Finite Group Databasebeta

← C31×#11087 #21467846

Subgroups — C31×#11087 #21467846

Order 7936.

1478 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C31×#99C211yesmaximal, characteristic
2C31×#2308C211yesmaximal, characteristic
3C2×C31×#386C211yesmaximal, characteristic
4C2×C31×#385C211yesmaximal, characteristic, complemented
5C2×C31×#342C211yesmaximal, characteristic, complemented
6C2×C31×#342C211yesmaximal, characteristic, complemented
7C31×C22⋊#95C211yesmaximal, characteristic, complemented
8C23×D4×C31C2211yescharacteristic
9C24×C4×C31C2211yescharacteristic
10C22×C4⋊C4×C31—21no—
11C22×C22⋊C4×C31—21no—
12C22×C22⋊C4×C31C2211yescharacteristic
13C22×C22⋊C4×C31C2211yescharacteristic
14C22×C22⋊C4×C31C2211yescharacteristic
15C22×C22⋊C4×C31C2211yescharacteristic
16C22×C22⋊C4×C31C2211yescharacteristic
17C2×C31×#99—22no—
18C2×C31×#99—22no—
19C2×C31×#99C414yescomplemented
20C31×#386—21no—
21C31×#386—21no—
22C31×#386—22no—
23C31×#386—22no—
24C31×#386—22no—
25C31×#385—22no—
26C31×#385—22no—
27C31×#381—21no—
28C31×#379—21no—
29C2×C31×#95—21no—
30C2×C31×#95—21no—
31C2×C31×#95—22no—
32C31×#342—22no—
33C31×#342—22no—
34C25×C31D411yescharacteristic
35C25×C31C2311yescharacteristic
36C22×D4×C31—21no—
37C22×D4×C31—21no—
38C22×D4×C31—21no—
39C22×D4×C31—21no—
40C22×D4×C31—21no—
41C22×D4×C31—21no—
42C22×D4×C31—21no—
43C22×D4×C31—21no—
44C22×D4×C31—21no—
45C22×D4×C31—21no—
46C22×D4×C31—21no—
47C22×D4×C31—21no—
48C22×D4×C31C2×C412yes—
49C22×D4×C31Q812yes—
50C23×C4×C31—21no—
51C23×C4×C31—21no—
52C23×C4×C31—21no—
53C23×C4×C31—21no—
54C23×C4×C31—21no—
55C23×C4×C31—21no—
56C23×C4×C31—21no—
57C23×C4×C31—21no—
58C23×C4×C31—21no—
59C23×C4×C31—44no—
60C23×C4×C31D411yescharacteristic
61C23×C4×C31D411yescharacteristic
62C23×C4×C31D411yescharacteristic
63C23×C4×C31D412yes—
64C23×C4×C31D412yes—
65C2×C4⋊C4×C31—24no—
66C2×C4⋊C4×C31—44no—
67C2×C22⋊C4×C31—21no—
68C2×C22⋊C4×C31—21no—
69C2×C22⋊C4×C31—21no—
70C2×C22⋊C4×C31—21no—
71C2×C22⋊C4×C31—21no—
72C2×C22⋊C4×C31—21no—
73C2×C22⋊C4×C31—21no—
74C2×C22⋊C4×C31—21no—
75C2×C22⋊C4×C31—21no—
76C2×C22⋊C4×C31—21no—
77C2×C22⋊C4×C31—21no—
78C2×C22⋊C4×C31—24no—
79C2×C22⋊C4×C31—21no—
80C2×C22⋊C4×C31—21no—
81C2×C22⋊C4×C31—21no—
82C2×C22⋊C4×C31—21no—
83C2×C22⋊C4×C31—21no—
84C2×C22⋊C4×C31—21no—
85C2×C22⋊C4×C31—21no—
86C2×C22⋊C4×C31—21no—
87C2×C22⋊C4×C31—21no—
88C2×C22⋊C4×C31—21no—
89C2×C22⋊C4×C31—21no—
90C2×C22⋊C4×C31—21no—
91C2×C22⋊C4×C31—21no—
92C2×C22⋊C4×C31—21no—
93C2×C22⋊C4×C31—22no—
94C2×C22⋊C4×C31—22no—
95C2×C22⋊C4×C31—44no—
96C2×C22⋊C4×C31C2×C412yes—
97C2×C22⋊C4×C31C2×C412yes—
98C2×C22⋊C4×C31D412yes—
99C2×C22⋊C4×C31D412yes—
100C2×C22⋊C4×C31D412yes—
101C31×#99—28no—
102C31×#95—24no—
103C31×#95—24no—
104C31×#95—22no—
105C31×#95—22no—
106C31×#95—44no—
107C24×C31—21no—
108C24×C31—21no—
109C24×C31—21no—
110C24×C31—21no—
111C24×C31—21no—
112C24×C31—21no—
113C24×C31—42no—
114C24×C31—42no—
115C24×C31—42no—
116C24×C31—42no—
117C24×C31C4⋊C412yescomplemented
118C24×C31C22×C411yescharacteristic
119C24×C31C2×D411yescharacteristic
120C24×C31C2×D411yescharacteristic
121C24×C31C2×D411yescharacteristic
122C24×C31C2×D411yescharacteristic
123C24×C31C2×D411yescharacteristic
124C24×C31C2×D411yescharacteristic
125C24×C31C2×D411yescharacteristic
126C24×C31C2×Q811yescharacteristic
127C24×C31#4111yescharacteristic
128C24×C31#4111yescharacteristic
129C24×C31#4111yescharacteristic
130C24×C31#4111yescharacteristic
131C24×C31#4111yescharacteristic
132C24×C31#4111yescharacteristic
133C2×D4×C31—22no—
134C2×D4×C31—22no—
135C2×D4×C31—22no—
136C2×D4×C31—22no—
137C2×D4×C31—22no—
138C2×D4×C31—22no—
139C2×D4×C31—22no—
140C2×D4×C31—22no—
141C2×D4×C31—22no—
142C2×D4×C31—22no—
143C2×D4×C31—22no—
144C2×D4×C31—22no—
145C2×D4×C31—41no—
146C2×D4×C31—41no—
147C2×D4×C31—41no—
148C2×D4×C31—41no—
149C2×D4×C31—41no—
150C2×D4×C31—41no—
151C2×D4×C31—41no—
152C2×D4×C31—41no—
153C2×D4×C31—41no—
154C2×D4×C31—41no—
155C2×D4×C31—41no—
156C2×D4×C31—41no—
157C2×D4×C31—41no—
158C2×D4×C31—41no—
159C2×D4×C31—41no—
160C2×D4×C31—41no—
161C22×C4×C31—24no—
162C22×C4×C31—24no—
163C22×C4×C31—24no—
164C22×C4×C31—22no—
165C22×C4×C31—21no—
166C22×C4×C31—22no—
167C22×C4×C31—22no—
168C22×C4×C31—22no—
169C22×C4×C31—21no—
170C22×C4×C31—22no—
171C22×C4×C31—22no—
172C22×C4×C31—21no—
173C22×C4×C31—21no—
174C22×C4×C31—21no—
175C22×C4×C31—21no—
176C22×C4×C31—22no—
177C22×C4×C31—21no—
178C22×C4×C31—22no—
179C22×C4×C31—21no—
180C22×C4×C31—21no—
181C22×C4×C31—21no—
182C22×C4×C31—22no—
183C22×C4×C31—22no—
184C22×C4×C31—21no—
185C22×C4×C31—21no—
186C22×C4×C31—22no—
187C22×C4×C31—44no—
188C22×C4×C31—44no—
189C22×C4×C31—44no—
190C22×C4×C31—44no—
191C22×C4×C31—42no—
192C22×C4×C31—42no—
193C22×C4×C31—42no—
194C22×C4×C31—42no—
195C22×C4×C31—42no—
196C22×C4×C31—41no—
197C22×C4×C31—41no—
198C22×C4×C31—41no—
199C22×C4×C31—41no—
200C22×C4×C31—42no—
201C22×C4×C31—42no—
202C22×C4×C31—42no—
203C22×C4×C31—42no—
204C22×C4×C31—42no—
205C22×C4×C31—42no—
206C22×C4×C31—42no—
207C22×C4×C31—42no—
208C22×C4×C31—41no—
209C22×C4×C31—41no—
210C22×C4×C31—41no—
211C22×C4×C31—41no—
212C22×C4×C31C4⋊C412yescomplemented
213C4⋊C4×C31—48no—
214C22⋊C4×C31—22no—
215C22⋊C4×C31—22no—
216C22⋊C4×C31—22no—
217C22⋊C4×C31—22no—
218C22⋊C4×C31—22no—
219C22⋊C4×C31—22no—
220C22⋊C4×C31—22no—
221C22⋊C4×C31—48no—
222C22⋊C4×C31—41no—
223C22⋊C4×C31—41no—
224C22⋊C4×C31—41no—
225C22⋊C4×C31—41no—
226C22⋊C4×C31—41no—
227C22⋊C4×C31—41no—
228C22⋊C4×C31—41no—
229C22⋊C4×C31—41no—
230C22⋊C4×C31—41no—
231C22⋊C4×C31—41no—
232C22⋊C4×C31—41no—
233C22⋊C4×C31—41no—
234C22⋊C4×C31—82no—
235C22⋊C4×C31—82no—
236C22⋊C4×C31C22⋊C414yescomplemented
237#11087C3111yesmaximal, characteristic, direct product factor, Sylow
238C23×C31—22no—
239C23×C31—22no—
240C23×C31—22no—
241C23×C31—22no—
242C23×C31—22no—
243C23×C31—22no—
244C23×C31—22no—
245C23×C31—22no—
246C23×C31—22no—
247C23×C31—41no—
248C23×C31—41no—
249C23×C31—41no—
250C23×C31—41no—
251C23×C31—42no—
252C23×C31—41no—
253C23×C31—41no—
254C23×C31—41no—
255C23×C31—42no—
256C23×C31—42no—
257C23×C31—42no—
258C23×C31—42no—
259C23×C31—41no—
260C23×C31—42no—
261C23×C31—42no—
262C23×C31—42no—
263C23×C31—44no—
264C23×C31—42no—
265C23×C31—42no—
266C23×C31—44no—
267C23×C31—41no—
268C23×C31—41no—
269C23×C31—41no—
270C23×C31—41no—
271C23×C31—42no—
272C23×C31—42no—
273C23×C31—82no—
274C23×C31—81no—
275C23×C31—81no—
276C23×C31—82no—
277C23×C31C2×C22⋊C411yescharacteristic
278C23×C31C2×C4⋊C411yescharacteristic
279C23×C31#11711yescharacteristic
280C23×C31C4×D411yescharacteristic
281C23×C31C4×D411yescharacteristic
282C23×C31C4×D411yescharacteristic
283C23×C31C4×D411yescharacteristic
284C23×C31#12011yescharacteristic
285C23×C31#12011yescharacteristic
286C23×C31#12011yescharacteristic
287C23×C31#12111yescharacteristic
288C23×C31#12111yescharacteristic
289C23×C31#12111yescharacteristic
290C23×C31#12111yescharacteristic
291C23×C31#12111yescharacteristic
292C23×C31#12111yescharacteristic
293C23×C31#12111yescharacteristic
294C23×C31#12111yescharacteristic
295C23×C31C22⋊Q811yescharacteristic
296C23×C31C22⋊Q811yescharacteristic
297C23×C31C22⋊Q811yescharacteristic
298C23×C31C22⋊Q811yescharacteristic
299C23×C31C22⋊Q811yescharacteristic
300C23×C31C22⋊Q811yescharacteristic
301C23×C31#12311yescharacteristic
302C23×C31#12311yescharacteristic
303C23×C31#12311yescharacteristic
304C23×C31#12311yescharacteristic
305C23×C31#12311yescharacteristic
306C23×C31#12411yescharacteristic
307C23×C31#12411yescharacteristic
308C23×C31#12411yescharacteristic
309C23×C31#12611yescharacteristic
310C23×C31#12611yescharacteristic
311C23×C31#12711yescharacteristic
312D4×C31—42no—
313D4×C31—42no—
314D4×C31—42no—
315D4×C31—42no—
316D4×C31—42no—
317D4×C31—42no—
318D4×C31—42no—
319D4×C31—42no—
320C2×C4×C31—24no—
321C2×C4×C31—24no—
322C2×C4×C31—24no—
323C2×C4×C31—22no—
324C2×C4×C31—22no—
325C2×C4×C31—22no—
326C2×C4×C31—24no—
327C2×C4×C31—42no—
328C2×C4×C31—44no—
329C2×C4×C31—42no—
330C2×C4×C31—44no—
331C2×C4×C31—42no—
332C2×C4×C31—42no—
333C2×C4×C31—42no—
334C2×C4×C31—44no—
335C2×C4×C31—44no—
336C2×C4×C31—44no—
337C2×C4×C31—42no—
338C2×C4×C31—41no—
339C2×C4×C31—41no—
340C2×C4×C31—41no—
341C2×C4×C31—41no—
342C2×C4×C31—44no—
343C2×C4×C31—42no—
344C2×C4×C31—42no—
345C2×C4×C31—44no—
346C2×C4×C31—42no—
347C2×C4×C31—42no—
348C2×C4×C31—44no—
349C2×C4×C31—42no—
350C2×C4×C31—41no—
351C2×C4×C31—41no—
352C2×C4×C31—42no—
353C2×C4×C31—42no—
354C2×C4×C31—42no—
355C2×C4×C31—42no—
356C2×C4×C31—42no—
357C2×C4×C31—42no—
358C2×C4×C31—82no—
359C2×C4×C31—81no—
360C2×C4×C31—81no—
361C2×C4×C31—82no—
362C2×C4×C31—82no—
363C2×C4×C31—81no—
364C2×C4×C31—81no—
365C2×C4×C31—82no—
366C22×#99C2×C3111yescharacteristic
367#2308C2×C3111yescharacteristic
368C2×#386C2×C3111yescharacteristic
369C2×#385C2×C3111yescharacteristic, complemented
370C2×#342C2×C3111yescharacteristic, complemented
371C2×#342C2×C3111yescharacteristic, complemented
372C22⋊#95C2×C3111yescharacteristic, complemented
373C22×C31—22no—
374C22×C31—22no—
375C22×C31—22no—
376C22×C31—22no—
377C22×C31—22no—
378C22×C31—22no—
379C22×C31—21no—
380C22×C31—21no—
381C22×C31—21no—
382C22×C31—21no—
383C22×C31—21no—
384C22×C31—21no—
385C22×C31—21no—
386C22×C31—21no—
387C22×C31—21no—
388C22×C31—21no—
389C22×C31—21no—
390C22×C31—21no—
391C22×C31—22no—
392C22×C31—22no—
393C22×C31—22no—
394C22×C31—22no—
395C22×C31—22no—
396C22×C31—22no—
397C22×C31—41no—
398C22×C31—41no—
399C22×C31—41no—
400C22×C31—41no—
401C22×C31—41no—
402C22×C31—41no—
403C22×C31—41no—
404C22×C31—41no—
405C22×C31—41no—
406C22×C31—41no—
407C22×C31—41no—
408C22×C31—41no—
409C22×C31—41no—
410C22×C31—41no—
411C22×C31—41no—
412C22×C31—41no—
413C22×C31—44no—
414C22×C31—44no—
415C22×C31—42no—
416C22×C31—82no—
417C22×C31—82no—
418C22×C31—82no—
419C22×C31—81no—
420C22×C31—81no—
421C22×C31—82no—
422C22×C31#38011yescharacteristic
423C22×C31#38511yescharacteristic
424C22×C31#38511yescharacteristic
425C22×C31#38611yescharacteristic
426C22×C31#38811yescharacteristic
427C22×C31#38811yescharacteristic
428C22×C31#39011yescharacteristic
429C22×C31#39211yescharacteristic
430C22×C31#39311yescharacteristic
431C22×C31#39411yescharacteristic
432C22×C31#39411yescharacteristic
433C22×C31#39611yescharacteristic
434C22×C31#39611yescharacteristic
435C22×C31#39711yescharacteristic
436C22×C31#39911yescharacteristic
437C22×C31B(4,𝔽2)12yes—
438C22×C31#45812yes—
439C4×C31—44no—
440C4×C31—42no—
441C4×C31—44no—
442C4×C31—82no—
443C4×C31—82no—
444C4×C31—81no—
445C4×C31—81no—
446C4×C31—82no—
447C23×D4C22×C3111yescharacteristic
448C24×C4C22×C3111yescharacteristic
449C22×C4⋊C4—21no—
450C22×C22⋊C4—21no—
451C22×C22⋊C4C22×C3111yescharacteristic
452C22×C22⋊C4C22×C3111yescharacteristic
453C22×C22⋊C4C22×C3111yescharacteristic
454C22×C22⋊C4C22×C3111yescharacteristic
455C22×C22⋊C4C22×C3111yescharacteristic
456C2×#99—22no—
457C2×#99—22no—
458C2×#99C4×C3114yescomplemented
459#386—21no—
460#386—21no—
461#386—22no—
462#386—22no—
463#386—22no—
464#385—22no—
465#385—22no—
466#381—21no—
467#379—21no—
468C2×#95—21no—
469C2×#95—21no—
470C2×#95—22no—
471#342—22no—
472#342—22no—
473C2×C31—21no—
474C2×C31—21no—
475C2×C31—21no—
476C2×C31—21no—
477C2×C31—21no—
478C2×C31—21no—
479C2×C31—21no—
480C2×C31—21no—
481C2×C31—21no—
482C2×C31—21no—
483C2×C31—21no—
484C2×C31—21no—
485C2×C31—82no—
486C2×C31#143911yescharacteristic
487C2×C31#186712yes—
488C2×C31#202111yescharacteristic
489C2×C31#202211yescharacteristic
490C2×C31#204412yes—
491C25D4×C3111yescharacteristic
492C25C23×C3111yescharacteristic
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4C2×C4×C3112yes—
506C22×D4Q8×C3112yes—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—21no—
510C23×C4—21no—
511C23×C4—21no—
512C23×C4—21no—
513C23×C4—21no—
514C23×C4—21no—
515C23×C4—21no—
516C23×C4—44no—
517C23×C4D4×C3111yescharacteristic
518C23×C4D4×C3111yescharacteristic
519C23×C4D4×C3111yescharacteristic
520C23×C4D4×C3112yes—
521C23×C4D4×C3112yes—
522C2×C4⋊C4—24no—
523C2×C4⋊C4—44no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—24no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—21no—
538C2×C22⋊C4—21no—
539C2×C22⋊C4—21no—
540C2×C22⋊C4—21no—
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—22no—
551C2×C22⋊C4—22no—
552C2×C22⋊C4—44no—
553C2×C22⋊C4C2×C4×C3112yes—
554C2×C22⋊C4C2×C4×C3112yes—
555C2×C22⋊C4D4×C3112yes—
556C2×C22⋊C4D4×C3112yes—
557C2×C22⋊C4D4×C3112yes—
558#99—28no—
559#95—24no—
560#95—24no—
561#95—22no—
562#95—22no—
563#95—44no—
564C31#1108711yescharacteristic, direct product factor, Sylow
565C24—21no—
566C24—21no—
567C24—21no—
568C24—21no—
569C24—21no—
570C24—21no—
571C24—42no—
572C24—42no—
573C24—42no—
574C24—42no—
575C24C4⋊C4×C3112yescomplemented
576C24C22×C4×C3111yescharacteristic
577C24C2×D4×C3111yescharacteristic
578C24C2×D4×C3111yescharacteristic
579C24C2×D4×C3111yescharacteristic
580C24C2×D4×C3111yescharacteristic
581C24C2×D4×C3111yescharacteristic
582C24C2×D4×C3111yescharacteristic
583C24C2×D4×C3111yescharacteristic
584C24C2×Q8×C3111yescharacteristic
585C24#41×C3111yescharacteristic
586C24#41×C3111yescharacteristic
587C24#41×C3111yescharacteristic
588C24#41×C3111yescharacteristic
589C24#41×C3111yescharacteristic
590C24#41×C3111yescharacteristic
591C2×D4—22no—
592C2×D4—22no—
593C2×D4—22no—
594C2×D4—22no—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—22no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—22no—
603C2×D4—41no—
604C2×D4—41no—
605C2×D4—41no—
606C2×D4—41no—
607C2×D4—41no—
608C2×D4—41no—
609C2×D4—41no—
610C2×D4—41no—
611C2×D4—41no—
612C2×D4—41no—
613C2×D4—41no—
614C2×D4—41no—
615C2×D4—41no—
616C2×D4—41no—
617C2×D4—41no—
618C2×D4—41no—
619C22×C4—24no—
620C22×C4—24no—
621C22×C4—24no—
622C22×C4—22no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—22no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—22no—
638C22×C4—21no—
639C22×C4—22no—
640C22×C4—21no—
641C22×C4—22no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—22no—
645C22×C4—44no—
646C22×C4—44no—
647C22×C4—44no—
648C22×C4—44no—
649C22×C4—42no—
650C22×C4—42no—
651C22×C4—42no—
652C22×C4—42no—
653C22×C4—42no—
654C22×C4—41no—
655C22×C4—41no—
656C22×C4—41no—
657C22×C4—41no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—42no—
661C22×C4—42no—
662C22×C4—42no—
663C22×C4—42no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4—41no—
667C22×C4—41no—
668C22×C4—41no—
669C22×C4—41no—
670C22×C4C4⋊C4×C3112yescomplemented
671C4⋊C4—48no—
672C22⋊C4—22no—
673C22⋊C4—22no—
674C22⋊C4—22no—
675C22⋊C4—22no—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—22no—
679C22⋊C4—48no—
680C22⋊C4—41no—
681C22⋊C4—41no—
682C22⋊C4—41no—
683C22⋊C4—41no—
684C22⋊C4—41no—
685C22⋊C4—41no—
686C22⋊C4—41no—
687C22⋊C4—41no—
688C22⋊C4—41no—
689C22⋊C4—41no—
690C22⋊C4—41no—
691C22⋊C4—41no—
692C22⋊C4—82no—
693C22⋊C4—82no—
694C22⋊C4C22⋊C4×C3114yescomplemented
695C23—22no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—41no—
705C23—41no—
706C23—41no—
707C23—41no—
708C23—42no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—41no—
717C23—42no—
718C23—42no—
719C23—42no—
720C23—44no—
721C23—42no—
722C23—42no—
723C23—44no—
724C23—41no—
725C23—42no—
726C23—42no—
727C23—41no—
728C23—41no—
729C23—41no—
730C23—82no—
731C23—81no—
732C23—81no—
733C23—82no—
734C23C2×C22⋊C4×C3111yescharacteristic
735C23C2×C4⋊C4×C3111yescharacteristic
736C23C31×#11711yescharacteristic
737C23C4×D4×C3111yescharacteristic
738C23C4×D4×C3111yescharacteristic
739C23C4×D4×C3111yescharacteristic
740C23C4×D4×C3111yescharacteristic
741C23C31×#12011yescharacteristic
742C23C31×#12011yescharacteristic
743C23C31×#12011yescharacteristic
744C23C31×#12111yescharacteristic
745C23C31×#12111yescharacteristic
746C23C31×#12111yescharacteristic
747C23C31×#12111yescharacteristic
748C23C31×#12111yescharacteristic
749C23C31×#12111yescharacteristic
750C23C31×#12111yescharacteristic
751C23C31×#12111yescharacteristic
752C23C31×C22⋊Q811yescharacteristic
753C23C31×C22⋊Q811yescharacteristic
754C23C31×C22⋊Q811yescharacteristic
755C23C31×C22⋊Q811yescharacteristic
756C23C31×C22⋊Q811yescharacteristic
757C23C31×C22⋊Q811yescharacteristic
758C23C31×#12311yescharacteristic
759C23C31×#12311yescharacteristic
760C23C31×#12311yescharacteristic
761C23C31×#12311yescharacteristic
762C23C31×#12311yescharacteristic
763C23C31×#12411yescharacteristic
764C23C31×#12411yescharacteristic
765C23C31×#12411yescharacteristic
766C23C31×#12611yescharacteristic
767C23C31×#12611yescharacteristic
768C23C31×#12711yescharacteristic
769D4—42no—
770D4—42no—
771D4—42no—
772D4—42no—
773D4—42no—
774D4—42no—
775D4—42no—
776D4—42no—
777C2×C4—24no—
778C2×C4—24no—
779C2×C4—24no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—24no—
784C2×C4—42no—
785C2×C4—44no—
786C2×C4—42no—
787C2×C4—44no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—44no—
792C2×C4—44no—
793C2×C4—44no—
794C2×C4—41no—
795C2×C4—44no—
796C2×C4—42no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—42no—
802C2×C4—44no—
803C2×C4—42no—
804C2×C4—42no—
805C2×C4—44no—
806C2×C4—42no—
807C2×C4—42no—
808C2×C4—42no—
809C2×C4—42no—
810C2×C4—42no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—82no—
816C2×C4—81no—
817C2×C4—81no—
818C2×C4—82no—
819C2×C4—82no—
820C2×C4—81no—
821C2×C4—81no—
822C2×C4—82no—
823C22—22no—
824C22—22no—
825C22—22no—
826C22—22no—
827C22—22no—
828C22—22no—
829C22—21no—
830C22—21no—
831C22—21no—
832C22—21no—
833C22—21no—
834C22—21no—
835C22—21no—
836C22—21no—
837C22—21no—
838C22—21no—
839C22—21no—
840C22—21no—
841C22—22no—
842C22—22no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—41no—
848C22—41no—
849C22—41no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—44no—
864C22—44no—
865C22—42no—
866C22—82no—
867C22—82no—
868C22—82no—
869C22—81no—
870C22—81no—
871C22—82no—
872C22C31×#38011yescharacteristic
873C22C31×#38511yescharacteristic
874C22C31×#38511yescharacteristic
875C22C31×#38611yescharacteristic
876C22C31×#38811yescharacteristic
877C22C31×#38811yescharacteristic
878C22C31×#39011yescharacteristic
879C22C31×#39211yescharacteristic
880C22C31×#39311yescharacteristic
881C22C31×#39411yescharacteristic
882C22C31×#39411yescharacteristic
883C22C31×#39611yescharacteristic
884C22C31×#39611yescharacteristic
885C22C31×#39711yescharacteristic
886C22C31×#39911yescharacteristic
887C22C31×B(4,𝔽2)12yes—
888C22C31×#45812yes—
889C4—44no—
890C4—42no—
891C4—44no—
892C4—82no—
893C4—82no—
894C4—81no—
895C4—81no—
896C4—82no—
897C2—21no—
898C2—21no—
899C2—21no—
900C2—21no—
901C2—21no—
902C2—21no—
903C2—21no—
904C2—21no—
905C2—21no—
906C2—21no—
907C2—21no—
908C2—21no—
909C2—82no—
910C2C31×#143911yescharacteristic
911C2C31×#186712yes—
912C2C31×#202111yescharacteristic
913C2C31×#202211yescharacteristic
914C2C31×#204412yes—
subgroupG/H
center, socleC23×C31#120
commutatorC24C22×C4×C31
Frattini, cosocleC25C23×C31
prime radicalC23×D4×C31C22
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C31 ◁ C25×C31 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C31×#385C2semidirect
5. C2×C31×#342C2semidirect
6. C2×C31×#342C2semidirect
7. C31×C22⋊#95C2semidirect
19. C2×C31×#99C4semidirect
117. C24×C31C4⋊C4semidirect
212. C22×C4×C31C4⋊C4semidirect
236. C22⋊C4×C31C22⋊C4semidirect
237. #11087C31direct (N × H)
369. C2×#385C2×C31semidirect
370. C2×#342C2×C31semidirect
371. C2×#342C2×C31semidirect
372. C22⋊#95C2×C31semidirect
458. C2×#99C4×C31semidirect
564. C31#11087direct (N × H)
575. C24C4⋊C4×C31semidirect
670. C22×C4C4⋊C4×C31semidirect
694. C22⋊C4C22⋊C4×C31semidirect

Maximal subgroups

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

subgroupindex
C22×C31×#992
C31×#23082
C2×C31×#3862
C2×C31×#3852
C2×C31×#3422
C31×C22⋊#952
#1108731