Finite Group Databasebeta

← #30615883

Subgroups — #30615883

Order 15616.

1142 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
1C2×#16840768C211yesmaximal, characteristic, complemented
2C2×#16840735C211yesmaximal, characteristic
3C2×#16840735C211yesmaximal, characteristic
4C2×C4×#11758217C211yesmaximal, characteristic, complemented
5#21461895C211yesmaximal, characteristic, complemented
6#21461894C211yesmaximal, characteristic, complemented
7#21461893C211yesmaximal, characteristic, complemented
8#21461892C211yesmaximal, characteristic, complemented
9#21461891C211yesmaximal, characteristic, complemented
10#21461890C211yesmaximal, characteristic, complemented
11#21461889C211yesmaximal, characteristic, complemented
12#21461888C211yesmaximal, characteristic, complemented
13#21461485C211yesmaximal, characteristic, complemented
14C2×#16840628C211yesmaximal, characteristic, complemented
15#21448304C211yesmaximal, characteristic
16C22×#11758217C2211yescharacteristic
17C22×#11758217C2211yescharacteristic
18C23×#92420C2211yescharacteristic
19C23×#92420C2211yescharacteristic
20#16840768—24no—
21C2×#14519844C2211yescharacteristic
22C2×#14519844C2211yescharacteristic
23C2×C4⋊#92420C2211yescharacteristic
24C2×C4⋊#92420C2211yescharacteristic
25#16840735—24no—
26#16840735—24no—
27C2×#14519834C2211yescharacteristic
28C2×#14519834C2211yescharacteristic
29C2×#14519834C2211yescharacteristic
30C2×#14519834C2211yescharacteristic
31C2×C22⋊#92420C2211yescharacteristic
32C2×C22⋊#92420C2211yescharacteristic
33C2×C22⋊#92420C2211yescharacteristic
34C2×C22⋊#92420C2211yescharacteristic
35C4×#11758217—24no—
36C2×#14519832C2211yescharacteristic
37C2×#14519832C2211yescharacteristic
38C2×C4×#92420C2211yescharacteristic
39C2×C4×#92420C2211yescharacteristic
40#16840628C2211yescharacteristic
41#16840628C2211yescharacteristic
42#16840628C2211yescharacteristic
43#16840628C2211yescharacteristic
44#16840628C2211yescharacteristic
45#16840628C2211yescharacteristic
46#16840628C2211yescharacteristic
47#16840628C2211yescharacteristic
48C22×#11758224C2211yescharacteristic
49C2×#14519733C2211yescharacteristic
50C22×C4×Dic61C2211yescharacteristic
51#16839666C411yescharacteristic
52#16839666C411yescharacteristic
53#16839662C411yescharacteristic
54#16839662C411yescharacteristic
55#16839642C411yescharacteristic
56#16839641C411yescharacteristic
57#16839639C411yescharacteristic
58C22⋊C4×Dic61C2211yescharacteristic
59C22⋊C4×Dic61C2211yescharacteristic
60#16839609C2211yescharacteristic
61#16839609C2211yescharacteristic
62C61×#386C411yescharacteristic
63C2×#11758217—22no—
64C2×#11758217—22no—
65C2×#11758217—22no—
66C2×#11758217—22no—
67C2×#11758217D414yes—
68C2×#11758217D414yes—
69C22×#92420—22no—
70C22×#92420—22no—
71C22×#92420—22no—
72C22×#92420—22no—
73C22×#92420—22no—
74C22×#92420—22no—
75C22×#92420C2311yescharacteristic
76C22×#92420C2311yescharacteristic
77C22×#92420C2311yescharacteristic
78C22×#92420C2311yescharacteristic
79C22×#92420C2311yescharacteristic
80C22×#92420C2311yescharacteristic
81C22×#92420C2311yescharacteristic
82C22×#92420C2311yescharacteristic
83#14519844—22no—
84#14519844—22no—
85C4⋊#92420—22no—
86C4⋊#92420—22no—
87#14519834—22no—
88#14519834—22no—
89#14519834—22no—
90#14519834—22no—
91C22⋊#92420—22no—
92C22⋊#92420—22no—
93C22⋊#92420—22no—
94C22⋊#92420—22no—
95#14519832—22no—
96#14519832—22no—
97C4×#92420—22no—
98C4×#92420—22no—
99C2×#11758224—22no—
100C2×#11758224—22no—
101C2×#11758224—22no—
102C2×#11758224—22no—
103C2×#11758224—22no—
104C2×#11758224—22no—
105C22×Dic122C2×C411yescharacteristic
106C22×C22⋊D61C2×C411yescharacteristic
107C22×C22⋊D61C2×C411yescharacteristic
108C23×Dic61C2×C411yescharacteristic
109C23×Dic61C2311yescharacteristic
110C23×Dic61C2311yescharacteristic
111C22×C4×D61C2311yescharacteristic
112#14519733—22no—
113#14519733—22no—
114C2×#11758196C2×C411yescharacteristic
115C2×#11758196C2×C411yescharacteristic
116C2×C22⋊Dic61C2×C411yescharacteristic
117C2×C22⋊Dic61C2×C411yescharacteristic
118C2×C22⋊Dic61C2×C411yescharacteristic
119C2×#11758198C2×C411yescharacteristic
120C2×#11758198C2×C411yescharacteristic
121C2×#11758198C2×C411yescharacteristic
122C2×#11758198C2×C411yescharacteristic
123C2×C4×Dic61—22no—
124C2×C4×Dic61—22no—
125C2×C4×Dic61C2×C411yescharacteristic
126C2×C4×Dic61C2×C411yescharacteristic
127C2×C4×Dic61C2311yescharacteristic
128C2×C4×Dic61C2311yescharacteristic
129C2×C4×Dic61C2311yescharacteristic
130C2×C4×Dic61C2311yescharacteristic
131#14519684C2×C411yescharacteristic
132#14519684C2×C411yescharacteristic
133#14519684C2×C411yescharacteristic
134#14519684C2×C411yescharacteristic
135#14519684C2×C411yescharacteristic
136#14519684C2×C411yescharacteristic
137C22×D4×C61C2×C411yescharacteristic
138C23×C4×C61C2×C411yescharacteristic
139C2×C22⋊C4×C61C2×C411yescharacteristic
140C2×C22⋊C4×C61C2×C411yescharacteristic
141C2×C22⋊C4×C61C2×C411yescharacteristic
142#95×C61C2×C411yescharacteristic
143#95×C61C2×C411yescharacteristic
144C24×C61C22×C411yescharacteristic
145C24×C61C22×C411yescharacteristic
146C23×D61C22×C411yescharacteristic
147C2×D4×C61—22no—
148C2×D4×C61—22no—
149C2×D4×C61—22no—
150C22×C4×C61—22no—
151C22×C4×C61—22no—
152C22×C4×C61—41no—
153C22×C4×C61C22×C411yescharacteristic
154C22×C4×C61C22×C411yescharacteristic
155C22×C4×C61C22×C411yescharacteristic
156C22×C4×C61C22×C411yescharacteristic
157C22×C4×C61C22×C411yescharacteristic
158C2×C22⋊D61—22no—
159C2×C22⋊D61—22no—
160C2×C22⋊D61—22no—
161C2×C22⋊D61—22no—
162C2×C22⋊D61—22no—
163C2×C22⋊D61—22no—
164C22×Dic61—22no—
165C22×Dic61—22no—
166C22×Dic61—21no—
167C22×Dic61—21no—
168C22×Dic61—21no—
169C22×Dic61—21no—
170C22×Dic61—21no—
171C22×Dic61—21no—
172C22×Dic61—41no—
173C22×Dic61C22×C411yescharacteristic
174C22×Dic61C22×C411yescharacteristic
175C22×Dic61C22×C411yescharacteristic
176C22×Dic61C22×C411yescharacteristic
177C22×Dic61C22×C411yescharacteristic
178C22×Dic61C22×C411yescharacteristic
179C22×Dic61C2×D412yes—
180C22×Dic61C2×D412yes—
181C22×Dic61#4112yes—
182C22×Dic61#4112yes—
183C22×Dic61#4112yes—
184C22×Dic61#4112yes—
185C22×Dic61C2411yescharacteristic
186#11758224—44no—
187#11758224—44no—
188#11758224—44no—
189#11758224—44no—
190C2×C4×D61—21no—
191C2×C4×D61—21no—
192C2×C4×D61—21no—
193C2×C4×D61—21no—
194C2×C4×D61—21no—
195C2×C4×D61—21no—
196C2×Dic122—22no—
197C2×Dic122—22no—
198C2×Dic122—22no—
199#11758217—28no—
200#11758217—28no—
201C2×#92420—21no—
202C2×#92420—21no—
203C2×#92420—21no—
204C2×#92420—21no—
205C2×#92420—21no—
206C2×#92420—21no—
207C2×#92420—21no—
208C2×#92420—21no—
209C2×#92420—21no—
210C2×#92420—21no—
211C2×#92420—21no—
212C2×#92420—21no—
213C2×#92420—21no—
214C2×#92420—21no—
215C2×#92420—21no—
216C2×#92420—21no—
217C2×#92420—21no—
218C2×#92420—21no—
219C2×#92420—21no—
220C2×#92420—21no—
221C2×#92420—44no—
222C2×#92420—44no—
223C2×#92420C2×D412yes—
224C2×#92420C2×D412yes—
225C2×#92420C2×D412yes—
226C2×#92420C2×D412yes—
227C22⋊C4×C61—22no—
228C22⋊C4×C61—22no—
229C22⋊C4×C61—41no—
230C22⋊Dic61—22no—
231C22⋊Dic61—22no—
232C22⋊Dic61—41no—
233#11758198—22no—
234#11758198—22no—
235#11758198—41no—
236#11758198—41no—
237#11758196—22no—
238#11758196—22no—
239C4×Dic61—22no—
240C4×Dic61—22no—
241C4×Dic61—21no—
242C4×Dic61—21no—
243C4×Dic61—21no—
244C4×Dic61—21no—
245C4×Dic61—21no—
246C4×Dic61—21no—
247C4×Dic61—21no—
248C4×Dic61—21no—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61—21no—
252C23×C61—21no—
253C23×C61—21no—
254C23×C61—21no—
255C23×C61—21no—
256C23×C61—21no—
257C23×C61—21no—
258C23×C61—21no—
259C23×C61—21no—
260C23×C61#11712yes—
261C23×C61C4×D412yes—
262C23×C61C4×D412yes—
263C23×C61C23×C411yescharacteristic
264C22×D61—21no—
265C22×D61—21no—
266C22×D61—21no—
267C22×D61—21no—
268C22×D61—21no—
269C22×D61—21no—
270C22×D61—21no—
271D4×C61—44no—
272C2×C4×C61—21no—
273C2×C4×C61—21no—
274C2×C4×C61—21no—
275C2×C4×C61—21no—
276C2×C4×C61—21no—
277C2×C4×C61—21no—
278C2×C4×C61—21no—
279C2×C4×C61—21no—
280C2×C4×C61—21no—
281C2×C4×C61—21no—
282C2×C4×C61—21no—
283C2×C4×C61—21no—
284C2×C4×C61—21no—
285C2×C4×C61—21no—
286C2×C4×C61—44no—
287C2×C4×C61#13112yes—
288C22⋊D61—44no—
289C22⋊D61—44no—
290C2×Dic61—21no—
291C2×Dic61—21no—
292C2×Dic61—21no—
293C2×Dic61—21no—
294C2×Dic61—21no—
295C2×Dic61—21no—
296C2×Dic61—21no—
297C2×Dic61—21no—
298C2×Dic61—21no—
299C2×Dic61—21no—
300C2×Dic61—21no—
301C2×Dic61—21no—
302C2×Dic61—21no—
303C2×Dic61—21no—
304C2×Dic61—44no—
305C2×Dic61—41no—
306C2×Dic61—41no—
307C2×Dic61—41no—
308C2×Dic61—41no—
309C2×Dic61#11712yes—
310C2×Dic61C4×D412yes—
311C2×Dic61C4×D412yes—
312C2×Dic61#12114yes—
313C2×Dic61#12314yes—
314C2×Dic61#12414yes—
315C2×Dic61#12614yes—
316C2×Dic61#13112yes—
317C2×Dic61C22×D411yescharacteristic
318C2×Dic61C22×D411yescharacteristic
319C2×Dic61C2×#4111yescharacteristic
320C2×Dic61C2×#4111yescharacteristic
321C2×Dic61C2×#4111yescharacteristic
322C2×Dic61C2×#4111yescharacteristic
323C4×D61—41no—
324C4×D61—41no—
325C4×D61—41no—
326C4×D61—41no—
327Dic122—44no—
328#92420—22no—
329#92420—22no—
330#92420—22no—
331#92420—22no—
332#92420—41no—
333#92420—41no—
334#92420—41no—
335#92420—41no—
336#21048—611nomaximal, Sylow
337C22×C61—22no—
338C22×C61—22no—
339C22×C61—22no—
340C22×C61—22no—
341C22×C61—22no—
342C22×C61—22no—
343C22×C61—41no—
344C22×C61—41no—
345C22×C61—41no—
346C22×C61—41no—
347C22×C61—41no—
348C22×C61—41no—
349C22×C61—41no—
350C22×C61#38814yes—
351C22×C61C2×#11711yescharacteristic
352C22×C61C2×C4×D411yescharacteristic
353C22×C61C2×C4×D411yescharacteristic
354C22×C61C2×#13111yescharacteristic
355C22×C61C2×#13111yescharacteristic
356C22×C61#56811yescharacteristic
357C22×C61#56811yescharacteristic
358C2×D61—41no—
359C2×D61—41no—
360C2×D61—41no—
361C2×D61—41no—
362C2×D61—41no—
363C2×D61—41no—
364C2×D61—41no—
365C4×C61—22no—
366C4×C61—41no—
367C4×C61—41no—
368C4×C61—41no—
369C4×C61—41no—
370Dic61—22no—
371Dic61—41no—
372Dic61—41no—
373Dic61—41no—
374Dic61—41no—
375Dic61#38814yes—
376Dic61C2×#12111yescharacteristic
377Dic61C2×#12311yescharacteristic
378Dic61C2×#12411yescharacteristic
379Dic61C2×#12611yescharacteristic
380C2×#424—611no—
381C2×#408—611no—
382C2×#408—611no—
383C2×C4×M16—611no—
384#2297—611no—
385#1924—611no—
386#1924—611no—
387#1924—611no—
388#1924—611no—
389#1923—611no—
390#1923—611no—
391#1923—611no—
392#1923—611no—
393#1729—611no—
394C2×#336—611no—
395C2×C61—24no—
396C2×C61—81no—
397C2×C61C2×#38811yescharacteristic
398C2×C61#292211yescharacteristic
399C2×C61#292311yescharacteristic
400C2×C61#293311yescharacteristic
401C2×C61#293311yescharacteristic
402C2×C61#293511yescharacteristic
403C2×C61#293511yescharacteristic
404D61—81no—
405C22×#41—611no—
406C22×M16—611no—
407C22×M16—611no—
408C23×C8—611no—
409C23×C8—611no—
410C2×#117—611no—
411C22×C42—611no—
412#424—1224no—
413C2×C4⋊C8—611no—
414C2×C4⋊C8—611no—
415C2×C4⋊C8—611no—
416C2×C4⋊C8—611no—
417#408—1224no—
418#408—1224no—
419C2×C22⋊C8—611no—
420C2×C22⋊C8—611no—
421C2×C22⋊C8—611no—
422C2×C22⋊C8—611no—
423C2×C22⋊C8—611no—
424C2×C22⋊C8—611no—
425C2×C22⋊C8—611no—
426C2×C22⋊C8—611no—
427C4×M16—1224no—
428C2×#97—611no—
429C2×#97—611no—
430C2×C4×C8—611no—
431C2×C4×C8—611no—
432#391—611no—
433#391—611no—
434#390—611no—
435#390—611no—
436#386—611no—
437#386—611no—
438#386—611no—
439#386#692311yescharacteristic
440C4×C22⋊C4—611no—
441C4×C22⋊C4—611no—
442C4×C22⋊C4—611no—
443C4×C22⋊C4—611no—
444#336—611no—
445#336—611no—
446#336—611no—
447#336—611no—
448#336—611no—
449#336—611no—
450#336—611no—
451#336—611no—
452C61#2104811yescharacteristic, complemented, Sylow
453C2×#41—1222no—
454C2×#41—1222no—
455C2×#41—1222no—
456C2×#41—1222no—
457C2×#41—1222no—
458C2×#41—1222no—
459C22×Q8—611no—
460C22×D4—611no—
461C22×D4—611no—
462C22×D4C2×#692311yescharacteristic
463C23×C4—611no—
464C23×C4—611no—
465C23×C4—611no—
466C23×C4—611no—
467C23×C4C2×#692311yescharacteristic
468C2×M16—614no—
469C2×M16—614no—
470C2×M16—1222no—
471C2×M16—1222no—
472C2×M16—1222no—
473C2×M16—1222no—
474C22×C8—611no—
475C22×C8—611no—
476C22×C8—611no—
477C22×C8—611no—
478C22×C8—611no—
479C22×C8—611no—
480C22×C8—611no—
481C22×C8—611no—
482C22×C8—1222no—
483C22×C8—1222no—
484C22×C8—1222no—
485C22×C8—1222no—
486C22×C8—1222no—
487C22×C8—1222no—
488#117—1222no—
489#117—1222no—
490C2×C4⋊C4—611no—
491C2×C4⋊C4—611no—
492C2×C22⋊C4—611no—
493C2×C22⋊C4—611no—
494C2×C22⋊C4—611no—
495C2×C22⋊C4—611no—
496C2×C22⋊C4—611no—
497C2×C22⋊C4—611no—
498C2×C22⋊C4—611no—
499C2×C22⋊C4C2×#692311yescharacteristic
500C2×C22⋊C4C2×#692311yescharacteristic
501C2×C22⋊C4C2×#692311yescharacteristic
502C2×C42—611no—
503C2×C42—611no—
504C2×C42—611no—
505C2×C42—611no—
506C2×C42—611no—
507C2×C42—611no—
508C2×C42—1222no—
509C2×C42—1222no—
510C4⋊C8—1222no—
511C4⋊C8—1222no—
512C4⋊C8—1222no—
513C4⋊C8—1222no—
514C22⋊C8—1222no—
515C22⋊C8—1222no—
516C22⋊C8—1222no—
517C22⋊C8—1222no—
518C22⋊C8—1222no—
519C22⋊C8—1222no—
520C22⋊C8—1222no—
521C22⋊C8—1222no—
522#97—1222no—
523#97—1222no—
524C4×C8—1222no—
525C4×C8—1222no—
526#95—611no—
527#95—611no—
528#95—611no—
529#95—611no—
530#95—611no—
531#95—611no—
532#95C2×#692311yescharacteristic
533#95C2×#692311yescharacteristic
534C24—611no—
535C24C22×#692311yescharacteristic
536C24C22×#692311yescharacteristic
537#41—2444no—
538#41—2444no—
539#41—2444no—
540#41—2444no—
541C2×Q8—1222no—
542C2×Q8—1222no—
543C2×Q8—1222no—
544C2×D4—22no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—1222no—
548C2×D4—1222no—
549C2×D4—1222no—
550C2×D4—1222no—
551C2×D4—1222no—
552C2×D4—1222no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—41no—
556C22×C4—612no—
557C22×C4—612no—
558C22×C4—612no—
559C22×C4—612no—
560C22×C4—612no—
561C22×C4—612no—
562C22×C4—611no—
563C22×C4—611no—
564C22×C4—611no—
565C22×C4—611no—
566C22×C4—611no—
567C22×C4—611no—
568C22×C4—611no—
569C22×C4—1221no—
570C22×C4—1221no—
571C22×C4—1221no—
572C22×C4—1221no—
573C22×C4—1221no—
574C22×C4—1221no—
575C22×C4—1221no—
576C22×C4—1221no—
577C22×C4—1221no—
578C22×C4—1221no—
579C22×C4—1221no—
580C22×C4—1221no—
581C22×C4—1222no—
582C22×C4—1222no—
583C22×C4—2441no—
584C22×C4C22×#692311yescharacteristic
585C22×C4C22×#692311yescharacteristic
586C22×C4C22×#692311yescharacteristic
587C22×C4C22×#692311yescharacteristic
588C22×C4C22×#692311yescharacteristic
589M16—1228no—
590M16—1228no—
591C2×C8—612no—
592C2×C8—612no—
593C2×C8—612no—
594C2×C8—612no—
595C2×C8—1221no—
596C2×C8—1221no—
597C2×C8—1221no—
598C2×C8—1221no—
599C2×C8—1221no—
600C2×C8—1221no—
601C2×C8—1221no—
602C2×C8—1221no—
603C2×C8—1221no—
604C2×C8—1221no—
605C2×C8—1221no—
606C2×C8—1221no—
607C2×C8—1221no—
608C2×C8—1221no—
609C2×C8—1221no—
610C2×C8—1221no—
611C2×C8—1221no—
612C2×C8—1221no—
613C2×C8—1221no—
614C2×C8—1221no—
615C2×C8—2444no—
616C2×C8—2444no—
617C4⋊C4—1222no—
618C4⋊C4—1222no—
619C22⋊C4—22no—
620C22⋊C4—22no—
621C22⋊C4—41no—
622C22⋊C4—1222no—
623C22⋊C4—1222no—
624C22⋊C4—1222no—
625C22⋊C4—1222no—
626C22⋊C4—2441no—
627C22⋊C4—2441no—
628C22⋊C4—2441no—
629C42—1221no—
630C42—1221no—
631C42—1221no—
632C42—1221no—
633C42—1222no—
634C42—1221no—
635C42—1222no—
636C42—1221no—
637C42—1221no—
638C42—1221no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—1221no—
651C23—1221no—
652C23—1221no—
653C23—1221no—
654C23—1221no—
655C23—1221no—
656C23—1221no—
657C23#1451985612yes—
658C23D4×#692312yes—
659C23D4×#692312yes—
660C23C23×#692311yescharacteristic
661Q8—2444no—
662D4—44no—
663D4—2444no—
664D4—2444no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—44no—
680C2×C4—614no—
681C2×C4—614no—
682C2×C4—614no—
683C2×C4—614no—
684C2×C4—612no—
685C2×C4—611no—
686C2×C4—611no—
687C2×C4—612no—
688C2×C4—612no—
689C2×C4—611no—
690C2×C4—611no—
691C2×C4—611no—
692C2×C4—611no—
693C2×C4—612no—
694C2×C4—1221no—
695C2×C4—1221no—
696C2×C4—1221no—
697C2×C4—1221no—
698C2×C4—1221no—
699C2×C4—1221no—
700C2×C4—1221no—
701C2×C4—1221no—
702C2×C4—1221no—
703C2×C4—1221no—
704C2×C4—1221no—
705C2×C4—1221no—
706C2×C4—1221no—
707C2×C4—1221no—
708C2×C4—2441no—
709C2×C4—2441no—
710C2×C4—2441no—
711C2×C4—2441no—
712C2×C4—2441no—
713C2×C4—2441no—
714C2×C4—2441no—
715C2×C4—2441no—
716C2×C4—2444no—
717C2×C4#1451986412yes—
718C8—1222no—
719C8—1222no—
720C8—1222no—
721C8—1222no—
722C8—2441no—
723C8—2441no—
724C8—2441no—
725C8—2441no—
726C22—22no—
727C22—22no—
728C22—22no—
729C22—22no—
730C22—22no—
731C22—22no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—2441no—
740C22—2441no—
741C22—2441no—
742C22—2441no—
743C22—2441no—
744C22—2441no—
745C22—2441no—
746C22#1684071214yes—
747C22C2×#1451985611yescharacteristic
748C22C2×D4×#692311yescharacteristic
749C22C2×D4×#692311yescharacteristic
750C22C2×#1451986411yescharacteristic
751C22D61⋊#13111yescharacteristic
752C22#1684084011yescharacteristic
753C22#1684084111yescharacteristic
754C4—22no—
755C4—41no—
756C4—41no—
757C4—41no—
758C4—41no—
759C4—611no—
760C4—611no—
761C4—611no—
762C4—611no—
763C4—614no—
764C4—1222no—
765C4—2441no—
766C4—2441no—
767C4—2441no—
768C4—2441no—
769C2—24no—
770C2—81no—
771C2—4881no—
772C2C2×#1684071211yescharacteristic
773C2#2146250211yescharacteristic
774C2#2146250511yescharacteristic
775C2#2146255111yescharacteristic
776C2#2146255311yescharacteristic
777C2#2146256111yescharacteristic
778C2#2146256311yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC61×#386C4
prime radicalC22×#11758224C22
cosocleC22×Dic61C24
hypercenter#386#6923
hypocenterC61#21048
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C2×#16840768C2semidirect
4. C2×C4×#11758217C2semidirect
5. #21461895C2semidirect
6. #21461894C2semidirect
7. #21461893C2semidirect
8. #21461892C2semidirect
9. #21461891C2semidirect
10. #21461890C2semidirect
11. #21461889C2semidirect
12. #21461888C2semidirect
13. #21461485C2semidirect
14. C2×#16840628C2semidirect
452. C61#21048semidirect

Maximal subgroups

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

subgroupindex
C2×#168407682
C2×#168407352
C2×C4×#117582172
#214618952
#214618942
#214618932
#214618922
#214618912
#214618902
#214618892
#214618882
#214614852
C2×#168406282
#214483042
#2104861