Finite Group Databasebeta

← C31×#13968 #21470727

Subgroups — C31×#13968 #21470727

Order 7936.

2742 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#123C211yesmaximal, characteristic
2C22×C4×D4×C31C211yesmaximal, characteristic
3C2×C31×#386C211yesmaximal, characteristic
4C2×C31×#381C211yesmaximal, characteristic, complemented
5C22×C31×#95C211yesmaximal, characteristic, complemented
6C31×#1441C212yesmaximal, complemented
7C31×#1440C212yesmaximal, complemented
8C31×#1436C212yesmaximal, complemented
9C31×C22⋊#95C211yesmaximal, characteristic, complemented
10C31×C22⋊#95C212yesmaximal, complemented
11C31×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×D4×C31C2211yescharacteristic
13C24×C4×C31C2211yescharacteristic
14C24×C4×C31C2211yescharacteristic
15C24×C4×C31C2211yescharacteristic
16C24×C4×C31C2211yescharacteristic
17C2×C31×#123—24no—
18C2×C31×#123—24no—
19C2×C31×#123C418yescomplemented
20C2×C4×D4×C31—24no—
21C2×C4×D4×C31—24no—
22C2×C4×D4×C31—24no—
23C22×C4⋊C4×C31C2211yescharacteristic
24C22×C4⋊C4×C31C2212yes—
25C22×C22⋊C4×C31C2211yescharacteristic
26C22×C22⋊C4×C31C2211yescharacteristic
27C22×C22⋊C4×C31C2212yes—
28C22×C22⋊C4×C31C2211yescharacteristic
29C22×C22⋊C4×C31C2212yes—
30C22×C22⋊C4×C31C2211yescharacteristic
31C22×C42×C31C2211yescharacteristic
32C31×#386—24no—
33C31×#381—24no—
34C2×C31×#95—24no—
35C2×C31×#95C2212yes—
36C2×C31×#95C2212yes—
37C2×C31×#95C2212yes—
38C2×C31×#95C2212yes—
39C2×C31×#95C2212yes—
40C2×C31×#95C2212yes—
41C2×C31×#95C2212yes—
42C2×C31×#95C2212yes—
43C2×C31×#95C2212yes—
44C25×C31C2311yescharacteristic
45C25×C31C2311yescharacteristic
46C22×D4×C31—22no—
47C22×D4×C31—22no—
48C22×D4×C31—22no—
49C22×D4×C31—22no—
50C22×D4×C31C2×C414yes—
51C22×D4×C31D414yes—
52C22×D4×C31D414yes—
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—22no—
60C23×C4×C31—22no—
61C23×C4×C31—22no—
62C23×C4×C31—22no—
63C23×C4×C31—22no—
64C23×C4×C31—22no—
65C23×C4×C31—24no—
66C23×C4×C31—24no—
67C23×C4×C31—22no—
68C23×C4×C31—22no—
69C23×C4×C31—24no—
70C23×C4×C31—42no—
71C23×C4×C31—42no—
72C23×C4×C31—42no—
73C23×C4×C31C2×C414yescomplemented
74C23×C4×C31D414yes—
75C23×C4×C31C2312yes—
76C23×C4×C31C2312yes—
77C23×C4×C31C2312yes—
78C23×C4×C31C2311yescharacteristic
79C23×C4×C31C2311yescharacteristic
80C23×C4×C31C2311yescharacteristic
81C23×C4×C31C2312yes—
82C23×C4×C31C2311yescharacteristic
83C23×C4×C31C2311yescharacteristic
84C31×#123—232no—
85C4×D4×C31—232no—
86C2×C4⋊C4×C31—22no—
87C2×C4⋊C4×C31—22no—
88C2×C4⋊C4×C31—22no—
89C2×C4⋊C4×C31—24no—
90C2×C4⋊C4×C31—24no—
91C2×C4⋊C4×C31C2×C418yescomplemented
92C2×C22⋊C4×C31—22no—
93C2×C22⋊C4×C31—22no—
94C2×C22⋊C4×C31—22no—
95C2×C22⋊C4×C31—22no—
96C2×C22⋊C4×C31—22no—
97C2×C22⋊C4×C31—24no—
98C2×C22⋊C4×C31—24no—
99C2×C22⋊C4×C31—22no—
100C2×C22⋊C4×C31—22no—
101C2×C22⋊C4×C31—22no—
102C2×C22⋊C4×C31—24no—
103C2×C22⋊C4×C31—22no—
104C2×C22⋊C4×C31—22no—
105C2×C22⋊C4×C31—24no—
106C2×C22⋊C4×C31—42no—
107C2×C22⋊C4×C31C2×C414yescomplemented
108C2×C22⋊C4×C31C2×C418yescomplemented
109C2×C22⋊C4×C31D414yes—
110C2×C42×C31—22no—
111C2×C42×C31—22no—
112C2×C42×C31—22no—
113C31×#95—24no—
114C31×#95—24no—
115C31×#95—24no—
116C31×#95—24no—
117C31×#95—24no—
118C31×#95—24no—
119C31×#95—24no—
120C31×#95—42no—
121C31×#95—42no—
122C24×C31—22no—
123C24×C31—22no—
124C24×C31—22no—
125C24×C31—22no—
126C24×C31—21no—
127C24×C31—21no—
128C24×C31—22no—
129C24×C31—22no—
130C24×C31—21no—
131C24×C31—21no—
132C24×C31—22no—
133C24×C31—22no—
134C24×C31C22×C412yes—
135C24×C31C22×C412yes—
136C24×C31C2×D412yes—
137C24×C31C2×D412yes—
138C24×C31C2×D412yes—
139C24×C31C2×D412yes—
140C24×C31C2×D412yes—
141C24×C31C2×D412yes—
142C24×C31#4112yes—
143C24×C31#4112yes—
144C24×C31C2411yescharacteristic
145C2×D4×C31—28no—
146C2×D4×C31—28no—
147C2×D4×C31—28no—
148C2×D4×C31—28no—
149C2×D4×C31—28no—
150C2×D4×C31—28no—
151C2×D4×C31C22⋊C4116yes—
152C22×C4×C31—21no—
153C22×C4×C31—21no—
154C22×C4×C31—21no—
155C22×C4×C31—21no—
156C22×C4×C31—21no—
157C22×C4×C31—21no—
158C22×C4×C31—22no—
159C22×C4×C31—28no—
160C22×C4×C31—28no—
161C22×C4×C31—28no—
162C22×C4×C31—28no—
163C22×C4×C31—28no—
164C22×C4×C31—28no—
165C22×C4×C31—22no—
166C22×C4×C31—22no—
167C22×C4×C31—22no—
168C22×C4×C31—22no—
169C22×C4×C31—21no—
170C22×C4×C31—21no—
171C22×C4×C31—22no—
172C22×C4×C31—22no—
173C22×C4×C31—22no—
174C22×C4×C31—22no—
175C22×C4×C31—21no—
176C22×C4×C31—21no—
177C22×C4×C31—21no—
178C22×C4×C31—21no—
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—22no—
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—28no—
196C22×C4×C31—22no—
197C22×C4×C31—22no—
198C22×C4×C31—22no—
199C22×C4×C31—22no—
200C22×C4×C31—22no—
201C22×C4×C31—22no—
202C22×C4×C31—22no—
203C22×C4×C31—44no—
204C22×C4×C31—48no—
205C22×C4×C31—48no—
206C22×C4×C31—48no—
207C22×C4×C31—48no—
208C22×C4×C31—48no—
209C22×C4×C31—48no—
210C22×C4×C31—44no—
211C22×C4×C31—44no—
212C22×C4×C31—44no—
213C22×C4×C31—44no—
214C22×C4×C31—44no—
215C22×C4×C31—44no—
216C22×C4×C31—44no—
217C22×C4×C31—44no—
218C22×C4×C31C22×C414yes—
219C22×C4×C31C22×C414yes—
220C22×C4×C31C22×C412yes—
221C22×C4×C31C2×D412yes—
222C22×C4×C31C2×D412yes—
223C22×C4×C31C2×D412yes—
224C22×C4×C31C2×D412yes—
225C22×C4×C31C2×D412yes—
226C22×C4×C31C2×D412yes—
227C22×C4×C31#4114yes—
228C22×C4×C31#4114yes—
229C4⋊C4×C31—28no—
230C4⋊C4×C31—216no—
231C22⋊C4×C31—28no—
232C22⋊C4×C31—28no—
233C22⋊C4×C31—216no—
234C22⋊C4×C31—28no—
235C22⋊C4×C31—48no—
236C22⋊C4×C31—44no—
237C42×C31—28no—
238#13968C3111yesmaximal, characteristic, direct product factor, Sylow
239C23×C31—24no—
240C23×C31—24no—
241C23×C31—22no—
242C23×C31—22no—
243C23×C31—24no—
244C23×C31—22no—
245C23×C31—22no—
246C23×C31—24no—
247C23×C31—24no—
248C23×C31—24no—
249C23×C31—24no—
250C23×C31—24no—
251C23×C31—24no—
252C23×C31—24no—
253C23×C31—24no—
254C23×C31—24no—
255C23×C31—22no—
256C23×C31—22no—
257C23×C31—24no—
258C23×C31—24no—
259C23×C31—22no—
260C23×C31—22no—
261C23×C31—22no—
262C23×C31—22no—
263C23×C31—24no—
264C23×C31—24no—
265C23×C31—24no—
266C23×C31—24no—
267C23×C31—41no—
268C23×C31—41no—
269C23×C31—42no—
270C23×C31—41no—
271C23×C31—41no—
272C23×C31—42no—
273C23×C31—42no—
274C23×C31—42no—
275C23×C31—42no—
276C23×C31—42no—
277C23×C31C2×C22⋊C414yes—
278C23×C31C2×C22⋊C414yes—
279C23×C31C4×D414yes—
280C23×C31C4×D414yes—
281C23×C31#12014yes—
282C23×C31#12114yes—
283C23×C31#12114yes—
284C23×C31#12314yes—
285C23×C31C23×C411yescharacteristic
286C23×C31C22×D411yescharacteristic
287C23×C31C22×D411yescharacteristic
288C23×C31C22×D411yescharacteristic
289C23×C31C22×D411yescharacteristic
290C23×C31C2×#4111yescharacteristic
291C23×C31C2×#4111yescharacteristic
292C23×C31C2×#4112yes—
293C23×C31C2×#4112yes—
294C23×C31H(5,𝔽2)12yes—
295C23×C312−1+412yes—
296D4×C31—232no—
297C2×C4×C31—22no—
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—24no—
306C2×C4×C31—24no—
307C2×C4×C31—24no—
308C2×C4×C31—24no—
309C2×C4×C31—24no—
310C2×C4×C31—24no—
311C2×C4×C31—24no—
312C2×C4×C31—24no—
313C2×C4×C31—22no—
314C2×C4×C31—22no—
315C2×C4×C31—22no—
316C2×C4×C31—22no—
317C2×C4×C31—24no—
318C2×C4×C31—22no—
319C2×C4×C31—24no—
320C2×C4×C31—24no—
321C2×C4×C31—24no—
322C2×C4×C31—24no—
323C2×C4×C31—416no—
324C2×C4×C31—416no—
325C2×C4×C31—416no—
326C2×C4×C31—42no—
327C2×C4×C31—42no—
328C2×C4×C31—42no—
329C2×C4×C31—42no—
330C2×C4×C31—41no—
331C2×C4×C31—42no—
332C2×C4×C31—41no—
333C2×C4×C31—41no—
334C2×C4×C31—42no—
335C2×C4×C31—41no—
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—416no—
347C2×C4×C31—42no—
348C2×C4×C31—42no—
349C2×C4×C31—42no—
350C2×C4×C31—42no—
351C2×C4×C31—42no—
352C2×C4×C31—42no—
353C2×C4×C31—42no—
354C2×C4×C31C2×C22⋊C414yes—
355C2×C4×C31#12314yescomplemented
356C22×#123C2×C3111yescharacteristic
357C22×C4×D4C2×C3111yescharacteristic
358C2×#386C2×C3111yescharacteristic
359C2×#381C2×C3111yescharacteristic, complemented
360C22×#95C2×C3111yescharacteristic, complemented
361#1441C2×C3112yescomplemented
362#1440C2×C3112yescomplemented
363#1436C2×C3112yescomplemented
364C22⋊#95C2×C3111yescharacteristic, complemented
365C22⋊#95C2×C3112yescomplemented
366C22⋊#95C2×C3111yescharacteristic, complemented
367C22×C31—24no—
368C22×C31—28no—
369C22×C31—28no—
370C22×C31—24no—
371C22×C31—24no—
372C22×C31—28no—
373C22×C31—28no—
374C22×C31—24no—
375C22×C31—24no—
376C22×C31—24no—
377C22×C31—28no—
378C22×C31—24no—
379C22×C31—42no—
380C22×C31—44no—
381C22×C31—42no—
382C22×C31—42no—
383C22×C31—44no—
384C22×C31—44no—
385C22×C31—42no—
386C22×C31—42no—
387C22×C31—42no—
388C22×C31#38618yes—
389C22×C31C22×C22⋊C411yescharacteristic
390C22×C31C2×C4×D411yescharacteristic
391C22×C31C2×C4×D411yescharacteristic
392C22×C31C4×#4112yes—
393C22×C31#52012yes—
394C22×C31C2×#12011yescharacteristic
395C22×C31C2×#12111yescharacteristic
396C22×C31C2×#12111yescharacteristic
397C22×C31C2×#12311yescharacteristic
398C22×C31C2×#12311yescharacteristic
399C22×C31#52511yescharacteristic
400C22×C31#52912yes—
401C22×C31#53411yescharacteristic
402C22×C31#53611yescharacteristic
403C22×C31#53912yes—
404C22×C31#54612yes—
405C22×C31#54612yes—
406C22×C31#54612yes—
407C22×C31#54712yes—
408C22×C31#54712yes—
409C22×C31#54712yes—
410C22×C31#55112yes—
411C22×C31#55212yes—
412C4×C31—24no—
413C4×C31—24no—
414C4×C31—44no—
415C4×C31—42no—
416C4×C31—42no—
417C4×C31—42no—
418C4×C31—44no—
419C4×C31—44no—
420C4×C31—82no—
421C23×D4C22×C3111yescharacteristic
422C24×C4C22×C3111yescharacteristic
423C24×C4C22×C3111yescharacteristic
424C24×C4C22×C3111yescharacteristic
425C24×C4C22×C3111yescharacteristic
426C2×#123—24no—
427C2×#123—24no—
428C2×#123C4×C3118yescomplemented
429C2×C4×D4—24no—
430C2×C4×D4—24no—
431C2×C4×D4—24no—
432C22×C4⋊C4C22×C3111yescharacteristic
433C22×C4⋊C4C22×C3112yes—
434C22×C22⋊C4C22×C3111yescharacteristic
435C22×C22⋊C4C22×C3111yescharacteristic
436C22×C22⋊C4C22×C3112yes—
437C22×C22⋊C4C22×C3111yescharacteristic
438C22×C22⋊C4C22×C3112yes—
439C22×C22⋊C4C22×C3111yescharacteristic
440C22×C42C22×C3111yescharacteristic
441#386—24no—
442#381—24no—
443C2×#95—24no—
444C2×#95C22×C3112yes—
445C2×#95C22×C3112yes—
446C2×#95C22×C3112yes—
447C2×#95C22×C3112yes—
448C2×#95C22×C3112yes—
449C2×#95C22×C3112yes—
450C2×#95C22×C3112yes—
451C2×#95C22×C3112yes—
452C2×#95C22×C3112yes—
453C2×C31—28no—
454C2×C31—44no—
455C2×C31C2×#38611yescharacteristic
456C2×C31C4×#12311yescharacteristic
457C2×C31#232211yescharacteristic
458C2×C31#233912yes—
459C2×C31#235912yes—
460C2×C31#240511yescharacteristic
461C2×C31#240611yescharacteristic
462C2×C31#241912yes—
463C2×C31#242512yes—
464C2×C31#248611yescharacteristic
465C2×C31#253411yescharacteristic
466C25C23×C3111yescharacteristic
467C25C23×C3111yescharacteristic
468C22×D4—22no—
469C22×D4—22no—
470C22×D4—22no—
471C22×D4—22no—
472C22×D4C2×C4×C3114yes—
473C22×D4D4×C3114yes—
474C22×D4D4×C3114yes—
475C23×C4—22no—
476C23×C4—22no—
477C23×C4—22no—
478C23×C4—22no—
479C23×C4—22no—
480C23×C4—22no—
481C23×C4—22no—
482C23×C4—22no—
483C23×C4—22no—
484C23×C4—22no—
485C23×C4—22no—
486C23×C4—22no—
487C23×C4—24no—
488C23×C4—24no—
489C23×C4—22no—
490C23×C4—22no—
491C23×C4—24no—
492C23×C4—42no—
493C23×C4—42no—
494C23×C4—42no—
495C23×C4C2×C4×C3114yescomplemented
496C23×C4D4×C3114yes—
497C23×C4C23×C3112yes—
498C23×C4C23×C3112yes—
499C23×C4C23×C3112yes—
500C23×C4C23×C3111yescharacteristic
501C23×C4C23×C3111yescharacteristic
502C23×C4C23×C3111yescharacteristic
503C23×C4C23×C3112yes—
504C23×C4C23×C3111yescharacteristic
505C23×C4C23×C3111yescharacteristic
506#123—232no—
507C4×D4—232no—
508C2×C4⋊C4—22no—
509C2×C4⋊C4—22no—
510C2×C4⋊C4—22no—
511C2×C4⋊C4—24no—
512C2×C4⋊C4—24no—
513C2×C4⋊C4C2×C4×C3118yescomplemented
514C2×C22⋊C4—22no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—22no—
517C2×C22⋊C4—22no—
518C2×C22⋊C4—22no—
519C2×C22⋊C4—24no—
520C2×C22⋊C4—24no—
521C2×C22⋊C4—22no—
522C2×C22⋊C4—22no—
523C2×C22⋊C4—22no—
524C2×C22⋊C4—24no—
525C2×C22⋊C4—22no—
526C2×C22⋊C4—22no—
527C2×C22⋊C4—24no—
528C2×C22⋊C4—42no—
529C2×C22⋊C4C2×C4×C3114yescomplemented
530C2×C22⋊C4C2×C4×C3118yescomplemented
531C2×C22⋊C4D4×C3114yes—
532C2×C42—22no—
533C2×C42—22no—
534C2×C42—22no—
535#95—24no—
536#95—24no—
537#95—24no—
538#95—24no—
539#95—24no—
540#95—24no—
541#95—24no—
542#95—42no—
543#95—42no—
544C31#1396811yescharacteristic, direct product factor, Sylow
545C24—22no—
546C24—22no—
547C24—22no—
548C24—22no—
549C24—21no—
550C24—21no—
551C24—22no—
552C24—22no—
553C24—21no—
554C24—21no—
555C24—22no—
556C24—22no—
557C24C22×C4×C3112yes—
558C24C22×C4×C3112yes—
559C24C2×D4×C3112yes—
560C24C2×D4×C3112yes—
561C24C2×D4×C3112yes—
562C24C2×D4×C3112yes—
563C24C2×D4×C3112yes—
564C24C2×D4×C3112yes—
565C24#41×C3112yes—
566C24#41×C3112yes—
567C24C24×C3111yescharacteristic
568C2×D4—28no—
569C2×D4—28no—
570C2×D4—28no—
571C2×D4—28no—
572C2×D4—28no—
573C2×D4—28no—
574C2×D4C22⋊C4×C31116yes—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—22no—
582C22×C4—28no—
583C22×C4—28no—
584C22×C4—28no—
585C22×C4—28no—
586C22×C4—28no—
587C22×C4—28no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—28no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—44no—
627C22×C4—48no—
628C22×C4—48no—
629C22×C4—48no—
630C22×C4—48no—
631C22×C4—48no—
632C22×C4—48no—
633C22×C4—44no—
634C22×C4—44no—
635C22×C4—44no—
636C22×C4—44no—
637C22×C4—44no—
638C22×C4—44no—
639C22×C4—44no—
640C22×C4—44no—
641C22×C4C22×C4×C3114yes—
642C22×C4C22×C4×C3114yes—
643C22×C4C22×C4×C3112yes—
644C22×C4C2×D4×C3112yes—
645C22×C4C2×D4×C3112yes—
646C22×C4C2×D4×C3112yes—
647C22×C4C2×D4×C3112yes—
648C22×C4C2×D4×C3112yes—
649C22×C4C2×D4×C3112yes—
650C22×C4#41×C3114yes—
651C22×C4#41×C3114yes—
652C4⋊C4—28no—
653C4⋊C4—216no—
654C22⋊C4—28no—
655C22⋊C4—28no—
656C22⋊C4—216no—
657C22⋊C4—28no—
658C22⋊C4—48no—
659C22⋊C4—44no—
660C42—28no—
661C23—24no—
662C23—24no—
663C23—22no—
664C23—22no—
665C23—24no—
666C23—22no—
667C23—22no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—24no—
676C23—24no—
677C23—22no—
678C23—22no—
679C23—24no—
680C23—24no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—24no—
686C23—24no—
687C23—24no—
688C23—24no—
689C23—41no—
690C23—41no—
691C23—42no—
692C23—41no—
693C23—41no—
694C23—42no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23C2×C22⋊C4×C3114yes—
700C23C2×C22⋊C4×C3114yes—
701C23C4×D4×C3114yes—
702C23C4×D4×C3114yes—
703C23C31×#12014yes—
704C23C31×#12114yes—
705C23C31×#12114yes—
706C23C31×#12314yes—
707C23C23×C4×C3111yescharacteristic
708C23C22×D4×C3111yescharacteristic
709C23C22×D4×C3111yescharacteristic
710C23C22×D4×C3111yescharacteristic
711C23C22×D4×C3111yescharacteristic
712C23C2×#41×C3111yescharacteristic
713C23C2×#41×C3111yescharacteristic
714C23C2×#41×C3112yes—
715C23C2×#41×C3112yes—
716C23C31×H(5,𝔽2)12yes—
717C23C31×2−1+412yes—
718D4—232no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—24no—
734C2×C4—24no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—24no—
740C2×C4—22no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—416no—
746C2×C4—416no—
747C2×C4—416no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—41no—
753C2×C4—42no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—42no—
757C2×C4—41no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—42no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—416no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4C2×C22⋊C4×C3114yes—
777C2×C4C31×#12314yescomplemented
778C22—24no—
779C22—28no—
780C22—28no—
781C22—24no—
782C22—24no—
783C22—28no—
784C22—28no—
785C22—24no—
786C22—24no—
787C22—24no—
788C22—28no—
789C22—24no—
790C22—42no—
791C22—44no—
792C22—42no—
793C22—42no—
794C22—44no—
795C22—44no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22C31×#38618yes—
800C22C22×C22⋊C4×C3111yescharacteristic
801C22C2×C4×D4×C3111yescharacteristic
802C22C2×C4×D4×C3111yescharacteristic
803C22C4×#41×C3112yes—
804C22C31×#52012yes—
805C22C2×C31×#12011yescharacteristic
806C22C2×C31×#12111yescharacteristic
807C22C2×C31×#12111yescharacteristic
808C22C2×C31×#12311yescharacteristic
809C22C2×C31×#12311yescharacteristic
810C22C31×#52511yescharacteristic
811C22C31×#52912yes—
812C22C31×#53411yescharacteristic
813C22C31×#53611yescharacteristic
814C22C31×#53912yes—
815C22C31×#54612yes—
816C22C31×#54612yes—
817C22C31×#54612yes—
818C22C31×#54712yes—
819C22C31×#54712yes—
820C22C31×#54712yes—
821C22C31×#55112yes—
822C22C31×#55212yes—
823C4—24no—
824C4—24no—
825C4—44no—
826C4—42no—
827C4—42no—
828C4—42no—
829C4—44no—
830C4—44no—
831C4—82no—
832C2—28no—
833C2—44no—
834C2C2×C31×#38611yescharacteristic
835C2C4×C31×#12311yescharacteristic
836C2C31×#232211yescharacteristic
837C2C31×#233912yes—
838C2C31×#235912yes—
839C2C31×#240511yescharacteristic
840C2C31×#240611yescharacteristic
841C2C31×#241912yes—
842C2C31×#242512yes—
843C2C31×#248611yescharacteristic
844C2C31×#253411yescharacteristic
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×#381C2semidirect
5. C22×C31×#95C2semidirect
6. C31×#1441C2semidirect
7. C31×#1440C2semidirect
8. C31×#1436C2semidirect
9. C31×C22⋊#95C2semidirect
10. C31×C22⋊#95C2semidirect
11. C31×C22⋊#95C2semidirect
19. C2×C31×#123C4semidirect
73. C23×C4×C31C2×C4semidirect
91. C2×C4⋊C4×C31C2×C4semidirect
107. C2×C22⋊C4×C31C2×C4semidirect
108. C2×C22⋊C4×C31C2×C4semidirect
238. #13968C31direct (N × H)
355. C2×C4×C31#123semidirect
359. C2×#381C2×C31semidirect
360. C22×#95C2×C31semidirect
361. #1441C2×C31semidirect
362. #1440C2×C31semidirect
363. #1436C2×C31semidirect
364. C22⋊#95C2×C31semidirect
365. C22⋊#95C2×C31semidirect
366. C22⋊#95C2×C31semidirect
428. C2×#123C4×C31semidirect
495. C23×C4C2×C4×C31semidirect
513. C2×C4⋊C4C2×C4×C31semidirect
529. C2×C22⋊C4C2×C4×C31semidirect
530. C2×C22⋊C4C2×C4×C31semidirect
544. C31#13968direct (N × H)
777. C2×C4C31×#123semidirect

Maximal subgroups

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

subgroupindex
C22×C31×#1232
C22×C4×D4×C312
C2×C31×#3862
C2×C31×#3812
C22×C31×#952
C31×#14412
C31×#14402
C31×#14362
C31×C22⋊#952
#1396831