Finite Group Databasebeta

← C31×#22427 #21479186

Subgroups — C31×#22427 #21479186

Order 7936.

1606 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#546C211yesmaximal, characteristic
2C2×C31×#436C211yesmaximal, characteristic, complemented
3C2×C31×#417C211yesmaximal, characteristic, complemented
4C2×C31×#418C211yesmaximal, characteristic, complemented
5C31×#2352C211yesmaximal, characteristic, complemented
6C31×#1983C211yesmaximal, characteristic, complemented
7C31×#1958C211yesmaximal, characteristic, complemented
8C31×#1895C211yesmaximal, characteristic, complemented
9C31×#1894C211yesmaximal, characteristic, complemented
10C31×#1874C211yesmaximal, characteristic, complemented
11C31×#1873C211yesmaximal, characteristic, complemented
12C31×#1804C211yesmaximal, characteristic, complemented
13C31×#1788C211yesmaximal, characteristic, complemented
14C31×#1786C211yesmaximal, characteristic, complemented
15C4×C31×#102C211yesmaximal, characteristic, complemented
16C22×#41×C31C2211yescharacteristic
17C23×D4×C31C2211yescharacteristic
18C22×M16×C31C2211yescharacteristic
19C22×M16×C31C2211yescharacteristic, complemented
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×C31C2211yescharacteristic
29C2×C4×D4×C31C2211yescharacteristic
30C2×C31×#117C2211yescharacteristic
31C22×C4⋊C4×C31C2211yescharacteristic, complemented
32C22×C22⋊C4×C31—21no—
33C31×#436—24no—
34C2×C31×C4⋊C8C2211yescharacteristic, complemented
35C31×#418—24no—
36C31×#417—24no—
37C2×C31×#103C2211yescharacteristic, complemented
38C2×C31×#103C2211yescharacteristic, complemented
39C2×C31×#103C2211yescharacteristic, complemented
40C2×C31×#103C2211yescharacteristic, complemented
41C2×C31×#102C2211yescharacteristic
42C2×C31×#102C2211yescharacteristic
43C2×C31×#102C2211yescharacteristic
44C2×C31×#102C2211yescharacteristic
45C2×C31×#102C2211yescharacteristic
46C2×C31×#102C2211yescharacteristic
47C2×C31×#102C2211yescharacteristic
48C2×C31×#102C2211yescharacteristic
49C2×C31×C22⋊C8C2211yescharacteristic
50C2×C31×C22⋊C8C2211yescharacteristic, complemented
51C2×C4×C8×C31C2211yescharacteristic, complemented
52C31×#388—21no—
53C31×#387—21no—
54C31×#386—21no—
55C31×#382C2211yescharacteristic, complemented
56C31×#380C2211yescharacteristic
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—
65C2×#41×C31—22no—
66C2×#41×C31—22no—
67C2×#41×C31—22no—
68C2×#41×C31—41no—
69C2×#41×C31—41no—
70C2×#41×C31C2×C414yes—
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×C31C2311yescharacteristic
88C23×C4×C31C2311yescharacteristic
89C2×M16×C31—22no—
90C2×M16×C31—22no—
91C2×M16×C31—22no—
92C2×M16×C31—22no—
93C2×M16×C31—41no—
94C2×M16×C31—41no—
95C22×C8×C31C2311yescharacteristic
96C22×C8×C31C2311yescharacteristic
97C22×C8×C31C2311yescharacteristic
98C22×C8×C31C2311yescharacteristic
99C31×#124—22no—
100C31×#124C2×C414yescomplemented
101C31×#123—28no—
102C31×C22⋊Q8—22no—
103C31×C22⋊Q8C2×C414yescomplemented
104C31×#121—22no—
105C31×#121—28no—
106C31×#121C2×C414yes—
107C31×#120—28no—
108C4×D4×C31—22no—
109C4×D4×C31C2×C414yes—
110C4×D4×C31C2×C414yescomplemented
111C4×D4×C31D414yes—
112C31×#117—22no—
113C31×#117—41no—
114C2×C4⋊C4×C31—21no—
115C2×C4⋊C4×C31—22no—
116C2×C4⋊C4×C31—21no—
117C2×C4⋊C4×C31—41no—
118C2×C4⋊C4×C31D411yescharacteristic
119C2×C4⋊C4×C31C2311yescharacteristic
120C2×C4⋊C4×C31C2311yescharacteristic
121C2×C4⋊C4×C31C2311yescharacteristic
122C2×C4⋊C4×C31C2311yescharacteristic
123C2×C4⋊C4×C31C2311yescharacteristic
124C2×C22⋊C4×C31—21no—
125C2×C22⋊C4×C31—21no—
126C2×C22⋊C4×C31—21no—
127C2×C22⋊C4×C31—21no—
128C2×C22⋊C4×C31—21no—
129C2×C22⋊C4×C31—28no—
130C2×C22⋊C4×C31—21no—
131C2×C22⋊C4×C31—21no—
132C2×C22⋊C4×C31—21no—
133C2×C22⋊C4×C31D411yescharacteristic
134C2×C22⋊C4×C31D411yescharacteristic
135C2×C42×C31—21no—
136C2×C42×C31—21no—
137C2×C42×C31C2311yescharacteristic
138C31×C4⋊C8—22no—
139C31×#103—22no—
140C31×#103—22no—
141C31×#103—41no—
142C31×#103—41no—
143C31×#102—22no—
144C31×#102—22no—
145C31×#102—22no—
146C31×#102—22no—
147C31×#102—22no—
148C31×#102—41no—
149C31×#102—41no—
150C31×#102D414yescomplemented
151C31×C22⋊C8—22no—
152C31×C22⋊C8—22no—
153C4×C8×C31—22no—
154C31×#95—21no—
155C31×#95—21no—
156C31×#95—21no—
157C31×#95—21no—
158C31×#95—21no—
159C24×C31—21no—
160C24×C31—21no—
161C24×C31—24no—
162C24×C31—42no—
163C24×C31—42no—
164C24×C31—42no—
165C24×C31—42no—
166C24×C31—81no—
167C24×C31—81no—
168C24×C31C2×D411yescharacteristic
169C24×C31C2×D411yescharacteristic
170#41×C31—28no—
171#41×C31—44no—
172#41×C31—44no—
173#41×C31—44no—
174C2×Q8×C31—21no—
175C2×Q8×C31—21no—
176C2×Q8×C31—21no—
177C2×Q8×C31—21no—
178C2×Q8×C31—21no—
179C2×Q8×C31C22×C412yes—
180C2×D4×C31—28no—
181C2×D4×C31—24no—
182C2×D4×C31—24no—
183C2×D4×C31—24no—
184C2×D4×C31—21no—
185C2×D4×C31—21no—
186C2×D4×C31—21no—
187C2×D4×C31—21no—
188C2×D4×C31—21no—
189C2×D4×C31—21no—
190C2×D4×C31—21no—
191C2×D4×C31—21no—
192C2×D4×C31—44no—
193C2×D4×C31—44no—
194C2×D4×C31—44no—
195C2×D4×C31—41no—
196C2×D4×C31—41no—
197C2×D4×C31—42no—
198C2×D4×C31—42no—
199C2×D4×C31—42no—
200C2×D4×C31—42no—
201C2×D4×C31—81no—
202C2×D4×C31—81no—
203C2×D4×C31C22⋊C414yes—
204C2×D4×C31C22×C412yes—
205C2×D4×C31C22×C412yes—
206C2×D4×C31C2×D412yes—
207C2×D4×C31#4112yes—
208C22×C4×C31—21no—
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—24no—
220C22×C4×C31—24no—
221C22×C4×C31—21no—
222C22×C4×C31—21no—
223C22×C4×C31—21no—
224C22×C4×C31—42no—
225C22×C4×C31—42no—
226C22×C4×C31—42no—
227C22×C4×C31—42no—
228C22×C4×C31—81no—
229C22×C4×C31—81no—
230C22×C4×C31—81no—
231C22×C4×C31C22×C412yes—
232C22×C4×C31C22×C412yes—
233C22×C4×C31C2×D411yescharacteristic
234C22×C4×C31C2×D411yescharacteristic
235C22×C4×C31C2×D411yescharacteristic
236C22×C4×C31C2×D411yescharacteristic
237C22×C4×C31C2×D412yes—
238C22×C4×C31C2×D412yes—
239C22×C4×C31C2411yescharacteristic
240M16×C31—44no—
241M16×C31—44no—
242C2×C8×C31—21no—
243C2×C8×C31—21no—
244C2×C8×C31—21no—
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×C31C2×D412yes—
254C4⋊C4×C31—24no—
255C4⋊C4×C31—21no—
256C4⋊C4×C31—21no—
257C4⋊C4×C31—21no—
258C4⋊C4×C31—21no—
259C4⋊C4×C31—21no—
260C4⋊C4×C31—21no—
261C4⋊C4×C31—21no—
262C4⋊C4×C31—21no—
263C4⋊C4×C31—42no—
264C4⋊C4×C31C22⋊C414yes—
265C4⋊C4×C31C22×C412yes—
266C4⋊C4×C31C2×D412yes—
267C22⋊C4×C31—24no—
268C22⋊C4×C31—24no—
269C22⋊C4×C31—24no—
270C22⋊C4×C31—24no—
271C22⋊C4×C31—24no—
272C22⋊C4×C31—42no—
273C22⋊C4×C31—42no—
274C22⋊C4×C31—81no—
275C22⋊C4×C31C22⋊C414yes—
276C22⋊C4×C31C22⋊C414yes—
277C42×C31—42no—
278C42×C31—81no—
279C42×C31C22×C412yes—
280C42×C31C2×D412yes—
281#22427C3111yesmaximal, characteristic, direct product factor, Sylow
282C23×C31—22no—
283C23×C31—21no—
284C23×C31—21no—
285C23×C31—22no—
286C23×C31—21no—
287C23×C31—21no—
288C23×C31—22no—
289C23×C31—21no—
290C23×C31—21no—
291C23×C31—21no—
292C23×C31—21no—
293C23×C31—21no—
294C23×C31—21no—
295C23×C31—21no—
296C23×C31—21no—
297C23×C31—22no—
298C23×C31—48no—
299C23×C31—48no—
300C23×C31—41no—
301C23×C31—41no—
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—84no—
311C23×C31—84no—
312C23×C31—84no—
313C23×C31—84no—
314C23×C31—84no—
315C23×C31C2×C22⋊C412yes—
316C23×C31C2×C22⋊C412yes—
317C23×C31C22×D411yescharacteristic
318Q8×C31—22no—
319Q8×C31—22no—
320Q8×C31—41no—
321Q8×C31—41no—
322D4×C31—22no—
323D4×C31—22no—
324D4×C31—22no—
325D4×C31—22no—
326D4×C31—22no—
327D4×C31—44no—
328D4×C31—48no—
329D4×C31—48no—
330D4×C31—41no—
331D4×C31—41no—
332D4×C31—84no—
333D4×C31C4×D414yes—
334C2×C4×C31—21no—
335C2×C4×C31—21no—
336C2×C4×C31—21no—
337C2×C4×C31—21no—
338C2×C4×C31—21no—
339C2×C4×C31—21no—
340C2×C4×C31—21no—
341C2×C4×C31—21no—
342C2×C4×C31—22no—
343C2×C4×C31—22no—
344C2×C4×C31—22no—
345C2×C4×C31—22no—
346C2×C4×C31—22no—
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—48no—
354C2×C4×C31—41no—
355C2×C4×C31—41no—
356C2×C4×C31—41no—
357C2×C4×C31—41no—
358C2×C4×C31—41no—
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—84no—
370C2×C4×C31—84no—
371C2×C4×C31C2×C22⋊C412yes—
372C2×C4×C31C2×C22⋊C412yes—
373C2×C4×C31C2×C22⋊C412yes—
374C2×C4×C31C2×C22⋊C412yes—
375C2×C4×C31C23×C411yescharacteristic
376C2×C4×C31C22×D411yescharacteristic
377C2×C4×C31C22×D411yescharacteristic
378C2×C4×C31C2×#4111yescharacteristic
379C2×C4×C31H(5,𝔽2)11yescharacteristic
380C2×C4×C31H(5,𝔽2)11yescharacteristic
381C8×C31—22no—
382C8×C31—41no—
383C8×C31—41no—
384C8×C31—41no—
385C2×#546C2×C3111yescharacteristic
386C2×#436C2×C3111yescharacteristic, complemented
387C2×#417C2×C3111yescharacteristic, complemented
388C2×#418C2×C3111yescharacteristic, complemented
389#2352C2×C3111yescharacteristic, complemented
390#1983C2×C3111yescharacteristic, complemented
391#1958C2×C3111yescharacteristic, complemented
392#1895C2×C3111yescharacteristic, complemented
393#1894C2×C3111yescharacteristic, complemented
394#1874C2×C3111yescharacteristic, complemented
395#1873C2×C3111yescharacteristic, complemented
396#1804C2×C3111yescharacteristic, complemented
397#1788C2×C3111yescharacteristic, complemented
398#1786C2×C3111yescharacteristic, complemented
399C4×#102C2×C3111yescharacteristic, complemented
400C22×C31—22no—
401C22×C31—22no—
402C22×C31—24no—
403C22×C31—22no—
404C22×C31—22no—
405C22×C31—22no—
406C22×C31—22no—
407C22×C31—42no—
408C22×C31—42no—
409C22×C31—41no—
410C22×C31—41no—
411C22×C31—42no—
412C22×C31—41no—
413C22×C31—41no—
414C22×C31—42no—
415C22×C31—41no—
416C22×C31—41no—
417C22×C31—42no—
418C22×C31—41no—
419C22×C31—41no—
420C22×C31—42no—
421C22×C31—42no—
422C22×C31—42no—
423C22×C31—42no—
424C22×C31—816no—
425C22×C31—81no—
426C22×C31—81no—
427C22×C31—81no—
428C22×C31—81no—
429C22×C31C22×C22⋊C411yescharacteristic
430C22×C31D4211yescharacteristic
431C22×C31#54611yescharacteristic
432C22×C31#57511yescharacteristic
433C22×C31#57511yescharacteristic
434C22×C31#57611yescharacteristic
435C22×C31#57711yescharacteristic
436C4×C31—22no—
437C4×C31—22no—
438C4×C31—22no—
439C4×C31—22no—
440C4×C31—42no—
441C4×C31—42no—
442C4×C31—42no—
443C4×C31—81no—
444C4×C31—81no—
445C4×C31—81no—
446C4×C31C2×C4×D411yescharacteristic
447C4×C31#51811yescharacteristic
448C4×C31D4211yescharacteristic
449C4×C31#54611yescharacteristic
450C22×#41C22×C3111yescharacteristic
451C23×D4C22×C3111yescharacteristic
452C22×M16C22×C3111yescharacteristic
453C22×M16C22×C3111yescharacteristic, complemented
454#546—24no—
455#546C4×C3118yescomplemented
456C2×#124C22×C3111yescharacteristic
457C2×#123—21no—
458C2×C22⋊Q8C22×C3111yescharacteristic
459C2×#121—21no—
460C2×#121C22×C3111yescharacteristic
461C2×#120—21no—
462C2×C4×D4C22×C3111yescharacteristic
463C2×C4×D4C22×C3111yescharacteristic
464C2×#117C22×C3111yescharacteristic
465C22×C4⋊C4C22×C3111yescharacteristic, complemented
466C22×C22⋊C4—21no—
467#436—24no—
468C2×C4⋊C8C22×C3111yescharacteristic, complemented
469#418—24no—
470#417—24no—
471C2×#103C22×C3111yescharacteristic, complemented
472C2×#103C22×C3111yescharacteristic, complemented
473C2×#103C22×C3111yescharacteristic, complemented
474C2×#103C22×C3111yescharacteristic, complemented
475C2×#102C22×C3111yescharacteristic
476C2×#102C22×C3111yescharacteristic
477C2×#102C22×C3111yescharacteristic
478C2×#102C22×C3111yescharacteristic
479C2×#102C22×C3111yescharacteristic
480C2×#102C22×C3111yescharacteristic
481C2×#102C22×C3111yescharacteristic
482C2×#102C22×C3111yescharacteristic
483C2×C22⋊C8C22×C3111yescharacteristic
484C2×C22⋊C8C22×C3111yescharacteristic, complemented
485C2×C4×C8C22×C3111yescharacteristic, complemented
486#388—21no—
487#387—21no—
488#386—21no—
489#382C22×C3111yescharacteristic, complemented
490#380C22×C3111yescharacteristic
491#380C22×C3111yescharacteristic, complemented
492C4×C4⋊C4C22×C3111yescharacteristic, complemented
493C4×C22⋊C4—21no—
494#340C22×C3111yescharacteristic, complemented
495#340C22×C3111yescharacteristic, complemented
496#340C22×C3111yescharacteristic, complemented
497#340C22×C3111yescharacteristic, complemented
498C2×C31—42no—
499C2×C31—42no—
500C2×C31—44no—
501C2×C31—82no—
502C2×C31D4×C22⋊C411yescharacteristic
503C2×C31#289611yescharacteristic
504C2×C31#289711yescharacteristic
505C2×C31#327311yescharacteristic
506C2×C31#327511yescharacteristic
507C2×C31#332211yescharacteristic
508C2×C31#332311yescharacteristic
509C25—21no—
510C2×#41—22no—
511C2×#41—22no—
512C2×#41—22no—
513C2×#41—41no—
514C2×#41—41no—
515C2×#41C2×C4×C3114yes—
516C22×Q8C23×C3111yescharacteristic
517C22×D4—22no—
518C22×D4—22no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—22no—
523C22×D4—41no—
524C22×D4—41no—
525C22×D4C2×C4×C3114yescomplemented
526C22×D4D4×C3111yescharacteristic
527C22×D4C23×C3111yescharacteristic
528C22×D4C23×C3111yescharacteristic
529C23×C4—21no—
530C23×C4—21no—
531C23×C4—21no—
532C23×C4C23×C3111yescharacteristic
533C23×C4C23×C3111yescharacteristic
534C2×M16—22no—
535C2×M16—22no—
536C2×M16—22no—
537C2×M16—22no—
538C2×M16—41no—
539C2×M16—41no—
540C22×C8C23×C3111yescharacteristic
541C22×C8C23×C3111yescharacteristic
542C22×C8C23×C3111yescharacteristic
543C22×C8C23×C3111yescharacteristic
544#124—22no—
545#124C2×C4×C3114yescomplemented
546#123—28no—
547C22⋊Q8—22no—
548C22⋊Q8C2×C4×C3114yescomplemented
549#121—22no—
550#121—28no—
551#121C2×C4×C3114yes—
552#120—28no—
553C4×D4—22no—
554C4×D4C2×C4×C3114yes—
555C4×D4C2×C4×C3114yescomplemented
556C4×D4D4×C3114yes—
557#117—22no—
558#117—41no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—22no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—41no—
563C2×C4⋊C4D4×C3111yescharacteristic
564C2×C4⋊C4C23×C3111yescharacteristic
565C2×C4⋊C4C23×C3111yescharacteristic
566C2×C4⋊C4C23×C3111yescharacteristic
567C2×C4⋊C4C23×C3111yescharacteristic
568C2×C4⋊C4C23×C3111yescharacteristic
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—28no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4—21no—
577C2×C22⋊C4—21no—
578C2×C22⋊C4D4×C3111yescharacteristic
579C2×C22⋊C4D4×C3111yescharacteristic
580C2×C42—21no—
581C2×C42—21no—
582C2×C42C23×C3111yescharacteristic
583C4⋊C8—22no—
584#103—22no—
585#103—22no—
586#103—41no—
587#103—41no—
588#102—22no—
589#102—22no—
590#102—22no—
591#102—22no—
592#102—22no—
593#102—41no—
594#102—41no—
595#102D4×C3114yescomplemented
596C22⋊C8—22no—
597C22⋊C8—22no—
598C4×C8—22no—
599#95—21no—
600#95—21no—
601#95—21no—
602#95—21no—
603#95—21no—
604C31#2242711yescharacteristic, direct product factor, Sylow
605C24—21no—
606C24—21no—
607C24—24no—
608C24—42no—
609C24—42no—
610C24—42no—
611C24—42no—
612C24—81no—
613C24—81no—
614C24C2×D4×C3111yescharacteristic
615C24C2×D4×C3111yescharacteristic
616#41—28no—
617#41—44no—
618#41—44no—
619#41—44no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8—21no—
625C2×Q8C22×C4×C3112yes—
626C2×D4—28no—
627C2×D4—24no—
628C2×D4—24no—
629C2×D4—24no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—44no—
639C2×D4—44no—
640C2×D4—44no—
641C2×D4—41no—
642C2×D4—41no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4—42no—
646C2×D4—42no—
647C2×D4—81no—
648C2×D4—81no—
649C2×D4C22⋊C4×C3114yes—
650C2×D4C22×C4×C3112yes—
651C2×D4C22×C4×C3112yes—
652C2×D4C2×D4×C3112yes—
653C2×D4#41×C3112yes—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—24no—
666C22×C4—24no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—42no—
671C22×C4—42no—
672C22×C4—42no—
673C22×C4—42no—
674C22×C4—81no—
675C22×C4—81no—
676C22×C4—81no—
677C22×C4C22×C4×C3112yes—
678C22×C4C22×C4×C3112yes—
679C22×C4C2×D4×C3111yescharacteristic
680C22×C4C2×D4×C3111yescharacteristic
681C22×C4C2×D4×C3111yescharacteristic
682C22×C4C2×D4×C3111yescharacteristic
683C22×C4C2×D4×C3112yes—
684C22×C4C2×D4×C3112yes—
685C22×C4C24×C3111yescharacteristic
686M16—44no—
687M16—44no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8C2×D4×C3112yes—
700C4⋊C4—24no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—21no—
708C4⋊C4—21no—
709C4⋊C4—42no—
710C4⋊C4C22⋊C4×C3114yes—
711C4⋊C4C22×C4×C3112yes—
712C4⋊C4C2×D4×C3112yes—
713C22⋊C4—24no—
714C22⋊C4—24no—
715C22⋊C4—24no—
716C22⋊C4—24no—
717C22⋊C4—24no—
718C22⋊C4—42no—
719C22⋊C4—42no—
720C22⋊C4—81no—
721C22⋊C4C22⋊C4×C3114yes—
722C22⋊C4C22⋊C4×C3114yes—
723C42—42no—
724C42—81no—
725C42C22×C4×C3112yes—
726C42C2×D4×C3112yes—
727C23—22no—
728C23—21no—
729C23—21no—
730C23—22no—
731C23—21no—
732C23—21no—
733C23—22no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—22no—
743C23—48no—
744C23—48no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—84no—
756C23—84no—
757C23—84no—
758C23—84no—
759C23—84no—
760C23C2×C22⋊C4×C3112yes—
761C23C2×C22⋊C4×C3112yes—
762C23C22×D4×C3111yescharacteristic
763Q8—22no—
764Q8—22no—
765Q8—41no—
766Q8—41no—
767D4—22no—
768D4—22no—
769D4—22no—
770D4—22no—
771D4—22no—
772D4—44no—
773D4—48no—
774D4—48no—
775D4—41no—
776D4—41no—
777D4—84no—
778D4C4×D4×C3114yes—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—48no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—84no—
815C2×C4—84no—
816C2×C4C2×C22⋊C4×C3112yes—
817C2×C4C2×C22⋊C4×C3112yes—
818C2×C4C2×C22⋊C4×C3112yes—
819C2×C4C2×C22⋊C4×C3112yes—
820C2×C4C23×C4×C3111yescharacteristic
821C2×C4C22×D4×C3111yescharacteristic
822C2×C4C22×D4×C3111yescharacteristic
823C2×C4C2×#41×C3111yescharacteristic
824C2×C4C31×H(5,𝔽2)11yescharacteristic
825C2×C4C31×H(5,𝔽2)11yescharacteristic
826C8—22no—
827C8—41no—
828C8—41no—
829C8—41no—
830C22—22no—
831C22—22no—
832C22—24no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—22no—
837C22—42no—
838C22—42no—
839C22—41no—
840C22—41no—
841C22—42no—
842C22—41no—
843C22—41no—
844C22—42no—
845C22—41no—
846C22—41no—
847C22—42no—
848C22—41no—
849C22—41no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—816no—
855C22—81no—
856C22—81no—
857C22—81no—
858C22—81no—
859C22C22×C22⋊C4×C3111yescharacteristic
860C22D42×C3111yescharacteristic
861C22C31×#54611yescharacteristic
862C22C31×#57511yescharacteristic
863C22C31×#57511yescharacteristic
864C22C31×#57611yescharacteristic
865C22C31×#57711yescharacteristic
866C4—22no—
867C4—22no—
868C4—22no—
869C4—22no—
870C4—42no—
871C4—42no—
872C4—42no—
873C4—81no—
874C4—81no—
875C4—81no—
876C4C2×C4×D4×C3111yescharacteristic
877C4C31×#51811yescharacteristic
878C4D42×C3111yescharacteristic
879C4C31×#54611yescharacteristic
880C2—42no—
881C2—42no—
882C2—44no—
883C2—82no—
884C2D4×C22⋊C4×C3111yescharacteristic
885C2C31×#289611yescharacteristic
886C2C31×#289711yescharacteristic
887C2C31×#327311yescharacteristic
888C2C31×#327511yescharacteristic
889C2C31×#332211yescharacteristic
890C2C31×#332311yescharacteristic
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×#436C2semidirect
3. C2×C31×#417C2semidirect
4. C2×C31×#418C2semidirect
5. C31×#2352C2semidirect
6. C31×#1983C2semidirect
7. C31×#1958C2semidirect
8. C31×#1895C2semidirect
9. C31×#1894C2semidirect
10. C31×#1874C2semidirect
11. C31×#1873C2semidirect
12. C31×#1804C2semidirect
13. C31×#1788C2semidirect
14. C31×#1786C2semidirect
15. C4×C31×#102C2semidirect
19. C22×M16×C31C22semidirect
21. C31×#546C4semidirect
31. C22×C4⋊C4×C31C22semidirect
34. C2×C31×C4⋊C8C22semidirect
37. C2×C31×#103C22semidirect
38. C2×C31×#103C22semidirect
39. C2×C31×#103C22semidirect
40. C2×C31×#103C22semidirect
50. C2×C31×C22⋊C8C22semidirect
51. C2×C4×C8×C31C22semidirect
55. C31×#382C22semidirect
57. C31×#380C22semidirect
58. C4×C4⋊C4×C31C22semidirect
60. C31×#340C22semidirect
61. C31×#340C22semidirect
62. C31×#340C22semidirect
63. C31×#340C22semidirect
80. C22×D4×C31C2×C4semidirect
100. C31×#124C2×C4semidirect
103. C31×C22⋊Q8C2×C4semidirect
110. C4×D4×C31C2×C4semidirect
150. C31×#102D4semidirect
281. #22427C31direct (N × H)
386. C2×#436C2×C31semidirect
387. C2×#417C2×C31semidirect
388. C2×#418C2×C31semidirect
389. #2352C2×C31semidirect
390. #1983C2×C31semidirect
391. #1958C2×C31semidirect
392. #1895C2×C31semidirect
393. #1894C2×C31semidirect
394. #1874C2×C31semidirect
395. #1873C2×C31semidirect
396. #1804C2×C31semidirect
397. #1788C2×C31semidirect
398. #1786C2×C31semidirect
399. C4×#102C2×C31semidirect
453. C22×M16C22×C31semidirect
455. #546C4×C31semidirect
465. C22×C4⋊C4C22×C31semidirect
468. C2×C4⋊C8C22×C31semidirect
471. C2×#103C22×C31semidirect
472. C2×#103C22×C31semidirect
473. C2×#103C22×C31semidirect
474. C2×#103C22×C31semidirect
484. C2×C22⋊C8C22×C31semidirect
485. C2×C4×C8C22×C31semidirect
489. #382C22×C31semidirect
491. #380C22×C31semidirect
492. C4×C4⋊C4C22×C31semidirect
494. #340C22×C31semidirect
495. #340C22×C31semidirect
496. #340C22×C31semidirect
497. #340C22×C31semidirect
525. C22×D4C2×C4×C31semidirect
545. #124C2×C4×C31semidirect
548. C22⋊Q8C2×C4×C31semidirect
555. C4×D4C2×C4×C31semidirect
595. #102D4×C31semidirect
604. C31#22427direct (N × H)

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×#4362
C2×C31×#4172
C2×C31×#4182
C31×#23522
C31×#19832
C31×#19582
C31×#18952
C31×#18942
C31×#18742
C31×#18732
C31×#18042
C31×#17882
C31×#17862
C4×C31×#1022
#2242731