Finite Group Databasebeta

← #30624913

Subgroups — #30624913

Order 15616.

2502 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462359C214yesmaximal, complemented
2#21462357C214yesmaximal, complemented
3#21462327C214yesmaximal, complemented
4#21462325C214yesmaximal, complemented
5#21462318C218yesmaximal, complemented
6#21462295C212yesmaximal, complemented
7#21462292C211yesmaximal, characteristic
8#21462291C211yesmaximal, characteristic
9#21462263C212yesmaximal, complemented
10C2×#123×D61C211yesmaximal, characteristic
11C2×#14519856C2212yes—
12C2×#14519856C2214yes—
13C22×C22⋊#6923C2212yes—
14#16840714C2214yes—
15#16840714C2214yes—
16#16840713C2218yescomplemented
17#16840712C2218yescomplemented
18#16840712C2218yescomplemented
19#16840712C2218yescomplemented
20#16840712C2218yescomplemented
21#16840711C2218yescomplemented
22#16840711C2218yescomplemented
23#16840710C2214yes—
24#16840710C2214yes—
25#16840709C2218yescomplemented
26#16840705C2212yes—
27#16840705C2214yes—
28#16840704C2214yes—
29#16840704C2214yescomplemented
30#16840704C2214yescomplemented
31#16840703C2212yes—
32#16840703C2212yes—
33#16840703C2212yes—
34C4⋊C4×#6923C2218yescomplemented
35C22⋊C4×#6923C2218yescomplemented
36C4×C22⋊#6923C2214yes—
37C4×C22⋊#6923C2214yescomplemented
38C4×C22⋊#6923C2214yescomplemented
39C22×D4×D61C2211yescharacteristic
40C23×C4×D61C2211yescharacteristic
41C2×#14519762C412yescomplemented
42C2×#14519761C411yescharacteristic, complemented
43C2×#14519760C411yescharacteristic, complemented
44C2×#14519759C412yescomplemented
45C2×#14519758C411yescharacteristic, complemented
46#123×D61C414yescomplemented
47#123×D61C412yescomplemented
48#123×D61C412yescomplemented
49#123×D61C2214yes—
50#123×D61C2212yes—
51#123×D61C2212yes—
52C2×C4⋊C4×D61C2212yes—
53C2×C22⋊C4×D61C2212yes—
54C2×C22⋊C4×D61C2211yescharacteristic
55C2×#123×C61C411yescharacteristic, complemented
56C23×#6923C2314yes—
57#14519856—48no—
58#14519856—44no—
59C2×C4⋊#6923C2318yes—
60C2×C4⋊#6923C2318yes—
61C2×C4⋊#6923C2314yes—
62C2×C22⋊#6923—44no—
63C2×C22⋊#6923C2314yes—
64C2×C22⋊#6923C2314yes—
65C2×C22⋊#6923C2314yes—
66C2×C22⋊#6923C2314yes—
67C2×C22⋊#6923C2314yes—
68C2×C22⋊#6923C2314yes—
69C2×C22⋊#6923C2318yes—
70C2×C22⋊#6923C2314yes—
71C2×C4×#6923C2314yes—
72C2×C4×#6923C2318yes—
73C2×C4×#6923C2318yes—
74(C2×#6923)⋊C4C2318yes—
75(C2×#6923)⋊C4C2318yes—
76(C2×#6923)⋊C4C2318yes—
77(C2×#6923)⋊C4C2318yes—
78(C2×#6923)⋊C4C2318yes—
79C24×D61C2311yescharacteristic
80C24×D61C2311yescharacteristic
81C22×D244C2×C411yescharacteristic
82C22×C22⋊D61C2×C411yescharacteristic
83C22×C22⋊D61C2×C411yescharacteristic
84C2×D4×D61—44no—
85C2×D4×D61C2×C412yes—
86C2×D4×D61C2×C412yes—
87C2×D4×D61C2312yes—
88C2×D4×D61C2312yes—
89C23×Dic61C2×C411yescharacteristic, complemented
90C22×C4×D61—44no—
91C22×C4×D61C2×C412yescomplemented
92C22×C4×D61C2×C411yescharacteristic, complemented
93C22×C4×D61C2×C411yescharacteristic, complemented
94C22×C4×D61C2×C412yescomplemented
95C22×C4×D61C2312yes—
96C22×C4×D61C2311yescharacteristic
97C22×C4×D61C2312yes—
98C22×C4×D61C2311yescharacteristic
99C22×C4×D61C2312yes—
100C22×C4×D61C2311yescharacteristic
101#14519762C2×C414yescomplemented
102#14519762C2×C414yescomplemented
103#14519762C2×C414yescomplemented
104#14519762C2×C414yescomplemented
105#14519761C2×C414yescomplemented
106#14519761C2×C412yescomplemented
107#14519761C2×C412yescomplemented
108#14519760C2×C414yescomplemented
109#14519760C2×C412yescomplemented
110#14519760C2×C412yescomplemented
111#14519759C2×C414yescomplemented
112#14519759C2×C414yescomplemented
113#14519759C2×C414yescomplemented
114#14519759C2×C414yescomplemented
115#14519758C2×C414yescomplemented
116#14519758C2×C412yescomplemented
117#14519758C2×C412yescomplemented
118C2×C4⋊Dic61C2×C412yescomplemented
119C2×#11758196C2×C412yescomplemented
120C2×#11758196C2×C412yescomplemented
121C4⋊C4×D61C2×C414yescomplemented
122C4⋊C4×D61C2×C414yescomplemented
123C4⋊C4×D61C2314yes—
124C4⋊C4×D61C2314yes—
125C2×C22⋊Dic61C2×C412yes—
126C2×C22⋊Dic61C2×C411yescharacteristic, complemented
127C2×#11758198C2×C412yes—
128C2×#11758198C2×C412yes—
129C2×#11758198C2×C412yescomplemented
130C22⋊C4×D61C2×C414yes—
131C22⋊C4×D61C2×C414yes—
132C22⋊C4×D61C2×C412yescomplemented
133C22⋊C4×D61C2×C412yescomplemented
134C22⋊C4×D61C2314yes—
135C22⋊C4×D61C2312yes—
136C22⋊C4×D61C2312yes—
137C22⋊C4×D61C2314yes—
138C22×D4×C61C2×C411yescharacteristic
139C23×C4×C61C2×C411yescharacteristic, complemented
140#123×C61C2×C414yescomplemented
141#123×C61C2×C412yescomplemented
142#123×C61C2×C412yescomplemented
143C2×C4⋊C4×C61C2×C412yescomplemented
144C2×C22⋊C4×C61C2×C412yes—
145C2×C22⋊C4×C61C2×C411yescharacteristic, complemented
146C24×C61C22×C411yescharacteristic
147C24×C61C22×C411yescharacteristic
148C23×D61—24no—
149C23×D61—24no—
150C23×D61—44no—
151C23×D61—44no—
152C23×D61C22×C411yescharacteristic
153C23×D61C22×C411yescharacteristic
154C23×D61C22×C411yescharacteristic
155C23×D61C22×C412yes—
156C23×D61C22×C411yescharacteristic
157C23×D61C2411yescharacteristic
158C23×D61C2411yescharacteristic
159C23×D61C2412yes—
160C23×D61C2411yescharacteristic
161C22×#6923—44no—
162C22×#6923—48no—
163C22×#6923C2418yes—
164C22×#6923C2418yes—
165C2×D4×C61—42no—
166C2×D4×C61C22×C412yes—
167C2×D4×C61C22×C412yes—
168C22×C4×C61—42no—
169C22×C4×C61C22×C412yes—
170C22×C4×C61C22×C411yescharacteristic
171C22×C4×C61C22×C411yescharacteristic
172C22×C4×C61C22×C412yes—
173C22×C4×C61C22×C411yescharacteristic
174C22×C4×C61C22×C412yes—
175C2×C22⋊D61—42no—
176C2×C22⋊D61—42no—
177C2×C22⋊D61C22×C412yes—
178C2×C22⋊D61C22×C412yes—
179C2×C22⋊D61C22×C412yes—
180C2×C22⋊D61C22×C412yes—
181C22×Dic61—42no—
182C22×Dic61C22×C412yes—
183C22×Dic61C22×C411yescharacteristic
184C22×Dic61C22×C411yescharacteristic
185C22×Dic61C22×C412yes—
186C22×Dic61C22×C411yescharacteristic
187C22×Dic61C22×C412yes—
188D4×D61—44no—
189D4×D61—44no—
190D4×D61—42no—
191D4×D61—42no—
192D4×D61—42no—
193D4×D61—42no—
194C2×D244—42no—
195C2×D244C22×C412yes—
196C2×D244C22×C412yes—
197C2×C4×D61—28no—
198C2×C4×D61—24no—
199C2×C4×D61—42no—
200C2×C4×D61—44no—
201C2×C4×D61—42no—
202C2×C4×D61—42no—
203C2×C4×D61—44no—
204C2×C4×D61—42no—
205C2×C4×D61—44no—
206C2×C4×D61—44no—
207C2×C4×D61C22×C412yes—
208C2×C4×D61C22×C412yes—
209C2×C4×D61C22×C412yes—
210C2×C4×D61C22×C412yes—
211C2×C4×D61C22×C412yes—
212C2×C4×D61C22×C412yes—
213C2×C4×D61C22×C412yes—
214C2×C4×D61C22×C414yes—
215C2×C4×D61C2412yes—
216C2×C4×D61C2412yes—
217C2×C4×D61C2412yes—
218C2×C4×D61C2414yes—
219C22⋊#6923—28no—
220C22⋊#6923—28no—
221C22⋊#6923—44no—
222C22⋊#6923—44no—
223C22⋊#6923—48no—
224C22⋊#6923—44no—
225C22⋊#6923—44no—
226C22⋊#6923—44no—
227C4⋊#6923—48no—
228C4⋊#6923—48no—
229C4⋊#6923—44no—
230C4×#6923—48no—
231C4×#6923—48no—
232C4×#6923—44no—
233C4⋊C4×C61C22×C414yes—
234C4⋊C4×C61C22×C414yes—
235C22⋊C4×C61C22×C414yes—
236C22⋊C4×C61C22×C414yes—
237C22⋊C4×C61C22×C412yes—
238C22⋊C4×C61C22×C412yes—
239C22⋊Dic61C22×C414yes—
240C22⋊Dic61C22×C414yes—
241C22⋊Dic61C22×C412yes—
242C22⋊Dic61C22×C412yes—
243#11758198C22×C414yes—
244#11758198C22×C414yes—
245#11758198C22×C414yes—
246#11758198C22×C414yes—
247#11758198C22×C414yes—
248#11758198C22×C414yes—
249C4⋊Dic61C22×C414yes—
250C4⋊Dic61C22×C414yes—
251#11758196C22×C414yes—
252#11758196C22×C414yes—
253#11758196C22×C414yes—
254#11758196C22×C414yes—
255C23×C61—22no—
256C23×C61—22no—
257C23×C61—42no—
258C23×C61—42no—
259C23×C61C23×C412yes—
260C23×C61C23×C411yescharacteristic
261C23×C61C23×C411yescharacteristic
262C23×C61C23×C411yescharacteristic
263C22×D61—24no—
264C22×D61—22no—
265C22×D61—22no—
266C22×D61—22no—
267C22×D61—22no—
268C22×D61—22no—
269C22×D61—22no—
270C22×D61—22no—
271C22×D61—22no—
272C22×D61—24no—
273C22×D61—24no—
274C22×D61—28no—
275C22×D61—24no—
276C22×D61—42no—
277C22×D61—42no—
278C22×D61—42no—
279C22×D61—44no—
280C22×D61—42no—
281C22×D61—416no—
282C22×D61—88no—
283C22×D61C23×C412yes—
284C22×D61C23×C411yescharacteristic
285C22×D61C23×C411yescharacteristic
286C22×D61C23×C411yescharacteristic
287C22×D61H(5,𝔽2)14yes—
288C22×D61C2511yescharacteristic
289C2×#6923—28no—
290C2×#6923—28no—
291C2×#6923—28no—
292C2×#6923—28no—
293C2×#6923—28no—
294C2×#6923—28no—
295C2×#6923—88no—
296D4×C61—42no—
297D4×C61—42no—
298C2×C4×C61—24no—
299C2×C4×C61—22no—
300C2×C4×C61—41no—
301C2×C4×C61—42no—
302C2×C4×C61—41no—
303C2×C4×C61—42no—
304C2×C4×C61C23×C412yes—
305C2×C4×C61C23×C412yes—
306C2×C4×C61C23×C412yes—
307C2×C4×C61C23×C414yes—
308C22⋊D61—42no—
309C22⋊D61—42no—
310C22⋊D61—42no—
311C22⋊D61—42no—
312C2×Dic61—24no—
313C2×Dic61—22no—
314C2×Dic61—41no—
315C2×Dic61—42no—
316C2×Dic61—41no—
317C2×Dic61—42no—
318C2×Dic61C23×C412yes—
319C2×Dic61C23×C414yes—
320C2×Dic61C23×C412yes—
321C2×Dic61C23×C412yes—
322D244—42no—
323D244—42no—
324C4×D61—24no—
325C4×D61—24no—
326C4×D61—24no—
327C4×D61—24no—
328C4×D61—22no—
329C4×D61—24no—
330C4×D61—22no—
331C4×D61—28no—
332C4×D61—42no—
333C4×D61—42no—
334C4×D61—42no—
335C4×D61—42no—
336C4×D61—44no—
337#34357—611nomaximal, Sylow
338C22×C61—22no—
339C22×C61—21no—
340C22×C61—21no—
341C22×C61—22no—
342C22×C61—22no—
343C22×C61—22no—
344C22×C61—24no—
345C22×C61—44no—
346C22×C61—82no—
347C22×C61#51812yes—
348C22×C61C24×C411yescharacteristic
349C2×D61—22no—
350C2×D61—28no—
351C2×D61—21no—
352C2×D61—21no—
353C2×D61—22no—
354C2×D61—22no—
355C2×D61—22no—
356C2×D61—24no—
357C2×D61—44no—
358C2×D61—44no—
359C2×D61—44no—
360C2×D61—44no—
361C2×D61—44no—
362C2×D61—44no—
363C2×D61—44no—
364C2×D61—84no—
365C2×D61—82no—
366C2×D61#51812yes—
367C2×D61C2×H(5,𝔽2)12yes—
368C2×D61#58514yes—
369#6923—48no—
370#6923—48no—
371C4×C61—22no—
372C4×C61—22no—
373C4×C61—22no—
374C4×C61—24no—
375Dic61—22no—
376Dic61—22no—
377Dic61—22no—
378Dic61—24no—
379C22×#123—611no—
380#2376—614no—
381#2374—614no—
382#2344—614no—
383#2342—614no—
384#2335—618no—
385#2312—612no—
386#2309—611no—
387#2308—611no—
388#2280—612no—
389C2×C61—22no—
390C2×C61—41no—
391C2×C61—41no—
392C2×C61—42no—
393C2×C61C2×#51811yescharacteristic
394C2×C61#342812yes—
395D61—22no—
396D61—41no—
397D61—41no—
398D61—42no—
399D61#353314yes—
400C23×D4—611no—
401C24×C4—611no—
402C2×#123—611no—
403C2×#123—611no—
404C2×#123—614no—
405C2×#123—612no—
406C2×#123—614no—
407C2×#123—612no—
408C2×#123—612no—
409C2×#123—612no—
410C2×#123—612no—
411C2×#123—612no—
412C2×#123—611no—
413C2×#123#692311yescharacteristic, complemented
414C2×#117—612no—
415C2×#117—614no—
416C22×C4⋊C4—612no—
417C22×C22⋊C4—612no—
418C22×C22⋊C4—611no—
419C22×C22⋊C4—612no—
420#390—614no—
421#390—614no—
422#389—618no—
423#388—618no—
424#388—618no—
425#388—618no—
426#388—618no—
427#387—618no—
428#387—618no—
429#386—614no—
430#386—614no—
431#385—618no—
432#381—612no—
433#381—614no—
434#380—614no—
435#380—614no—
436#380—614no—
437#379—612no—
438#379—612no—
439#379—612no—
440C4×C4⋊C4—618no—
441C4×C22⋊C4—614no—
442C4×C22⋊C4—614no—
443C4×C22⋊C4—618no—
444C4×C22⋊C4—614no—
445C61#3435711yescharacteristic, complemented, Sylow
446C25—611no—
447C25—611no—
448C22×D4—611no—
449C22×D4—611no—
450C22×D4—612no—
451C22×D4—612no—
452C22×D4—612no—
453C22×D4—612no—
454C22×D4—611no—
455C22×D4—2444no—
456C22×D4C2×#692311yescharacteristic
457C23×C4—611no—
458C23×C4—612no—
459C23×C4—611no—
460C23×C4—612no—
461C23×C4—612no—
462C23×C4—611no—
463C23×C4—612no—
464C23×C4—611no—
465C23×C4—611no—
466C23×C4—612no—
467C23×C4—611no—
468C23×C4—614no—
469C23×C4—2444no—
470C23×C4C2×#692311yescharacteristic, complemented
471#123—614no—
472#123—612no—
473#123—612no—
474#123—614no—
475#123—612no—
476#123—612no—
477#123—614no—
478#123—614no—
479#123—614no—
480#123—614no—
481#123—614no—
482#123—614no—
483#123—614no—
484#123—614no—
485#123—614no—
486#123—612no—
487#123—612no—
488#123C2×#692314yescomplemented
489#123C2×#692312yescomplemented
490#123C2×#692312yescomplemented
491#117—2448no—
492#117—2444no—
493C2×C4⋊C4—612no—
494C2×C4⋊C4—612no—
495C2×C4⋊C4—612no—
496C2×C4⋊C4—614no—
497C2×C4⋊C4—614no—
498C2×C4⋊C4—614no—
499C2×C4⋊C4—614no—
500C2×C4⋊C4—618no—
501C2×C4⋊C4—614no—
502C2×C4⋊C4—618no—
503C2×C4⋊C4C2×#692312yescomplemented
504C2×C22⋊C4—612no—
505C2×C22⋊C4—611no—
506C2×C22⋊C4—612no—
507C2×C22⋊C4—612no—
508C2×C22⋊C4—612no—
509C2×C22⋊C4—614no—
510C2×C22⋊C4—614no—
511C2×C22⋊C4—612no—
512C2×C22⋊C4—612no—
513C2×C22⋊C4—614no—
514C2×C22⋊C4—614no—
515C2×C22⋊C4—612no—
516C2×C22⋊C4—612no—
517C2×C22⋊C4—614no—
518C2×C22⋊C4—614no—
519C2×C22⋊C4—614no—
520C2×C22⋊C4—614no—
521C2×C22⋊C4—614no—
522C2×C22⋊C4—614no—
523C2×C22⋊C4—614no—
524C2×C22⋊C4—618no—
525C2×C22⋊C4—2444no—
526C2×C22⋊C4C2×#692312yes—
527C2×C22⋊C4C2×#692311yescharacteristic, complemented
528C2×C42—618no—
529C2×C42—614no—
530C2×C42—618no—
531#95—618no—
532#95—618no—
533#95—618no—
534#95—618no—
535#95—618no—
536C24—611no—
537C24—612no—
538C24—611no—
539C24—611no—
540C24—612no—
541C24—611no—
542C24—611no—
543C24—611no—
544C24—611no—
545C24—1224no—
546C24—1224no—
547C24—2444no—
548C24—2444no—
549C24C22×#692311yescharacteristic
550C24C22×#692311yescharacteristic
551C2×D4—42no—
552C2×D4—612no—
553C2×D4—612no—
554C2×D4—612no—
555C2×D4—612no—
556C2×D4—612no—
557C2×D4—612no—
558C2×D4—2442no—
559C2×D4—2442no—
560C2×D4—2442no—
561C2×D4—2442no—
562C2×D4—2442no—
563C2×D4—2444no—
564C2×D4—2444no—
565C2×D4—2442no—
566C2×D4—2442no—
567C2×D4C22×#692312yes—
568C2×D4C22×#692312yes—
569C22×C4—42no—
570C22×C4—612no—
571C22×C4—611no—
572C22×C4—612no—
573C22×C4—611no—
574C22×C4—612no—
575C22×C4—611no—
576C22×C4—612no—
577C22×C4—614no—
578C22×C4—612no—
579C22×C4—612no—
580C22×C4—612no—
581C22×C4—612no—
582C22×C4—612no—
583C22×C4—614no—
584C22×C4—612no—
585C22×C4—612no—
586C22×C4—612no—
587C22×C4—612no—
588C22×C4—618no—
589C22×C4—618no—
590C22×C4—1228no—
591C22×C4—1224no—
592C22×C4—2444no—
593C22×C4—2442no—
594C22×C4—2444no—
595C22×C4—2442no—
596C22×C4—2442no—
597C22×C4—2444no—
598C22×C4—2442no—
599C22×C4—2444no—
600C22×C4—2444no—
601C22×C4—2448no—
602C22×C4—2442no—
603C22×C4C22×#692312yes—
604C22×C4C22×#692311yescharacteristic
605C22×C4C22×#692312yes—
606C22×C4C22×#692311yescharacteristic
607C22×C4C22×#692312yes—
608C22×C4C22×#692311yescharacteristic
609C4⋊C4—614no—
610C4⋊C4—614no—
611C4⋊C4—614no—
612C4⋊C4—614no—
613C4⋊C4—614no—
614C4⋊C4—614no—
615C4⋊C4—2448no—
616C4⋊C4—2444no—
617C4⋊C4—2448no—
618C4⋊C4C22×#692314yes—
619C4⋊C4C22×#692314yes—
620C22⋊C4—612no—
621C22⋊C4—612no—
622C22⋊C4—614no—
623C22⋊C4—614no—
624C22⋊C4—614no—
625C22⋊C4—614no—
626C22⋊C4—614no—
627C22⋊C4—614no—
628C22⋊C4—614no—
629C22⋊C4—614no—
630C22⋊C4—1228no—
631C22⋊C4—1228no—
632C22⋊C4—2444no—
633C22⋊C4—2444no—
634C22⋊C4—2448no—
635C22⋊C4—2444no—
636C22⋊C4—2444no—
637C22⋊C4—2444no—
638C22⋊C4C22×#692314yes—
639C22⋊C4C22×#692314yes—
640C22⋊C4C22×#692312yes—
641C22⋊C4C22×#692312yes—
642C42—2448no—
643C42—2444no—
644C42—2448no—
645C23—22no—
646C23—22no—
647C23—42no—
648C23—42no—
649C23—611no—
650C23—614no—
651C23—611no—
652C23—612no—
653C23—611no—
654C23—611no—
655C23—1224no—
656C23—1224no—
657C23—1222no—
658C23—1224no—
659C23—1224no—
660C23—1228no—
661C23—1222no—
662C23—1222no—
663C23—1222no—
664C23—1222no—
665C23—1222no—
666C23—1222no—
667C23—1222no—
668C23—4888no—
669C23—2442no—
670C23—2444no—
671C23—2442no—
672C23—2442no—
673C23—2442no—
674C23—24416no—
675C23C23×#692312yes—
676C23C23×#692311yescharacteristic
677C23C23×#692311yescharacteristic
678C23C23×#692311yescharacteristic
679D4—42no—
680D4—42no—
681D4—2442no—
682D4—2442no—
683D4—2442no—
684D4—2442no—
685D4—2442no—
686D4—2442no—
687C2×C4—24no—
688C2×C4—22no—
689C2×C4—41no—
690C2×C4—42no—
691C2×C4—41no—
692C2×C4—42no—
693C2×C4—614no—
694C2×C4—612no—
695C2×C4—612no—
696C2×C4—612no—
697C2×C4—1224no—
698C2×C4—1222no—
699C2×C4—1228no—
700C2×C4—1224no—
701C2×C4—1222no—
702C2×C4—1224no—
703C2×C4—1224no—
704C2×C4—1224no—
705C2×C4—1224no—
706C2×C4—1222no—
707C2×C4—1228no—
708C2×C4—1228no—
709C2×C4—1228no—
710C2×C4—1228no—
711C2×C4—1228no—
712C2×C4—1228no—
713C2×C4—4888no—
714C2×C4—2444no—
715C2×C4—2442no—
716C2×C4—2442no—
717C2×C4—2442no—
718C2×C4—2442no—
719C2×C4—2442no—
720C2×C4—2441no—
721C2×C4—2442no—
722C2×C4—2441no—
723C2×C4C23×#692314yes—
724C2×C4C23×#692312yes—
725C2×C4C23×#692312yes—
726C2×C4C23×#692312yes—
727C22—22no—
728C22—21no—
729C22—21no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—24no—
734C22—44no—
735C22—82no—
736C22—612no—
737C22—614no—
738C22—612no—
739C22—1228no—
740C22—1222no—
741C22—1221no—
742C22—1221no—
743C22—1222no—
744C22—1224no—
745C22—1222no—
746C22—1222no—
747C22—4882no—
748C22—4884no—
749C22—2444no—
750C22—2444no—
751C22—2444no—
752C22—2444no—
753C22—2444no—
754C22—2444no—
755C22—2444no—
756C22#1684082912yes—
757C22C24×#692311yescharacteristic
758C4—22no—
759C4—22no—
760C4—22no—
761C4—24no—
762C4—1222no—
763C4—1222no—
764C4—1222no—
765C4—1224no—
766C4—2448no—
767C4—2448no—
768C2—22no—
769C2—41no—
770C2—41no—
771C2—42no—
772C2—614no—
773C2—1222no—
774C2—2442no—
775C2—2441no—
776C2—2441no—
777C2C2×#1684082911yescharacteristic
778C2#2146279912yes—
subgroupG/H
center, FrattiniC22C24×#6923
commutator, socleC22×C61C24×C4
FittingC2×#123×C61C4
prime radicalC22×D4×D61C22
cosocleC22×D61C25
hypercenterC2×#123#6923
hypocenterC61#34357
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. #21462359C2semidirect
2. #21462357C2semidirect
3. #21462327C2semidirect
4. #21462325C2semidirect
5. #21462318C2semidirect
6. #21462295C2semidirect
9. #21462263C2semidirect
16. #16840713C22semidirect
17. #16840712C22semidirect
18. #16840712C22semidirect
19. #16840712C22semidirect
20. #16840712C22semidirect
21. #16840711C22semidirect
22. #16840711C22semidirect
25. #16840709C22semidirect
29. #16840704C22semidirect
30. #16840704C22semidirect
34. C4⋊C4×#6923C22semidirect
35. C22⋊C4×#6923C22semidirect
37. C4×C22⋊#6923C22semidirect
38. C4×C22⋊#6923C22semidirect
41. C2×#14519762C4semidirect
42. C2×#14519761C4semidirect
43. C2×#14519760C4semidirect
44. C2×#14519759C4semidirect
45. C2×#14519758C4semidirect
46. #123×D61C4semidirect
47. #123×D61C4semidirect
48. #123×D61C4semidirect
55. C2×#123×C61C4semidirect
89. C23×Dic61C2×C4semidirect
91. C22×C4×D61C2×C4semidirect
92. C22×C4×D61C2×C4semidirect
93. C22×C4×D61C2×C4semidirect
94. C22×C4×D61C2×C4semidirect
101. #14519762C2×C4semidirect
102. #14519762C2×C4semidirect
103. #14519762C2×C4semidirect
104. #14519762C2×C4semidirect
105. #14519761C2×C4semidirect
106. #14519761C2×C4semidirect
107. #14519761C2×C4semidirect
108. #14519760C2×C4semidirect
109. #14519760C2×C4semidirect
110. #14519760C2×C4semidirect
111. #14519759C2×C4semidirect
112. #14519759C2×C4semidirect
113. #14519759C2×C4semidirect
114. #14519759C2×C4semidirect
115. #14519758C2×C4semidirect
116. #14519758C2×C4semidirect
117. #14519758C2×C4semidirect
118. C2×C4⋊Dic61C2×C4semidirect
119. C2×#11758196C2×C4semidirect
120. C2×#11758196C2×C4semidirect
121. C4⋊C4×D61C2×C4semidirect
122. C4⋊C4×D61C2×C4semidirect
126. C2×C22⋊Dic61C2×C4semidirect
129. C2×#11758198C2×C4semidirect
132. C22⋊C4×D61C2×C4semidirect
133. C22⋊C4×D61C2×C4semidirect
139. C23×C4×C61C2×C4semidirect
140. #123×C61C2×C4semidirect
141. #123×C61C2×C4semidirect
142. #123×C61C2×C4semidirect
143. C2×C4⋊C4×C61C2×C4semidirect
145. C2×C22⋊C4×C61C2×C4semidirect
413. C2×#123#6923semidirect
445. C61#34357semidirect
470. C23×C4C2×#6923semidirect
488. #123C2×#6923semidirect
489. #123C2×#6923semidirect
490. #123C2×#6923semidirect
503. C2×C4⋊C4C2×#6923semidirect
527. C2×C22⋊C4C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214623592
#214623572
#214623272
#214623252
#214623182
#214622952
#214622922
#214622912
#214622632
C2×#123×D612
#3435761