Finite Group Databasebeta

← C31×#26724 #21483483

Subgroups — C31×#26724 #21483483

Order 7936.

826 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C31×#2491C211yesmaximal, characteristic
2C31×#2360C211yesmaximal, characteristic, complemented
3C31×#2055C211yesmaximal, characteristic, complemented
4C31×#2035C211yesmaximal, characteristic, complemented
5C31×#2024C211yesmaximal, characteristic, complemented
6C31×#2000C211yesmaximal, characteristic
7C31×#1988C211yesmaximal, characteristic, complemented
8C31×#1934C211yesmaximal, characteristic, complemented
9C31×#1926C211yesmaximal, characteristic, complemented
10C31×#1923C211yesmaximal, characteristic, complemented
11C31×#1920C211yesmaximal, characteristic, complemented
12C31×#1880C211yesmaximal, characteristic, complemented
13C31×#1874C211yesmaximal, characteristic
14C31×#1824C211yesmaximal, characteristic, complemented
15C4×C31×#103C211yesmaximal, characteristic, complemented
16C22×SD16×C31C2211yescharacteristic
17C2×C31×C4⋊Q8C2211yescharacteristic
18C2×C31×#124—21no—
19C2×C31×C22⋊Q8C2211yescharacteristic
20C2×C31×#121C2211yescharacteristic
21C2×C4×Q8×C31C2211yescharacteristic
22C22×C4⋊C4×C31C2211yescharacteristic
23C2×C31×#106C2211yescharacteristic
24C2×C31×C4⋊C8C2211yescharacteristic
25C2×C31×#103C2211yescharacteristic
26C2×C31×#103C2211yescharacteristic
27C2×C31×#103C2211yescharacteristic
28C2×C31×#102C2211yescharacteristic
29C2×C31×#102C2211yescharacteristic
30C2×C31×#102C2211yescharacteristic
31C2×C31×C22⋊C8C2211yescharacteristic
32C2×C31×C22⋊C8C2211yescharacteristic
33C2×C4×C8×C31C2211yescharacteristic
34C31×#394—21no—
35C31×#393—21no—
36C31×#391C2211yescharacteristic
37C31×#390C2211yescharacteristic
38C31×#390C2211yescharacteristic
39C31×#389—21no—
40C31×#389C2211yescharacteristic
41C31×#388—21no—
42C31×#387—21no—
43C31×#385—21no—
44C31×#380C2211yescharacteristic
45C4×C4⋊C4×C31C2211yescharacteristic
46C4×C4⋊C4×C31C2211yescharacteristic
47C4×C22⋊C4×C31—21no—
48C4×C22⋊C4×C31C2211yescharacteristic
49C31×#340C2211yescharacteristic
50C31×#340C2211yescharacteristic
51C31×#340C2211yescharacteristic
52C31×#340C2211yescharacteristic
53C31×#340C2211yescharacteristic
54C31×#340C2211yescharacteristic
55C31×#340C2211yescharacteristic
56C31×#340C2211yescharacteristic
57C31×#336C2211yescharacteristic
58C31×#336C2211yescharacteristic
59C22×Q8×C31—21no—
60C22×Q8×C31C2311yescharacteristic
61C22×D4×C31—21no—
62C22×D4×C31C2311yescharacteristic
63C23×C4×C31—21no—
64C23×C4×C31C2311yescharacteristic
65C2×SD16×C31—22no—
66C2×SD16×C31—41no—
67C2×SD16×C31—41no—
68C22×C8×C31C2311yescharacteristic
69C22×C8×C31C2311yescharacteristic
70C22×C8×C31C2311yescharacteristic
71C22×C8×C31C2311yescharacteristic
72C31×C4⋊Q8—22no—
73C31×C4⋊Q8—41no—
74C31×#124—44no—
75C31×C22⋊Q8—22no—
76C31×C22⋊Q8—22no—
77C31×#121—22no—
78C31×#121—41no—
79C4×Q8×C31—22no—
80C4×Q8×C31—41no—
81C2×C4⋊C4×C31—21no—
82C2×C4⋊C4×C31—22no—
83C2×C4⋊C4×C31—21no—
84C2×C4⋊C4×C31—21no—
85C2×C4⋊C4×C31—21no—
86C2×C4⋊C4×C31—21no—
87C2×C4⋊C4×C31—41no—
88C2×C4⋊C4×C31C2311yescharacteristic
89C2×C4⋊C4×C31C2311yescharacteristic
90C2×C4⋊C4×C31C2311yescharacteristic
91C2×C4⋊C4×C31C2311yescharacteristic
92C2×C4⋊C4×C31C2311yescharacteristic
93C2×C4⋊C4×C31C2311yescharacteristic
94C2×C22⋊C4×C31—21no—
95C2×C22⋊C4×C31—21no—
96C2×C22⋊C4×C31—21no—
97C2×C22⋊C4×C31—21no—
98C2×C22⋊C4×C31—21no—
99C2×C22⋊C4×C31—21no—
100C2×C22⋊C4×C31—21no—
101C2×C22⋊C4×C31D411yescharacteristic
102C2×C22⋊C4×C31D411yescharacteristic
103C2×C42×C31—21no—
104C2×C42×C31—21no—
105C2×C42×C31—21no—
106C2×C42×C31C2311yescharacteristic
107C2×C42×C31C2311yescharacteristic
108C31×#106—22no—
109C31×C4⋊C8—41no—
110C31×#103—22no—
111C31×#103—22no—
112C31×#103—41no—
113C31×#102—22no—
114C31×#102—22no—
115C31×#102—41no—
116C31×C22⋊C8—41no—
117C31×C22⋊C8—41no—
118C4×C8×C31—41no—
119C31×#95—21no—
120C31×#95—21no—
121C31×#95—21no—
122C31×#95—21no—
123C31×#95—21no—
124C31×#95—21no—
125C31×#95D411yescharacteristic
126C31×#95D411yescharacteristic
127C24×C31—21no—
128C24×C31C2×D411yescharacteristic
129C2×Q8×C31—21no—
130C2×Q8×C31—21no—
131C2×Q8×C31—21no—
132C2×Q8×C31—21no—
133C2×Q8×C31—21no—
134C2×Q8×C31—42no—
135C2×Q8×C31—42no—
136C2×Q8×C31—81no—
137C2×Q8×C31#4112yes—
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—81no—
147C22×C4×C31—21no—
148C22×C4×C31—21no—
149C22×C4×C31—21no—
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—42no—
161C22×C4×C31—42no—
162C22×C4×C31—81no—
163C22×C4×C31C2×D411yescharacteristic
164C22×C4×C31C2×D411yescharacteristic
165C22×C4×C31C2×D411yescharacteristic
166C22×C4×C31C2×D411yescharacteristic
167C22×C4×C31C2×D411yescharacteristic
168C22×C4×C31C2411yescharacteristic
169SD16×C31—44no—
170C2×C8×C31—21no—
171C2×C8×C31—21no—
172C2×C8×C31—21no—
173C2×C8×C31—21no—
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—
182C4⋊C4×C31—24no—
183C4⋊C4×C31—21no—
184C4⋊C4×C31—21no—
185C4⋊C4×C31—21no—
186C4⋊C4×C31—21no—
187C4⋊C4×C31—21no—
188C4⋊C4×C31—21no—
189C4⋊C4×C31—21no—
190C4⋊C4×C31—21no—
191C4⋊C4×C31—21no—
192C4⋊C4×C31—42no—
193C4⋊C4×C31—42no—
194C4⋊C4×C31—42no—
195C4⋊C4×C31—81no—
196C4⋊C4×C31#4112yes—
197C4⋊C4×C31#4112yes—
198C4⋊C4×C31#4112yes—
199C22⋊C4×C31—24no—
200C22⋊C4×C31—41no—
201C22⋊C4×C31—42no—
202C22⋊C4×C31—42no—
203C22⋊C4×C31—42no—
204C22⋊C4×C31—42no—
205C22⋊C4×C31—42no—
206C22⋊C4×C31—81no—
207C22⋊C4×C31SD1614yescomplemented
208C42×C31—21no—
209C42×C31—21no—
210C42×C31—21no—
211C42×C31—21no—
212C42×C31—42no—
213C42×C31—42no—
214C42×C31—81no—
215#26724C3111yesmaximal, characteristic, direct product factor, Sylow
216C23×C31—21no—
217C23×C31—21no—
218C23×C31—21no—
219C23×C31—21no—
220C23×C31—21no—
221C23×C31—21no—
222C23×C31—41no—
223C23×C31—41no—
224C23×C31—41no—
225C23×C31—41no—
226C23×C31—41no—
227C23×C31—41no—
228C23×C31—41no—
229C23×C31C2×SD1612yes—
230C23×C31C22×D411yescharacteristic
231Q8×C31—22no—
232Q8×C31—22no—
233Q8×C31—41no—
234Q8×C31—41no—
235Q8×C31—84no—
236D4×C31—41no—
237D4×C31—41no—
238D4×C31—41no—
239D4×C31—41no—
240D4×C31—84no—
241C2×C4×C31—21no—
242C2×C4×C31—21no—
243C2×C4×C31—21no—
244C2×C4×C31—21no—
245C2×C4×C31—22no—
246C2×C4×C31—22no—
247C2×C4×C31—21no—
248C2×C4×C31—21no—
249C2×C4×C31—21no—
250C2×C4×C31—22no—
251C2×C4×C31—21no—
252C2×C4×C31—22no—
253C2×C4×C31—21no—
254C2×C4×C31—21no—
255C2×C4×C31—21no—
256C2×C4×C31—21no—
257C2×C4×C31—21no—
258C2×C4×C31—41no—
259C2×C4×C31—41no—
260C2×C4×C31—41no—
261C2×C4×C31—41no—
262C2×C4×C31—41no—
263C2×C4×C31—41no—
264C2×C4×C31—41no—
265C2×C4×C31—41no—
266C2×C4×C31—41no—
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—84no—
280C2×C4×C31C2×SD1612yes—
281C2×C4×C31C2×SD1612yes—
282C2×C4×C31C2×#4111yescharacteristic
283C2×C4×C31C2×#4111yescharacteristic
284C2×C4×C31C2×#4111yescharacteristic
285C2×C4×C31C2×#4111yescharacteristic
286C2×C4×C31H(5,𝔽2)11yescharacteristic
287C2×C4×C31H(5,𝔽2)11yescharacteristic
288C8×C31—41no—
289C8×C31—41no—
290C8×C31—41no—
291C8×C31—41no—
292#2491C2×C3111yescharacteristic
293#2360C2×C3111yescharacteristic, complemented
294#2055C2×C3111yescharacteristic, complemented
295#2035C2×C3111yescharacteristic, complemented
296#2024C2×C3111yescharacteristic, complemented
297#2000C2×C3111yescharacteristic
298#1988C2×C3111yescharacteristic, complemented
299#1934C2×C3111yescharacteristic, complemented
300#1926C2×C3111yescharacteristic, complemented
301#1923C2×C3111yescharacteristic, complemented
302#1920C2×C3111yescharacteristic, complemented
303#1880C2×C3111yescharacteristic, complemented
304#1874C2×C3111yescharacteristic
305#1824C2×C3111yescharacteristic, complemented
306C4×#103C2×C3111yescharacteristic, complemented
307C22×C31—22no—
308C22×C31—22no—
309C22×C31—22no—
310C22×C31—41no—
311C22×C31—41no—
312C22×C31—41no—
313C22×C31—41no—
314C22×C31—81no—
315C22×C31—81no—
316C22×C31—81no—
317C22×C31—81no—
318C22×C31—81no—
319C22×C31—81no—
320C22×C31—81no—
321C22×C31#52511yescharacteristic
322C22×C31#54611yescharacteristic
323C22×C31#54611yescharacteristic
324C22×C31C22×SD1611yescharacteristic
325C22×C31#57511yescharacteristic
326C22×C31#57611yescharacteristic
327C22×C31#57811yescharacteristic
328C4×C31—22no—
329C4×C31—22no—
330C4×C31—42no—
331C4×C31—41no—
332C4×C31—42no—
333C4×C31—42no—
334C4×C31—41no—
335C4×C31—42no—
336C4×C31—41no—
337C4×C31—81no—
338C4×C31—81no—
339C4×C31—81no—
340C4×C31#52911yescharacteristic
341C4×C31#53811yescharacteristic
342C4×C31#55511yescharacteristic
343C4×C31#55911yescharacteristic
344C22×SD16C22×C3111yescharacteristic
345C2×C4⋊Q8C22×C3111yescharacteristic
346C2×#124—21no—
347C2×C22⋊Q8C22×C3111yescharacteristic
348C2×#121C22×C3111yescharacteristic
349C2×C4×Q8C22×C3111yescharacteristic
350C22×C4⋊C4C22×C3111yescharacteristic
351C2×#106C22×C3111yescharacteristic
352C2×C4⋊C8C22×C3111yescharacteristic
353C2×#103C22×C3111yescharacteristic
354C2×#103C22×C3111yescharacteristic
355C2×#103C22×C3111yescharacteristic
356C2×#102C22×C3111yescharacteristic
357C2×#102C22×C3111yescharacteristic
358C2×#102C22×C3111yescharacteristic
359C2×C22⋊C8C22×C3111yescharacteristic
360C2×C22⋊C8C22×C3111yescharacteristic
361C2×C4×C8C22×C3111yescharacteristic
362#394—21no—
363#393—21no—
364#391C22×C3111yescharacteristic
365#390C22×C3111yescharacteristic
366#390C22×C3111yescharacteristic
367#389—21no—
368#389C22×C3111yescharacteristic
369#388—21no—
370#387—21no—
371#385—21no—
372#380C22×C3111yescharacteristic
373C4×C4⋊C4C22×C3111yescharacteristic
374C4×C4⋊C4C22×C3111yescharacteristic
375C4×C22⋊C4—21no—
376C4×C22⋊C4C22×C3111yescharacteristic
377#340C22×C3111yescharacteristic
378#340C22×C3111yescharacteristic
379#340C22×C3111yescharacteristic
380#340C22×C3111yescharacteristic
381#340C22×C3111yescharacteristic
382#340C22×C3111yescharacteristic
383#340C22×C3111yescharacteristic
384#340C22×C3111yescharacteristic
385#336C22×C3111yescharacteristic
386#336C22×C3111yescharacteristic
387C2×C31—42no—
388C2×C31—161no—
389C2×C31#245911yescharacteristic
390C2×C31#310311yescharacteristic
391C2×C31#312411yescharacteristic
392C2×C31#329511yescharacteristic
393C2×C31#329811yescharacteristic
394C2×C31#331911yescharacteristic
395C2×C31#332711yescharacteristic
396C22×Q8—21no—
397C22×Q8C23×C3111yescharacteristic
398C22×D4—21no—
399C22×D4C23×C3111yescharacteristic
400C23×C4—21no—
401C23×C4C23×C3111yescharacteristic
402C2×SD16—22no—
403C2×SD16—41no—
404C2×SD16—41no—
405C22×C8C23×C3111yescharacteristic
406C22×C8C23×C3111yescharacteristic
407C22×C8C23×C3111yescharacteristic
408C22×C8C23×C3111yescharacteristic
409C4⋊Q8—22no—
410C4⋊Q8—41no—
411#124—44no—
412C22⋊Q8—22no—
413C22⋊Q8—22no—
414#121—22no—
415#121—41no—
416C4×Q8—22no—
417C4×Q8—41no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—22no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—41no—
425C2×C4⋊C4C23×C3111yescharacteristic
426C2×C4⋊C4C23×C3111yescharacteristic
427C2×C4⋊C4C23×C3111yescharacteristic
428C2×C4⋊C4C23×C3111yescharacteristic
429C2×C4⋊C4C23×C3111yescharacteristic
430C2×C4⋊C4C23×C3111yescharacteristic
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4D4×C3111yescharacteristic
439C2×C22⋊C4D4×C3111yescharacteristic
440C2×C42—21no—
441C2×C42—21no—
442C2×C42—21no—
443C2×C42C23×C3111yescharacteristic
444C2×C42C23×C3111yescharacteristic
445#106—22no—
446C4⋊C8—41no—
447#103—22no—
448#103—22no—
449#103—41no—
450#102—22no—
451#102—22no—
452#102—41no—
453C22⋊C8—41no—
454C22⋊C8—41no—
455C4×C8—41no—
456#95—21no—
457#95—21no—
458#95—21no—
459#95—21no—
460#95—21no—
461#95—21no—
462#95D4×C3111yescharacteristic
463#95D4×C3111yescharacteristic
464C31#2672411yescharacteristic, direct product factor, Sylow
465C24—21no—
466C24C2×D4×C3111yescharacteristic
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—42no—
473C2×Q8—42no—
474C2×Q8—81no—
475C2×Q8#41×C3112yes—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—42no—
483C2×D4—42no—
484C2×D4—81no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—42no—
499C22×C4—42no—
500C22×C4—81no—
501C22×C4C2×D4×C3111yescharacteristic
502C22×C4C2×D4×C3111yescharacteristic
503C22×C4C2×D4×C3111yescharacteristic
504C22×C4C2×D4×C3111yescharacteristic
505C22×C4C2×D4×C3111yescharacteristic
506C22×C4C24×C3111yescharacteristic
507SD16—44no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C4⋊C4—24no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—42no—
531C4⋊C4—42no—
532C4⋊C4—42no—
533C4⋊C4—81no—
534C4⋊C4#41×C3112yes—
535C4⋊C4#41×C3112yes—
536C4⋊C4#41×C3112yes—
537C22⋊C4—24no—
538C22⋊C4—41no—
539C22⋊C4—42no—
540C22⋊C4—42no—
541C22⋊C4—42no—
542C22⋊C4—42no—
543C22⋊C4—42no—
544C22⋊C4—81no—
545C22⋊C4SD16×C3114yescomplemented
546C42—21no—
547C42—21no—
548C42—21no—
549C42—21no—
550C42—42no—
551C42—42no—
552C42—81no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23—41no—
566C23C2×SD16×C3112yes—
567C23C22×D4×C3111yescharacteristic
568Q8—22no—
569Q8—22no—
570Q8—41no—
571Q8—41no—
572Q8—84no—
573D4—41no—
574D4—41no—
575D4—41no—
576D4—41no—
577D4—84no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—22no—
588C2×C4—21no—
589C2×C4—22no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
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—84no—
617C2×C4C2×SD16×C3112yes—
618C2×C4C2×SD16×C3112yes—
619C2×C4C2×#41×C3111yescharacteristic
620C2×C4C2×#41×C3111yescharacteristic
621C2×C4C2×#41×C3111yescharacteristic
622C2×C4C2×#41×C3111yescharacteristic
623C2×C4C31×H(5,𝔽2)11yescharacteristic
624C2×C4C31×H(5,𝔽2)11yescharacteristic
625C8—41no—
626C8—41no—
627C8—41no—
628C8—41no—
629C22—22no—
630C22—22no—
631C22—22no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—81no—
637C22—81no—
638C22—81no—
639C22—81no—
640C22—81no—
641C22—81no—
642C22—81no—
643C22C31×#52511yescharacteristic
644C22C31×#54611yescharacteristic
645C22C31×#54611yescharacteristic
646C22C22×SD16×C3111yescharacteristic
647C22C31×#57511yescharacteristic
648C22C31×#57611yescharacteristic
649C22C31×#57811yescharacteristic
650C4—22no—
651C4—22no—
652C4—42no—
653C4—41no—
654C4—42no—
655C4—42no—
656C4—41no—
657C4—42no—
658C4—41no—
659C4—81no—
660C4—81no—
661C4—81no—
662C4C31×#52911yescharacteristic
663C4C31×#53811yescharacteristic
664C4C31×#55511yescharacteristic
665C4C31×#55911yescharacteristic
666C2—42no—
667C2—161no—
668C2C31×#245911yescharacteristic
669C2C31×#310311yescharacteristic
670C2C31×#312411yescharacteristic
671C2C31×#329511yescharacteristic
672C2C31×#329811yescharacteristic
673C2C31×#331911yescharacteristic
674C2C31×#332711yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C4×C22⋊C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#2360C2semidirect
3. C31×#2055C2semidirect
4. C31×#2035C2semidirect
5. C31×#2024C2semidirect
7. C31×#1988C2semidirect
8. C31×#1934C2semidirect
9. C31×#1926C2semidirect
10. C31×#1923C2semidirect
11. C31×#1920C2semidirect
12. C31×#1880C2semidirect
14. C31×#1824C2semidirect
15. C4×C31×#103C2semidirect
207. C22⋊C4×C31SD16semidirect
215. #26724C31direct (N × H)
293. #2360C2×C31semidirect
294. #2055C2×C31semidirect
295. #2035C2×C31semidirect
296. #2024C2×C31semidirect
298. #1988C2×C31semidirect
299. #1934C2×C31semidirect
300. #1926C2×C31semidirect
301. #1923C2×C31semidirect
302. #1920C2×C31semidirect
303. #1880C2×C31semidirect
305. #1824C2×C31semidirect
306. C4×#103C2×C31semidirect
464. C31#26724direct (N × H)
545. C22⋊C4SD16×C31semidirect

Maximal subgroups

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

subgroupindex
C31×#24912
C31×#23602
C31×#20552
C31×#20352
C31×#20242
C31×#20002
C31×#19882
C31×#19342
C31×#19262
C31×#19232
C31×#19202
C31×#18802
C31×#18742
C31×#18242
C4×C31×#1032
#2672431