Finite Group Databasebeta

← C31×#26163 #21482922

Subgroups — C31×#26163 #21482922

Order 7936.

918 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#460C211yesmaximal, characteristic
2C2×C4×SD16×C31C211yesmaximal, characteristic, complemented
3C31×#2445C211yesmaximal, characteristic
4Q8×C4⋊C4×C31C211yesmaximal, characteristic, complemented
5C31×#2094C211yesmaximal, characteristic, complemented
6C31×#2088C211yesmaximal, characteristic, complemented
7C31×#2071C211yesmaximal, characteristic, complemented
8C31×#2041C211yesmaximal, characteristic
9C31×#1934C211yesmaximal, characteristic, complemented
10C31×#1916C211yesmaximal, characteristic, complemented
11C31×#1880C211yesmaximal, characteristic, complemented
12C31×#1880C211yesmaximal, characteristic, complemented
13C31×#1880C211yesmaximal, characteristic, complemented
14C31×#1865C211yesmaximal, characteristic, complemented
15C31×#1864C211yesmaximal, characteristic, complemented
16C22×SD16×C31C2211yescharacteristic
17C22×SD16×C31C2211yescharacteristic
18C2×C31×#127C2211yescharacteristic
19C2×C31×#123—21no—
20C2×C4×Q8×C31C2211yescharacteristic
21C2×C4×Q8×C31C2211yescharacteristic
22C2×C4×Q8×C31C2211yescharacteristic
23C2×C4×D4×C31C2211yescharacteristic
24C31×#460—24no—
25C4×SD16×C31—24no—
26C2×C31×#106C2211yescharacteristic
27C2×C31×#106C2211yescharacteristic
28C2×C31×C4⋊C8C2211yescharacteristic
29C2×C31×#103C2211yescharacteristic
30C2×C31×#103C2211yescharacteristic
31C2×C31×#102C2211yescharacteristic
32C2×C31×#102C2211yescharacteristic
33C2×C31×#102C2211yescharacteristic
34C2×C31×#102C2211yescharacteristic
35C2×C31×#102C2211yescharacteristic
36C2×C31×#102C2211yescharacteristic
37C2×C4×C8×C31C2211yescharacteristic
38C31×#394—21no—
39C31×#394—21no—
40C31×#390C2211yescharacteristic
41C31×#390C2211yescharacteristic
42C31×#390C2211yescharacteristic
43C31×#389—21no—
44C31×#389—21no—
45C31×#389C2211yescharacteristic
46C31×#389C2211yescharacteristic
47C31×#389C2211yescharacteristic
48C31×#386—21no—
49C31×#384—21no—
50C31×#384C2211yescharacteristic
51C4×C4⋊C4×C31—21no—
52C4×C4⋊C4×C31C2211yescharacteristic
53C31×#340C2211yescharacteristic
54C31×#340C2211yescharacteristic
55C31×#340C2211yescharacteristic
56C31×#340C2211yescharacteristic
57C31×#336C2211yescharacteristic
58C31×#336C2211yescharacteristic
59C31×#336C2211yescharacteristic
60C31×#336C2211yescharacteristic
61C22×Q8×C31C2311yescharacteristic
62C22×D4×C31—21no—
63C22×D4×C31—21no—
64C22×D4×C31C2311yescharacteristic
65C22×D4×C31C2311yescharacteristic
66C23×C4×C31—21no—
67C2×SD16×C31—22no—
68C2×SD16×C31—22no—
69C2×SD16×C31—22no—
70C2×SD16×C31—22no—
71C2×SD16×C31—22no—
72C2×SD16×C31D414yes—
73C22×C8×C31C2311yescharacteristic
74C22×C8×C31C2311yescharacteristic
75C22×C8×C31C2311yescharacteristic
76C22×C8×C31C2311yescharacteristic
77C31×#127—22no—
78C31×#127—41no—
79C31×#123—44no—
80C4×Q8×C31—22no—
81C4×Q8×C31—22no—
82C4×Q8×C31—22no—
83C4×Q8×C31—22no—
84C4×Q8×C31—41no—
85C4×Q8×C31—41no—
86C4×D4×C31—22no—
87C4×D4×C31—41no—
88C2×C4⋊C4×C31—21no—
89C2×C4⋊C4×C31—21no—
90C2×C4⋊C4×C31—21no—
91C2×C4⋊C4×C31—21no—
92C2×C4⋊C4×C31—21no—
93C2×C4⋊C4×C31—21no—
94C2×C4⋊C4×C31—21no—
95C2×C4⋊C4×C31—21no—
96C2×C4⋊C4×C31D411yescharacteristic
97C2×C4⋊C4×C31D411yescharacteristic
98C2×C4⋊C4×C31C2311yescharacteristic
99C2×C4⋊C4×C31C2311yescharacteristic
100C2×C4⋊C4×C31C2311yescharacteristic
101C2×C4⋊C4×C31C2311yescharacteristic
102C2×C4⋊C4×C31C2311yescharacteristic
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×C31—21no—
109C2×C22⋊C4×C31—21no—
110C2×C42×C31—21no—
111C2×C42×C31—21no—
112C2×C42×C31—21no—
113C2×C42×C31C2311yescharacteristic
114C2×C42×C31C2311yescharacteristic
115C2×C42×C31C2311yescharacteristic
116C31×#106—22no—
117C31×#106—41no—
118C31×C4⋊C8—22no—
119C31×#103—22no—
120C31×#103—22no—
121C31×#102—22no—
122C31×#102—22no—
123C31×#102—22no—
124C31×#102—22no—
125C31×#102—22no—
126C31×#102—41no—
127C4×C8×C31—22no—
128C31×#95—21no—
129C31×#95—21no—
130C31×#95—21no—
131C31×#95D411yescharacteristic
132C31×#95D411yescharacteristic
133C24×C31—21no—
134C24×C31—21no—
135C2×Q8×C31—21no—
136C2×Q8×C31—21no—
137C2×Q8×C31—21no—
138C2×Q8×C31C2×D412yes—
139C2×Q8×C31#4112yes—
140C2×Q8×C31#4112yes—
141C2×D4×C31—21no—
142C2×D4×C31—21no—
143C2×D4×C31—21no—
144C2×D4×C31—21no—
145C2×D4×C31—21no—
146C2×D4×C31—21no—
147C2×D4×C31—21no—
148C2×D4×C31—21no—
149C2×D4×C31—21no—
150C2×D4×C31—21no—
151C2×D4×C31—21no—
152C2×D4×C31—42no—
153C2×D4×C31—42no—
154C2×D4×C31—42no—
155C2×D4×C31—42no—
156C2×D4×C31—81no—
157C2×D4×C31—81no—
158C2×D4×C31C2×D412yes—
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—42no—
166C22×C4×C31—42no—
167C22×C4×C31—81no—
168C22×C4×C31C2×D411yescharacteristic
169C22×C4×C31C2×D411yescharacteristic
170C22×C4×C31C2×D411yescharacteristic
171C22×C4×C31C2×D411yescharacteristic
172C22×C4×C31C2×D411yescharacteristic
173C22×C4×C31C2×D411yescharacteristic
174C22×C4×C31C2411yescharacteristic
175SD16×C31—28no—
176SD16×C31—44no—
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×D412yes—
189C4⋊C4×C31—24no—
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—41no—
200C4⋊C4×C31—42no—
201C4⋊C4×C31—42no—
202C4⋊C4×C31—42no—
203C4⋊C4×C31—42no—
204C4⋊C4×C31—81no—
205C4⋊C4×C31—81no—
206C4⋊C4×C31—81no—
207C4⋊C4×C31SD1614yescomplemented
208C4⋊C4×C31#4112yes—
209C22⋊C4×C31—42no—
210C22⋊C4×C31—42no—
211C22⋊C4×C31—42no—
212C22⋊C4×C31—42no—
213C22⋊C4×C31—81no—
214C22⋊C4×C31—81no—
215C22⋊C4×C31—81no—
216C42×C31—24no—
217C42×C31—21no—
218C42×C31—21no—
219C42×C31—21no—
220C42×C31—21no—
221C42×C31—21no—
222C42×C31—21no—
223C42×C31—42no—
224C42×C31—42no—
225#26163C3111yesmaximal, characteristic, direct product factor, Sylow
226C23×C31—22no—
227C23×C31—41no—
228C23×C31—41no—
229C23×C31—41no—
230C23×C31—41no—
231C23×C31—41no—
232C23×C31—41no—
233C23×C31—41no—
234C23×C31—41no—
235C23×C31—41no—
236C23×C31—41no—
237C23×C31—41no—
238C23×C31—41no—
239C23×C31—41no—
240C23×C31C22×D411yescharacteristic
241Q8×C31—22no—
242Q8×C31—22no—
243Q8×C31—22no—
244Q8×C31#12314yescomplemented
245D4×C31—22no—
246D4×C31—22no—
247D4×C31—41no—
248D4×C31—41no—
249D4×C31—41no—
250D4×C31—41no—
251D4×C31—41no—
252D4×C31—41no—
253D4×C31—84no—
254D4×C31—84no—
255C2×C4×C31—21no—
256C2×C4×C31—22no—
257C2×C4×C31—21no—
258C2×C4×C31—21no—
259C2×C4×C31—22no—
260C2×C4×C31—22no—
261C2×C4×C31—21no—
262C2×C4×C31—21no—
263C2×C4×C31—21no—
264C2×C4×C31—21no—
265C2×C4×C31—22no—
266C2×C4×C31—21no—
267C2×C4×C31—21no—
268C2×C4×C31—21no—
269C2×C4×C31—21no—
270C2×C4×C31—21no—
271C2×C4×C31—21no—
272C2×C4×C31—21no—
273C2×C4×C31—21no—
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—84no—
289C2×C4×C31C2×SD1612yes—
290C2×C4×C31C2×SD1612yes—
291C2×C4×C31C2×SD1612yes—
292C2×C4×C31C22×D411yescharacteristic
293C2×C4×C31C2×#4111yescharacteristic
294C2×C4×C31C2×#4111yescharacteristic
295C2×C4×C31C2×#4111yescharacteristic
296C2×C4×C31H(5,𝔽2)11yescharacteristic
297C2×C4×C312−1+411yescharacteristic
298C8×C31—22no—
299C8×C31—41no—
300C8×C31—41no—
301C8×C31—41no—
302C2×#460C2×C3111yescharacteristic
303C2×C4×SD16C2×C3111yescharacteristic, complemented
304#2445C2×C3111yescharacteristic
305Q8×C4⋊C4C2×C3111yescharacteristic, complemented
306#2094C2×C3111yescharacteristic, complemented
307#2088C2×C3111yescharacteristic, complemented
308#2071C2×C3111yescharacteristic, complemented
309#2041C2×C3111yescharacteristic
310#1934C2×C3111yescharacteristic, complemented
311#1916C2×C3111yescharacteristic, complemented
312#1880C2×C3111yescharacteristic, complemented
313#1880C2×C3111yescharacteristic, complemented
314#1880C2×C3111yescharacteristic, complemented
315#1865C2×C3111yescharacteristic, complemented
316#1864C2×C3111yescharacteristic, complemented
317C22×C31—42no—
318C22×C31—42no—
319C22×C31—42no—
320C22×C31—81no—
321C22×C31—81no—
322C22×C31—81no—
323C22×C31—81no—
324C22×C31—81no—
325C22×C31—81no—
326C22×C31—81no—
327C22×C31—81no—
328C22×C31—81no—
329C22×C31—81no—
330C22×C31—81no—
331C22×C31#52511yescharacteristic
332C22×C31D4211yescharacteristic
333C22×C31#54811yescharacteristic
334C22×C31C22×SD1611yescharacteristic
335C22×C31#57511yescharacteristic
336C22×C31#57611yescharacteristic
337C22×C31#57711yescharacteristic
338C4×C31—22no—
339C4×C31—24no—
340C4×C31—22no—
341C4×C31—22no—
342C4×C31—41no—
343C4×C31—42no—
344C4×C31—41no—
345C4×C31—41no—
346C4×C31—81no—
347C4×C31—81no—
348C4×C31—81no—
349C4×C31—81no—
350C4×C31C2×#12311yescharacteristic
351C4×C31#53911yescharacteristic
352C4×C31#54711yescharacteristic
353C4×C31#55311yescharacteristic
354C22×SD16C22×C3111yescharacteristic
355C22×SD16C22×C3111yescharacteristic
356C2×#127C22×C3111yescharacteristic
357C2×#123—21no—
358C2×C4×Q8C22×C3111yescharacteristic
359C2×C4×Q8C22×C3111yescharacteristic
360C2×C4×Q8C22×C3111yescharacteristic
361C2×C4×D4C22×C3111yescharacteristic
362#460—24no—
363C4×SD16—24no—
364C2×#106C22×C3111yescharacteristic
365C2×#106C22×C3111yescharacteristic
366C2×C4⋊C8C22×C3111yescharacteristic
367C2×#103C22×C3111yescharacteristic
368C2×#103C22×C3111yescharacteristic
369C2×#102C22×C3111yescharacteristic
370C2×#102C22×C3111yescharacteristic
371C2×#102C22×C3111yescharacteristic
372C2×#102C22×C3111yescharacteristic
373C2×#102C22×C3111yescharacteristic
374C2×#102C22×C3111yescharacteristic
375C2×C4×C8C22×C3111yescharacteristic
376#394—21no—
377#394—21no—
378#390C22×C3111yescharacteristic
379#390C22×C3111yescharacteristic
380#390C22×C3111yescharacteristic
381#389—21no—
382#389—21no—
383#389C22×C3111yescharacteristic
384#389C22×C3111yescharacteristic
385#389C22×C3111yescharacteristic
386#386—21no—
387#384—21no—
388#384C22×C3111yescharacteristic
389C4×C4⋊C4—21no—
390C4×C4⋊C4C22×C3111yescharacteristic
391#340C22×C3111yescharacteristic
392#340C22×C3111yescharacteristic
393#340C22×C3111yescharacteristic
394#340C22×C3111yescharacteristic
395#336C22×C3111yescharacteristic
396#336C22×C3111yescharacteristic
397#336C22×C3111yescharacteristic
398#336C22×C3111yescharacteristic
399C2×C31—82no—
400C2×C31—161no—
401C2×C31#244311yescharacteristic
402C2×C31#310311yescharacteristic
403C2×C31#311911yescharacteristic
404C2×C31#326811yescharacteristic
405C2×C31D4×SD1611yescharacteristic
406C2×C31#336211yescharacteristic
407C2×C31#337111yescharacteristic
408C22×Q8C23×C3111yescharacteristic
409C22×D4—21no—
410C22×D4—21no—
411C22×D4C23×C3111yescharacteristic
412C22×D4C23×C3111yescharacteristic
413C23×C4—21no—
414C2×SD16—22no—
415C2×SD16—22no—
416C2×SD16—22no—
417C2×SD16—22no—
418C2×SD16—22no—
419C2×SD16D4×C3114yes—
420C22×C8C23×C3111yescharacteristic
421C22×C8C23×C3111yescharacteristic
422C22×C8C23×C3111yescharacteristic
423C22×C8C23×C3111yescharacteristic
424#127—22no—
425#127—41no—
426#123—44no—
427C4×Q8—22no—
428C4×Q8—22no—
429C4×Q8—22no—
430C4×Q8—22no—
431C4×Q8—41no—
432C4×Q8—41no—
433C4×D4—22no—
434C4×D4—41no—
435C2×C4⋊C4—21no—
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⋊C4D4×C3111yescharacteristic
444C2×C4⋊C4D4×C3111yescharacteristic
445C2×C4⋊C4C23×C3111yescharacteristic
446C2×C4⋊C4C23×C3111yescharacteristic
447C2×C4⋊C4C23×C3111yescharacteristic
448C2×C4⋊C4C23×C3111yescharacteristic
449C2×C4⋊C4C23×C3111yescharacteristic
450C2×C22⋊C4—21no—
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C42—21no—
458C2×C42—21no—
459C2×C42—21no—
460C2×C42C23×C3111yescharacteristic
461C2×C42C23×C3111yescharacteristic
462C2×C42C23×C3111yescharacteristic
463#106—22no—
464#106—41no—
465C4⋊C8—22no—
466#103—22no—
467#103—22no—
468#102—22no—
469#102—22no—
470#102—22no—
471#102—22no—
472#102—22no—
473#102—41no—
474C4×C8—22no—
475#95—21no—
476#95—21no—
477#95—21no—
478#95D4×C3111yescharacteristic
479#95D4×C3111yescharacteristic
480C31#2616311yescharacteristic, direct product factor, Sylow
481C24—21no—
482C24—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8C2×D4×C3112yes—
487C2×Q8#41×C3112yes—
488C2×Q8#41×C3112yes—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
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—42no—
504C2×D4—81no—
505C2×D4—81no—
506C2×D4C2×D4×C3112yes—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—42no—
514C22×C4—42no—
515C22×C4—81no—
516C22×C4C2×D4×C3111yescharacteristic
517C22×C4C2×D4×C3111yescharacteristic
518C22×C4C2×D4×C3111yescharacteristic
519C22×C4C2×D4×C3111yescharacteristic
520C22×C4C2×D4×C3111yescharacteristic
521C22×C4C2×D4×C3111yescharacteristic
522C22×C4C24×C3111yescharacteristic
523SD16—28no—
524SD16—44no—
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×C8—21no—
535C2×C8—21no—
536C2×C8C2×D4×C3112yes—
537C4⋊C4—24no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—41no—
548C4⋊C4—42no—
549C4⋊C4—42no—
550C4⋊C4—42no—
551C4⋊C4—42no—
552C4⋊C4—81no—
553C4⋊C4—81no—
554C4⋊C4—81no—
555C4⋊C4SD16×C3114yescomplemented
556C4⋊C4#41×C3112yes—
557C22⋊C4—42no—
558C22⋊C4—42no—
559C22⋊C4—42no—
560C22⋊C4—42no—
561C22⋊C4—81no—
562C22⋊C4—81no—
563C22⋊C4—81no—
564C42—24no—
565C42—21no—
566C42—21no—
567C42—21no—
568C42—21no—
569C42—21no—
570C42—21no—
571C42—42no—
572C42—42no—
573C23—22no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23C22×D4×C3111yescharacteristic
588Q8—22no—
589Q8—22no—
590Q8—22no—
591Q8C31×#12314yescomplemented
592D4—22no—
593D4—22no—
594D4—41no—
595D4—41no—
596D4—41no—
597D4—41no—
598D4—41no—
599D4—41no—
600D4—84no—
601D4—84no—
602C2×C4—21no—
603C2×C4—22no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—22no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—41no—
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—84no—
636C2×C4C2×SD16×C3112yes—
637C2×C4C2×SD16×C3112yes—
638C2×C4C2×SD16×C3112yes—
639C2×C4C22×D4×C3111yescharacteristic
640C2×C4C2×#41×C3111yescharacteristic
641C2×C4C2×#41×C3111yescharacteristic
642C2×C4C2×#41×C3111yescharacteristic
643C2×C4C31×H(5,𝔽2)11yescharacteristic
644C2×C4C31×2−1+411yescharacteristic
645C8—22no—
646C8—41no—
647C8—41no—
648C8—41no—
649C22—42no—
650C22—42no—
651C22—42no—
652C22—81no—
653C22—81no—
654C22—81no—
655C22—81no—
656C22—81no—
657C22—81no—
658C22—81no—
659C22—81no—
660C22—81no—
661C22—81no—
662C22—81no—
663C22C31×#52511yescharacteristic
664C22D42×C3111yescharacteristic
665C22C31×#54811yescharacteristic
666C22C22×SD16×C3111yescharacteristic
667C22C31×#57511yescharacteristic
668C22C31×#57611yescharacteristic
669C22C31×#57711yescharacteristic
670C4—22no—
671C4—24no—
672C4—22no—
673C4—22no—
674C4—41no—
675C4—42no—
676C4—41no—
677C4—41no—
678C4—81no—
679C4—81no—
680C4—81no—
681C4—81no—
682C4C2×C31×#12311yescharacteristic
683C4C31×#53911yescharacteristic
684C4C31×#54711yescharacteristic
685C4C31×#55311yescharacteristic
686C2—82no—
687C2—161no—
688C2C31×#244311yescharacteristic
689C2C31×#310311yescharacteristic
690C2C31×#311911yescharacteristic
691C2C31×#326811yescharacteristic
692C2D4×SD16×C3111yescharacteristic
693C2C31×#336211yescharacteristic
694C2C31×#337111yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#127C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C4×C4⋊C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×SD16×C31C2semidirect
4. Q8×C4⋊C4×C31C2semidirect
5. C31×#2094C2semidirect
6. C31×#2088C2semidirect
7. C31×#2071C2semidirect
9. C31×#1934C2semidirect
10. C31×#1916C2semidirect
11. C31×#1880C2semidirect
12. C31×#1880C2semidirect
13. C31×#1880C2semidirect
14. C31×#1865C2semidirect
15. C31×#1864C2semidirect
207. C4⋊C4×C31SD16semidirect
225. #26163C31direct (N × H)
244. Q8×C31#123semidirect
303. C2×C4×SD16C2×C31semidirect
305. Q8×C4⋊C4C2×C31semidirect
306. #2094C2×C31semidirect
307. #2088C2×C31semidirect
308. #2071C2×C31semidirect
310. #1934C2×C31semidirect
311. #1916C2×C31semidirect
312. #1880C2×C31semidirect
313. #1880C2×C31semidirect
314. #1880C2×C31semidirect
315. #1865C2×C31semidirect
316. #1864C2×C31semidirect
480. C31#26163direct (N × H)
555. C4⋊C4SD16×C31semidirect
591. Q8C31×#123semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#4602
C2×C4×SD16×C312
C31×#24452
Q8×C4⋊C4×C312
C31×#20942
C31×#20882
C31×#20712
C31×#20412
C31×#19342
C31×#19162
C31×#18802
C31×#18652
C31×#18642
#2616331