Finite Group Databasebeta

← C31×#22678 #21479437

Subgroups — C31×#22678 #21479437

Order 7936.

982 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#440C211yesmaximal, characteristic
2C2×C31×#440C211yesmaximal, characteristic
3C2×C4×SD16×C31C211yesmaximal, characteristic
4Q8×C4⋊C4×C31C211yesmaximal, characteristic, complemented
5C31×#2349C211yesmaximal, characteristic
6C31×#1943C211yesmaximal, characteristic, complemented
7C31×#1942C211yesmaximal, characteristic, complemented
8C31×#1865C211yesmaximal, characteristic, complemented
9C31×#1864C211yesmaximal, characteristic
10C31×#1863C211yesmaximal, characteristic, complemented
11C31×#1862C211yesmaximal, characteristic
12C31×#1847C211yesmaximal, characteristic, complemented
13C31×#1805C211yesmaximal, characteristic, complemented
14C31×#1802C211yesmaximal, characteristic
15C31×#1771C211yesmaximal, characteristic, complemented
16C22×SD16×C31C2211yescharacteristic
17C2×C4×Q8×C31C2211yescharacteristic
18C2×C4×Q8×C31C2211yescharacteristic
19C2×C4×Q8×C31C2211yescharacteristic
20C2×C4×D4×C31C2211yescharacteristic
21C2×C4×D4×C31C2211yescharacteristic
22C2×C4×D4×C31C2211yescharacteristic
23C31×#440—24no—
24C31×#440C418yescomplemented
25C4×SD16×C31—24no—
26C2×C31×#107C2211yescharacteristic
27C2×C31×#107C2211yescharacteristic
28C2×C31×#107C2211yescharacteristic
29C2×C31×#106C2211yescharacteristic
30C2×C31×#106C2211yescharacteristic
31C2×C31×C4⋊C8C2211yescharacteristic
32C2×C31×#103C2211yescharacteristic
33C2×C31×#103C2211yescharacteristic
34C2×C31×#103C2211yescharacteristic
35C2×C31×#102C2211yescharacteristic
36C2×C31×#102C2211yescharacteristic
37C2×C31×#102C2211yescharacteristic
38C2×C31×#97C2211yescharacteristic
39C2×C31×#97C2211yescharacteristic
40C2×C4×C8×C31C2211yescharacteristic
41C31×#389—21no—
42C31×#389—21no—
43C31×#389C2211yescharacteristic
44C31×#389C2211yescharacteristic
45C31×#389C2211yescharacteristic
46C31×#389C2211yescharacteristic
47C31×#385—21no—
48C31×#385—21no—
49C31×#384—21no—
50C31×#384C2211yescharacteristic
51C31×#382C2211yescharacteristic
52C31×#380—21no—
53C4×C4⋊C4×C31—21no—
54C4×C4⋊C4×C31C2211yescharacteristic
55C2×C31×#95—21no—
56C31×#340C2211yescharacteristic
57C31×#340C2211yescharacteristic
58C31×#340C2211yescharacteristic
59C31×#340C2211yescharacteristic
60C31×#336C2211yescharacteristic
61C31×#336C2211yescharacteristic
62C22×Q8×C31C2311yescharacteristic
63C22×D4×C31C2311yescharacteristic
64C23×C4×C31—21no—
65C23×C4×C31—21no—
66C23×C4×C31—21no—
67C2×SD16×C31C2×C414yes—
68C2×SD16×C31D414yes—
69C2×SD16×C31Q814yes—
70C22×C8×C31C2311yescharacteristic
71C22×C8×C31C2311yescharacteristic
72C22×C8×C31C2311yescharacteristic
73C22×C8×C31C2311yescharacteristic
74C4×Q8×C31—22no—
75C4×Q8×C31—22no—
76C4×Q8×C31—22no—
77C4×Q8×C31—41no—
78C4×Q8×C31—41no—
79C4×Q8×C31C2×C414yescomplemented
80C4×D4×C31—22no—
81C4×D4×C31—22no—
82C4×D4×C31—22no—
83C4×D4×C31—41no—
84C4×D4×C31—41no—
85C4×D4×C31C2×C414yes—
86C2×C4⋊C4×C31—21no—
87C2×C4⋊C4×C31—21no—
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×C31D411yescharacteristic
96C2×C4⋊C4×C31D411yescharacteristic
97C2×C4⋊C4×C31C2311yescharacteristic
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×C42×C31—21no—
107C2×C42×C31—21no—
108C2×C42×C31—21no—
109C2×C42×C31C2311yescharacteristic
110C2×C42×C31C2311yescharacteristic
111C2×C42×C31C2311yescharacteristic
112C31×#107—22no—
113C31×#107—41no—
114C31×#107C2×C414yescomplemented
115C31×#106—22no—
116C31×#106—41no—
117C31×C4⋊C8—22no—
118C31×#103—22no—
119C31×#103—22no—
120C31×#103C2×C414yescomplemented
121C31×#102—22no—
122C31×#102—22no—
123C31×#102C2×C414yes—
124C31×#97—22no—
125C31×#97C2×C414yescomplemented
126C4×C8×C31—22no—
127C31×#95—21no—
128C31×#95—21no—
129C31×#95—21no—
130C31×#95—21no—
131C31×#95—21no—
132C31×#95—21no—
133C31×#95D411yescharacteristic
134C31×#95D411yescharacteristic
135C24×C31—21no—
136C2×Q8×C31—21no—
137C2×Q8×C31—21no—
138C2×Q8×C31—21no—
139C2×Q8×C31C22×C412yes—
140C2×Q8×C31C2×D412yes—
141C2×Q8×C31C2×Q812yes—
142C2×D4×C31—21no—
143C2×D4×C31—21no—
144C2×D4×C31—21no—
145C2×D4×C31C22×C412yes—
146C2×D4×C31C2×D412yes—
147C2×D4×C31C2×Q812yes—
148C22×C4×C31—21no—
149C22×C4×C31—21no—
150C22×C4×C31—21no—
151C22×C4×C31—24no—
152C22×C4×C31—21no—
153C22×C4×C31—21no—
154C22×C4×C31—21no—
155C22×C4×C31—21no—
156C22×C4×C31—42no—
157C22×C4×C31—42no—
158C22×C4×C31—42no—
159C22×C4×C31—42no—
160C22×C4×C31—81no—
161C22×C4×C31—81no—
162C22×C4×C31—81no—
163C22×C4×C31—81no—
164C22×C4×C31C2×D411yescharacteristic
165C22×C4×C31C2×D411yescharacteristic
166C22×C4×C31C2×D411yescharacteristic
167C22×C4×C31C2×D411yescharacteristic
168C22×C4×C31C2×D411yescharacteristic
169C22×C4×C31C2×D411yescharacteristic
170C22×C4×C31C2411yescharacteristic
171SD16×C31C4⋊C4116yescomplemented
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×C31C22×C412yes—
181C2×C8×C31C22×C412yes—
182C2×C8×C31C2×D412yes—
183C2×C8×C31C2×Q812yes—
184C4⋊C4×C31—24no—
185C4⋊C4×C31—22no—
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—21no—
193C4⋊C4×C31—21no—
194C4⋊C4×C31—21no—
195C4⋊C4×C31—21no—
196C4⋊C4×C31—41no—
197C4⋊C4×C31—42no—
198C4⋊C4×C31—42no—
199C4⋊C4×C31—42no—
200C4⋊C4×C31—81no—
201C4⋊C4×C31—81no—
202C4⋊C4×C31—81no—
203C4⋊C4×C31—81no—
204C4⋊C4×C31—81no—
205C4⋊C4×C31C22×C412yes—
206C4⋊C4×C31C22×C412yes—
207C22⋊C4×C31—24no—
208C22⋊C4×C31—42no—
209C22⋊C4×C31—42no—
210C42×C31—24no—
211C42×C31—21no—
212C42×C31—21no—
213C42×C31—21no—
214C42×C31—21no—
215C42×C31—42no—
216C42×C31—42no—
217C42×C31C22×C412yes—
218C42×C31#4112yes—
219#22678C3111yesmaximal, characteristic, direct product factor, Sylow
220C23×C31—22no—
221C23×C31—22no—
222C23×C31—22no—
223C23×C31—41no—
224C23×C31—41no—
225C23×C31—41no—
226C23×C31—41no—
227C23×C31C22×D411yescharacteristic
228Q8×C31—22no—
229Q8×C31—22no—
230Q8×C31—22no—
231Q8×C31C2×C4⋊C414yes—
232D4×C31—22no—
233D4×C31—22no—
234D4×C31—22no—
235D4×C31C2×C4⋊C414yes—
236C2×C4×C31—22no—
237C2×C4×C31—21no—
238C2×C4×C31—22no—
239C2×C4×C31—22no—
240C2×C4×C31—21no—
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—21no—
251C2×C4×C31—21no—
252C2×C4×C31—21no—
253C2×C4×C31—21no—
254C2×C4×C31—21no—
255C2×C4×C31—21no—
256C2×C4×C31—41no—
257C2×C4×C31—41no—
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—84no—
273C2×C4×C31—84no—
274C2×C4×C31—84no—
275C2×C4×C31C4×D412yes—
276C2×C4×C31C4×D412yes—
277C2×C4×C31#13712yes—
278C2×C4×C31C23×C411yescharacteristic
279C2×C4×C31C22×D411yescharacteristic
280C2×C4×C31C22×Q811yescharacteristic
281C2×C4×C31C2×#4111yescharacteristic
282C2×C4×C31H(5,𝔽2)11yescharacteristic
283C2×C4×C312−1+411yescharacteristic
284C8×C31—22no—
285C8×C31—41no—
286C8×C31—41no—
287C8×C31C2×C4⋊C414yes—
288C2×#440C2×C3111yescharacteristic
289C2×#440C2×C3111yescharacteristic
290C2×C4×SD16C2×C3111yescharacteristic
291Q8×C4⋊C4C2×C3111yescharacteristic, complemented
292#2349C2×C3111yescharacteristic
293#1943C2×C3111yescharacteristic, complemented
294#1942C2×C3111yescharacteristic, complemented
295#1865C2×C3111yescharacteristic, complemented
296#1864C2×C3111yescharacteristic
297#1863C2×C3111yescharacteristic, complemented
298#1862C2×C3111yescharacteristic
299#1847C2×C3111yescharacteristic, complemented
300#1805C2×C3111yescharacteristic, complemented
301#1802C2×C3111yescharacteristic
302#1771C2×C3111yescharacteristic, complemented
303C22×C31—24no—
304C22×C31—42no—
305C22×C31—42no—
306C22×C31—42no—
307C22×C31—42no—
308C22×C31—42no—
309C22×C31—42no—
310C22×C31C2×C4×D411yescharacteristic
311C22×C31D4211yescharacteristic
312C22×C31D4×Q811yescharacteristic
313C22×C31C2×#13711yescharacteristic
314C22×C31#57511yescharacteristic
315C22×C31#57611yescharacteristic
316C22×C31#57711yescharacteristic
317C4×C31—24no—
318C4×C31—22no—
319C4×C31—22no—
320C4×C31—22no—
321C4×C31—42no—
322C4×C31—42no—
323C4×C31—41no—
324C4×C31—41no—
325C4×C31—41no—
326C4×C31—81no—
327C4×C31—81no—
328C4×C31—81no—
329C4×C31—81no—
330C4×C31C22×C4⋊C411yescharacteristic
331C4×C31#52011yescharacteristic
332C4×C31#54711yescharacteristic
333C4×C31#55411yescharacteristic
334C22×SD16C22×C3111yescharacteristic
335C2×C4×Q8C22×C3111yescharacteristic
336C2×C4×Q8C22×C3111yescharacteristic
337C2×C4×Q8C22×C3111yescharacteristic
338C2×C4×D4C22×C3111yescharacteristic
339C2×C4×D4C22×C3111yescharacteristic
340C2×C4×D4C22×C3111yescharacteristic
341#440—24no—
342#440C4×C3118yescomplemented
343C4×SD16—24no—
344C2×#107C22×C3111yescharacteristic
345C2×#107C22×C3111yescharacteristic
346C2×#107C22×C3111yescharacteristic
347C2×#106C22×C3111yescharacteristic
348C2×#106C22×C3111yescharacteristic
349C2×C4⋊C8C22×C3111yescharacteristic
350C2×#103C22×C3111yescharacteristic
351C2×#103C22×C3111yescharacteristic
352C2×#103C22×C3111yescharacteristic
353C2×#102C22×C3111yescharacteristic
354C2×#102C22×C3111yescharacteristic
355C2×#102C22×C3111yescharacteristic
356C2×#97C22×C3111yescharacteristic
357C2×#97C22×C3111yescharacteristic
358C2×C4×C8C22×C3111yescharacteristic
359#389—21no—
360#389—21no—
361#389C22×C3111yescharacteristic
362#389C22×C3111yescharacteristic
363#389C22×C3111yescharacteristic
364#389C22×C3111yescharacteristic
365#385—21no—
366#385—21no—
367#384—21no—
368#384C22×C3111yescharacteristic
369#382C22×C3111yescharacteristic
370#380—21no—
371C4×C4⋊C4—21no—
372C4×C4⋊C4C22×C3111yescharacteristic
373C2×#95—21no—
374#340C22×C3111yescharacteristic
375#340C22×C3111yescharacteristic
376#340C22×C3111yescharacteristic
377#340C22×C3111yescharacteristic
378#336C22×C3111yescharacteristic
379#336C22×C3111yescharacteristic
380C2×C31—44no—
381C2×C31D4×C4⋊C411yescharacteristic
382C2×C31C4×#13711yescharacteristic
383C2×C31#294611yescharacteristic
384C2×C31#326611yescharacteristic
385C2×C31#326811yescharacteristic
386C2×C31#338511yescharacteristic
387C2×C31#338811yescharacteristic
388C22×Q8C23×C3111yescharacteristic
389C22×D4C23×C3111yescharacteristic
390C23×C4—21no—
391C23×C4—21no—
392C23×C4—21no—
393C2×SD16C2×C4×C3114yes—
394C2×SD16D4×C3114yes—
395C2×SD16Q8×C3114yes—
396C22×C8C23×C3111yescharacteristic
397C22×C8C23×C3111yescharacteristic
398C22×C8C23×C3111yescharacteristic
399C22×C8C23×C3111yescharacteristic
400C4×Q8—22no—
401C4×Q8—22no—
402C4×Q8—22no—
403C4×Q8—41no—
404C4×Q8—41no—
405C4×Q8C2×C4×C3114yescomplemented
406C4×D4—22no—
407C4×D4—22no—
408C4×D4—22no—
409C4×D4—41no—
410C4×D4—41no—
411C4×D4C2×C4×C3114yes—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4D4×C3111yescharacteristic
422C2×C4⋊C4D4×C3111yescharacteristic
423C2×C4⋊C4C23×C3111yescharacteristic
424C2×C4⋊C4C23×C3111yescharacteristic
425C2×C4⋊C4C23×C3111yescharacteristic
426C2×C4⋊C4C23×C3111yescharacteristic
427C2×C4⋊C4C23×C3111yescharacteristic
428C2×C4⋊C4C23×C3111yescharacteristic
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C42—21no—
433C2×C42—21no—
434C2×C42—21no—
435C2×C42C23×C3111yescharacteristic
436C2×C42C23×C3111yescharacteristic
437C2×C42C23×C3111yescharacteristic
438#107—22no—
439#107—41no—
440#107C2×C4×C3114yescomplemented
441#106—22no—
442#106—41no—
443C4⋊C8—22no—
444#103—22no—
445#103—22no—
446#103C2×C4×C3114yescomplemented
447#102—22no—
448#102—22no—
449#102C2×C4×C3114yes—
450#97—22no—
451#97C2×C4×C3114yescomplemented
452C4×C8—22no—
453#95—21no—
454#95—21no—
455#95—21no—
456#95—21no—
457#95—21no—
458#95—21no—
459#95D4×C3111yescharacteristic
460#95D4×C3111yescharacteristic
461C31#2267811yescharacteristic, direct product factor, Sylow
462C24—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8C22×C4×C3112yes—
467C2×Q8C2×D4×C3112yes—
468C2×Q8C2×Q8×C3112yes—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4C22×C4×C3112yes—
473C2×D4C2×D4×C3112yes—
474C2×D4C2×Q8×C3112yes—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—24no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4—81no—
488C22×C4—81no—
489C22×C4—81no—
490C22×C4—81no—
491C22×C4C2×D4×C3111yescharacteristic
492C22×C4C2×D4×C3111yescharacteristic
493C22×C4C2×D4×C3111yescharacteristic
494C22×C4C2×D4×C3111yescharacteristic
495C22×C4C2×D4×C3111yescharacteristic
496C22×C4C2×D4×C3111yescharacteristic
497C22×C4C24×C3111yescharacteristic
498SD16C4⋊C4×C31116yescomplemented
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8C22×C4×C3112yes—
508C2×C8C22×C4×C3112yes—
509C2×C8C2×D4×C3112yes—
510C2×C8C2×Q8×C3112yes—
511C4⋊C4—24no—
512C4⋊C4—22no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—41no—
524C4⋊C4—42no—
525C4⋊C4—42no—
526C4⋊C4—42no—
527C4⋊C4—81no—
528C4⋊C4—81no—
529C4⋊C4—81no—
530C4⋊C4—81no—
531C4⋊C4—81no—
532C4⋊C4C22×C4×C3112yes—
533C4⋊C4C22×C4×C3112yes—
534C22⋊C4—24no—
535C22⋊C4—42no—
536C22⋊C4—42no—
537C42—24no—
538C42—21no—
539C42—21no—
540C42—21no—
541C42—21no—
542C42—42no—
543C42—42no—
544C42C22×C4×C3112yes—
545C42#41×C3112yes—
546C23—22no—
547C23—22no—
548C23—22no—
549C23—41no—
550C23—41no—
551C23—41no—
552C23—41no—
553C23C22×D4×C3111yescharacteristic
554Q8—22no—
555Q8—22no—
556Q8—22no—
557Q8C2×C4⋊C4×C3114yes—
558D4—22no—
559D4—22no—
560D4—22no—
561D4C2×C4⋊C4×C3114yes—
562C2×C4—22no—
563C2×C4—21no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—84no—
599C2×C4—84no—
600C2×C4—84no—
601C2×C4C4×D4×C3112yes—
602C2×C4C4×D4×C3112yes—
603C2×C4C31×#13712yes—
604C2×C4C23×C4×C3111yescharacteristic
605C2×C4C22×D4×C3111yescharacteristic
606C2×C4C22×Q8×C3111yescharacteristic
607C2×C4C2×#41×C3111yescharacteristic
608C2×C4C31×H(5,𝔽2)11yescharacteristic
609C2×C4C31×2−1+411yescharacteristic
610C8—22no—
611C8—41no—
612C8—41no—
613C8C2×C4⋊C4×C3114yes—
614C22—24no—
615C22—42no—
616C22—42no—
617C22—42no—
618C22—42no—
619C22—42no—
620C22—42no—
621C22C2×C4×D4×C3111yescharacteristic
622C22D42×C3111yescharacteristic
623C22D4×Q8×C3111yescharacteristic
624C22C2×C31×#13711yescharacteristic
625C22C31×#57511yescharacteristic
626C22C31×#57611yescharacteristic
627C22C31×#57711yescharacteristic
628C4—24no—
629C4—22no—
630C4—22no—
631C4—22no—
632C4—42no—
633C4—42no—
634C4—41no—
635C4—41no—
636C4—41no—
637C4—81no—
638C4—81no—
639C4—81no—
640C4—81no—
641C4C22×C4⋊C4×C3111yescharacteristic
642C4C31×#52011yescharacteristic
643C4C31×#54711yescharacteristic
644C4C31×#55411yescharacteristic
645C2—44no—
646C2D4×C4⋊C4×C3111yescharacteristic
647C2C4×C31×#13711yescharacteristic
648C2C31×#294611yescharacteristic
649C2C31×#326611yescharacteristic
650C2C31×#326811yescharacteristic
651C2C31×#338511yescharacteristic
652C2C31×#338811yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutatorC2×C4C23×C4×C31
Frattini, cosocleC22×C4C24×C31
prime radicalC22×D4×C31C23
LCSG ▷ C2×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
4. Q8×C4⋊C4×C31C2semidirect
6. C31×#1943C2semidirect
7. C31×#1942C2semidirect
8. C31×#1865C2semidirect
10. C31×#1863C2semidirect
12. C31×#1847C2semidirect
13. C31×#1805C2semidirect
15. C31×#1771C2semidirect
24. C31×#440C4semidirect
79. C4×Q8×C31C2×C4semidirect
114. C31×#107C2×C4semidirect
120. C31×#103C2×C4semidirect
125. C31×#97C2×C4semidirect
171. SD16×C31C4⋊C4semidirect
219. #22678C31direct (N × H)
291. Q8×C4⋊C4C2×C31semidirect
293. #1943C2×C31semidirect
294. #1942C2×C31semidirect
295. #1865C2×C31semidirect
297. #1863C2×C31semidirect
299. #1847C2×C31semidirect
300. #1805C2×C31semidirect
302. #1771C2×C31semidirect
342. #440C4×C31semidirect
405. C4×Q8C2×C4×C31semidirect
440. #107C2×C4×C31semidirect
446. #103C2×C4×C31semidirect
451. #97C2×C4×C31semidirect
461. C31#22678direct (N × H)
498. SD16C4⋊C4×C31semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#4402
C2×C4×SD16×C312
Q8×C4⋊C4×C312
C31×#23492
C31×#19432
C31×#19422
C31×#18652
C31×#18642
C31×#18632
C31×#18622
C31×#18472
C31×#18052
C31×#18022
C31×#17712
#2267831