Finite Group Databasebeta

← C31×#22419 #21479178

Subgroups — C31×#22419 #21479178

Order 7936.

1670 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#546C211yesmaximal, characteristic
2C2×C31×#435C211yesmaximal, characteristic, complemented
3C2×C31×#417C211yesmaximal, characteristic, complemented
4C22×C31×#102C211yesmaximal, characteristic, complemented
5D4×C4⋊C4×C31C211yesmaximal, characteristic, complemented
6C31×#1983C211yesmaximal, characteristic, complemented
7C31×#1959C211yesmaximal, characteristic, complemented
8C31×#1895C211yesmaximal, characteristic, complemented
9C31×#1892C211yesmaximal, characteristic, complemented
10C31×#1874C211yesmaximal, characteristic, complemented
11C31×#1872C211yesmaximal, characteristic, complemented
12C31×#1802C211yesmaximal, characteristic, complemented
13C31×#1788C211yesmaximal, characteristic, complemented
14C31×#1786C211yesmaximal, characteristic, complemented
15C31×#1762C211yesmaximal, characteristic, complemented
16C22×#41×C31C2211yescharacteristic
17C23×D4×C31C2211yescharacteristic
18C22×M16×C31C2211yescharacteristic, complemented
19C23×C8×C31C2211yescharacteristic
20C31×#546—24no—
21C31×#546C418yescomplemented
22C2×C31×#124C2211yescharacteristic
23C2×C31×#123—21no—
24C2×C31×C22⋊Q8C2211yescharacteristic
25C2×C31×#121—21no—
26C2×C31×#121C2211yescharacteristic
27C2×C31×#120—21no—
28C2×C4×D4×C31—21no—
29C2×C4×D4×C31C2211yescharacteristic
30C2×C4×D4×C31C2211yescharacteristic
31C22×C4⋊C4×C31C2211yescharacteristic
32C22×C4⋊C4×C31C2211yescharacteristic, complemented
33C22×C22⋊C4×C31—21no—
34C31×#435—24no—
35C2×C31×C4⋊C8C2211yescharacteristic, complemented
36C31×#417—24no—
37C2×C31×#103C2211yescharacteristic, complemented
38C2×C31×#103C2211yescharacteristic, complemented
39C2×C31×#103C2211yescharacteristic, complemented
40C2×C31×#103C2211yescharacteristic, complemented
41C2×C31×#102—24no—
42C2×C31×#102C2211yescharacteristic
43C2×C31×#102C2211yescharacteristic
44C2×C31×#102C2211yescharacteristic
45C2×C31×#102C2211yescharacteristic
46C2×C31×#102C2211yescharacteristic
47C2×C31×#102C2211yescharacteristic
48C2×C31×#102C2211yescharacteristic
49C2×C31×#102C2211yescharacteristic
50C2×C31×C22⋊C8C2211yescharacteristic
51C2×C31×C22⋊C8C2211yescharacteristic, complemented
52C2×C31×#97C2211yescharacteristic, complemented
53C31×#389—21no—
54C31×#385—21no—
55C31×#385—21no—
56C31×#384C2211yescharacteristic, complemented
57C31×#380C2211yescharacteristic
58C31×#380C2211yescharacteristic, complemented
59C4×C4⋊C4×C31C2211yescharacteristic, complemented
60C31×#340C2211yescharacteristic, complemented
61C31×#340C2211yescharacteristic, complemented
62C31×#340C2211yescharacteristic, complemented
63C31×#340C2211yescharacteristic, complemented
64C25×C31—21no—
65C2×#41×C31—22no—
66C2×#41×C31—22no—
67C2×#41×C31—22no—
68C2×#41×C31—41no—
69C2×#41×C31—41no—
70C2×#41×C31C2×C414yescomplemented
71C22×Q8×C31C2311yescharacteristic
72C22×D4×C31—22no—
73C22×D4×C31—22no—
74C22×D4×C31—21no—
75C22×D4×C31—21no—
76C22×D4×C31—21no—
77C22×D4×C31—22no—
78C22×D4×C31—41no—
79C22×D4×C31—41no—
80C22×D4×C31C2×C414yescomplemented
81C22×D4×C31D411yescharacteristic
82C22×D4×C31C2311yescharacteristic
83C22×D4×C31C2311yescharacteristic
84C23×C4×C31—21no—
85C23×C4×C31—21no—
86C23×C4×C31—21no—
87C23×C4×C31—21no—
88C23×C4×C31C2311yescharacteristic
89C23×C4×C31C2311yescharacteristic
90C2×M16×C31—22no—
91C2×M16×C31—22no—
92C2×M16×C31—41no—
93C22×C8×C31—22no—
94C22×C8×C31—22no—
95C22×C8×C31—41no—
96C22×C8×C31C2311yescharacteristic
97C22×C8×C31C2311yescharacteristic
98C22×C8×C31C2311yescharacteristic
99C22×C8×C31C2311yescharacteristic
100C31×#124—22no—
101C31×#124C2×C414yescomplemented
102C31×#123—28no—
103C31×C22⋊Q8—22no—
104C31×C22⋊Q8C2×C414yescomplemented
105C31×#121—22no—
106C31×#121—28no—
107C31×#121C2×C414yescomplemented
108C31×#120—28no—
109C4×D4×C31—22no—
110C4×D4×C31—44no—
111C4×D4×C31C2×C414yes—
112C4×D4×C31C2×C414yescomplemented
113C4×D4×C31D414yes—
114C2×C4⋊C4×C31—21no—
115C2×C4⋊C4×C31—22no—
116C2×C4⋊C4×C31—22no—
117C2×C4⋊C4×C31—21no—
118C2×C4⋊C4×C31—21no—
119C2×C4⋊C4×C31—21no—
120C2×C4⋊C4×C31—21no—
121C2×C4⋊C4×C31—41no—
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—28no—
135C2×C22⋊C4×C31—21no—
136C2×C22⋊C4×C31—21no—
137C2×C22⋊C4×C31D411yescharacteristic
138C2×C22⋊C4×C31D411yescharacteristic
139C2×C42×C31—21no—
140C2×C42×C31C2311yescharacteristic
141C31×C4⋊C8—22no—
142C31×#103—22no—
143C31×#103—22no—
144C31×#103—41no—
145C31×#103—41no—
146C31×#102—22no—
147C31×#102—22no—
148C31×#102—22no—
149C31×#102—22no—
150C31×#102—22no—
151C31×#102—41no—
152C31×#102—41no—
153C31×#102D414yescomplemented
154C31×C22⋊C8—22no—
155C31×C22⋊C8—22no—
156C31×#97—22no—
157C31×#95—21no—
158C31×#95—21no—
159C31×#95—21no—
160C24×C31—21no—
161C24×C31—21no—
162C24×C31—24no—
163C24×C31—42no—
164C24×C31—42no—
165C24×C31—42no—
166C24×C31—42no—
167C24×C31—81no—
168C24×C31—81no—
169C24×C31C2×D411yescharacteristic
170C24×C31C2×D411yescharacteristic
171#41×C31—28no—
172#41×C31—44no—
173#41×C31—44no—
174#41×C31—44no—
175C2×Q8×C31—21no—
176C2×Q8×C31—21no—
177C2×Q8×C31—21no—
178C2×Q8×C31—21no—
179C2×Q8×C31—21no—
180C2×Q8×C31C22×C412yes—
181C2×D4×C31—22no—
182C2×D4×C31—22no—
183C2×D4×C31—28no—
184C2×D4×C31—24no—
185C2×D4×C31—24no—
186C2×D4×C31—24no—
187C2×D4×C31—21no—
188C2×D4×C31—21no—
189C2×D4×C31—21no—
190C2×D4×C31—21no—
191C2×D4×C31—21no—
192C2×D4×C31—21no—
193C2×D4×C31—21no—
194C2×D4×C31—21no—
195C2×D4×C31—44no—
196C2×D4×C31—44no—
197C2×D4×C31—44no—
198C2×D4×C31—42no—
199C2×D4×C31—42no—
200C2×D4×C31—42no—
201C2×D4×C31—42no—
202C2×D4×C31—81no—
203C2×D4×C31—81no—
204C2×D4×C31C22⋊C414yes—
205C2×D4×C31C22×C412yes—
206C2×D4×C31C22×C412yes—
207C2×D4×C31C2×D412yes—
208C2×D4×C31#4112yes—
209C22×C4×C31—21no—
210C22×C4×C31—21no—
211C22×C4×C31—21no—
212C22×C4×C31—21no—
213C22×C4×C31—21no—
214C22×C4×C31—21no—
215C22×C4×C31—21no—
216C22×C4×C31—21no—
217C22×C4×C31—21no—
218C22×C4×C31—21no—
219C22×C4×C31—21no—
220C22×C4×C31—24no—
221C22×C4×C31—24no—
222C22×C4×C31—21no—
223C22×C4×C31—21no—
224C22×C4×C31—21no—
225C22×C4×C31—42no—
226C22×C4×C31—42no—
227C22×C4×C31—42no—
228C22×C4×C31—42no—
229C22×C4×C31—42no—
230C22×C4×C31—42no—
231C22×C4×C31—81no—
232C22×C4×C31—81no—
233C22×C4×C31—81no—
234C22×C4×C31—81no—
235C22×C4×C31C22×C412yes—
236C22×C4×C31C22×C412yes—
237C22×C4×C31C2×D411yescharacteristic
238C22×C4×C31C2×D411yescharacteristic
239C22×C4×C31C2×D411yescharacteristic
240C22×C4×C31C2×D411yescharacteristic
241C22×C4×C31C2×D412yes—
242C22×C4×C31C2×D412yes—
243C22×C4×C31C2411yescharacteristic
244M16×C31—44no—
245C2×C8×C31—21no—
246C2×C8×C31—21no—
247C2×C8×C31—21no—
248C2×C8×C31—21no—
249C2×C8×C31—21no—
250C2×C8×C31—21no—
251C2×C8×C31—21no—
252C2×C8×C31—21no—
253C2×C8×C31—21no—
254C2×C8×C31—21no—
255C2×C8×C31—21no—
256C2×C8×C31—44no—
257C2×C8×C31C2×D412yes—
258C4⋊C4×C31—24no—
259C4⋊C4×C31—21no—
260C4⋊C4×C31—21no—
261C4⋊C4×C31—21no—
262C4⋊C4×C31—21no—
263C4⋊C4×C31—21no—
264C4⋊C4×C31—21no—
265C4⋊C4×C31—21no—
266C4⋊C4×C31—21no—
267C4⋊C4×C31—42no—
268C4⋊C4×C31—42no—
269C4⋊C4×C31—42no—
270C4⋊C4×C31—81no—
271C4⋊C4×C31C22⋊C414yes—
272C4⋊C4×C31C22×C412yes—
273C4⋊C4×C31C2×D412yes—
274C22⋊C4×C31—24no—
275C22⋊C4×C31—24no—
276C22⋊C4×C31—24no—
277C22⋊C4×C31—24no—
278C22⋊C4×C31—24no—
279C22⋊C4×C31—42no—
280C22⋊C4×C31—42no—
281C22⋊C4×C31C22⋊C414yes—
282C22⋊C4×C31C22⋊C414yes—
283C42×C31—42no—
284C42×C31C22×C412yes—
285C42×C31C2×D412yes—
286#22419C3111yesmaximal, characteristic, direct product factor, Sylow
287C23×C31—21no—
288C23×C31—21no—
289C23×C31—21no—
290C23×C31—21no—
291C23×C31—22no—
292C23×C31—21no—
293C23×C31—22no—
294C23×C31—21no—
295C23×C31—22no—
296C23×C31—21no—
297C23×C31—21no—
298C23×C31—21no—
299C23×C31—21no—
300C23×C31—22no—
301C23×C31—48no—
302C23×C31—41no—
303C23×C31—41no—
304C23×C31—41no—
305C23×C31—41no—
306C23×C31—41no—
307C23×C31—41no—
308C23×C31—41no—
309C23×C31—41no—
310C23×C31—41no—
311C23×C31—41no—
312C23×C31—48no—
313C23×C31—84no—
314C23×C31—84no—
315C23×C31—84no—
316C23×C31—84no—
317C23×C31—84no—
318C23×C31C2×C22⋊C412yes—
319C23×C31C2×C22⋊C412yes—
320C23×C31AGL(1,ℤ/8)12yes—
321C23×C31#13712yes—
322C23×C31C22×D411yescharacteristic
323Q8×C31—22no—
324Q8×C31—22no—
325Q8×C31—41no—
326Q8×C31—41no—
327D4×C31—28no—
328D4×C31—22no—
329D4×C31—22no—
330D4×C31—22no—
331D4×C31—22no—
332D4×C31—22no—
333D4×C31—48no—
334D4×C31—48no—
335D4×C31—41no—
336D4×C31—41no—
337D4×C31—84no—
338D4×C31C4×D414yescomplemented
339C2×C4×C31—21no—
340C2×C4×C31—21no—
341C2×C4×C31—21no—
342C2×C4×C31—21no—
343C2×C4×C31—21no—
344C2×C4×C31—21no—
345C2×C4×C31—21no—
346C2×C4×C31—21no—
347C2×C4×C31—22no—
348C2×C4×C31—22no—
349C2×C4×C31—22no—
350C2×C4×C31—22no—
351C2×C4×C31—22no—
352C2×C4×C31—22no—
353C2×C4×C31—22no—
354C2×C4×C31—22no—
355C2×C4×C31—22no—
356C2×C4×C31—22no—
357C2×C4×C31—22no—
358C2×C4×C31—48no—
359C2×C4×C31—41no—
360C2×C4×C31—41no—
361C2×C4×C31—41no—
362C2×C4×C31—41no—
363C2×C4×C31—41no—
364C2×C4×C31—41no—
365C2×C4×C31—41no—
366C2×C4×C31—41no—
367C2×C4×C31—41no—
368C2×C4×C31—41no—
369C2×C4×C31—41no—
370C2×C4×C31—41no—
371C2×C4×C31—41no—
372C2×C4×C31—41no—
373C2×C4×C31—41no—
374C2×C4×C31—84no—
375C2×C4×C31—84no—
376C2×C4×C31—84no—
377C2×C4×C31C2×C22⋊C412yes—
378C2×C4×C31C2×C22⋊C412yes—
379C2×C4×C31C2×C22⋊C412yes—
380C2×C4×C31C2×C22⋊C412yes—
381C2×C4×C31C23×C411yescharacteristic
382C2×C4×C31C22×D411yescharacteristic
383C2×C4×C31C22×D411yescharacteristic
384C2×C4×C31C2×#4111yescharacteristic
385C2×C4×C31H(5,𝔽2)11yescharacteristic
386C2×C4×C31H(5,𝔽2)11yescharacteristic
387C8×C31—22no—
388C8×C31—41no—
389C8×C31—41no—
390C8×C31—41no—
391C2×#546C2×C3111yescharacteristic
392C2×#435C2×C3111yescharacteristic, complemented
393C2×#417C2×C3111yescharacteristic, complemented
394C22×#102C2×C3111yescharacteristic, complemented
395D4×C4⋊C4C2×C3111yescharacteristic, complemented
396#1983C2×C3111yescharacteristic, complemented
397#1959C2×C3111yescharacteristic, complemented
398#1895C2×C3111yescharacteristic, complemented
399#1892C2×C3111yescharacteristic, complemented
400#1874C2×C3111yescharacteristic, complemented
401#1872C2×C3111yescharacteristic, complemented
402#1802C2×C3111yescharacteristic, complemented
403#1788C2×C3111yescharacteristic, complemented
404#1786C2×C3111yescharacteristic, complemented
405#1762C2×C3111yescharacteristic, complemented
406C22×C31—22no—
407C22×C31—22no—
408C22×C31—22no—
409C22×C31—22no—
410C22×C31—22no—
411C22×C31—22no—
412C22×C31—22no—
413C22×C31—24no—
414C22×C31—22no—
415C22×C31—22no—
416C22×C31—42no—
417C22×C31—42no—
418C22×C31—41no—
419C22×C31—42no—
420C22×C31—41no—
421C22×C31—42no—
422C22×C31—41no—
423C22×C31—42no—
424C22×C31—41no—
425C22×C31—42no—
426C22×C31—42no—
427C22×C31—42no—
428C22×C31—42no—
429C22×C31—816no—
430C22×C31—81no—
431C22×C31—81no—
432C22×C31—81no—
433C22×C31—81no—
434C22×C31#41714yescomplemented
435C22×C31C22×C22⋊C411yescharacteristic
436C22×C31D4211yescharacteristic
437C22×C31#54611yescharacteristic
438C22×C31C2×AGL(1,ℤ/8)11yescharacteristic
439C22×C31C2×#13711yescharacteristic
440C22×C31#57611yescharacteristic
441C22×C31#57711yescharacteristic
442C4×C31—22no—
443C4×C31—22no—
444C4×C31—22no—
445C4×C31—22no—
446C4×C31—42no—
447C4×C31—42no—
448C4×C31—42no—
449C4×C31—81no—
450C4×C31—81no—
451C4×C31—81no—
452C4×C31C2×C4×D411yescharacteristic
453C4×C31#51811yescharacteristic
454C4×C31D4211yescharacteristic
455C4×C31#54611yescharacteristic
456C22×#41C22×C3111yescharacteristic
457C23×D4C22×C3111yescharacteristic
458C22×M16C22×C3111yescharacteristic, complemented
459C23×C8C22×C3111yescharacteristic
460#546—24no—
461#546C4×C3118yescomplemented
462C2×#124C22×C3111yescharacteristic
463C2×#123—21no—
464C2×C22⋊Q8C22×C3111yescharacteristic
465C2×#121—21no—
466C2×#121C22×C3111yescharacteristic
467C2×#120—21no—
468C2×C4×D4—21no—
469C2×C4×D4C22×C3111yescharacteristic
470C2×C4×D4C22×C3111yescharacteristic
471C22×C4⋊C4C22×C3111yescharacteristic
472C22×C4⋊C4C22×C3111yescharacteristic, complemented
473C22×C22⋊C4—21no—
474#435—24no—
475C2×C4⋊C8C22×C3111yescharacteristic, complemented
476#417—24no—
477C2×#103C22×C3111yescharacteristic, complemented
478C2×#103C22×C3111yescharacteristic, complemented
479C2×#103C22×C3111yescharacteristic, complemented
480C2×#103C22×C3111yescharacteristic, complemented
481C2×#102—24no—
482C2×#102C22×C3111yescharacteristic
483C2×#102C22×C3111yescharacteristic
484C2×#102C22×C3111yescharacteristic
485C2×#102C22×C3111yescharacteristic
486C2×#102C22×C3111yescharacteristic
487C2×#102C22×C3111yescharacteristic
488C2×#102C22×C3111yescharacteristic
489C2×#102C22×C3111yescharacteristic
490C2×C22⋊C8C22×C3111yescharacteristic
491C2×C22⋊C8C22×C3111yescharacteristic, complemented
492C2×#97C22×C3111yescharacteristic, complemented
493#389—21no—
494#385—21no—
495#385—21no—
496#384C22×C3111yescharacteristic, complemented
497#380C22×C3111yescharacteristic
498#380C22×C3111yescharacteristic, complemented
499C4×C4⋊C4C22×C3111yescharacteristic, complemented
500#340C22×C3111yescharacteristic, complemented
501#340C22×C3111yescharacteristic, complemented
502#340C22×C3111yescharacteristic, complemented
503#340C22×C3111yescharacteristic, complemented
504C2×C31—24no—
505C2×C31—42no—
506C2×C31—44no—
507C2×C31—82no—
508C2×C31D4×C22⋊C411yescharacteristic
509C2×C31C2×#41711yescharacteristic
510C2×C31#289711yescharacteristic
511C2×C31#326411yescharacteristic
512C2×C31#326611yescharacteristic
513C2×C31#330611yescharacteristic
514C2×C31#331411yescharacteristic
515C25—21no—
516C2×#41—22no—
517C2×#41—22no—
518C2×#41—22no—
519C2×#41—41no—
520C2×#41—41no—
521C2×#41C2×C4×C3114yescomplemented
522C22×Q8C23×C3111yescharacteristic
523C22×D4—22no—
524C22×D4—22no—
525C22×D4—21no—
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—22no—
529C22×D4—41no—
530C22×D4—41no—
531C22×D4C2×C4×C3114yescomplemented
532C22×D4D4×C3111yescharacteristic
533C22×D4C23×C3111yescharacteristic
534C22×D4C23×C3111yescharacteristic
535C23×C4—21no—
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—21no—
539C23×C4C23×C3111yescharacteristic
540C23×C4C23×C3111yescharacteristic
541C2×M16—22no—
542C2×M16—22no—
543C2×M16—41no—
544C22×C8—22no—
545C22×C8—22no—
546C22×C8—41no—
547C22×C8C23×C3111yescharacteristic
548C22×C8C23×C3111yescharacteristic
549C22×C8C23×C3111yescharacteristic
550C22×C8C23×C3111yescharacteristic
551#124—22no—
552#124C2×C4×C3114yescomplemented
553#123—28no—
554C22⋊Q8—22no—
555C22⋊Q8C2×C4×C3114yescomplemented
556#121—22no—
557#121—28no—
558#121C2×C4×C3114yescomplemented
559#120—28no—
560C4×D4—22no—
561C4×D4—44no—
562C4×D4C2×C4×C3114yes—
563C4×D4C2×C4×C3114yescomplemented
564C4×D4D4×C3114yes—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—22no—
567C2×C4⋊C4—22no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—41no—
573C2×C4⋊C4—41no—
574C2×C4⋊C4D4×C3111yescharacteristic
575C2×C4⋊C4C23×C3111yescharacteristic
576C2×C4⋊C4C23×C3111yescharacteristic
577C2×C4⋊C4C23×C3111yescharacteristic
578C2×C4⋊C4C23×C3111yescharacteristic
579C2×C4⋊C4C23×C3111yescharacteristic
580C2×C22⋊C4—21no—
581C2×C22⋊C4—21no—
582C2×C22⋊C4—21no—
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—28no—
586C2×C22⋊C4—21no—
587C2×C22⋊C4—21no—
588C2×C22⋊C4D4×C3111yescharacteristic
589C2×C22⋊C4D4×C3111yescharacteristic
590C2×C42—21no—
591C2×C42C23×C3111yescharacteristic
592C4⋊C8—22no—
593#103—22no—
594#103—22no—
595#103—41no—
596#103—41no—
597#102—22no—
598#102—22no—
599#102—22no—
600#102—22no—
601#102—22no—
602#102—41no—
603#102—41no—
604#102D4×C3114yescomplemented
605C22⋊C8—22no—
606C22⋊C8—22no—
607#97—22no—
608#95—21no—
609#95—21no—
610#95—21no—
611C31#2241911yescharacteristic, direct product factor, Sylow
612C24—21no—
613C24—21no—
614C24—24no—
615C24—42no—
616C24—42no—
617C24—42no—
618C24—42no—
619C24—81no—
620C24—81no—
621C24C2×D4×C3111yescharacteristic
622C24C2×D4×C3111yescharacteristic
623#41—28no—
624#41—44no—
625#41—44no—
626#41—44no—
627C2×Q8—21no—
628C2×Q8—21no—
629C2×Q8—21no—
630C2×Q8—21no—
631C2×Q8—21no—
632C2×Q8C22×C4×C3112yes—
633C2×D4—22no—
634C2×D4—22no—
635C2×D4—28no—
636C2×D4—24no—
637C2×D4—24no—
638C2×D4—24no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—21no—
647C2×D4—44no—
648C2×D4—44no—
649C2×D4—44no—
650C2×D4—42no—
651C2×D4—42no—
652C2×D4—42no—
653C2×D4—42no—
654C2×D4—81no—
655C2×D4—81no—
656C2×D4C22⋊C4×C3114yes—
657C2×D4C22×C4×C3112yes—
658C2×D4C22×C4×C3112yes—
659C2×D4C2×D4×C3112yes—
660C2×D4#41×C3112yes—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—24no—
673C22×C4—24no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—42no—
678C22×C4—42no—
679C22×C4—42no—
680C22×C4—42no—
681C22×C4—42no—
682C22×C4—42no—
683C22×C4—81no—
684C22×C4—81no—
685C22×C4—81no—
686C22×C4—81no—
687C22×C4C22×C4×C3112yes—
688C22×C4C22×C4×C3112yes—
689C22×C4C2×D4×C3111yescharacteristic
690C22×C4C2×D4×C3111yescharacteristic
691C22×C4C2×D4×C3111yescharacteristic
692C22×C4C2×D4×C3111yescharacteristic
693C22×C4C2×D4×C3112yes—
694C22×C4C2×D4×C3112yes—
695C22×C4C24×C3111yescharacteristic
696M16—44no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—21no—
702C2×C8—21no—
703C2×C8—21no—
704C2×C8—21no—
705C2×C8—21no—
706C2×C8—21no—
707C2×C8—21no—
708C2×C8—44no—
709C2×C8C2×D4×C3112yes—
710C4⋊C4—24no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—42no—
720C4⋊C4—42no—
721C4⋊C4—42no—
722C4⋊C4—81no—
723C4⋊C4C22⋊C4×C3114yes—
724C4⋊C4C22×C4×C3112yes—
725C4⋊C4C2×D4×C3112yes—
726C22⋊C4—24no—
727C22⋊C4—24no—
728C22⋊C4—24no—
729C22⋊C4—24no—
730C22⋊C4—24no—
731C22⋊C4—42no—
732C22⋊C4—42no—
733C22⋊C4C22⋊C4×C3114yes—
734C22⋊C4C22⋊C4×C3114yes—
735C42—42no—
736C42C22×C4×C3112yes—
737C42C2×D4×C3112yes—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—22no—
743C23—21no—
744C23—22no—
745C23—21no—
746C23—22no—
747C23—21no—
748C23—21no—
749C23—21no—
750C23—21no—
751C23—22no—
752C23—48no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—48no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—84no—
765C23—84no—
766C23—84no—
767C23—84no—
768C23—84no—
769C23C2×C22⋊C4×C3112yes—
770C23C2×C22⋊C4×C3112yes—
771C23C31×AGL(1,ℤ/8)12yes—
772C23C31×#13712yes—
773C23C22×D4×C3111yescharacteristic
774Q8—22no—
775Q8—22no—
776Q8—41no—
777Q8—41no—
778D4—28no—
779D4—22no—
780D4—22no—
781D4—22no—
782D4—22no—
783D4—22no—
784D4—48no—
785D4—48no—
786D4—41no—
787D4—41no—
788D4—84no—
789D4C4×D4×C3114yescomplemented
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—48no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—84no—
826C2×C4—84no—
827C2×C4—84no—
828C2×C4C2×C22⋊C4×C3112yes—
829C2×C4C2×C22⋊C4×C3112yes—
830C2×C4C2×C22⋊C4×C3112yes—
831C2×C4C2×C22⋊C4×C3112yes—
832C2×C4C23×C4×C3111yescharacteristic
833C2×C4C22×D4×C3111yescharacteristic
834C2×C4C22×D4×C3111yescharacteristic
835C2×C4C2×#41×C3111yescharacteristic
836C2×C4C31×H(5,𝔽2)11yescharacteristic
837C2×C4C31×H(5,𝔽2)11yescharacteristic
838C8—22no—
839C8—41no—
840C8—41no—
841C8—41no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—24no—
850C22—22no—
851C22—22no—
852C22—42no—
853C22—42no—
854C22—41no—
855C22—42no—
856C22—41no—
857C22—42no—
858C22—41no—
859C22—42no—
860C22—41no—
861C22—42no—
862C22—42no—
863C22—42no—
864C22—42no—
865C22—816no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22—81no—
870C22C31×#41714yescomplemented
871C22C22×C22⋊C4×C3111yescharacteristic
872C22D42×C3111yescharacteristic
873C22C31×#54611yescharacteristic
874C22C2×C31×AGL(1,ℤ/8)11yescharacteristic
875C22C2×C31×#13711yescharacteristic
876C22C31×#57611yescharacteristic
877C22C31×#57711yescharacteristic
878C4—22no—
879C4—22no—
880C4—22no—
881C4—22no—
882C4—42no—
883C4—42no—
884C4—42no—
885C4—81no—
886C4—81no—
887C4—81no—
888C4C2×C4×D4×C3111yescharacteristic
889C4C31×#51811yescharacteristic
890C4D42×C3111yescharacteristic
891C4C31×#54611yescharacteristic
892C2—24no—
893C2—42no—
894C2—44no—
895C2—82no—
896C2D4×C22⋊C4×C3111yescharacteristic
897C2C2×C31×#41711yescharacteristic
898C2C31×#289711yescharacteristic
899C2C31×#326411yescharacteristic
900C2C31×#326611yescharacteristic
901C2C31×#330611yescharacteristic
902C2C31×#331411yescharacteristic
subgroupG/H
center, socleC23×C31C22×D4
commutatorC2×C4C23×C4×C31
Frattini, cosocleC22×C4C24×C31
prime radicalC2×C31×#546C2
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×#417C2semidirect
4. C22×C31×#102C2semidirect
5. D4×C4⋊C4×C31C2semidirect
6. C31×#1983C2semidirect
7. C31×#1959C2semidirect
8. C31×#1895C2semidirect
9. C31×#1892C2semidirect
10. C31×#1874C2semidirect
11. C31×#1872C2semidirect
12. C31×#1802C2semidirect
13. C31×#1788C2semidirect
14. C31×#1786C2semidirect
15. C31×#1762C2semidirect
18. C22×M16×C31C22semidirect
21. C31×#546C4semidirect
32. C22×C4⋊C4×C31C22semidirect
35. C2×C31×C4⋊C8C22semidirect
37. C2×C31×#103C22semidirect
38. C2×C31×#103C22semidirect
39. C2×C31×#103C22semidirect
40. C2×C31×#103C22semidirect
51. C2×C31×C22⋊C8C22semidirect
52. C2×C31×#97C22semidirect
56. C31×#384C22semidirect
58. C31×#380C22semidirect
59. C4×C4⋊C4×C31C22semidirect
60. C31×#340C22semidirect
61. C31×#340C22semidirect
62. C31×#340C22semidirect
63. C31×#340C22semidirect
70. C2×#41×C31C2×C4semidirect
80. C22×D4×C31C2×C4semidirect
101. C31×#124C2×C4semidirect
104. C31×C22⋊Q8C2×C4semidirect
107. C31×#121C2×C4semidirect
112. C4×D4×C31C2×C4semidirect
153. C31×#102D4semidirect
286. #22419C31direct (N × H)
338. D4×C31C4×D4semidirect
392. C2×#435C2×C31semidirect
393. C2×#417C2×C31semidirect
394. C22×#102C2×C31semidirect
395. D4×C4⋊C4C2×C31semidirect
396. #1983C2×C31semidirect
397. #1959C2×C31semidirect
398. #1895C2×C31semidirect
399. #1892C2×C31semidirect
400. #1874C2×C31semidirect
401. #1872C2×C31semidirect
402. #1802C2×C31semidirect
403. #1788C2×C31semidirect
404. #1786C2×C31semidirect
405. #1762C2×C31semidirect
434. C22×C31#417semidirect
458. C22×M16C22×C31semidirect
461. #546C4×C31semidirect
472. C22×C4⋊C4C22×C31semidirect
475. C2×C4⋊C8C22×C31semidirect
477. C2×#103C22×C31semidirect
478. C2×#103C22×C31semidirect
479. C2×#103C22×C31semidirect
480. C2×#103C22×C31semidirect
491. C2×C22⋊C8C22×C31semidirect
492. C2×#97C22×C31semidirect
496. #384C22×C31semidirect
498. #380C22×C31semidirect
499. C4×C4⋊C4C22×C31semidirect
500. #340C22×C31semidirect
501. #340C22×C31semidirect
502. #340C22×C31semidirect
503. #340C22×C31semidirect
521. C2×#41C2×C4×C31semidirect
531. C22×D4C2×C4×C31semidirect
552. #124C2×C4×C31semidirect
555. C22⋊Q8C2×C4×C31semidirect
558. #121C2×C4×C31semidirect
563. C4×D4C2×C4×C31semidirect
604. #102D4×C31semidirect
611. C31#22419direct (N × H)
789. D4C4×D4×C31semidirect
870. C22C31×#417semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#5462
C2×C31×#4352
C2×C31×#4172
C22×C31×#1022
D4×C4⋊C4×C312
C31×#19832
C31×#19592
C31×#18952
C31×#18922
C31×#18742
C31×#18722
C31×#18022
C31×#17882
C31×#17862
C31×#17622
#2241931