Finite Group Databasebeta

← C31×#23938 #21480697

Subgroups — C31×#23938 #21480697

Order 7936.

1308 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#529C211yesmaximal, characteristic, complemented
2C2×C31×#452C211yesmaximal, characteristic, complemented
3C2×C31×#449C211yesmaximal, characteristic
4C31×#2297C211yesmaximal, characteristic, complemented
5C31×#2026C211yesmaximal, characteristic, complemented
6C31×#2025C211yesmaximal, characteristic, complemented
7C31×#2015C211yesmaximal, characteristic, complemented
8C31×#2012C211yesmaximal, characteristic, complemented
9C31×#1880C211yesmaximal, characteristic, complemented
10C31×#1879C211yesmaximal, characteristic, complemented
11C31×#1878C211yesmaximal, characteristic, complemented
12C31×#1877C211yesmaximal, characteristic, complemented
13C31×#1875C211yesmaximal, characteristic, complemented
14C31×#1873C211yesmaximal, characteristic, complemented
15C31×#1817C211yesmaximal, characteristic, complemented
16C22×#41×C31C2211yescharacteristic
17C22×Q16×C31C2211yescharacteristic
18C22×SD16×C31C2211yescharacteristic
19C22×SD16×C31C2211yescharacteristic
20C22×D8×C31C2211yescharacteristic
21C31×#529—24no—
22C31×#529—24no—
23C2×C31×#126—21no—
24C2×C31×#125C2211yescharacteristic
25C2×C31×#124C2211yescharacteristic
26C2×C31×#123—21no—
27C2×C31×C22⋊Q8C2211yescharacteristic
28C2×C31×#121C2211yescharacteristic
29C2×C4×Q8×C31C2211yescharacteristic
30C2×C4×D4×C31—21no—
31C2×C4×D4×C31C2211yescharacteristic
32C2×C31×#117—21no—
33C2×C31×#117C2211yescharacteristic
34C22×C42×C31C2211yescharacteristic
35C31×#452—24no—
36C31×#449—24no—
37C2×C31×#103C2211yescharacteristic
38C2×C31×#103C2211yescharacteristic
39C2×C31×#103C2211yescharacteristic
40C2×C31×#103C2211yescharacteristic
41C2×C31×#102C2211yescharacteristic
42C2×C31×#102C2211yescharacteristic
43C2×C31×#102C2211yescharacteristic
44C2×C31×#102C2211yescharacteristic
45C2×C31×C22⋊C8C2211yescharacteristic
46C2×C31×C22⋊C8C2211yescharacteristic
47C31×#391C2211yescharacteristic
48C31×#391C2211yescharacteristic
49C31×#390C2211yescharacteristic
50C31×#390C2211yescharacteristic
51C31×#386—21no—
52C31×#386—21no—
53C4×C22⋊C4×C31—21no—
54C4×C22⋊C4×C31—21no—
55C31×#340C2211yescharacteristic
56C31×#340C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#336C2211yescharacteristic
60C31×#336C2211yescharacteristic
61C31×#336C2211yescharacteristic
62C31×#336C2211yescharacteristic
63C2×#41×C31—22no—
64C2×#41×C31—22no—
65C2×#41×C31—22no—
66C2×#41×C31—22no—
67C2×#41×C31—41no—
68C2×#41×C31—41no—
69C22×Q8×C31C2311yescharacteristic
70C22×Q8×C31C2311yescharacteristic
71C22×D4×C31—21no—
72C22×D4×C31—21no—
73C22×D4×C31C2311yescharacteristic
74C22×D4×C31C2311yescharacteristic
75C23×C4×C31—21no—
76C23×C4×C31—21no—
77C23×C4×C31D411yescharacteristic
78C23×C4×C31D411yescharacteristic
79C23×C4×C31C2311yescharacteristic
80C2×Q16×C31—22no—
81C2×Q16×C31—22no—
82C2×Q16×C31—41no—
83C2×SD16×C31—22no—
84C2×SD16×C31—22no—
85C2×SD16×C31—22no—
86C2×SD16×C31—22no—
87C2×SD16×C31—41no—
88C2×SD16×C31—41no—
89C2×D8×C31—22no—
90C2×D8×C31—22no—
91C2×D8×C31—41no—
92C22×C8×C31C2311yescharacteristic
93C22×C8×C31C2311yescharacteristic
94C22×C8×C31C2311yescharacteristic
95C22×C8×C31C2311yescharacteristic
96C31×#126—28no—
97C31×#125—22no—
98C31×#125—22no—
99C31×#124—22no—
100C31×#124—22no—
101C31×#123—28no—
102C31×C22⋊Q8—22no—
103C31×C22⋊Q8D414yes—
104C31×#121—22no—
105C31×#121D414yes—
106C4×Q8×C31—22no—
107C4×Q8×C31—22no—
108C4×D4×C31—28no—
109C4×D4×C31—22no—
110C4×D4×C31—22no—
111C31×#117—28no—
112C31×#117—41no—
113C31×#117—41no—
114C2×C4⋊C4×C31—21no—
115C2×C4⋊C4×C31—21no—
116C2×C4⋊C4×C31—21no—
117C2×C4⋊C4×C31—21no—
118C2×C4⋊C4×C31C2311yescharacteristic
119C2×C4⋊C4×C31C2311yescharacteristic
120C2×C4⋊C4×C31C2311yescharacteristic
121C2×C4⋊C4×C31C2311yescharacteristic
122C2×C22⋊C4×C31—21no—
123C2×C22⋊C4×C31—21no—
124C2×C22⋊C4×C31—21no—
125C2×C22⋊C4×C31—21no—
126C2×C22⋊C4×C31—21no—
127C2×C22⋊C4×C31—21no—
128C2×C22⋊C4×C31—21no—
129C2×C22⋊C4×C31—21no—
130C2×C22⋊C4×C31—21no—
131C2×C22⋊C4×C31—21no—
132C2×C42×C31—22no—
133C2×C42×C31—22no—
134C2×C42×C31—21no—
135C2×C42×C31—21no—
136C2×C42×C31D411yescharacteristic
137C2×C42×C31D411yescharacteristic
138C2×C42×C31C2311yescharacteristic
139C2×C42×C31C2311yescharacteristic
140C31×#103—22no—
141C31×#103—22no—
142C31×#103—41no—
143C31×#103—41no—
144C31×#102—22no—
145C31×#102—22no—
146C31×#102—41no—
147C31×#102—41no—
148C31×C22⋊C8—22no—
149C31×C22⋊C8—22no—
150C31×#95—21no—
151C31×#95—21no—
152C31×#95—21no—
153C31×#95—21no—
154C24×C31—21no—
155C24×C31—21no—
156C24×C31C2×D411yescharacteristic
157#41×C31—44no—
158#41×C31—44no—
159#41×C31—44no—
160#41×C31—44no—
161C2×Q8×C31—21no—
162C2×Q8×C31—21no—
163C2×Q8×C31—21no—
164C2×Q8×C31—21no—
165C2×Q8×C31—21no—
166C2×Q8×C31—21no—
167C2×Q8×C31—21no—
168C2×Q8×C31—21no—
169C2×Q8×C31—21no—
170C2×Q8×C31—21no—
171C2×Q8×C31C2×D412yes—
172C2×Q8×C31#4112yes—
173C2×D4×C31—24no—
174C2×D4×C31—24no—
175C2×D4×C31—21no—
176C2×D4×C31—21no—
177C2×D4×C31—21no—
178C2×D4×C31—21no—
179C2×D4×C31—21no—
180C2×D4×C31—21no—
181C2×D4×C31—21no—
182C2×D4×C31—21no—
183C2×D4×C31—21no—
184C2×D4×C31—21no—
185C2×D4×C31—42no—
186C2×D4×C31—42no—
187C2×D4×C31—42no—
188C2×D4×C31—42no—
189C2×D4×C31C2×D412yes—
190C2×D4×C31#4112yes—
191C22×C4×C31—21no—
192C22×C4×C31—21no—
193C22×C4×C31—21no—
194C22×C4×C31—21no—
195C22×C4×C31—24no—
196C22×C4×C31—24no—
197C22×C4×C31—22no—
198C22×C4×C31—22no—
199C22×C4×C31—21no—
200C22×C4×C31—21no—
201C22×C4×C31—21no—
202C22×C4×C31—21no—
203C22×C4×C31—22no—
204C22×C4×C31—21no—
205C22×C4×C31—21no—
206C22×C4×C31—41no—
207C22×C4×C31—41no—
208C22×C4×C31—41no—
209C22×C4×C31—42no—
210C22×C4×C31—42no—
211C22×C4×C31—42no—
212C22×C4×C31—42no—
213C22×C4×C31C2×D411yescharacteristic
214C22×C4×C31C2×D411yescharacteristic
215C22×C4×C31C2×D411yescharacteristic
216C22×C4×C31C2×D411yescharacteristic
217C22×C4×C31C2×D412yes—
218C22×C4×C31C2×D412yes—
219C22×C4×C31C2×D411yescharacteristic
220C22×C4×C31C2411yescharacteristic
221Q16×C31—44no—
222SD16×C31—44no—
223SD16×C31—44no—
224D8×C31—44no—
225C2×C8×C31—21no—
226C2×C8×C31—21no—
227C2×C8×C31—21no—
228C2×C8×C31—21no—
229C2×C8×C31—21no—
230C2×C8×C31—21no—
231C2×C8×C31—21no—
232C2×C8×C31—21no—
233C2×C8×C31—21no—
234C2×C8×C31—21no—
235C2×C8×C31—21no—
236C2×C8×C31—21no—
237C4⋊C4×C31—24no—
238C4⋊C4×C31—24no—
239C4⋊C4×C31—24no—
240C4⋊C4×C31—24no—
241C4⋊C4×C31—21no—
242C4⋊C4×C31—21no—
243C4⋊C4×C31—21no—
244C4⋊C4×C31—21no—
245C4⋊C4×C31—21no—
246C4⋊C4×C31—21no—
247C4⋊C4×C31C2×D412yes—
248C4⋊C4×C31C2×D412yes—
249C22⋊C4×C31—24no—
250C22⋊C4×C31—24no—
251C22⋊C4×C31—24no—
252C22⋊C4×C31—24no—
253C22⋊C4×C31—24no—
254C22⋊C4×C31—42no—
255C22⋊C4×C31—42no—
256C22⋊C4×C31—42no—
257C22⋊C4×C31—42no—
258C22⋊C4×C31—42no—
259C42×C31—24no—
260C42×C31—22no—
261C42×C31—22no—
262C42×C31—21no—
263C42×C31—21no—
264C42×C31—21no—
265C42×C31—21no—
266C42×C31—42no—
267#23938C3111yesmaximal, characteristic, direct product factor, Sylow
268C23×C31—21no—
269C23×C31—21no—
270C23×C31—21no—
271C23×C31—21no—
272C23×C31—21no—
273C23×C31—21no—
274C23×C31—22no—
275C23×C31—22no—
276C23×C31—41no—
277C23×C31—41no—
278C23×C31—41no—
279C23×C31—41no—
280C23×C31—41no—
281C23×C31—41no—
282C23×C31—41no—
283C23×C31—41no—
284C23×C31—41no—
285C23×C31—41no—
286C23×C31—41no—
287C23×C31—41no—
288C23×C31#12012yes—
289C23×C31C22×D411yescharacteristic
290Q8×C31—22no—
291Q8×C31—22no—
292Q8×C31—22no—
293Q8×C31—22no—
294Q8×C31—41no—
295Q8×C31—41no—
296Q8×C31—41no—
297Q8×C31—41no—
298D4×C31—22no—
299D4×C31—22no—
300D4×C31—22no—
301D4×C31—22no—
302D4×C31—48no—
303D4×C31—48no—
304D4×C31—41no—
305D4×C31—41no—
306D4×C31—41no—
307D4×C31—41no—
308C2×C4×C31—21no—
309C2×C4×C31—21no—
310C2×C4×C31—21no—
311C2×C4×C31—21no—
312C2×C4×C31—22no—
313C2×C4×C31—22no—
314C2×C4×C31—22no—
315C2×C4×C31—22no—
316C2×C4×C31—21no—
317C2×C4×C31—21no—
318C2×C4×C31—21no—
319C2×C4×C31—22no—
320C2×C4×C31—22no—
321C2×C4×C31—22no—
322C2×C4×C31—22no—
323C2×C4×C31—21no—
324C2×C4×C31—21no—
325C2×C4×C31—21no—
326C2×C4×C31—21no—
327C2×C4×C31—21no—
328C2×C4×C31—21no—
329C2×C4×C31—44no—
330C2×C4×C31—48no—
331C2×C4×C31—48no—
332C2×C4×C31—44no—
333C2×C4×C31—41no—
334C2×C4×C31—41no—
335C2×C4×C31—41no—
336C2×C4×C31—41no—
337C2×C4×C31—41no—
338C2×C4×C31—41no—
339C2×C4×C31—41no—
340C2×C4×C31—41no—
341C2×C4×C31—41no—
342C2×C4×C31—41no—
343C2×C4×C31—41no—
344C2×C4×C31—41no—
345C2×C4×C31—41no—
346C2×C4×C31—41no—
347C2×C4×C31#12012yes—
348C2×C4×C31#13512yes—
349C2×C4×C31C22×D411yescharacteristic
350C2×C4×C31C22×D411yescharacteristic
351C2×C4×C31C2×#4111yescharacteristic
352C2×C4×C31C2×#4111yescharacteristic
353C2×C4×C31H(5,𝔽2)11yescharacteristic
354C2×C4×C31H(5,𝔽2)11yescharacteristic
355C8×C31—41no—
356C8×C31—41no—
357C8×C31—41no—
358C8×C31—41no—
359C2×#529C2×C3111yescharacteristic, complemented
360C2×#452C2×C3111yescharacteristic, complemented
361C2×#449C2×C3111yescharacteristic
362#2297C2×C3111yescharacteristic, complemented
363#2026C2×C3111yescharacteristic, complemented
364#2025C2×C3111yescharacteristic, complemented
365#2015C2×C3111yescharacteristic, complemented
366#2012C2×C3111yescharacteristic, complemented
367#1880C2×C3111yescharacteristic, complemented
368#1879C2×C3111yescharacteristic, complemented
369#1878C2×C3111yescharacteristic, complemented
370#1877C2×C3111yescharacteristic, complemented
371#1875C2×C3111yescharacteristic, complemented
372#1873C2×C3111yescharacteristic, complemented
373#1817C2×C3111yescharacteristic, complemented
374C22×C31—22no—
375C22×C31—22no—
376C22×C31—22no—
377C22×C31—41no—
378C22×C31—41no—
379C22×C31—41no—
380C22×C31—41no—
381C22×C31—42no—
382C22×C31—42no—
383C22×C31—42no—
384C22×C31—42no—
385C22×C31—42no—
386C22×C31—42no—
387C22×C31—81no—
388C22×C31—81no—
389C22×C31—81no—
390C22×C31—81no—
391C22×C31—81no—
392C22×C31—81no—
393C22×C31—81no—
394C22×C31—81no—
395C22×C31C2×#12011yescharacteristic
396C22×C31#52511yescharacteristic
397C22×C31#53511yescharacteristic
398C22×C31C2×#13511yescharacteristic
399C22×C31#57511yescharacteristic
400C22×C31#57511yescharacteristic
401C22×C31#57511yescharacteristic
402C4×C31—22no—
403C4×C31—22no—
404C4×C31—42no—
405C4×C31—42no—
406C4×C31—41no—
407C4×C31—42no—
408C4×C31—41no—
409C4×C31—41no—
410C4×C31—42no—
411C4×C31—81no—
412C4×C31—81no—
413C4×C31#54611yescharacteristic
414C4×C31#54611yescharacteristic
415C4×C31#54611yescharacteristic
416C4×C31#54611yescharacteristic
417C22×#41C22×C3111yescharacteristic
418C22×Q16C22×C3111yescharacteristic
419C22×SD16C22×C3111yescharacteristic
420C22×SD16C22×C3111yescharacteristic
421C22×D8C22×C3111yescharacteristic
422#529—24no—
423#529—24no—
424C2×#126—21no—
425C2×#125C22×C3111yescharacteristic
426C2×#124C22×C3111yescharacteristic
427C2×#123—21no—
428C2×C22⋊Q8C22×C3111yescharacteristic
429C2×#121C22×C3111yescharacteristic
430C2×C4×Q8C22×C3111yescharacteristic
431C2×C4×D4—21no—
432C2×C4×D4C22×C3111yescharacteristic
433C2×#117—21no—
434C2×#117C22×C3111yescharacteristic
435C22×C42C22×C3111yescharacteristic
436#452—24no—
437#449—24no—
438C2×#103C22×C3111yescharacteristic
439C2×#103C22×C3111yescharacteristic
440C2×#103C22×C3111yescharacteristic
441C2×#103C22×C3111yescharacteristic
442C2×#102C22×C3111yescharacteristic
443C2×#102C22×C3111yescharacteristic
444C2×#102C22×C3111yescharacteristic
445C2×#102C22×C3111yescharacteristic
446C2×C22⋊C8C22×C3111yescharacteristic
447C2×C22⋊C8C22×C3111yescharacteristic
448#391C22×C3111yescharacteristic
449#391C22×C3111yescharacteristic
450#390C22×C3111yescharacteristic
451#390C22×C3111yescharacteristic
452#386—21no—
453#386—21no—
454C4×C22⋊C4—21no—
455C4×C22⋊C4—21no—
456#340C22×C3111yescharacteristic
457#340C22×C3111yescharacteristic
458#340C22×C3111yescharacteristic
459#340C22×C3111yescharacteristic
460#336C22×C3111yescharacteristic
461#336C22×C3111yescharacteristic
462#336C22×C3111yescharacteristic
463#336C22×C3111yescharacteristic
464C2×C31—42no—
465C2×C31—82no—
466C2×C31—82no—
467C2×C31#240411yescharacteristic
468C2×C31#300211yescharacteristic
469C2×C31#300511yescharacteristic
470C2×C31#310211yescharacteristic
471C2×C31#311111yescharacteristic
472C2×C31#321211yescharacteristic
473C2×C31#321911yescharacteristic
474C2×#41—22no—
475C2×#41—22no—
476C2×#41—22no—
477C2×#41—22no—
478C2×#41—41no—
479C2×#41—41no—
480C22×Q8C23×C3111yescharacteristic
481C22×Q8C23×C3111yescharacteristic
482C22×D4—21no—
483C22×D4—21no—
484C22×D4C23×C3111yescharacteristic
485C22×D4C23×C3111yescharacteristic
486C23×C4—21no—
487C23×C4—21no—
488C23×C4D4×C3111yescharacteristic
489C23×C4D4×C3111yescharacteristic
490C23×C4C23×C3111yescharacteristic
491C2×Q16—22no—
492C2×Q16—22no—
493C2×Q16—41no—
494C2×SD16—22no—
495C2×SD16—22no—
496C2×SD16—22no—
497C2×SD16—22no—
498C2×SD16—41no—
499C2×SD16—41no—
500C2×D8—22no—
501C2×D8—22no—
502C2×D8—41no—
503C22×C8C23×C3111yescharacteristic
504C22×C8C23×C3111yescharacteristic
505C22×C8C23×C3111yescharacteristic
506C22×C8C23×C3111yescharacteristic
507#126—28no—
508#125—22no—
509#125—22no—
510#124—22no—
511#124—22no—
512#123—28no—
513C22⋊Q8—22no—
514C22⋊Q8D4×C3114yes—
515#121—22no—
516#121D4×C3114yes—
517C4×Q8—22no—
518C4×Q8—22no—
519C4×D4—28no—
520C4×D4—22no—
521C4×D4—22no—
522#117—28no—
523#117—41no—
524#117—41no—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4C23×C3111yescharacteristic
530C2×C4⋊C4C23×C3111yescharacteristic
531C2×C4⋊C4C23×C3111yescharacteristic
532C2×C4⋊C4C23×C3111yescharacteristic
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C42—21no—
544C2×C42—22no—
545C2×C42—22no—
546C2×C42—21no—
547C2×C42D4×C3111yescharacteristic
548C2×C42D4×C3111yescharacteristic
549C2×C42C23×C3111yescharacteristic
550C2×C42C23×C3111yescharacteristic
551#103—22no—
552#103—22no—
553#103—41no—
554#103—41no—
555#102—22no—
556#102—22no—
557#102—41no—
558#102—41no—
559C22⋊C8—22no—
560C22⋊C8—22no—
561#95—21no—
562#95—21no—
563#95—21no—
564#95—21no—
565C31#2393811yescharacteristic, direct product factor, Sylow
566C24—21no—
567C24—21no—
568C24C2×D4×C3111yescharacteristic
569#41—44no—
570#41—44no—
571#41—44no—
572#41—44no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8C2×D4×C3112yes—
584C2×Q8#41×C3112yes—
585C2×D4—24no—
586C2×D4—24no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—42no—
598C2×D4—42no—
599C2×D4—42no—
600C2×D4—42no—
601C2×D4C2×D4×C3112yes—
602C2×D4#41×C3112yes—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—24no—
608C22×C4—24no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—22no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—41no—
619C22×C4—41no—
620C22×C4—41no—
621C22×C4—42no—
622C22×C4—42no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4C2×D4×C3111yescharacteristic
626C22×C4C2×D4×C3111yescharacteristic
627C22×C4C2×D4×C3111yescharacteristic
628C22×C4C2×D4×C3111yescharacteristic
629C22×C4C2×D4×C3112yes—
630C22×C4C2×D4×C3112yes—
631C22×C4C2×D4×C3111yescharacteristic
632C22×C4C24×C3111yescharacteristic
633Q16—44no—
634SD16—44no—
635SD16—44no—
636D8—44no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C4⋊C4—24no—
650C4⋊C4—24no—
651C4⋊C4—24no—
652C4⋊C4—24no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—21no—
659C4⋊C4C2×D4×C3112yes—
660C4⋊C4C2×D4×C3112yes—
661C22⋊C4—24no—
662C22⋊C4—24no—
663C22⋊C4—24no—
664C22⋊C4—24no—
665C22⋊C4—24no—
666C22⋊C4—42no—
667C22⋊C4—42no—
668C22⋊C4—42no—
669C22⋊C4—42no—
670C22⋊C4—42no—
671C42—24no—
672C42—22no—
673C42—22no—
674C42—21no—
675C42—21no—
676C42—21no—
677C42—21no—
678C42—42no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—22no—
686C23—22no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—41no—
697C23—41no—
698C23—41no—
699C23C31×#12012yes—
700C23C22×D4×C3111yescharacteristic
701Q8—22no—
702Q8—22no—
703Q8—22no—
704Q8—22no—
705Q8—41no—
706Q8—41no—
707Q8—41no—
708Q8—41no—
709D4—22no—
710D4—22no—
711D4—22no—
712D4—22no—
713D4—48no—
714D4—48no—
715D4—41no—
716D4—41no—
717D4—41no—
718D4—41no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—44no—
741C2×C4—48no—
742C2×C4—48no—
743C2×C4—44no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4C31×#12012yes—
759C2×C4C31×#13512yes—
760C2×C4C22×D4×C3111yescharacteristic
761C2×C4C22×D4×C3111yescharacteristic
762C2×C4C2×#41×C3111yescharacteristic
763C2×C4C2×#41×C3111yescharacteristic
764C2×C4C31×H(5,𝔽2)11yescharacteristic
765C2×C4C31×H(5,𝔽2)11yescharacteristic
766C8—41no—
767C8—41no—
768C8—41no—
769C8—41no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22C2×C31×#12011yescharacteristic
792C22C31×#52511yescharacteristic
793C22C31×#53511yescharacteristic
794C22C2×C31×#13511yescharacteristic
795C22C31×#57511yescharacteristic
796C22C31×#57511yescharacteristic
797C22C31×#57511yescharacteristic
798C4—22no—
799C4—22no—
800C4—42no—
801C4—42no—
802C4—41no—
803C4—42no—
804C4—41no—
805C4—41no—
806C4—42no—
807C4—81no—
808C4—81no—
809C4C31×#54611yescharacteristic
810C4C31×#54611yescharacteristic
811C4C31×#54611yescharacteristic
812C4C31×#54611yescharacteristic
813C2—42no—
814C2—82no—
815C2—82no—
816C2C31×#240411yescharacteristic
817C2C31×#300211yescharacteristic
818C2C31×#300511yescharacteristic
819C2C31×#310211yescharacteristic
820C2C31×#311111yescharacteristic
821C2C31×#321211yescharacteristic
822C2C31×#321911yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#449C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C22×C42×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#529C2semidirect
2. C2×C31×#452C2semidirect
4. C31×#2297C2semidirect
5. C31×#2026C2semidirect
6. C31×#2025C2semidirect
7. C31×#2015C2semidirect
8. C31×#2012C2semidirect
9. C31×#1880C2semidirect
10. C31×#1879C2semidirect
11. C31×#1878C2semidirect
12. C31×#1877C2semidirect
13. C31×#1875C2semidirect
14. C31×#1873C2semidirect
15. C31×#1817C2semidirect
267. #23938C31direct (N × H)
359. C2×#529C2×C31semidirect
360. C2×#452C2×C31semidirect
362. #2297C2×C31semidirect
363. #2026C2×C31semidirect
364. #2025C2×C31semidirect
365. #2015C2×C31semidirect
366. #2012C2×C31semidirect
367. #1880C2×C31semidirect
368. #1879C2×C31semidirect
369. #1878C2×C31semidirect
370. #1877C2×C31semidirect
371. #1875C2×C31semidirect
372. #1873C2×C31semidirect
373. #1817C2×C31semidirect
565. C31#23938direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5292
C2×C31×#4522
C2×C31×#4492
C31×#22972
C31×#20262
C31×#20252
C31×#20152
C31×#20122
C31×#18802
C31×#18792
C31×#18782
C31×#18772
C31×#18752
C31×#18732
C31×#18172
#2393831