Finite Group Databasebeta

← C31×#24334 #21481093

Subgroups — C31×#24334 #21481093

Order 7936.

1042 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#557C211yesmaximal, characteristic, complemented
2C2×C31×#478C211yesmaximal, characteristic
3C2×C4×SD16×C31C211yesmaximal, characteristic
4C31×#2580C211yesmaximal, characteristic
5C31×#2059C211yesmaximal, characteristic, complemented
6C31×#2058C211yesmaximal, characteristic, complemented
7C31×#2025C211yesmaximal, characteristic
8C31×#2023C211yesmaximal, characteristic
9C31×#1991C211yesmaximal, characteristic, complemented
10C31×#1984C211yesmaximal, characteristic, complemented
11C31×#1880C211yesmaximal, characteristic
12C31×#1880C211yesmaximal, characteristic
13C31×#1865C211yesmaximal, characteristic, complemented
14C31×#1863C211yesmaximal, characteristic, complemented
15C31×#1805C211yesmaximal, characteristic, complemented
16C22×SD16×C31C2211yescharacteristic
17C31×#557—24no—
18C31×#557—24no—
19C2×C31×C4⋊Q8—21no—
20C2×C31×C4⋊Q8C2211yescharacteristic
21C2×C31×#125—21no—
22C2×C31×#125—21no—
23C2×C31×#125C2211yescharacteristic
24C2×C31×#125C2211yescharacteristic
25C2×C4×Q8×C31—21no—
26C2×C4×Q8×C31C2211yescharacteristic
27C2×C4×Q8×C31C2211yescharacteristic
28C2×C4×Q8×C31C2211yescharacteristic
29C2×C4×Q8×C31C2211yescharacteristic
30C2×C4×D4×C31C2211yescharacteristic
31C31×#478—24no—
32C4×SD16×C31—24no—
33C2×C31×#107C2211yescharacteristic
34C2×C31×#106C2211yescharacteristic
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×C4×C8×C31C2211yescharacteristic
44C31×#399—21no—
45C31×#393—21no—
46C31×#390C2211yescharacteristic
47C31×#390C2211yescharacteristic
48C31×#389C2211yescharacteristic
49C31×#389C2211yescharacteristic
50C31×#385—21no—
51C31×#385—21no—
52C31×#382C2211yescharacteristic
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—
68C2×SD16×C31—22no—
69C2×SD16×C31—22no—
70C2×SD16×C31Q814yescomplemented
71C22×C8×C31C2311yescharacteristic
72C22×C8×C31C2311yescharacteristic
73C22×C8×C31C2311yescharacteristic
74C22×C8×C31C2311yescharacteristic
75C31×C4⋊Q8—28no—
76C31×C4⋊Q8—22no—
77C31×C4⋊Q8—22no—
78C31×#125—28no—
79C31×#125—28no—
80C31×#125—22no—
81C31×#125—22no—
82C31×#125—22no—
83C31×#125D414yes—
84C4×Q8×C31—28no—
85C4×Q8×C31—22no—
86C4×Q8×C31—22no—
87C4×Q8×C31—22no—
88C4×Q8×C31—22no—
89C4×Q8×C31—22no—
90C4×Q8×C31—22no—
91C4×Q8×C31—22no—
92C4×Q8×C31D414yes—
93C4×D4×C31—22no—
94C4×D4×C31—22no—
95C2×C4⋊C4×C31—21no—
96C2×C4⋊C4×C31—21no—
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×C31D411yescharacteristic
106C2×C4⋊C4×C31D411yescharacteristic
107C2×C4⋊C4×C31D411yescharacteristic
108C2×C4⋊C4×C31C2311yescharacteristic
109C2×C4⋊C4×C31C2311yescharacteristic
110C2×C4⋊C4×C31C2311yescharacteristic
111C2×C4⋊C4×C31C2311yescharacteristic
112C2×C4⋊C4×C31C2311yescharacteristic
113C2×C4⋊C4×C31C2311yescharacteristic
114C2×C22⋊C4×C31—21no—
115C2×C22⋊C4×C31—21no—
116C2×C22⋊C4×C31—21no—
117C2×C22⋊C4×C31—21no—
118C2×C22⋊C4×C31—21no—
119C2×C42×C31—21no—
120C2×C42×C31—21no—
121C2×C42×C31—21no—
122C2×C42×C31C2311yescharacteristic
123C2×C42×C31C2311yescharacteristic
124C2×C42×C31C2311yescharacteristic
125C31×#107—22no—
126C31×#106—22no—
127C31×#106—22no—
128C31×C4⋊C8—22no—
129C31×#103—22no—
130C31×#103—22no—
131C31×#103—22no—
132C31×#102—22no—
133C31×#102—22no—
134C31×#102—22no—
135C4×C8×C31—22no—
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—41no—
148C2×Q8×C31—42no—
149C2×Q8×C31—42no—
150C2×Q8×C31C2×D412yes—
151C2×Q8×C31C2×Q812yes—
152C2×Q8×C31#4112yes—
153C2×D4×C31—21no—
154C2×D4×C31—21no—
155C2×D4×C31—21no—
156C2×D4×C31—21no—
157C2×D4×C31—21no—
158C2×D4×C31C2×Q812yes—
159C22×C4×C31—21no—
160C22×C4×C31—21no—
161C22×C4×C31—21no—
162C22×C4×C31—21no—
163C22×C4×C31—21no—
164C22×C4×C31—21no—
165C22×C4×C31—21no—
166C22×C4×C31—42no—
167C22×C4×C31—81no—
168C22×C4×C31—81no—
169C22×C4×C31C2×D411yescharacteristic
170C22×C4×C31C2×D411yescharacteristic
171C22×C4×C31C2×D411yescharacteristic
172C22×C4×C31C2×D411yescharacteristic
173C22×C4×C31C2×D411yescharacteristic
174C22×C4×C31C2×D411yescharacteristic
175C22×C4×C31C2411yescharacteristic
176SD16×C31—28no—
177C2×C8×C31—21no—
178C2×C8×C31—21no—
179C2×C8×C31—21no—
180C2×C8×C31—21no—
181C2×C8×C31—21no—
182C2×C8×C31—21no—
183C2×C8×C31—21no—
184C2×C8×C31—21no—
185C2×C8×C31—21no—
186C2×C8×C31—21no—
187C2×C8×C31—21no—
188C2×C8×C31C2×Q812yes—
189C4⋊C4×C31—24no—
190C4⋊C4×C31—24no—
191C4⋊C4×C31—24no—
192C4⋊C4×C31—24no—
193C4⋊C4×C31—24no—
194C4⋊C4×C31—24no—
195C4⋊C4×C31—24no—
196C4⋊C4×C31—24no—
197C4⋊C4×C31—22no—
198C4⋊C4×C31—22no—
199C4⋊C4×C31—22no—
200C4⋊C4×C31—21no—
201C4⋊C4×C31—21no—
202C4⋊C4×C31—21no—
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—81no—
210C4⋊C4×C31—81no—
211C4⋊C4×C31C2×D412yes—
212C4⋊C4×C31C2×D412yes—
213C4⋊C4×C31C2×D412yes—
214C22⋊C4×C31—42no—
215C22⋊C4×C31—42no—
216C22⋊C4×C31—42no—
217C22⋊C4×C31—81no—
218C22⋊C4×C31—81no—
219C42×C31—24no—
220C42×C31—24no—
221C42×C31—24no—
222C42×C31—21no—
223C42×C31—21no—
224C42×C31—21no—
225C42×C31—21no—
226C42×C31C2×D412yes—
227C42×C31C2×D412yes—
228#24334C3111yesmaximal, characteristic, direct product factor, Sylow
229C23×C31—22no—
230C23×C31—41no—
231C23×C31—41no—
232C23×C31—41no—
233C23×C31—41no—
234C23×C31—41no—
235C23×C31—41no—
236C23×C31C22×D411yescharacteristic
237Q8×C31—22no—
238Q8×C31—22no—
239Q8×C31—22no—
240Q8×C31—44no—
241Q8×C31—48no—
242Q8×C31C22⋊Q814yes—
243D4×C31—22no—
244D4×C31—22no—
245D4×C31—41no—
246D4×C31—41no—
247C2×C4×C31—22no—
248C2×C4×C31—21no—
249C2×C4×C31—22no—
250C2×C4×C31—22no—
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—21no—
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—41no—
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—84no—
284C2×C4×C31#12012yes—
285C2×C4×C31#12012yes—
286C2×C4×C31#13512yes—
287C2×C4×C31C22×D411yescharacteristic
288C2×C4×C31C22×D411yescharacteristic
289C2×C4×C31C22×Q811yescharacteristic
290C2×C4×C31C2×#4111yescharacteristic
291C2×C4×C312−1+411yescharacteristic
292C2×C4×C312−1+411yescharacteristic
293C8×C31—22no—
294C8×C31—41no—
295C8×C31—41no—
296C8×C31—41no—
297C2×#557C2×C3111yescharacteristic, complemented
298C2×#478C2×C3111yescharacteristic
299C2×C4×SD16C2×C3111yescharacteristic
300#2580C2×C3111yescharacteristic
301#2059C2×C3111yescharacteristic, complemented
302#2058C2×C3111yescharacteristic, complemented
303#2025C2×C3111yescharacteristic
304#2023C2×C3111yescharacteristic
305#1991C2×C3111yescharacteristic, complemented
306#1984C2×C3111yescharacteristic, complemented
307#1880C2×C3111yescharacteristic
308#1880C2×C3111yescharacteristic
309#1865C2×C3111yescharacteristic, complemented
310#1863C2×C3111yescharacteristic, complemented
311#1805C2×C3111yescharacteristic, complemented
312C22×C31—42no—
313C22×C31—42no—
314C22×C31—42no—
315C22×C31—81no—
316C22×C31—81no—
317C22×C31—81no—
318C22×C31—81no—
319C22×C31C2×#12011yescharacteristic
320C22×C31#54811yescharacteristic
321C22×C31D4×Q811yescharacteristic
322C22×C31C2×#13511yescharacteristic
323C22×C31#57511yescharacteristic
324C22×C31#57711yescharacteristic
325C22×C31#57711yescharacteristic
326C4×C31—24no—
327C4×C31—22no—
328C4×C31—22no—
329C4×C31—22no—
330C4×C31—41no—
331C4×C31—42no—
332C4×C31—42no—
333C4×C31—41no—
334C4×C31—41no—
335C4×C31—42no—
336C4×C31—81no—
337C4×C31—81no—
338C4×C31—81no—
339C4×C31C2×C22⋊Q811yescharacteristic
340C4×C31#53611yescharacteristic
341C4×C31#54811yescharacteristic
342C4×C31D4×Q811yescharacteristic
343C22×SD16C22×C3111yescharacteristic
344#557—24no—
345#557—24no—
346C2×C4⋊Q8—21no—
347C2×C4⋊Q8C22×C3111yescharacteristic
348C2×#125—21no—
349C2×#125—21no—
350C2×#125C22×C3111yescharacteristic
351C2×#125C22×C3111yescharacteristic
352C2×C4×Q8—21no—
353C2×C4×Q8C22×C3111yescharacteristic
354C2×C4×Q8C22×C3111yescharacteristic
355C2×C4×Q8C22×C3111yescharacteristic
356C2×C4×Q8C22×C3111yescharacteristic
357C2×C4×D4C22×C3111yescharacteristic
358#478—24no—
359C4×SD16—24no—
360C2×#107C22×C3111yescharacteristic
361C2×#106C22×C3111yescharacteristic
362C2×#106C22×C3111yescharacteristic
363C2×C4⋊C8C22×C3111yescharacteristic
364C2×#103C22×C3111yescharacteristic
365C2×#103C22×C3111yescharacteristic
366C2×#103C22×C3111yescharacteristic
367C2×#102C22×C3111yescharacteristic
368C2×#102C22×C3111yescharacteristic
369C2×#102C22×C3111yescharacteristic
370C2×C4×C8C22×C3111yescharacteristic
371#399—21no—
372#393—21no—
373#390C22×C3111yescharacteristic
374#390C22×C3111yescharacteristic
375#389C22×C3111yescharacteristic
376#389C22×C3111yescharacteristic
377#385—21no—
378#385—21no—
379#382C22×C3111yescharacteristic
380#340C22×C3111yescharacteristic
381#340C22×C3111yescharacteristic
382#340C22×C3111yescharacteristic
383#340C22×C3111yescharacteristic
384#340C22×C3111yescharacteristic
385#340C22×C3111yescharacteristic
386#336C22×C3111yescharacteristic
387#336C22×C3111yescharacteristic
388#336C22×C3111yescharacteristic
389#336C22×C3111yescharacteristic
390C2×C31—82no—
391C2×C31#240911yescharacteristic
392C2×C31#300211yescharacteristic
393C2×C31#301011yescharacteristic
394C2×C31#336511yescharacteristic
395C2×C31#337111yescharacteristic
396C2×C31#338111yescharacteristic
397C2×C31#338811yescharacteristic
398C22×Q8—21no—
399C22×Q8D4×C3111yescharacteristic
400C22×Q8C23×C3111yescharacteristic
401C22×D4C23×C3111yescharacteristic
402C23×C4—21no—
403C2×SD16—22no—
404C2×SD16—22no—
405C2×SD16Q8×C3114yescomplemented
406C22×C8C23×C3111yescharacteristic
407C22×C8C23×C3111yescharacteristic
408C22×C8C23×C3111yescharacteristic
409C22×C8C23×C3111yescharacteristic
410C4⋊Q8—28no—
411C4⋊Q8—22no—
412C4⋊Q8—22no—
413#125—28no—
414#125—28no—
415#125—22no—
416#125—22no—
417#125—22no—
418#125D4×C3114yes—
419C4×Q8—28no—
420C4×Q8—22no—
421C4×Q8—22no—
422C4×Q8—22no—
423C4×Q8—22no—
424C4×Q8—22no—
425C4×Q8—22no—
426C4×Q8—22no—
427C4×Q8D4×C3114yes—
428C4×D4—22no—
429C4×D4—22no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4D4×C3111yescharacteristic
441C2×C4⋊C4D4×C3111yescharacteristic
442C2×C4⋊C4D4×C3111yescharacteristic
443C2×C4⋊C4C23×C3111yescharacteristic
444C2×C4⋊C4C23×C3111yescharacteristic
445C2×C4⋊C4C23×C3111yescharacteristic
446C2×C4⋊C4C23×C3111yescharacteristic
447C2×C4⋊C4C23×C3111yescharacteristic
448C2×C4⋊C4C23×C3111yescharacteristic
449C2×C22⋊C4—21no—
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C42—21no—
455C2×C42—21no—
456C2×C42—21no—
457C2×C42C23×C3111yescharacteristic
458C2×C42C23×C3111yescharacteristic
459C2×C42C23×C3111yescharacteristic
460#107—22no—
461#106—22no—
462#106—22no—
463C4⋊C8—22no—
464#103—22no—
465#103—22no—
466#103—22no—
467#102—22no—
468#102—22no—
469#102—22no—
470C4×C8—22no—
471#95—21no—
472#95—21no—
473#95—21no—
474#95—21no—
475C31#2433411yescharacteristic, direct product factor, Sylow
476C24—21no—
477C2×Q8—24no—
478C2×Q8—22no—
479C2×Q8—22no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—41no—
484C2×Q8—42no—
485C2×Q8—42no—
486C2×Q8C2×D4×C3112yes—
487C2×Q8C2×Q8×C3112yes—
488C2×Q8#41×C3112yes—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4C2×Q8×C3112yes—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—42no—
503C22×C4—81no—
504C22×C4—81no—
505C22×C4C2×D4×C3111yescharacteristic
506C22×C4C2×D4×C3111yescharacteristic
507C22×C4C2×D4×C3111yescharacteristic
508C22×C4C2×D4×C3111yescharacteristic
509C22×C4C2×D4×C3111yescharacteristic
510C22×C4C2×D4×C3111yescharacteristic
511C22×C4C24×C3111yescharacteristic
512SD16—28no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8C2×Q8×C3112yes—
525C4⋊C4—24no—
526C4⋊C4—24no—
527C4⋊C4—24no—
528C4⋊C4—24no—
529C4⋊C4—24no—
530C4⋊C4—24no—
531C4⋊C4—24no—
532C4⋊C4—24no—
533C4⋊C4—22no—
534C4⋊C4—22no—
535C4⋊C4—22no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—81no—
546C4⋊C4—81no—
547C4⋊C4C2×D4×C3112yes—
548C4⋊C4C2×D4×C3112yes—
549C4⋊C4C2×D4×C3112yes—
550C22⋊C4—42no—
551C22⋊C4—42no—
552C22⋊C4—42no—
553C22⋊C4—81no—
554C22⋊C4—81no—
555C42—24no—
556C42—24no—
557C42—24no—
558C42—21no—
559C42—21no—
560C42—21no—
561C42—21no—
562C42C2×D4×C3112yes—
563C42C2×D4×C3112yes—
564C23—22no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23C22×D4×C3111yescharacteristic
572Q8—22no—
573Q8—22no—
574Q8—22no—
575Q8—44no—
576Q8—48no—
577Q8C31×C22⋊Q814yes—
578D4—22no—
579D4—22no—
580D4—41no—
581D4—41no—
582C2×C4—22no—
583C2×C4—21no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—22no—
594C2×C4—21no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
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—84no—
619C2×C4C31×#12012yes—
620C2×C4C31×#12012yes—
621C2×C4C31×#13512yes—
622C2×C4C22×D4×C3111yescharacteristic
623C2×C4C22×D4×C3111yescharacteristic
624C2×C4C22×Q8×C3111yescharacteristic
625C2×C4C2×#41×C3111yescharacteristic
626C2×C4C31×2−1+411yescharacteristic
627C2×C4C31×2−1+411yescharacteristic
628C8—22no—
629C8—41no—
630C8—41no—
631C8—41no—
632C22—42no—
633C22—42no—
634C22—42no—
635C22—81no—
636C22—81no—
637C22—81no—
638C22—81no—
639C22C2×C31×#12011yescharacteristic
640C22C31×#54811yescharacteristic
641C22D4×Q8×C3111yescharacteristic
642C22C2×C31×#13511yescharacteristic
643C22C31×#57511yescharacteristic
644C22C31×#57711yescharacteristic
645C22C31×#57711yescharacteristic
646C4—24no—
647C4—22no—
648C4—22no—
649C4—22no—
650C4—41no—
651C4—42no—
652C4—42no—
653C4—41no—
654C4—41no—
655C4—42no—
656C4—81no—
657C4—81no—
658C4—81no—
659C4C2×C31×C22⋊Q811yescharacteristic
660C4C31×#53611yescharacteristic
661C4C31×#54811yescharacteristic
662C4D4×Q8×C3111yescharacteristic
663C2—82no—
664C2C31×#240911yescharacteristic
665C2C31×#300211yescharacteristic
666C2C31×#301011yescharacteristic
667C2C31×#336511yescharacteristic
668C2C31×#337111yescharacteristic
669C2C31×#338111yescharacteristic
670C2C31×#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
1. C2×C31×#557C2semidirect
5. C31×#2059C2semidirect
6. C31×#2058C2semidirect
9. C31×#1991C2semidirect
10. C31×#1984C2semidirect
13. C31×#1865C2semidirect
14. C31×#1863C2semidirect
15. C31×#1805C2semidirect
70. C2×SD16×C31Q8semidirect
228. #24334C31direct (N × H)
297. C2×#557C2×C31semidirect
301. #2059C2×C31semidirect
302. #2058C2×C31semidirect
305. #1991C2×C31semidirect
306. #1984C2×C31semidirect
309. #1865C2×C31semidirect
310. #1863C2×C31semidirect
311. #1805C2×C31semidirect
405. C2×SD16Q8×C31semidirect
475. C31#24334direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5572
C2×C31×#4782
C2×C4×SD16×C312
C31×#25802
C31×#20592
C31×#20582
C31×#20252
C31×#20232
C31×#19912
C31×#19842
C31×#18802
C31×#18652
C31×#18632
C31×#18052
#2433431