Finite Group Databasebeta

← C31×#24424 #21481183

Subgroups — C31×#24424 #21481183

Order 7936.

1992 conjugacy classes of subgroups.

The subgroup lattice has 1036 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D42×C31C211yesmaximal, characteristic, complemented
2C2×C31×#466C211yesmaximal, characteristic, complemented
3C2×C31×#447C211yesmaximal, characteristic, complemented
4C2×C31×#447C211yesmaximal, characteristic, complemented
5C22×C31×#102C211yesmaximal, characteristic, complemented
6C31×#2416C211yesmaximal, characteristic, complemented
7C31×#2041C211yesmaximal, characteristic, complemented
8C31×#2033C211yesmaximal, characteristic, complemented
9C31×#2011C211yesmaximal, characteristic, complemented
10C31×#1999C211yesmaximal, characteristic, complemented
11C31×#1879C211yesmaximal, characteristic, complemented
12C31×#1874C211yesmaximal, characteristic, complemented
13C31×#1869C211yesmaximal, characteristic, complemented
14C31×#1862C211yesmaximal, characteristic, complemented
15C31×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C31—21no—
17C23×D4×C31C2211yescharacteristic
18C23×D4×C31C2211yescharacteristic
19C22×D8×C31C2211yescharacteristic
20C22×D8×C31C2211yescharacteristic, complemented
21C22×D8×C31C2211yescharacteristic, complemented
22C23×C8×C31C2211yescharacteristic, complemented
23D42×C31—24no—
24D42×C31—24no—
25C2×C31×#127C2211yescharacteristic
26C2×C31×#121—21no—
27C2×C31×#121—21no—
28C2×C31×#121C2211yescharacteristic
29C2×C31×#121C2211yescharacteristic
30C2×C31×#121C2211yescharacteristic, complemented
31C2×C31×#121C2211yescharacteristic, complemented
32C2×C31×#120—21no—
33C2×C31×#120—21no—
34C2×C4×D4×C31C2211yescharacteristic
35C2×C4×D4×C31C2211yescharacteristic
36C22×C4⋊C4×C31C2211yescharacteristic, complemented
37C31×#466—24no—
38C31×#447—24no—
39C31×#447—24no—
40C2×C31×#107C2211yescharacteristic, complemented
41C2×C31×#102—24no—
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×#102C2211yescharacteristic, complemented
52C2×C31×C22⋊C8C2211yescharacteristic, complemented
53C2×C31×C22⋊C8C2211yescharacteristic, complemented
54C2×C31×C22⋊C8C2211yescharacteristic, complemented
55C31×#396—21no—
56C31×#394—21no—
57C31×#390C2211yescharacteristic, complemented
58C31×#389C2211yescharacteristic, complemented
59C31×#386—21no—
60C31×#380C2211yescharacteristic, complemented
61C31×#340C2211yescharacteristic, complemented
62C31×#340C2211yescharacteristic, complemented
63C31×#336C2211yescharacteristic, complemented
64C31×#336C2211yescharacteristic, complemented
65C25×C31—21no—
66C25×C31—21no—
67C22×D4×C31—22no—
68C22×D4×C31—22no—
69C22×D4×C31—28no—
70C22×D4×C31—21no—
71C22×D4×C31—21no—
72C22×D4×C31—22no—
73C22×D4×C31—22no—
74C22×D4×C31—22no—
75C22×D4×C31—22no—
76C22×D4×C31—21no—
77C22×D4×C31—21no—
78C22×D4×C31—21no—
79C22×D4×C31—21no—
80C22×D4×C31—21no—
81C22×D4×C31—22no—
82C22×D4×C31—21no—
83C22×D4×C31—41no—
84C22×D4×C31—41no—
85C22×D4×C31—41no—
86C22×D4×C31—41no—
87C22×D4×C31—44no—
88C22×D4×C31—44no—
89C22×D4×C31D411yescharacteristic
90C22×D4×C31D414yescomplemented
91C22×D4×C31C2311yescharacteristic
92C22×D4×C31C2311yescharacteristic
93C22×D4×C31C2311yescharacteristic
94C22×D4×C31C2311yescharacteristic
95C23×C4×C31—21no—
96C23×C4×C31—21no—
97C23×C4×C31C2311yescharacteristic
98C23×C4×C31C2311yescharacteristic
99C2×D8×C31—22no—
100C2×D8×C31—22no—
101C2×D8×C31—22no—
102C2×D8×C31—22no—
103C2×D8×C31—22no—
104C2×D8×C31—22no—
105C2×D8×C31—41no—
106C2×D8×C31—41no—
107C2×D8×C31—41no—
108C22×C8×C31—22no—
109C22×C8×C31—22no—
110C22×C8×C31—41no—
111C22×C8×C31C2311yescharacteristic
112C22×C8×C31C2311yescharacteristic
113C22×C8×C31C2311yescharacteristic
114C22×C8×C31C2311yescharacteristic
115C31×#127—22no—
116C31×#127—22no—
117C31×#121—28no—
118C31×#121—22no—
119C31×#121—22no—
120C31×#121—22no—
121C31×#121—22no—
122C31×#121—22no—
123C31×#121—22no—
124C31×#121—41no—
125C31×#121—44no—
126C31×#121D414yescomplemented
127C31×#120—28no—
128C31×#120—28no—
129C4×D4×C31—22no—
130C4×D4×C31—22no—
131C4×D4×C31—22no—
132C4×D4×C31—22no—
133C2×C4⋊C4×C31—22no—
134C2×C4⋊C4×C31—21no—
135C2×C4⋊C4×C31—21no—
136C2×C4⋊C4×C31—41no—
137C2×C4⋊C4×C31D411yescharacteristic
138C2×C4⋊C4×C31C2311yescharacteristic
139C2×C4⋊C4×C31C2311yescharacteristic
140C2×C4⋊C4×C31C2311yescharacteristic
141C2×C4⋊C4×C31C2311yescharacteristic
142C2×C22⋊C4×C31—21no—
143C2×C22⋊C4×C31—21no—
144C2×C22⋊C4×C31—21no—
145C2×C22⋊C4×C31—21no—
146C2×C22⋊C4×C31—21no—
147C2×C22⋊C4×C31—21no—
148C2×C22⋊C4×C31—21no—
149C2×C22⋊C4×C31—21no—
150C2×C22⋊C4×C31D411yescharacteristic
151C2×C22⋊C4×C31D411yescharacteristic
152C2×C42×C31C2311yescharacteristic
153C31×#107—22no—
154C31×#102—22no—
155C31×#102—22no—
156C31×#102—22no—
157C31×#102—22no—
158C31×#102—22no—
159C31×#102—22no—
160C31×#102—22no—
161C31×#102—22no—
162C31×#102—41no—
163C31×#102D414yescomplemented
164C31×C22⋊C8—22no—
165C31×C22⋊C8—22no—
166C31×C22⋊C8—41no—
167C31×#95—21no—
168C31×#95—21no—
169C24×C31—21no—
170C24×C31—24no—
171C24×C31—21no—
172C24×C31—21no—
173C24×C31—24no—
174C24×C31—21no—
175C24×C31—42no—
176C24×C31—42no—
177C24×C31—42no—
178C24×C31—42no—
179C24×C31—42no—
180C24×C31—42no—
181C24×C31—42no—
182C24×C31—42no—
183C24×C31—81no—
184C24×C31—81no—
185C24×C31—81no—
186C24×C31—81no—
187C24×C31C2×D411yescharacteristic
188C24×C31C2×D411yescharacteristic
189C2×D4×C31—22no—
190C2×D4×C31—22no—
191C2×D4×C31—28no—
192C2×D4×C31—24no—
193C2×D4×C31—24no—
194C2×D4×C31—24no—
195C2×D4×C31—24no—
196C2×D4×C31—24no—
197C2×D4×C31—24no—
198C2×D4×C31—21no—
199C2×D4×C31—21no—
200C2×D4×C31—21no—
201C2×D4×C31—21no—
202C2×D4×C31—21no—
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—21no—
217C2×D4×C31—44no—
218C2×D4×C31—44no—
219C2×D4×C31—44no—
220C2×D4×C31—42no—
221C2×D4×C31—42no—
222C2×D4×C31—42no—
223C2×D4×C31—42no—
224C2×D4×C31—42no—
225C2×D4×C31—42no—
226C2×D4×C31—44no—
227C2×D4×C31—44no—
228C2×D4×C31—432no—
229C2×D4×C31—44no—
230C2×D4×C31—42no—
231C2×D4×C31—42no—
232C2×D4×C31—42no—
233C2×D4×C31—42no—
234C2×D4×C31—44no—
235C2×D4×C31—42no—
236C2×D4×C31—42no—
237C2×D4×C31—42no—
238C2×D4×C31—42no—
239C2×D4×C31—42no—
240C2×D4×C31—81no—
241C2×D4×C31—81no—
242C2×D4×C31—81no—
243C2×D4×C31D814yescomplemented
244C2×D4×C31C2×D412yes—
245C2×D4×C31C2×D412yes—
246C2×D4×C31C2×D412yes—
247C2×D4×C31C2×D412yes—
248C2×D4×C31#4112yes—
249C22×C4×C31—21no—
250C22×C4×C31—21no—
251C22×C4×C31—21no—
252C22×C4×C31—21no—
253C22×C4×C31—24no—
254C22×C4×C31—21no—
255C22×C4×C31—21no—
256C22×C4×C31—21no—
257C22×C4×C31—21no—
258C22×C4×C31—21no—
259C22×C4×C31—21no—
260C22×C4×C31—21no—
261C22×C4×C31—21no—
262C22×C4×C31—21no—
263C22×C4×C31—21no—
264C22×C4×C31—42no—
265C22×C4×C31—42no—
266C22×C4×C31—42no—
267C22×C4×C31—42no—
268C22×C4×C31—81no—
269C22×C4×C31C2×D411yescharacteristic
270C22×C4×C31C2×D411yescharacteristic
271C22×C4×C31C2×D411yescharacteristic
272C22×C4×C31C2×D412yes—
273C22×C4×C31C2×D412yes—
274C22×C4×C31C2×D411yescharacteristic
275C22×C4×C31C2411yescharacteristic
276D8×C31—44no—
277D8×C31—44no—
278D8×C31—44no—
279C2×C8×C31—21no—
280C2×C8×C31—21no—
281C2×C8×C31—21no—
282C2×C8×C31—21no—
283C2×C8×C31—21no—
284C2×C8×C31—21no—
285C2×C8×C31—21no—
286C2×C8×C31—21no—
287C2×C8×C31—21no—
288C2×C8×C31—21no—
289C2×C8×C31—21no—
290C2×C8×C31—44no—
291C2×C8×C31C2×D412yescomplemented
292C4⋊C4×C31—22no—
293C4⋊C4×C31—21no—
294C4⋊C4×C31—21no—
295C4⋊C4×C31—21no—
296C4⋊C4×C31—21no—
297C4⋊C4×C31—21no—
298C4⋊C4×C31—21no—
299C4⋊C4×C31—42no—
300C4⋊C4×C31—42no—
301C4⋊C4×C31C2×D412yes—
302C4⋊C4×C31C2×D412yescomplemented
303C22⋊C4×C31—24no—
304C22⋊C4×C31—24no—
305C22⋊C4×C31—22no—
306C22⋊C4×C31—24no—
307C22⋊C4×C31—22no—
308C22⋊C4×C31—42no—
309C22⋊C4×C31—42no—
310C22⋊C4×C31—42no—
311C22⋊C4×C31—42no—
312C22⋊C4×C31—81no—
313C42×C31—21no—
314C42×C31—21no—
315#24424C3111yesmaximal, characteristic, direct product factor, Sylow
316C23×C31—21no—
317C23×C31—21no—
318C23×C31—21no—
319C23×C31—21no—
320C23×C31—21no—
321C23×C31—22no—
322C23×C31—21no—
323C23×C31—22no—
324C23×C31—21no—
325C23×C31—22no—
326C23×C31—21no—
327C23×C31—21no—
328C23×C31—21no—
329C23×C31—22no—
330C23×C31—22no—
331C23×C31—48no—
332C23×C31—48no—
333C23×C31—48no—
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—41no—
345C23×C31—41no—
346C23×C31—41no—
347C23×C31—41no—
348C23×C31—41no—
349C23×C31—41no—
350C23×C31—48no—
351C23×C31—41no—
352C23×C31—41no—
353C23×C31—41no—
354C23×C31—41no—
355C23×C31—41no—
356C23×C31—41no—
357C23×C31—41no—
358C23×C31—84no—
359C23×C31—84no—
360C23×C31—84no—
361C23×C31—84no—
362C23×C31—84no—
363C23×C31—84no—
364C23×C31—84no—
365C23×C31—84no—
366C23×C31—84no—
367C23×C31—84no—
368C23×C31#12012yes—
369C23×C31C2×D812yes—
370C23×C31C2×D812yes—
371C23×C31AGL(1,ℤ/8)12yes—
372C23×C31C22×D411yescharacteristic
373D4×C31—28no—
374D4×C31—22no—
375D4×C31—22no—
376D4×C31—22no—
377D4×C31—22no—
378D4×C31—22no—
379D4×C31—22no—
380D4×C31—22no—
381D4×C31—48no—
382D4×C31—48no—
383D4×C31—48no—
384D4×C31—48no—
385D4×C31—48no—
386D4×C31—41no—
387D4×C31—41no—
388D4×C31—41no—
389D4×C31—41no—
390D4×C31—41no—
391D4×C31—41no—
392D4×C31—41no—
393D4×C31—41no—
394D4×C31—84no—
395D4×C31—84no—
396D4×C31—84no—
397D4×C31#12114yescomplemented
398C2×C4×C31—21no—
399C2×C4×C31—21no—
400C2×C4×C31—21no—
401C2×C4×C31—21no—
402C2×C4×C31—22no—
403C2×C4×C31—22no—
404C2×C4×C31—22no—
405C2×C4×C31—22no—
406C2×C4×C31—21no—
407C2×C4×C31—21no—
408C2×C4×C31—22no—
409C2×C4×C31—21no—
410C2×C4×C31—22no—
411C2×C4×C31—21no—
412C2×C4×C31—21no—
413C2×C4×C31—21no—
414C2×C4×C31—48no—
415C2×C4×C31—41no—
416C2×C4×C31—41no—
417C2×C4×C31—41no—
418C2×C4×C31—41no—
419C2×C4×C31—41no—
420C2×C4×C31—41no—
421C2×C4×C31—41no—
422C2×C4×C31—41no—
423C2×C4×C31—41no—
424C2×C4×C31—41no—
425C2×C4×C31—41no—
426C2×C4×C31—41no—
427C2×C4×C31—41no—
428C2×C4×C31—41no—
429C2×C4×C31—84no—
430C2×C4×C31#12012yes—
431C2×C4×C31C2×D812yes—
432C2×C4×C31C22×D411yescharacteristic
433C2×C4×C31C22×D411yescharacteristic
434C2×C4×C31C22×D411yescharacteristic
435C2×C4×C31C2×#4111yescharacteristic
436C2×C4×C31H(5,𝔽2)11yescharacteristic
437C2×C4×C31H(5,𝔽2)11yescharacteristic
438C8×C31—22no—
439C8×C31—41no—
440C8×C31—41no—
441C8×C31—41no—
442C2×D42C2×C3111yescharacteristic, complemented
443C2×#466C2×C3111yescharacteristic, complemented
444C2×#447C2×C3111yescharacteristic, complemented
445C2×#447C2×C3111yescharacteristic, complemented
446C22×#102C2×C3111yescharacteristic, complemented
447#2416C2×C3111yescharacteristic, complemented
448#2041C2×C3111yescharacteristic, complemented
449#2033C2×C3111yescharacteristic, complemented
450#2011C2×C3111yescharacteristic, complemented
451#1999C2×C3111yescharacteristic, complemented
452#1879C2×C3111yescharacteristic, complemented
453#1874C2×C3111yescharacteristic, complemented
454#1869C2×C3111yescharacteristic, complemented
455#1862C2×C3111yescharacteristic, complemented
456#1786C2×C3111yescharacteristic, complemented
457C22×C31—22no—
458C22×C31—22no—
459C22×C31—22no—
460C22×C31—22no—
461C22×C31—22no—
462C22×C31—22no—
463C22×C31—24no—
464C22×C31—22no—
465C22×C31—22no—
466C22×C31—22no—
467C22×C31—41no—
468C22×C31—42no—
469C22×C31—41no—
470C22×C31—42no—
471C22×C31—41no—
472C22×C31—42no—
473C22×C31—42no—
474C22×C31—42no—
475C22×C31—41no—
476C22×C31—42no—
477C22×C31—42no—
478C22×C31—42no—
479C22×C31—42no—
480C22×C31—42no—
481C22×C31—42no—
482C22×C31—42no—
483C22×C31—816no—
484C22×C31—816no—
485C22×C31—81no—
486C22×C31—81no—
487C22×C31—81no—
488C22×C31—81no—
489C22×C31—81no—
490C22×C31—81no—
491C22×C31—81no—
492C22×C31—81no—
493C22×C31—81no—
494C22×C31—81no—
495C22×C31—81no—
496C22×C31—81no—
497C22×C31—81no—
498C22×C31—81no—
499C22×C31—81no—
500C22×C31#44714yescomplemented
501C22×C31C2×#12011yescharacteristic
502C22×C31D4211yescharacteristic
503C22×C31#54611yescharacteristic
504C22×C31C22×D811yescharacteristic
505C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
506C22×C31#57611yescharacteristic
507C22×C31#57711yescharacteristic
508C4×C31—22no—
509C4×C31—22no—
510C4×C31—41no—
511C4×C31—42no—
512C4×C31—41no—
513C4×C31—42no—
514C4×C31—81no—
515C4×C31—81no—
516C4×C31C2×#12111yescharacteristic
517C4×C31#53411yescharacteristic
518C4×C31D4211yescharacteristic
519C4×C31#54611yescharacteristic
520C23×D4—21no—
521C23×D4C22×C3111yescharacteristic
522C23×D4C22×C3111yescharacteristic
523C22×D8C22×C3111yescharacteristic
524C22×D8C22×C3111yescharacteristic, complemented
525C22×D8C22×C3111yescharacteristic, complemented
526C23×C8C22×C3111yescharacteristic, complemented
527D42—24no—
528D42—24no—
529C2×#127C22×C3111yescharacteristic
530C2×#121—21no—
531C2×#121—21no—
532C2×#121C22×C3111yescharacteristic
533C2×#121C22×C3111yescharacteristic
534C2×#121C22×C3111yescharacteristic, complemented
535C2×#121C22×C3111yescharacteristic, complemented
536C2×#120—21no—
537C2×#120—21no—
538C2×C4×D4C22×C3111yescharacteristic
539C2×C4×D4C22×C3111yescharacteristic
540C22×C4⋊C4C22×C3111yescharacteristic, complemented
541#466—24no—
542#447—24no—
543#447—24no—
544C2×#107C22×C3111yescharacteristic, complemented
545C2×#102—24no—
546C2×#102C22×C3111yescharacteristic
547C2×#102C22×C3111yescharacteristic
548C2×#102C22×C3111yescharacteristic
549C2×#102C22×C3111yescharacteristic, complemented
550C2×#102C22×C3111yescharacteristic, complemented
551C2×#102C22×C3111yescharacteristic, complemented
552C2×#102C22×C3111yescharacteristic, complemented
553C2×#102C22×C3111yescharacteristic, complemented
554C2×#102C22×C3111yescharacteristic, complemented
555C2×#102C22×C3111yescharacteristic, complemented
556C2×C22⋊C8C22×C3111yescharacteristic, complemented
557C2×C22⋊C8C22×C3111yescharacteristic, complemented
558C2×C22⋊C8C22×C3111yescharacteristic, complemented
559#396—21no—
560#394—21no—
561#390C22×C3111yescharacteristic, complemented
562#389C22×C3111yescharacteristic, complemented
563#386—21no—
564#380C22×C3111yescharacteristic, complemented
565#340C22×C3111yescharacteristic, complemented
566#340C22×C3111yescharacteristic, complemented
567#336C22×C3111yescharacteristic, complemented
568#336C22×C3111yescharacteristic, complemented
569C2×C31—24no—
570C2×C31—42no—
571C2×C31—44no—
572C2×C31—82no—
573C2×C31—82no—
574C2×C31—161no—
575C2×C31#241011yescharacteristic
576C2×C31C2×#44711yescharacteristic
577C2×C31#301211yescharacteristic
578C2×C31#326511yescharacteristic
579C2×C31D4×D811yescharacteristic
580C2×C31#329411yescharacteristic
581C2×C31#331811yescharacteristic
582C25—21no—
583C25—21no—
584C22×D4—22no—
585C22×D4—22no—
586C22×D4—28no—
587C22×D4—21no—
588C22×D4—21no—
589C22×D4—22no—
590C22×D4—22no—
591C22×D4—22no—
592C22×D4—22no—
593C22×D4—21no—
594C22×D4—21no—
595C22×D4—21no—
596C22×D4—21no—
597C22×D4—21no—
598C22×D4—22no—
599C22×D4—21no—
600C22×D4—41no—
601C22×D4—41no—
602C22×D4—41no—
603C22×D4—41no—
604C22×D4—44no—
605C22×D4—44no—
606C22×D4D4×C3111yescharacteristic
607C22×D4D4×C3114yescomplemented
608C22×D4C23×C3111yescharacteristic
609C22×D4C23×C3111yescharacteristic
610C22×D4C23×C3111yescharacteristic
611C22×D4C23×C3111yescharacteristic
612C23×C4—21no—
613C23×C4—21no—
614C23×C4C23×C3111yescharacteristic
615C23×C4C23×C3111yescharacteristic
616C2×D8—22no—
617C2×D8—22no—
618C2×D8—22no—
619C2×D8—22no—
620C2×D8—22no—
621C2×D8—22no—
622C2×D8—41no—
623C2×D8—41no—
624C2×D8—41no—
625C22×C8—22no—
626C22×C8—22no—
627C22×C8—41no—
628C22×C8C23×C3111yescharacteristic
629C22×C8C23×C3111yescharacteristic
630C22×C8C23×C3111yescharacteristic
631C22×C8C23×C3111yescharacteristic
632#127—22no—
633#127—22no—
634#121—28no—
635#121—22no—
636#121—22no—
637#121—22no—
638#121—22no—
639#121—22no—
640#121—22no—
641#121—41no—
642#121—44no—
643#121D4×C3114yescomplemented
644#120—28no—
645#120—28no—
646C4×D4—22no—
647C4×D4—22no—
648C4×D4—22no—
649C4×D4—22no—
650C2×C4⋊C4—22no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—41no—
654C2×C4⋊C4D4×C3111yescharacteristic
655C2×C4⋊C4C23×C3111yescharacteristic
656C2×C4⋊C4C23×C3111yescharacteristic
657C2×C4⋊C4C23×C3111yescharacteristic
658C2×C4⋊C4C23×C3111yescharacteristic
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4D4×C3111yescharacteristic
668C2×C22⋊C4D4×C3111yescharacteristic
669C2×C42C23×C3111yescharacteristic
670#107—22no—
671#102—22no—
672#102—22no—
673#102—22no—
674#102—22no—
675#102—22no—
676#102—22no—
677#102—22no—
678#102—22no—
679#102—41no—
680#102D4×C3114yescomplemented
681C22⋊C8—22no—
682C22⋊C8—22no—
683C22⋊C8—41no—
684#95—21no—
685#95—21no—
686C31#2442411yescharacteristic, direct product factor, Sylow
687C24—21no—
688C24—24no—
689C24—21no—
690C24—21no—
691C24—24no—
692C24—21no—
693C24—42no—
694C24—42no—
695C24—42no—
696C24—42no—
697C24—42no—
698C24—42no—
699C24—42no—
700C24—42no—
701C24—81no—
702C24—81no—
703C24—81no—
704C24—81no—
705C24C2×D4×C3111yescharacteristic
706C24C2×D4×C3111yescharacteristic
707C2×D4—22no—
708C2×D4—22no—
709C2×D4—28no—
710C2×D4—24no—
711C2×D4—24no—
712C2×D4—24no—
713C2×D4—24no—
714C2×D4—24no—
715C2×D4—24no—
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—21no—
720C2×D4—21no—
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—44no—
736C2×D4—44no—
737C2×D4—44no—
738C2×D4—42no—
739C2×D4—42no—
740C2×D4—42no—
741C2×D4—42no—
742C2×D4—42no—
743C2×D4—42no—
744C2×D4—44no—
745C2×D4—44no—
746C2×D4—432no—
747C2×D4—44no—
748C2×D4—42no—
749C2×D4—42no—
750C2×D4—42no—
751C2×D4—42no—
752C2×D4—44no—
753C2×D4—42no—
754C2×D4—42no—
755C2×D4—42no—
756C2×D4—42no—
757C2×D4—42no—
758C2×D4—81no—
759C2×D4—81no—
760C2×D4—81no—
761C2×D4D8×C3114yescomplemented
762C2×D4C2×D4×C3112yes—
763C2×D4C2×D4×C3112yes—
764C2×D4C2×D4×C3112yes—
765C2×D4C2×D4×C3112yes—
766C2×D4#41×C3112yes—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—24no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—42no—
783C22×C4—42no—
784C22×C4—42no—
785C22×C4—42no—
786C22×C4—81no—
787C22×C4C2×D4×C3111yescharacteristic
788C22×C4C2×D4×C3111yescharacteristic
789C22×C4C2×D4×C3111yescharacteristic
790C22×C4C2×D4×C3112yes—
791C22×C4C2×D4×C3112yes—
792C22×C4C2×D4×C3111yescharacteristic
793C22×C4C24×C3111yescharacteristic
794D8—44no—
795D8—44no—
796D8—44no—
797C2×C8—21no—
798C2×C8—21no—
799C2×C8—21no—
800C2×C8—21no—
801C2×C8—21no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8—21no—
807C2×C8—21no—
808C2×C8—44no—
809C2×C8C2×D4×C3112yescomplemented
810C4⋊C4—22no—
811C4⋊C4—21no—
812C4⋊C4—21no—
813C4⋊C4—21no—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—42no—
818C4⋊C4—42no—
819C4⋊C4C2×D4×C3112yes—
820C4⋊C4C2×D4×C3112yescomplemented
821C22⋊C4—24no—
822C22⋊C4—24no—
823C22⋊C4—22no—
824C22⋊C4—24no—
825C22⋊C4—22no—
826C22⋊C4—42no—
827C22⋊C4—42no—
828C22⋊C4—42no—
829C22⋊C4—42no—
830C22⋊C4—81no—
831C42—21no—
832C42—21no—
833C23—21no—
834C23—21no—
835C23—21no—
836C23—21no—
837C23—21no—
838C23—22no—
839C23—21no—
840C23—22no—
841C23—21no—
842C23—22no—
843C23—21no—
844C23—21no—
845C23—21no—
846C23—22no—
847C23—22no—
848C23—48no—
849C23—48no—
850C23—48no—
851C23—41no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—48no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—41no—
870C23—41no—
871C23—41no—
872C23—41no—
873C23—41no—
874C23—41no—
875C23—84no—
876C23—84no—
877C23—84no—
878C23—84no—
879C23—84no—
880C23—84no—
881C23—84no—
882C23—84no—
883C23—84no—
884C23—84no—
885C23C31×#12012yes—
886C23C2×D8×C3112yes—
887C23C2×D8×C3112yes—
888C23C31×AGL(1,ℤ/8)12yes—
889C23C22×D4×C3111yescharacteristic
890D4—28no—
891D4—22no—
892D4—22no—
893D4—22no—
894D4—22no—
895D4—22no—
896D4—22no—
897D4—22no—
898D4—48no—
899D4—48no—
900D4—48no—
901D4—48no—
902D4—48no—
903D4—41no—
904D4—41no—
905D4—41no—
906D4—41no—
907D4—41no—
908D4—41no—
909D4—41no—
910D4—41no—
911D4—84no—
912D4—84no—
913D4—84no—
914D4C31×#12114yescomplemented
915C2×C4—21no—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—22no—
926C2×C4—21no—
927C2×C4—22no—
928C2×C4—21no—
929C2×C4—21no—
930C2×C4—21no—
931C2×C4—48no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—84no—
947C2×C4C31×#12012yes—
948C2×C4C2×D8×C3112yes—
949C2×C4C22×D4×C3111yescharacteristic
950C2×C4C22×D4×C3111yescharacteristic
951C2×C4C22×D4×C3111yescharacteristic
952C2×C4C2×#41×C3111yescharacteristic
953C2×C4C31×H(5,𝔽2)11yescharacteristic
954C2×C4C31×H(5,𝔽2)11yescharacteristic
955C8—22no—
956C8—41no—
957C8—41no—
958C8—41no—
959C22—22no—
960C22—22no—
961C22—22no—
962C22—22no—
963C22—22no—
964C22—22no—
965C22—24no—
966C22—22no—
967C22—22no—
968C22—22no—
969C22—41no—
970C22—42no—
971C22—41no—
972C22—42no—
973C22—41no—
974C22—42no—
975C22—42no—
976C22—42no—
977C22—41no—
978C22—42no—
979C22—42no—
980C22—42no—
981C22—42no—
982C22—42no—
983C22—42no—
984C22—42no—
985C22—816no—
986C22—816no—
987C22—81no—
988C22—81no—
989C22—81no—
990C22—81no—
991C22—81no—
992C22—81no—
993C22—81no—
994C22—81no—
995C22—81no—
996C22—81no—
997C22—81no—
998C22—81no—
999C22—81no—
1000C22—81no—
1001C22—81no—
1002C22C31×#44714yescomplemented
1003C22C2×C31×#12011yescharacteristic
1004C22D42×C3111yescharacteristic
1005C22C31×#54611yescharacteristic
1006C22C22×D8×C3111yescharacteristic
1007C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
1008C22C31×#57611yescharacteristic
1009C22C31×#57711yescharacteristic
1010C4—22no—
1011C4—22no—
1012C4—41no—
1013C4—42no—
1014C4—41no—
1015C4—42no—
1016C4—81no—
1017C4—81no—
1018C4C2×C31×#12111yescharacteristic
1019C4C31×#53411yescharacteristic
1020C4D42×C3111yescharacteristic
1021C4C31×#54611yescharacteristic
1022C2—24no—
1023C2—42no—
1024C2—44no—
1025C2—82no—
1026C2—82no—
1027C2—161no—
1028C2C31×#241011yescharacteristic
1029C2C2×C31×#44711yescharacteristic
1030C2C31×#301211yescharacteristic
1031C2C31×#326511yescharacteristic
1032C2D4×D8×C3111yescharacteristic
1033C2C31×#329411yescharacteristic
1034C2C31×#331811yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutator, Frattini, cosocleC22×C4C24×C31
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
1. C2×D42×C31C2semidirect
2. C2×C31×#466C2semidirect
3. C2×C31×#447C2semidirect
4. C2×C31×#447C2semidirect
5. C22×C31×#102C2semidirect
6. C31×#2416C2semidirect
7. C31×#2041C2semidirect
8. C31×#2033C2semidirect
9. C31×#2011C2semidirect
10. C31×#1999C2semidirect
11. C31×#1879C2semidirect
12. C31×#1874C2semidirect
13. C31×#1869C2semidirect
14. C31×#1862C2semidirect
15. C31×#1786C2semidirect
20. C22×D8×C31C22semidirect
21. C22×D8×C31C22semidirect
22. C23×C8×C31C22semidirect
30. C2×C31×#121C22semidirect
31. C2×C31×#121C22semidirect
36. C22×C4⋊C4×C31C22semidirect
40. C2×C31×#107C22semidirect
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×#102C22semidirect
52. C2×C31×C22⋊C8C22semidirect
53. C2×C31×C22⋊C8C22semidirect
54. C2×C31×C22⋊C8C22semidirect
57. C31×#390C22semidirect
58. C31×#389C22semidirect
60. C31×#380C22semidirect
61. C31×#340C22semidirect
62. C31×#340C22semidirect
63. C31×#336C22semidirect
64. C31×#336C22semidirect
90. C22×D4×C31D4semidirect
126. C31×#121D4semidirect
163. C31×#102D4semidirect
243. C2×D4×C31D8semidirect
291. C2×C8×C31C2×D4semidirect
302. C4⋊C4×C31C2×D4semidirect
315. #24424C31direct (N × H)
397. D4×C31#121semidirect
442. C2×D42C2×C31semidirect
443. C2×#466C2×C31semidirect
444. C2×#447C2×C31semidirect
445. C2×#447C2×C31semidirect
446. C22×#102C2×C31semidirect
447. #2416C2×C31semidirect
448. #2041C2×C31semidirect
449. #2033C2×C31semidirect
450. #2011C2×C31semidirect
451. #1999C2×C31semidirect
452. #1879C2×C31semidirect
453. #1874C2×C31semidirect
454. #1869C2×C31semidirect
455. #1862C2×C31semidirect
456. #1786C2×C31semidirect
500. C22×C31#447semidirect
524. C22×D8C22×C31semidirect
525. C22×D8C22×C31semidirect
526. C23×C8C22×C31semidirect
534. C2×#121C22×C31semidirect
535. C2×#121C22×C31semidirect
540. C22×C4⋊C4C22×C31semidirect
544. C2×#107C22×C31semidirect
549. C2×#102C22×C31semidirect
550. C2×#102C22×C31semidirect
551. C2×#102C22×C31semidirect
552. C2×#102C22×C31semidirect
553. C2×#102C22×C31semidirect
554. C2×#102C22×C31semidirect
555. C2×#102C22×C31semidirect
556. C2×C22⋊C8C22×C31semidirect
557. C2×C22⋊C8C22×C31semidirect
558. C2×C22⋊C8C22×C31semidirect
561. #390C22×C31semidirect
562. #389C22×C31semidirect
564. #380C22×C31semidirect
565. #340C22×C31semidirect
566. #340C22×C31semidirect
567. #336C22×C31semidirect
568. #336C22×C31semidirect
607. C22×D4D4×C31semidirect
643. #121D4×C31semidirect
680. #102D4×C31semidirect
686. C31#24424direct (N × H)
761. C2×D4D8×C31semidirect
809. C2×C8C2×D4×C31semidirect
820. C4⋊C4C2×D4×C31semidirect
914. D4C31×#121semidirect
1002. C22C31×#447semidirect

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×#4662
C2×C31×#4472
C22×C31×#1022
C31×#24162
C31×#20412
C31×#20332
C31×#20112
C31×#19992
C31×#18792
C31×#18742
C31×#18692
C31×#18622
C31×#17862
#2442431