Finite Group Databasebeta

← C31×#25237 #21481996

Subgroups — C31×#25237 #21481996

Order 7936.

904 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#482C211yesmaximal, characteristic, complemented
2C2×C8×D4×C31C211yesmaximal, characteristic, complemented
3C31×#2485C211yesmaximal, characteristic, complemented
4C31×#2414C211yesmaximal, characteristic
5C31×#2088C211yesmaximal, characteristic, complemented
6C31×#2076C211yesmaximal, characteristic, complemented
7C31×#2065C211yesmaximal, characteristic, complemented
8C31×#2033C211yesmaximal, characteristic, complemented
9C31×#1942C211yesmaximal, characteristic, complemented
10C31×#1934C211yesmaximal, characteristic, complemented
11C31×#1893C211yesmaximal, characteristic, complemented
12C31×#1893C211yesmaximal, characteristic, complemented
13C31×#1854C211yesmaximal, characteristic, complemented
14C31×#1807C211yesmaximal, characteristic, complemented
15C31×#1735C211yesmaximal, characteristic, complemented
16C23×C8×C31C2211yescharacteristic
17C23×C8×C31C2211yescharacteristic
18C2×C31×#121C2211yescharacteristic
19C2×C31×#121C2211yescharacteristic
20C2×C4×D4×C31C2211yescharacteristic
21C2×C31×#117C2211yescharacteristic
22C2×C31×#117C2211yescharacteristic
23C31×#482—24no—
24C8×D4×C31—24no—
25C2×C31×#107C2211yescharacteristic
26C2×C31×#107C2211yescharacteristic
27C2×C31×#106C2211yescharacteristic
28C2×C31×#106C2211yescharacteristic
29C2×C31×C4⋊C8C2211yescharacteristic
30C2×C31×#102C2211yescharacteristic
31C2×C31×#102C2211yescharacteristic
32C2×C31×#102C2211yescharacteristic
33C2×C31×#102C2211yescharacteristic
34C2×C31×C22⋊C8C2211yescharacteristic
35C2×C31×C22⋊C8C2211yescharacteristic
36C2×C4×C8×C31C2211yescharacteristic
37C31×#397—21no—
38C31×#394—21no—
39C31×#394—21no—
40C31×#392—21no—
41C31×#390—21no—
42C31×#390C2211yescharacteristic
43C31×#389C2211yescharacteristic
44C31×#389C2211yescharacteristic
45C31×#389C2211yescharacteristic
46C31×#388—21no—
47C31×#388—21no—
48C31×#387—21no—
49C31×#380C2211yescharacteristic
50C31×#380C2211yescharacteristic
51C31×#380C2211yescharacteristic
52C31×#380C2211yescharacteristic
53C31×#340C2211yescharacteristic
54C31×#340C2211yescharacteristic
55C31×#340C2211yescharacteristic
56C31×#340C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#340C2211yescharacteristic
60C31×#340C2211yescharacteristic
61C22×D4×C31—21no—
62C22×D4×C31—21no—
63C22×D4×C31D411yescharacteristic
64C22×D4×C31C2311yescharacteristic
65C23×C4×C31C2311yescharacteristic
66C23×C4×C31C2311yescharacteristic
67C22×C8×C31—22no—
68C22×C8×C31—22no—
69C22×C8×C31—22no—
70C22×C8×C31—22no—
71C22×C8×C31—41no—
72C22×C8×C31—41no—
73C22×C8×C31C2311yescharacteristic
74C22×C8×C31C2311yescharacteristic
75C22×C8×C31C2311yescharacteristic
76C22×C8×C31C2311yescharacteristic
77C31×#121—22no—
78C31×#121—22no—
79C31×#121—22no—
80C31×#121—41no—
81C4×D4×C31—22no—
82C4×D4×C31—22no—
83C31×#117—22no—
84C31×#117—22no—
85C31×#117—22no—
86C31×#117—41no—
87C2×C4⋊C4×C31—21no—
88C2×C4⋊C4×C31—21no—
89C2×C4⋊C4×C31—21no—
90C2×C4⋊C4×C31D411yescharacteristic
91C2×C4⋊C4×C31C2311yescharacteristic
92C2×C4⋊C4×C31C2311yescharacteristic
93C2×C4⋊C4×C31C2311yescharacteristic
94C2×C4⋊C4×C31C2311yescharacteristic
95C2×C4⋊C4×C31C2311yescharacteristic
96C2×C4⋊C4×C31C2311yescharacteristic
97C2×C4⋊C4×C31C2311yescharacteristic
98C2×C22⋊C4×C31—21no—
99C2×C22⋊C4×C31—21no—
100C2×C22⋊C4×C31—21no—
101C2×C22⋊C4×C31—21no—
102C2×C22⋊C4×C31—21no—
103C2×C22⋊C4×C31—21no—
104C2×C22⋊C4×C31—21no—
105C2×C22⋊C4×C31—21no—
106C2×C22⋊C4×C31—21no—
107C2×C22⋊C4×C31—21no—
108C2×C22⋊C4×C31D411yescharacteristic
109C2×C22⋊C4×C31D411yescharacteristic
110C2×C42×C31—21no—
111C2×C42×C31—21no—
112C2×C42×C31C2311yescharacteristic
113C31×#107—22no—
114C31×#107—22no—
115C31×#106—22no—
116C31×#106—41no—
117C31×C4⋊C8—22no—
118C31×#102—22no—
119C31×#102—22no—
120C31×#102—22no—
121C31×#102—41no—
122C31×C22⋊C8—22no—
123C31×C22⋊C8D414yescomplemented
124C4×C8×C31—22no—
125C31×#95—21no—
126C31×#95—21no—
127C31×#95—21no—
128C31×#95—21no—
129C31×#95—21no—
130C31×#95—21no—
131C31×#95—21no—
132C24×C31—21no—
133C24×C31C2×D411yescharacteristic
134C24×C31C2×D411yescharacteristic
135C2×D4×C31—22no—
136C2×D4×C31—22no—
137C2×D4×C31—22no—
138C2×D4×C31—21no—
139C2×D4×C31—21no—
140C2×D4×C31—21no—
141C2×D4×C31—21no—
142C2×D4×C31—21no—
143C2×D4×C31—21no—
144C2×D4×C31—42no—
145C2×D4×C31—42no—
146C2×D4×C31—42no—
147C2×D4×C31—81no—
148C2×D4×C31—81no—
149C2×D4×C31—81no—
150C22×C4×C31—21no—
151C22×C4×C31—21no—
152C22×C4×C31—21no—
153C22×C4×C31—21no—
154C22×C4×C31—21no—
155C22×C4×C31—21no—
156C22×C4×C31—21no—
157C22×C4×C31—21no—
158C22×C4×C31—21no—
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—21no—
167C22×C4×C31C2×D411yescharacteristic
168C22×C4×C31C2×D411yescharacteristic
169C22×C4×C31C2×D411yescharacteristic
170C22×C4×C31C2×D412yes—
171C22×C4×C31C2×D411yescharacteristic
172C22×C4×C31#4112yes—
173C22×C4×C31C2411yescharacteristic
174C2×C8×C31—21no—
175C2×C8×C31—21no—
176C2×C8×C31—21no—
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—44no—
184C2×C8×C31—44no—
185C2×C8×C31C2×D412yes—
186C2×C8×C31C2×D412yes—
187C2×C8×C31#4112yes—
188C4⋊C4×C31—22no—
189C4⋊C4×C31—21no—
190C4⋊C4×C31—21no—
191C4⋊C4×C31—21no—
192C4⋊C4×C31—21no—
193C4⋊C4×C31—21no—
194C4⋊C4×C31—21no—
195C4⋊C4×C31—21no—
196C4⋊C4×C31—21no—
197C4⋊C4×C31—21no—
198C4⋊C4×C31—21no—
199C4⋊C4×C31—21no—
200C4⋊C4×C31—21no—
201C4⋊C4×C31—21no—
202C4⋊C4×C31—42no—
203C4⋊C4×C31—81no—
204C4⋊C4×C31—81no—
205C4⋊C4×C31#4112yes—
206C22⋊C4×C31—22no—
207C22⋊C4×C31—22no—
208C22⋊C4×C31—42no—
209C22⋊C4×C31—42no—
210C22⋊C4×C31—42no—
211C22⋊C4×C31—42no—
212C22⋊C4×C31—42no—
213C22⋊C4×C31—42no—
214C22⋊C4×C31—81no—
215C22⋊C4×C31—81no—
216C22⋊C4×C31—81no—
217C22⋊C4×C31—81no—
218C42×C31—21no—
219C42×C31—21no—
220C42×C31—42no—
221C42×C31—42no—
222#25237C3111yesmaximal, characteristic, direct product factor, Sylow
223C23×C31—21no—
224C23×C31—21no—
225C23×C31—21no—
226C23×C31—21no—
227C23×C31—21no—
228C23×C31—21no—
229C23×C31—21no—
230C23×C31—21no—
231C23×C31—21no—
232C23×C31—21no—
233C23×C31—21no—
234C23×C31—21no—
235C23×C31—41no—
236C23×C31—41no—
237C23×C31—41no—
238C23×C31—41no—
239C23×C31—41no—
240C23×C31—41no—
241C23×C31—41no—
242C23×C31#12112yes—
243C23×C31#13512yes—
244C23×C31C22×D411yescharacteristic
245D4×C31—28no—
246D4×C31—41no—
247D4×C31—41no—
248D4×C31—41no—
249D4×C31—41no—
250D4×C31—84no—
251D4×C31—84no—
252C2×C4×C31—21no—
253C2×C4×C31—21no—
254C2×C4×C31—21no—
255C2×C4×C31—21no—
256C2×C4×C31—22no—
257C2×C4×C31—22no—
258C2×C4×C31—22no—
259C2×C4×C31—22no—
260C2×C4×C31—21no—
261C2×C4×C31—21no—
262C2×C4×C31—22no—
263C2×C4×C31—21no—
264C2×C4×C31—21no—
265C2×C4×C31—21no—
266C2×C4×C31—21no—
267C2×C4×C31—41no—
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—41no—
284C2×C4×C31—41no—
285C2×C4×C31—41no—
286C2×C4×C31—41no—
287C2×C4×C31—41no—
288C2×C4×C31—41no—
289C2×C4×C31—41no—
290C2×C4×C31—41no—
291C2×C4×C31#12112yes—
292C2×C4×C31#13512yes—
293C2×C4×C31C22×D411yescharacteristic
294C2×C4×C31C2×#4111yescharacteristic
295C2×C4×C31C2×#4111yescharacteristic
296C2×C4×C31C2×#4111yescharacteristic
297C2×C4×C31H(5,𝔽2)11yescharacteristic
298C2×C4×C312−1+411yescharacteristic
299C8×C31—22no—
300C8×C31—22no—
301C8×C31—22no—
302C8×C31—41no—
303C2×#482C2×C3111yescharacteristic, complemented
304C2×C8×D4C2×C3111yescharacteristic, complemented
305#2485C2×C3111yescharacteristic, complemented
306#2414C2×C3111yescharacteristic
307#2088C2×C3111yescharacteristic, complemented
308#2076C2×C3111yescharacteristic, complemented
309#2065C2×C3111yescharacteristic, complemented
310#2033C2×C3111yescharacteristic, complemented
311#1942C2×C3111yescharacteristic, complemented
312#1934C2×C3111yescharacteristic, complemented
313#1893C2×C3111yescharacteristic, complemented
314#1893C2×C3111yescharacteristic, complemented
315#1854C2×C3111yescharacteristic, complemented
316#1807C2×C3111yescharacteristic, complemented
317#1735C2×C3111yescharacteristic, complemented
318C22×C31—22no—
319C22×C31—22no—
320C22×C31—22no—
321C22×C31—22no—
322C22×C31—22no—
323C22×C31—22no—
324C22×C31—41no—
325C22×C31—41no—
326C22×C31—41no—
327C22×C31—41no—
328C22×C31—41no—
329C22×C31—41no—
330C22×C31—41no—
331C22×C31—41no—
332C22×C31—81no—
333C22×C31—81no—
334C22×C31—81no—
335C22×C31—81no—
336C22×C31—81no—
337C22×C31—81no—
338C22×C31—81no—
339C22×C31C2×#12111yescharacteristic
340C22×C31#54611yescharacteristic
341C22×C31#54711yescharacteristic
342C22×C31C2×#13511yescharacteristic
343C22×C31C2×#13511yescharacteristic
344C22×C31#57611yescharacteristic
345C22×C31#57711yescharacteristic
346C4×C31—22no—
347C4×C31—22no—
348C4×C31—41no—
349C4×C31—42no—
350C4×C31—41no—
351C4×C31—81no—
352C4×C31—81no—
353C4×C31—81no—
354C4×C31—81no—
355C4×C31—81no—
356C4×C31—81no—
357C4×C31#52911yescharacteristic
358C4×C31#53911yescharacteristic
359C4×C31#54611yescharacteristic
360C4×C31#54711yescharacteristic
361C23×C8C22×C3111yescharacteristic
362C23×C8C22×C3111yescharacteristic
363C2×#121C22×C3111yescharacteristic
364C2×#121C22×C3111yescharacteristic
365C2×C4×D4C22×C3111yescharacteristic
366C2×#117C22×C3111yescharacteristic
367C2×#117C22×C3111yescharacteristic
368#482—24no—
369C8×D4—24no—
370C2×#107C22×C3111yescharacteristic
371C2×#107C22×C3111yescharacteristic
372C2×#106C22×C3111yescharacteristic
373C2×#106C22×C3111yescharacteristic
374C2×C4⋊C8C22×C3111yescharacteristic
375C2×#102C22×C3111yescharacteristic
376C2×#102C22×C3111yescharacteristic
377C2×#102C22×C3111yescharacteristic
378C2×#102C22×C3111yescharacteristic
379C2×C22⋊C8C22×C3111yescharacteristic
380C2×C22⋊C8C22×C3111yescharacteristic
381C2×C4×C8C22×C3111yescharacteristic
382#397—21no—
383#394—21no—
384#394—21no—
385#392—21no—
386#390—21no—
387#390C22×C3111yescharacteristic
388#389C22×C3111yescharacteristic
389#389C22×C3111yescharacteristic
390#389C22×C3111yescharacteristic
391#388—21no—
392#388—21no—
393#387—21no—
394#380C22×C3111yescharacteristic
395#380C22×C3111yescharacteristic
396#380C22×C3111yescharacteristic
397#380C22×C3111yescharacteristic
398#340C22×C3111yescharacteristic
399#340C22×C3111yescharacteristic
400#340C22×C3111yescharacteristic
401#340C22×C3111yescharacteristic
402#340C22×C3111yescharacteristic
403#340C22×C3111yescharacteristic
404#340C22×C3111yescharacteristic
405#340C22×C3111yescharacteristic
406C2×C31—42no—
407C2×C31—42no—
408C2×C31—161no—
409C2×C31#242511yescharacteristic
410C2×C31#305011yescharacteristic
411C2×C31#306211yescharacteristic
412C2×C31#329711yescharacteristic
413C2×C31#330411yescharacteristic
414C2×C31#333711yescharacteristic
415C2×C31#334111yescharacteristic
416C22×D4—21no—
417C22×D4—21no—
418C22×D4D4×C3111yescharacteristic
419C22×D4C23×C3111yescharacteristic
420C23×C4C23×C3111yescharacteristic
421C23×C4C23×C3111yescharacteristic
422C22×C8—22no—
423C22×C8—22no—
424C22×C8—22no—
425C22×C8—22no—
426C22×C8—41no—
427C22×C8—41no—
428C22×C8C23×C3111yescharacteristic
429C22×C8C23×C3111yescharacteristic
430C22×C8C23×C3111yescharacteristic
431C22×C8C23×C3111yescharacteristic
432#121—22no—
433#121—22no—
434#121—22no—
435#121—41no—
436C4×D4—22no—
437C4×D4—22no—
438#117—22no—
439#117—22no—
440#117—22no—
441#117—41no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4D4×C3111yescharacteristic
446C2×C4⋊C4C23×C3111yescharacteristic
447C2×C4⋊C4C23×C3111yescharacteristic
448C2×C4⋊C4C23×C3111yescharacteristic
449C2×C4⋊C4C23×C3111yescharacteristic
450C2×C4⋊C4C23×C3111yescharacteristic
451C2×C4⋊C4C23×C3111yescharacteristic
452C2×C4⋊C4C23×C3111yescharacteristic
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4—21no—
459C2×C22⋊C4—21no—
460C2×C22⋊C4—21no—
461C2×C22⋊C4—21no—
462C2×C22⋊C4—21no—
463C2×C22⋊C4D4×C3111yescharacteristic
464C2×C22⋊C4D4×C3111yescharacteristic
465C2×C42—21no—
466C2×C42—21no—
467C2×C42C23×C3111yescharacteristic
468#107—22no—
469#107—22no—
470#106—22no—
471#106—41no—
472C4⋊C8—22no—
473#102—22no—
474#102—22no—
475#102—22no—
476#102—41no—
477C22⋊C8—22no—
478C22⋊C8D4×C3114yescomplemented
479C4×C8—22no—
480#95—21no—
481#95—21no—
482#95—21no—
483#95—21no—
484#95—21no—
485#95—21no—
486#95—21no—
487C31#2523711yescharacteristic, direct product factor, Sylow
488C24—21no—
489C24C2×D4×C3111yescharacteristic
490C24C2×D4×C3111yescharacteristic
491C2×D4—22no—
492C2×D4—22no—
493C2×D4—22no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—42no—
501C2×D4—42no—
502C2×D4—42no—
503C2×D4—81no—
504C2×D4—81no—
505C2×D4—81no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4C2×D4×C3111yescharacteristic
524C22×C4C2×D4×C3111yescharacteristic
525C22×C4C2×D4×C3111yescharacteristic
526C22×C4C2×D4×C3112yes—
527C22×C4C2×D4×C3111yescharacteristic
528C22×C4#41×C3112yes—
529C22×C4C24×C3111yescharacteristic
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—44no—
540C2×C8—44no—
541C2×C8C2×D4×C3112yes—
542C2×C8C2×D4×C3112yes—
543C2×C8#41×C3112yes—
544C4⋊C4—22no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—42no—
559C4⋊C4—81no—
560C4⋊C4—81no—
561C4⋊C4#41×C3112yes—
562C22⋊C4—22no—
563C22⋊C4—22no—
564C22⋊C4—42no—
565C22⋊C4—42no—
566C22⋊C4—42no—
567C22⋊C4—42no—
568C22⋊C4—42no—
569C22⋊C4—42no—
570C22⋊C4—81no—
571C22⋊C4—81no—
572C22⋊C4—81no—
573C22⋊C4—81no—
574C42—21no—
575C42—21no—
576C42—42no—
577C42—42no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23C31×#12112yes—
598C23C31×#13512yes—
599C23C22×D4×C3111yescharacteristic
600D4—28no—
601D4—41no—
602D4—41no—
603D4—41no—
604D4—41no—
605D4—84no—
606D4—84no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—22no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4C31×#12112yes—
647C2×C4C31×#13512yes—
648C2×C4C22×D4×C3111yescharacteristic
649C2×C4C2×#41×C3111yescharacteristic
650C2×C4C2×#41×C3111yescharacteristic
651C2×C4C2×#41×C3111yescharacteristic
652C2×C4C31×H(5,𝔽2)11yescharacteristic
653C2×C4C31×2−1+411yescharacteristic
654C8—22no—
655C8—22no—
656C8—22no—
657C8—41no—
658C22—22no—
659C22—22no—
660C22—22no—
661C22—22no—
662C22—22no—
663C22—22no—
664C22—41no—
665C22—41no—
666C22—41no—
667C22—41no—
668C22—41no—
669C22—41no—
670C22—41no—
671C22—41no—
672C22—81no—
673C22—81no—
674C22—81no—
675C22—81no—
676C22—81no—
677C22—81no—
678C22—81no—
679C22C2×C31×#12111yescharacteristic
680C22C31×#54611yescharacteristic
681C22C31×#54711yescharacteristic
682C22C2×C31×#13511yescharacteristic
683C22C2×C31×#13511yescharacteristic
684C22C31×#57611yescharacteristic
685C22C31×#57711yescharacteristic
686C4—22no—
687C4—22no—
688C4—41no—
689C4—42no—
690C4—41no—
691C4—81no—
692C4—81no—
693C4—81no—
694C4—81no—
695C4—81no—
696C4—81no—
697C4C31×#52911yescharacteristic
698C4C31×#53911yescharacteristic
699C4C31×#54611yescharacteristic
700C4C31×#54711yescharacteristic
701C2—42no—
702C2—42no—
703C2—161no—
704C2C31×#242511yescharacteristic
705C2C31×#305011yescharacteristic
706C2C31×#306211yescharacteristic
707C2C31×#329711yescharacteristic
708C2C31×#330411yescharacteristic
709C2C31×#333711yescharacteristic
710C2C31×#334111yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC31×#2414C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C4×D4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C31×#482C2semidirect
2. C2×C8×D4×C31C2semidirect
3. C31×#2485C2semidirect
5. C31×#2088C2semidirect
6. C31×#2076C2semidirect
7. C31×#2065C2semidirect
8. C31×#2033C2semidirect
9. C31×#1942C2semidirect
10. C31×#1934C2semidirect
11. C31×#1893C2semidirect
12. C31×#1893C2semidirect
13. C31×#1854C2semidirect
14. C31×#1807C2semidirect
15. C31×#1735C2semidirect
123. C31×C22⋊C8D4semidirect
222. #25237C31direct (N × H)
303. C2×#482C2×C31semidirect
304. C2×C8×D4C2×C31semidirect
305. #2485C2×C31semidirect
307. #2088C2×C31semidirect
308. #2076C2×C31semidirect
309. #2065C2×C31semidirect
310. #2033C2×C31semidirect
311. #1942C2×C31semidirect
312. #1934C2×C31semidirect
313. #1893C2×C31semidirect
314. #1893C2×C31semidirect
315. #1854C2×C31semidirect
316. #1807C2×C31semidirect
317. #1735C2×C31semidirect
478. C22⋊C8D4×C31semidirect
487. C31#25237direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#4822
C2×C8×D4×C312
C31×#24852
C31×#24142
C31×#20882
C31×#20762
C31×#20652
C31×#20332
C31×#19422
C31×#19342
C31×#18932
C31×#18542
C31×#18072
C31×#17352
#2523731