Finite Group Databasebeta

← C31×#24349 #21481108

Subgroups — C31×#24349 #21481108

Order 7936.

1072 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#554C211yesmaximal, characteristic
2C2×C31×#479C211yesmaximal, characteristic, complemented
3C2×C31×#440C211yesmaximal, characteristic
4C31×#2582C211yesmaximal, characteristic, complemented
5C31×#2059C211yesmaximal, characteristic, complemented
6C31×#2057C211yesmaximal, characteristic, complemented
7C31×#2026C211yesmaximal, characteristic, complemented
8C31×#2024C211yesmaximal, characteristic, complemented
9C31×#1992C211yesmaximal, characteristic, complemented
10C31×#1985C211yesmaximal, characteristic, complemented
11C31×#1877C211yesmaximal, characteristic
12C31×#1877C211yesmaximal, characteristic
13C31×#1864C211yesmaximal, characteristic
14C31×#1862C211yesmaximal, characteristic
15C31×#1802C211yesmaximal, characteristic
16C22×SD16×C31C2211yescharacteristic
17C31×#554—24no—
18C31×#554—24no—
19C2×C31×C4⋊Q8C2211yescharacteristic
20C2×C31×#125C2211yescharacteristic
21C2×C31×#125C2211yescharacteristic
22C2×C31×C22⋊Q8—21no—
23C2×C31×C22⋊Q8—21no—
24C2×C31×C22⋊Q8—21no—
25C2×C4×Q8×C31C2211yescharacteristic
26C2×C4×Q8×C31C2211yescharacteristic
27C2×C4×D4×C31C2211yescharacteristic
28C2×C4×D4×C31C2211yescharacteristic
29C2×C4×D4×C31C2211yescharacteristic
30C22×C4⋊C4×C31—21no—
31C31×#479—24no—
32C31×#440—24no—
33C2×C31×#107C2211yescharacteristic
34C2×C31×#107C2211yescharacteristic
35C2×C31×#106C2211yescharacteristic
36C2×C31×C4⋊C8C2211yescharacteristic
37C2×C31×#103C2211yescharacteristic
38C2×C31×#103C2211yescharacteristic
39C2×C31×#103C2211yescharacteristic
40C2×C31×#102C2211yescharacteristic
41C2×C31×#102C2211yescharacteristic
42C2×C31×#102C2211yescharacteristic
43C2×C31×#97C2211yescharacteristic
44C31×#398—21no—
45C31×#398—21no—
46C31×#391—21no—
47C31×#391C2211yescharacteristic
48C31×#391C2211yescharacteristic
49C31×#389—21no—
50C31×#389C2211yescharacteristic
51C31×#389C2211yescharacteristic
52C31×#384C2211yescharacteristic
53C31×#340C2211yescharacteristic
54C31×#340C2211yescharacteristic
55C31×#340C2211yescharacteristic
56C31×#340C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#336C2211yescharacteristic
60C31×#336C2211yescharacteristic
61C31×#336C2211yescharacteristic
62C31×#336C2211yescharacteristic
63C22×Q8×C31—21no—
64C22×Q8×C31D411yescharacteristic
65C22×Q8×C31C2311yescharacteristic
66C22×D4×C31C2311yescharacteristic
67C23×C4×C31—21no—
68C23×C4×C31—21no—
69C23×C4×C31—21no—
70C2×SD16×C31—22no—
71C2×SD16×C31—22no—
72C2×SD16×C31Q814yescomplemented
73C22×C8×C31C2311yescharacteristic
74C22×C8×C31C2311yescharacteristic
75C22×C8×C31C2311yescharacteristic
76C22×C8×C31C2311yescharacteristic
77C31×C4⋊Q8—22no—
78C31×C4⋊Q8—22no—
79C31×#125—22no—
80C31×#125—22no—
81C31×#125—22no—
82C31×#125D414yes—
83C31×C22⋊Q8—28no—
84C31×C22⋊Q8—28no—
85C31×C22⋊Q8—28no—
86C4×Q8×C31—22no—
87C4×Q8×C31—22no—
88C4×Q8×C31—22no—
89C4×Q8×C31—22no—
90C4×D4×C31—22no—
91C4×D4×C31—22no—
92C4×D4×C31—22no—
93C4×D4×C31—22no—
94C4×D4×C31—22no—
95C4×D4×C31D414yes—
96C2×C4⋊C4×C31—28no—
97C2×C4⋊C4×C31—21no—
98C2×C4⋊C4×C31—21no—
99C2×C4⋊C4×C31—21no—
100C2×C4⋊C4×C31—21no—
101C2×C4⋊C4×C31—21no—
102C2×C4⋊C4×C31—21no—
103C2×C4⋊C4×C31—21no—
104C2×C4⋊C4×C31—21no—
105C2×C4⋊C4×C31—21no—
106C2×C4⋊C4×C31—21no—
107C2×C4⋊C4×C31D411yescharacteristic
108C2×C4⋊C4×C31D411yescharacteristic
109C2×C4⋊C4×C31D411yescharacteristic
110C2×C4⋊C4×C31C2311yescharacteristic
111C2×C4⋊C4×C31C2311yescharacteristic
112C2×C4⋊C4×C31C2311yescharacteristic
113C2×C4⋊C4×C31C2311yescharacteristic
114C2×C4⋊C4×C31C2311yescharacteristic
115C2×C4⋊C4×C31C2311yescharacteristic
116C2×C22⋊C4×C31—21no—
117C2×C22⋊C4×C31—21no—
118C2×C22⋊C4×C31—21no—
119C2×C42×C31—21no—
120C2×C42×C31C2311yescharacteristic
121C2×C42×C31C2311yescharacteristic
122C2×C42×C31C2311yescharacteristic
123C31×#107—22no—
124C31×#107—22no—
125C31×#106—22no—
126C31×C4⋊C8—22no—
127C31×#103—22no—
128C31×#103—22no—
129C31×#103—22no—
130C31×#102—22no—
131C31×#102—22no—
132C31×#102—22no—
133C31×#97—22no—
134C31×#95—21no—
135C31×#95—21no—
136C31×#95—21no—
137C31×#95—21no—
138C31×#95—21no—
139C31×#95—21no—
140C24×C31—21no—
141C2×Q8×C31—24no—
142C2×Q8×C31—22no—
143C2×Q8×C31—22no—
144C2×Q8×C31—21no—
145C2×Q8×C31—21no—
146C2×Q8×C31—21no—
147C2×Q8×C31—21no—
148C2×Q8×C31—21no—
149C2×Q8×C31—41no—
150C2×Q8×C31—81no—
151C2×Q8×C31—81no—
152C2×Q8×C31C2×Q812yes—
153C2×D4×C31—21no—
154C2×D4×C31—21no—
155C2×D4×C31—21no—
156C2×D4×C31C2×D412yes—
157C2×D4×C31C2×Q812yes—
158C2×D4×C31#4112yes—
159C22×C4×C31—24no—
160C22×C4×C31—21no—
161C22×C4×C31—21no—
162C22×C4×C31—21no—
163C22×C4×C31—21no—
164C22×C4×C31—24no—
165C22×C4×C31—24no—
166C22×C4×C31—21no—
167C22×C4×C31—21no—
168C22×C4×C31—21no—
169C22×C4×C31—42no—
170C22×C4×C31—42no—
171C22×C4×C31—81no—
172C22×C4×C31—81no—
173C22×C4×C31—81no—
174C22×C4×C31—81no—
175C22×C4×C31C2×D411yescharacteristic
176C22×C4×C31C2×D411yescharacteristic
177C22×C4×C31C2×D411yescharacteristic
178C22×C4×C31C2×D411yescharacteristic
179C22×C4×C31C2×D411yescharacteristic
180C22×C4×C31C2×D411yescharacteristic
181C22×C4×C31C2411yescharacteristic
182SD16×C31—28no—
183C2×C8×C31—21no—
184C2×C8×C31—21no—
185C2×C8×C31—21no—
186C2×C8×C31—21no—
187C2×C8×C31—21no—
188C2×C8×C31—21no—
189C2×C8×C31—21no—
190C2×C8×C31—21no—
191C2×C8×C31—21no—
192C2×C8×C31—21no—
193C2×C8×C31—21no—
194C2×C8×C31C2×Q812yes—
195C4⋊C4×C31—24no—
196C4⋊C4×C31—24no—
197C4⋊C4×C31—24no—
198C4⋊C4×C31—22no—
199C4⋊C4×C31—24no—
200C4⋊C4×C31—24no—
201C4⋊C4×C31—22no—
202C4⋊C4×C31—22no—
203C4⋊C4×C31—21no—
204C4⋊C4×C31—21no—
205C4⋊C4×C31—21no—
206C4⋊C4×C31—21no—
207C4⋊C4×C31—21no—
208C4⋊C4×C31—21no—
209C4⋊C4×C31—21no—
210C4⋊C4×C31—21no—
211C4⋊C4×C31—21no—
212C4⋊C4×C31—42no—
213C4⋊C4×C31—42no—
214C4⋊C4×C31—81no—
215C4⋊C4×C31—81no—
216C4⋊C4×C31—81no—
217C4⋊C4×C31C2×D412yes—
218C4⋊C4×C31C2×D412yes—
219C4⋊C4×C31C2×D412yes—
220C22⋊C4×C31—24no—
221C22⋊C4×C31—24no—
222C22⋊C4×C31—24no—
223C42×C31—21no—
224C42×C31—21no—
225C42×C31—21no—
226C42×C31—21no—
227C42×C31—42no—
228C42×C31C2×D412yes—
229C42×C31C2×D412yes—
230#24349C3111yesmaximal, characteristic, direct product factor, Sylow
231C23×C31—22no—
232C23×C31—22no—
233C23×C31—22no—
234C23×C31—41no—
235C23×C31—41no—
236C23×C31—41no—
237C23×C31—41no—
238C23×C31C22×D411yescharacteristic
239Q8×C31—22no—
240Q8×C31—22no—
241Q8×C31—44no—
242Q8×C31—41no—
243Q8×C31—41no—
244Q8×C31—84no—
245D4×C31—22no—
246D4×C31—22no—
247D4×C31—22no—
248D4×C31C22⋊Q814yes—
249C2×C4×C31—21no—
250C2×C4×C31—21no—
251C2×C4×C31—21no—
252C2×C4×C31—21no—
253C2×C4×C31—21no—
254C2×C4×C31—21no—
255C2×C4×C31—21no—
256C2×C4×C31—21no—
257C2×C4×C31—21no—
258C2×C4×C31—22no—
259C2×C4×C31—22no—
260C2×C4×C31—22no—
261C2×C4×C31—22no—
262C2×C4×C31—21no—
263C2×C4×C31—21no—
264C2×C4×C31—21no—
265C2×C4×C31—21no—
266C2×C4×C31—21no—
267C2×C4×C31—21no—
268C2×C4×C31—48no—
269C2×C4×C31—41no—
270C2×C4×C31—41no—
271C2×C4×C31—41no—
272C2×C4×C31—41no—
273C2×C4×C31—41no—
274C2×C4×C31—41no—
275C2×C4×C31—41no—
276C2×C4×C31—41no—
277C2×C4×C31—41no—
278C2×C4×C31—41no—
279C2×C4×C31—41no—
280C2×C4×C31—41no—
281C2×C4×C31—41no—
282C2×C4×C31—41no—
283C2×C4×C31—41no—
284C2×C4×C31—41no—
285C2×C4×C31—41no—
286C2×C4×C31—84no—
287C2×C4×C31—84no—
288C2×C4×C31#12012yes—
289C2×C4×C31#12012yes—
290C2×C4×C31#13712yes—
291C2×C4×C31C22×D411yescharacteristic
292C2×C4×C31C22×D411yescharacteristic
293C2×C4×C31C22×Q811yescharacteristic
294C2×C4×C31C2×#4111yescharacteristic
295C2×C4×C312−1+411yescharacteristic
296C2×C4×C312−1+411yescharacteristic
297C8×C31—22no—
298C8×C31—41no—
299C8×C31—41no—
300C8×C31—41no—
301C2×#554C2×C3111yescharacteristic
302C2×#479C2×C3111yescharacteristic, complemented
303C2×#440C2×C3111yescharacteristic
304#2582C2×C3111yescharacteristic, complemented
305#2059C2×C3111yescharacteristic, complemented
306#2057C2×C3111yescharacteristic, complemented
307#2026C2×C3111yescharacteristic, complemented
308#2024C2×C3111yescharacteristic, complemented
309#1992C2×C3111yescharacteristic, complemented
310#1985C2×C3111yescharacteristic, complemented
311#1877C2×C3111yescharacteristic
312#1877C2×C3111yescharacteristic
313#1864C2×C3111yescharacteristic
314#1862C2×C3111yescharacteristic
315#1802C2×C3111yescharacteristic
316C22×C31—24no—
317C22×C31—42no—
318C22×C31—42no—
319C22×C31—42no—
320C22×C31—42no—
321C22×C31—42no—
322C22×C31—42no—
323C22×C31C2×#12011yescharacteristic
324C22×C31#54811yescharacteristic
325C22×C31D4×Q811yescharacteristic
326C22×C31C2×#13711yescharacteristic
327C22×C31#57511yescharacteristic
328C22×C31#57611yescharacteristic
329C22×C31#57711yescharacteristic
330C4×C31—22no—
331C4×C31—22no—
332C4×C31—22no—
333C4×C31—42no—
334C4×C31—41no—
335C4×C31—42no—
336C4×C31—41no—
337C4×C31—41no—
338C4×C31—42no—
339C4×C31—42no—
340C4×C31—81no—
341C4×C31—81no—
342C4×C31—81no—
343C4×C31C2×C22⋊Q811yescharacteristic
344C4×C31#53611yescharacteristic
345C4×C31#54811yescharacteristic
346C4×C31D4×Q811yescharacteristic
347C22×SD16C22×C3111yescharacteristic
348#554—24no—
349#554—24no—
350C2×C4⋊Q8C22×C3111yescharacteristic
351C2×#125C22×C3111yescharacteristic
352C2×#125C22×C3111yescharacteristic
353C2×C22⋊Q8—21no—
354C2×C22⋊Q8—21no—
355C2×C22⋊Q8—21no—
356C2×C4×Q8C22×C3111yescharacteristic
357C2×C4×Q8C22×C3111yescharacteristic
358C2×C4×D4C22×C3111yescharacteristic
359C2×C4×D4C22×C3111yescharacteristic
360C2×C4×D4C22×C3111yescharacteristic
361C22×C4⋊C4—21no—
362#479—24no—
363#440—24no—
364C2×#107C22×C3111yescharacteristic
365C2×#107C22×C3111yescharacteristic
366C2×#106C22×C3111yescharacteristic
367C2×C4⋊C8C22×C3111yescharacteristic
368C2×#103C22×C3111yescharacteristic
369C2×#103C22×C3111yescharacteristic
370C2×#103C22×C3111yescharacteristic
371C2×#102C22×C3111yescharacteristic
372C2×#102C22×C3111yescharacteristic
373C2×#102C22×C3111yescharacteristic
374C2×#97C22×C3111yescharacteristic
375#398—21no—
376#398—21no—
377#391—21no—
378#391C22×C3111yescharacteristic
379#391C22×C3111yescharacteristic
380#389—21no—
381#389C22×C3111yescharacteristic
382#389C22×C3111yescharacteristic
383#384C22×C3111yescharacteristic
384#340C22×C3111yescharacteristic
385#340C22×C3111yescharacteristic
386#340C22×C3111yescharacteristic
387#340C22×C3111yescharacteristic
388#340C22×C3111yescharacteristic
389#340C22×C3111yescharacteristic
390#336C22×C3111yescharacteristic
391#336C22×C3111yescharacteristic
392#336C22×C3111yescharacteristic
393#336C22×C3111yescharacteristic
394C2×C31—44no—
395C2×C31#240911yescharacteristic
396C2×C31#300711yescharacteristic
397C2×C31#301211yescharacteristic
398C2×C31#337011yescharacteristic
399C2×C31#337211yescharacteristic
400C2×C31#338511yescharacteristic
401C2×C31#338811yescharacteristic
402C22×Q8—21no—
403C22×Q8D4×C3111yescharacteristic
404C22×Q8C23×C3111yescharacteristic
405C22×D4C23×C3111yescharacteristic
406C23×C4—21no—
407C23×C4—21no—
408C23×C4—21no—
409C2×SD16—22no—
410C2×SD16—22no—
411C2×SD16Q8×C3114yescomplemented
412C22×C8C23×C3111yescharacteristic
413C22×C8C23×C3111yescharacteristic
414C22×C8C23×C3111yescharacteristic
415C22×C8C23×C3111yescharacteristic
416C4⋊Q8—22no—
417C4⋊Q8—22no—
418#125—22no—
419#125—22no—
420#125—22no—
421#125D4×C3114yes—
422C22⋊Q8—28no—
423C22⋊Q8—28no—
424C22⋊Q8—28no—
425C4×Q8—22no—
426C4×Q8—22no—
427C4×Q8—22no—
428C4×Q8—22no—
429C4×D4—22no—
430C4×D4—22no—
431C4×D4—22no—
432C4×D4—22no—
433C4×D4—22no—
434C4×D4D4×C3114yes—
435C2×C4⋊C4—28no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4D4×C3111yescharacteristic
447C2×C4⋊C4D4×C3111yescharacteristic
448C2×C4⋊C4D4×C3111yescharacteristic
449C2×C4⋊C4C23×C3111yescharacteristic
450C2×C4⋊C4C23×C3111yescharacteristic
451C2×C4⋊C4C23×C3111yescharacteristic
452C2×C4⋊C4C23×C3111yescharacteristic
453C2×C4⋊C4C23×C3111yescharacteristic
454C2×C4⋊C4C23×C3111yescharacteristic
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C42—21no—
459C2×C42C23×C3111yescharacteristic
460C2×C42C23×C3111yescharacteristic
461C2×C42C23×C3111yescharacteristic
462#107—22no—
463#107—22no—
464#106—22no—
465C4⋊C8—22no—
466#103—22no—
467#103—22no—
468#103—22no—
469#102—22no—
470#102—22no—
471#102—22no—
472#97—22no—
473#95—21no—
474#95—21no—
475#95—21no—
476#95—21no—
477#95—21no—
478#95—21no—
479C31#2434911yescharacteristic, direct product factor, Sylow
480C24—21no—
481C2×Q8—24no—
482C2×Q8—22no—
483C2×Q8—22no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—41no—
490C2×Q8—81no—
491C2×Q8—81no—
492C2×Q8C2×Q8×C3112yes—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4C2×D4×C3112yes—
497C2×D4C2×Q8×C3112yes—
498C2×D4#41×C3112yes—
499C22×C4—24no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—24no—
505C22×C4—24no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—81no—
512C22×C4—81no—
513C22×C4—81no—
514C22×C4—81no—
515C22×C4C2×D4×C3111yescharacteristic
516C22×C4C2×D4×C3111yescharacteristic
517C22×C4C2×D4×C3111yescharacteristic
518C22×C4C2×D4×C3111yescharacteristic
519C22×C4C2×D4×C3111yescharacteristic
520C22×C4C2×D4×C3111yescharacteristic
521C22×C4C24×C3111yescharacteristic
522SD16—28no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8C2×Q8×C3112yes—
535C4⋊C4—24no—
536C4⋊C4—24no—
537C4⋊C4—24no—
538C4⋊C4—22no—
539C4⋊C4—24no—
540C4⋊C4—24no—
541C4⋊C4—22no—
542C4⋊C4—22no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—42no—
553C4⋊C4—42no—
554C4⋊C4—81no—
555C4⋊C4—81no—
556C4⋊C4—81no—
557C4⋊C4C2×D4×C3112yes—
558C4⋊C4C2×D4×C3112yes—
559C4⋊C4C2×D4×C3112yes—
560C22⋊C4—24no—
561C22⋊C4—24no—
562C22⋊C4—24no—
563C42—21no—
564C42—21no—
565C42—21no—
566C42—21no—
567C42—42no—
568C42C2×D4×C3112yes—
569C42C2×D4×C3112yes—
570C23—22no—
571C23—22no—
572C23—22no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23C22×D4×C3111yescharacteristic
578Q8—22no—
579Q8—22no—
580Q8—44no—
581Q8—41no—
582Q8—41no—
583Q8—84no—
584D4—22no—
585D4—22no—
586D4—22no—
587D4C31×C22⋊Q814yes—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—48no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—84no—
626C2×C4—84no—
627C2×C4C31×#12012yes—
628C2×C4C31×#12012yes—
629C2×C4C31×#13712yes—
630C2×C4C22×D4×C3111yescharacteristic
631C2×C4C22×D4×C3111yescharacteristic
632C2×C4C22×Q8×C3111yescharacteristic
633C2×C4C2×#41×C3111yescharacteristic
634C2×C4C31×2−1+411yescharacteristic
635C2×C4C31×2−1+411yescharacteristic
636C8—22no—
637C8—41no—
638C8—41no—
639C8—41no—
640C22—24no—
641C22—42no—
642C22—42no—
643C22—42no—
644C22—42no—
645C22—42no—
646C22—42no—
647C22C2×C31×#12011yescharacteristic
648C22C31×#54811yescharacteristic
649C22D4×Q8×C3111yescharacteristic
650C22C2×C31×#13711yescharacteristic
651C22C31×#57511yescharacteristic
652C22C31×#57611yescharacteristic
653C22C31×#57711yescharacteristic
654C4—22no—
655C4—22no—
656C4—22no—
657C4—42no—
658C4—41no—
659C4—42no—
660C4—41no—
661C4—41no—
662C4—42no—
663C4—42no—
664C4—81no—
665C4—81no—
666C4—81no—
667C4C2×C31×C22⋊Q811yescharacteristic
668C4C31×#53611yescharacteristic
669C4C31×#54811yescharacteristic
670C4D4×Q8×C3111yescharacteristic
671C2—44no—
672C2C31×#240911yescharacteristic
673C2C31×#300711yescharacteristic
674C2C31×#301211yescharacteristic
675C2C31×#337011yescharacteristic
676C2C31×#337211yescharacteristic
677C2C31×#338511yescharacteristic
678C2C31×#338811yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC22×D4×C31C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C4×Q8×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#479C2semidirect
4. C31×#2582C2semidirect
5. C31×#2059C2semidirect
6. C31×#2057C2semidirect
7. C31×#2026C2semidirect
8. C31×#2024C2semidirect
9. C31×#1992C2semidirect
10. C31×#1985C2semidirect
72. C2×SD16×C31Q8semidirect
230. #24349C31direct (N × H)
302. C2×#479C2×C31semidirect
304. #2582C2×C31semidirect
305. #2059C2×C31semidirect
306. #2057C2×C31semidirect
307. #2026C2×C31semidirect
308. #2024C2×C31semidirect
309. #1992C2×C31semidirect
310. #1985C2×C31semidirect
411. C2×SD16Q8×C31semidirect
479. C31#24349direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5542
C2×C31×#4792
C2×C31×#4402
C31×#25822
C31×#20592
C31×#20572
C31×#20262
C31×#20242
C31×#19922
C31×#19852
C31×#18772
C31×#18642
C31×#18622
C31×#18022
#2434931