Finite Group Databasebeta

← C31×#17542 #21474301

Subgroups — C31×#17542 #21474301

Order 7936.

1574 conjugacy classes of subgroups.

The subgroup lattice has 784 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
3C2×C4×C22⋊C4×C31C211yesmaximal, characteristic, complemented
4C31×#1508C212yesmaximal, complemented
5C31×#1507C212yesmaximal, complemented
6C31×#1504C214yesmaximal, 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×#117C411yescharacteristic, complemented
28C22×C22⋊C4×C31—21no—
29C22×C42×C31—21no—
30C31×#407—21no—
31C31×#407—21no—
32C31×#407C2212yes—
33C31×#407C2212yescomplemented
34C2×C31×C22⋊C8—21no—
35C2×C31×C22⋊C8C2212yescomplemented
36C4×C22⋊C4×C31—21no—
37C4×C22⋊C4×C31—21no—
38C4×C22⋊C4×C31C2212yes—
39C4×C22⋊C4×C31C2212yescomplemented
40C2×C31×#95C2212yescomplemented
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×C412yescomplemented
49C22×Q8×C31C2×C411yescharacteristic, complemented
50C22×D4×C31—21no—
51C22×D4×C31—21no—
52C22×D4×C31—21no—
53C22×D4×C31C2×C411yescharacteristic, complemented
54C23×C4×C31—22no—
55C23×C4×C31—21no—
56C23×C4×C31—44no—
57C23×C4×C31C2×C411yescharacteristic
58C23×C4×C31C2×C411yescharacteristic
59C23×C4×C31C2×C411yescharacteristic
60C23×C4×C31C2×C411yescharacteristic
61C23×C4×C31D411yescharacteristic
62C23×C4×C31D411yescharacteristic
63C23×C4×C31D411yescharacteristic
64C23×C4×C31D411yescharacteristic
65C23×C4×C31D411yescharacteristic
66C23×C4×C31D411yescharacteristic
67C23×C4×C31D411yescharacteristic
68C23×C4×C31C2311yescharacteristic
69C23×C4×C31C2311yescharacteristic
70C23×C4×C31C2311yescharacteristic
71C2×M16×C31—22no—
72C2×M16×C31—22no—
73C2×M16×C31—44no—
74C22×C8×C31—22no—
75C31×#123—22no—
76C31×#123—22no—
77C31×#123—22no—
78C31×#123—22no—
79C31×C22⋊Q8—21no—
80C31×C22⋊Q8—21no—
81C31×C22⋊Q8—21no—
82C31×C22⋊Q8—21no—
83C31×C22⋊Q8C2×C412yes—
84C31×C22⋊Q8C2×C412yescomplemented
85C31×C22⋊Q8C2×C412yescomplemented
86C31×C22⋊Q8C2312yes—
87C31×#121—21no—
88C31×#121—21no—
89C31×#121—21no—
90C31×#121—21no—
91C31×#121C2×C412yes—
92C31×#121C2×C412yescomplemented
93C31×#121C2×C412yescomplemented
94C31×#121C2312yes—
95C31×#120—22no—
96C31×#120—22no—
97C31×#120—22no—
98C31×#120—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—
106C4×D4×C31—22no—
107C31×#117—21no—
108C31×#117—21no—
109C31×#117C2×C412yes—
110C31×#117C2×C412yescomplemented
111C2×C4⋊C4×C31—21no—
112C2×C4⋊C4×C31—21no—
113C2×C4⋊C4×C31C2×C411yescharacteristic, complemented
114C2×C4⋊C4×C31C2×C411yescharacteristic, complemented
115C2×C22⋊C4×C31—28no—
116C2×C22⋊C4×C31—21no—
117C2×C22⋊C4×C31—21no—
118C2×C22⋊C4×C31—22no—
119C2×C22⋊C4×C31—22no—
120C2×C22⋊C4×C31—21no—
121C2×C22⋊C4×C31—21no—
122C2×C22⋊C4×C31—21no—
123C2×C42×C31—21no—
124C2×C42×C31—22no—
125C2×C42×C31—22no—
126C2×C42×C31—44no—
127C31×C22⋊C8—22no—
128C31×C22⋊C8—22no—
129C31×C22⋊C8—22no—
130C31×C22⋊C8C2314yes—
131C31×#95—22no—
132C31×#95C2314yes—
133C24×C31—24no—
134C24×C31—21no—
135C24×C31—42no—
136C24×C31—42no—
137C24×C31C22⋊C411yescharacteristic
138C24×C31C22⋊C411yescharacteristic
139C24×C31C22⋊C411yescharacteristic
140C24×C31C22⋊C411yescharacteristic
141C24×C31C2×D411yescharacteristic
142C24×C31C2×D411yescharacteristic
143C24×C31C2×D411yescharacteristic
144#41×C31—44no—
145#41×C31—44no—
146#41×C31—44no—
147#41×C31—44no—
148C2×Q8×C31—21no—
149C2×Q8×C31—42no—
150C2×Q8×C31C22×C412yes—
151C2×D4×C31—22no—
152C2×D4×C31—22no—
153C2×D4×C31—22no—
154C2×D4×C31—22no—
155C2×D4×C31—22no—
156C2×D4×C31—22no—
157C2×D4×C31—21no—
158C2×D4×C31—42no—
159C2×D4×C31—44no—
160C2×D4×C31—44no—
161C2×D4×C31—44no—
162C2×D4×C31C22×C412yes—
163C22×C4×C31—24no—
164C22×C4×C31—24no—
165C22×C4×C31—24no—
166C22×C4×C31—28no—
167C22×C4×C31—21no—
168C22×C4×C31—21no—
169C22×C4×C31—21no—
170C22×C4×C31—24no—
171C22×C4×C31—22no—
172C22×C4×C31—22no—
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—42no—
183C22×C4×C31—42no—
184C22×C4×C31—44no—
185C22×C4×C31—44no—
186C22×C4×C31—44no—
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×C31C22×C411yescharacteristic
202C22×C4×C31C22×C411yescharacteristic
203C22×C4×C31C22×C411yescharacteristic
204C22×C4×C31C22×C411yescharacteristic
205C22×C4×C31C2×D411yescharacteristic
206C22×C4×C31C2×D411yescharacteristic
207C22×C4×C31C2×D411yescharacteristic
208C22×C4×C31C2×D411yescharacteristic
209C22×C4×C31C2×D411yescharacteristic
210C22×C4×C31C2×D411yescharacteristic
211C22×C4×C31C2×D411yescharacteristic
212C22×C4×C31C2×D411yescharacteristic
213C22×C4×C31C2×D411yescharacteristic
214C22×C4×C31C2411yescharacteristic
215M16×C31—44no—
216M16×C31—44no—
217C2×C8×C31—24no—
218C2×C8×C31—44no—
219C4⋊C4×C31—22no—
220C4⋊C4×C31—22no—
221C4⋊C4×C31—22no—
222C4⋊C4×C31—21no—
223C4⋊C4×C31—21no—
224C4⋊C4×C31—22no—
225C4⋊C4×C31C22×C412yes—
226C4⋊C4×C31C22×C412yes—
227C22⋊C4×C31—28no—
228C22⋊C4×C31—28no—
229C22⋊C4×C31—22no—
230C22⋊C4×C31—22no—
231C22⋊C4×C31—22no—
232C22⋊C4×C31—22no—
233C22⋊C4×C31—22no—
234C22⋊C4×C31—22no—
235C22⋊C4×C31—22no—
236C22⋊C4×C31—22no—
237C22⋊C4×C31—22no—
238C22⋊C4×C31—22no—
239C42×C31—22no—
240C42×C31—22no—
241C42×C31—44no—
242C42×C31—44no—
243#17542C3111yesmaximal, characteristic, direct product factor, Sylow
244C23×C31—22no—
245C23×C31—22no—
246C23×C31—22no—
247C23×C31—22no—
248C23×C31—22no—
249C23×C31—22no—
250C23×C31—22no—
251C23×C31—22no—
252C23×C31—22no—
253C23×C31—22no—
254C23×C31—22no—
255C23×C31—22no—
256C23×C31—22no—
257C23×C31—41no—
258C23×C31—41no—
259C23×C31—41no—
260C23×C31—41no—
261C23×C31—41no—
262C23×C31—41no—
263C23×C31—41no—
264C23×C31—41no—
265C23×C31—416no—
266C23×C31—42no—
267C23×C31—42no—
268C23×C31—42no—
269C23×C31#10414yes—
270C23×C31C2×C22⋊C411yescharacteristic
271C23×C31C2×C22⋊C411yescharacteristic
272C23×C31C2×C22⋊C411yescharacteristic
273C23×C31C2×C22⋊C411yescharacteristic
274C23×C31C2×C22⋊C411yescharacteristic
275C23×C31C2×C22⋊C411yescharacteristic
276C23×C31C22×D411yescharacteristic
277Q8×C31—42no—
278Q8×C31—42no—
279D4×C31—42no—
280D4×C31—44no—
281D4×C31—44no—
282D4×C31—44no—
283D4×C31—44no—
284D4×C31—44no—
285D4×C31—44no—
286D4×C31—42no—
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—28no—
303C2×C4×C31—22no—
304C2×C4×C31—22no—
305C2×C4×C31—22no—
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—41no—
315C2×C4×C31—41no—
316C2×C4×C31—41no—
317C2×C4×C31—41no—
318C2×C4×C31—44no—
319C2×C4×C31—44no—
320C2×C4×C31—416no—
321C2×C4×C31—42no—
322C2×C4×C31—42no—
323C2×C4×C31—44no—
324C2×C4×C31—42no—
325C2×C4×C31—44no—
326C2×C4×C31#9914yes—
327C2×C4×C31C2×C22⋊C411yescharacteristic
328C2×C4×C31C2×C22⋊C411yescharacteristic
329C2×C4×C31C2×C22⋊C411yescharacteristic
330C2×C4×C31C2×C22⋊C411yescharacteristic
331C2×C4×C31C2×C22⋊C411yescharacteristic
332C2×C4×C31C2×C22⋊C411yescharacteristic
333C2×C4×C31C23×C411yescharacteristic
334C2×C4×C31C22×D411yescharacteristic
335C8×C31—44no—
336C2×#525C2×C3111yescharacteristic
337C2×#407C2×C3111yescharacteristic, complemented
338C2×C4×C22⋊C4C2×C3111yescharacteristic, complemented
339#1508C2×C3112yescomplemented
340#1507C2×C3112yescomplemented
341#1504C2×C3114yescomplemented
342#1501C2×C3114yescomplemented
343C22×C31—28no—
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—21no—
358C22×C31—21no—
359C22×C31—21no—
360C22×C31—44no—
361C22×C31—44no—
362C22×C31—44no—
363C22×C31—44no—
364C22×C31—44no—
365C22×C31—44no—
366C22×C31—42no—
367C22×C31—42no—
368C22×C31—42no—
369C22×C31—84no—
370C22×C31C2×#9912yes—
371C22×C31C2×#10412yes—
372C22×C31C2×#10412yes—
373C22×C31C2×#10412yes—
374C22×C31C22×C22⋊C411yescharacteristic
375C22×C31#57512yes—
376C4×C31—21no—
377C4×C31—21no—
378C4×C31—21no—
379C4×C31—21no—
380C4×C31—21no—
381C4×C31—21no—
382C4×C31—48no—
383C4×C31—42no—
384C4×C31—42no—
385C4×C31—42no—
386C4×C31C2×#9912yes—
387C4×C31C2×#9912yes—
388C22×#41C4×C3111yescharacteristic, complemented
389C24×C4C22×C3111yescharacteristic
390C22×M16—21no—
391#525—21no—
392#525—21no—
393#525—21no—
394#525—21no—
395#525C4×C3112yescomplemented
396#525C4×C3112yescomplemented
397#525C22×C3112yes—
398#525C22×C3112yes—
399C2×#123—21no—
400C2×C22⋊Q8C4×C3111yescharacteristic, complemented
401C2×C22⋊Q8C22×C3111yescharacteristic
402C2×#121C4×C3111yescharacteristic, complemented
403C2×#121C22×C3111yescharacteristic
404C2×#120—21no—
405C2×C4×D4—21no—
406C2×C4×D4—21no—
407C2×#117C4×C3111yescharacteristic, complemented
408C22×C22⋊C4—21no—
409C22×C42—21no—
410#407—21no—
411#407—21no—
412#407C22×C3112yes—
413#407C22×C3112yescomplemented
414C2×C22⋊C8—21no—
415C2×C22⋊C8C22×C3112yescomplemented
416C4×C22⋊C4—21no—
417C4×C22⋊C4—21no—
418C4×C22⋊C4C22×C3112yes—
419C4×C22⋊C4C22×C3112yescomplemented
420C2×#95C22×C3112yescomplemented
421#328C22×C3118yescomplemented
422#327C22×C3118yescomplemented
423C2×C31—22no—
424C2×C31—22no—
425C2×C31—22no—
426C2×C31—22no—
427C2×C31—22no—
428C2×C31—41no—
429C2×C31—41no—
430C2×C31—82no—
431C2×C31C22×#9911yescharacteristic
432C2×C31#289611yescharacteristic
433C2×C31C22×#10411yescharacteristic
434C25D4×C3111yescharacteristic
435C2×#41—21no—
436C2×#41—21no—
437C2×#41—44no—
438C2×#41C2×C4×C3112yes—
439C2×#41C2×C4×C3112yescomplemented
440C22×Q8C2×C4×C3111yescharacteristic, complemented
441C22×D4—21no—
442C22×D4—21no—
443C22×D4—21no—
444C22×D4C2×C4×C3111yescharacteristic, complemented
445C23×C4—22no—
446C23×C4—21no—
447C23×C4—44no—
448C23×C4C2×C4×C3111yescharacteristic
449C23×C4C2×C4×C3111yescharacteristic
450C23×C4C2×C4×C3111yescharacteristic
451C23×C4C2×C4×C3111yescharacteristic
452C23×C4D4×C3111yescharacteristic
453C23×C4D4×C3111yescharacteristic
454C23×C4D4×C3111yescharacteristic
455C23×C4D4×C3111yescharacteristic
456C23×C4D4×C3111yescharacteristic
457C23×C4D4×C3111yescharacteristic
458C23×C4D4×C3111yescharacteristic
459C23×C4C23×C3111yescharacteristic
460C23×C4C23×C3111yescharacteristic
461C23×C4C23×C3111yescharacteristic
462C2×M16—22no—
463C2×M16—22no—
464C2×M16—44no—
465C22×C8—22no—
466#123—22no—
467#123—22no—
468#123—22no—
469#123—22no—
470C22⋊Q8—21no—
471C22⋊Q8—21no—
472C22⋊Q8—21no—
473C22⋊Q8—21no—
474C22⋊Q8C2×C4×C3112yes—
475C22⋊Q8C2×C4×C3112yescomplemented
476C22⋊Q8C2×C4×C3112yescomplemented
477C22⋊Q8C23×C3112yes—
478#121—21no—
479#121—21no—
480#121—21no—
481#121—21no—
482#121C2×C4×C3112yes—
483#121C2×C4×C3112yescomplemented
484#121C2×C4×C3112yescomplemented
485#121C23×C3112yes—
486#120—22no—
487#120—22no—
488#120—22no—
489#120—22no—
490C4×D4—22no—
491C4×D4—22no—
492C4×D4—22no—
493C4×D4—22no—
494C4×D4—22no—
495C4×D4—22no—
496C4×D4—22no—
497C4×D4—22no—
498#117—21no—
499#117—21no—
500#117C2×C4×C3112yes—
501#117C2×C4×C3112yescomplemented
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4C2×C4×C3111yescharacteristic, complemented
505C2×C4⋊C4C2×C4×C3111yescharacteristic, complemented
506C2×C22⋊C4—28no—
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C42—21no—
515C2×C42—22no—
516C2×C42—22no—
517C2×C42—44no—
518C22⋊C8—22no—
519C22⋊C8—22no—
520C22⋊C8—22no—
521C22⋊C8C23×C3114yes—
522#95—22no—
523#95C23×C3114yes—
524C31#1754211yescharacteristic, direct product factor, Sylow
525C24—24no—
526C24—21no—
527C24—42no—
528C24—42no—
529C24C22⋊C4×C3111yescharacteristic
530C24C22⋊C4×C3111yescharacteristic
531C24C22⋊C4×C3111yescharacteristic
532C24C22⋊C4×C3111yescharacteristic
533C24C2×D4×C3111yescharacteristic
534C24C2×D4×C3111yescharacteristic
535C24C2×D4×C3111yescharacteristic
536#41—44no—
537#41—44no—
538#41—44no—
539#41—44no—
540C2×Q8—21no—
541C2×Q8—42no—
542C2×Q8C22×C4×C3112yes—
543C2×D4—22no—
544C2×D4—22no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—22no—
549C2×D4—21no—
550C2×D4—42no—
551C2×D4—44no—
552C2×D4—44no—
553C2×D4—44no—
554C2×D4C22×C4×C3112yes—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—24no—
558C22×C4—28no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—24no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—44no—
577C22×C4—44no—
578C22×C4—44no—
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×C4C22⋊C4×C3111yescharacteristic
590C22×C4C22⋊C4×C3111yescharacteristic
591C22×C4C22×C4×C3111yescharacteristic
592C22×C4C22×C4×C3111yescharacteristic
593C22×C4C22×C4×C3111yescharacteristic
594C22×C4C22×C4×C3111yescharacteristic
595C22×C4C22×C4×C3111yescharacteristic
596C22×C4C22×C4×C3111yescharacteristic
597C22×C4C2×D4×C3111yescharacteristic
598C22×C4C2×D4×C3111yescharacteristic
599C22×C4C2×D4×C3111yescharacteristic
600C22×C4C2×D4×C3111yescharacteristic
601C22×C4C2×D4×C3111yescharacteristic
602C22×C4C2×D4×C3111yescharacteristic
603C22×C4C2×D4×C3111yescharacteristic
604C22×C4C2×D4×C3111yescharacteristic
605C22×C4C2×D4×C3111yescharacteristic
606C22×C4C24×C3111yescharacteristic
607M16—44no—
608M16—44no—
609C2×C8—24no—
610C2×C8—44no—
611C4⋊C4—22no—
612C4⋊C4—22no—
613C4⋊C4—22no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—22no—
617C4⋊C4C22×C4×C3112yes—
618C4⋊C4C22×C4×C3112yes—
619C22⋊C4—28no—
620C22⋊C4—28no—
621C22⋊C4—22no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—22no—
625C22⋊C4—22no—
626C22⋊C4—22no—
627C22⋊C4—22no—
628C22⋊C4—22no—
629C22⋊C4—22no—
630C22⋊C4—22no—
631C42—22no—
632C42—22no—
633C42—44no—
634C42—44no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—416no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23C31×#10414yes—
661C23C2×C22⋊C4×C3111yescharacteristic
662C23C2×C22⋊C4×C3111yescharacteristic
663C23C2×C22⋊C4×C3111yescharacteristic
664C23C2×C22⋊C4×C3111yescharacteristic
665C23C2×C22⋊C4×C3111yescharacteristic
666C23C2×C22⋊C4×C3111yescharacteristic
667C23C22×D4×C3111yescharacteristic
668Q8—42no—
669Q8—42no—
670D4—42no—
671D4—44no—
672D4—44no—
673D4—44no—
674D4—44no—
675D4—44no—
676D4—44no—
677D4—42no—
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—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—28no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—44no—
710C2×C4—44no—
711C2×C4—416no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—44no—
716C2×C4—44no—
717C2×C4C31×#9914yes—
718C2×C4C2×C22⋊C4×C3111yescharacteristic
719C2×C4C2×C22⋊C4×C3111yescharacteristic
720C2×C4C2×C22⋊C4×C3111yescharacteristic
721C2×C4C2×C22⋊C4×C3111yescharacteristic
722C2×C4C2×C22⋊C4×C3111yescharacteristic
723C2×C4C2×C22⋊C4×C3111yescharacteristic
724C2×C4C23×C4×C3111yescharacteristic
725C2×C4C22×D4×C3111yescharacteristic
726C8—44no—
727C22—28no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—21no—
738C22—21no—
739C22—21no—
740C22—21no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—44no—
745C22—44no—
746C22—44no—
747C22—44no—
748C22—44no—
749C22—44no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—84no—
754C22C2×C31×#9912yes—
755C22C2×C31×#10412yes—
756C22C2×C31×#10412yes—
757C22C2×C31×#10412yes—
758C22C22×C22⋊C4×C3111yescharacteristic
759C22C31×#57512yes—
760C4—21no—
761C4—21no—
762C4—21no—
763C4—21no—
764C4—21no—
765C4—21no—
766C4—48no—
767C4—42no—
768C4—42no—
769C4—42no—
770C4C2×C31×#9912yes—
771C4C2×C31×#9912yes—
772C2—22no—
773C2—22no—
774C2—22no—
775C2—22no—
776C2—22no—
777C2—41no—
778C2—41no—
779C2—82no—
780C2C22×C31×#9911yescharacteristic
781C2C31×#289611yescharacteristic
782C2C22×C31×#10411yescharacteristic
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. C2×C4×C22⋊C4×C31C2semidirect
4. C31×#1508C2semidirect
5. C31×#1507C2semidirect
6. C31×#1504C2semidirect
7. C31×#1501C2semidirect
8. C22×#41×C31C4semidirect
15. C31×#525C4semidirect
16. C31×#525C4semidirect
20. C2×C31×C22⋊Q8C4semidirect
22. C2×C31×#121C4semidirect
27. C2×C31×#117C4semidirect
33. C31×#407C22semidirect
35. C2×C31×C22⋊C8C22semidirect
39. C4×C22⋊C4×C31C22semidirect
40. C2×C31×#95C22semidirect
41. C31×#328C22semidirect
42. C31×#327C22semidirect
48. C2×#41×C31C2×C4semidirect
49. C22×Q8×C31C2×C4semidirect
53. C22×D4×C31C2×C4semidirect
84. C31×C22⋊Q8C2×C4semidirect
85. C31×C22⋊Q8C2×C4semidirect
92. C31×#121C2×C4semidirect
93. C31×#121C2×C4semidirect
110. C31×#117C2×C4semidirect
113. C2×C4⋊C4×C31C2×C4semidirect
114. C2×C4⋊C4×C31C2×C4semidirect
243. #17542C31direct (N × H)
337. C2×#407C2×C31semidirect
338. C2×C4×C22⋊C4C2×C31semidirect
339. #1508C2×C31semidirect
340. #1507C2×C31semidirect
341. #1504C2×C31semidirect
342. #1501C2×C31semidirect
388. C22×#41C4×C31semidirect
395. #525C4×C31semidirect
396. #525C4×C31semidirect
400. C2×C22⋊Q8C4×C31semidirect
402. C2×#121C4×C31semidirect
407. C2×#117C4×C31semidirect
413. #407C22×C31semidirect
415. C2×C22⋊C8C22×C31semidirect
419. C4×C22⋊C4C22×C31semidirect
420. C2×#95C22×C31semidirect
421. #328C22×C31semidirect
422. #327C22×C31semidirect
439. C2×#41C2×C4×C31semidirect
440. C22×Q8C2×C4×C31semidirect
444. C22×D4C2×C4×C31semidirect
475. C22⋊Q8C2×C4×C31semidirect
476. C22⋊Q8C2×C4×C31semidirect
483. #121C2×C4×C31semidirect
484. #121C2×C4×C31semidirect
501. #117C2×C4×C31semidirect
504. C2×C4⋊C4C2×C4×C31semidirect
505. C2×C4⋊C4C2×C4×C31semidirect
524. C31#17542direct (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
C2×C4×C22⋊C4×C312
C31×#15082
C31×#15072
C31×#15042
C31×#15012
#1754231