Finite Group Databasebeta

← C31×#21874 #21478633

Subgroups — C31×#21874 #21478633

Order 7936.

1598 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C31×#525C211yesmaximal, characteristic
2C31×#2280C211yesmaximal, characteristic, complemented
3C2×C31×#380C211yesmaximal, characteristic, complemented
4C31×#1996C212yesmaximal, complemented
5C31×#1964C212yesmaximal, complemented
6C31×#1898C214yesmaximal, complemented
7C31×#1799C214yesmaximal, complemented
8C22×#41×C31C411yescharacteristic, complemented
9C24×C4×C31C2211yescharacteristic
10C31×#525—21no—
11C31×#525—21no—
12C31×#525—21no—
13C31×#525—21no—
14C31×#525—21no—
15C31×#525—21no—
16C31×#525—21no—
17C31×#525—21no—
18C2×C31×#123C412yescomplemented
19C2×C31×C22⋊Q8C411yescharacteristic, complemented
20C2×C31×C22⋊Q8C2211yescharacteristic
21C2×C31×#121C411yescharacteristic, complemented
22C2×C31×#121C2211yescharacteristic
23C2×C31×#120C2212yes—
24C2×C4×D4×C31C412yescomplemented
25C2×C4×D4×C31C2212yes—
26C2×C31×#117—21no—
27C2×C31×#117C411yescharacteristic, complemented
28C22×C4⋊C4×C31—21no—
29C22×C22⋊C4×C31C2212yes—
30C2×C31×#99C2218yes—
31C31×#381—21no—
32C31×#380—21no—
33C31×#380—21no—
34C31×#380—21no—
35C31×#380C2212yes—
36C31×#380C2212yes—
37C31×#380C2212yes—
38C31×#379C2212yes—
39C4×C22⋊C4×C31—21no—
40C4×C22⋊C4×C31C2212yes—
41C2×C31×#95—21no—
42C31×#342C2218yes—
43C25×C31C2311yescharacteristic
44C2×#41×C31—21no—
45C2×#41×C31—21no—
46C2×#41×C31—21no—
47C2×#41×C31—21no—
48C2×#41×C31—44no—
49C22×Q8×C31C2×C411yescharacteristic, complemented
50C22×D4×C31C2×C412yes—
51C22×D4×C31C2×C412yes—
52C22×D4×C31C2×C411yescharacteristic, complemented
53C22×D4×C31C2312yes—
54C23×C4×C31—22no—
55C23×C4×C31—44no—
56C23×C4×C31C2×C411yescharacteristic
57C23×C4×C31C2×C411yescharacteristic
58C23×C4×C31C2×C411yescharacteristic
59C23×C4×C31C2×C411yescharacteristic
60C23×C4×C31C2×C412yescomplemented
61C23×C4×C31D411yescharacteristic
62C23×C4×C31D411yescharacteristic
63C23×C4×C31D411yescharacteristic
64C23×C4×C31D411yescharacteristic
65C23×C4×C31D411yescharacteristic
66C23×C4×C31D411yescharacteristic
67C23×C4×C31D411yescharacteristic
68C23×C4×C31D411yescharacteristic
69C23×C4×C31C2311yescharacteristic
70C23×C4×C31C2311yescharacteristic
71C31×#123—22no—
72C31×#123—22no—
73C31×#123—22no—
74C31×#123—22no—
75C31×C22⋊Q8—21no—
76C31×C22⋊Q8—21no—
77C31×C22⋊Q8—21no—
78C31×C22⋊Q8—21no—
79C31×C22⋊Q8—21no—
80C31×C22⋊Q8—21no—
81C31×C22⋊Q8—21no—
82C31×C22⋊Q8—21no—
83C31×#121—21no—
84C31×#121—21no—
85C31×#121—21no—
86C31×#121—21no—
87C31×#121—21no—
88C31×#121—21no—
89C31×#121—21no—
90C31×#121—21no—
91C31×#120—22no—
92C31×#120—22no—
93C31×#120—22no—
94C31×#120—22no—
95C4×D4×C31—22no—
96C4×D4×C31—22no—
97C4×D4×C31—22no—
98C4×D4×C31—22no—
99C4×D4×C31—22no—
100C4×D4×C31—22no—
101C4×D4×C31—22no—
102C4×D4×C31—22no—
103C31×#117—21no—
104C31×#117—21no—
105C31×#117—21no—
106C31×#117—21no—
107C31×#117—44no—
108C2×C4⋊C4×C31—22no—
109C2×C4⋊C4×C31—22no—
110C2×C4⋊C4×C31—22no—
111C2×C4⋊C4×C31—44no—
112C2×C4⋊C4×C31C2×C411yescharacteristic, complemented
113C2×C4⋊C4×C31C2×C411yescharacteristic, complemented
114C2×C4⋊C4×C31C2×C412yescomplemented
115C2×C4⋊C4×C31C2×C412yescomplemented
116C2×C22⋊C4×C31—22no—
117C2×C22⋊C4×C31—22no—
118C2×C22⋊C4×C31—22no—
119C2×C22⋊C4×C31—44no—
120C2×C22⋊C4×C31C2×C412yes—
121C2×C22⋊C4×C31C2×C412yes—
122C2×C22⋊C4×C31C2×C412yescomplemented
123C2×C22⋊C4×C31C2×C412yescomplemented
124C2×C22⋊C4×C31C2314yes—
125C2×C22⋊C4×C31C2314yes—
126C2×C22⋊C4×C31C2312yes—
127C2×C42×C31—22no—
128C2×C42×C31C2×C412yescomplemented
129C31×#99—48no—
130C31×#95—22no—
131C31×#95—22no—
132C31×#95—22no—
133C31×#95—22no—
134C24×C31—22no—
135C24×C31—22no—
136C24×C31—42no—
137C24×C31—42no—
138C24×C31C22×C411yescharacteristic
139C24×C31C22×C411yescharacteristic
140C24×C31C22×C412yes—
141C24×C31C2×D411yescharacteristic
142C24×C31C2×D411yescharacteristic
143C24×C31C2×D411yescharacteristic
144C24×C31C2×D411yescharacteristic
145C24×C31C2411yescharacteristic
146#41×C31—44no—
147#41×C31—44no—
148#41×C31—44no—
149#41×C31—44no—
150C2×Q8×C31—21no—
151C2×Q8×C31—21no—
152C2×Q8×C31—42no—
153C2×D4×C31—22no—
154C2×D4×C31—22no—
155C2×D4×C31—22no—
156C2×D4×C31—22no—
157C2×D4×C31—22no—
158C2×D4×C31—22no—
159C2×D4×C31—24no—
160C2×D4×C31—24no—
161C2×D4×C31—21no—
162C2×D4×C31—21no—
163C2×D4×C31—42no—
164C2×D4×C31—44no—
165C2×D4×C31—44no—
166C22×C4×C31—24no—
167C22×C4×C31—24no—
168C22×C4×C31—24no—
169C22×C4×C31—22no—
170C22×C4×C31—22no—
171C22×C4×C31—24no—
172C22×C4×C31—24no—
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×C31—44no—
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×C412yes—
205C22×C4×C31C22×C411yescharacteristic
206C22×C4×C31C22×C411yescharacteristic
207C22×C4×C31C22×C412yes—
208C22×C4×C31C22×C412yes—
209C22×C4×C31C22×C411yescharacteristic
210C22×C4×C31C22×C411yescharacteristic
211C22×C4×C31C2×D411yescharacteristic
212C22×C4×C31C2×D411yescharacteristic
213C22×C4×C31C2×D411yescharacteristic
214C22×C4×C31C2×D411yescharacteristic
215C22×C4×C31C2×D411yescharacteristic
216C22×C4×C31C2×D411yescharacteristic
217C22×C4×C31C2×D411yescharacteristic
218C22×C4×C31C2×D411yescharacteristic
219C4⋊C4×C31—21no—
220C4⋊C4×C31—21no—
221C4⋊C4×C31—21no—
222C4⋊C4×C31—21no—
223C4⋊C4×C31—22no—
224C4⋊C4×C31—22no—
225C4⋊C4×C31—22no—
226C4⋊C4×C31—22no—
227C4⋊C4×C31—44no—
228C4⋊C4×C31—44no—
229C4⋊C4×C31—44no—
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—
239C22⋊C4×C31—22no—
240C22⋊C4×C31—24no—
241C22⋊C4×C31—28no—
242C22⋊C4×C31—24no—
243C22⋊C4×C31—44no—
244C22⋊C4×C31—44no—
245C22⋊C4×C31—44no—
246C42×C31—22no—
247C42×C31—22no—
248C42×C31—44no—
249#21874C3111yesmaximal, characteristic, direct product factor, Sylow
250C23×C31—21no—
251C23×C31—21no—
252C23×C31—22no—
253C23×C31—22no—
254C23×C31—22no—
255C23×C31—22no—
256C23×C31—21no—
257C23×C31—21no—
258C23×C31—22no—
259C23×C31—22no—
260C23×C31—22no—
261C23×C31—22no—
262C23×C31—22no—
263C23×C31—22no—
264C23×C31—22no—
265C23×C31—24no—
266C23×C31—41no—
267C23×C31—41no—
268C23×C31—41no—
269C23×C31—41no—
270C23×C31—41no—
271C23×C31—41no—
272C23×C31—41no—
273C23×C31—41no—
274C23×C31—48no—
275C23×C31—48no—
276C23×C31—42no—
277C23×C31—42no—
278C23×C31C2×C22⋊C411yescharacteristic
279C23×C31C2×C22⋊C411yescharacteristic
280C23×C31C2×C22⋊C411yescharacteristic
281C23×C31C2×C22⋊C411yescharacteristic
282C23×C31C23×C411yescharacteristic
283C23×C31C22×D411yescharacteristic
284C23×C31C22×D411yescharacteristic
285C23×C31H(5,𝔽2)12yes—
286C23×C312−1+412yes—
287Q8×C31—42no—
288Q8×C31—42no—
289D4×C31—42no—
290D4×C31—44no—
291D4×C31—44no—
292D4×C31—42no—
293D4×C31—42no—
294D4×C31—44no—
295D4×C31—44no—
296D4×C31—44no—
297D4×C31—42no—
298C2×C4×C31—22no—
299C2×C4×C31—22no—
300C2×C4×C31—22no—
301C2×C4×C31—22no—
302C2×C4×C31—22no—
303C2×C4×C31—22no—
304C2×C4×C31—22no—
305C2×C4×C31—22no—
306C2×C4×C31—22no—
307C2×C4×C31—22no—
308C2×C4×C31—22no—
309C2×C4×C31—22no—
310C2×C4×C31—22no—
311C2×C4×C31—22no—
312C2×C4×C31—22no—
313C2×C4×C31—22no—
314C2×C4×C31—22no—
315C2×C4×C31—22no—
316C2×C4×C31—24no—
317C2×C4×C31—41no—
318C2×C4×C31—41no—
319C2×C4×C31—41no—
320C2×C4×C31—41no—
321C2×C4×C31—41no—
322C2×C4×C31—41no—
323C2×C4×C31—41no—
324C2×C4×C31—41no—
325C2×C4×C31—41no—
326C2×C4×C31—41no—
327C2×C4×C31—41no—
328C2×C4×C31—41no—
329C2×C4×C31—44no—
330C2×C4×C31—44no—
331C2×C4×C31—42no—
332C2×C4×C31—42no—
333C2×C4×C31—44no—
334C2×C4×C31—44no—
335C2×C4×C31—44no—
336C2×C4×C31—44no—
337C2×C4×C31—44no—
338C2×C4×C31—44no—
339C2×C4×C31—88no—
340C2×C4×C31#9914yescomplemented
341C2×C4×C31C2×C22⋊C411yescharacteristic
342C2×C4×C31C2×C22⋊C411yescharacteristic
343C2×C4×C31C2×C22⋊C411yescharacteristic
344C2×C4×C31C2×C22⋊C411yescharacteristic
345C2×C4×C31C2×C22⋊C411yescharacteristic
346C2×C4×C31C2×C22⋊C411yescharacteristic
347C2×C4×C31C2×C22⋊C411yescharacteristic
348C2×C4×C31C2×C22⋊C411yescharacteristic
349C2×#525C2×C3111yescharacteristic
350#2280C2×C3111yescharacteristic, complemented
351C2×#380C2×C3111yescharacteristic, complemented
352#1996C2×C3112yescomplemented
353#1964C2×C3112yescomplemented
354#1898C2×C3114yescomplemented
355#1799C2×C3114yescomplemented
356C22×C31—24no—
357C22×C31—24no—
358C22×C31—21no—
359C22×C31—21no—
360C22×C31—21no—
361C22×C31—21no—
362C22×C31—21no—
363C22×C31—21no—
364C22×C31—21no—
365C22×C31—21no—
366C22×C31—21no—
367C22×C31—21no—
368C22×C31—21no—
369C22×C31—21no—
370C22×C31—21no—
371C22×C31—21no—
372C22×C31—21no—
373C22×C31—21no—
374C22×C31—42no—
375C22×C31—42no—
376C22×C31—44no—
377C22×C31—44no—
378C22×C31—44no—
379C22×C31—44no—
380C22×C31—42no—
381C22×C31—42no—
382C22×C31—42no—
383C22×C31—42no—
384C22×C31—42no—
385C22×C31—84no—
386C22×C31C2×#9912yes—
387C22×C31#41012yes—
388C22×C31C22×C22⋊C411yescharacteristic
389C22×C31#52012yes—
390C22×C31#53511yescharacteristic
391C22×C31#53611yescharacteristic
392C22×C31#53712yes—
393C4×C31—21no—
394C4×C31—21no—
395C4×C31—21no—
396C4×C31—21no—
397C4×C31—21no—
398C4×C31—21no—
399C4×C31—42no—
400C4×C31—42no—
401C4×C31—42no—
402C4×C31—84no—
403C4×C31—84no—
404C4×C31C2×#9912yes—
405C4×C31C2×#9912yes—
406C22×#41C4×C3111yescharacteristic, complemented
407C24×C4C22×C3111yescharacteristic
408#525—21no—
409#525—21no—
410#525—21no—
411#525—21no—
412#525—21no—
413#525—21no—
414#525—21no—
415#525—21no—
416C2×#123C4×C3112yescomplemented
417C2×C22⋊Q8C4×C3111yescharacteristic, complemented
418C2×C22⋊Q8C22×C3111yescharacteristic
419C2×#121C4×C3111yescharacteristic, complemented
420C2×#121C22×C3111yescharacteristic
421C2×#120C22×C3112yes—
422C2×C4×D4C4×C3112yescomplemented
423C2×C4×D4C22×C3112yes—
424C2×#117—21no—
425C2×#117C4×C3111yescharacteristic, complemented
426C22×C4⋊C4—21no—
427C22×C22⋊C4C22×C3112yes—
428C2×#99C22×C3118yes—
429#381—21no—
430#380—21no—
431#380—21no—
432#380—21no—
433#380C22×C3112yes—
434#380C22×C3112yes—
435#380C22×C3112yes—
436#379C22×C3112yes—
437C4×C22⋊C4—21no—
438C4×C22⋊C4C22×C3112yes—
439C2×#95—21no—
440#342C22×C3118yes—
441C2×C31—21no—
442C2×C31—22no—
443C2×C31—21no—
444C2×C31—22no—
445C2×C31—22no—
446C2×C31—22no—
447C2×C31—41no—
448C2×C31—41no—
449C2×C31—82no—
450C2×C31#231111yescharacteristic
451C2×C31C22×#9911yescharacteristic
452C2×C31C2×#41011yescharacteristic
453C25C23×C3111yescharacteristic
454C2×#41—21no—
455C2×#41—21no—
456C2×#41—21no—
457C2×#41—21no—
458C2×#41—44no—
459C22×Q8C2×C4×C3111yescharacteristic, complemented
460C22×D4C2×C4×C3112yes—
461C22×D4C2×C4×C3112yes—
462C22×D4C2×C4×C3111yescharacteristic, complemented
463C22×D4C23×C3112yes—
464C23×C4—22no—
465C23×C4—44no—
466C23×C4C2×C4×C3111yescharacteristic
467C23×C4C2×C4×C3111yescharacteristic
468C23×C4C2×C4×C3111yescharacteristic
469C23×C4C2×C4×C3111yescharacteristic
470C23×C4C2×C4×C3112yescomplemented
471C23×C4D4×C3111yescharacteristic
472C23×C4D4×C3111yescharacteristic
473C23×C4D4×C3111yescharacteristic
474C23×C4D4×C3111yescharacteristic
475C23×C4D4×C3111yescharacteristic
476C23×C4D4×C3111yescharacteristic
477C23×C4D4×C3111yescharacteristic
478C23×C4D4×C3111yescharacteristic
479C23×C4C23×C3111yescharacteristic
480C23×C4C23×C3111yescharacteristic
481#123—22no—
482#123—22no—
483#123—22no—
484#123—22no—
485C22⋊Q8—21no—
486C22⋊Q8—21no—
487C22⋊Q8—21no—
488C22⋊Q8—21no—
489C22⋊Q8—21no—
490C22⋊Q8—21no—
491C22⋊Q8—21no—
492C22⋊Q8—21no—
493#121—21no—
494#121—21no—
495#121—21no—
496#121—21no—
497#121—21no—
498#121—21no—
499#121—21no—
500#121—21no—
501#120—22no—
502#120—22no—
503#120—22no—
504#120—22no—
505C4×D4—22no—
506C4×D4—22no—
507C4×D4—22no—
508C4×D4—22no—
509C4×D4—22no—
510C4×D4—22no—
511C4×D4—22no—
512C4×D4—22no—
513#117—21no—
514#117—21no—
515#117—21no—
516#117—21no—
517#117—44no—
518C2×C4⋊C4—22no—
519C2×C4⋊C4—22no—
520C2×C4⋊C4—22no—
521C2×C4⋊C4—44no—
522C2×C4⋊C4C2×C4×C3111yescharacteristic, complemented
523C2×C4⋊C4C2×C4×C3111yescharacteristic, complemented
524C2×C4⋊C4C2×C4×C3112yescomplemented
525C2×C4⋊C4C2×C4×C3112yescomplemented
526C2×C22⋊C4—22no—
527C2×C22⋊C4—22no—
528C2×C22⋊C4—22no—
529C2×C22⋊C4—44no—
530C2×C22⋊C4C2×C4×C3112yes—
531C2×C22⋊C4C2×C4×C3112yes—
532C2×C22⋊C4C2×C4×C3112yescomplemented
533C2×C22⋊C4C2×C4×C3112yescomplemented
534C2×C22⋊C4C23×C3114yes—
535C2×C22⋊C4C23×C3114yes—
536C2×C22⋊C4C23×C3112yes—
537C2×C42—22no—
538C2×C42C2×C4×C3112yescomplemented
539#99—48no—
540#95—22no—
541#95—22no—
542#95—22no—
543#95—22no—
544C31#2187411yescharacteristic, direct product factor, Sylow
545C24—22no—
546C24—22no—
547C24—42no—
548C24—42no—
549C24C22×C4×C3111yescharacteristic
550C24C22×C4×C3111yescharacteristic
551C24C22×C4×C3112yes—
552C24C2×D4×C3111yescharacteristic
553C24C2×D4×C3111yescharacteristic
554C24C2×D4×C3111yescharacteristic
555C24C2×D4×C3111yescharacteristic
556C24C24×C3111yescharacteristic
557#41—44no—
558#41—44no—
559#41—44no—
560#41—44no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—42no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—24no—
571C2×D4—24no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—42no—
575C2×D4—44no—
576C2×D4—44no—
577C22×C4—24no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—24no—
583C22×C4—24no—
584C22×C4—42no—
585C22×C4—42no—
586C22×C4—42no—
587C22×C4—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—42no—
594C22×C4—42no—
595C22×C4—44no—
596C22×C4—44no—
597C22×C4—44no—
598C22×C4—44no—
599C22×C4C22⋊C4×C3111yescharacteristic
600C22×C4C22⋊C4×C3111yescharacteristic
601C22×C4C22⋊C4×C3111yescharacteristic
602C22×C4C22⋊C4×C3111yescharacteristic
603C22×C4C22⋊C4×C3111yescharacteristic
604C22×C4C22⋊C4×C3111yescharacteristic
605C22×C4C22⋊C4×C3111yescharacteristic
606C22×C4C22⋊C4×C3111yescharacteristic
607C22×C4C22⋊C4×C3111yescharacteristic
608C22×C4C22⋊C4×C3111yescharacteristic
609C22×C4C22⋊C4×C3111yescharacteristic
610C22×C4C22⋊C4×C3111yescharacteristic
611C22×C4C22⋊C4×C3111yescharacteristic
612C22×C4C22⋊C4×C3111yescharacteristic
613C22×C4C22⋊C4×C3111yescharacteristic
614C22×C4C22⋊C4×C3111yescharacteristic
615C22×C4C22×C4×C3112yes—
616C22×C4C22×C4×C3111yescharacteristic
617C22×C4C22×C4×C3111yescharacteristic
618C22×C4C22×C4×C3112yes—
619C22×C4C22×C4×C3112yes—
620C22×C4C22×C4×C3111yescharacteristic
621C22×C4C22×C4×C3111yescharacteristic
622C22×C4C2×D4×C3111yescharacteristic
623C22×C4C2×D4×C3111yescharacteristic
624C22×C4C2×D4×C3111yescharacteristic
625C22×C4C2×D4×C3111yescharacteristic
626C22×C4C2×D4×C3111yescharacteristic
627C22×C4C2×D4×C3111yescharacteristic
628C22×C4C2×D4×C3111yescharacteristic
629C22×C4C2×D4×C3111yescharacteristic
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4—22no—
637C4⋊C4—22no—
638C4⋊C4—44no—
639C4⋊C4—44no—
640C4⋊C4—44no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—22no—
646C22⋊C4—22no—
647C22⋊C4—22no—
648C22⋊C4—22no—
649C22⋊C4—22no—
650C22⋊C4—22no—
651C22⋊C4—24no—
652C22⋊C4—28no—
653C22⋊C4—24no—
654C22⋊C4—44no—
655C22⋊C4—44no—
656C22⋊C4—44no—
657C42—22no—
658C42—22no—
659C42—44no—
660C23—22no—
661C23—22no—
662C23—21no—
663C23—21no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—21no—
671C23—21no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—24no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—48no—
685C23—48no—
686C23—42no—
687C23—42no—
688C23C2×C22⋊C4×C3111yescharacteristic
689C23C2×C22⋊C4×C3111yescharacteristic
690C23C2×C22⋊C4×C3111yescharacteristic
691C23C2×C22⋊C4×C3111yescharacteristic
692C23C23×C4×C3111yescharacteristic
693C23C22×D4×C3111yescharacteristic
694C23C22×D4×C3111yescharacteristic
695C23C31×H(5,𝔽2)12yes—
696C23C31×2−1+412yes—
697Q8—42no—
698Q8—42no—
699D4—42no—
700D4—44no—
701D4—44no—
702D4—44no—
703D4—44no—
704D4—42no—
705D4—42no—
706D4—44no—
707D4—42no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—24no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—44no—
740C2×C4—44no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—44no—
744C2×C4—44no—
745C2×C4—44no—
746C2×C4—44no—
747C2×C4—44no—
748C2×C4—44no—
749C2×C4—88no—
750C2×C4C31×#9914yescomplemented
751C2×C4C2×C22⋊C4×C3111yescharacteristic
752C2×C4C2×C22⋊C4×C3111yescharacteristic
753C2×C4C2×C22⋊C4×C3111yescharacteristic
754C2×C4C2×C22⋊C4×C3111yescharacteristic
755C2×C4C2×C22⋊C4×C3111yescharacteristic
756C2×C4C2×C22⋊C4×C3111yescharacteristic
757C2×C4C2×C22⋊C4×C3111yescharacteristic
758C2×C4C2×C22⋊C4×C3111yescharacteristic
759C22—24no—
760C22—24no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—21no—
765C22—21no—
766C22—21no—
767C22—21no—
768C22—21no—
769C22—21no—
770C22—21no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—21no—
775C22—21no—
776C22—21no—
777C22—42no—
778C22—42no—
779C22—44no—
780C22—44no—
781C22—44no—
782C22—44no—
783C22—42no—
784C22—42no—
785C22—42no—
786C22—42no—
787C22—42no—
788C22—84no—
789C22C2×C31×#9912yes—
790C22C31×#41012yes—
791C22C22×C22⋊C4×C3111yescharacteristic
792C22C31×#52012yes—
793C22C31×#53511yescharacteristic
794C22C31×#53611yescharacteristic
795C22C31×#53712yes—
796C4—21no—
797C4—21no—
798C4—21no—
799C4—21no—
800C4—21no—
801C4—21no—
802C4—42no—
803C4—42no—
804C4—42no—
805C4—84no—
806C4—84no—
807C4C2×C31×#9912yes—
808C4C2×C31×#9912yes—
809C2—21no—
810C2—22no—
811C2—22no—
812C2—22no—
813C2—21no—
814C2—22no—
815C2—41no—
816C2—41no—
817C2—82no—
818C2C31×#231111yescharacteristic
819C2C22×C31×#9911yescharacteristic
820C2C2×C31×#41011yescharacteristic
subgroupG/H
center, socleC22×C31C22×C22⋊C4
commutatorC23C23×C4×C31
Frattini, cosocleC24C24×C31
prime radicalC2×C31×#525C2
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C31 ◁ C24×C4×C31 ◁ G

Complements

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

NH ≅ G/Ntype
2. C31×#2280C2semidirect
3. C2×C31×#380C2semidirect
4. C31×#1996C2semidirect
5. C31×#1964C2semidirect
6. C31×#1898C2semidirect
7. C31×#1799C2semidirect
8. C22×#41×C31C4semidirect
18. C2×C31×#123C4semidirect
19. C2×C31×C22⋊Q8C4semidirect
21. C2×C31×#121C4semidirect
24. C2×C4×D4×C31C4semidirect
27. C2×C31×#117C4semidirect
49. C22×Q8×C31C2×C4semidirect
52. C22×D4×C31C2×C4semidirect
60. C23×C4×C31C2×C4semidirect
112. C2×C4⋊C4×C31C2×C4semidirect
113. C2×C4⋊C4×C31C2×C4semidirect
114. C2×C4⋊C4×C31C2×C4semidirect
115. C2×C4⋊C4×C31C2×C4semidirect
122. C2×C22⋊C4×C31C2×C4semidirect
123. C2×C22⋊C4×C31C2×C4semidirect
128. C2×C42×C31C2×C4semidirect
249. #21874C31direct (N × H)
340. C2×C4×C31#99semidirect
350. #2280C2×C31semidirect
351. C2×#380C2×C31semidirect
352. #1996C2×C31semidirect
353. #1964C2×C31semidirect
354. #1898C2×C31semidirect
355. #1799C2×C31semidirect
406. C22×#41C4×C31semidirect
416. C2×#123C4×C31semidirect
417. C2×C22⋊Q8C4×C31semidirect
419. C2×#121C4×C31semidirect
422. C2×C4×D4C4×C31semidirect
425. C2×#117C4×C31semidirect
459. C22×Q8C2×C4×C31semidirect
462. C22×D4C2×C4×C31semidirect
470. C23×C4C2×C4×C31semidirect
522. C2×C4⋊C4C2×C4×C31semidirect
523. C2×C4⋊C4C2×C4×C31semidirect
524. C2×C4⋊C4C2×C4×C31semidirect
525. C2×C4⋊C4C2×C4×C31semidirect
532. C2×C22⋊C4C2×C4×C31semidirect
533. C2×C22⋊C4C2×C4×C31semidirect
538. C2×C42C2×C4×C31semidirect
544. C31#21874direct (N × H)
750. C2×C4C31×#99semidirect

Maximal subgroups

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

subgroupindex
C2×C31×#5252
C31×#22802
C2×C31×#3802
C31×#19962
C31×#19642
C31×#18982
C31×#17992
#2187431