Finite Group Databasebeta

← C31×#14015 #21470774

Subgroups — C31×#14015 #21470774

Order 7936.

2950 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D4×C31C211yesmaximal, characteristic
2C23×C4⋊C4×C31C211yesmaximal, characteristic, complemented
3C2×C31×#386C211yesmaximal, characteristic
4C2×C31×#386C211yesmaximal, characteristic
5C2×C31×#385C212yesmaximal, complemented
6C2×C31×#385C211yesmaximal, characteristic, complemented
7C31×#1444C212yesmaximal, complemented
8C31×#1439C212yesmaximal, complemented
9C31×#1436C212yesmaximal, complemented
10C31×C22⋊#95C211yesmaximal, characteristic, complemented
11C31×C22⋊#95C211yesmaximal, characteristic, 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×C31—24no—
21C22×C4⋊C4×C31—28no—
22C22×C4⋊C4×C31C2212yes—
23C22×C4⋊C4×C31C2211yescharacteristic
24C22×C4⋊C4×C31C2212yes—
25C22×C4⋊C4×C31C2212yes—
26C22×C22⋊C4×C31C2211yescharacteristic
27C22×C22⋊C4×C31C2211yescharacteristic
28C22×C22⋊C4×C31C2212yes—
29C22×C22⋊C4×C31C2211yescharacteristic
30C22×C22⋊C4×C31C2212yes—
31C22×C22⋊C4×C31C2211yescharacteristic
32C22×C42×C31C2211yescharacteristic
33C31×#386—24no—
34C31×#386C418yescomplemented
35C31×#385—28no—
36C31×#385—24no—
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×C31Q814yes—
53C23×C4×C31—22no—
54C23×C4×C31—22no—
55C23×C4×C31—24no—
56C23×C4×C31—24no—
57C23×C4×C31—22no—
58C23×C4×C31—22no—
59C23×C4×C31—22no—
60C23×C4×C31—22no—
61C23×C4×C31—24no—
62C23×C4×C31—24no—
63C23×C4×C31—22no—
64C23×C4×C31—22no—
65C23×C4×C31—22no—
66C23×C4×C31—22no—
67C23×C4×C31—24no—
68C23×C4×C31—42no—
69C23×C4×C31—42no—
70C23×C4×C31—42no—
71C23×C4×C31C2×C414yescomplemented
72C23×C4×C31D414yes—
73C23×C4×C31C2312yes—
74C23×C4×C31C2312yes—
75C23×C4×C31C2311yescharacteristic
76C23×C4×C31C2312yes—
77C23×C4×C31C2311yescharacteristic
78C23×C4×C31C2311yescharacteristic
79C23×C4×C31C2311yescharacteristic
80C23×C4×C31C2312yes—
81C23×C4×C31C2311yescharacteristic
82C4×D4×C31—232no—
83C2×C4⋊C4×C31—232no—
84C2×C4⋊C4×C31—24no—
85C2×C4⋊C4×C31—24no—
86C2×C4⋊C4×C31—24no—
87C2×C4⋊C4×C31—24no—
88C2×C4⋊C4×C31—24no—
89C2×C4⋊C4×C31—22no—
90C2×C4⋊C4×C31—22no—
91C2×C4⋊C4×C31—22no—
92C2×C4⋊C4×C31—24no—
93C2×C4⋊C4×C31—24no—
94C2×C4⋊C4×C31—42no—
95C2×C4⋊C4×C31D418yescomplemented
96C2×C22⋊C4×C31—22no—
97C2×C22⋊C4×C31—22no—
98C2×C22⋊C4×C31—22no—
99C2×C22⋊C4×C31—22no—
100C2×C22⋊C4×C31—22no—
101C2×C22⋊C4×C31—22no—
102C2×C22⋊C4×C31—22no—
103C2×C22⋊C4×C31—24no—
104C2×C22⋊C4×C31—24no—
105C2×C22⋊C4×C31—24no—
106C2×C22⋊C4×C31—22no—
107C2×C22⋊C4×C31—22no—
108C2×C22⋊C4×C31—22no—
109C2×C22⋊C4×C31—24no—
110C2×C22⋊C4×C31—42no—
111C2×C22⋊C4×C31C2×C414yescomplemented
112C2×C22⋊C4×C31C2×C418yescomplemented
113C2×C22⋊C4×C31D414yes—
114C2×C42×C31—22no—
115C2×C42×C31—22no—
116C2×C42×C31—22no—
117C31×#95—24no—
118C31×#95—24no—
119C31×#95—24no—
120C31×#95—24no—
121C31×#95—24no—
122C31×#95—42no—
123C31×#95C2×C418yescomplemented
124C24×C31—22no—
125C24×C31—22no—
126C24×C31—22no—
127C24×C31—22no—
128C24×C31—22no—
129C24×C31—21no—
130C24×C31—21no—
131C24×C31—22no—
132C24×C31—21no—
133C24×C31—21no—
134C24×C31—22no—
135C24×C31—22no—
136C24×C31C22×C412yes—
137C24×C31C22×C412yes—
138C24×C31C2×D412yes—
139C24×C31C2×D412yes—
140C24×C31C2×D412yes—
141C24×C31C2×D412yes—
142C24×C31C2×Q812yes—
143C24×C31C2×Q812yes—
144C24×C31#4112yes—
145C24×C31#4112yes—
146C24×C31C2411yescharacteristic
147C2×D4×C31—28no—
148C2×D4×C31—28no—
149C2×D4×C31—28no—
150C2×D4×C31—28no—
151C2×D4×C31—28no—
152C2×D4×C31—28no—
153C2×D4×C31C4⋊C4116yescomplemented
154C22×C4×C31—28no—
155C22×C4×C31—216no—
156C22×C4×C31—28no—
157C22×C4×C31—28no—
158C22×C4×C31—21no—
159C22×C4×C31—21no—
160C22×C4×C31—21no—
161C22×C4×C31—21no—
162C22×C4×C31—22no—
163C22×C4×C31—22no—
164C22×C4×C31—22no—
165C22×C4×C31—22no—
166C22×C4×C31—21no—
167C22×C4×C31—21no—
168C22×C4×C31—22no—
169C22×C4×C31—216no—
170C22×C4×C31—28no—
171C22×C4×C31—28no—
172C22×C4×C31—28no—
173C22×C4×C31—22no—
174C22×C4×C31—22no—
175C22×C4×C31—22no—
176C22×C4×C31—22no—
177C22×C4×C31—22no—
178C22×C4×C31—21no—
179C22×C4×C31—21no—
180C22×C4×C31—21no—
181C22×C4×C31—21no—
182C22×C4×C31—21no—
183C22×C4×C31—21no—
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—22no—
196C22×C4×C31—22no—
197C22×C4×C31—28no—
198C22×C4×C31—22no—
199C22×C4×C31—22no—
200C22×C4×C31—22no—
201C22×C4×C31—22no—
202C22×C4×C31—22no—
203C22×C4×C31—22no—
204C22×C4×C31—22no—
205C22×C4×C31—44no—
206C22×C4×C31—48no—
207C22×C4×C31—48no—
208C22×C4×C31—48no—
209C22×C4×C31—48no—
210C22×C4×C31—48no—
211C22×C4×C31—48no—
212C22×C4×C31—44no—
213C22×C4×C31—44no—
214C22×C4×C31—44no—
215C22×C4×C31—44no—
216C22×C4×C31C22×C414yes—
217C22×C4×C31C22×C412yes—
218C22×C4×C31C22×C414yes—
219C22×C4×C31C2×D412yes—
220C22×C4×C31C2×D412yes—
221C22×C4×C31C2×D414yes—
222C22×C4×C31C2×D412yes—
223C22×C4×C31C2×D412yes—
224C22×C4×C31C2×D414yes—
225C22×C4×C31C2×D414yes—
226C22×C4×C31C2×D412yes—
227C22×C4×C31C2×Q812yes—
228C22×C4×C31#4114yes—
229C4⋊C4×C31—216no—
230C4⋊C4×C31—28no—
231C4⋊C4×C31—216no—
232C4⋊C4×C31—48no—
233C22⋊C4×C31—28no—
234C22⋊C4×C31—28no—
235C22⋊C4×C31—28no—
236C22⋊C4×C31—216no—
237C22⋊C4×C31—48no—
238C22⋊C4×C31—44no—
239C42×C31—28no—
240#14015C3111yesmaximal, characteristic, direct product factor, Sylow
241C23×C31—24no—
242C23×C31—24no—
243C23×C31—22no—
244C23×C31—22no—
245C23×C31—24no—
246C23×C31—22no—
247C23×C31—22no—
248C23×C31—24no—
249C23×C31—24no—
250C23×C31—24no—
251C23×C31—24no—
252C23×C31—24no—
253C23×C31—24no—
254C23×C31—24no—
255C23×C31—24no—
256C23×C31—24no—
257C23×C31—24no—
258C23×C31—22no—
259C23×C31—22no—
260C23×C31—24no—
261C23×C31—22no—
262C23×C31—22no—
263C23×C31—22no—
264C23×C31—22no—
265C23×C31—24no—
266C23×C31—24no—
267C23×C31—24no—
268C23×C31—24no—
269C23×C31—41no—
270C23×C31—41no—
271C23×C31—42no—
272C23×C31—41no—
273C23×C31—41no—
274C23×C31—42no—
275C23×C31—42no—
276C23×C31—42no—
277C23×C31—42no—
278C23×C31—42no—
279C23×C31C2×C4⋊C414yes—
280C23×C31C2×C4⋊C414yescomplemented
281C23×C31C4×D414yes—
282C23×C31C4×D414yes—
283C23×C31#12014yes—
284C23×C31C22⋊Q814yes—
285C23×C31C22⋊Q814yes—
286C23×C31#12314yes—
287C23×C31C23×C411yescharacteristic
288C23×C31C22×D411yescharacteristic
289C23×C31C22×D411yescharacteristic
290C23×C31C22×D411yescharacteristic
291C23×C31C22×D412yes—
292C23×C31C22×Q811yescharacteristic
293C23×C31C2×#4111yescharacteristic
294C23×C31C2×#4111yescharacteristic
295C23×C31C2×#4112yes—
296C23×C31H(5,𝔽2)12yes—
297C23×C312−1+412yes—
298D4×C31—232no—
299C2×C4×C31—232no—
300C2×C4×C31—24no—
301C2×C4×C31—24no—
302C2×C4×C31—22no—
303C2×C4×C31—22no—
304C2×C4×C31—22no—
305C2×C4×C31—22no—
306C2×C4×C31—24no—
307C2×C4×C31—22no—
308C2×C4×C31—22no—
309C2×C4×C31—22no—
310C2×C4×C31—24no—
311C2×C4×C31—24no—
312C2×C4×C31—24no—
313C2×C4×C31—22no—
314C2×C4×C31—24no—
315C2×C4×C31—24no—
316C2×C4×C31—24no—
317C2×C4×C31—24no—
318C2×C4×C31—24no—
319C2×C4×C31—22no—
320C2×C4×C31—22no—
321C2×C4×C31—22no—
322C2×C4×C31—22no—
323C2×C4×C31—24no—
324C2×C4×C31—22no—
325C2×C4×C31—24no—
326C2×C4×C31—24no—
327C2×C4×C31—24no—
328C2×C4×C31—24no—
329C2×C4×C31—416no—
330C2×C4×C31—416no—
331C2×C4×C31—416no—
332C2×C4×C31—42no—
333C2×C4×C31—41no—
334C2×C4×C31—41no—
335C2×C4×C31—41no—
336C2×C4×C31—42no—
337C2×C4×C31—41no—
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×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×C31—42no—
355C2×C4×C31C2×C4⋊C414yescomplemented
356C2×C4×C31C4×D418yescomplemented
357C2×C4×C31#12014yes—
358C22×C4×D4C2×C3111yescharacteristic
359C23×C4⋊C4C2×C3111yescharacteristic, complemented
360C2×#386C2×C3111yescharacteristic
361C2×#386C2×C3111yescharacteristic
362C2×#385C2×C3112yescomplemented
363C2×#385C2×C3111yescharacteristic, complemented
364#1444C2×C3112yescomplemented
365#1439C2×C3112yescomplemented
366#1436C2×C3112yescomplemented
367C22⋊#95C2×C3111yescharacteristic, complemented
368C22⋊#95C2×C3111yescharacteristic, complemented
369C22×C31—24no—
370C22×C31—24no—
371C22×C31—28no—
372C22×C31—28no—
373C22×C31—24no—
374C22×C31—24no—
375C22×C31—24no—
376C22×C31—28no—
377C22×C31—28no—
378C22×C31—24no—
379C22×C31—28no—
380C22×C31—24no—
381C22×C31—42no—
382C22×C31—42no—
383C22×C31—44no—
384C22×C31—42no—
385C22×C31—42no—
386C22×C31—42no—
387C22×C31—44no—
388C22×C31—44no—
389C22×C31—42no—
390C22×C31#38518yescomplemented
391C22×C31C22×C4⋊C411yescharacteristic
392C22×C31C2×C4×D411yescharacteristic
393C22×C31C2×C4×D412yes—
394C22×C31C2×C4×D411yescharacteristic
395C22×C31#52012yes—
396C22×C31C2×#12011yescharacteristic
397C22×C31C2×#12011yescharacteristic
398C22×C31C2×C22⋊Q811yescharacteristic
399C22×C31C2×C22⋊Q811yescharacteristic
400C22×C31C2×#12311yescharacteristic
401C22×C31#52511yescharacteristic
402C22×C31#52512yes—
403C22×C31#53411yescharacteristic
404C22×C31#53611yescharacteristic
405C22×C31#53912yes—
406C22×C31D4212yes—
407C22×C31D4212yes—
408C22×C31#54712yes—
409C22×C31#54712yes—
410C22×C31#54812yes—
411C22×C31D4×Q812yes—
412C22×C31#55312yes—
413C22×C31#55412yes—
414C4×C31—24no—
415C4×C31—24no—
416C4×C31—28no—
417C4×C31—44no—
418C4×C31—42no—
419C4×C31—42no—
420C4×C31—44no—
421C4×C31—42no—
422C4×C31—82no—
423C23×D4C22×C3111yescharacteristic
424C24×C4C22×C3111yescharacteristic
425C24×C4C22×C3111yescharacteristic
426C24×C4C22×C3111yescharacteristic
427C24×C4C22×C3111yescharacteristic
428C2×C4×D4—24no—
429C2×C4×D4—24no—
430C2×C4×D4—24no—
431C22×C4⋊C4—24no—
432C22×C4⋊C4—28no—
433C22×C4⋊C4C22×C3112yes—
434C22×C4⋊C4C22×C3111yescharacteristic
435C22×C4⋊C4C22×C3112yes—
436C22×C4⋊C4C22×C3112yes—
437C22×C22⋊C4C22×C3111yescharacteristic
438C22×C22⋊C4C22×C3111yescharacteristic
439C22×C22⋊C4C22×C3112yes—
440C22×C22⋊C4C22×C3111yescharacteristic
441C22×C22⋊C4C22×C3112yes—
442C22×C22⋊C4C22×C3111yescharacteristic
443C22×C42C22×C3111yescharacteristic
444#386—24no—
445#386C4×C3118yescomplemented
446#385—28no—
447#385—24no—
448C2×#95C22×C3112yes—
449C2×#95C22×C3112yes—
450C2×#95C22×C3112yes—
451C2×#95C22×C3112yes—
452C2×#95C22×C3112yes—
453C2×#95C22×C3112yes—
454C2×#95C22×C3112yes—
455C2×C31—28no—
456C2×C31—44no—
457C2×C31C2×#38511yescharacteristic
458C2×C31C4×#12011yescharacteristic
459C2×C31#232211yescharacteristic
460C2×C31D4×C4⋊C412yes—
461C2×C31#236112yes—
462C2×C31#240311yescharacteristic
463C2×C31#240611yescharacteristic
464C2×C31#240911yescharacteristic
465C2×C31#244312yes—
466C2×C31#244912yes—
467C2×C31#257911yescharacteristic
468C25C23×C3111yescharacteristic
469C25C23×C3111yescharacteristic
470C22×D4—22no—
471C22×D4—22no—
472C22×D4—22no—
473C22×D4—22no—
474C22×D4C2×C4×C3114yes—
475C22×D4D4×C3114yes—
476C22×D4Q8×C3114yes—
477C23×C4—22no—
478C23×C4—22no—
479C23×C4—24no—
480C23×C4—24no—
481C23×C4—22no—
482C23×C4—22no—
483C23×C4—22no—
484C23×C4—22no—
485C23×C4—24no—
486C23×C4—24no—
487C23×C4—22no—
488C23×C4—22no—
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×C3111yescharacteristic
500C23×C4C23×C3112yes—
501C23×C4C23×C3111yescharacteristic
502C23×C4C23×C3111yescharacteristic
503C23×C4C23×C3111yescharacteristic
504C23×C4C23×C3112yes—
505C23×C4C23×C3111yescharacteristic
506C4×D4—232no—
507C2×C4⋊C4—232no—
508C2×C4⋊C4—24no—
509C2×C4⋊C4—24no—
510C2×C4⋊C4—24no—
511C2×C4⋊C4—24no—
512C2×C4⋊C4—24no—
513C2×C4⋊C4—22no—
514C2×C4⋊C4—22no—
515C2×C4⋊C4—22no—
516C2×C4⋊C4—24no—
517C2×C4⋊C4—24no—
518C2×C4⋊C4—42no—
519C2×C4⋊C4D4×C3118yescomplemented
520C2×C22⋊C4—22no—
521C2×C22⋊C4—22no—
522C2×C22⋊C4—22no—
523C2×C22⋊C4—22no—
524C2×C22⋊C4—22no—
525C2×C22⋊C4—22no—
526C2×C22⋊C4—22no—
527C2×C22⋊C4—24no—
528C2×C22⋊C4—24no—
529C2×C22⋊C4—24no—
530C2×C22⋊C4—22no—
531C2×C22⋊C4—22no—
532C2×C22⋊C4—22no—
533C2×C22⋊C4—24no—
534C2×C22⋊C4—42no—
535C2×C22⋊C4C2×C4×C3114yescomplemented
536C2×C22⋊C4C2×C4×C3118yescomplemented
537C2×C22⋊C4D4×C3114yes—
538C2×C42—22no—
539C2×C42—22no—
540C2×C42—22no—
541#95—24no—
542#95—24no—
543#95—24no—
544#95—24no—
545#95—24no—
546#95—42no—
547#95C2×C4×C3118yescomplemented
548C31#1401511yescharacteristic, direct product factor, Sylow
549C24—22no—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—21no—
555C24—21no—
556C24—22no—
557C24—21no—
558C24—21no—
559C24—22no—
560C24—22no—
561C24C22×C4×C3112yes—
562C24C22×C4×C3112yes—
563C24C2×D4×C3112yes—
564C24C2×D4×C3112yes—
565C24C2×D4×C3112yes—
566C24C2×D4×C3112yes—
567C24C2×Q8×C3112yes—
568C24C2×Q8×C3112yes—
569C24#41×C3112yes—
570C24#41×C3112yes—
571C24C24×C3111yescharacteristic
572C2×D4—28no—
573C2×D4—28no—
574C2×D4—28no—
575C2×D4—28no—
576C2×D4—28no—
577C2×D4—28no—
578C2×D4C4⋊C4×C31116yescomplemented
579C22×C4—28no—
580C22×C4—216no—
581C22×C4—28no—
582C22×C4—28no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—22no—
594C22×C4—216no—
595C22×C4—28no—
596C22×C4—28no—
597C22×C4—28no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
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—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—28no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—44no—
631C22×C4—48no—
632C22×C4—48no—
633C22×C4—48no—
634C22×C4—48no—
635C22×C4—48no—
636C22×C4—48no—
637C22×C4—44no—
638C22×C4—44no—
639C22×C4—44no—
640C22×C4—44no—
641C22×C4C22×C4×C3114yes—
642C22×C4C22×C4×C3112yes—
643C22×C4C22×C4×C3114yes—
644C22×C4C2×D4×C3112yes—
645C22×C4C2×D4×C3112yes—
646C22×C4C2×D4×C3114yes—
647C22×C4C2×D4×C3112yes—
648C22×C4C2×D4×C3112yes—
649C22×C4C2×D4×C3114yes—
650C22×C4C2×D4×C3114yes—
651C22×C4C2×D4×C3112yes—
652C22×C4C2×Q8×C3112yes—
653C22×C4#41×C3114yes—
654C4⋊C4—216no—
655C4⋊C4—28no—
656C4⋊C4—216no—
657C4⋊C4—48no—
658C22⋊C4—28no—
659C22⋊C4—28no—
660C22⋊C4—28no—
661C22⋊C4—216no—
662C22⋊C4—48no—
663C22⋊C4—44no—
664C42—28no—
665C23—24no—
666C23—24no—
667C23—22no—
668C23—22no—
669C23—24no—
670C23—22no—
671C23—22no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—24no—
676C23—24no—
677C23—24no—
678C23—24no—
679C23—24no—
680C23—24no—
681C23—24no—
682C23—22no—
683C23—22no—
684C23—24no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—24no—
690C23—24no—
691C23—24no—
692C23—24no—
693C23—41no—
694C23—41no—
695C23—42no—
696C23—41no—
697C23—41no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23C2×C4⋊C4×C3114yes—
704C23C2×C4⋊C4×C3114yescomplemented
705C23C4×D4×C3114yes—
706C23C4×D4×C3114yes—
707C23C31×#12014yes—
708C23C31×C22⋊Q814yes—
709C23C31×C22⋊Q814yes—
710C23C31×#12314yes—
711C23C23×C4×C3111yescharacteristic
712C23C22×D4×C3111yescharacteristic
713C23C22×D4×C3111yescharacteristic
714C23C22×D4×C3111yescharacteristic
715C23C22×D4×C3112yes—
716C23C22×Q8×C3111yescharacteristic
717C23C2×#41×C3111yescharacteristic
718C23C2×#41×C3111yescharacteristic
719C23C2×#41×C3112yes—
720C23C31×H(5,𝔽2)12yes—
721C23C31×2−1+412yes—
722D4—232no—
723C2×C4—232no—
724C2×C4—24no—
725C2×C4—24no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—24no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—24no—
735C2×C4—24no—
736C2×C4—24no—
737C2×C4—22no—
738C2×C4—24no—
739C2×C4—24no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—24no—
748C2×C4—22no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—416no—
754C2×C4—416no—
755C2×C4—416no—
756C2×C4—42no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—42no—
761C2×C4—41no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4C2×C4⋊C4×C3114yescomplemented
780C2×C4C4×D4×C3118yescomplemented
781C2×C4C31×#12014yes—
782C22—24no—
783C22—24no—
784C22—28no—
785C22—28no—
786C22—24no—
787C22—24no—
788C22—24no—
789C22—28no—
790C22—28no—
791C22—24no—
792C22—28no—
793C22—24no—
794C22—42no—
795C22—42no—
796C22—44no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—44no—
801C22—44no—
802C22—42no—
803C22C31×#38518yescomplemented
804C22C22×C4⋊C4×C3111yescharacteristic
805C22C2×C4×D4×C3111yescharacteristic
806C22C2×C4×D4×C3112yes—
807C22C2×C4×D4×C3111yescharacteristic
808C22C31×#52012yes—
809C22C2×C31×#12011yescharacteristic
810C22C2×C31×#12011yescharacteristic
811C22C2×C31×C22⋊Q811yescharacteristic
812C22C2×C31×C22⋊Q811yescharacteristic
813C22C2×C31×#12311yescharacteristic
814C22C31×#52511yescharacteristic
815C22C31×#52512yes—
816C22C31×#53411yescharacteristic
817C22C31×#53611yescharacteristic
818C22C31×#53912yes—
819C22D42×C3112yes—
820C22D42×C3112yes—
821C22C31×#54712yes—
822C22C31×#54712yes—
823C22C31×#54812yes—
824C22D4×Q8×C3112yes—
825C22C31×#55312yes—
826C22C31×#55412yes—
827C4—24no—
828C4—24no—
829C4—28no—
830C4—44no—
831C4—42no—
832C4—42no—
833C4—44no—
834C4—42no—
835C4—82no—
836C2—28no—
837C2—44no—
838C2C2×C31×#38511yescharacteristic
839C2C4×C31×#12011yescharacteristic
840C2C31×#232211yescharacteristic
841C2D4×C4⋊C4×C3112yes—
842C2C31×#236112yes—
843C2C31×#240311yescharacteristic
844C2C31×#240611yescharacteristic
845C2C31×#240911yescharacteristic
846C2C31×#244312yes—
847C2C31×#244912yes—
848C2C31×#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
2. C23×C4⋊C4×C31C2semidirect
5. C2×C31×#385C2semidirect
6. C2×C31×#385C2semidirect
7. C31×#1444C2semidirect
8. C31×#1439C2semidirect
9. C31×#1436C2semidirect
10. C31×C22⋊#95C2semidirect
11. C31×C22⋊#95C2semidirect
34. C31×#386C4semidirect
71. C23×C4×C31C2×C4semidirect
95. C2×C4⋊C4×C31D4semidirect
111. C2×C22⋊C4×C31C2×C4semidirect
112. C2×C22⋊C4×C31C2×C4semidirect
123. C31×#95C2×C4semidirect
153. C2×D4×C31C4⋊C4semidirect
240. #14015C31direct (N × H)
280. C23×C31C2×C4⋊C4semidirect
355. C2×C4×C31C2×C4⋊C4semidirect
356. C2×C4×C31C4×D4semidirect
359. C23×C4⋊C4C2×C31semidirect
362. C2×#385C2×C31semidirect
363. C2×#385C2×C31semidirect
364. #1444C2×C31semidirect
365. #1439C2×C31semidirect
366. #1436C2×C31semidirect
367. C22⋊#95C2×C31semidirect
368. C22⋊#95C2×C31semidirect
390. C22×C31#385semidirect
445. #386C4×C31semidirect
495. C23×C4C2×C4×C31semidirect
519. C2×C4⋊C4D4×C31semidirect
535. C2×C22⋊C4C2×C4×C31semidirect
536. C2×C22⋊C4C2×C4×C31semidirect
547. #95C2×C4×C31semidirect
548. C31#14015direct (N × H)
578. C2×D4C4⋊C4×C31semidirect
704. C23C2×C4⋊C4×C31semidirect
779. C2×C4C2×C4⋊C4×C31semidirect
780. C2×C4C4×D4×C31semidirect
803. C22C31×#385semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D4×C312
C23×C4⋊C4×C312
C2×C31×#3862
C2×C31×#3852
C31×#14442
C31×#14392
C31×#14362
C31×C22⋊#952
#1401531