Finite Group Databasebeta

← C31×#22423 #21479182

Subgroups — C31×#22423 #21479182

Order 7936.

1930 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D42×C31C211yesmaximal, characteristic
2C2×C31×#435C211yesmaximal, characteristic, complemented
3C2×C31×#418C211yesmaximal, characteristic, complemented
4C22×C31×#102C211yesmaximal, characteristic, complemented
5C31×#2352C211yesmaximal, characteristic, complemented
6C31×#1982C211yesmaximal, characteristic, complemented
7C31×#1961C211yesmaximal, characteristic, complemented
8C31×#1895C211yesmaximal, characteristic, complemented
9C31×#1893C211yesmaximal, characteristic, complemented
10C31×#1875C211yesmaximal, characteristic, complemented
11C31×#1874C211yesmaximal, characteristic, complemented
12C31×#1804C211yesmaximal, characteristic, complemented
13C31×#1786C211yesmaximal, characteristic, complemented
14C31×#1786C211yesmaximal, characteristic, complemented
15C31×#1762C211yesmaximal, characteristic, complemented
16C23×D4×C31—21no—
17C23×D4×C31C2211yescharacteristic
18C23×D4×C31C2211yescharacteristic
19C22×M16×C31C2211yescharacteristic, complemented
20C23×C8×C31C2211yescharacteristic, complemented
21D42×C31—24no—
22D42×C31C418yescomplemented
23C2×C31×#127C2211yescharacteristic
24C2×C31×#121—21no—
25C2×C31×#121C2211yescharacteristic
26C2×C31×#121C2211yescharacteristic
27C2×C31×#120—21no—
28C2×C31×#120—21no—
29C2×C4×D4×C31C2211yescharacteristic
30C2×C4×D4×C31C2211yescharacteristic
31C2×C31×#117C2211yescharacteristic, complemented
32C22×C4⋊C4×C31C2211yescharacteristic, complemented
33C31×#435—24no—
34C2×C31×C4⋊C8C2211yescharacteristic, complemented
35C31×#418—24no—
36C2×C31×#102—24no—
37C2×C31×#102C2211yescharacteristic
38C2×C31×#102C2211yescharacteristic
39C2×C31×#102C2211yescharacteristic
40C2×C31×#102C2211yescharacteristic
41C2×C31×#102C2211yescharacteristic, complemented
42C2×C31×#102C2211yescharacteristic, complemented
43C2×C31×#102C2211yescharacteristic, complemented
44C2×C31×#102C2211yescharacteristic, complemented
45C2×C31×#102C2211yescharacteristic, complemented
46C2×C31×#102C2211yescharacteristic, complemented
47C2×C31×#102C2211yescharacteristic, complemented
48C2×C31×#102C2211yescharacteristic, complemented
49C2×C31×C22⋊C8C2211yescharacteristic, complemented
50C2×C31×C22⋊C8C2211yescharacteristic, complemented
51C2×C31×#97C2211yescharacteristic, complemented
52C31×#388—21no—
53C31×#387—21no—
54C31×#386—21no—
55C31×#382C2211yescharacteristic, complemented
56C31×#380C2211yescharacteristic, complemented
57C31×#380C2211yescharacteristic, complemented
58C4×C4⋊C4×C31C2211yescharacteristic, complemented
59C4×C22⋊C4×C31—21no—
60C31×#340C2211yescharacteristic, complemented
61C31×#340C2211yescharacteristic, complemented
62C31×#340C2211yescharacteristic, complemented
63C31×#340C2211yescharacteristic, complemented
64C25×C31—21no—
65C25×C31—21no—
66C22×D4×C31—22no—
67C22×D4×C31—22no—
68C22×D4×C31—22no—
69C22×D4×C31—22no—
70C22×D4×C31—21no—
71C22×D4×C31—21no—
72C22×D4×C31—28no—
73C22×D4×C31—21no—
74C22×D4×C31—21no—
75C22×D4×C31—21no—
76C22×D4×C31—22no—
77C22×D4×C31—22no—
78C22×D4×C31—21no—
79C22×D4×C31—41no—
80C22×D4×C31—41no—
81C22×D4×C31—41no—
82C22×D4×C31—41no—
83C22×D4×C31—44no—
84C22×D4×C31—44no—
85C22×D4×C31C2×C414yes—
86C22×D4×C31C2×C414yescomplemented
87C22×D4×C31D411yescharacteristic
88C22×D4×C31C2311yescharacteristic
89C22×D4×C31C2311yescharacteristic
90C22×D4×C31C2311yescharacteristic
91C23×C4×C31—21no—
92C23×C4×C31—21no—
93C23×C4×C31C2311yescharacteristic
94C23×C4×C31C2311yescharacteristic
95C2×M16×C31—22no—
96C2×M16×C31—22no—
97C2×M16×C31—41no—
98C22×C8×C31—22no—
99C22×C8×C31—22no—
100C22×C8×C31—41no—
101C22×C8×C31C2311yescharacteristic
102C22×C8×C31C2311yescharacteristic
103C22×C8×C31C2311yescharacteristic
104C22×C8×C31C2311yescharacteristic
105C31×#127—22no—
106C31×#127C2×C414yescomplemented
107C31×#121—22no—
108C31×#121—22no—
109C31×#121—28no—
110C31×#121C2×C414yes—
111C31×#121C2×C414yescomplemented
112C31×#120—28no—
113C31×#120—28no—
114C4×D4×C31—22no—
115C4×D4×C31C2×C414yes—
116C4×D4×C31C2×C414yescomplemented
117C4×D4×C31D414yes—
118C31×#117—22no—
119C31×#117—41no—
120C2×C4⋊C4×C31—22no—
121C2×C4⋊C4×C31—21no—
122C2×C4⋊C4×C31—41no—
123C2×C4⋊C4×C31D411yescharacteristic
124C2×C4⋊C4×C31C2311yescharacteristic
125C2×C4⋊C4×C31C2311yescharacteristic
126C2×C4⋊C4×C31C2311yescharacteristic
127C2×C4⋊C4×C31C2311yescharacteristic
128C2×C4⋊C4×C31C2311yescharacteristic
129C2×C22⋊C4×C31—21no—
130C2×C22⋊C4×C31—21no—
131C2×C22⋊C4×C31—21no—
132C2×C22⋊C4×C31—21no—
133C2×C22⋊C4×C31—21no—
134C2×C22⋊C4×C31—21no—
135C2×C22⋊C4×C31D411yescharacteristic
136C2×C22⋊C4×C31D411yescharacteristic
137C2×C42×C31—21no—
138C2×C42×C31—21no—
139C2×C42×C31C2311yescharacteristic
140C31×C4⋊C8—22no—
141C31×#102—22no—
142C31×#102—22no—
143C31×#102—22no—
144C31×#102—22no—
145C31×#102—22no—
146C31×#102—22no—
147C31×#102—22no—
148C31×#102—41no—
149C31×#102—41no—
150C31×#102—41no—
151C31×#102—41no—
152C31×#102D414yescomplemented
153C31×C22⋊C8—22no—
154C31×C22⋊C8—22no—
155C31×#97—22no—
156C31×#95—21no—
157C31×#95—21no—
158C31×#95—21no—
159C31×#95—21no—
160C31×#95—21no—
161C24×C31—21no—
162C24×C31—21no—
163C24×C31—21no—
164C24×C31—24no—
165C24×C31—24no—
166C24×C31—42no—
167C24×C31—42no—
168C24×C31—42no—
169C24×C31—42no—
170C24×C31—42no—
171C24×C31—42no—
172C24×C31—42no—
173C24×C31—42no—
174C24×C31—81no—
175C24×C31—81no—
176C24×C31—81no—
177C24×C31—81no—
178C24×C31C2×D411yescharacteristic
179C24×C31C2×D411yescharacteristic
180C2×D4×C31—22no—
181C2×D4×C31—22no—
182C2×D4×C31—28no—
183C2×D4×C31—28no—
184C2×D4×C31—24no—
185C2×D4×C31—24no—
186C2×D4×C31—24no—
187C2×D4×C31—24no—
188C2×D4×C31—24no—
189C2×D4×C31—24no—
190C2×D4×C31—21no—
191C2×D4×C31—21no—
192C2×D4×C31—21no—
193C2×D4×C31—21no—
194C2×D4×C31—21no—
195C2×D4×C31—21no—
196C2×D4×C31—21no—
197C2×D4×C31—21no—
198C2×D4×C31—21no—
199C2×D4×C31—21no—
200C2×D4×C31—21no—
201C2×D4×C31—21no—
202C2×D4×C31—21no—
203C2×D4×C31—44no—
204C2×D4×C31—44no—
205C2×D4×C31—44no—
206C2×D4×C31—44no—
207C2×D4×C31—44no—
208C2×D4×C31—44no—
209C2×D4×C31—42no—
210C2×D4×C31—42no—
211C2×D4×C31—42no—
212C2×D4×C31—42no—
213C2×D4×C31—42no—
214C2×D4×C31—42no—
215C2×D4×C31—432no—
216C2×D4×C31—42no—
217C2×D4×C31—42no—
218C2×D4×C31—42no—
219C2×D4×C31—42no—
220C2×D4×C31—81no—
221C2×D4×C31—81no—
222C2×D4×C31C22⋊C414yes—
223C2×D4×C31C22×C412yes—
224C2×D4×C31C22×C412yes—
225C2×D4×C31C22×C412yes—
226C2×D4×C31C2×D412yes—
227C2×D4×C31#4112yes—
228C22×C4×C31—21no—
229C22×C4×C31—21no—
230C22×C4×C31—21no—
231C22×C4×C31—21no—
232C22×C4×C31—21no—
233C22×C4×C31—21no—
234C22×C4×C31—21no—
235C22×C4×C31—21no—
236C22×C4×C31—21no—
237C22×C4×C31—21no—
238C22×C4×C31—24no—
239C22×C4×C31—21no—
240C22×C4×C31—21no—
241C22×C4×C31—21no—
242C22×C4×C31—42no—
243C22×C4×C31—42no—
244C22×C4×C31—42no—
245C22×C4×C31—42no—
246C22×C4×C31—81no—
247C22×C4×C31C22×C412yes—
248C22×C4×C31C22×C412yes—
249C22×C4×C31C2×D411yescharacteristic
250C22×C4×C31C2×D411yescharacteristic
251C22×C4×C31C2×D411yescharacteristic
252C22×C4×C31C2×D411yescharacteristic
253C22×C4×C31C2×D412yes—
254C22×C4×C31C2×D412yes—
255C22×C4×C31C2411yescharacteristic
256M16×C31—44no—
257C2×C8×C31—21no—
258C2×C8×C31—21no—
259C2×C8×C31—21no—
260C2×C8×C31—21no—
261C2×C8×C31—21no—
262C2×C8×C31—21no—
263C2×C8×C31—21no—
264C2×C8×C31—21no—
265C2×C8×C31—21no—
266C2×C8×C31—21no—
267C2×C8×C31—21no—
268C2×C8×C31—44no—
269C2×C8×C31C2×D412yescomplemented
270C4⋊C4×C31—21no—
271C4⋊C4×C31—21no—
272C4⋊C4×C31—21no—
273C4⋊C4×C31—21no—
274C4⋊C4×C31—21no—
275C4⋊C4×C31—21no—
276C4⋊C4×C31—21no—
277C4⋊C4×C31—21no—
278C4⋊C4×C31—42no—
279C4⋊C4×C31C22⋊C414yes—
280C4⋊C4×C31C22×C412yes—
281C4⋊C4×C31C2×D412yescomplemented
282C22⋊C4×C31—24no—
283C22⋊C4×C31—24no—
284C22⋊C4×C31—24no—
285C22⋊C4×C31—42no—
286C22⋊C4×C31—42no—
287C22⋊C4×C31—81no—
288C22⋊C4×C31C22⋊C414yes—
289C22⋊C4×C31C22⋊C414yes—
290C42×C31—42no—
291C42×C31—81no—
292C42×C31C22×C412yes—
293C42×C31C2×D412yes—
294#22423C3111yesmaximal, characteristic, direct product factor, Sylow
295C23×C31—21no—
296C23×C31—21no—
297C23×C31—21no—
298C23×C31—21no—
299C23×C31—22no—
300C23×C31—21no—
301C23×C31—22no—
302C23×C31—21no—
303C23×C31—22no—
304C23×C31—21no—
305C23×C31—21no—
306C23×C31—21no—
307C23×C31—21no—
308C23×C31—22no—
309C23×C31—22no—
310C23×C31—48no—
311C23×C31—48no—
312C23×C31—48no—
313C23×C31—41no—
314C23×C31—41no—
315C23×C31—41no—
316C23×C31—41no—
317C23×C31—41no—
318C23×C31—41no—
319C23×C31—41no—
320C23×C31—41no—
321C23×C31—41no—
322C23×C31—41no—
323C23×C31—41no—
324C23×C31—41no—
325C23×C31—41no—
326C23×C31—41no—
327C23×C31—41no—
328C23×C31—41no—
329C23×C31—48no—
330C23×C31—84no—
331C23×C31—84no—
332C23×C31—84no—
333C23×C31—84no—
334C23×C31—84no—
335C23×C31—84no—
336C23×C31—84no—
337C23×C31—84no—
338C23×C31—84no—
339C23×C31—84no—
340C23×C31C2×C22⋊C412yes—
341C23×C31C2×C22⋊C412yes—
342C23×C31AGL(1,ℤ/8)12yes—
343C23×C31AGL(1,ℤ/8)12yes—
344C23×C31C22×D411yescharacteristic
345D4×C31—28no—
346D4×C31—22no—
347D4×C31—22no—
348D4×C31—22no—
349D4×C31—22no—
350D4×C31—22no—
351D4×C31—22no—
352D4×C31—22no—
353D4×C31—48no—
354D4×C31—48no—
355D4×C31—48no—
356D4×C31—48no—
357D4×C31—48no—
358D4×C31—41no—
359D4×C31—41no—
360D4×C31—41no—
361D4×C31—41no—
362D4×C31—84no—
363D4×C31C4×D414yes—
364C2×C4×C31—21no—
365C2×C4×C31—21no—
366C2×C4×C31—21no—
367C2×C4×C31—21no—
368C2×C4×C31—21no—
369C2×C4×C31—21no—
370C2×C4×C31—21no—
371C2×C4×C31—21no—
372C2×C4×C31—22no—
373C2×C4×C31—22no—
374C2×C4×C31—22no—
375C2×C4×C31—22no—
376C2×C4×C31—22no—
377C2×C4×C31—22no—
378C2×C4×C31—22no—
379C2×C4×C31—22no—
380C2×C4×C31—22no—
381C2×C4×C31—22no—
382C2×C4×C31—48no—
383C2×C4×C31—41no—
384C2×C4×C31—41no—
385C2×C4×C31—41no—
386C2×C4×C31—41no—
387C2×C4×C31—41no—
388C2×C4×C31—41no—
389C2×C4×C31—41no—
390C2×C4×C31—41no—
391C2×C4×C31—41no—
392C2×C4×C31—41no—
393C2×C4×C31—41no—
394C2×C4×C31—41no—
395C2×C4×C31—41no—
396C2×C4×C31—84no—
397C2×C4×C31C2×C22⋊C412yes—
398C2×C4×C31C2×C22⋊C412yes—
399C2×C4×C31C2×C22⋊C412yes—
400C2×C4×C31C2×C22⋊C412yes—
401C2×C4×C31C23×C411yescharacteristic
402C2×C4×C31C22×D411yescharacteristic
403C2×C4×C31C22×D411yescharacteristic
404C2×C4×C31C2×#4111yescharacteristic
405C2×C4×C31H(5,𝔽2)11yescharacteristic
406C2×C4×C31H(5,𝔽2)11yescharacteristic
407C8×C31—22no—
408C8×C31—41no—
409C8×C31—41no—
410C8×C31—41no—
411C2×D42C2×C3111yescharacteristic
412C2×#435C2×C3111yescharacteristic, complemented
413C2×#418C2×C3111yescharacteristic, complemented
414C22×#102C2×C3111yescharacteristic, complemented
415#2352C2×C3111yescharacteristic, complemented
416#1982C2×C3111yescharacteristic, complemented
417#1961C2×C3111yescharacteristic, complemented
418#1895C2×C3111yescharacteristic, complemented
419#1893C2×C3111yescharacteristic, complemented
420#1875C2×C3111yescharacteristic, complemented
421#1874C2×C3111yescharacteristic, complemented
422#1804C2×C3111yescharacteristic, complemented
423#1786C2×C3111yescharacteristic, complemented
424#1786C2×C3111yescharacteristic, complemented
425#1762C2×C3111yescharacteristic, complemented
426C22×C31—22no—
427C22×C31—22no—
428C22×C31—22no—
429C22×C31—22no—
430C22×C31—22no—
431C22×C31—22no—
432C22×C31—22no—
433C22×C31—24no—
434C22×C31—22no—
435C22×C31—22no—
436C22×C31—42no—
437C22×C31—42no—
438C22×C31—41no—
439C22×C31—42no—
440C22×C31—41no—
441C22×C31—42no—
442C22×C31—41no—
443C22×C31—42no—
444C22×C31—41no—
445C22×C31—42no—
446C22×C31—42no—
447C22×C31—42no—
448C22×C31—42no—
449C22×C31—42no—
450C22×C31—42no—
451C22×C31—42no—
452C22×C31—816no—
453C22×C31—816no—
454C22×C31—81no—
455C22×C31—81no—
456C22×C31—81no—
457C22×C31—81no—
458C22×C31—81no—
459C22×C31—81no—
460C22×C31—81no—
461C22×C31—81no—
462C22×C31#41814yescomplemented
463C22×C31C22×C22⋊C411yescharacteristic
464C22×C31D4211yescharacteristic
465C22×C31#54611yescharacteristic
466C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
467C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
468C22×C31#57611yescharacteristic
469C22×C31#57711yescharacteristic
470C4×C31—22no—
471C4×C31—22no—
472C4×C31—22no—
473C4×C31—22no—
474C4×C31—42no—
475C4×C31—42no—
476C4×C31—81no—
477C4×C31—81no—
478C4×C31—81no—
479C4×C31C2×C4×D411yescharacteristic
480C4×C31#51811yescharacteristic
481C4×C31D4211yescharacteristic
482C4×C31#54611yescharacteristic
483C23×D4—21no—
484C23×D4C22×C3111yescharacteristic
485C23×D4C22×C3111yescharacteristic
486C22×M16C22×C3111yescharacteristic, complemented
487C23×C8C22×C3111yescharacteristic, complemented
488D42—24no—
489D42C4×C3118yescomplemented
490C2×#127C22×C3111yescharacteristic
491C2×#121—21no—
492C2×#121C22×C3111yescharacteristic
493C2×#121C22×C3111yescharacteristic
494C2×#120—21no—
495C2×#120—21no—
496C2×C4×D4C22×C3111yescharacteristic
497C2×C4×D4C22×C3111yescharacteristic
498C2×#117C22×C3111yescharacteristic, complemented
499C22×C4⋊C4C22×C3111yescharacteristic, complemented
500#435—24no—
501C2×C4⋊C8C22×C3111yescharacteristic, complemented
502#418—24no—
503C2×#102—24no—
504C2×#102C22×C3111yescharacteristic
505C2×#102C22×C3111yescharacteristic
506C2×#102C22×C3111yescharacteristic
507C2×#102C22×C3111yescharacteristic
508C2×#102C22×C3111yescharacteristic, complemented
509C2×#102C22×C3111yescharacteristic, complemented
510C2×#102C22×C3111yescharacteristic, complemented
511C2×#102C22×C3111yescharacteristic, complemented
512C2×#102C22×C3111yescharacteristic, complemented
513C2×#102C22×C3111yescharacteristic, complemented
514C2×#102C22×C3111yescharacteristic, complemented
515C2×#102C22×C3111yescharacteristic, complemented
516C2×C22⋊C8C22×C3111yescharacteristic, complemented
517C2×C22⋊C8C22×C3111yescharacteristic, complemented
518C2×#97C22×C3111yescharacteristic, complemented
519#388—21no—
520#387—21no—
521#386—21no—
522#382C22×C3111yescharacteristic, complemented
523#380C22×C3111yescharacteristic, complemented
524#380C22×C3111yescharacteristic, complemented
525C4×C4⋊C4C22×C3111yescharacteristic, complemented
526C4×C22⋊C4—21no—
527#340C22×C3111yescharacteristic, complemented
528#340C22×C3111yescharacteristic, complemented
529#340C22×C3111yescharacteristic, complemented
530#340C22×C3111yescharacteristic, complemented
531C2×C31—24no—
532C2×C31—42no—
533C2×C31—44no—
534C2×C31—82no—
535C2×C31—82no—
536C2×C31D4×C22⋊C411yescharacteristic
537C2×C31C2×#41811yescharacteristic
538C2×C31#289711yescharacteristic
539C2×C31#326411yescharacteristic
540C2×C31#326511yescharacteristic
541C2×C31#331011yescharacteristic
542C2×C31#331811yescharacteristic
543C25—21no—
544C25—21no—
545C22×D4—22no—
546C22×D4—22no—
547C22×D4—22no—
548C22×D4—22no—
549C22×D4—21no—
550C22×D4—21no—
551C22×D4—28no—
552C22×D4—21no—
553C22×D4—21no—
554C22×D4—21no—
555C22×D4—22no—
556C22×D4—22no—
557C22×D4—21no—
558C22×D4—41no—
559C22×D4—41no—
560C22×D4—41no—
561C22×D4—41no—
562C22×D4—44no—
563C22×D4—44no—
564C22×D4C2×C4×C3114yes—
565C22×D4C2×C4×C3114yescomplemented
566C22×D4D4×C3111yescharacteristic
567C22×D4C23×C3111yescharacteristic
568C22×D4C23×C3111yescharacteristic
569C22×D4C23×C3111yescharacteristic
570C23×C4—21no—
571C23×C4—21no—
572C23×C4C23×C3111yescharacteristic
573C23×C4C23×C3111yescharacteristic
574C2×M16—22no—
575C2×M16—22no—
576C2×M16—41no—
577C22×C8—22no—
578C22×C8—22no—
579C22×C8—41no—
580C22×C8C23×C3111yescharacteristic
581C22×C8C23×C3111yescharacteristic
582C22×C8C23×C3111yescharacteristic
583C22×C8C23×C3111yescharacteristic
584#127—22no—
585#127C2×C4×C3114yescomplemented
586#121—22no—
587#121—22no—
588#121—28no—
589#121C2×C4×C3114yes—
590#121C2×C4×C3114yescomplemented
591#120—28no—
592#120—28no—
593C4×D4—22no—
594C4×D4C2×C4×C3114yes—
595C4×D4C2×C4×C3114yescomplemented
596C4×D4D4×C3114yes—
597#117—22no—
598#117—41no—
599C2×C4⋊C4—22no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—41no—
602C2×C4⋊C4D4×C3111yescharacteristic
603C2×C4⋊C4C23×C3111yescharacteristic
604C2×C4⋊C4C23×C3111yescharacteristic
605C2×C4⋊C4C23×C3111yescharacteristic
606C2×C4⋊C4C23×C3111yescharacteristic
607C2×C4⋊C4C23×C3111yescharacteristic
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4D4×C3111yescharacteristic
615C2×C22⋊C4D4×C3111yescharacteristic
616C2×C42—21no—
617C2×C42—21no—
618C2×C42C23×C3111yescharacteristic
619C4⋊C8—22no—
620#102—22no—
621#102—22no—
622#102—22no—
623#102—22no—
624#102—22no—
625#102—22no—
626#102—22no—
627#102—41no—
628#102—41no—
629#102—41no—
630#102—41no—
631#102D4×C3114yescomplemented
632C22⋊C8—22no—
633C22⋊C8—22no—
634#97—22no—
635#95—21no—
636#95—21no—
637#95—21no—
638#95—21no—
639#95—21no—
640C31#2242311yescharacteristic, direct product factor, Sylow
641C24—21no—
642C24—21no—
643C24—21no—
644C24—24no—
645C24—24no—
646C24—42no—
647C24—42no—
648C24—42no—
649C24—42no—
650C24—42no—
651C24—42no—
652C24—42no—
653C24—42no—
654C24—81no—
655C24—81no—
656C24—81no—
657C24—81no—
658C24C2×D4×C3111yescharacteristic
659C24C2×D4×C3111yescharacteristic
660C2×D4—22no—
661C2×D4—22no—
662C2×D4—28no—
663C2×D4—28no—
664C2×D4—24no—
665C2×D4—24no—
666C2×D4—24no—
667C2×D4—24no—
668C2×D4—24no—
669C2×D4—24no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—44no—
684C2×D4—44no—
685C2×D4—44no—
686C2×D4—44no—
687C2×D4—44no—
688C2×D4—44no—
689C2×D4—42no—
690C2×D4—42no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—42no—
694C2×D4—42no—
695C2×D4—432no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—42no—
699C2×D4—42no—
700C2×D4—81no—
701C2×D4—81no—
702C2×D4C22⋊C4×C3114yes—
703C2×D4C22×C4×C3112yes—
704C2×D4C22×C4×C3112yes—
705C2×D4C22×C4×C3112yes—
706C2×D4C2×D4×C3112yes—
707C2×D4#41×C3112yes—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—24no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—42no—
723C22×C4—42no—
724C22×C4—42no—
725C22×C4—42no—
726C22×C4—81no—
727C22×C4C22×C4×C3112yes—
728C22×C4C22×C4×C3112yes—
729C22×C4C2×D4×C3111yescharacteristic
730C22×C4C2×D4×C3111yescharacteristic
731C22×C4C2×D4×C3111yescharacteristic
732C22×C4C2×D4×C3111yescharacteristic
733C22×C4C2×D4×C3112yes—
734C22×C4C2×D4×C3112yes—
735C22×C4C24×C3111yescharacteristic
736M16—44no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—44no—
749C2×C8C2×D4×C3112yescomplemented
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—42no—
759C4⋊C4C22⋊C4×C3114yes—
760C4⋊C4C22×C4×C3112yes—
761C4⋊C4C2×D4×C3112yescomplemented
762C22⋊C4—24no—
763C22⋊C4—24no—
764C22⋊C4—24no—
765C22⋊C4—42no—
766C22⋊C4—42no—
767C22⋊C4—81no—
768C22⋊C4C22⋊C4×C3114yes—
769C22⋊C4C22⋊C4×C3114yes—
770C42—42no—
771C42—81no—
772C42C22×C4×C3112yes—
773C42C2×D4×C3112yes—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—22no—
779C23—21no—
780C23—22no—
781C23—21no—
782C23—22no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—22no—
788C23—22no—
789C23—48no—
790C23—48no—
791C23—48no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—48no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—84no—
810C23—84no—
811C23—84no—
812C23—84no—
813C23—84no—
814C23—84no—
815C23—84no—
816C23—84no—
817C23—84no—
818C23—84no—
819C23C2×C22⋊C4×C3112yes—
820C23C2×C22⋊C4×C3112yes—
821C23C31×AGL(1,ℤ/8)12yes—
822C23C31×AGL(1,ℤ/8)12yes—
823C23C22×D4×C3111yescharacteristic
824D4—28no—
825D4—22no—
826D4—22no—
827D4—22no—
828D4—22no—
829D4—22no—
830D4—22no—
831D4—22no—
832D4—48no—
833D4—48no—
834D4—48no—
835D4—48no—
836D4—48no—
837D4—41no—
838D4—41no—
839D4—41no—
840D4—41no—
841D4—84no—
842D4C4×D4×C3114yes—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—48no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—84no—
876C2×C4C2×C22⋊C4×C3112yes—
877C2×C4C2×C22⋊C4×C3112yes—
878C2×C4C2×C22⋊C4×C3112yes—
879C2×C4C2×C22⋊C4×C3112yes—
880C2×C4C23×C4×C3111yescharacteristic
881C2×C4C22×D4×C3111yescharacteristic
882C2×C4C22×D4×C3111yescharacteristic
883C2×C4C2×#41×C3111yescharacteristic
884C2×C4C31×H(5,𝔽2)11yescharacteristic
885C2×C4C31×H(5,𝔽2)11yescharacteristic
886C8—22no—
887C8—41no—
888C8—41no—
889C8—41no—
890C22—22no—
891C22—22no—
892C22—22no—
893C22—22no—
894C22—22no—
895C22—22no—
896C22—22no—
897C22—24no—
898C22—22no—
899C22—22no—
900C22—42no—
901C22—42no—
902C22—41no—
903C22—42no—
904C22—41no—
905C22—42no—
906C22—41no—
907C22—42no—
908C22—41no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—816no—
917C22—816no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22C31×#41814yescomplemented
927C22C22×C22⋊C4×C3111yescharacteristic
928C22D42×C3111yescharacteristic
929C22C31×#54611yescharacteristic
930C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
931C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
932C22C31×#57611yescharacteristic
933C22C31×#57711yescharacteristic
934C4—22no—
935C4—22no—
936C4—22no—
937C4—22no—
938C4—42no—
939C4—42no—
940C4—81no—
941C4—81no—
942C4—81no—
943C4C2×C4×D4×C3111yescharacteristic
944C4C31×#51811yescharacteristic
945C4D42×C3111yescharacteristic
946C4C31×#54611yescharacteristic
947C2—24no—
948C2—42no—
949C2—44no—
950C2—82no—
951C2—82no—
952C2D4×C22⋊C4×C3111yescharacteristic
953C2C2×C31×#41811yescharacteristic
954C2C31×#289711yescharacteristic
955C2C31×#326411yescharacteristic
956C2C31×#326511yescharacteristic
957C2C31×#331011yescharacteristic
958C2C31×#331811yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutatorC2×C4C23×C4×C31
Frattini, cosocleC22×C4C24×C31
prime radicalC2×D42×C31C2
LCSG ▷ C2×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×#435C2semidirect
3. C2×C31×#418C2semidirect
4. C22×C31×#102C2semidirect
5. C31×#2352C2semidirect
6. C31×#1982C2semidirect
7. C31×#1961C2semidirect
8. C31×#1895C2semidirect
9. C31×#1893C2semidirect
10. C31×#1875C2semidirect
11. C31×#1874C2semidirect
12. C31×#1804C2semidirect
13. C31×#1786C2semidirect
14. C31×#1786C2semidirect
15. C31×#1762C2semidirect
19. C22×M16×C31C22semidirect
20. C23×C8×C31C22semidirect
22. D42×C31C4semidirect
31. C2×C31×#117C22semidirect
32. C22×C4⋊C4×C31C22semidirect
34. C2×C31×C4⋊C8C22semidirect
41. C2×C31×#102C22semidirect
42. C2×C31×#102C22semidirect
43. C2×C31×#102C22semidirect
44. C2×C31×#102C22semidirect
45. C2×C31×#102C22semidirect
46. C2×C31×#102C22semidirect
47. C2×C31×#102C22semidirect
48. C2×C31×#102C22semidirect
49. C2×C31×C22⋊C8C22semidirect
50. C2×C31×C22⋊C8C22semidirect
51. C2×C31×#97C22semidirect
55. C31×#382C22semidirect
56. C31×#380C22semidirect
57. C31×#380C22semidirect
58. C4×C4⋊C4×C31C22semidirect
60. C31×#340C22semidirect
61. C31×#340C22semidirect
62. C31×#340C22semidirect
63. C31×#340C22semidirect
86. C22×D4×C31C2×C4semidirect
106. C31×#127C2×C4semidirect
111. C31×#121C2×C4semidirect
116. C4×D4×C31C2×C4semidirect
152. C31×#102D4semidirect
269. C2×C8×C31C2×D4semidirect
281. C4⋊C4×C31C2×D4semidirect
294. #22423C31direct (N × H)
412. C2×#435C2×C31semidirect
413. C2×#418C2×C31semidirect
414. C22×#102C2×C31semidirect
415. #2352C2×C31semidirect
416. #1982C2×C31semidirect
417. #1961C2×C31semidirect
418. #1895C2×C31semidirect
419. #1893C2×C31semidirect
420. #1875C2×C31semidirect
421. #1874C2×C31semidirect
422. #1804C2×C31semidirect
423. #1786C2×C31semidirect
424. #1786C2×C31semidirect
425. #1762C2×C31semidirect
462. C22×C31#418semidirect
486. C22×M16C22×C31semidirect
487. C23×C8C22×C31semidirect
489. D42C4×C31semidirect
498. C2×#117C22×C31semidirect
499. C22×C4⋊C4C22×C31semidirect
501. C2×C4⋊C8C22×C31semidirect
508. C2×#102C22×C31semidirect
509. C2×#102C22×C31semidirect
510. C2×#102C22×C31semidirect
511. C2×#102C22×C31semidirect
512. C2×#102C22×C31semidirect
513. C2×#102C22×C31semidirect
514. C2×#102C22×C31semidirect
515. C2×#102C22×C31semidirect
516. C2×C22⋊C8C22×C31semidirect
517. C2×C22⋊C8C22×C31semidirect
518. C2×#97C22×C31semidirect
522. #382C22×C31semidirect
523. #380C22×C31semidirect
524. #380C22×C31semidirect
525. C4×C4⋊C4C22×C31semidirect
527. #340C22×C31semidirect
528. #340C22×C31semidirect
529. #340C22×C31semidirect
530. #340C22×C31semidirect
565. C22×D4C2×C4×C31semidirect
585. #127C2×C4×C31semidirect
590. #121C2×C4×C31semidirect
595. C4×D4C2×C4×C31semidirect
631. #102D4×C31semidirect
640. C31#22423direct (N × H)
749. C2×C8C2×D4×C31semidirect
761. C4⋊C4C2×D4×C31semidirect
926. C22C31×#418semidirect

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×#4352
C2×C31×#4182
C22×C31×#1022
C31×#23522
C31×#19822
C31×#19612
C31×#18952
C31×#18932
C31×#18752
C31×#18742
C31×#18042
C31×#17862
C31×#17622
#2242331