22×D4×C31C2311yescharacteristic
80C22×D4×C31C2311yescharacteristic
81C23×C4×C31—22no—
82C23×C4×C31—21no—
83C23×C4×C31—22no—
84C23×C4×C31—22no—
85C23×C4×C31—22no—
86C23×C4×C31—41no—
87C23×C4×C31—41no—
88C23×C4×C31D411yescharacteristic
89C23×C4×C31D411yescharacteristic
90C23×C4×C31D411yescharacteristic
91C23×C4×C31C2311yescharacteristic
92C23×C4×C31C2311yescharacteristic
93C23×C4×C31C2311yescharacteristic
94C2×SD16×C31—22no—
95C2×SD16×C31—22no—
96C2×SD16×C31—41no—
97C2×D8×C31—22no—
98C2×D8×C31—22no—
99C2×D8×C31—41no—
100C2×M16×C31—22no—
101C2×M16×C31—22no—
102C2×M16×C31—22no—
103C2×M16×C31—22no—
104C2×M16×C31—41no—
105C2×M16×C31—41no—
106C22×C8×C31C2311yescharacteristic
107C22×C8×C31C2311yescharacteristic
108C22×C8×C31C2311yescharacteristic
109C22×C8×C31C2311yescharacteristic
110C31×#123—28no—
111C31×C22⋊Q8—22no—
112C31×C22⋊Q8—22no—
113C31×C22⋊Q8—22no—
114C31×C22⋊Q8D414yescomplemented
115C31×#121—22no—
116C31×#121—22no—
117C31×#121—22no—
118C31×#121—22no—
119C31×#121—22no—
120C31×#121—22no—
121C31×#121—22no—
122C31×#121—41no—
123C31×#121—41no—
124C31×#121D414yescomplemented
125C31×#120—28no—
126C31×#120—44no—
127C4×D4×C31—28no—
128C4×D4×C31—28no—
129C31×#117—22no—
130C31×#117—22no—
131C2×C4⋊C4×C31—21no—
132C2×C4⋊C4×C31—21no—
133C2×C4⋊C4×C31C2311yescharacteristic
134C2×C4⋊C4×C31C2311yescharacteristic
135C2×C4⋊C4×C31C2311yescharacteristic
136C2×C4⋊C4×C31C2311yescharacteristic
137C2×C4⋊C4×C31C2311yescharacteristic
138C2×C22⋊C4×C31—21no—
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—
149C2×C42×C31—21no—
150C31×#107—22no—
151C31×#106—22no—
152C31×#103—22no—
153C31×#103—22no—
154C31×#103—41no—
155C31×#102—22no—
156C31×#102—22no—
157C31×#102—22no—
158C31×#102—22no—
159C31×#102—41no—
160C31×C22⋊C8—22no—
161C31×C22⋊C8—22no—
162C31×C22⋊C8—22no—
163C31×C22⋊C8D414yescomplemented
164C31×#95—21no—
165C31×#95—21no—
166C31×#95—21no—
167C24×C31—22no—
168C24×C31—22no—
169C24×C31—22no—
170C24×C31—21no—
171C24×C31—21no—
172C24×C31—41no—
173C24×C31—41no—
174C24×C31—41no—
175C24×C31—41no—
176C24×C31C2×D411yescharacteristic
177C24×C31C2×D411yescharacteristic
178C24×C31C2×D411yescharacteristic
179#41×C31—44no—
180#41×C31—44no—
181#41×C31—44no—
182#41×C31—44no—
183C2×Q8×C31—21no—
184C2×Q8×C31—21no—
185C2×Q8×C31—21no—
186C2×Q8×C31—21no—
187C2×Q8×C31—21no—
188C2×Q8×C31C2×D412yes—
189C2×D4×C31—24no—
190C2×D4×C31—24no—
191C2×D4×C31—24no—
192C2×D4×C31—21no—
193C2×D4×C31—21no—
194C2×D4×C31—21no—
195C2×D4×C31—21no—
196C2×D4×C31—21no—
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—42no—
204C2×D4×C31—42no—
205C2×D4×C31—42no—
206C2×D4×C31—42no—
207C2×D4×C31—42no—
208C2×D4×C31—42no—
209C2×D4×C31—42no—
210C2×D4×C31—42no—
211C2×D4×C31—42no—
212C2×D4×C31—42no—
213C2×D4×C31—42no—
214C2×D4×C31—42no—
215C2×D4×C31—42no—
216C2×D4×C31—42no—
217C2×D4×C31—42no—
218C2×D4×C31C2×D412yes—
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—24no—
228C22×C4×C31—22no—
229C22×C4×C31—22no—
230C22×C4×C31—21no—
231C22×C4×C31—21no—
232C22×C4×C31—21no—
233C22×C4×C31—22no—
234C22×C4×C31—22no—
235C22×C4×C31—22no—
236C22×C4×C31—22no—
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—41no—
247C22×C4×C31—41no—
248C22×C4×C31—41no—
249C22×C4×C31—44no—
250C22×C4×C31—44no—
251C22×C4×C31—44no—
252C22×C4×C31—44no—
253C22×C4×C31—42no—
254C22×C4×C31—42no—
255C22×C4×C31C2×D411yescharacteristic
256C22×C4×C31C2×D411yescharacteristic
257C22×C4×C31C2×D412yes—
258C22×C4×C31C2×D412yes—
259C22×C4×C31C2×D411yescharacteristic
260C22×C4×C31C2×D412yes—
261C22×C4×C31#4112yes—
262C22×C4×C31C2411yescharacteristic
263SD16×C31—44no—
264D8×C31—44no—
265M16×C31—44no—
266M16×C31—44no—
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—21no—
275C2×C8×C31—21no—
276C2×C8×C31—21no—
277C2×C8×C31C2×D412yes—
278C2×C8×C31C2×D412yes—
279C4⋊C4×C31—24no—
280C4⋊C4×C31—24no—
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×C31—21no—
289C4⋊C4×C31C2×D412yes—
290C4⋊C4×C31C2×D412yes—
291C22⋊C4×C31—24no—
292C22⋊C4×C31—24no—
293C22⋊C4×C31—24no—
294C22⋊C4×C31—24no—
295C22⋊C4×C31—24no—
296C22⋊C4×C31—42no—
297C22⋊C4×C31—42no—
298C22⋊C4×C31—42no—
299C22⋊C4×C31—42no—
300C22⋊C4×C31—42no—
301C22⋊C4×C31—42no—
302C42×C31—24no—
303#24388C3111yesmaximal, characteristic, direct product factor, Sylow
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—21no—
315C23×C31—21no—
316C23×C31—21no—
317C23×C31—21no—
318C23×C31—21no—
319C23×C31—21no—
320C23×C31—21no—
321C23×C31—21no—
322C23×C31—22no—
323C23×C31—44no—
324C23×C31—44no—
325C23×C31—44no—
326C23×C31—44no—
327C23×C31—44no—
328C23×C31—44no—
329C23×C31—44no—
330C23×C31—41no—
331C23×C31—41no—
332C23×C31—41no—
333C23×C31—41no—
334C23×C31—41no—
335C23×C31—41no—
336C23×C31—41no—
337C23×C31—41no—
338C23×C31—41no—
339C23×C31—41no—
340C23×C31—41no—
341C23×C31—41no—
342C23×C31—41no—
343C23×C31#12012yes—
344C23×C31#12112yes—
345C23×C31AGL(1,ℤ/8)12yes—
346C23×C31C22×D411yescharacteristic
347Q8×C31—22no—
348Q8×C31—22no—
349Q8×C31—41no—
350Q8×C31—41no—
351D4×C31—22no—
352D4×C31—22no—
353D4×C31—48no—
354D4×C31—48no—
355D4×C31—48no—
356D4×C31—41no—
357D4×C31—41no—
358D4×C31—41no—
359D4×C31—41no—
360D4×C31—41no—
361D4×C31—41no—
362D4×C31—84no—
363D4×C31—84no—
364D4×C31—84no—
365C2×C4×C31—21no—
366C2×C4×C31—21no—
367C2×C4×C31—21no—
368C2×C4×C31—21no—
369C2×C4×C31—22no—
370C2×C4×C31—22no—
371C2×C4×C31—22no—
372C2×C4×C31—22no—
373C2×C4×C31—22no—
374C2×C4×C31—22no—
375C2×C4×C31—22no—
376C2×C4×C31—22no—
377C2×C4×C31—22no—
378C2×C4×C31—22no—
379C2×C4×C31—21no—
380C2×C4×C31—22no—
381C2×C4×C31—21no—
382C2×C4×C31—21no—
383C2×C4×C31—44no—
384C2×C4×C31—44no—
385C2×C4×C31—44no—
386C2×C4×C31—48no—
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—41no—
398C2×C4×C31—41no—
399C2×C4×C31—41no—
400C2×C4×C31—41no—
401C2×C4×C31—41no—
402C2×C4×C31—41no—
403C2×C4×C31—41no—
404C2×C4×C31—41no—
405C2×C4×C31—41no—
406C2×C4×C31#12012yes—
407C2×C4×C31#12112yes—
408C2×C4×C31C22×D411yescharacteristic
409C2×C4×C31C22×D411yescharacteristic
410C2×C4×C31C22×D411yescharacteristic
411C2×C4×C31C2×#4111yescharacteristic
412C2×C4×C31H(5,𝔽2)11yescharacteristic
413C2×C4×C31H(5,𝔽2)11yescharacteristic
414C8×C31—22no—
415C8×C31—22no—
416C8×C31—41no—
417C8×C31—41no—
418C2×#525C2×C3111yescharacteristic, complemented
419C2×#469C2×C3111yescharacteristic, complemented
420C2×#468C2×C3111yescharacteristic, complemented
421C2×#449C2×C3111yescharacteristic, complemented
422C2×#407C2×C3111yescharacteristic, complemented
423#2847C2×C3111yescharacteristic, complemented
424#2035C2×C3111yescharacteristic, complemented
425#2033C2×C3111yescharacteristic, complemented
426#2000C2×C3111yescharacteristic, complemented
427#1999C2×C3111yescharacteristic, complemented
428#1895C2×C3111yescharacteristic, complemented
429#1894C2×C3111yescharacteristic, complemented
430#1875C2×C3111yescharacteristic, complemented
431#1854C2×C3111yescharacteristic, complemented
432#1788C2×C3111yescharacteristic, complemented
433C22×C31—22no—
434C22×C31—22no—
435C22×C31—22no—
436C22×C31—22no—
437C22×C31—22no—
438C22×C31—22no—
439C22×C31—22no—
440C22×C31—22no—
441C22×C31—22no—
442C22×C31—416no—
443C22×C31—41no—
444C22×C31—41no—
445C22×C31—41no—
446C22×C31—41no—
447C22×C31—41no—
448C22×C31—41no—
449C22×C31—41no—
450C22×C31—41no—
451C22×C31—41no—
452C22×C31—41no—
453C22×C31—41no—
454C22×C31—41no—
455C22×C31—42no—
456C22×C31—42no—
457C22×C31—42no—
458C22×C31—81no—
459C22×C31—81no—
460C22×C31—81no—
461C22×C31—81no—
462C22×C31—81no—
463C22×C31—81no—
464C22×C31—81no—
465C22×C31—81no—
466C22×C31—81no—
467C22×C31—81no—
468C22×C31—81no—
469C22×C31C2×#12011yescharacteristic
470C22×C31C2×#12111yescharacteristic
471C22×C31#53411yescharacteristic
472C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
473C22×C31#57511yescharacteristic
474C22×C31#57511yescharacteristic
475C22×C31#57511yescharacteristic
476C4×C31—22no—
477C4×C31—22no—
478C4×C31—41no—
479C4×C31—42no—
480C4×C31—42no—
481C4×C31—42no—
482C4×C31—81no—
483C4×C31—81no—
484C4×C31—81no—
485C4×C31D4211yescharacteristic
486C4×C31D4211yescharacteristic
487C4×C31#54611yescharacteristic
488C4×C31#54611yescharacteristic
489C22×#41C22×C3111yescharacteristic
490C24×C4C22×C3111yescharacteristic
491C22×SD16C22×C3111yescharacteristic, complemented
492C22×D8C22×C3111yescharacteristic, complemented
493C22×M16C22×C3111yescharacteristic
494C22×M16C22×C3111yescharacteristic
495#525—24no—
496#525—24no—
497C2×#123—21no—
498C2×C22⋊Q8C22×C3111yescharacteristic
499C2×C22⋊Q8C22×C3111yescharacteristic
500C2×#121C22×C3111yescharacteristic
501C2×#121C22×C3111yescharacteristic
502C2×#121C22×C3111yescharacteristic
503C2×#121C22×C3111yescharacteristic
504C2×#121C22×C3111yescharacteristic
505C2×#120—21no—
506C2×#120—21no—
507C2×C4×D4—21no—
508C2×C4×D4—21no—
509C2×#117C22×C3111yescharacteristic
510#469—24no—
511#468—24no—
512#449—24no—
513C2×#107C22×C3111yescharacteristic, complemented
514C2×#106C22×C3111yescharacteristic, complemented
515C2×#103C22×C3111yescharacteristic, complemented
516C2×#103C22×C3111yescharacteristic, complemented
517C2×#103C22×C3111yescharacteristic, complemented
518C2×#102C22×C3111yescharacteristic, complemented
519C2×#102C22×C3111yescharacteristic, complemented
520C2×#102C22×C3111yescharacteristic, complemented
521C2×#102C22×C3111yescharacteristic, complemented
522C2×#102C22×C3111yescharacteristic, complemented
523#407—24no—
524C2×C22⋊C8C22×C3111yescharacteristic
525C2×C22⋊C8C22×C3111yescharacteristic
526C2×C22⋊C8C22×C3111yescharacteristic
527C2×C22⋊C8C22×C3111yescharacteristic
528#386—21no—
529#386—21no—
530#386—21no—
531#380C22×C3111yescharacteristic
532#380C22×C3111yescharacteristic
533#380C22×C3111yescharacteristic
534#340C22×C3111yescharacteristic, complemented
535#340C22×C3111yescharacteristic, complemented
536#340C22×C3111yescharacteristic, complemented
537#340C22×C3111yescharacteristic, complemented
538C2×C31—42no—
539C2×C31—42no—
540C2×C31—42no—
541C2×C31—82no—
542C2×C31—161no—
543C2×C31#241011yescharacteristic
544C2×C31#300511yescharacteristic
545C2×C31#300611yescharacteristic
546C2×C31#305411yescharacteristic
547C2×C31#305511yescharacteristic
548C2×C31#319411yescharacteristic
549C2×C31#319711yescharacteristic
550C25D4×C3111yescharacteristic
551C2×#41—22no—
552C2×#41—22no—
553C2×#41—22no—
554C2×#41—22no—
555C2×#41—41no—
556C2×#41—41no—
557C22×Q8C23×C3111yescharacteristic
558C22×D4—21no—
559C22×D4—21no—
560C22×D4—21no—
561C22×D4—21no—
562C22×D4—21no—
563C22×D4—21no—
564C22×D4C23×C3111yescharacteristic
565C22×D4C23×C3111yescharacteristic
566C23×C4—21no—
567C23×C4—22no—
568C23×C4—22no—
569C23×C4—22no—
570C23×C4—22no—
571C23×C4—41no—
572C23×C4—41no—
573C23×C4D4×C3111yescharacteristic
574C23×C4D4×C3111yescharacteristic
575C23×C4D4×C3111yescharacteristic
576C23×C4C23×C3111yescharacteristic
577C23×C4C23×C3111yescharacteristic
578C23×C4C23×C3111yescharacteristic
579C2×SD16—22no—
580C2×SD16—22no—
581C2×SD16—41no—
582C2×D8—22no—
583C2×D8—22no—
584C2×D8—41no—
585C2×M16—22no—
586C2×M16—22no—
587C2×M16—22no—
588C2×M16—22no—
589C2×M16—41no—
590C2×M16—41no—
591C22×C8C23×C3111yescharacteristic
592C22×C8C23×C3111yescharacteristic
593C22×C8C23×C3111yescharacteristic
594C22×C8C23×C3111yescharacteristic
595#123—28no—
596C22⋊Q8—22no—
597C22⋊Q8—22no—
598C22⋊Q8—22no—
599C22⋊Q8D4×C3114yescomplemented
600#121—22no—
601#121—22no—
602#121—22no—
603#121—22no—
604#121—22no—
605#121—22no—
606#121—22no—
607#121—41no—
608#121—41no—
609#121D4×C3114yescomplemented
610#120—28no—
611#120—44no—
612C4×D4—28no—
613C4×D4—28no—
614#117—22no—
615#117—22no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4C23×C3111yescharacteristic
619C2×C4⋊C4C23×C3111yescharacteristic
620C2×C4⋊C4C23×C3111yescharacteristic
621C2×C4⋊C4C23×C3111yescharacteristic
622C2×C4⋊C4C23×C3111yescharacteristic
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C42—21no—
635#107—22no—
636#106—22no—
637#103—22no—
638#103—22no—
639#103—41no—
640#102—22no—
641#102—22no—
642#102—22no—
643#102—22no—
644#102—41no—
645C22⋊C8—22no—
646C22⋊C8—22no—
647C22⋊C8—22no—
648C22⋊C8D4×C3114yescomplemented
649#95—21no—
650#95—21no—
651#95—21no—
652C31#2438811yescharacteristic, direct product factor, Sylow
653C24—22no—
654C24—22no—
655C24—22no—
656C24—21no—
657C24—21no—
658C24—41no—
659C24—41no—
660C24—41no—
661C24—41no—
662C24C2×D4×C3111yescharacteristic
663C24C2×D4×C3111yescharacteristic
664C24C2×D4×C3111yescharacteristic
665#41—44no—
666#41—44no—
667#41—44no—
668#41—44no—
669C2×Q8—21no—
670C2×Q8—21no—
671C2×Q8—21no—
672C2×Q8—21no—
673C2×Q8—21no—
674C2×Q8C2×D4×C3112yes—
675C2×D4—24no—
676C2×D4—24no—
677C2×D4—24no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—42no—
690C2×D4—42no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—42no—
694C2×D4—42no—
695C2×D4—42no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—42no—
699C2×D4—42no—
700C2×D4—42no—
701C2×D4—42no—
702C2×D4—42no—
703C2×D4—42no—
704C2×D4C2×D4×C3112yes—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—24no—
714C22×C4—22no—
715C22×C4—22no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—22no—
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—22no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—41no—
733C22×C4—41no—
734C22×C4—41no—
735C22×C4—44no—
736C22×C4—44no—
737C22×C4—44no—
738C22×C4—44no—
739C22×C4—42no—
740C22×C4—42no—
741C22×C4C2×D4×C3111yescharacteristic
742C22×C4C2×D4×C3111yescharacteristic
743C22×C4C2×D4×C3112yes—
744C22×C4C2×D4×C3112yes—
745C22×C4C2×D4×C3111yescharacteristic
746C22×C4C2×D4×C3112yes—
747C22×C4#41×C3112yes—
748C22×C4C24×C3111yescharacteristic
749SD16—44no—
750D8—44no—
751M16—44no—
752M16—44no—
753C2×C8—21no—
754C2×C8—21no—
755C2×C8—21no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8—21no—
761C2×C8—21no—
762C2×C8—21no—
763C2×C8C2×D4×C3112yes—
764C2×C8C2×D4×C3112yes—
765C4⋊C4—24no—
766C4⋊C4—24no—
767C4⋊C4—21no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—21no—
771C4⋊C4—21no—
772C4⋊C4—21no—
773C4⋊C4—21no—
774C4⋊C4—21no—
775C4⋊C4C2×D4×C3112yes—
776C4⋊C4C2×D4×C3112yes—
777C22⋊C4—24no—
778C22⋊C4—24no—
779C22⋊C4—24no—
780C22⋊C4—24no—
781C22⋊C4—24no—
782C22⋊C4—42no—
783C22⋊C4—42no—
784C22⋊C4—42no—
785C22⋊C4—42no—
786C22⋊C4—42no—
787C22⋊C4—42no—
788C42—24no—
789C23—21no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—21no—
796C23—21no—
797C23—21no—
798C23—21no—
799C23—21no—
800C23—21no—
801C23—21no—
802C23—21no—
803C23—21no—
804C23—21no—
805C23—21no—
806C23—21no—
807C23—22no—
808C23—44no—
809C23—44no—
810C23—44no—
811C23—44no—
812C23—44no—
813C23—44no—
814C23—44no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23C31×#12012yes—
829C23C31×#12112yes—
830C23C31×AGL(1,ℤ/8)12yes—
831C23C22×D4×C3111yescharacteristic
832Q8—22no—
833Q8—22no—
834Q8—41no—
835Q8—41no—
836D4—22no—
837D4—22no—
838D4—48no—
839D4—48no—
840D4—48no—
841D4—41no—
842D4—41no—
843D4—41no—
844D4—41no—
845D4—41no—
846D4—41no—
847D4—84no—
848D4—84no—
849D4—84no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—21no—
865C2×C4—22no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—44no—
869C2×C4—44no—
870C2×C4—44no—
871C2×C4—48no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4C31×#12012yes—
892C2×C4C31×#12112yes—
893C2×C4C22×D4×C3111yescharacteristic
894C2×C4C22×D4×C3111yescharacteristic
895C2×C4C22×D4×C3111yescharacteristic
896C2×C4C2×#41×C3111yescharacteristic
897C2×C4C31×H(5,𝔽2)11yescharacteristic
898C2×C4C31×H(5,𝔽2)11yescharacteristic
899C8—22no—
900C8—22no—
901C8—41no—
902C8—41no—
903C22—22no—
904C22—22no—
905C22—22no—
906C22—22no—
907C22—22no—
908C22—22no—
909C22—22no—
910C22—22no—
911C22—22no—
912C22—416no—
913C22—41no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—41no—
921C22—41no—
922C22—41no—
923C22—41no—
924C22—41no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—81no—
933C22—81no—
934C22—81no—
935C22—81no—
936C22—81no—
937C22—81no—
938C22—81no—
939C22C2×C31×#12011yescharacteristic
940C22C2×C31×#12111yescharacteristic
941C22C31×#53411yescharacteristic
942C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
943C22C31×#57511yescharacteristic
944C22C31×#57511yescharacteristic
945C22C31×#57511yescharacteristic
946C4—22no—
947C4—22no—
948C4—41no—
949C4—42no—
950C4—42no—
951C4—42no—
952C4—81no—
953C4—81no—
954C4—81no—
955C4D42×C3111yescharacteristic
956C4D42×C3111yescharacteristic
957C4C31×#54611yescharacteristic
958C4C31×#54611yescharacteristic
959C2—42no—
960C2—42no—
961C2—42no—
962C2—82no—
963C2—161no—
964C2C31×#241011yescharacteristic
965C2C31×#300511yescharacteristic
966C2C31×#300611yescharacteristic
967C2C31×#305411yescharacteristic
968C2C31×#305511yescharacteristic
969C2C31×#319411yescharacteristic
970C2C31×#319711yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C24×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#525C2semidirect
2. C2×C31×#469C2semidirect
3. C2×C31×#468C2semidirect
4. C2×C31×#449C2semidirect
5. C2×C31×#407C2semidirect
6. C31×#2847C2semidirect
7. C31×#2035C2semidirect
8. C31×#2033C2semidirect
9. C31×#2000C2semidirect
10. C31×#1999C2semidirect
11. C31×#1895C2semidirect
12. C31×#1894C2semidirect
13. C31×#1875C2semidirect
14. C31×#1854C2semidirect
15. C31×#1788C2semidirect
18. C22×SD16×C31C22semidirect
19. C22×D8×C31C22semidirect
40. C2×C31×#107C22semidirect
41. C2×C31×#106C22semidirect
42. C2×C31×#103C22semidirect
43. C2×C31×#103C22semidirect
44. C2×C31×#103C22semidirect
45. C2×C31×#102C22semidirect
46. C2×C31×#102C22semidirect
47. C2×C31×#102C22semidirect
48. C2×C31×#102C22semidirect
49. C2×C31×#102C22semidirect
61. C31×#340C22semidirect
62. C31×#340C22semidirect
63. C31×#340C22semidirect
64. C31×#340C22semidirect
114. C31×C22⋊Q8D4semidirect
124. C31×#121D4semidirect
163. C31×C22⋊C8D4semidirect
303. #24388C31direct (N × H)
418. C2×#525C2×C31semidirect
419. C2×#469C2×C31semidirect
420. C2×#468C2×C31semidirect
421. C2×#449C2×C31semidirect
422. C2×#407C2×C31semidirect
423. #2847C2×C31semidirect
424. #2035C2×C31semidirect
425. #2033C2×C31semidirect
426. #2000C2×C31semidirect
427. #1999C2×C31semidirect
428. #1895C2×C31semidirect
429. #1894C2×C31semidirect
430. #1875C2×C31semidirect
431. #1854C2×C31semidirect
432. #1788C2×C31semidirect
491. C22×SD16C22×C31semidirect
492. C22×D8C22×C31semidirect
513. C2×#107C22×C31semidirect
514. C2×#106C22×C31semidirect
515. C2×#103C22×C31semidirect
516. C2×#103C22×C31semidirect
517. C2×#103C22×C31semidirect
518. C2×#102C22×C31semidirect
519. C2×#102C22×C31semidirect
520. C2×#102C22×C31semidirect
521. C2×#102C22×C31semidirect
522. C2×#102C22×C31semidirect
534. #340C22×C31semidirect
535. #340C22×C31semidirect
536. #340C22×C31semidirect
537. #340C22×C31semidirect
599. C22⋊Q8D4×C31semidirect
609. #121D4×C31semidirect
648. C22⋊C8D4×C31semidirect
652. C31#24388direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5252
C2×C31×#4692
C2×C31×#4682
C2×C31×#4492
C2×C31×#4072
C31×#28472
C31×#20352
C31×#20332
C31×#20002
C31×#19992
C31×#18952
C31×#18942
C31×#18752
C31×#18542
C31×#17882
#2438831