Finite Group Databasebeta

← C31×#14016 #21470775

Subgroups — C31×#14016 #21470775

Order 7936.

2590 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D4×C31C211yesmaximal, characteristic
2C2×C31×#386C211yesmaximal, characteristic
3C2×C31×#386C211yesmaximal, characteristic
4C2×C31×#385C211yesmaximal, characteristic, complemented
5C22×C31×#95C211yesmaximal, characteristic, complemented
6C31×#1442C212yesmaximal, complemented
7C31×#1439C212yesmaximal, complemented
8C31×#1436C212yesmaximal, complemented
9C31×C22⋊#95C211yesmaximal, characteristic, complemented
10C31×C22⋊#95C211yesmaximal, characteristic, complemented
11C31×C22⋊#95C212yesmaximal, complemented
12C23×D4×C31C2211yescharacteristic
13C24×C4×C31C2211yescharacteristic
14C24×C4×C31C2211yescharacteristic
15C24×C4×C31C2211yescharacteristic
16C24×C4×C31C2211yescharacteristic
17C2×C4×D4×C31—24no—
18C2×C4×D4×C31—24no—
19C2×C4×D4×C31—24no—
20C22×C4⋊C4×C31C2211yescharacteristic
21C22×C4⋊C4×C31C2212yes—
22C22×C22⋊C4×C31C2211yescharacteristic
23C22×C22⋊C4×C31C2211yescharacteristic
24C22×C22⋊C4×C31C2212yes—
25C22×C22⋊C4×C31C2211yescharacteristic
26C22×C22⋊C4×C31C2211yescharacteristic
27C22×C22⋊C4×C31C2212yes—
28C22×C42×C31C2211yescharacteristic
29C31×#386—24no—
30C31×#386C418yescomplemented
31C31×#385—24no—
32C2×C31×#95—24no—
33C2×C31×#95C2212yes—
34C2×C31×#95C2212yes—
35C2×C31×#95C2212yes—
36C2×C31×#95C2212yes—
37C2×C31×#95C2212yes—
38C2×C31×#95C2212yes—
39C2×C31×#95C2212yes—
40C2×C31×#95C2212yes—
41C2×C31×#95C2212yes—
42C25×C31C2311yescharacteristic
43C25×C31C2311yescharacteristic
44C22×D4×C31—22no—
45C22×D4×C31—22no—
46C22×D4×C31—22no—
47C22×D4×C31—22no—
48C22×D4×C31C2×C414yes—
49C22×D4×C31D414yes—
50C22×D4×C31Q814yes—
51C23×C4×C31—22no—
52C23×C4×C31—22no—
53C23×C4×C31—22no—
54C23×C4×C31—22no—
55C23×C4×C31—22no—
56C23×C4×C31—22no—
57C23×C4×C31—22no—
58C23×C4×C31—22no—
59C23×C4×C31—24no—
60C23×C4×C31—24no—
61C23×C4×C31—22no—
62C23×C4×C31—22no—
63C23×C4×C31—24no—
64C23×C4×C31—42no—
65C23×C4×C31—42no—
66C23×C4×C31—42no—
67C23×C4×C31—42no—
68C23×C4×C31—42no—
69C23×C4×C31C2×C414yescomplemented
70C23×C4×C31D414yes—
71C23×C4×C31C2312yes—
72C23×C4×C31C2312yes—
73C23×C4×C31C2312yes—
74C23×C4×C31C2311yescharacteristic
75C23×C4×C31C2311yescharacteristic
76C23×C4×C31C2311yescharacteristic
77C23×C4×C31C2312yes—
78C23×C4×C31C2311yescharacteristic
79C23×C4×C31C2311yescharacteristic
80C4×D4×C31—232no—
81C2×C4⋊C4×C31—22no—
82C2×C4⋊C4×C31—22no—
83C2×C4⋊C4×C31—22no—
84C2×C4⋊C4×C31—24no—
85C2×C4⋊C4×C31—24no—
86C2×C4⋊C4×C31—42no—
87C2×C22⋊C4×C31—22no—
88C2×C22⋊C4×C31—22no—
89C2×C22⋊C4×C31—22no—
90C2×C22⋊C4×C31—22no—
91C2×C22⋊C4×C31—22no—
92C2×C22⋊C4×C31—22no—
93C2×C22⋊C4×C31—22no—
94C2×C22⋊C4×C31—24no—
95C2×C22⋊C4×C31—22no—
96C2×C22⋊C4×C31—22no—
97C2×C22⋊C4×C31—22no—
98C2×C22⋊C4×C31—24no—
99C2×C22⋊C4×C31—42no—
100C2×C22⋊C4×C31—42no—
101C2×C22⋊C4×C31—42no—
102C2×C22⋊C4×C31C2×C414yescomplemented
103C2×C22⋊C4×C31C2×C418yescomplemented
104C2×C22⋊C4×C31D414yes—
105C2×C42×C31—22no—
106C2×C42×C31—22no—
107C2×C42×C31—22no—
108C31×#95—24no—
109C31×#95—24no—
110C31×#95—24no—
111C31×#95—24no—
112C31×#95—24no—
113C31×#95—42no—
114C31×#95—42no—
115C31×#95—42no—
116C31×#95C2×C418yescomplemented
117C24×C31—22no—
118C24×C31—22no—
119C24×C31—22no—
120C24×C31—22no—
121C24×C31—21no—
122C24×C31—21no—
123C24×C31—22no—
124C24×C31—22no—
125C24×C31—21no—
126C24×C31—21no—
127C24×C31—22no—
128C24×C31—22no—
129C24×C31C22×C412yes—
130C24×C31C22×C412yes—
131C24×C31C2×D412yes—
132C24×C31C2×D412yes—
133C24×C31C2×D412yes—
134C24×C31C2×D412yes—
135C24×C31C2×Q812yes—
136C24×C31C2×Q812yes—
137C24×C31#4112yes—
138C24×C31#4112yes—
139C24×C31C2411yescharacteristic
140C2×D4×C31—28no—
141C2×D4×C31—28no—
142C2×D4×C31—28no—
143C2×D4×C31—28no—
144C2×D4×C31—28no—
145C2×D4×C31—28no—
146C2×D4×C31C4⋊C4116yescomplemented
147C22×C4×C31—21no—
148C22×C4×C31—21no—
149C22×C4×C31—21no—
150C22×C4×C31—21no—
151C22×C4×C31—21no—
152C22×C4×C31—21no—
153C22×C4×C31—22no—
154C22×C4×C31—28no—
155C22×C4×C31—28no—
156C22×C4×C31—28no—
157C22×C4×C31—28no—
158C22×C4×C31—22no—
159C22×C4×C31—22no—
160C22×C4×C31—22no—
161C22×C4×C31—22no—
162C22×C4×C31—22no—
163C22×C4×C31—21no—
164C22×C4×C31—21no—
165C22×C4×C31—21no—
166C22×C4×C31—21no—
167C22×C4×C31—21no—
168C22×C4×C31—21no—
169C22×C4×C31—22no—
170C22×C4×C31—22no—
171C22×C4×C31—22no—
172C22×C4×C31—22no—
173C22×C4×C31—22no—
174C22×C4×C31—22no—
175C22×C4×C31—22no—
176C22×C4×C31—22no—
177C22×C4×C31—22no—
178C22×C4×C31—22no—
179C22×C4×C31—22no—
180C22×C4×C31—22no—
181C22×C4×C31—22no—
182C22×C4×C31—22no—
183C22×C4×C31—22no—
184C22×C4×C31—22no—
185C22×C4×C31—22no—
186C22×C4×C31—22no—
187C22×C4×C31—22no—
188C22×C4×C31—28no—
189C22×C4×C31—22no—
190C22×C4×C31—22no—
191C22×C4×C31—22no—
192C22×C4×C31—22no—
193C22×C4×C31—22no—
194C22×C4×C31—22no—
195C22×C4×C31—22no—
196C22×C4×C31—48no—
197C22×C4×C31—44no—
198C22×C4×C31—48no—
199C22×C4×C31—48no—
200C22×C4×C31—48no—
201C22×C4×C31—48no—
202C22×C4×C31—48no—
203C22×C4×C31—48no—
204C22×C4×C31—44no—
205C22×C4×C31—44no—
206C22×C4×C31—44no—
207C22×C4×C31—44no—
208C22×C4×C31—48no—
209C22×C4×C31—44no—
210C22×C4×C31—44no—
211C22×C4×C31C22×C414yes—
212C22×C4×C31C22×C414yes—
213C22×C4×C31C22×C412yes—
214C22×C4×C31C2×D412yes—
215C22×C4×C31C2×D412yes—
216C22×C4×C31C2×D412yes—
217C22×C4×C31C2×D412yes—
218C22×C4×C31C2×D412yes—
219C22×C4×C31C2×Q812yes—
220C22×C4×C31#4114yes—
221C22×C4×C31#4114yes—
222C4⋊C4×C31—28no—
223C4⋊C4×C31—48no—
224C22⋊C4×C31—28no—
225C22⋊C4×C31—28no—
226C22⋊C4×C31—28no—
227C22⋊C4×C31—48no—
228C22⋊C4×C31—48no—
229C22⋊C4×C31—44no—
230C42×C31—28no—
231#14016C3111yesmaximal, characteristic, direct product factor, Sylow
232C23×C31—24no—
233C23×C31—24no—
234C23×C31—22no—
235C23×C31—22no—
236C23×C31—24no—
237C23×C31—22no—
238C23×C31—22no—
239C23×C31—24no—
240C23×C31—24no—
241C23×C31—24no—
242C23×C31—24no—
243C23×C31—24no—
244C23×C31—24no—
245C23×C31—24no—
246C23×C31—24no—
247C23×C31—24no—
248C23×C31—22no—
249C23×C31—22no—
250C23×C31—24no—
251C23×C31—24no—
252C23×C31—22no—
253C23×C31—22no—
254C23×C31—22no—
255C23×C31—22no—
256C23×C31—24no—
257C23×C31—24no—
258C23×C31—24no—
259C23×C31—24no—
260C23×C31—41no—
261C23×C31—41no—
262C23×C31—42no—
263C23×C31—41no—
264C23×C31—41no—
265C23×C31—42no—
266C23×C31—42no—
267C23×C31—42no—
268C23×C31—42no—
269C23×C31—42no—
270C23×C31C2×C4⋊C414yes—
271C23×C31C2×C4⋊C414yes—
272C23×C31C4×D414yes—
273C23×C31C4×D414yes—
274C23×C31#12014yes—
275C23×C31C22⋊Q814yes—
276C23×C31C22⋊Q814yes—
277C23×C31#12314yes—
278C23×C31C23×C411yescharacteristic
279C23×C31C22×D411yescharacteristic
280C23×C31C22×D411yescharacteristic
281C23×C31C22×D411yescharacteristic
282C23×C31C22×Q811yescharacteristic
283C23×C31C2×#4111yescharacteristic
284C23×C31C2×#4111yescharacteristic
285C23×C31C2×#4112yes—
286C23×C31C2×#4112yes—
287C23×C31H(5,𝔽2)12yes—
288C23×C31H(5,𝔽2)12yes—
289D4×C31—232no—
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—24no—
299C2×C4×C31—24no—
300C2×C4×C31—24no—
301C2×C4×C31—24no—
302C2×C4×C31—24no—
303C2×C4×C31—24no—
304C2×C4×C31—24no—
305C2×C4×C31—24no—
306C2×C4×C31—22no—
307C2×C4×C31—22no—
308C2×C4×C31—22no—
309C2×C4×C31—22no—
310C2×C4×C31—24no—
311C2×C4×C31—22no—
312C2×C4×C31—24no—
313C2×C4×C31—24no—
314C2×C4×C31—24no—
315C2×C4×C31—24no—
316C2×C4×C31—416no—
317C2×C4×C31—416no—
318C2×C4×C31—416no—
319C2×C4×C31—416no—
320C2×C4×C31—42no—
321C2×C4×C31—41no—
322C2×C4×C31—41no—
323C2×C4×C31—42no—
324C2×C4×C31—41no—
325C2×C4×C31—41no—
326C2×C4×C31—42no—
327C2×C4×C31—42no—
328C2×C4×C31—42no—
329C2×C4×C31—42no—
330C2×C4×C31—42no—
331C2×C4×C31—42no—
332C2×C4×C31—42no—
333C2×C4×C31—42no—
334C2×C4×C31—42no—
335C2×C4×C31—42no—
336C2×C4×C31—42no—
337C2×C4×C31—42no—
338C2×C4×C31—42no—
339C2×C4×C31—42no—
340C2×C4×C31—42no—
341C2×C4×C31—42no—
342C2×C4×C31—42no—
343C2×C4×C31—42no—
344C2×C4×C31—42no—
345C2×C4×C31—42no—
346C2×C4×C31—42no—
347C2×C4×C31C2×C4⋊C414yes—
348C2×C4×C31#12314yes—
349C22×C4×D4C2×C3111yescharacteristic
350C2×#386C2×C3111yescharacteristic
351C2×#386C2×C3111yescharacteristic
352C2×#385C2×C3111yescharacteristic, complemented
353C22×#95C2×C3111yescharacteristic, complemented
354#1442C2×C3112yescomplemented
355#1439C2×C3112yescomplemented
356#1436C2×C3112yescomplemented
357C22⋊#95C2×C3111yescharacteristic, complemented
358C22⋊#95C2×C3111yescharacteristic, complemented
359C22⋊#95C2×C3112yescomplemented
360C22×C31—24no—
361C22×C31—24no—
362C22×C31—28no—
363C22×C31—28no—
364C22×C31—24no—
365C22×C31—24no—
366C22×C31—28no—
367C22×C31—28no—
368C22×C31—24no—
369C22×C31—24no—
370C22×C31—28no—
371C22×C31—24no—
372C22×C31—42no—
373C22×C31—42no—
374C22×C31—44no—
375C22×C31—42no—
376C22×C31—42no—
377C22×C31—44no—
378C22×C31—44no—
379C22×C31—42no—
380C22×C31—42no—
381C22×C31#38518yes—
382C22×C31C22×C4⋊C411yescharacteristic
383C22×C31C2×C4×D411yescharacteristic
384C22×C31C2×C4×D411yescharacteristic
385C22×C31C4×#4112yes—
386C22×C31#51812yes—
387C22×C31C2×#12011yescharacteristic
388C22×C31C2×C22⋊Q811yescharacteristic
389C22×C31C2×C22⋊Q811yescharacteristic
390C22×C31C2×#12311yescharacteristic
391C22×C31C2×#12311yescharacteristic
392C22×C31#52511yescharacteristic
393C22×C31#52912yes—
394C22×C31#53411yescharacteristic
395C22×C31#53511yescharacteristic
396C22×C31#53812yes—
397C22×C31#54612yes—
398C22×C31#54612yes—
399C22×C31#54612yes—
400C22×C31#54612yes—
401C22×C31#55312yes—
402C22×C31#55312yes—
403C22×C31#55412yes—
404C22×C31#55412yes—
405C4×C31—24no—
406C4×C31—24no—
407C4×C31—44no—
408C4×C31—44no—
409C4×C31—42no—
410C4×C31—44no—
411C4×C31—42no—
412C4×C31—42no—
413C4×C31—82no—
414C23×D4C22×C3111yescharacteristic
415C24×C4C22×C3111yescharacteristic
416C24×C4C22×C3111yescharacteristic
417C24×C4C22×C3111yescharacteristic
418C24×C4C22×C3111yescharacteristic
419C2×C4×D4—24no—
420C2×C4×D4—24no—
421C2×C4×D4—24no—
422C22×C4⋊C4C22×C3111yescharacteristic
423C22×C4⋊C4C22×C3112yes—
424C22×C22⋊C4C22×C3111yescharacteristic
425C22×C22⋊C4C22×C3111yescharacteristic
426C22×C22⋊C4C22×C3112yes—
427C22×C22⋊C4C22×C3111yescharacteristic
428C22×C22⋊C4C22×C3111yescharacteristic
429C22×C22⋊C4C22×C3112yes—
430C22×C42C22×C3111yescharacteristic
431#386—24no—
432#386C4×C3118yescomplemented
433#385—24no—
434C2×#95—24no—
435C2×#95C22×C3112yes—
436C2×#95C22×C3112yes—
437C2×#95C22×C3112yes—
438C2×#95C22×C3112yes—
439C2×#95C22×C3112yes—
440C2×#95C22×C3112yes—
441C2×#95C22×C3112yes—
442C2×#95C22×C3112yes—
443C2×#95C22×C3112yes—
444C2×C31—28no—
445C2×C31—44no—
446C2×C31C2×#38511yescharacteristic
447C2×C31C4×#12311yescharacteristic
448C2×C31#232111yescharacteristic
449C2×C31#234912yes—
450C2×C31#236412yes—
451C2×C31#240411yescharacteristic
452C2×C31#240511yescharacteristic
453C2×C31#244412yes—
454C2×C31#245012yes—
455C2×C31#248711yescharacteristic
456C2×C31#257911yescharacteristic
457C25C23×C3111yescharacteristic
458C25C23×C3111yescharacteristic
459C22×D4—22no—
460C22×D4—22no—
461C22×D4—22no—
462C22×D4—22no—
463C22×D4C2×C4×C3114yes—
464C22×D4D4×C3114yes—
465C22×D4Q8×C3114yes—
466C23×C4—22no—
467C23×C4—22no—
468C23×C4—22no—
469C23×C4—22no—
470C23×C4—22no—
471C23×C4—22no—
472C23×C4—22no—
473C23×C4—22no—
474C23×C4—24no—
475C23×C4—24no—
476C23×C4—22no—
477C23×C4—22no—
478C23×C4—24no—
479C23×C4—42no—
480C23×C4—42no—
481C23×C4—42no—
482C23×C4—42no—
483C23×C4—42no—
484C23×C4C2×C4×C3114yescomplemented
485C23×C4D4×C3114yes—
486C23×C4C23×C3112yes—
487C23×C4C23×C3112yes—
488C23×C4C23×C3112yes—
489C23×C4C23×C3111yescharacteristic
490C23×C4C23×C3111yescharacteristic
491C23×C4C23×C3111yescharacteristic
492C23×C4C23×C3112yes—
493C23×C4C23×C3111yescharacteristic
494C23×C4C23×C3111yescharacteristic
495C4×D4—232no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—22no—
499C2×C4⋊C4—24no—
500C2×C4⋊C4—24no—
501C2×C4⋊C4—42no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—22no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—22no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—24no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—24no—
514C2×C22⋊C4—42no—
515C2×C22⋊C4—42no—
516C2×C22⋊C4—42no—
517C2×C22⋊C4C2×C4×C3114yescomplemented
518C2×C22⋊C4C2×C4×C3118yescomplemented
519C2×C22⋊C4D4×C3114yes—
520C2×C42—22no—
521C2×C42—22no—
522C2×C42—22no—
523#95—24no—
524#95—24no—
525#95—24no—
526#95—24no—
527#95—24no—
528#95—42no—
529#95—42no—
530#95—42no—
531#95C2×C4×C3118yescomplemented
532C31#1401611yescharacteristic, direct product factor, Sylow
533C24—22no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—21no—
538C24—21no—
539C24—22no—
540C24—22no—
541C24—21no—
542C24—21no—
543C24—22no—
544C24—22no—
545C24C22×C4×C3112yes—
546C24C22×C4×C3112yes—
547C24C2×D4×C3112yes—
548C24C2×D4×C3112yes—
549C24C2×D4×C3112yes—
550C24C2×D4×C3112yes—
551C24C2×Q8×C3112yes—
552C24C2×Q8×C3112yes—
553C24#41×C3112yes—
554C24#41×C3112yes—
555C24C24×C3111yescharacteristic
556C2×D4—28no—
557C2×D4—28no—
558C2×D4—28no—
559C2×D4—28no—
560C2×D4—28no—
561C2×D4—28no—
562C2×D4C4⋊C4×C31116yescomplemented
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—22no—
570C22×C4—28no—
571C22×C4—28no—
572C22×C4—28no—
573C22×C4—28no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—28no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—48no—
613C22×C4—44no—
614C22×C4—48no—
615C22×C4—48no—
616C22×C4—48no—
617C22×C4—48no—
618C22×C4—48no—
619C22×C4—48no—
620C22×C4—44no—
621C22×C4—44no—
622C22×C4—44no—
623C22×C4—44no—
624C22×C4—48no—
625C22×C4—44no—
626C22×C4—44no—
627C22×C4C22×C4×C3114yes—
628C22×C4C22×C4×C3114yes—
629C22×C4C22×C4×C3112yes—
630C22×C4C2×D4×C3112yes—
631C22×C4C2×D4×C3112yes—
632C22×C4C2×D4×C3112yes—
633C22×C4C2×D4×C3112yes—
634C22×C4C2×D4×C3112yes—
635C22×C4C2×Q8×C3112yes—
636C22×C4#41×C3114yes—
637C22×C4#41×C3114yes—
638C4⋊C4—28no—
639C4⋊C4—48no—
640C22⋊C4—28no—
641C22⋊C4—28no—
642C22⋊C4—28no—
643C22⋊C4—48no—
644C22⋊C4—48no—
645C22⋊C4—44no—
646C42—28no—
647C23—24no—
648C23—24no—
649C23—22no—
650C23—22no—
651C23—24no—
652C23—22no—
653C23—22no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—24no—
662C23—24no—
663C23—22no—
664C23—22no—
665C23—24no—
666C23—24no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—22no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—41no—
676C23—41no—
677C23—42no—
678C23—41no—
679C23—41no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23C2×C4⋊C4×C3114yes—
686C23C2×C4⋊C4×C3114yes—
687C23C4×D4×C3114yes—
688C23C4×D4×C3114yes—
689C23C31×#12014yes—
690C23C31×C22⋊Q814yes—
691C23C31×C22⋊Q814yes—
692C23C31×#12314yes—
693C23C23×C4×C3111yescharacteristic
694C23C22×D4×C3111yescharacteristic
695C23C22×D4×C3111yescharacteristic
696C23C22×D4×C3111yescharacteristic
697C23C22×Q8×C3111yescharacteristic
698C23C2×#41×C3111yescharacteristic
699C23C2×#41×C3111yescharacteristic
700C23C2×#41×C3112yes—
701C23C2×#41×C3112yes—
702C23C31×H(5,𝔽2)12yes—
703C23C31×H(5,𝔽2)12yes—
704D4—232no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—24no—
726C2×C4—22no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—416no—
732C2×C4—416no—
733C2×C4—416no—
734C2×C4—416no—
735C2×C4—42no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—42no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4C2×C4⋊C4×C3114yes—
763C2×C4C31×#12314yes—
764C22—24no—
765C22—24no—
766C22—28no—
767C22—28no—
768C22—24no—
769C22—24no—
770C22—28no—
771C22—28no—
772C22—24no—
773C22—24no—
774C22—28no—
775C22—24no—
776C22—42no—
777C22—42no—
778C22—44no—
779C22—42no—
780C22—42no—
781C22—44no—
782C22—44no—
783C22—42no—
784C22—42no—
785C22C31×#38518yes—
786C22C22×C4⋊C4×C3111yescharacteristic
787C22C2×C4×D4×C3111yescharacteristic
788C22C2×C4×D4×C3111yescharacteristic
789C22C4×#41×C3112yes—
790C22C31×#51812yes—
791C22C2×C31×#12011yescharacteristic
792C22C2×C31×C22⋊Q811yescharacteristic
793C22C2×C31×C22⋊Q811yescharacteristic
794C22C2×C31×#12311yescharacteristic
795C22C2×C31×#12311yescharacteristic
796C22C31×#52511yescharacteristic
797C22C31×#52912yes—
798C22C31×#53411yescharacteristic
799C22C31×#53511yescharacteristic
800C22C31×#53812yes—
801C22C31×#54612yes—
802C22C31×#54612yes—
803C22C31×#54612yes—
804C22C31×#54612yes—
805C22C31×#55312yes—
806C22C31×#55312yes—
807C22C31×#55412yes—
808C22C31×#55412yes—
809C4—24no—
810C4—24no—
811C4—44no—
812C4—44no—
813C4—44no—
814C4—42no—
815C4—42no—
816C4—42no—
817C4—82no—
818C2—28no—
819C2—44no—
820C2C2×C31×#38511yescharacteristic
821C2C4×C31×#12311yescharacteristic
822C2C31×#232111yescharacteristic
823C2C31×#234912yes—
824C2C31×#236412yes—
825C2C31×#240411yescharacteristic
826C2C31×#240511yescharacteristic
827C2C31×#244412yes—
828C2C31×#245012yes—
829C2C31×#248711yescharacteristic
830C2C31×#257911yescharacteristic
subgroupG/H
center, socleC24×C31C24
commutatorC23C23×C4×C31
Frattini, cosocleC24C24×C31
prime radicalC23×D4×C31C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C31 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C31×#385C2semidirect
5. C22×C31×#95C2semidirect
6. C31×#1442C2semidirect
7. C31×#1439C2semidirect
8. C31×#1436C2semidirect
9. C31×C22⋊#95C2semidirect
10. C31×C22⋊#95C2semidirect
11. C31×C22⋊#95C2semidirect
30. C31×#386C4semidirect
69. C23×C4×C31C2×C4semidirect
102. C2×C22⋊C4×C31C2×C4semidirect
103. C2×C22⋊C4×C31C2×C4semidirect
116. C31×#95C2×C4semidirect
146. C2×D4×C31C4⋊C4semidirect
231. #14016C31direct (N × H)
352. C2×#385C2×C31semidirect
353. C22×#95C2×C31semidirect
354. #1442C2×C31semidirect
355. #1439C2×C31semidirect
356. #1436C2×C31semidirect
357. C22⋊#95C2×C31semidirect
358. C22⋊#95C2×C31semidirect
359. C22⋊#95C2×C31semidirect
432. #386C4×C31semidirect
484. C23×C4C2×C4×C31semidirect
517. C2×C22⋊C4C2×C4×C31semidirect
518. C2×C22⋊C4C2×C4×C31semidirect
531. #95C2×C4×C31semidirect
532. C31#14016direct (N × H)
562. C2×D4C4⋊C4×C31semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D4×C312
C2×C31×#3862
C2×C31×#3852
C22×C31×#952
C31×#14422
C31×#14392
C31×#14362
C31×C22⋊#952
#1401631