Finite Group Databasebeta

← C31×#24448 #21481207

Subgroups — C31×#24448 #21481207

Order 7936.

1888 conjugacy classes of subgroups.

The subgroup lattice has 990 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D42×C31C211yesmaximal, characteristic
2C2×C31×#468C211yesmaximal, characteristic, complemented
3C2×C31×#450C211yesmaximal, characteristic, complemented
4C2×C31×#450C211yesmaximal, characteristic, complemented
5C2×C31×#418C211yesmaximal, characteristic, complemented
6C31×#2415C211yesmaximal, characteristic, complemented
7C31×#2041C211yesmaximal, characteristic, complemented
8C31×#2033C211yesmaximal, characteristic, complemented
9C31×#2014C211yesmaximal, characteristic, complemented
10C31×#2000C211yesmaximal, characteristic, complemented
11C31×#1877C211yesmaximal, characteristic, complemented
12C31×#1875C211yesmaximal, characteristic, complemented
13C31×#1870C211yesmaximal, characteristic, complemented
14C31×#1862C211yesmaximal, characteristic, complemented
15C31×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C31—21no—
17C23×D4×C31C2211yescharacteristic
18C23×D4×C31C2211yescharacteristic
19C22×SD16×C31C2211yescharacteristic
20C22×SD16×C31C2211yescharacteristic, complemented
21C22×SD16×C31C2211yescharacteristic, complemented
22C22×M16×C31C2211yescharacteristic, complemented
23D42×C31—24no—
24D42×C31—24no—
25C2×C31×#127C2211yescharacteristic
26C2×C31×C22⋊Q8C2211yescharacteristic, complemented
27C2×C31×C22⋊Q8C2211yescharacteristic, complemented
28C2×C31×#121—21no—
29C2×C31×#121C2211yescharacteristic
30C2×C31×#121C2211yescharacteristic
31C2×C31×#120—21no—
32C2×C31×#120—21no—
33C2×C4×D4×C31C2211yescharacteristic
34C2×C4×D4×C31C2211yescharacteristic
35C2×C31×#117C2211yescharacteristic, complemented
36C31×#468—24no—
37C31×#450—24no—
38C31×#450—24no—
39C2×C31×#107C2211yescharacteristic, complemented
40C31×#418—24no—
41C2×C31×#103C2211yescharacteristic, complemented
42C2×C31×#102C2211yescharacteristic
43C2×C31×#102C2211yescharacteristic
44C2×C31×#102C2211yescharacteristic
45C2×C31×#102C2211yescharacteristic, complemented
46C2×C31×#102C2211yescharacteristic, complemented
47C2×C31×#102C2211yescharacteristic, complemented
48C2×C31×#102C2211yescharacteristic, complemented
49C2×C31×#102C2211yescharacteristic, complemented
50C2×C31×#102C2211yescharacteristic, complemented
51C2×C31×C22⋊C8C2211yescharacteristic, complemented
52C2×C31×C22⋊C8C2211yescharacteristic, complemented
53C2×C31×C22⋊C8C2211yescharacteristic, complemented
54C31×#397—21no—
55C31×#394—21no—
56C31×#391C2211yescharacteristic, complemented
57C31×#389—21no—
58C31×#389C2211yescharacteristic, complemented
59C31×#388—21no—
60C31×#380C2211yescharacteristic, complemented
61C31×#340C2211yescharacteristic, complemented
62C31×#340C2211yescharacteristic, complemented
63C31×#336C2211yescharacteristic, complemented
64C31×#336C2211yescharacteristic, complemented
65C25×C31—21no—
66C25×C31—21no—
67C22×Q8×C31C2311yescharacteristic
68C22×D4×C31—22no—
69C22×D4×C31—22no—
70C22×D4×C31—28no—
71C22×D4×C31—21no—
72C22×D4×C31—21no—
73C22×D4×C31—22no—
74C22×D4×C31—22no—
75C22×D4×C31—22no—
76C22×D4×C31—22no—
77C22×D4×C31—21no—
78C22×D4×C31—21no—
79C22×D4×C31—21no—
80C22×D4×C31—22no—
81C22×D4×C31—21no—
82C22×D4×C31—41no—
83C22×D4×C31—41no—
84C22×D4×C31—41no—
85C22×D4×C31—41no—
86C22×D4×C31—44no—
87C22×D4×C31—44no—
88C22×D4×C31D411yescharacteristic
89C22×D4×C31D414yes—
90C22×D4×C31C2311yescharacteristic
91C22×D4×C31C2311yescharacteristic
92C22×D4×C31C2311yescharacteristic
93C23×C4×C31—21no—
94C23×C4×C31C2311yescharacteristic
95C23×C4×C31C2311yescharacteristic
96C2×SD16×C31—22no—
97C2×SD16×C31—22no—
98C2×SD16×C31—22no—
99C2×SD16×C31—22no—
100C2×SD16×C31—22no—
101C2×SD16×C31—22no—
102C2×SD16×C31—41no—
103C2×SD16×C31—41no—
104C2×SD16×C31—41no—
105C2×M16×C31—22no—
106C2×M16×C31—22no—
107C2×M16×C31—41no—
108C22×C8×C31C2311yescharacteristic
109C22×C8×C31C2311yescharacteristic
110C22×C8×C31C2311yescharacteristic
111C22×C8×C31C2311yescharacteristic
112C31×#127—22no—
113C31×#127—22no—
114C31×C22⋊Q8—22no—
115C31×C22⋊Q8—22no—
116C31×C22⋊Q8—22no—
117C31×C22⋊Q8—41no—
118C31×#121—28no—
119C31×#121—22no—
120C31×#121—22no—
121C31×#121—22no—
122C31×#121D414yes—
123C31×#120—28no—
124C31×#120—28no—
125C4×D4×C31—22no—
126C4×D4×C31—22no—
127C4×D4×C31—22no—
128C4×D4×C31—22no—
129C31×#117—22no—
130C31×#117—41no—
131C2×C4⋊C4×C31—21no—
132C2×C4⋊C4×C31—21no—
133C2×C4⋊C4×C31—21no—
134C2×C4⋊C4×C31D411yescharacteristic
135C2×C4⋊C4×C31C2311yescharacteristic
136C2×C4⋊C4×C31C2311yescharacteristic
137C2×C4⋊C4×C31C2311yescharacteristic
138C2×C4⋊C4×C31C2311yescharacteristic
139C2×C22⋊C4×C31—21no—
140C2×C22⋊C4×C31—21no—
141C2×C22⋊C4×C31—21no—
142C2×C22⋊C4×C31—21no—
143C2×C22⋊C4×C31—21no—
144C2×C22⋊C4×C31—21no—
145C2×C22⋊C4×C31—21no—
146C2×C22⋊C4×C31D411yescharacteristic
147C2×C22⋊C4×C31D411yescharacteristic
148C2×C42×C31—21no—
149C2×C42×C31C2311yescharacteristic
150C31×#107—22no—
151C31×#103—22no—
152C31×#102—22no—
153C31×#102—22no—
154C31×#102—22no—
155C31×#102—22no—
156C31×#102—22no—
157C31×#102—22no—
158C31×#102—22no—
159C31×#102—41no—
160C31×#102D414yescomplemented
161C31×C22⋊C8—22no—
162C31×C22⋊C8—22no—
163C31×C22⋊C8—41no—
164C31×#95—21no—
165C31×#95—21no—
166C31×#95—21no—
167C31×#95—21no—
168C24×C31—21no—
169C24×C31—24no—
170C24×C31—21no—
171C24×C31—21no—
172C24×C31—24no—
173C24×C31—42no—
174C24×C31—42no—
175C24×C31—42no—
176C24×C31—42no—
177C24×C31—42no—
178C24×C31—42no—
179C24×C31—42no—
180C24×C31—42no—
181C24×C31—81no—
182C24×C31—81no—
183C24×C31—81no—
184C24×C31—81no—
185C24×C31C2×D411yescharacteristic
186C24×C31C2×D411yescharacteristic
187C2×Q8×C31—21no—
188C2×Q8×C31—21no—
189C2×Q8×C31—21no—
190C2×Q8×C31—21no—
191C2×Q8×C31—21no—
192C2×Q8×C31—21no—
193C2×D4×C31—22no—
194C2×D4×C31—22no—
195C2×D4×C31—28no—
196C2×D4×C31—24no—
197C2×D4×C31—24no—
198C2×D4×C31—24no—
199C2×D4×C31—24no—
200C2×D4×C31—24no—
201C2×D4×C31—24no—
202C2×D4×C31—22no—
203C2×D4×C31—21no—
204C2×D4×C31—21no—
205C2×D4×C31—21no—
206C2×D4×C31—21no—
207C2×D4×C31—21no—
208C2×D4×C31—21no—
209C2×D4×C31—21no—
210C2×D4×C31—21no—
211C2×D4×C31—21no—
212C2×D4×C31—21no—
213C2×D4×C31—21no—
214C2×D4×C31—21no—
215C2×D4×C31—21no—
216C2×D4×C31—44no—
217C2×D4×C31—44no—
218C2×D4×C31—44no—
219C2×D4×C31—42no—
220C2×D4×C31—42no—
221C2×D4×C31—42no—
222C2×D4×C31—42no—
223C2×D4×C31—42no—
224C2×D4×C31—44no—
225C2×D4×C31—44no—
226C2×D4×C31—432no—
227C2×D4×C31—44no—
228C2×D4×C31—42no—
229C2×D4×C31—42no—
230C2×D4×C31—42no—
231C2×D4×C31—42no—
232C2×D4×C31—44no—
233C2×D4×C31—42no—
234C2×D4×C31—81no—
235C2×D4×C31—81no—
236C2×D4×C31C2×D412yes—
237C2×D4×C31C2×D412yes—
238C2×D4×C31C2×D412yes—
239C2×D4×C31C2×D412yes—
240C2×D4×C31#4112yes—
241C22×C4×C31—21no—
242C22×C4×C31—21no—
243C22×C4×C31—21no—
244C22×C4×C31—21no—
245C22×C4×C31—24no—
246C22×C4×C31—21no—
247C22×C4×C31—21no—
248C22×C4×C31—21no—
249C22×C4×C31—21no—
250C22×C4×C31—21no—
251C22×C4×C31—21no—
252C22×C4×C31—21no—
253C22×C4×C31—21no—
254C22×C4×C31—21no—
255C22×C4×C31—21no—
256C22×C4×C31—21no—
257C22×C4×C31—42no—
258C22×C4×C31—42no—
259C22×C4×C31C2×D411yescharacteristic
260C22×C4×C31C2×D411yescharacteristic
261C22×C4×C31C2×D411yescharacteristic
262C22×C4×C31C2×D412yes—
263C22×C4×C31C2×D412yes—
264C22×C4×C31C2×D411yescharacteristic
265C22×C4×C31C2411yescharacteristic
266SD16×C31—44no—
267SD16×C31—44no—
268SD16×C31—44no—
269M16×C31—44no—
270C2×C8×C31—21no—
271C2×C8×C31—21no—
272C2×C8×C31—21no—
273C2×C8×C31—21no—
274C2×C8×C31—21no—
275C2×C8×C31—21no—
276C2×C8×C31—21no—
277C2×C8×C31—21no—
278C2×C8×C31—21no—
279C2×C8×C31—21no—
280C2×C8×C31—21no—
281C2×C8×C31C2×D412yescomplemented
282C4⋊C4×C31—22no—
283C4⋊C4×C31—21no—
284C4⋊C4×C31—21no—
285C4⋊C4×C31—21no—
286C4⋊C4×C31—21no—
287C4⋊C4×C31—21no—
288C4⋊C4×C31—21no—
289C4⋊C4×C31—42no—
290C4⋊C4×C31—42no—
291C4⋊C4×C31—42no—
292C4⋊C4×C31C2×D412yes—
293C4⋊C4×C31C2×D412yescomplemented
294C22⋊C4×C31—24no—
295C22⋊C4×C31—24no—
296C22⋊C4×C31—22no—
297C22⋊C4×C31—24no—
298C22⋊C4×C31—22no—
299C22⋊C4×C31—42no—
300C22⋊C4×C31—42no—
301C22⋊C4×C31—42no—
302C22⋊C4×C31—42no—
303C42×C31—21no—
304C42×C31—21no—
305C42×C31—42no—
306#24448C3111yesmaximal, characteristic, direct product factor, Sylow
307C23×C31—21no—
308C23×C31—22no—
309C23×C31—21no—
310C23×C31—21no—
311C23×C31—22no—
312C23×C31—21no—
313C23×C31—21no—
314C23×C31—22no—
315C23×C31—21no—
316C23×C31—21no—
317C23×C31—21no—
318C23×C31—21no—
319C23×C31—21no—
320C23×C31—21no—
321C23×C31—21no—
322C23×C31—22no—
323C23×C31—22no—
324C23×C31—48no—
325C23×C31—48no—
326C23×C31—48no—
327C23×C31—48no—
328C23×C31—41no—
329C23×C31—41no—
330C23×C31—41no—
331C23×C31—41no—
332C23×C31—41no—
333C23×C31—41no—
334C23×C31—41no—
335C23×C31—41no—
336C23×C31—41no—
337C23×C31—41no—
338C23×C31—41no—
339C23×C31—41no—
340C23×C31—41no—
341C23×C31—41no—
342C23×C31—41no—
343C23×C31—41no—
344C23×C31—84no—
345C23×C31—84no—
346C23×C31—84no—
347C23×C31—84no—
348C23×C31—84no—
349C23×C31—84no—
350C23×C31—84no—
351C23×C31—84no—
352C23×C31—84no—
353C23×C31—84no—
354C23×C31#12012yes—
355C23×C31AGL(1,ℤ/8)12yes—
356C23×C31C22×D411yescharacteristic
357Q8×C31—41no—
358Q8×C31—41no—
359Q8×C31—41no—
360Q8×C31—41no—
361D4×C31—28no—
362D4×C31—22no—
363D4×C31—22no—
364D4×C31—22no—
365D4×C31—22no—
366D4×C31—22no—
367D4×C31—22no—
368D4×C31—22no—
369D4×C31—48no—
370D4×C31—48no—
371D4×C31—48no—
372D4×C31—48no—
373D4×C31—48no—
374D4×C31—41no—
375D4×C31—41no—
376D4×C31—41no—
377D4×C31—41no—
378D4×C31—84no—
379D4×C31#12114yes—
380C2×C4×C31—21no—
381C2×C4×C31—21no—
382C2×C4×C31—21no—
383C2×C4×C31—21no—
384C2×C4×C31—22no—
385C2×C4×C31—22no—
386C2×C4×C31—22no—
387C2×C4×C31—22no—
388C2×C4×C31—21no—
389C2×C4×C31—21no—
390C2×C4×C31—22no—
391C2×C4×C31—22no—
392C2×C4×C31—21no—
393C2×C4×C31—21no—
394C2×C4×C31—21no—
395C2×C4×C31—21no—
396C2×C4×C31—48no—
397C2×C4×C31—41no—
398C2×C4×C31—41no—
399C2×C4×C31—41no—
400C2×C4×C31—41no—
401C2×C4×C31—41no—
402C2×C4×C31—41no—
403C2×C4×C31—41no—
404C2×C4×C31—41no—
405C2×C4×C31—41no—
406C2×C4×C31—41no—
407C2×C4×C31—41no—
408C2×C4×C31—41no—
409C2×C4×C31—41no—
410C2×C4×C31—41no—
411C2×C4×C31—41no—
412C2×C4×C31—41no—
413C2×C4×C31—41no—
414C2×C4×C31#12012yes—
415C2×C4×C31AGL(1,ℤ/8)12yes—
416C2×C4×C31C22×D411yescharacteristic
417C2×C4×C31C22×D411yescharacteristic
418C2×C4×C31C22×D411yescharacteristic
419C2×C4×C31C2×#4111yescharacteristic
420C2×C4×C31H(5,𝔽2)11yescharacteristic
421C2×C4×C31H(5,𝔽2)11yescharacteristic
422C8×C31—22no—
423C8×C31—41no—
424C8×C31—41no—
425C8×C31—41no—
426C2×D42C2×C3111yescharacteristic
427C2×#468C2×C3111yescharacteristic, complemented
428C2×#450C2×C3111yescharacteristic, complemented
429C2×#450C2×C3111yescharacteristic, complemented
430C2×#418C2×C3111yescharacteristic, complemented
431#2415C2×C3111yescharacteristic, complemented
432#2041C2×C3111yescharacteristic, complemented
433#2033C2×C3111yescharacteristic, complemented
434#2014C2×C3111yescharacteristic, complemented
435#2000C2×C3111yescharacteristic, complemented
436#1877C2×C3111yescharacteristic, complemented
437#1875C2×C3111yescharacteristic, complemented
438#1870C2×C3111yescharacteristic, complemented
439#1862C2×C3111yescharacteristic, complemented
440#1786C2×C3111yescharacteristic, complemented
441C22×C31—22no—
442C22×C31—24no—
443C22×C31—22no—
444C22×C31—22no—
445C22×C31—22no—
446C22×C31—22no—
447C22×C31—22no—
448C22×C31—41no—
449C22×C31—42no—
450C22×C31—41no—
451C22×C31—42no—
452C22×C31—41no—
453C22×C31—42no—
454C22×C31—41no—
455C22×C31—41no—
456C22×C31—42no—
457C22×C31—41no—
458C22×C31—42no—
459C22×C31—41no—
460C22×C31—41no—
461C22×C31—42no—
462C22×C31—42no—
463C22×C31—42no—
464C22×C31—42no—
465C22×C31—42no—
466C22×C31—42no—
467C22×C31—42no—
468C22×C31—816no—
469C22×C31—816no—
470C22×C31—81no—
471C22×C31—81no—
472C22×C31—81no—
473C22×C31—81no—
474C22×C31—81no—
475C22×C31—81no—
476C22×C31—81no—
477C22×C31—81no—
478C22×C31C2×#12011yescharacteristic
479C22×C31D4211yescharacteristic
480C22×C31#54611yescharacteristic
481C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
482C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
483C22×C31#57711yescharacteristic
484C22×C31#57711yescharacteristic
485C4×C31—22no—
486C4×C31—22no—
487C4×C31—41no—
488C4×C31—42no—
489C4×C31—41no—
490C4×C31—42no—
491C4×C31—81no—
492C4×C31—81no—
493C4×C31—81no—
494C4×C31C2×#12111yescharacteristic
495C4×C31#53411yescharacteristic
496C4×C31D4211yescharacteristic
497C4×C31#54611yescharacteristic
498C23×D4—21no—
499C23×D4C22×C3111yescharacteristic
500C23×D4C22×C3111yescharacteristic
501C22×SD16C22×C3111yescharacteristic
502C22×SD16C22×C3111yescharacteristic, complemented
503C22×SD16C22×C3111yescharacteristic, complemented
504C22×M16C22×C3111yescharacteristic, complemented
505D42—24no—
506D42—24no—
507C2×#127C22×C3111yescharacteristic
508C2×C22⋊Q8C22×C3111yescharacteristic, complemented
509C2×C22⋊Q8C22×C3111yescharacteristic, complemented
510C2×#121—21no—
511C2×#121C22×C3111yescharacteristic
512C2×#121C22×C3111yescharacteristic
513C2×#120—21no—
514C2×#120—21no—
515C2×C4×D4C22×C3111yescharacteristic
516C2×C4×D4C22×C3111yescharacteristic
517C2×#117C22×C3111yescharacteristic, complemented
518#468—24no—
519#450—24no—
520#450—24no—
521C2×#107C22×C3111yescharacteristic, complemented
522#418—24no—
523C2×#103C22×C3111yescharacteristic, complemented
524C2×#102C22×C3111yescharacteristic
525C2×#102C22×C3111yescharacteristic
526C2×#102C22×C3111yescharacteristic
527C2×#102C22×C3111yescharacteristic, complemented
528C2×#102C22×C3111yescharacteristic, complemented
529C2×#102C22×C3111yescharacteristic, complemented
530C2×#102C22×C3111yescharacteristic, complemented
531C2×#102C22×C3111yescharacteristic, complemented
532C2×#102C22×C3111yescharacteristic, complemented
533C2×C22⋊C8C22×C3111yescharacteristic, complemented
534C2×C22⋊C8C22×C3111yescharacteristic, complemented
535C2×C22⋊C8C22×C3111yescharacteristic, complemented
536#397—21no—
537#394—21no—
538#391C22×C3111yescharacteristic, complemented
539#389—21no—
540#389C22×C3111yescharacteristic, complemented
541#388—21no—
542#380C22×C3111yescharacteristic, complemented
543#340C22×C3111yescharacteristic, complemented
544#340C22×C3111yescharacteristic, complemented
545#336C22×C3111yescharacteristic, complemented
546#336C22×C3111yescharacteristic, complemented
547C2×C31—42no—
548C2×C31—42no—
549C2×C31—44no—
550C2×C31—82no—
551C2×C31—82no—
552C2×C31#241011yescharacteristic
553C2×C31#300311yescharacteristic
554C2×C31#300911yescharacteristic
555C2×C31#326511yescharacteristic
556C2×C31#327211yescharacteristic
557C2×C31#331011yescharacteristic
558C2×C31#332411yescharacteristic
559C25—21no—
560C25—21no—
561C22×Q8C23×C3111yescharacteristic
562C22×D4—22no—
563C22×D4—22no—
564C22×D4—28no—
565C22×D4—21no—
566C22×D4—21no—
567C22×D4—22no—
568C22×D4—22no—
569C22×D4—22no—
570C22×D4—22no—
571C22×D4—21no—
572C22×D4—21no—
573C22×D4—21no—
574C22×D4—22no—
575C22×D4—21no—
576C22×D4—41no—
577C22×D4—41no—
578C22×D4—41no—
579C22×D4—41no—
580C22×D4—44no—
581C22×D4—44no—
582C22×D4D4×C3111yescharacteristic
583C22×D4D4×C3114yes—
584C22×D4C23×C3111yescharacteristic
585C22×D4C23×C3111yescharacteristic
586C22×D4C23×C3111yescharacteristic
587C23×C4—21no—
588C23×C4C23×C3111yescharacteristic
589C23×C4C23×C3111yescharacteristic
590C2×SD16—22no—
591C2×SD16—22no—
592C2×SD16—22no—
593C2×SD16—22no—
594C2×SD16—22no—
595C2×SD16—22no—
596C2×SD16—41no—
597C2×SD16—41no—
598C2×SD16—41no—
599C2×M16—22no—
600C2×M16—22no—
601C2×M16—41no—
602C22×C8C23×C3111yescharacteristic
603C22×C8C23×C3111yescharacteristic
604C22×C8C23×C3111yescharacteristic
605C22×C8C23×C3111yescharacteristic
606#127—22no—
607#127—22no—
608C22⋊Q8—22no—
609C22⋊Q8—22no—
610C22⋊Q8—22no—
611C22⋊Q8—41no—
612#121—28no—
613#121—22no—
614#121—22no—
615#121—22no—
616#121D4×C3114yes—
617#120—28no—
618#120—28no—
619C4×D4—22no—
620C4×D4—22no—
621C4×D4—22no—
622C4×D4—22no—
623#117—22no—
624#117—41no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4D4×C3111yescharacteristic
629C2×C4⋊C4C23×C3111yescharacteristic
630C2×C4⋊C4C23×C3111yescharacteristic
631C2×C4⋊C4C23×C3111yescharacteristic
632C2×C4⋊C4C23×C3111yescharacteristic
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4D4×C3111yescharacteristic
641C2×C22⋊C4D4×C3111yescharacteristic
642C2×C42—21no—
643C2×C42C23×C3111yescharacteristic
644#107—22no—
645#103—22no—
646#102—22no—
647#102—22no—
648#102—22no—
649#102—22no—
650#102—22no—
651#102—22no—
652#102—22no—
653#102—41no—
654#102D4×C3114yescomplemented
655C22⋊C8—22no—
656C22⋊C8—22no—
657C22⋊C8—41no—
658#95—21no—
659#95—21no—
660#95—21no—
661#95—21no—
662C31#2444811yescharacteristic, direct product factor, Sylow
663C24—21no—
664C24—24no—
665C24—21no—
666C24—21no—
667C24—24no—
668C24—42no—
669C24—42no—
670C24—42no—
671C24—42no—
672C24—42no—
673C24—42no—
674C24—42no—
675C24—42no—
676C24—81no—
677C24—81no—
678C24—81no—
679C24—81no—
680C24C2×D4×C3111yescharacteristic
681C24C2×D4×C3111yescharacteristic
682C2×Q8—21no—
683C2×Q8—21no—
684C2×Q8—21no—
685C2×Q8—21no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×D4—22no—
689C2×D4—22no—
690C2×D4—28no—
691C2×D4—24no—
692C2×D4—24no—
693C2×D4—24no—
694C2×D4—24no—
695C2×D4—24no—
696C2×D4—24no—
697C2×D4—22no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—44no—
712C2×D4—44no—
713C2×D4—44no—
714C2×D4—42no—
715C2×D4—42no—
716C2×D4—42no—
717C2×D4—42no—
718C2×D4—42no—
719C2×D4—44no—
720C2×D4—44no—
721C2×D4—432no—
722C2×D4—44no—
723C2×D4—42no—
724C2×D4—42no—
725C2×D4—42no—
726C2×D4—42no—
727C2×D4—44no—
728C2×D4—42no—
729C2×D4—81no—
730C2×D4—81no—
731C2×D4C2×D4×C3112yes—
732C2×D4C2×D4×C3112yes—
733C2×D4C2×D4×C3112yes—
734C2×D4C2×D4×C3112yes—
735C2×D4#41×C3112yes—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—24no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—42no—
753C22×C4—42no—
754C22×C4C2×D4×C3111yescharacteristic
755C22×C4C2×D4×C3111yescharacteristic
756C22×C4C2×D4×C3111yescharacteristic
757C22×C4C2×D4×C3112yes—
758C22×C4C2×D4×C3112yes—
759C22×C4C2×D4×C3111yescharacteristic
760C22×C4C24×C3111yescharacteristic
761SD16—44no—
762SD16—44no—
763SD16—44no—
764M16—44no—
765C2×C8—21no—
766C2×C8—21no—
767C2×C8—21no—
768C2×C8—21no—
769C2×C8—21no—
770C2×C8—21no—
771C2×C8—21no—
772C2×C8—21no—
773C2×C8—21no—
774C2×C8—21no—
775C2×C8—21no—
776C2×C8C2×D4×C3112yescomplemented
777C4⋊C4—22no—
778C4⋊C4—21no—
779C4⋊C4—21no—
780C4⋊C4—21no—
781C4⋊C4—21no—
782C4⋊C4—21no—
783C4⋊C4—21no—
784C4⋊C4—42no—
785C4⋊C4—42no—
786C4⋊C4—42no—
787C4⋊C4C2×D4×C3112yes—
788C4⋊C4C2×D4×C3112yescomplemented
789C22⋊C4—24no—
790C22⋊C4—24no—
791C22⋊C4—22no—
792C22⋊C4—24no—
793C22⋊C4—22no—
794C22⋊C4—42no—
795C22⋊C4—42no—
796C22⋊C4—42no—
797C22⋊C4—42no—
798C42—21no—
799C42—21no—
800C42—42no—
801C23—21no—
802C23—22no—
803C23—21no—
804C23—21no—
805C23—22no—
806C23—21no—
807C23—21no—
808C23—22no—
809C23—21no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—21no—
816C23—22no—
817C23—22no—
818C23—48no—
819C23—48no—
820C23—48no—
821C23—48no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—84no—
839C23—84no—
840C23—84no—
841C23—84no—
842C23—84no—
843C23—84no—
844C23—84no—
845C23—84no—
846C23—84no—
847C23—84no—
848C23C31×#12012yes—
849C23C31×AGL(1,ℤ/8)12yes—
850C23C22×D4×C3111yescharacteristic
851Q8—41no—
852Q8—41no—
853Q8—41no—
854Q8—41no—
855D4—28no—
856D4—22no—
857D4—22no—
858D4—22no—
859D4—22no—
860D4—22no—
861D4—22no—
862D4—22no—
863D4—48no—
864D4—48no—
865D4—48no—
866D4—48no—
867D4—48no—
868D4—41no—
869D4—41no—
870D4—41no—
871D4—41no—
872D4—84no—
873D4C31×#12114yes—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—21no—
883C2×C4—21no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—21no—
887C2×C4—21no—
888C2×C4—21no—
889C2×C4—21no—
890C2×C4—48no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4C31×#12012yes—
909C2×C4C31×AGL(1,ℤ/8)12yes—
910C2×C4C22×D4×C3111yescharacteristic
911C2×C4C22×D4×C3111yescharacteristic
912C2×C4C22×D4×C3111yescharacteristic
913C2×C4C2×#41×C3111yescharacteristic
914C2×C4C31×H(5,𝔽2)11yescharacteristic
915C2×C4C31×H(5,𝔽2)11yescharacteristic
916C8—22no—
917C8—41no—
918C8—41no—
919C8—41no—
920C22—22no—
921C22—24no—
922C22—22no—
923C22—22no—
924C22—22no—
925C22—22no—
926C22—22no—
927C22—41no—
928C22—42no—
929C22—41no—
930C22—42no—
931C22—41no—
932C22—42no—
933C22—41no—
934C22—41no—
935C22—42no—
936C22—41no—
937C22—42no—
938C22—41no—
939C22—41no—
940C22—42no—
941C22—42no—
942C22—42no—
943C22—42no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—816no—
948C22—816no—
949C22—81no—
950C22—81no—
951C22—81no—
952C22—81no—
953C22—81no—
954C22—81no—
955C22—81no—
956C22—81no—
957C22C2×C31×#12011yescharacteristic
958C22D42×C3111yescharacteristic
959C22C31×#54611yescharacteristic
960C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
961C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
962C22C31×#57711yescharacteristic
963C22C31×#57711yescharacteristic
964C4—22no—
965C4—22no—
966C4—41no—
967C4—42no—
968C4—41no—
969C4—42no—
970C4—81no—
971C4—81no—
972C4—81no—
973C4C2×C31×#12111yescharacteristic
974C4C31×#53411yescharacteristic
975C4D42×C3111yescharacteristic
976C4C31×#54611yescharacteristic
977C2—42no—
978C2—42no—
979C2—44no—
980C2—82no—
981C2—82no—
982C2C31×#241011yescharacteristic
983C2C31×#300311yescharacteristic
984C2C31×#300911yescharacteristic
985C2C31×#326511yescharacteristic
986C2C31×#327211yescharacteristic
987C2C31×#331011yescharacteristic
988C2C31×#332411yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
prime radicalC2×D42×C31C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C2×C4×D4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#468C2semidirect
3. C2×C31×#450C2semidirect
4. C2×C31×#450C2semidirect
5. C2×C31×#418C2semidirect
6. C31×#2415C2semidirect
7. C31×#2041C2semidirect
8. C31×#2033C2semidirect
9. C31×#2014C2semidirect
10. C31×#2000C2semidirect
11. C31×#1877C2semidirect
12. C31×#1875C2semidirect
13. C31×#1870C2semidirect
14. C31×#1862C2semidirect
15. C31×#1786C2semidirect
20. C22×SD16×C31C22semidirect
21. C22×SD16×C31C22semidirect
22. C22×M16×C31C22semidirect
26. C2×C31×C22⋊Q8C22semidirect
27. C2×C31×C22⋊Q8C22semidirect
35. C2×C31×#117C22semidirect
39. C2×C31×#107C22semidirect
41. C2×C31×#103C22semidirect
45. C2×C31×#102C22semidirect
46. C2×C31×#102C22semidirect
47. C2×C31×#102C22semidirect
48. C2×C31×#102C22semidirect
49. C2×C31×#102C22semidirect
50. C2×C31×#102C22semidirect
51. C2×C31×C22⋊C8C22semidirect
52. C2×C31×C22⋊C8C22semidirect
53. C2×C31×C22⋊C8C22semidirect
56. C31×#391C22semidirect
58. C31×#389C22semidirect
60. C31×#380C22semidirect
61. C31×#340C22semidirect
62. C31×#340C22semidirect
63. C31×#336C22semidirect
64. C31×#336C22semidirect
160. C31×#102D4semidirect
281. C2×C8×C31C2×D4semidirect
293. C4⋊C4×C31C2×D4semidirect
306. #24448C31direct (N × H)
427. C2×#468C2×C31semidirect
428. C2×#450C2×C31semidirect
429. C2×#450C2×C31semidirect
430. C2×#418C2×C31semidirect
431. #2415C2×C31semidirect
432. #2041C2×C31semidirect
433. #2033C2×C31semidirect
434. #2014C2×C31semidirect
435. #2000C2×C31semidirect
436. #1877C2×C31semidirect
437. #1875C2×C31semidirect
438. #1870C2×C31semidirect
439. #1862C2×C31semidirect
440. #1786C2×C31semidirect
502. C22×SD16C22×C31semidirect
503. C22×SD16C22×C31semidirect
504. C22×M16C22×C31semidirect
508. C2×C22⋊Q8C22×C31semidirect
509. C2×C22⋊Q8C22×C31semidirect
517. C2×#117C22×C31semidirect
521. C2×#107C22×C31semidirect
523. C2×#103C22×C31semidirect
527. C2×#102C22×C31semidirect
528. C2×#102C22×C31semidirect
529. C2×#102C22×C31semidirect
530. C2×#102C22×C31semidirect
531. C2×#102C22×C31semidirect
532. C2×#102C22×C31semidirect
533. C2×C22⋊C8C22×C31semidirect
534. C2×C22⋊C8C22×C31semidirect
535. C2×C22⋊C8C22×C31semidirect
538. #391C22×C31semidirect
540. #389C22×C31semidirect
542. #380C22×C31semidirect
543. #340C22×C31semidirect
544. #340C22×C31semidirect
545. #336C22×C31semidirect
546. #336C22×C31semidirect
654. #102D4×C31semidirect
662. C31#24448direct (N × H)
776. C2×C8C2×D4×C31semidirect
788. C4⋊C4C2×D4×C31semidirect

Maximal subgroups

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

subgroupindex
C2×D42×C312
C2×C31×#4682
C2×C31×#4502
C2×C31×#4182
C31×#24152
C31×#20412
C31×#20332
C31×#20142
C31×#20002
C31×#18772
C31×#18752
C31×#18702
C31×#18622
C31×#17862
#2444831