Finite Group Databasebeta

← C31×#21459 #21478218

Subgroups — C31×#21459 #21478218

Order 7936.

1560 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#518C211yesmaximal, characteristic
2C2×C31×#450C211yesmaximal, characteristic
3C2×C31×#440C211yesmaximal, characteristic, complemented
4C2×C4×SD16×C31C211yesmaximal, characteristic, complemented
5C31×#2323C211yesmaximal, characteristic, complemented
6C31×#1877C211yesmaximal, characteristic, complemented
7C31×#1877C211yesmaximal, characteristic, complemented
8C31×#1873C211yesmaximal, characteristic, complemented
9C31×#1864C211yesmaximal, characteristic, complemented
10C31×#1862C211yesmaximal, characteristic, complemented
11C31×#1854C211yesmaximal, characteristic, complemented
12C31×#1786C211yesmaximal, characteristic
13C31×#1762C211yesmaximal, characteristic, complemented
14C4×C31×#102C211yesmaximal, characteristic, complemented
15C31×#1750C211yesmaximal, characteristic, complemented
16C23×D4×C31C2211yescharacteristic
17C22×SD16×C31C2211yescharacteristic
18C22×SD16×C31C2211yescharacteristic
19C2×C31×C22⋊Q8C2211yescharacteristic
20C31×#518—24no—
21C31×#518—24no—
22C2×C4×Q8×C31C2211yescharacteristic, complemented
23C2×C4×D4×C31—21no—
24C2×C4×D4×C31—21no—
25C2×C4×D4×C31C2211yescharacteristic
26C2×C4×D4×C31C2211yescharacteristic
27C2×C4×D4×C31C2211yescharacteristic
28C2×C4×D4×C31C2211yescharacteristic
29C2×C31×#117C2211yescharacteristic
30C2×C31×#117C2211yescharacteristic
31C22×C22⋊C4×C31—21no—
32C22×C22⋊C4×C31—21no—
33C31×#450C418yescomplemented
34C31×#440—24no—
35C4×SD16×C31—24no—
36C2×C31×#107C2211yescharacteristic, complemented
37C2×C31×#106C2211yescharacteristic, complemented
38C2×C31×#103C2211yescharacteristic, complemented
39C2×C31×#103C2211yescharacteristic, complemented
40C2×C31×#102C2211yescharacteristic
41C2×C31×#102C2211yescharacteristic
42C2×C31×#102C2211yescharacteristic
43C2×C31×#102C2211yescharacteristic
44C2×C31×#102C2211yescharacteristic
45C2×C31×#102C2211yescharacteristic
46C2×C31×C22⋊C8C2211yescharacteristic
47C2×C31×C22⋊C8C2211yescharacteristic
48C2×C31×#97C2211yescharacteristic, complemented
49C2×C4×C8×C31C2211yescharacteristic, complemented
50C31×#391C2211yescharacteristic, complemented
51C31×#389—21no—
52C31×#389C2211yescharacteristic, complemented
53C31×#388—21no—
54C31×#388—21no—
55C31×#387—21no—
56C31×#380C2211yescharacteristic
57C4×C4⋊C4×C31C2211yescharacteristic, complemented
58C31×#340C2211yescharacteristic, complemented
59C31×#340C2211yescharacteristic, complemented
60C31×#340C2211yescharacteristic, complemented
61C31×#340C2211yescharacteristic, complemented
62C31×#336C2211yescharacteristic, complemented
63C31×#336C2211yescharacteristic, complemented
64C25×C31—21no—
65C22×Q8×C31C2311yescharacteristic
66C22×D4×C31—22no—
67C22×D4×C31—22no—
68C22×D4×C31—22no—
69C22×D4×C31—22no—
70C22×D4×C31—21no—
71C22×D4×C31—22no—
72C22×D4×C31C2×C414yes—
73C22×D4×C31C2311yescharacteristic
74C22×D4×C31C2311yescharacteristic
75C23×C4×C31—21no—
76C23×C4×C31—21no—
77C23×C4×C31—21no—
78C23×C4×C31—21no—
79C23×C4×C31C2311yescharacteristic
80C2×SD16×C31—22no—
81C2×SD16×C31—22no—
82C2×SD16×C31—22no—
83C2×SD16×C31—22no—
84C2×SD16×C31C2×C414yescomplemented
85C2×SD16×C31C2×C414yescomplemented
86C22×C8×C31C2311yescharacteristic
87C22×C8×C31C2311yescharacteristic
88C22×C8×C31C2311yescharacteristic
89C22×C8×C31C2311yescharacteristic
90C31×C22⋊Q8—22no—
91C31×C22⋊Q8C2×C414yescomplemented
92C4×Q8×C31—22no—
93C4×Q8×C31—22no—
94C4×D4×C31—28no—
95C4×D4×C31—28no—
96C4×D4×C31—22no—
97C4×D4×C31—22no—
98C4×D4×C31—22no—
99C4×D4×C31—22no—
100C4×D4×C31—22no—
101C4×D4×C31—22no—
102C4×D4×C31D414yes—
103C4×D4×C31D414yes—
104C31×#117—22no—
105C31×#117—22no—
106C31×#117—22no—
107C31×#117—22no—
108C2×C4⋊C4×C31—21no—
109C2×C4⋊C4×C31—21no—
110C2×C4⋊C4×C31—21no—
111C2×C4⋊C4×C31D411yescharacteristic
112C2×C4⋊C4×C31D411yescharacteristic
113C2×C4⋊C4×C31C2311yescharacteristic
114C2×C4⋊C4×C31C2311yescharacteristic
115C2×C4⋊C4×C31C2311yescharacteristic
116C2×C4⋊C4×C31C2311yescharacteristic
117C2×C4⋊C4×C31C2311yescharacteristic
118C2×C22⋊C4×C31—28no—
119C2×C22⋊C4×C31—28no—
120C2×C22⋊C4×C31—21no—
121C2×C22⋊C4×C31—21no—
122C2×C22⋊C4×C31—21no—
123C2×C22⋊C4×C31—21no—
124C2×C22⋊C4×C31—21no—
125C2×C22⋊C4×C31—21no—
126C2×C22⋊C4×C31—21no—
127C2×C22⋊C4×C31D411yescharacteristic
128C2×C22⋊C4×C31D411yescharacteristic
129C2×C42×C31—21no—
130C2×C42×C31—21no—
131C2×C42×C31—21no—
132C2×C42×C31C2311yescharacteristic
133C2×C42×C31C2311yescharacteristic
134C31×#107—22no—
135C31×#106—22no—
136C31×#103—22no—
137C31×#103—22no—
138C31×#102—22no—
139C31×#102—22no—
140C31×#102—22no—
141C31×#102—22no—
142C31×#102C2×C414yescomplemented
143C31×#102C2×C414yescomplemented
144C31×C22⋊C8—22no—
145C31×C22⋊C8C2×C414yescomplemented
146C31×#97—22no—
147C4×C8×C31—22no—
148C31×#95—21no—
149C31×#95—21no—
150C31×#95—21no—
151C31×#95—21no—
152C31×#95—21no—
153C24×C31—24no—
154C24×C31—24no—
155C24×C31—21no—
156C24×C31—21no—
157C24×C31—24no—
158C24×C31—81no—
159C24×C31—81no—
160C24×C31—81no—
161C24×C31—81no—
162C24×C31C2×D411yescharacteristic
163C2×Q8×C31—21no—
164C2×Q8×C31—21no—
165C2×Q8×C31—21no—
166C2×Q8×C31—21no—
167C2×Q8×C31—21no—
168C2×Q8×C31C22×C412yes—
169C2×D4×C31—24no—
170C2×D4×C31—24no—
171C2×D4×C31—28no—
172C2×D4×C31—28no—
173C2×D4×C31—28no—
174C2×D4×C31—28no—
175C2×D4×C31—24no—
176C2×D4×C31—21no—
177C2×D4×C31—21no—
178C2×D4×C31—21no—
179C2×D4×C31—21no—
180C2×D4×C31—21no—
181C2×D4×C31—21no—
182C2×D4×C31C22×C412yes—
183C2×D4×C31C22×C412yes—
184C2×D4×C31C2×D412yes—
185C2×D4×C31C2×D412yes—
186C2×D4×C31#4112yes—
187C2×D4×C31#4112yes—
188C22×C4×C31—21no—
189C22×C4×C31—21no—
190C22×C4×C31—21no—
191C22×C4×C31—21no—
192C22×C4×C31—21no—
193C22×C4×C31—21no—
194C22×C4×C31—21no—
195C22×C4×C31—21no—
196C22×C4×C31—24no—
197C22×C4×C31—24no—
198C22×C4×C31—24no—
199C22×C4×C31—24no—
200C22×C4×C31—21no—
201C22×C4×C31—21no—
202C22×C4×C31—81no—
203C22×C4×C31—81no—
204C22×C4×C31—81no—
205C22×C4×C31—81no—
206C22×C4×C31—81no—
207C22×C4×C31—81no—
208C22×C4×C31—81no—
209C22×C4×C31—81no—
210C22×C4×C31C22×C412yes—
211C22×C4×C31C2×D411yescharacteristic
212C22×C4×C31C2×D411yescharacteristic
213C22×C4×C31C2×D411yescharacteristic
214C22×C4×C31C2×D411yescharacteristic
215C22×C4×C31C2×D411yescharacteristic
216C22×C4×C31#4112yes—
217C22×C4×C31C2411yescharacteristic
218SD16×C31—28no—
219SD16×C31—28no—
220C2×C8×C31—21no—
221C2×C8×C31—21no—
222C2×C8×C31—21no—
223C2×C8×C31—21no—
224C2×C8×C31—21no—
225C2×C8×C31—21no—
226C2×C8×C31—21no—
227C2×C8×C31—21no—
228C2×C8×C31—21no—
229C2×C8×C31—21no—
230C2×C8×C31C22×C412yes—
231C2×C8×C31C22×C412yes—
232C4⋊C4×C31—24no—
233C4⋊C4×C31—22no—
234C4⋊C4×C31—22no—
235C4⋊C4×C31—21no—
236C4⋊C4×C31—21no—
237C4⋊C4×C31—21no—
238C4⋊C4×C31—21no—
239C4⋊C4×C31—21no—
240C4⋊C4×C31—21no—
241C4⋊C4×C31—21no—
242C4⋊C4×C31—42no—
243C4⋊C4×C31—81no—
244C4⋊C4×C31C22×C412yes—
245C4⋊C4×C31C2×D412yes—
246C4⋊C4×C31C2×D412yes—
247C22⋊C4×C31—24no—
248C22⋊C4×C31—24no—
249C22⋊C4×C31—24no—
250C22⋊C4×C31—24no—
251C22⋊C4×C31—22no—
252C22⋊C4×C31—22no—
253C22⋊C4×C31—24no—
254C22⋊C4×C31—24no—
255C22⋊C4×C31—81no—
256C42×C31—24no—
257C42×C31—21no—
258C42×C31—21no—
259C42×C31—42no—
260C42×C31—81no—
261C42×C31C2×D412yes—
262C42×C31C2×D412yes—
263#21459C3111yesmaximal, characteristic, direct product factor, Sylow
264C23×C31—216no—
265C23×C31—22no—
266C23×C31—22no—
267C23×C31—21no—
268C23×C31—22no—
269C23×C31—22no—
270C23×C31—21no—
271C23×C31—22no—
272C23×C31—22no—
273C23×C31—21no—
274C23×C31—21no—
275C23×C31—21no—
276C23×C31—21no—
277C23×C31—41no—
278C23×C31—41no—
279C23×C31—41no—
280C23×C31—41no—
281C23×C31—41no—
282C23×C31—41no—
283C23×C31—41no—
284C23×C31—41no—
285C23×C31—84no—
286C23×C31—84no—
287C23×C31—84no—
288C23×C31—84no—
289C23×C31—84no—
290C23×C31—84no—
291C23×C31C4×D412yes—
292C23×C31C22×D411yescharacteristic
293Q8×C31—22no—
294Q8×C31—22no—
295Q8×C31—41no—
296Q8×C31—41no—
297D4×C31—216no—
298D4×C31—22no—
299D4×C31—22no—
300D4×C31—22no—
301D4×C31—22no—
302D4×C31—22no—
303D4×C31—22no—
304D4×C31C4×D414yes—
305D4×C31C4×D414yes—
306C2×C4×C31—21no—
307C2×C4×C31—21no—
308C2×C4×C31—21no—
309C2×C4×C31—21no—
310C2×C4×C31—21no—
311C2×C4×C31—21no—
312C2×C4×C31—22no—
313C2×C4×C31—22no—
314C2×C4×C31—22no—
315C2×C4×C31—22no—
316C2×C4×C31—22no—
317C2×C4×C31—22no—
318C2×C4×C31—21no—
319C2×C4×C31—21no—
320C2×C4×C31—22no—
321C2×C4×C31—22no—
322C2×C4×C31—21no—
323C2×C4×C31—21no—
324C2×C4×C31—21no—
325C2×C4×C31—21no—
326C2×C4×C31—41no—
327C2×C4×C31—41no—
328C2×C4×C31—41no—
329C2×C4×C31—41no—
330C2×C4×C31—41no—
331C2×C4×C31—41no—
332C2×C4×C31—41no—
333C2×C4×C31—41no—
334C2×C4×C31—41no—
335C2×C4×C31—41no—
336C2×C4×C31—41no—
337C2×C4×C31—41no—
338C2×C4×C31—41no—
339C2×C4×C31—41no—
340C2×C4×C31—84no—
341C2×C4×C31—84no—
342C2×C4×C31—84no—
343C2×C4×C31—84no—
344C2×C4×C31C4×D412yes—
345C2×C4×C31#12012yes—
346C2×C4×C31#12012yes—
347C2×C4×C31C23×C411yescharacteristic
348C2×C4×C31C22×D411yescharacteristic
349C2×C4×C31C22×D411yescharacteristic
350C2×C4×C31C2×#4111yescharacteristic
351C2×C4×C31C2×#4111yescharacteristic
352C2×C4×C31C2×#4111yescharacteristic
353C8×C31—22no—
354C8×C31—22no—
355C8×C31—41no—
356C8×C31—41no—
357C2×#518C2×C3111yescharacteristic
358C2×#450C2×C3111yescharacteristic
359C2×#440C2×C3111yescharacteristic, complemented
360C2×C4×SD16C2×C3111yescharacteristic, complemented
361#2323C2×C3111yescharacteristic, complemented
362#1877C2×C3111yescharacteristic, complemented
363#1877C2×C3111yescharacteristic, complemented
364#1873C2×C3111yescharacteristic, complemented
365#1864C2×C3111yescharacteristic, complemented
366#1862C2×C3111yescharacteristic, complemented
367#1854C2×C3111yescharacteristic, complemented
368#1786C2×C3111yescharacteristic
369#1762C2×C3111yescharacteristic, complemented
370C4×#102C2×C3111yescharacteristic, complemented
371#1750C2×C3111yescharacteristic, complemented
372C22×C31—22no—
373C22×C31—22no—
374C22×C31—22no—
375C22×C31—24no—
376C22×C31—24no—
377C22×C31—41no—
378C22×C31—42no—
379C22×C31—42no—
380C22×C31—41no—
381C22×C31—42no—
382C22×C31—42no—
383C22×C31—42no—
384C22×C31—42no—
385C22×C31—42no—
386C22×C31—42no—
387C22×C31—42no—
388C22×C31—42no—
389C22×C31—41no—
390C22×C31—42no—
391C22×C31—42no—
392C22×C31—41no—
393C22×C31—816no—
394C22×C31C2×C4×D411yescharacteristic
395C22×C31C2×#12011yescharacteristic
396C22×C31#52511yescharacteristic
397C22×C31#57611yescharacteristic
398C22×C31#57711yescharacteristic
399C22×C31#57711yescharacteristic
400C22×C31#57711yescharacteristic
401C4×C31—22no—
402C4×C31—22no—
403C4×C31—22no—
404C4×C31—42no—
405C4×C31—41no—
406C4×C31—42no—
407C4×C31—41no—
408C4×C31—42no—
409C4×C31—42no—
410C4×C31—81no—
411C4×C31—81no—
412C4×C31C2×C4×D411yescharacteristic
413C4×C31C2×C4×D411yescharacteristic
414C4×C31#52511yescharacteristic
415C4×C31#52511yescharacteristic
416C23×D4C22×C3111yescharacteristic
417C22×SD16C22×C3111yescharacteristic
418C22×SD16C22×C3111yescharacteristic
419C2×C22⋊Q8C22×C3111yescharacteristic
420#518—24no—
421#518—24no—
422C2×C4×Q8C22×C3111yescharacteristic, complemented
423C2×C4×D4—21no—
424C2×C4×D4—21no—
425C2×C4×D4C22×C3111yescharacteristic
426C2×C4×D4C22×C3111yescharacteristic
427C2×C4×D4C22×C3111yescharacteristic
428C2×C4×D4C22×C3111yescharacteristic
429C2×#117C22×C3111yescharacteristic
430C2×#117C22×C3111yescharacteristic
431C22×C22⋊C4—21no—
432C22×C22⋊C4—21no—
433#450C4×C3118yescomplemented
434#440—24no—
435C4×SD16—24no—
436C2×#107C22×C3111yescharacteristic, complemented
437C2×#106C22×C3111yescharacteristic, complemented
438C2×#103C22×C3111yescharacteristic, complemented
439C2×#103C22×C3111yescharacteristic, complemented
440C2×#102C22×C3111yescharacteristic
441C2×#102C22×C3111yescharacteristic
442C2×#102C22×C3111yescharacteristic
443C2×#102C22×C3111yescharacteristic
444C2×#102C22×C3111yescharacteristic
445C2×#102C22×C3111yescharacteristic
446C2×C22⋊C8C22×C3111yescharacteristic
447C2×C22⋊C8C22×C3111yescharacteristic
448C2×#97C22×C3111yescharacteristic, complemented
449C2×C4×C8C22×C3111yescharacteristic, complemented
450#391C22×C3111yescharacteristic, complemented
451#389—21no—
452#389C22×C3111yescharacteristic, complemented
453#388—21no—
454#388—21no—
455#387—21no—
456#380C22×C3111yescharacteristic
457C4×C4⋊C4C22×C3111yescharacteristic, complemented
458#340C22×C3111yescharacteristic, complemented
459#340C22×C3111yescharacteristic, complemented
460#340C22×C3111yescharacteristic, complemented
461#340C22×C3111yescharacteristic, complemented
462#336C22×C3111yescharacteristic, complemented
463#336C22×C3111yescharacteristic, complemented
464C2×C31—42no—
465C2×C31—44no—
466C2×C31—44no—
467C2×C31C4×#12011yescharacteristic
468C2×C31#294611yescharacteristic
469C2×C31#294911yescharacteristic
470C2×C31#300911yescharacteristic
471C2×C31#301211yescharacteristic
472C2×C31#311811yescharacteristic
473C2×C31#312311yescharacteristic
474C25—21no—
475C22×Q8C23×C3111yescharacteristic
476C22×D4—22no—
477C22×D4—22no—
478C22×D4—22no—
479C22×D4—22no—
480C22×D4—21no—
481C22×D4—22no—
482C22×D4C2×C4×C3114yes—
483C22×D4C23×C3111yescharacteristic
484C22×D4C23×C3111yescharacteristic
485C23×C4—21no—
486C23×C4—21no—
487C23×C4—21no—
488C23×C4—21no—
489C23×C4C23×C3111yescharacteristic
490C2×SD16—22no—
491C2×SD16—22no—
492C2×SD16—22no—
493C2×SD16—22no—
494C2×SD16C2×C4×C3114yescomplemented
495C2×SD16C2×C4×C3114yescomplemented
496C22×C8C23×C3111yescharacteristic
497C22×C8C23×C3111yescharacteristic
498C22×C8C23×C3111yescharacteristic
499C22×C8C23×C3111yescharacteristic
500C22⋊Q8—22no—
501C22⋊Q8C2×C4×C3114yescomplemented
502C4×Q8—22no—
503C4×Q8—22no—
504C4×D4—28no—
505C4×D4—28no—
506C4×D4—22no—
507C4×D4—22no—
508C4×D4—22no—
509C4×D4—22no—
510C4×D4—22no—
511C4×D4—22no—
512C4×D4D4×C3114yes—
513C4×D4D4×C3114yes—
514#117—22no—
515#117—22no—
516#117—22no—
517#117—22no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4D4×C3111yescharacteristic
522C2×C4⋊C4D4×C3111yescharacteristic
523C2×C4⋊C4C23×C3111yescharacteristic
524C2×C4⋊C4C23×C3111yescharacteristic
525C2×C4⋊C4C23×C3111yescharacteristic
526C2×C4⋊C4C23×C3111yescharacteristic
527C2×C4⋊C4C23×C3111yescharacteristic
528C2×C22⋊C4—28no—
529C2×C22⋊C4—28no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4D4×C3111yescharacteristic
538C2×C22⋊C4D4×C3111yescharacteristic
539C2×C42—21no—
540C2×C42—21no—
541C2×C42—21no—
542C2×C42C23×C3111yescharacteristic
543C2×C42C23×C3111yescharacteristic
544#107—22no—
545#106—22no—
546#103—22no—
547#103—22no—
548#102—22no—
549#102—22no—
550#102—22no—
551#102—22no—
552#102C2×C4×C3114yescomplemented
553#102C2×C4×C3114yescomplemented
554C22⋊C8—22no—
555C22⋊C8C2×C4×C3114yescomplemented
556#97—22no—
557C4×C8—22no—
558#95—21no—
559#95—21no—
560#95—21no—
561#95—21no—
562#95—21no—
563C31#2145911yescharacteristic, direct product factor, Sylow
564C24—24no—
565C24—24no—
566C24—21no—
567C24—21no—
568C24—24no—
569C24—81no—
570C24—81no—
571C24—81no—
572C24—81no—
573C24C2×D4×C3111yescharacteristic
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8C22×C4×C3112yes—
580C2×D4—24no—
581C2×D4—24no—
582C2×D4—28no—
583C2×D4—28no—
584C2×D4—28no—
585C2×D4—28no—
586C2×D4—24no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4C22×C4×C3112yes—
594C2×D4C22×C4×C3112yes—
595C2×D4C2×D4×C3112yes—
596C2×D4C2×D4×C3112yes—
597C2×D4#41×C3112yes—
598C2×D4#41×C3112yes—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—24no—
608C22×C4—24no—
609C22×C4—24no—
610C22×C4—24no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—81no—
614C22×C4—81no—
615C22×C4—81no—
616C22×C4—81no—
617C22×C4—81no—
618C22×C4—81no—
619C22×C4—81no—
620C22×C4—81no—
621C22×C4C22×C4×C3112yes—
622C22×C4C2×D4×C3111yescharacteristic
623C22×C4C2×D4×C3111yescharacteristic
624C22×C4C2×D4×C3111yescharacteristic
625C22×C4C2×D4×C3111yescharacteristic
626C22×C4C2×D4×C3111yescharacteristic
627C22×C4#41×C3112yes—
628C22×C4C24×C3111yescharacteristic
629SD16—28no—
630SD16—28no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8C22×C4×C3112yes—
642C2×C8C22×C4×C3112yes—
643C4⋊C4—24no—
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—42no—
654C4⋊C4—81no—
655C4⋊C4C22×C4×C3112yes—
656C4⋊C4C2×D4×C3112yes—
657C4⋊C4C2×D4×C3112yes—
658C22⋊C4—24no—
659C22⋊C4—24no—
660C22⋊C4—24no—
661C22⋊C4—24no—
662C22⋊C4—22no—
663C22⋊C4—22no—
664C22⋊C4—24no—
665C22⋊C4—24no—
666C22⋊C4—81no—
667C42—24no—
668C42—21no—
669C42—21no—
670C42—42no—
671C42—81no—
672C42C2×D4×C3112yes—
673C42C2×D4×C3112yes—
674C23—216no—
675C23—22no—
676C23—22no—
677C23—21no—
678C23—22no—
679C23—22no—
680C23—21no—
681C23—22no—
682C23—22no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—84no—
696C23—84no—
697C23—84no—
698C23—84no—
699C23—84no—
700C23—84no—
701C23C4×D4×C3112yes—
702C23C22×D4×C3111yescharacteristic
703Q8—22no—
704Q8—22no—
705Q8—41no—
706Q8—41no—
707D4—216no—
708D4—22no—
709D4—22no—
710D4—22no—
711D4—22no—
712D4—22no—
713D4—22no—
714D4C4×D4×C3114yes—
715D4C4×D4×C3114yes—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—84no—
751C2×C4—84no—
752C2×C4—84no—
753C2×C4—84no—
754C2×C4C4×D4×C3112yes—
755C2×C4C31×#12012yes—
756C2×C4C31×#12012yes—
757C2×C4C23×C4×C3111yescharacteristic
758C2×C4C22×D4×C3111yescharacteristic
759C2×C4C22×D4×C3111yescharacteristic
760C2×C4C2×#41×C3111yescharacteristic
761C2×C4C2×#41×C3111yescharacteristic
762C2×C4C2×#41×C3111yescharacteristic
763C8—22no—
764C8—22no—
765C8—41no—
766C8—41no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—24no—
771C22—24no—
772C22—41no—
773C22—42no—
774C22—42no—
775C22—41no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—41no—
785C22—42no—
786C22—42no—
787C22—41no—
788C22—816no—
789C22C2×C4×D4×C3111yescharacteristic
790C22C2×C31×#12011yescharacteristic
791C22C31×#52511yescharacteristic
792C22C31×#57611yescharacteristic
793C22C31×#57711yescharacteristic
794C22C31×#57711yescharacteristic
795C22C31×#57711yescharacteristic
796C4—22no—
797C4—22no—
798C4—22no—
799C4—42no—
800C4—41no—
801C4—42no—
802C4—41no—
803C4—42no—
804C4—42no—
805C4—81no—
806C4—81no—
807C4C2×C4×D4×C3111yescharacteristic
808C4C2×C4×D4×C3111yescharacteristic
809C4C31×#52511yescharacteristic
810C4C31×#52511yescharacteristic
811C2—42no—
812C2—44no—
813C2—44no—
814C2C4×C31×#12011yescharacteristic
815C2C31×#294611yescharacteristic
816C2C31×#294911yescharacteristic
817C2C31×#300911yescharacteristic
818C2C31×#301211yescharacteristic
819C2C31×#311811yescharacteristic
820C2C31×#312311yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutatorC2×C4C23×C4×C31
Frattini, cosocleC22×C4C24×C31
prime radicalC23×D4×C31C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C31×#117 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C31×#440C2semidirect
4. C2×C4×SD16×C31C2semidirect
5. C31×#2323C2semidirect
6. C31×#1877C2semidirect
7. C31×#1877C2semidirect
8. C31×#1873C2semidirect
9. C31×#1864C2semidirect
10. C31×#1862C2semidirect
11. C31×#1854C2semidirect
13. C31×#1762C2semidirect
14. C4×C31×#102C2semidirect
15. C31×#1750C2semidirect
22. C2×C4×Q8×C31C22semidirect
33. C31×#450C4semidirect
36. C2×C31×#107C22semidirect
37. C2×C31×#106C22semidirect
38. C2×C31×#103C22semidirect
39. C2×C31×#103C22semidirect
48. C2×C31×#97C22semidirect
49. C2×C4×C8×C31C22semidirect
50. C31×#391C22semidirect
52. C31×#389C22semidirect
57. C4×C4⋊C4×C31C22semidirect
58. C31×#340C22semidirect
59. C31×#340C22semidirect
60. C31×#340C22semidirect
61. C31×#340C22semidirect
62. C31×#336C22semidirect
63. C31×#336C22semidirect
84. C2×SD16×C31C2×C4semidirect
85. C2×SD16×C31C2×C4semidirect
91. C31×C22⋊Q8C2×C4semidirect
142. C31×#102C2×C4semidirect
143. C31×#102C2×C4semidirect
145. C31×C22⋊C8C2×C4semidirect
263. #21459C31direct (N × H)
359. C2×#440C2×C31semidirect
360. C2×C4×SD16C2×C31semidirect
361. #2323C2×C31semidirect
362. #1877C2×C31semidirect
363. #1877C2×C31semidirect
364. #1873C2×C31semidirect
365. #1864C2×C31semidirect
366. #1862C2×C31semidirect
367. #1854C2×C31semidirect
369. #1762C2×C31semidirect
370. C4×#102C2×C31semidirect
371. #1750C2×C31semidirect
422. C2×C4×Q8C22×C31semidirect
433. #450C4×C31semidirect
436. C2×#107C22×C31semidirect
437. C2×#106C22×C31semidirect
438. C2×#103C22×C31semidirect
439. C2×#103C22×C31semidirect
448. C2×#97C22×C31semidirect
449. C2×C4×C8C22×C31semidirect
450. #391C22×C31semidirect
452. #389C22×C31semidirect
457. C4×C4⋊C4C22×C31semidirect
458. #340C22×C31semidirect
459. #340C22×C31semidirect
460. #340C22×C31semidirect
461. #340C22×C31semidirect
462. #336C22×C31semidirect
463. #336C22×C31semidirect
494. C2×SD16C2×C4×C31semidirect
495. C2×SD16C2×C4×C31semidirect
501. C22⋊Q8C2×C4×C31semidirect
552. #102C2×C4×C31semidirect
553. #102C2×C4×C31semidirect
555. C22⋊C8C2×C4×C31semidirect
563. C31#21459direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5182
C2×C31×#4502
C2×C31×#4402
C2×C4×SD16×C312
C31×#23232
C31×#18772
C31×#18732
C31×#18642
C31×#18622
C31×#18542
C31×#17862
C31×#17622
C4×C31×#1022
C31×#17502
#2145931