Finite Group Databasebeta

← #30621689

Subgroups — #30621689

Order 15616.

1306 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840795C211yesmaximal, characteristic, complemented
2C2×#16840791C211yesmaximal, characteristic, complemented
3C2×#16840732C211yesmaximal, characteristic, complemented
4C22×C22⋊#92420C211yesmaximal, characteristic, complemented
5#21461942C211yesmaximal, characteristic, complemented
6#21461892C211yesmaximal, characteristic, complemented
7#21461888C211yesmaximal, characteristic, complemented
8#21461798C211yesmaximal, characteristic, complemented
9#21461797C211yesmaximal, characteristic, complemented
10#21461794C211yesmaximal, characteristic, complemented
11#21461766C211yesmaximal, characteristic, complemented
12#21461763C211yesmaximal, characteristic, complemented
13#21461561C211yesmaximal, characteristic, complemented
14C22⋊C4×#92420C211yesmaximal, characteristic, complemented
15#21448318C211yesmaximal, characteristic
16C22×#11758213C2211yescharacteristic, complemented
17C22×#11758217C2211yescharacteristic
18C22×#11758217C2211yescharacteristic
19C23×#92420C2211yescharacteristic
20C23×#92420C2211yescharacteristic
21#16840795—24no—
22#16840791—24no—
23C2×#14519844C2211yescharacteristic, complemented
24C2×#14519844C2211yescharacteristic, complemented
25C2×C4⋊#92420C2211yescharacteristic, complemented
26#16840732—24no—
27C2×#14519834C2211yescharacteristic, complemented
28C2×#14519834C2211yescharacteristic, complemented
29C2×#14519834C2211yescharacteristic, complemented
30C2×C22⋊#92420—24no—
31C2×C22⋊#92420C2211yescharacteristic
32C2×C22⋊#92420C2211yescharacteristic
33C2×C22⋊#92420C2211yescharacteristic
34C2×C22⋊#92420C2211yescharacteristic
35C2×C22⋊#92420C2211yescharacteristic
36C2×C22⋊#92420C2211yescharacteristic
37C2×C22⋊#92420C2211yescharacteristic
38C2×C22⋊#92420C2211yescharacteristic
39C2×#14519832C2211yescharacteristic, complemented
40C2×C4×#92420C2211yescharacteristic, complemented
41C2×C4×#92420C2211yescharacteristic, complemented
42#16840628C2211yescharacteristic, complemented
43#16840628C2211yescharacteristic, complemented
44#16840628C2211yescharacteristic, complemented
45#16840628C2211yescharacteristic, complemented
46#16840628C2211yescharacteristic, complemented
47#16840628C2211yescharacteristic, complemented
48C24×Dic61C2211yescharacteristic
49C2×#14519746C411yescharacteristic
50C2×#14519737C2211yescharacteristic
51C2×#14519737C2211yescharacteristic
52C2×#14519737C2211yescharacteristic
53#16839639C411yescharacteristic
54#16839639C411yescharacteristic
55#16839639C411yescharacteristic
56#16839634C411yescharacteristic
57#16839634C411yescharacteristic
58#16839634C411yescharacteristic
59C22⋊C4×Dic61C2211yescharacteristic
60C22⋊C4×Dic61C2211yescharacteristic
61C22⋊C4×Dic61C2211yescharacteristic
62C61×#379C411yescharacteristic
63C2×#11758213—22no—
64C2×#11758213—22no—
65C2×#11758213—41no—
66C2×#11758217—22no—
67C2×#11758217—22no—
68C2×#11758217—22no—
69C2×#11758217—22no—
70C2×#11758217—41no—
71C2×#11758217—41no—
72C22×#92420—22no—
73C22×#92420—22no—
74C22×#92420—22no—
75C22×#92420—22no—
76C22×#92420—41no—
77C22×#92420—41no—
78C22×#92420C2311yescharacteristic
79C22×#92420C2311yescharacteristic
80C22×#92420C2311yescharacteristic
81C22×#92420C2311yescharacteristic
82C22×#92420C2311yescharacteristic
83C22×#92420C2311yescharacteristic
84C22×#92420C2311yescharacteristic
85C22×#92420C2311yescharacteristic
86#14519844—22no—
87#14519844—41no—
88C4⋊#92420—22no—
89#14519834—22no—
90#14519834—22no—
91#14519834—41no—
92C22⋊#92420—22no—
93C22⋊#92420—22no—
94C22⋊#92420—22no—
95C22⋊#92420—22no—
96C22⋊#92420—22no—
97C22⋊#92420—22no—
98C22⋊#92420D414yescomplemented
99C22⋊#92420D414yescomplemented
100#14519832—22no—
101C4×#92420—22no—
102C4×#92420—41no—
103C22×C22⋊D61C2×C411yescharacteristic
104C22×C22⋊D61C2×C411yescharacteristic
105C22×C22⋊D61C2×C411yescharacteristic
106C23×Dic61—22no—
107C23×Dic61—22no—
108C23×Dic61—22no—
109C23×Dic61—22no—
110C23×Dic61—41no—
111C23×Dic61—41no—
112C23×Dic61C2×C411yescharacteristic
113C23×Dic61C2×C411yescharacteristic
114C23×Dic61C2×C411yescharacteristic
115C23×Dic61C2311yescharacteristic
116C23×Dic61C2311yescharacteristic
117C23×Dic61C2311yescharacteristic
118C22×C4×D61C2311yescharacteristic
119#14519746—24no—
120#14519737—22no—
121#14519737—22no—
122#14519737—22no—
123#14519737—22no—
124#14519737—41no—
125#14519737—41no—
126C2×#11758196C2×C411yescharacteristic
127C2×#11758196C2×C411yescharacteristic
128C2×#11758196C2×C411yescharacteristic
129C2×C22⋊Dic61C2×C411yescharacteristic
130C2×C22⋊Dic61C2×C411yescharacteristic
131C2×C22⋊Dic61C2×C411yescharacteristic
132C2×#11758198C2×C411yescharacteristic
133C2×#11758198C2×C411yescharacteristic
134C2×#11758198C2×C411yescharacteristic
135C2×C4×Dic61C2311yescharacteristic
136C2×C4×Dic61C2311yescharacteristic
137C2×C4×Dic61C2311yescharacteristic
138#14519684C2×C411yescharacteristic
139#14519684C2×C411yescharacteristic
140#14519684C2×C411yescharacteristic
141#14519684C2×C411yescharacteristic
142#14519684C2×C411yescharacteristic
143#14519684C2×C411yescharacteristic
144C25×C61C2×C411yescharacteristic
145C2×C22⋊C4×C61C2×C411yescharacteristic
146C2×C22⋊C4×C61C2×C411yescharacteristic
147C2×C22⋊C4×C61C2×C411yescharacteristic
148C2×C22⋊C4×C61C2×C411yescharacteristic
149C2×C22⋊C4×C61C2×C411yescharacteristic
150C2×C22⋊C4×C61C2×C411yescharacteristic
151C24×C61—22no—
152C24×C61—22no—
153C24×C61—22no—
154C24×C61—22no—
155C24×C61—22no—
156C24×C61—41no—
157C24×C61—41no—
158C24×C61C22×C411yescharacteristic
159C24×C61C22×C411yescharacteristic
160C24×C61C22×C411yescharacteristic
161C23×D61C22×C411yescharacteristic
162C22×C4×C61C22×C411yescharacteristic
163C22×C4×C61C22×C411yescharacteristic
164C22×C4×C61C22×C411yescharacteristic
165C22×C4×C61C22×C411yescharacteristic
166C2×C22⋊D61—22no—
167C2×C22⋊D61—22no—
168C2×C22⋊D61—22no—
169C2×C22⋊D61—22no—
170C2×C22⋊D61—22no—
171C2×C22⋊D61—22no—
172C2×C22⋊D61—22no—
173C2×C22⋊D61—41no—
174C2×C22⋊D61—41no—
175C22×Dic61—21no—
176C22×Dic61—21no—
177C22×Dic61—21no—
178C22×Dic61—21no—
179C22×Dic61—21no—
180C22×Dic61—21no—
181C22×Dic61—21no—
182C22×Dic61—21no—
183C22×Dic61—22no—
184C22×Dic61—22no—
185C22×Dic61—22no—
186C22×Dic61—22no—
187C22×Dic61—22no—
188C22×Dic61—22no—
189C22×Dic61—21no—
190C22×Dic61—21no—
191C22×Dic61—21no—
192C22×Dic61—21no—
193C22×Dic61—21no—
194C22×Dic61—21no—
195C22×Dic61—41no—
196C22×Dic61—41no—
197C22×Dic61—41no—
198C22×Dic61—44no—
199C22×Dic61—44no—
200C22×Dic61—44no—
201C22×Dic61—44no—
202C22×Dic61C22×C411yescharacteristic
203C22×Dic61C22×C411yescharacteristic
204C22×Dic61C22×C411yescharacteristic
205C22×Dic61C22×C411yescharacteristic
206C22×Dic61C22×C411yescharacteristic
207C22×Dic61C22×C411yescharacteristic
208C22×Dic61C2×D412yes—
209C22×Dic61C2×D412yes—
210C22×Dic61#4112yes—
211C22×Dic61#4112yes—
212C22×Dic61C2411yescharacteristic
213C2×C4×D61—21no—
214C2×C4×D61—21no—
215C2×C4×D61—21no—
216C2×C4×D61—21no—
217C2×C4×D61—21no—
218C2×C4×D61—21no—
219#11758217—44no—
220#11758217—44no—
221C2×#92420—21no—
222C2×#92420—21no—
223C2×#92420—21no—
224C2×#92420—21no—
225C2×#92420—21no—
226C2×#92420—21no—
227C2×#92420—21no—
228C2×#92420—21no—
229C2×#92420—21no—
230C2×#92420—21no—
231C2×#92420—21no—
232C2×#92420—21no—
233C2×#92420—21no—
234C2×#92420—21no—
235C2×#92420—21no—
236C2×#92420—21no—
237C2×#92420—21no—
238C2×#92420—21no—
239C2×#92420—21no—
240C2×#92420—21no—
241C2×#92420—44no—
242C2×#92420—44no—
243C2×#92420C2×D412yes—
244C2×#92420C2×D412yes—
245C2×#92420C2×D412yes—
246C2×#92420C2×D412yes—
247#11758213—44no—
248C22⋊C4×C61—22no—
249C22⋊C4×C61—22no—
250C22⋊C4×C61—22no—
251C22⋊C4×C61—22no—
252C22⋊C4×C61—41no—
253C22⋊C4×C61—41no—
254C22⋊Dic61—22no—
255C22⋊Dic61—22no—
256C22⋊Dic61M1614yescomplemented
257#11758198—22no—
258#11758198—22no—
259#11758198—41no—
260#11758196—22no—
261#11758196—22no—
262#11758196—41no—
263C4×Dic61—21no—
264C4×Dic61—21no—
265C4×Dic61—21no—
266C4×Dic61—21no—
267C4×Dic61—21no—
268C4×Dic61—21no—
269C23×C61—21no—
270C23×C61—21no—
271C23×C61—21no—
272C23×C61—21no—
273C23×C61—28no—
274C23×C61—21no—
275C23×C61—21no—
276C23×C61—21no—
277C23×C61—21no—
278C23×C61—21no—
279C23×C61—21no—
280C23×C61—21no—
281C23×C61—21no—
282C23×C61—21no—
283C23×C61—21no—
284C23×C61—21no—
285C23×C61—21no—
286C23×C61—44no—
287C23×C61—44no—
288C23×C61—44no—
289C23×C61—44no—
290C23×C61—44no—
291C23×C61—44no—
292C23×C61C4×D412yes—
293C23×C61C4×D412yes—
294C23×C61C2×M1612yes—
295C23×C61#13112yes—
296C23×C61#13112yes—
297C23×C61C23×C411yescharacteristic
298C22×D61—21no—
299C22×D61—21no—
300C22×D61—21no—
301C22×D61—21no—
302C22×D61—21no—
303C22×D61—21no—
304C22×D61—21no—
305C2×C4×C61—21no—
306C2×C4×C61—21no—
307C2×C4×C61—21no—
308C2×C4×C61—21no—
309C2×C4×C61—21no—
310C2×C4×C61—21no—
311C2×C4×C61—21no—
312C2×C4×C61—21no—
313C2×C4×C61—21no—
314C2×C4×C61—21no—
315C2×C4×C61—21no—
316C2×C4×C61—21no—
317C22⋊D61—44no—
318C22⋊D61—44no—
319C22⋊D61—44no—
320C2×Dic61—21no—
321C2×Dic61—21no—
322C2×Dic61—21no—
323C2×Dic61—21no—
324C2×Dic61—21no—
325C2×Dic61—21no—
326C2×Dic61—21no—
327C2×Dic61—21no—
328C2×Dic61—22no—
329C2×Dic61—22no—
330C2×Dic61—22no—
331C2×Dic61—22no—
332C2×Dic61—22no—
333C2×Dic61—22no—
334C2×Dic61—22no—
335C2×Dic61—22no—
336C2×Dic61—21no—
337C2×Dic61—21no—
338C2×Dic61—21no—
339C2×Dic61—21no—
340C2×Dic61—21no—
341C2×Dic61—21no—
342C2×Dic61—44no—
343C2×Dic61—44no—
344C2×Dic61—44no—
345C2×Dic61—41no—
346C2×Dic61—41no—
347C2×Dic61—41no—
348C2×Dic61—41no—
349C2×Dic61C4×D412yes—
350C2×Dic61C4×D412yes—
351C2×Dic61C2×M1612yes—
352C2×Dic61C2×M1612yes—
353C2×Dic61C22×D411yescharacteristic
354C2×Dic61C22×D411yescharacteristic
355C2×Dic61C2×#4111yescharacteristic
356C2×Dic61C2×#4111yescharacteristic
357C2×Dic61H(5,𝔽2)11yescharacteristic
358C2×Dic61H(5,𝔽2)11yescharacteristic
359C4×D61—41no—
360C4×D61—41no—
361C4×D61—41no—
362C4×D61—41no—
363#92420—22no—
364#92420—22no—
365#92420—22no—
366#92420—22no—
367#92420—41no—
368#92420—41no—
369#92420—41no—
370#92420—41no—
371#22848—611nomaximal, Sylow
372C22×C61—22no—
373C22×C61—22no—
374C22×C61—22no—
375C22×C61—22no—
376C22×C61—22no—
377C22×C61—22no—
378C22×C61—22no—
379C22×C61—22no—
380C22×C61—22no—
381C22×C61—22no—
382C22×C61—22no—
383C22×C61—22no—
384C22×C61—416no—
385C22×C61—41no—
386C22×C61—41no—
387C22×C61—41no—
388C22×C61—41no—
389C22×C61—41no—
390C22×C61—41no—
391C22×C61—41no—
392C22×C61—41no—
393C22×C61#43614yescomplemented
394C22×C61C2×C4×D411yescharacteristic
395C22×C61C2×C4×D411yescharacteristic
396C22×C61#51811yescharacteristic
397C22×C61C22×M1611yescharacteristic
398C22×C61C2×#13111yescharacteristic
399C22×C61C2×#13111yescharacteristic
400C22×C61#56811yescharacteristic
401C2×D61—41no—
402C2×D61—41no—
403C2×D61—41no—
404C2×D61—41no—
405C2×D61—41no—
406C2×D61—41no—
407C2×D61—41no—
408C4×C61—41no—
409C4×C61—41no—
410C4×C61—41no—
411C4×C61—41no—
412Dic61—22no—
413Dic61—22no—
414Dic61—22no—
415Dic61—22no—
416Dic61—41no—
417Dic61—41no—
418Dic61D4211yescharacteristic
419Dic61#54611yescharacteristic
420Dic61#54611yescharacteristic
421Dic61#55111yescharacteristic
422C2×#436—611no—
423C2×#435—611no—
424C2×#407—611no—
425C22×C22⋊C8—611no—
426C4×#120—611no—
427#1954—611no—
428#1924—611no—
429#1923—611no—
430#1870—611no—
431#1870—611no—
432#1869—611no—
433#1851—611no—
434#1850—611no—
435#1753—611no—
436C8×C22⋊C4—611no—
437C2×C61—24no—
438C2×C61—42no—
439C2×C61—42no—
440C2×C61#235811yescharacteristic
441C2×C61C2×#43611yescharacteristic
442C2×C61#292911yescharacteristic
443C2×C61#293311yescharacteristic
444C2×C61D4×M1611yescharacteristic
445C2×C61#297411yescharacteristic
446C2×C61#297611yescharacteristic
447D61—81no—
448C24×C4—611no—
449C22×M16—611no—
450C22×M16—611no—
451C22×M16—611no—
452C23×C8—611no—
453C23×C8—611no—
454C2×#120—611no—
455C2×C4×D4—611no—
456C2×C4×D4—611no—
457C2×C4×D4—611no—
458#436—1224no—
459#435—1224no—
460C2×C4⋊C8—611no—
461C2×C4⋊C8—611no—
462C2×C4⋊C8—611no—
463#407—1224no—
464C2×C22⋊C8—611no—
465C2×C22⋊C8—611no—
466C2×C22⋊C8—611no—
467C2×C22⋊C8—611no—
468C2×C22⋊C8—611no—
469C2×C22⋊C8—611no—
470C2×C22⋊C8—611no—
471C2×C22⋊C8—611no—
472C2×C22⋊C8—611no—
473C2×C22⋊C8—611no—
474C2×C22⋊C8—611no—
475C2×C22⋊C8—1224no—
476C2×#97—611no—
477C2×C4×C8—611no—
478C2×C4×C8—611no—
479#386—611no—
480#386—611no—
481#386—611no—
482#385—611no—
483#385—611no—
484#385—611no—
485#379#692311yescharacteristic
486C4×C22⋊C4—611no—
487C4×C22⋊C4—611no—
488C4×C22⋊C4—611no—
489#336—611no—
490#336—611no—
491#336—611no—
492#336—611no—
493#336—611no—
494#336—611no—
495C61#2284811yescharacteristic, complemented, Sylow
496C25C2×#692311yescharacteristic
497C22×D4—611no—
498C22×D4—611no—
499C22×D4—611no—
500C23×C4—611no—
501C23×C4—611no—
502C23×C4—611no—
503C23×C4—611no—
504C23×C4—611no—
505C23×C4—611no—
506C23×C4—611no—
507C23×C4—1222no—
508C23×C4—1222no—
509C23×C4—1222no—
510C23×C4—1222no—
511C23×C4—2441no—
512C23×C4—2441no—
513C2×M16—1222no—
514C2×M16—1222no—
515C2×M16—1222no—
516C2×M16—1222no—
517C2×M16—1222no—
518C2×M16—1222no—
519C2×M16—2441no—
520C2×M16—2441no—
521C2×M16—2441no—
522C22×C8—611no—
523C22×C8—611no—
524C22×C8—611no—
525C22×C8—611no—
526C22×C8—611no—
527C22×C8—611no—
528C22×C8—611no—
529C22×C8—611no—
530C22×C8—1222no—
531C22×C8—1222no—
532C22×C8—1222no—
533C22×C8—1222no—
534C22×C8—2441no—
535C22×C8—2441no—
536#120—1224no—
537C4×D4—1222no—
538C4×D4—1222no—
539C4×D4—1222no—
540C4×D4—1222no—
541C4×D4—2441no—
542C4×D4—2441no—
543C2×C4⋊C4—611no—
544C2×C4⋊C4—611no—
545C2×C4⋊C4—611no—
546C2×C22⋊C4—611no—
547C2×C22⋊C4—611no—
548C2×C22⋊C4—611no—
549C2×C22⋊C4—611no—
550C2×C22⋊C4—611no—
551C2×C22⋊C4—611no—
552C2×C22⋊C4C2×#692311yescharacteristic
553C2×C22⋊C4C2×#692311yescharacteristic
554C2×C22⋊C4C2×#692311yescharacteristic
555C2×C22⋊C4C2×#692311yescharacteristic
556C2×C22⋊C4C2×#692311yescharacteristic
557C2×C22⋊C4C2×#692311yescharacteristic
558C2×C42—611no—
559C2×C42—611no—
560C2×C42—611no—
561C4⋊C8—1222no—
562C4⋊C8—1222no—
563C4⋊C8—2441no—
564C22⋊C8—614no—
565C22⋊C8—614no—
566C22⋊C8—1222no—
567C22⋊C8—1222no—
568C22⋊C8—1222no—
569C22⋊C8—1222no—
570C22⋊C8—1222no—
571C22⋊C8—1222no—
572C22⋊C8—1222no—
573C22⋊C8—1222no—
574C22⋊C8—2441no—
575#97—1222no—
576C4×C8—1222no—
577C4×C8—2441no—
578#95—611no—
579#95—611no—
580#95—611no—
581#95—611no—
582#95—611no—
583#95—611no—
584C24—22no—
585C24—22no—
586C24—22no—
587C24—22no—
588C24—22no—
589C24—41no—
590C24—41no—
591C24—611no—
592C24C22×#692311yescharacteristic
593C24C22×#692311yescharacteristic
594C24C22×#692311yescharacteristic
595C2×D4—1222no—
596C2×D4—1222no—
597C2×D4—1222no—
598C2×D4—1222no—
599C2×D4—1222no—
600C2×D4—1222no—
601C2×D4—1222no—
602C2×D4—2441no—
603C2×D4—2441no—
604C22×C4—611no—
605C22×C4—612no—
606C22×C4—612no—
607C22×C4—612no—
608C22×C4—612no—
609C22×C4—611no—
610C22×C4—611no—
611C22×C4—611no—
612C22×C4—611no—
613C22×C4—611no—
614C22×C4—611no—
615C22×C4—1221no—
616C22×C4—1221no—
617C22×C4—1221no—
618C22×C4—1221no—
619C22×C4—1221no—
620C22×C4—1221no—
621C22×C4—1221no—
622C22×C4—1221no—
623C22×C4—1221no—
624C22×C4—1221no—
625C22×C4—1221no—
626C22×C4—1221no—
627C22×C4—1221no—
628C22×C4—1221no—
629C22×C4—1221no—
630C22×C4—1221no—
631C22×C4—1221no—
632C22×C4—1221no—
633C22×C4—1221no—
634C22×C4—1221no—
635C22×C4—1222no—
636C22×C4—1222no—
637C22×C4—1222no—
638C22×C4—1222no—
639C22×C4—1222no—
640C22×C4—1222no—
641C22×C4—2441no—
642C22×C4—2441no—
643C22×C4—2441no—
644C22×C4—2444no—
645C22×C4—2444no—
646C22×C4—2444no—
647C22×C4—2444no—
648C22×C4C22×#692311yescharacteristic
649C22×C4C22×#692311yescharacteristic
650C22×C4C22×#692311yescharacteristic
651C22×C4C22×#692311yescharacteristic
652M16—2444no—
653M16—2444no—
654M16—2444no—
655C2×C8—612no—
656C2×C8—612no—
657C2×C8—612no—
658C2×C8—612no—
659C2×C8—1221no—
660C2×C8—1221no—
661C2×C8—1221no—
662C2×C8—1221no—
663C2×C8—1221no—
664C2×C8—1221no—
665C2×C8—1221no—
666C2×C8—1221no—
667C2×C8—1221no—
668C2×C8—1221no—
669C2×C8—1221no—
670C2×C8—1221no—
671C2×C8—1221no—
672C2×C8—1221no—
673C2×C8—1221no—
674C2×C8—1221no—
675C2×C8—1221no—
676C2×C8—1221no—
677C2×C8—1221no—
678C2×C8—1221no—
679C2×C8—2444no—
680C2×C8—2444no—
681C4⋊C4—1222no—
682C4⋊C4—1222no—
683C4⋊C4—2441no—
684C22⋊C4—22no—
685C22⋊C4—22no—
686C22⋊C4—22no—
687C22⋊C4—22no—
688C22⋊C4—41no—
689C22⋊C4—41no—
690C22⋊C4—614no—
691C22⋊C4—1222no—
692C22⋊C4—1222no—
693C22⋊C4—1222no—
694C22⋊C4—1222no—
695C22⋊C4—2441no—
696C42—1221no—
697C42—1221no—
698C42—1221no—
699C42—1221no—
700C42—1221no—
701C42—1221no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—28no—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—44no—
720C23—44no—
721C23—44no—
722C23—44no—
723C23—44no—
724C23—44no—
725C23—1221no—
726C23—1221no—
727C23—1221no—
728C23—1221no—
729C23—1221no—
730C23—1221no—
731C23—1221no—
732C23D4×#692312yes—
733C23D4×#692312yes—
734C23D61⋊M1612yes—
735C23#1451986412yes—
736C23#1451986412yes—
737C23C23×#692311yescharacteristic
738D4—2444no—
739D4—2444no—
740D4—2444no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—611no—
754C2×C4—611no—
755C2×C4—611no—
756C2×C4—611no—
757C2×C4—611no—
758C2×C4—611no—
759C2×C4—612no—
760C2×C4—612no—
761C2×C4—612no—
762C2×C4—612no—
763C2×C4—1222no—
764C2×C4—1222no—
765C2×C4—1222no—
766C2×C4—1222no—
767C2×C4—1222no—
768C2×C4—1222no—
769C2×C4—1222no—
770C2×C4—1222no—
771C2×C4—1221no—
772C2×C4—1221no—
773C2×C4—1221no—
774C2×C4—1221no—
775C2×C4—1221no—
776C2×C4—1221no—
777C2×C4—1221no—
778C2×C4—1221no—
779C2×C4—1221no—
780C2×C4—1221no—
781C2×C4—1221no—
782C2×C4—1221no—
783C2×C4—1221no—
784C2×C4—1221no—
785C2×C4—2441no—
786C2×C4—2441no—
787C2×C4—2441no—
788C2×C4—2441no—
789C2×C4—2441no—
790C2×C4—2441no—
791C2×C4—2441no—
792C2×C4—2441no—
793C2×C4—2444no—
794C2×C4—2444no—
795C2×C4—2444no—
796C8—1222no—
797C8—1222no—
798C8—1222no—
799C8—1222no—
800C8—2441no—
801C8—2441no—
802C8—2441no—
803C8—2441no—
804C22—22no—
805C22—22no—
806C22—22no—
807C22—22no—
808C22—22no—
809C22—22no—
810C22—22no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—22no—
816C22—416no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—2441no—
826C22—2441no—
827C22—2441no—
828C22—2441no—
829C22—2441no—
830C22—2441no—
831C22—2441no—
832C22#1684079514yescomplemented
833C22C2×D4×#692311yescharacteristic
834C22C2×D4×#692311yescharacteristic
835C22#1684082911yescharacteristic
836C22C2×D61⋊M1611yescharacteristic
837C22C2×#1451986411yescharacteristic
838C22C2×#1451986411yescharacteristic
839C22#1684084011yescharacteristic
840C4—41no—
841C4—41no—
842C4—41no—
843C4—41no—
844C4—611no—
845C4—611no—
846C4—611no—
847C4—611no—
848C4—1222no—
849C4—1222no—
850C4—1222no—
851C4—1222no—
852C4—2441no—
853C4—2441no—
854C2—24no—
855C2—42no—
856C2—42no—
857C2—4881no—
858C2#2146234111yescharacteristic
859C2C2×#1684079511yescharacteristic
860C2#2146253411yescharacteristic
861C2#2146255111yescharacteristic
862C2#2146255711yescharacteristic
863C2#2146267811yescharacteristic
864C2#2146268511yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC61×#379C4
prime radicalC2×#14519746C4
cosocleC22×Dic61C24
hypercenter#379#6923
hypocenterC61#22848
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
1. C2×#16840795C2semidirect
2. C2×#16840791C2semidirect
3. C2×#16840732C2semidirect
4. C22×C22⋊#92420C2semidirect
5. #21461942C2semidirect
6. #21461892C2semidirect
7. #21461888C2semidirect
8. #21461798C2semidirect
9. #21461797C2semidirect
10. #21461794C2semidirect
11. #21461766C2semidirect
12. #21461763C2semidirect
13. #21461561C2semidirect
14. C22⋊C4×#92420C2semidirect
16. C22×#11758213C22semidirect
23. C2×#14519844C22semidirect
24. C2×#14519844C22semidirect
25. C2×C4⋊#92420C22semidirect
27. C2×#14519834C22semidirect
28. C2×#14519834C22semidirect
29. C2×#14519834C22semidirect
39. C2×#14519832C22semidirect
40. C2×C4×#92420C22semidirect
41. C2×C4×#92420C22semidirect
42. #16840628C22semidirect
43. #16840628C22semidirect
44. #16840628C22semidirect
45. #16840628C22semidirect
46. #16840628C22semidirect
47. #16840628C22semidirect
98. C22⋊#92420D4semidirect
99. C22⋊#92420D4semidirect
256. C22⋊Dic61M16semidirect
393. C22×C61#436semidirect
495. C61#22848semidirect
832. C22#16840795semidirect

Maximal subgroups

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

subgroupindex
C2×#168407952
C2×#168407912
C2×#168407322
C22×C22⋊#924202
#214619422
#214618922
#214618882
#214617982
#214617972
#214617942
#214617662
#214617632
#214615612
C22⋊C4×#924202
#214483182
#2284861