Finite Group Databasebeta

← C31×#17559 #21474318

Subgroups — C31×#17559 #21474318

Order 7936.

1438 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#525C211yesmaximal, characteristic
2C2×C31×#407C211yesmaximal, characteristic, complemented
3C31×#2280C211yesmaximal, characteristic, complemented
4C31×#1513C214yesmaximal, complemented
5C31×#1511C212yesmaximal, complemented
6C31×#1510C212yesmaximal, complemented
7C31×#1501C214yesmaximal, complemented
8C22×#41×C31C411yescharacteristic, complemented
9C24×C4×C31C2211yescharacteristic
10C22×M16×C31—21no—
11C31×#525—21no—
12C31×#525—21no—
13C31×#525—21no—
14C31×#525—21no—
15C31×#525C412yescomplemented
16C31×#525C412yescomplemented
17C31×#525C2212yes—
18C31×#525C2212yes—
19C2×C31×#123—21no—
20C2×C31×C22⋊Q8C411yescharacteristic, complemented
21C2×C31×C22⋊Q8C2211yescharacteristic
22C2×C31×#121C411yescharacteristic, complemented
23C2×C31×#121C2211yescharacteristic
24C2×C31×#120—21no—
25C2×C4×D4×C31—21no—
26C2×C4×D4×C31—21no—
27C2×C31×#117—21no—
28C2×C31×#117C411yescharacteristic, complemented
29C31×#407—21no—
30C31×#407—21no—
31C31×#407C2212yes—
32C31×#407C2212yescomplemented
33C2×C31×C22⋊C8—21no—
34C2×C31×C22⋊C8C2212yescomplemented
35C31×#381C2212yes—
36C31×#380—21no—
37C31×#380C2212yescomplemented
38C31×#379—21no—
39C4×C22⋊C4×C31—21no—
40C4×C22⋊C4×C31C2212yescomplemented
41C31×#328C2218yescomplemented
42C31×#327C2218yescomplemented
43C25×C31D411yescharacteristic
44C2×#41×C31—21no—
45C2×#41×C31—21no—
46C2×#41×C31—44no—
47C2×#41×C31C2×C412yes—
48C2×#41×C31C2×C412yes—
49C22×Q8×C31C2×C411yescharacteristic
50C22×D4×C31—21no—
51C22×D4×C31—21no—
52C22×D4×C31—21no—
53C22×D4×C31C2×C411yescharacteristic
54C23×C4×C31—21no—
55C23×C4×C31—44no—
56C23×C4×C31C2×C411yescharacteristic
57C23×C4×C31C2×C411yescharacteristic
58C23×C4×C31C2×C411yescharacteristic
59C23×C4×C31C2×C411yescharacteristic
60C23×C4×C31D411yescharacteristic
61C23×C4×C31D411yescharacteristic
62C23×C4×C31D411yescharacteristic
63C23×C4×C31D411yescharacteristic
64C23×C4×C31D411yescharacteristic
65C23×C4×C31D411yescharacteristic
66C23×C4×C31D411yescharacteristic
67C23×C4×C31C2311yescharacteristic
68C23×C4×C31C2311yescharacteristic
69C23×C4×C31C2311yescharacteristic
70C2×M16×C31—22no—
71C2×M16×C31—22no—
72C2×M16×C31—44no—
73C22×C8×C31—22no—
74C31×#123—22no—
75C31×#123—22no—
76C31×#123—22no—
77C31×#123—22no—
78C31×C22⋊Q8—21no—
79C31×C22⋊Q8—21no—
80C31×C22⋊Q8—21no—
81C31×C22⋊Q8—21no—
82C31×C22⋊Q8C2×C412yes—
83C31×C22⋊Q8C2×C412yes—
84C31×C22⋊Q8C2×C412yes—
85C31×C22⋊Q8C2312yes—
86C31×#121—21no—
87C31×#121—21no—
88C31×#121—21no—
89C31×#121—21no—
90C31×#121C2×C412yes—
91C31×#121C2×C412yes—
92C31×#121C2×C412yes—
93C31×#121C2312yes—
94C31×#120—22no—
95C31×#120—22no—
96C31×#120—22no—
97C31×#120—22no—
98C4×D4×C31—22no—
99C4×D4×C31—22no—
100C4×D4×C31—22no—
101C4×D4×C31—22no—
102C4×D4×C31—22no—
103C4×D4×C31—22no—
104C4×D4×C31—22no—
105C4×D4×C31—22no—
106C31×#117—21no—
107C31×#117—21no—
108C31×#117—44no—
109C31×#117C2×C412yes—
110C31×#117C2×C412yes—
111C2×C4⋊C4×C31—21no—
112C2×C4⋊C4×C31—21no—
113C2×C4⋊C4×C31—22no—
114C2×C4⋊C4×C31C2×C411yescharacteristic
115C2×C4⋊C4×C31C2×C411yescharacteristic
116C2×C22⋊C4×C31—21no—
117C2×C22⋊C4×C31—21no—
118C2×C22⋊C4×C31—21no—
119C2×C22⋊C4×C31—21no—
120C2×C22⋊C4×C31—21no—
121C2×C22⋊C4×C31—22no—
122C2×C22⋊C4×C31—22no—
123C2×C22⋊C4×C31—22no—
124C2×C42×C31—21no—
125C2×C42×C31—22no—
126C31×C22⋊C8—22no—
127C31×C22⋊C8—22no—
128C31×C22⋊C8—22no—
129C31×C22⋊C8C2314yes—
130C31×#95—22no—
131C31×#95C2314yes—
132C24×C31—21no—
133C24×C31—42no—
134C24×C31—42no—
135C24×C31—42no—
136C24×C31C22⋊C411yescharacteristic
137C24×C31C22⋊C411yescharacteristic
138C24×C31C22⋊C411yescharacteristic
139C24×C31C22⋊C411yescharacteristic
140C24×C31C2×D411yescharacteristic
141C24×C31C2×D411yescharacteristic
142C24×C31C2×D411yescharacteristic
143#41×C31—44no—
144#41×C31—44no—
145#41×C31—44no—
146#41×C31—44no—
147C2×Q8×C31—21no—
148C2×Q8×C31—42no—
149C2×Q8×C31C22×C412yes—
150C2×D4×C31—22no—
151C2×D4×C31—22no—
152C2×D4×C31—22no—
153C2×D4×C31—22no—
154C2×D4×C31—22no—
155C2×D4×C31—22no—
156C2×D4×C31—21no—
157C2×D4×C31—42no—
158C2×D4×C31—44no—
159C2×D4×C31—44no—
160C2×D4×C31—44no—
161C2×D4×C31C22×C412yes—
162C22×C4×C31—24no—
163C22×C4×C31—24no—
164C22×C4×C31—24no—
165C22×C4×C31—21no—
166C22×C4×C31—21no—
167C22×C4×C31—21no—
168C22×C4×C31—22no—
169C22×C4×C31—22no—
170C22×C4×C31—24no—
171C22×C4×C31—42no—
172C22×C4×C31—42no—
173C22×C4×C31—42no—
174C22×C4×C31—42no—
175C22×C4×C31—42no—
176C22×C4×C31—42no—
177C22×C4×C31—42no—
178C22×C4×C31—42no—
179C22×C4×C31—42no—
180C22×C4×C31—42no—
181C22×C4×C31—42no—
182C22×C4×C31—44no—
183C22×C4×C31C22⋊C411yescharacteristic
184C22×C4×C31C22⋊C411yescharacteristic
185C22×C4×C31C22⋊C411yescharacteristic
186C22×C4×C31C22⋊C411yescharacteristic
187C22×C4×C31C22⋊C411yescharacteristic
188C22×C4×C31C22⋊C411yescharacteristic
189C22×C4×C31C22⋊C411yescharacteristic
190C22×C4×C31C22⋊C411yescharacteristic
191C22×C4×C31C22⋊C411yescharacteristic
192C22×C4×C31C22⋊C411yescharacteristic
193C22×C4×C31C22⋊C411yescharacteristic
194C22×C4×C31C22⋊C411yescharacteristic
195C22×C4×C31C22×C411yescharacteristic
196C22×C4×C31C22×C411yescharacteristic
197C22×C4×C31C22×C411yescharacteristic
198C22×C4×C31C22×C411yescharacteristic
199C22×C4×C31C22×C411yescharacteristic
200C22×C4×C31C22×C411yescharacteristic
201C22×C4×C31C2×D411yescharacteristic
202C22×C4×C31C2×D411yescharacteristic
203C22×C4×C31C2×D411yescharacteristic
204C22×C4×C31C2×D411yescharacteristic
205C22×C4×C31C2×D411yescharacteristic
206C22×C4×C31C2×D411yescharacteristic
207C22×C4×C31C2×D411yescharacteristic
208C22×C4×C31C2×D411yescharacteristic
209C22×C4×C31C2×D411yescharacteristic
210C22×C4×C31C2411yescharacteristic
211M16×C31—44no—
212M16×C31—44no—
213C2×C8×C31—24no—
214C2×C8×C31—44no—
215C4⋊C4×C31—22no—
216C4⋊C4×C31—22no—
217C4⋊C4×C31—22no—
218C4⋊C4×C31—21no—
219C4⋊C4×C31—21no—
220C4⋊C4×C31—22no—
221C4⋊C4×C31—44no—
222C4⋊C4×C31C22×C412yes—
223C4⋊C4×C31C22×C412yes—
224C22⋊C4×C31—22no—
225C22⋊C4×C31—22no—
226C22⋊C4×C31—22no—
227C22⋊C4×C31—22no—
228C22⋊C4×C31—22no—
229C22⋊C4×C31—22no—
230C22⋊C4×C31—22no—
231C22⋊C4×C31—22no—
232C22⋊C4×C31—22no—
233C22⋊C4×C31—22no—
234C22⋊C4×C31—44no—
235C22⋊C4×C31—44no—
236C22⋊C4×C31—44no—
237C42×C31—22no—
238C42×C31—22no—
239C42×C31—44no—
240#17559C3111yesmaximal, characteristic, direct product factor, Sylow
241C23×C31—22no—
242C23×C31—22no—
243C23×C31—22no—
244C23×C31—22no—
245C23×C31—22no—
246C23×C31—22no—
247C23×C31—22no—
248C23×C31—22no—
249C23×C31—22no—
250C23×C31—22no—
251C23×C31—41no—
252C23×C31—41no—
253C23×C31—41no—
254C23×C31—41no—
255C23×C31—41no—
256C23×C31—41no—
257C23×C31—41no—
258C23×C31—41no—
259C23×C31—41no—
260C23×C31—41no—
261C23×C31—41no—
262C23×C31—41no—
263C23×C31—42no—
264C23×C31—42no—
265C23×C31—416no—
266C23×C31—42no—
267C23×C31C2×C22⋊C411yescharacteristic
268C23×C31C2×C22⋊C411yescharacteristic
269C23×C31C2×C22⋊C411yescharacteristic
270C23×C31C2×C22⋊C411yescharacteristic
271C23×C31C2×C22⋊C411yescharacteristic
272C23×C31C2×C22⋊C411yescharacteristic
273C23×C31C22×D411yescharacteristic
274Q8×C31—42no—
275Q8×C31—42no—
276D4×C31—42no—
277D4×C31—42no—
278D4×C31—44no—
279D4×C31—44no—
280D4×C31—44no—
281D4×C31—44no—
282D4×C31—44no—
283D4×C31—44no—
284C2×C4×C31—22no—
285C2×C4×C31—22no—
286C2×C4×C31—22no—
287C2×C4×C31—22no—
288C2×C4×C31—22no—
289C2×C4×C31—22no—
290C2×C4×C31—22no—
291C2×C4×C31—22no—
292C2×C4×C31—22no—
293C2×C4×C31—22no—
294C2×C4×C31—22no—
295C2×C4×C31—22no—
296C2×C4×C31—22no—
297C2×C4×C31—22no—
298C2×C4×C31—22no—
299C2×C4×C31—22no—
300C2×C4×C31—22no—
301C2×C4×C31—22no—
302C2×C4×C31—41no—
303C2×C4×C31—41no—
304C2×C4×C31—41no—
305C2×C4×C31—41no—
306C2×C4×C31—41no—
307C2×C4×C31—41no—
308C2×C4×C31—41no—
309C2×C4×C31—41no—
310C2×C4×C31—41no—
311C2×C4×C31—41no—
312C2×C4×C31—41no—
313C2×C4×C31—41no—
314C2×C4×C31—42no—
315C2×C4×C31—42no—
316C2×C4×C31—42no—
317C2×C4×C31—44no—
318C2×C4×C31—44no—
319C2×C4×C31—44no—
320C2×C4×C31—44no—
321C2×C4×C31—44no—
322C2×C4×C31#9914yes—
323C2×C4×C31C2×C22⋊C411yescharacteristic
324C2×C4×C31C2×C22⋊C411yescharacteristic
325C2×C4×C31C2×C22⋊C411yescharacteristic
326C2×C4×C31C2×C22⋊C411yescharacteristic
327C2×C4×C31C2×C22⋊C411yescharacteristic
328C2×C4×C31C2×C22⋊C411yescharacteristic
329C2×C4×C31C23×C411yescharacteristic
330C2×C4×C31C22×D411yescharacteristic
331C8×C31—44no—
332C2×#525C2×C3111yescharacteristic
333C2×#407C2×C3111yescharacteristic, complemented
334#2280C2×C3111yescharacteristic, complemented
335#1513C2×C3114yescomplemented
336#1511C2×C3112yescomplemented
337#1510C2×C3112yescomplemented
338#1501C2×C3114yescomplemented
339C22×C31—21no—
340C22×C31—21no—
341C22×C31—21no—
342C22×C31—21no—
343C22×C31—21no—
344C22×C31—21no—
345C22×C31—21no—
346C22×C31—21no—
347C22×C31—21no—
348C22×C31—21no—
349C22×C31—21no—
350C22×C31—21no—
351C22×C31—21no—
352C22×C31—21no—
353C22×C31—21no—
354C22×C31—21no—
355C22×C31—21no—
356C22×C31—21no—
357C22×C31—44no—
358C22×C31—44no—
359C22×C31—44no—
360C22×C31—44no—
361C22×C31—44no—
362C22×C31—44no—
363C22×C31—44no—
364C22×C31—42no—
365C22×C31—42no—
366C22×C31—42no—
367C22×C31—84no—
368C22×C31C2×#9912yes—
369C22×C31#42112yes—
370C22×C31C22×C22⋊C411yescharacteristic
371C22×C31#57512yes—
372C4×C31—21no—
373C4×C31—21no—
374C4×C31—21no—
375C4×C31—21no—
376C4×C31—21no—
377C4×C31—21no—
378C4×C31—42no—
379C4×C31—42no—
380C4×C31—42no—
381C4×C31—84no—
382C4×C31C2×#9912yes—
383C4×C31C2×#9912yes—
384C22×#41C4×C3111yescharacteristic, complemented
385C24×C4C22×C3111yescharacteristic
386C22×M16—21no—
387#525—21no—
388#525—21no—
389#525—21no—
390#525—21no—
391#525C4×C3112yescomplemented
392#525C4×C3112yescomplemented
393#525C22×C3112yes—
394#525C22×C3112yes—
395C2×#123—21no—
396C2×C22⋊Q8C4×C3111yescharacteristic, complemented
397C2×C22⋊Q8C22×C3111yescharacteristic
398C2×#121C4×C3111yescharacteristic, complemented
399C2×#121C22×C3111yescharacteristic
400C2×#120—21no—
401C2×C4×D4—21no—
402C2×C4×D4—21no—
403C2×#117—21no—
404C2×#117C4×C3111yescharacteristic, complemented
405#407—21no—
406#407—21no—
407#407C22×C3112yes—
408#407C22×C3112yescomplemented
409C2×C22⋊C8—21no—
410C2×C22⋊C8C22×C3112yescomplemented
411#381C22×C3112yes—
412#380—21no—
413#380C22×C3112yescomplemented
414#379—21no—
415C4×C22⋊C4—21no—
416C4×C22⋊C4C22×C3112yescomplemented
417#328C22×C3118yescomplemented
418#327C22×C3118yescomplemented
419C2×C31—22no—
420C2×C31—22no—
421C2×C31—22no—
422C2×C31—41no—
423C2×C31—41no—
424C2×C31—41no—
425C2×C31—41no—
426C2×C31—82no—
427C2×C31C22×#9911yescharacteristic
428C2×C31#289611yescharacteristic
429C2×C31C2×#42111yescharacteristic
430C25D4×C3111yescharacteristic
431C2×#41—21no—
432C2×#41—21no—
433C2×#41—44no—
434C2×#41C2×C4×C3112yes—
435C2×#41C2×C4×C3112yes—
436C22×Q8C2×C4×C3111yescharacteristic
437C22×D4—21no—
438C22×D4—21no—
439C22×D4—21no—
440C22×D4C2×C4×C3111yescharacteristic
441C23×C4—21no—
442C23×C4—44no—
443C23×C4C2×C4×C3111yescharacteristic
444C23×C4C2×C4×C3111yescharacteristic
445C23×C4C2×C4×C3111yescharacteristic
446C23×C4C2×C4×C3111yescharacteristic
447C23×C4D4×C3111yescharacteristic
448C23×C4D4×C3111yescharacteristic
449C23×C4D4×C3111yescharacteristic
450C23×C4D4×C3111yescharacteristic
451C23×C4D4×C3111yescharacteristic
452C23×C4D4×C3111yescharacteristic
453C23×C4D4×C3111yescharacteristic
454C23×C4C23×C3111yescharacteristic
455C23×C4C23×C3111yescharacteristic
456C23×C4C23×C3111yescharacteristic
457C2×M16—22no—
458C2×M16—22no—
459C2×M16—44no—
460C22×C8—22no—
461#123—22no—
462#123—22no—
463#123—22no—
464#123—22no—
465C22⋊Q8—21no—
466C22⋊Q8—21no—
467C22⋊Q8—21no—
468C22⋊Q8—21no—
469C22⋊Q8C2×C4×C3112yes—
470C22⋊Q8C2×C4×C3112yes—
471C22⋊Q8C2×C4×C3112yes—
472C22⋊Q8C23×C3112yes—
473#121—21no—
474#121—21no—
475#121—21no—
476#121—21no—
477#121C2×C4×C3112yes—
478#121C2×C4×C3112yes—
479#121C2×C4×C3112yes—
480#121C23×C3112yes—
481#120—22no—
482#120—22no—
483#120—22no—
484#120—22no—
485C4×D4—22no—
486C4×D4—22no—
487C4×D4—22no—
488C4×D4—22no—
489C4×D4—22no—
490C4×D4—22no—
491C4×D4—22no—
492C4×D4—22no—
493#117—21no—
494#117—21no—
495#117—44no—
496#117C2×C4×C3112yes—
497#117C2×C4×C3112yes—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4C2×C4×C3111yescharacteristic
502C2×C4⋊C4C2×C4×C3111yescharacteristic
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—22no—
511C2×C42—21no—
512C2×C42—22no—
513C22⋊C8—22no—
514C22⋊C8—22no—
515C22⋊C8—22no—
516C22⋊C8C23×C3114yes—
517#95—22no—
518#95C23×C3114yes—
519C31#1755911yescharacteristic, direct product factor, Sylow
520C24—21no—
521C24—42no—
522C24—42no—
523C24—42no—
524C24C22⋊C4×C3111yescharacteristic
525C24C22⋊C4×C3111yescharacteristic
526C24C22⋊C4×C3111yescharacteristic
527C24C22⋊C4×C3111yescharacteristic
528C24C2×D4×C3111yescharacteristic
529C24C2×D4×C3111yescharacteristic
530C24C2×D4×C3111yescharacteristic
531#41—44no—
532#41—44no—
533#41—44no—
534#41—44no—
535C2×Q8—21no—
536C2×Q8—42no—
537C2×Q8C22×C4×C3112yes—
538C2×D4—22no—
539C2×D4—22no—
540C2×D4—22no—
541C2×D4—22no—
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—21no—
545C2×D4—42no—
546C2×D4—44no—
547C2×D4—44no—
548C2×D4—44no—
549C2×D4C22×C4×C3112yes—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—24no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—24no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—44no—
571C22×C4C22⋊C4×C3111yescharacteristic
572C22×C4C22⋊C4×C3111yescharacteristic
573C22×C4C22⋊C4×C3111yescharacteristic
574C22×C4C22⋊C4×C3111yescharacteristic
575C22×C4C22⋊C4×C3111yescharacteristic
576C22×C4C22⋊C4×C3111yescharacteristic
577C22×C4C22⋊C4×C3111yescharacteristic
578C22×C4C22⋊C4×C3111yescharacteristic
579C22×C4C22⋊C4×C3111yescharacteristic
580C22×C4C22⋊C4×C3111yescharacteristic
581C22×C4C22⋊C4×C3111yescharacteristic
582C22×C4C22⋊C4×C3111yescharacteristic
583C22×C4C22×C4×C3111yescharacteristic
584C22×C4C22×C4×C3111yescharacteristic
585C22×C4C22×C4×C3111yescharacteristic
586C22×C4C22×C4×C3111yescharacteristic
587C22×C4C22×C4×C3111yescharacteristic
588C22×C4C22×C4×C3111yescharacteristic
589C22×C4C2×D4×C3111yescharacteristic
590C22×C4C2×D4×C3111yescharacteristic
591C22×C4C2×D4×C3111yescharacteristic
592C22×C4C2×D4×C3111yescharacteristic
593C22×C4C2×D4×C3111yescharacteristic
594C22×C4C2×D4×C3111yescharacteristic
595C22×C4C2×D4×C3111yescharacteristic
596C22×C4C2×D4×C3111yescharacteristic
597C22×C4C2×D4×C3111yescharacteristic
598C22×C4C24×C3111yescharacteristic
599M16—44no—
600M16—44no—
601C2×C8—24no—
602C2×C8—44no—
603C4⋊C4—22no—
604C4⋊C4—22no—
605C4⋊C4—22no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—22no—
609C4⋊C4—44no—
610C4⋊C4C22×C4×C3112yes—
611C4⋊C4C22×C4×C3112yes—
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—22no—
619C22⋊C4—22no—
620C22⋊C4—22no—
621C22⋊C4—22no—
622C22⋊C4—44no—
623C22⋊C4—44no—
624C22⋊C4—44no—
625C42—22no—
626C42—22no—
627C42—44no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—42no—
651C23—42no—
652C23—416no—
653C23—42no—
654C23C2×C22⋊C4×C3111yescharacteristic
655C23C2×C22⋊C4×C3111yescharacteristic
656C23C2×C22⋊C4×C3111yescharacteristic
657C23C2×C22⋊C4×C3111yescharacteristic
658C23C2×C22⋊C4×C3111yescharacteristic
659C23C2×C22⋊C4×C3111yescharacteristic
660C23C22×D4×C3111yescharacteristic
661Q8—42no—
662Q8—42no—
663D4—42no—
664D4—42no—
665D4—44no—
666D4—44no—
667D4—44no—
668D4—44no—
669D4—44no—
670D4—44no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—44no—
705C2×C4—44no—
706C2×C4—44no—
707C2×C4—44no—
708C2×C4—44no—
709C2×C4C31×#9914yes—
710C2×C4C2×C22⋊C4×C3111yescharacteristic
711C2×C4C2×C22⋊C4×C3111yescharacteristic
712C2×C4C2×C22⋊C4×C3111yescharacteristic
713C2×C4C2×C22⋊C4×C3111yescharacteristic
714C2×C4C2×C22⋊C4×C3111yescharacteristic
715C2×C4C2×C22⋊C4×C3111yescharacteristic
716C2×C4C23×C4×C3111yescharacteristic
717C2×C4C22×D4×C3111yescharacteristic
718C8—44no—
719C22—21no—
720C22—21no—
721C22—21no—
722C22—21no—
723C22—21no—
724C22—21no—
725C22—21no—
726C22—21no—
727C22—21no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—44no—
738C22—44no—
739C22—44no—
740C22—44no—
741C22—44no—
742C22—44no—
743C22—44no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—84no—
748C22C2×C31×#9912yes—
749C22C31×#42112yes—
750C22C22×C22⋊C4×C3111yescharacteristic
751C22C31×#57512yes—
752C4—21no—
753C4—21no—
754C4—21no—
755C4—21no—
756C4—21no—
757C4—21no—
758C4—42no—
759C4—42no—
760C4—42no—
761C4—84no—
762C4C2×C31×#9912yes—
763C4C2×C31×#9912yes—
764C2—22no—
765C2—22no—
766C2—22no—
767C2—41no—
768C2—41no—
769C2—41no—
770C2—41no—
771C2—82no—
772C2C22×C31×#9911yescharacteristic
773C2C31×#289611yescharacteristic
774C2C2×C31×#42111yescharacteristic
subgroupG/H
centerC2×C4×C31C2×C22⋊C4
commutatorC2×C4C23×C4×C31
Frattini, cosocleC22×C4C24×C31
socleC22×C31C22×C22⋊C4
prime radicalC2×C31×#525C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C31 ◁ C24×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C31×#407C2semidirect
3. C31×#2280C2semidirect
4. C31×#1513C2semidirect
5. C31×#1511C2semidirect
6. C31×#1510C2semidirect
7. C31×#1501C2semidirect
8. C22×#41×C31C4semidirect
15. C31×#525C4semidirect
16. C31×#525C4semidirect
20. C2×C31×C22⋊Q8C4semidirect
22. C2×C31×#121C4semidirect
28. C2×C31×#117C4semidirect
32. C31×#407C22semidirect
34. C2×C31×C22⋊C8C22semidirect
37. C31×#380C22semidirect
40. C4×C22⋊C4×C31C22semidirect
41. C31×#328C22semidirect
42. C31×#327C22semidirect
240. #17559C31direct (N × H)
333. C2×#407C2×C31semidirect
334. #2280C2×C31semidirect
335. #1513C2×C31semidirect
336. #1511C2×C31semidirect
337. #1510C2×C31semidirect
338. #1501C2×C31semidirect
384. C22×#41C4×C31semidirect
391. #525C4×C31semidirect
392. #525C4×C31semidirect
396. C2×C22⋊Q8C4×C31semidirect
398. C2×#121C4×C31semidirect
404. C2×#117C4×C31semidirect
408. #407C22×C31semidirect
410. C2×C22⋊C8C22×C31semidirect
413. #380C22×C31semidirect
416. C4×C22⋊C4C22×C31semidirect
417. #328C22×C31semidirect
418. #327C22×C31semidirect
519. C31#17559direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C31×#5252
C2×C31×#4072
C31×#22802
C31×#15132
C31×#15112
C31×#15102
C31×#15012
#1755931