Finite Group Databasebeta

← C31×#25156 #21481915

Subgroups — C31×#25156 #21481915

Order 7936.

1268 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#461C211yesmaximal, characteristic, complemented
2C2×C31×#450C211yesmaximal, characteristic
3C2×C31×#450C211yesmaximal, characteristic
4C2×C4×SD16×C31C211yesmaximal, characteristic, complemented
5C31×#2429C211yesmaximal, characteristic, complemented
6D4×C22⋊C4×C31C211yesmaximal, characteristic
7C31×#2065C211yesmaximal, characteristic, complemented
8C31×#2035C211yesmaximal, characteristic, complemented
9C31×#2035C211yesmaximal, characteristic, complemented
10C31×#2013C211yesmaximal, characteristic, complemented
11C31×#1968C211yesmaximal, characteristic, complemented
12C31×#1923C211yesmaximal, characteristic, complemented
13C31×#1880C211yesmaximal, characteristic, complemented
14C31×#1877C211yesmaximal, characteristic, complemented
15C31×#1864C211yesmaximal, characteristic, complemented
16C23×D4×C31C2211yescharacteristic
17C22×SD16×C31C2211yescharacteristic
18C22×SD16×C31C2211yescharacteristic
19C22×SD16×C31C2211yescharacteristic
20C22×SD16×C31C2211yescharacteristic
21C2×C31×C4⋊Q8C2211yescharacteristic, complemented
22C2×C31×C22⋊Q8C2211yescharacteristic
23C2×C31×C22⋊Q8C2211yescharacteristic
24C2×C4×Q8×C31C2211yescharacteristic, complemented
25C2×C4×D4×C31C2211yescharacteristic
26C2×C4×D4×C31C2211yescharacteristic
27C22×C22⋊C4×C31—21no—
28C31×#461—24no—
29C31×#450—24no—
30C31×#450—24no—
31C4×SD16×C31—24no—
32C2×C31×#106C2211yescharacteristic, complemented
33C2×C31×#106C2211yescharacteristic, complemented
34C2×C31×C4⋊C8C2211yescharacteristic, complemented
35C2×C31×#103C2211yescharacteristic, complemented
36C2×C31×#103C2211yescharacteristic, complemented
37C2×C31×#103C2211yescharacteristic, complemented
38C2×C31×#103C2211yescharacteristic, complemented
39C2×C31×#102C2211yescharacteristic
40C2×C31×#102C2211yescharacteristic
41C2×C31×#102C2211yescharacteristic
42C2×C31×#102C2211yescharacteristic
43C2×C31×C22⋊C8C2211yescharacteristic
44C2×C31×C22⋊C8C2211yescharacteristic
45C2×C4×C8×C31C2211yescharacteristic, complemented
46C31×#398—21no—
47C31×#396—21no—
48C31×#391C2211yescharacteristic, complemented
49C31×#390C2211yescharacteristic
50C31×#390C2211yescharacteristic
51C31×#389—21no—
52C31×#389C2211yescharacteristic, complemented
53C31×#388—21no—
54C31×#386—21no—
55C31×#386—21no—
56C31×#380C2211yescharacteristic
57C31×#379—21no—
58C4×C22⋊C4×C31C2211yescharacteristic
59C31×#340C2211yescharacteristic, complemented
60C31×#340C2211yescharacteristic, complemented
61C31×#336C2211yescharacteristic, complemented
62C31×#336C2211yescharacteristic, complemented
63C25×C31—21no—
64C22×Q8×C31C2311yescharacteristic
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—41no—
72C22×D4×C31—41no—
73C22×D4×C31C2311yescharacteristic
74C22×D4×C31C2311yescharacteristic
75C23×C4×C31—21no—
76C23×C4×C31—21no—
77C23×C4×C31C2311yescharacteristic
78C2×SD16×C31—22no—
79C2×SD16×C31—22no—
80C2×SD16×C31—22no—
81C2×SD16×C31—22no—
82C2×SD16×C31—22no—
83C2×SD16×C31—22no—
84C2×SD16×C31—22no—
85C2×SD16×C31—22no—
86C2×SD16×C31—22no—
87C2×SD16×C31—41no—
88C2×SD16×C31—41no—
89C2×SD16×C31D414yes—
90C22×C8×C31C2311yescharacteristic
91C22×C8×C31C2311yescharacteristic
92C22×C8×C31C2311yescharacteristic
93C22×C8×C31C2311yescharacteristic
94C31×C4⋊Q8—22no—
95C31×C4⋊Q8—41no—
96C31×C22⋊Q8—22no—
97C31×C22⋊Q8—22no—
98C31×C22⋊Q8—41no—
99C31×C22⋊Q8—41no—
100C4×Q8×C31—22no—
101C4×Q8×C31—41no—
102C4×D4×C31—22no—
103C4×D4×C31—22no—
104C4×D4×C31—41no—
105C4×D4×C31—41no—
106C2×C4⋊C4×C31—21no—
107C2×C4⋊C4×C31—21no—
108C2×C4⋊C4×C31—21no—
109C2×C4⋊C4×C31—21no—
110C2×C4⋊C4×C31—21no—
111C2×C4⋊C4×C31—21no—
112C2×C4⋊C4×C31C2311yescharacteristic
113C2×C4⋊C4×C31C2311yescharacteristic
114C2×C4⋊C4×C31C2311yescharacteristic
115C2×C4⋊C4×C31C2311yescharacteristic
116C2×C22⋊C4×C31—21no—
117C2×C22⋊C4×C31—21no—
118C2×C22⋊C4×C31—21no—
119C2×C22⋊C4×C31—21no—
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—44no—
126C2×C22⋊C4×C31D411yescharacteristic
127C2×C22⋊C4×C31D411yescharacteristic
128C2×C42×C31—21no—
129C2×C42×C31C2311yescharacteristic
130C2×C42×C31C2311yescharacteristic
131C31×#106—22no—
132C31×#106—41no—
133C31×C4⋊C8—22no—
134C31×#103—22no—
135C31×#103—22no—
136C31×#103—22no—
137C31×#103—41no—
138C31×#102—22no—
139C31×#102—22no—
140C31×#102—22no—
141C31×#102D414yes—
142C31×C22⋊C8—22no—
143C31×C22⋊C8—22no—
144C4×C8×C31—22no—
145C31×#95—21no—
146C31×#95—21no—
147C31×#95—21no—
148C31×#95—21no—
149C31×#95D411yescharacteristic
150C31×#95D411yescharacteristic
151C24×C31—21no—
152C24×C31—24no—
153C24×C31—21no—
154C24×C31—42no—
155C24×C31—42no—
156C24×C31—42no—
157C24×C31—42no—
158C24×C31—81no—
159C24×C31—81no—
160C24×C31C2×D411yescharacteristic
161C2×Q8×C31—21no—
162C2×Q8×C31—21no—
163C2×Q8×C31—21no—
164C2×Q8×C31—21no—
165C2×Q8×C31—21no—
166C2×Q8×C31—21no—
167C2×Q8×C31—21no—
168C2×Q8×C31—21no—
169C2×Q8×C31—21no—
170C2×Q8×C31—21no—
171C2×Q8×C31—21no—
172C2×Q8×C31C2×D412yes—
173C2×D4×C31—24no—
174C2×D4×C31—21no—
175C2×D4×C31—21no—
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×C31—42no—
183C2×D4×C31—42no—
184C2×D4×C31—44no—
185C2×D4×C31—44no—
186C2×D4×C31—44no—
187C2×D4×C31—44no—
188C2×D4×C31C2×D412yes—
189C2×D4×C31C2×D412yes—
190C2×D4×C31#4112yes—
191C2×D4×C31#4112yes—
192C22×C4×C31—21no—
193C22×C4×C31—21no—
194C22×C4×C31—21no—
195C22×C4×C31—21no—
196C22×C4×C31—21no—
197C22×C4×C31—21no—
198C22×C4×C31—21no—
199C22×C4×C31—21no—
200C22×C4×C31—21no—
201C22×C4×C31—21no—
202C22×C4×C31—21no—
203C22×C4×C31—21no—
204C22×C4×C31—42no—
205C22×C4×C31—42no—
206C22×C4×C31—42no—
207C22×C4×C31—42no—
208C22×C4×C31—81no—
209C22×C4×C31—81no—
210C22×C4×C31C2×D411yescharacteristic
211C22×C4×C31C2×D411yescharacteristic
212C22×C4×C31C2×D411yescharacteristic
213C22×C4×C31C2×D411yescharacteristic
214C22×C4×C31C2×D411yescharacteristic
215C22×C4×C31C2411yescharacteristic
216SD16×C31—28no—
217SD16×C31—44no—
218SD16×C31—44no—
219SD16×C31—44no—
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×C31C2×D412yes—
231C2×C8×C31C2×D412yes—
232C4⋊C4×C31—21no—
233C4⋊C4×C31—21no—
234C4⋊C4×C31—21no—
235C4⋊C4×C31—21no—
236C4⋊C4×C31—21no—
237C4⋊C4×C31—21no—
238C4⋊C4×C31—21no—
239C4⋊C4×C31—42no—
240C4⋊C4×C31—42no—
241C4⋊C4×C31—42no—
242C4⋊C4×C31—42no—
243C4⋊C4×C31—42no—
244C4⋊C4×C31—42no—
245C4⋊C4×C31C2×D412yes—
246C22⋊C4×C31—41no—
247C22⋊C4×C31—42no—
248C22⋊C4×C31—42no—
249C22⋊C4×C31—42no—
250C22⋊C4×C31—42no—
251C22⋊C4×C31—42no—
252C22⋊C4×C31—42no—
253C22⋊C4×C31—42no—
254C22⋊C4×C31—81no—
255C22⋊C4×C31—81no—
256C22⋊C4×C31SD1614yescomplemented
257C42×C31—21no—
258C42×C31—21no—
259C42×C31—21no—
260C42×C31—21no—
261C42×C31—42no—
262#25156C3111yesmaximal, characteristic, direct product factor, Sylow
263C23×C31—21no—
264C23×C31—22no—
265C23×C31—21no—
266C23×C31—21no—
267C23×C31—22no—
268C23×C31—22no—
269C23×C31—21no—
270C23×C31—21no—
271C23×C31—21no—
272C23×C31—22no—
273C23×C31—48no—
274C23×C31—48no—
275C23×C31—41no—
276C23×C31—41no—
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×C31C2×SD1612yes—
291C23×C31C22×D411yescharacteristic
292Q8×C31—22no—
293Q8×C31—22no—
294Q8×C31—41no—
295Q8×C31—41no—
296Q8×C31—41no—
297Q8×C31—41no—
298Q8×C31—41no—
299Q8×C31—41no—
300D4×C31—22no—
301D4×C31—22no—
302D4×C31—22no—
303D4×C31—22no—
304D4×C31—22no—
305D4×C31—48no—
306D4×C31—41no—
307D4×C31—41no—
308D4×C31#12114yes—
309C2×C4×C31—21no—
310C2×C4×C31—21no—
311C2×C4×C31—21no—
312C2×C4×C31—21no—
313C2×C4×C31—21no—
314C2×C4×C31—21no—
315C2×C4×C31—21no—
316C2×C4×C31—22no—
317C2×C4×C31—22no—
318C2×C4×C31—21no—
319C2×C4×C31—21no—
320C2×C4×C31—21no—
321C2×C4×C31—21no—
322C2×C4×C31—21no—
323C2×C4×C31—21no—
324C2×C4×C31—41no—
325C2×C4×C31—41no—
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—41no—
341C2×C4×C31—41no—
342C2×C4×C31—41no—
343C2×C4×C31—41no—
344C2×C4×C31—84no—
345C2×C4×C31—84no—
346C2×C4×C31C2×SD1612yes—
347C2×C4×C31C2×SD1612yes—
348C2×C4×C31C22×D411yescharacteristic
349C2×C4×C31C22×D411yescharacteristic
350C2×C4×C31C2×#4111yescharacteristic
351C2×C4×C31C2×#4111yescharacteristic
352C2×C4×C31H(5,𝔽2)11yescharacteristic
353C2×C4×C31H(5,𝔽2)11yescharacteristic
354C8×C31—22no—
355C8×C31—22no—
356C8×C31—41no—
357C8×C31—41no—
358C2×#461C2×C3111yescharacteristic, complemented
359C2×#450C2×C3111yescharacteristic
360C2×#450C2×C3111yescharacteristic
361C2×C4×SD16C2×C3111yescharacteristic, complemented
362#2429C2×C3111yescharacteristic, complemented
363D4×C22⋊C4C2×C3111yescharacteristic
364#2065C2×C3111yescharacteristic, complemented
365#2035C2×C3111yescharacteristic, complemented
366#2035C2×C3111yescharacteristic, complemented
367#2013C2×C3111yescharacteristic, complemented
368#1968C2×C3111yescharacteristic, complemented
369#1923C2×C3111yescharacteristic, complemented
370#1880C2×C3111yescharacteristic, complemented
371#1877C2×C3111yescharacteristic, complemented
372#1864C2×C3111yescharacteristic, complemented
373C22×C31—22no—
374C22×C31—24no—
375C22×C31—22no—
376C22×C31—22no—
377C22×C31—42no—
378C22×C31—41no—
379C22×C31—42no—
380C22×C31—41no—
381C22×C31—41no—
382C22×C31—42no—
383C22×C31—41no—
384C22×C31—42no—
385C22×C31—42no—
386C22×C31—42no—
387C22×C31—42no—
388C22×C31—42no—
389C22×C31—42no—
390C22×C31—816no—
391C22×C31—81no—
392C22×C31—81no—
393C22×C31—81no—
394C22×C31—81no—
395C22×C31#52511yescharacteristic
396C22×C31D4211yescharacteristic
397C22×C31D4211yescharacteristic
398C22×C31C22×SD1611yescharacteristic
399C22×C31#57511yescharacteristic
400C22×C31#57711yescharacteristic
401C22×C31#57711yescharacteristic
402C4×C31—22no—
403C4×C31—22no—
404C4×C31—41no—
405C4×C31—42no—
406C4×C31—41no—
407C4×C31—42no—
408C4×C31—41no—
409C4×C31—81no—
410C4×C31—81no—
411C4×C31—81no—
412C4×C31—81no—
413C4×C31C2×#12111yescharacteristic
414C4×C31#53811yescharacteristic
415C4×C31#54611yescharacteristic
416C4×C31#54611yescharacteristic
417C23×D4C22×C3111yescharacteristic
418C22×SD16C22×C3111yescharacteristic
419C22×SD16C22×C3111yescharacteristic
420C22×SD16C22×C3111yescharacteristic
421C22×SD16C22×C3111yescharacteristic
422C2×C4⋊Q8C22×C3111yescharacteristic, complemented
423C2×C22⋊Q8C22×C3111yescharacteristic
424C2×C22⋊Q8C22×C3111yescharacteristic
425C2×C4×Q8C22×C3111yescharacteristic, complemented
426C2×C4×D4C22×C3111yescharacteristic
427C2×C4×D4C22×C3111yescharacteristic
428C22×C22⋊C4—21no—
429#461—24no—
430#450—24no—
431#450—24no—
432C4×SD16—24no—
433C2×#106C22×C3111yescharacteristic, complemented
434C2×#106C22×C3111yescharacteristic, complemented
435C2×C4⋊C8C22×C3111yescharacteristic, complemented
436C2×#103C22×C3111yescharacteristic, complemented
437C2×#103C22×C3111yescharacteristic, complemented
438C2×#103C22×C3111yescharacteristic, complemented
439C2×#103C22×C3111yescharacteristic, complemented
440C2×#102C22×C3111yescharacteristic
441C2×#102C22×C3111yescharacteristic
442C2×#102C22×C3111yescharacteristic
443C2×#102C22×C3111yescharacteristic
444C2×C22⋊C8C22×C3111yescharacteristic
445C2×C22⋊C8C22×C3111yescharacteristic
446C2×C4×C8C22×C3111yescharacteristic, complemented
447#398—21no—
448#396—21no—
449#391C22×C3111yescharacteristic, complemented
450#390C22×C3111yescharacteristic
451#390C22×C3111yescharacteristic
452#389—21no—
453#389C22×C3111yescharacteristic, complemented
454#388—21no—
455#386—21no—
456#386—21no—
457#380C22×C3111yescharacteristic
458#379—21no—
459C4×C22⋊C4C22×C3111yescharacteristic
460#340C22×C3111yescharacteristic, complemented
461#340C22×C3111yescharacteristic, complemented
462#336C22×C3111yescharacteristic, complemented
463#336C22×C3111yescharacteristic, complemented
464C2×C31—42no—
465C2×C31—44no—
466C2×C31—82no—
467C2×C31#242411yescharacteristic
468C2×C31#310111yescharacteristic
469C2×C31#312311yescharacteristic
470C2×C31#326711yescharacteristic
471C2×C31#327511yescharacteristic
472C2×C31D4×SD1611yescharacteristic
473C2×C31D4×SD1611yescharacteristic
474C25—21no—
475C22×Q8C23×C3111yescharacteristic
476C22×Q8C23×C3111yescharacteristic
477C22×D4—22no—
478C22×D4—22no—
479C22×D4—22no—
480C22×D4—22no—
481C22×D4—21no—
482C22×D4—41no—
483C22×D4—41no—
484C22×D4C23×C3111yescharacteristic
485C22×D4C23×C3111yescharacteristic
486C23×C4—21no—
487C23×C4—21no—
488C23×C4C23×C3111yescharacteristic
489C2×SD16—22no—
490C2×SD16—22no—
491C2×SD16—22no—
492C2×SD16—22no—
493C2×SD16—22no—
494C2×SD16—22no—
495C2×SD16—22no—
496C2×SD16—22no—
497C2×SD16—22no—
498C2×SD16—41no—
499C2×SD16—41no—
500C2×SD16D4×C3114yes—
501C22×C8C23×C3111yescharacteristic
502C22×C8C23×C3111yescharacteristic
503C22×C8C23×C3111yescharacteristic
504C22×C8C23×C3111yescharacteristic
505C4⋊Q8—22no—
506C4⋊Q8—41no—
507C22⋊Q8—22no—
508C22⋊Q8—22no—
509C22⋊Q8—41no—
510C22⋊Q8—41no—
511C4×Q8—22no—
512C4×Q8—41no—
513C4×D4—22no—
514C4×D4—22no—
515C4×D4—41no—
516C4×D4—41no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—21no—
523C2×C4⋊C4C23×C3111yescharacteristic
524C2×C4⋊C4C23×C3111yescharacteristic
525C2×C4⋊C4C23×C3111yescharacteristic
526C2×C4⋊C4C23×C3111yescharacteristic
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
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—44no—
537C2×C22⋊C4D4×C3111yescharacteristic
538C2×C22⋊C4D4×C3111yescharacteristic
539C2×C42—21no—
540C2×C42C23×C3111yescharacteristic
541C2×C42C23×C3111yescharacteristic
542#106—22no—
543#106—41no—
544C4⋊C8—22no—
545#103—22no—
546#103—22no—
547#103—22no—
548#103—41no—
549#102—22no—
550#102—22no—
551#102—22no—
552#102D4×C3114yes—
553C22⋊C8—22no—
554C22⋊C8—22no—
555C4×C8—22no—
556#95—21no—
557#95—21no—
558#95—21no—
559#95—21no—
560#95D4×C3111yescharacteristic
561#95D4×C3111yescharacteristic
562C31#2515611yescharacteristic, direct product factor, Sylow
563C24—21no—
564C24—24no—
565C24—21no—
566C24—42no—
567C24—42no—
568C24—42no—
569C24—42no—
570C24—81no—
571C24—81no—
572C24C2×D4×C3111yescharacteristic
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—21no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8C2×D4×C3112yes—
585C2×D4—24no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—42no—
595C2×D4—42no—
596C2×D4—44no—
597C2×D4—44no—
598C2×D4—44no—
599C2×D4—44no—
600C2×D4C2×D4×C3112yes—
601C2×D4C2×D4×C3112yes—
602C2×D4#41×C3112yes—
603C2×D4#41×C3112yes—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—42no—
617C22×C4—42no—
618C22×C4—42no—
619C22×C4—42no—
620C22×C4—81no—
621C22×C4—81no—
622C22×C4C2×D4×C3111yescharacteristic
623C22×C4C2×D4×C3111yescharacteristic
624C22×C4C2×D4×C3111yescharacteristic
625C22×C4C2×D4×C3111yescharacteristic
626C22×C4C2×D4×C3111yescharacteristic
627C22×C4C24×C3111yescharacteristic
628SD16—28no—
629SD16—44no—
630SD16—44no—
631SD16—44no—
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×C8—21no—
642C2×C8C2×D4×C3112yes—
643C2×C8C2×D4×C3112yes—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—42no—
652C4⋊C4—42no—
653C4⋊C4—42no—
654C4⋊C4—42no—
655C4⋊C4—42no—
656C4⋊C4—42no—
657C4⋊C4C2×D4×C3112yes—
658C22⋊C4—41no—
659C22⋊C4—42no—
660C22⋊C4—42no—
661C22⋊C4—42no—
662C22⋊C4—42no—
663C22⋊C4—42no—
664C22⋊C4—42no—
665C22⋊C4—42no—
666C22⋊C4—81no—
667C22⋊C4—81no—
668C22⋊C4SD16×C3114yescomplemented
669C42—21no—
670C42—21no—
671C42—21no—
672C42—21no—
673C42—42no—
674C23—21no—
675C23—22no—
676C23—21no—
677C23—21no—
678C23—22no—
679C23—22no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—22no—
684C23—48no—
685C23—48no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—41no—
696C23—84no—
697C23—84no—
698C23—84no—
699C23—84no—
700C23—84no—
701C23C2×SD16×C3112yes—
702C23C22×D4×C3111yescharacteristic
703Q8—22no—
704Q8—22no—
705Q8—41no—
706Q8—41no—
707Q8—41no—
708Q8—41no—
709Q8—41no—
710Q8—41no—
711D4—22no—
712D4—22no—
713D4—22no—
714D4—22no—
715D4—22no—
716D4—48no—
717D4—41no—
718D4—41no—
719D4C31×#12114yes—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—41no—
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—41no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—84no—
756C2×C4—84no—
757C2×C4C2×SD16×C3112yes—
758C2×C4C2×SD16×C3112yes—
759C2×C4C22×D4×C3111yescharacteristic
760C2×C4C22×D4×C3111yescharacteristic
761C2×C4C2×#41×C3111yescharacteristic
762C2×C4C2×#41×C3111yescharacteristic
763C2×C4C31×H(5,𝔽2)11yescharacteristic
764C2×C4C31×H(5,𝔽2)11yescharacteristic
765C8—22no—
766C8—22no—
767C8—41no—
768C8—41no—
769C22—22no—
770C22—24no—
771C22—22no—
772C22—22no—
773C22—42no—
774C22—41no—
775C22—42no—
776C22—41no—
777C22—41no—
778C22—42no—
779C22—41no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—816no—
787C22—81no—
788C22—81no—
789C22—81no—
790C22—81no—
791C22C31×#52511yescharacteristic
792C22D42×C3111yescharacteristic
793C22D42×C3111yescharacteristic
794C22C22×SD16×C3111yescharacteristic
795C22C31×#57511yescharacteristic
796C22C31×#57711yescharacteristic
797C22C31×#57711yescharacteristic
798C4—22no—
799C4—22no—
800C4—41no—
801C4—42no—
802C4—41no—
803C4—42no—
804C4—41no—
805C4—81no—
806C4—81no—
807C4—81no—
808C4—81no—
809C4C2×C31×#12111yescharacteristic
810C4C31×#53811yescharacteristic
811C4C31×#54611yescharacteristic
812C4C31×#54611yescharacteristic
813C2—42no—
814C2—44no—
815C2—82no—
816C2C31×#242411yescharacteristic
817C2C31×#310111yescharacteristic
818C2C31×#312311yescharacteristic
819C2C31×#326711yescharacteristic
820C2C31×#327511yescharacteristic
821C2D4×SD16×C3111yescharacteristic
822C2D4×SD16×C3111yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC23×D4×C31C22
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
1. C2×C31×#461C2semidirect
4. C2×C4×SD16×C31C2semidirect
5. C31×#2429C2semidirect
7. C31×#2065C2semidirect
8. C31×#2035C2semidirect
9. C31×#2035C2semidirect
10. C31×#2013C2semidirect
11. C31×#1968C2semidirect
12. C31×#1923C2semidirect
13. C31×#1880C2semidirect
14. C31×#1877C2semidirect
15. C31×#1864C2semidirect
21. C2×C31×C4⋊Q8C22semidirect
24. C2×C4×Q8×C31C22semidirect
32. C2×C31×#106C22semidirect
33. C2×C31×#106C22semidirect
34. C2×C31×C4⋊C8C22semidirect
35. C2×C31×#103C22semidirect
36. C2×C31×#103C22semidirect
37. C2×C31×#103C22semidirect
38. C2×C31×#103C22semidirect
45. C2×C4×C8×C31C22semidirect
48. C31×#391C22semidirect
52. C31×#389C22semidirect
59. C31×#340C22semidirect
60. C31×#340C22semidirect
61. C31×#336C22semidirect
62. C31×#336C22semidirect
256. C22⋊C4×C31SD16semidirect
262. #25156C31direct (N × H)
358. C2×#461C2×C31semidirect
361. C2×C4×SD16C2×C31semidirect
362. #2429C2×C31semidirect
364. #2065C2×C31semidirect
365. #2035C2×C31semidirect
366. #2035C2×C31semidirect
367. #2013C2×C31semidirect
368. #1968C2×C31semidirect
369. #1923C2×C31semidirect
370. #1880C2×C31semidirect
371. #1877C2×C31semidirect
372. #1864C2×C31semidirect
422. C2×C4⋊Q8C22×C31semidirect
425. C2×C4×Q8C22×C31semidirect
433. C2×#106C22×C31semidirect
434. C2×#106C22×C31semidirect
435. C2×C4⋊C8C22×C31semidirect
436. C2×#103C22×C31semidirect
437. C2×#103C22×C31semidirect
438. C2×#103C22×C31semidirect
439. C2×#103C22×C31semidirect
446. C2×C4×C8C22×C31semidirect
449. #391C22×C31semidirect
453. #389C22×C31semidirect
460. #340C22×C31semidirect
461. #340C22×C31semidirect
462. #336C22×C31semidirect
463. #336C22×C31semidirect
562. C31#25156direct (N × H)
668. C22⋊C4SD16×C31semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#4612
C2×C31×#4502
C2×C4×SD16×C312
C31×#24292
D4×C22⋊C4×C312
C31×#20652
C31×#20352
C31×#20132
C31×#19682
C31×#19232
C31×#18802
C31×#18772
C31×#18642
#2515631