Finite Group Databasebeta

← #30615718

Subgroups — #30615718

Order 15616.

1994 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519856C211yesmaximal, characteristic, complemented
2C2×#16840743C212yesmaximal, complemented
3#21462263C211yesmaximal, characteristic, complemented
4#21461843C214yesmaximal, complemented
5#21461841C214yesmaximal, complemented
6#21461519C212yesmaximal, complemented
7C2×#16840275C211yesmaximal, characteristic
8C2×#14519856—28no—
9C2×#14519856—21no—
10C2×#14519856—21no—
11C2×#14519856C2212yes—
12C2×#14519856C2212yes—
13C2×#14519856C2212yes—
14C22×C4⋊#6923—21no—
15C22×C22⋊#6923C2212yes—
16C22×C4×#6923—21no—
17#16840743—28no—
18C2×#14519836C2218yes—
19#16840705C2212yes—
20#16840704—21no—
21#16840704—21no—
22#16840703C2212yes—
23C4×C22⋊#6923—21no—
24C4×C22⋊#6923—21no—
25#16840640C2218yes—
26C22×#11758226C2211yescharacteristic
27C23×C4×D61C2211yescharacteristic
28#16840275—21no—
29#16840275—21no—
30#16840275—21no—
31#16840275—21no—
32#16840275—21no—
33#16840275—21no—
34#16840275—21no—
35#16840275—21no—
36C2×#14519762C2212yes—
37C2×#14519753C411yescharacteristic, complemented
38C2×#14519752C411yescharacteristic, complemented
39C2×#14519751C411yescharacteristic, complemented
40C2×#14519747C2212yes—
41C2×#14519739C412yescomplemented
42C2×#14519737C412yescomplemented
43C2×#14519735C2211yescharacteristic
44C2×C22⋊Q8×C61C411yescharacteristic, complemented
45C23×#6923—22no—
46#14519856—28no—
47#14519856—28no—
48#14519856—24no—
49#14519856—28no—
50#14519856—24no—
51#14519856—24no—
52#14519856D418yescomplemented
53C2×C4⋊#6923—28no—
54C2×C4⋊#6923—22no—
55C2×C4⋊#6923—22no—
56C2×C4⋊#6923—22no—
57C2×C22⋊#6923—22no—
58C2×C22⋊#6923—28no—
59C2×C22⋊#6923—22no—
60C2×C22⋊#6923—22no—
61C2×C22⋊#6923C2314yes—
62C2×C22⋊#6923C2314yes—
63C2×C4×#6923—28no—
64C2×C4×#6923—22no—
65C2×C4×#6923—22no—
66C2×C4×#6923—22no—
67#14519836—216no—
68(C2×#6923)⋊C4—22no—
69(C2×#6923)⋊C4—22no—
70C24×D61C2311yescharacteristic
71C2×#11758226—24no—
72C2×#11758226—21no—
73C2×#11758226—21no—
74C2×#11758226—21no—
75C2×#11758226—21no—
76C2×#11758226—24no—
77C22×D244C2×C412yes—
78C22×D244C2×C411yescharacteristic, complemented
79C22×D244C2312yes—
80C22×C22⋊D61C2×C412yes—
81C23×Dic61C2×C411yescharacteristic
82C22×C4×D61—24no—
83C22×C4×D61—24no—
84C22×C4×D61C2×C411yescharacteristic
85C22×C4×D61C2×C411yescharacteristic
86C22×C4×D61C2×C412yescomplemented
87C22×C4×D61D411yescharacteristic
88C22×C4×D61D411yescharacteristic
89C22×C4×D61D411yescharacteristic
90C22×C4×D61D411yescharacteristic
91C22×C4×D61D411yescharacteristic
92C22×C4×D61D411yescharacteristic
93C22×C4×D61D411yescharacteristic
94C22×C4×D61D411yescharacteristic
95C22×C4×D61C2311yescharacteristic
96C22×C4×D61C2311yescharacteristic
97#14519762—22no—
98#14519762—22no—
99#14519762—22no—
100#14519762—22no—
101#14519753—21no—
102#14519753—21no—
103#14519753—21no—
104#14519753—21no—
105#14519752—21no—
106#14519752—21no—
107#14519752—21no—
108#14519752—21no—
109#14519751—21no—
110#14519751—21no—
111#14519751—21no—
112#14519751—21no—
113#14519747—22no—
114#14519747—22no—
115#14519747—22no—
116#14519747—22no—
117#14519739—22no—
118#14519739—22no—
119#14519739—22no—
120#14519739—22no—
121#14519737—22no—
122#14519737—22no—
123#14519737—22no—
124#14519737—22no—
125#14519735—21no—
126#14519735—21no—
127#14519735—21no—
128#14519735—21no—
129C2×C4⋊Dic61C2×C411yescharacteristic, complemented
130C2×#11758196C2×C412yescomplemented
131C2×#11758198C2×C412yes—
132C2×#11758198C2×C412yescomplemented
133C2×#11758198C2×C412yescomplemented
134C2×#11758198C2312yes—
135C2×C4×Dic61C2×C412yescomplemented
136C22×Q8×C61C2×C411yescharacteristic, complemented
137C23×C4×C61C2×C411yescharacteristic
138C22⋊Q8×C61—21no—
139C22⋊Q8×C61—21no—
140C22⋊Q8×C61—21no—
141C22⋊Q8×C61—21no—
142C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
143C2×C4⋊C4×C61C2×C412yescomplemented
144C2×C22⋊C4×C61C2×C412yes—
145C24×C61C22×C411yescharacteristic
146C23×D61—22no—
147C23×D61—22no—
148C23×D61—42no—
149C23×D61—42no—
150C23×D61C22×C411yescharacteristic
151C23×D61C22×C412yes—
152C23×D61C2×D411yescharacteristic
153C23×D61C2×D411yescharacteristic
154C23×D61C2×D411yescharacteristic
155C23×D61C2×D411yescharacteristic
156C23×D61C2411yescharacteristic
157C22×#6923—28no—
158C22×#6923—24no—
159C22×#6923—24no—
160C22×#6923—44no—
161C22×#6923—44no—
162C2×Q8×C61—21no—
163C2×Q8×C61—21no—
164C2×Q8×C61—24no—
165C22×C4×C61—24no—
166C22×C4×C61C22⋊C411yescharacteristic
167C22×C4×C61C22⋊C411yescharacteristic
168C22×C4×C61C22⋊C411yescharacteristic
169C22×C4×C61C22⋊C411yescharacteristic
170C22×C4×C61C22×C412yes—
171C22×C4×C61C22×C411yescharacteristic
172C22×C4×C61C22×C412yes—
173C22×C4×C61C22×C411yescharacteristic
174C2×C22⋊D61—22no—
175C2×C22⋊D61—22no—
176C2×C22⋊D61—44no—
177C22×Dic61—24no—
178C22×Dic61C22⋊C411yescharacteristic
179C22×Dic61C22⋊C411yescharacteristic
180C22×Dic61C22⋊C411yescharacteristic
181C22×Dic61C22⋊C411yescharacteristic
182C22×Dic61C22×C411yescharacteristic
183C22×Dic61C22×C412yes—
184C22×Dic61C22×C411yescharacteristic
185#11758226—42no—
186#11758226—42no—
187#11758226—44no—
188#11758226—44no—
189#11758226—42no—
190#11758226—42no—
191C2×D244—22no—
192C2×D244—22no—
193C2×D244—24no—
194C2×D244—22no—
195C2×D244—22no—
196C2×D244—24no—
197C2×D244—21no—
198C2×D244—21no—
199C2×D244—24no—
200C2×D244—44no—
201C2×C4×D61—22no—
202C2×C4×D61—22no—
203C2×C4×D61—24no—
204C2×C4×D61—24no—
205C2×C4×D61—22no—
206C2×C4×D61—22no—
207C2×C4×D61—22no—
208C2×C4×D61—22no—
209C2×C4×D61—24no—
210C2×C4×D61—24no—
211C2×C4×D61—24no—
212C2×C4×D61—24no—
213C2×C4×D61—22no—
214C2×C4×D61—22no—
215C2×C4×D61—22no—
216C2×C4×D61—22no—
217C2×C4×D61—22no—
218C2×C4×D61—22no—
219C2×C4×D61—28no—
220C2×C4×D61C22⋊C411yescharacteristic
221C2×C4×D61C22⋊C411yescharacteristic
222C2×C4×D61C22⋊C411yescharacteristic
223C2×C4×D61C22⋊C411yescharacteristic
224C2×C4×D61C22⋊C411yescharacteristic
225C2×C4×D61C22⋊C411yescharacteristic
226C2×C4×D61C22⋊C411yescharacteristic
227C2×C4×D61C22⋊C411yescharacteristic
228C2×C4×D61C2×D411yescharacteristic
229C2×C4×D61C2×D411yescharacteristic
230C2×C4×D61C2×D411yescharacteristic
231C2×C4×D61C2×D411yescharacteristic
232C2×C4×D61C2×D414yes—
233C2×C4×D61C2×D411yescharacteristic
234C2×C4×D61C2×D411yescharacteristic
235C2×C4×D61C2×D411yescharacteristic
236C2×C4×D61C2×D411yescharacteristic
237C2×C4×D61#4114yes—
238C22⋊#6923—28no—
239C22⋊#6923—24no—
240C22⋊#6923—24no—
241C22⋊#6923—24no—
242C22⋊#6923—44no—
243C22⋊#6923—44no—
244C22⋊#6923C2×D418yes—
245C4⋊#6923—28no—
246C4⋊#6923—28no—
247C4⋊#6923—44no—
248C4×#6923—28no—
249C4×#6923—28no—
250C4×#6923—44no—
251C4⋊C4×C61—21no—
252C4⋊C4×C61—21no—
253C4⋊C4×C61—22no—
254C4⋊C4×C61—22no—
255C22⋊C4×C61—22no—
256C22⋊C4×C61—22no—
257#11758198—22no—
258#11758198—22no—
259#11758198—22no—
260#11758198—22no—
261#11758198—22no—
262#11758198—22no—
263#11758198—22no—
264#11758198—22no—
265C4⋊Dic61—21no—
266C4⋊Dic61—21no—
267#11758196—22no—
268#11758196—22no—
269C4×Dic61—22no—
270C4×Dic61—22no—
271C23×C61—22no—
272C23×C61—22no—
273C23×C61—41no—
274C23×C61C2×C22⋊C411yescharacteristic
275C23×C61C2×C22⋊C411yescharacteristic
276C23×C61C23×C411yescharacteristic
277C22×D61—22no—
278C22×D61—21no—
279C22×D61—21no—
280C22×D61—22no—
281C22×D61—22no—
282C22×D61—22no—
283C22×D61—21no—
284C22×D61—22no—
285C22×D61—22no—
286C22×D61—21no—
287C22×D61—22no—
288C22×D61—22no—
289C22×D61—22no—
290C22×D61—24no—
291C22×D61—41no—
292C22×D61—41no—
293C22×D61—41no—
294C22×D61—41no—
295C22×D61—41no—
296C22×D61—41no—
297C22×D61—41no—
298C22×D61—48no—
299C22×D61—48no—
300C22×D61—42no—
301C22×D61—42no—
302C22×D61C2×C22⋊C411yescharacteristic
303C22×D61C2×C22⋊C411yescharacteristic
304C22×D61C22×D411yescharacteristic
305C22×D61C22×D411yescharacteristic
306C22×D61C22×D412yes—
307C22×D61C2×#4112yes—
308C2×#6923—28no—
309C2×#6923—416no—
310C2×#6923—44no—
311C2×#6923—44no—
312C2×#6923—44no—
313C2×#6923—44no—
314C2×#6923—44no—
315Q8×C61—42no—
316Q8×C61—42no—
317C2×C4×C61—22no—
318C2×C4×C61—22no—
319C2×C4×C61—22no—
320C2×C4×C61—22no—
321C2×C4×C61—22no—
322C2×C4×C61—22no—
323C2×C4×C61—22no—
324C2×C4×C61—24no—
325C2×C4×C61—42no—
326C2×C4×C61C2×C22⋊C411yescharacteristic
327C2×C4×C61C2×C22⋊C411yescharacteristic
328C2×C4×C61C2×C22⋊C411yescharacteristic
329C2×C4×C61C2×C22⋊C411yescharacteristic
330C2×C4×C61C4×D414yes—
331C22⋊D61—44no—
332C22⋊D61—44no—
333C2×Dic61—22no—
334C2×Dic61—22no—
335C2×Dic61—22no—
336C2×Dic61—22no—
337C2×Dic61—22no—
338C2×Dic61—22no—
339C2×Dic61—42no—
340C2×Dic61C2×C22⋊C411yescharacteristic
341C2×Dic61C2×C22⋊C411yescharacteristic
342C2×Dic61C2×C22⋊C411yescharacteristic
343C2×Dic61C2×C22⋊C411yescharacteristic
344C2×Dic61C4×D414yes—
345D244—44no—
346D244—42no—
347D244—44no—
348D244—42no—
349D244—44no—
350D244—42no—
351D244—42no—
352C4×D61—21no—
353C4×D61—21no—
354C4×D61—22no—
355C4×D61—22no—
356C4×D61—21no—
357C4×D61—21no—
358C4×D61—22no—
359C4×D61—22no—
360C4×D61—22no—
361C4×D61—22no—
362C4×D61—22no—
363C4×D61—22no—
364C4×D61—22no—
365C4×D61—22no—
366C4×D61—44no—
367C4×D61—44no—
368C4×D61#12012yes—
369C4×D61#12012yes—
370C4×D61#12114yes—
371C4×D61#12114yes—
372C4×D61#12312yes—
373C4×D61#12312yes—
374#20983—611nomaximal, Sylow
375C22×C61—21no—
376C22×C61—21no—
377C22×C61—21no—
378C22×C61—21no—
379C22×C61—21no—
380C22×C61—21no—
381C22×C61—21no—
382C22×C61—44no—
383C22×C61#41012yescomplemented
384C22×C61C22×C22⋊C411yescharacteristic
385C22×C61C2×C4×D412yes—
386C2×D61—24no—
387C2×D61—24no—
388C2×D61—21no—
389C2×D61—21no—
390C2×D61—21no—
391C2×D61—21no—
392C2×D61—21no—
393C2×D61—21no—
394C2×D61—21no—
395C2×D61—21no—
396C2×D61—21no—
397C2×D61—42no—
398C2×D61—42no—
399C2×D61—44no—
400C2×D61—44no—
401C2×D61—44no—
402C2×D61—42no—
403C2×D61—42no—
404C2×D61—42no—
405C2×D61—42no—
406C2×D61—42no—
407C2×D61—84no—
408C2×D61#41012yescomplemented
409C2×D61C2×#12011yescharacteristic
410C2×D61C2×#12112yes—
411C2×D61C2×#12311yescharacteristic
412#6923—48no—
413#6923—84no—
414C4×C61—21no—
415C4×C61—21no—
416C4×C61—42no—
417C4×C61—42no—
418C4×C61#38612yes—
419C4×C61#38612yes—
420Dic61—21no—
421Dic61—21no—
422Dic61—42no—
423Dic61#38612yes—
424Dic61#38612yes—
425C2×#525—611no—
426C22×#117—611no—
427C2×#410—612no—
428#2280—611no—
429#1899—614no—
430#1898—614no—
431#1740—612no—
432C2×C61—22no—
433C2×C61—22no—
434C2×C61—41no—
435C2×C61C2×#38611yescharacteristic
436C2×C61C2×#41011yescharacteristic
437C2×C61C2×#41011yescharacteristic
438D61—21no—
439D61—22no—
440D61—21no—
441D61—22no—
442D61—41no—
443D61—82no—
444C22×#41—611no—
445C24×C4—611no—
446#525—1221no—
447#525—1221no—
448#525—1221no—
449#525—1221no—
450#525—1221no—
451#525—1221no—
452#525—1221no—
453#525—1221no—
454C2×#123—612no—
455C2×C22⋊Q8—611no—
456C2×C22⋊Q8#692311yescharacteristic, complemented
457C2×#121—611no—
458C2×#121—611no—
459C2×#120—612no—
460C2×C4×D4—612no—
461C2×C4×D4—612no—
462C2×#117—611no—
463C2×#117—612no—
464C2×#117—612no—
465C2×#117—612no—
466C2×#117—1228no—
467C2×#117—1221no—
468C2×#117—1221no—
469C22×C4⋊C4—1221no—
470C22×C22⋊C4—612no—
471C22×C42—1221no—
472#410—1228no—
473C2×#99—618no—
474#381—612no—
475#380—1221no—
476#380—1221no—
477#379—612no—
478C4×C22⋊C4—1221no—
479C4×C22⋊C4—1221no—
480#342—618no—
481C61#2098311yescharacteristic, complemented, Sylow
482C25—611no—
483C2×#41—1221no—
484C2×#41—1221no—
485C2×#41—1221no—
486C2×#41—1221no—
487C2×#41—1224no—
488C2×#41—1224no—
489C22×Q8C2×#692311yescharacteristic, complemented
490C22×D4—612no—
491C22×D4—611no—
492C22×D4—612no—
493C22×D4—612no—
494C23×C4—611no—
495C23×C4—611no—
496C23×C4—611no—
497C23×C4—611no—
498C23×C4—611no—
499C23×C4—611no—
500C23×C4—611no—
501C23×C4—611no—
502C23×C4—611no—
503C23×C4—611no—
504C23×C4—611no—
505C23×C4—611no—
506C23×C4—611no—
507C23×C4—612no—
508C23×C4—1224no—
509C23×C4—1224no—
510C23×C4—1222no—
511C23×C4C2×#692311yescharacteristic
512#123—1222no—
513#123—1222no—
514#123—1222no—
515#123—1222no—
516C22⋊Q8—21no—
517C22⋊Q8—21no—
518C22⋊Q8—21no—
519C22⋊Q8—21no—
520C22⋊Q8—1221no—
521C22⋊Q8—1221no—
522C22⋊Q8—1221no—
523C22⋊Q8—1221no—
524#121—1221no—
525#121—1221no—
526#121—1221no—
527#121—1221no—
528#121—1221no—
529#121—1221no—
530#121—1221no—
531#121—1221no—
532#120—1222no—
533#120—1222no—
534#120—1222no—
535#120—1222no—
536C4×D4—1222no—
537C4×D4—1222no—
538C4×D4—1222no—
539C4×D4—1222no—
540C4×D4—1222no—
541C4×D4—1222no—
542C4×D4—1222no—
543C4×D4—1222no—
544#117—618no—
545#117—1228no—
546#117—1221no—
547#117—1221no—
548#117—1221no—
549#117—1221no—
550#117—1224no—
551#117—1228no—
552#117—1228no—
553#117—1224no—
554#117—1224no—
555C2×C4⋊C4—611no—
556C2×C4⋊C4—612no—
557C2×C4⋊C4—1222no—
558C2×C4⋊C4—1222no—
559C2×C4⋊C4—1228no—
560C2×C4⋊C4—1222no—
561C2×C4⋊C4C2×#692311yescharacteristic, complemented
562C2×C4⋊C4C2×#692312yescomplemented
563C2×C22⋊C4—614no—
564C2×C22⋊C4—612no—
565C2×C22⋊C4—612no—
566C2×C22⋊C4—612no—
567C2×C22⋊C4—612no—
568C2×C22⋊C4—614no—
569C2×C22⋊C4—1228no—
570C2×C22⋊C4—1222no—
571C2×C22⋊C4—1222no—
572C2×C22⋊C4—1222no—
573C2×C22⋊C4C2×#692312yes—
574C2×C42—612no—
575C2×C42—1222no—
576C2×C42—1222no—
577C2×C42—1228no—
578C2×C42—1222no—
579#99—12216no—
580#95—1222no—
581#95—1222no—
582C24—611no—
583C24—611no—
584C24—611no—
585C24—611no—
586C24—611no—
587C24—611no—
588C24—612no—
589C24—1222no—
590C24—1222no—
591C24—2442no—
592C24—2442no—
593C24C22×#692311yescharacteristic
594#41—2442no—
595#41—2442no—
596#41—2444no—
597#41—2444no—
598#41—2442no—
599#41—2442no—
600C2×Q8—21no—
601C2×Q8—21no—
602C2×Q8—24no—
603C2×D4—1224no—
604C2×D4—1222no—
605C2×D4—1222no—
606C2×D4—1222no—
607C2×D4—1222no—
608C2×D4—1224no—
609C2×D4—1222no—
610C2×D4—1222no—
611C2×D4—1221no—
612C2×D4—1221no—
613C2×D4—1224no—
614C2×D4—2444no—
615C2×D4—2444no—
616C22×C4—24no—
617C22×C4—611no—
618C22×C4—611no—
619C22×C4—611no—
620C22×C4—611no—
621C22×C4—611no—
622C22×C4—614no—
623C22×C4—614no—
624C22×C4—611no—
625C22×C4—611no—
626C22×C4—611no—
627C22×C4—611no—
628C22×C4—611no—
629C22×C4—611no—
630C22×C4—611no—
631C22×C4—611no—
632C22×C4—611no—
633C22×C4—611no—
634C22×C4—611no—
635C22×C4—611no—
636C22×C4—611no—
637C22×C4—611no—
638C22×C4—611no—
639C22×C4—611no—
640C22×C4—611no—
641C22×C4—612no—
642C22×C4—1222no—
643C22×C4—1222no—
644C22×C4—1222no—
645C22×C4—1222no—
646C22×C4—1224no—
647C22×C4—1224no—
648C22×C4—1224no—
649C22×C4—1224no—
650C22×C4—1224no—
651C22×C4—1222no—
652C22×C4—1222no—
653C22×C4—1222no—
654C22×C4—1222no—
655C22×C4—1222no—
656C22×C4—1222no—
657C22×C4—1228no—
658C22×C4—1222no—
659C22×C4—1222no—
660C22×C4—1224no—
661C22×C4—1224no—
662C22×C4—1224no—
663C22×C4—1228no—
664C22×C4—1224no—
665C22×C4—2444no—
666C22×C4—2444no—
667C22×C4C22⋊#692311yescharacteristic
668C22×C4C22⋊#692311yescharacteristic
669C22×C4C22⋊#692311yescharacteristic
670C22×C4C22⋊#692311yescharacteristic
671C22×C4C22×#692312yes—
672C22×C4C22×#692311yescharacteristic
673C22×C4C22×#692312yes—
674C22×C4C22×#692311yescharacteristic
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—22no—
678C4⋊C4—22no—
679C4⋊C4—1222no—
680C4⋊C4—1222no—
681C4⋊C4—1228no—
682C4⋊C4—1228no—
683C4⋊C4—1221no—
684C4⋊C4—1221no—
685C4⋊C4—2444no—
686C22⋊C4—22no—
687C22⋊C4—22no—
688C22⋊C4—618no—
689C22⋊C4—1222no—
690C22⋊C4—1222no—
691C22⋊C4—1222no—
692C22⋊C4—1222no—
693C22⋊C4—1222no—
694C22⋊C4—1222no—
695C22⋊C4—1224no—
696C22⋊C4—1228no—
697C22⋊C4—1222no—
698C22⋊C4—1222no—
699C22⋊C4—1224no—
700C22⋊C4—1224no—
701C22⋊C4—2444no—
702C22⋊C4—2444no—
703C42—1222no—
704C42—1222no—
705C42—1228no—
706C42—1228no—
707C42—2444no—
708C23—22no—
709C23—22no—
710C23—41no—
711C23—611no—
712C23—611no—
713C23—611no—
714C23—612no—
715C23—612no—
716C23—611no—
717C23—1221no—
718C23—1221no—
719C23—1222no—
720C23—1221no—
721C23—1222no—
722C23—1222no—
723C23—1222no—
724C23—1221no—
725C23—1222no—
726C23—1222no—
727C23—1222no—
728C23—1222no—
729C23—1224no—
730C23—1222no—
731C23—2441no—
732C23—2441no—
733C23—2441no—
734C23—2441no—
735C23—2441no—
736C23—2441no—
737C23—2441no—
738C23—2442no—
739C23—2442no—
740C23—2448no—
741C23—2448no—
742C23C2×C22⋊#692311yescharacteristic
743C23C2×C22⋊#692311yescharacteristic
744C23C23×#692311yescharacteristic
745Q8—42no—
746Q8—42no—
747D4—2442no—
748D4—2444no—
749D4—2442no—
750D4—2444no—
751D4—2444no—
752D4—2444no—
753D4—2444no—
754D4—2442no—
755D4—2442no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—24no—
764C2×C4—42no—
765C2×C4—611no—
766C2×C4—611no—
767C2×C4—614no—
768C2×C4—612no—
769C2×C4—612no—
770C2×C4—614no—
771C2×C4—614no—
772C2×C4—612no—
773C2×C4—612no—
774C2×C4—611no—
775C2×C4—611no—
776C2×C4—1222no—
777C2×C4—1222no—
778C2×C4—1222no—
779C2×C4—1222no—
780C2×C4—1221no—
781C2×C4—1221no—
782C2×C4—1222no—
783C2×C4—1222no—
784C2×C4—1221no—
785C2×C4—1221no—
786C2×C4—1222no—
787C2×C4—1222no—
788C2×C4—1222no—
789C2×C4—1222no—
790C2×C4—1222no—
791C2×C4—1222no—
792C2×C4—1222no—
793C2×C4—1222no—
794C2×C4—1222no—
795C2×C4—1228no—
796C2×C4—1222no—
797C2×C4—2444no—
798C2×C4—2444no—
799C2×C4—2444no—
800C2×C4—2444no—
801C2×C4—2444no—
802C2×C4—24416no—
803C2×C4—2444no—
804C2×C4—2444no—
805C2×C4—2442no—
806C2×C4C2×C22⋊#692311yescharacteristic
807C2×C4C2×C22⋊#692311yescharacteristic
808C2×C4C2×C22⋊#692311yescharacteristic
809C2×C4C2×C22⋊#692311yescharacteristic
810C2×C4D4×#692314yes—
811C22—21no—
812C22—21no—
813C22—21no—
814C22—21no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—44no—
819C22—612no—
820C22—611no—
821C22—612no—
822C22—611no—
823C22—1224no—
824C22—1224no—
825C22—1221no—
826C22—1221no—
827C22—1221no—
828C22—1221no—
829C22—1221no—
830C22—1221no—
831C22—1221no—
832C22—1221no—
833C22—1221no—
834C22—4884no—
835C22—2442no—
836C22—2442no—
837C22—2444no—
838C22—2444no—
839C22—2444no—
840C22—2442no—
841C22—2442no—
842C22—2442no—
843C22—2442no—
844C22—2442no—
845C22#1684074312yescomplemented
846C22C22×C22⋊#692311yescharacteristic
847C22C2×D4×#692312yes—
848C4—21no—
849C4—21no—
850C4—42no—
851C4—42no—
852C4—612no—
853C4—612no—
854C4—1221no—
855C4—1221no—
856C4—4884no—
857C4—2448no—
858C4—2442no—
859C4#1684071012yes—
860C4#1684071012yes—
861C2—22no—
862C2—22no—
863C2—41no—
864C2—1222no—
865C2—1221no—
866C2—1222no—
867C2—1221no—
868C2—4882no—
869C2—2441no—
870C2C2×#1684071011yescharacteristic
871C2D61⋊#41011yescharacteristic
872C2C2×#1684074311yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×C22⋊Q8×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840275C2
cosocleC23×D61C24
hypercenterC2×C22⋊Q8#6923
hypocenterC61#20983
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×#14519856C2semidirect
2. C2×#16840743C2semidirect
3. #21462263C2semidirect
4. #21461843C2semidirect
5. #21461841C2semidirect
6. #21461519C2semidirect
37. C2×#14519753C4semidirect
38. C2×#14519752C4semidirect
39. C2×#14519751C4semidirect
41. C2×#14519739C4semidirect
42. C2×#14519737C4semidirect
44. C2×C22⋊Q8×C61C4semidirect
52. #14519856D4semidirect
78. C22×D244C2×C4semidirect
86. C22×C4×D61C2×C4semidirect
129. C2×C4⋊Dic61C2×C4semidirect
130. C2×#11758196C2×C4semidirect
132. C2×#11758198C2×C4semidirect
133. C2×#11758198C2×C4semidirect
135. C2×C4×Dic61C2×C4semidirect
136. C22×Q8×C61C2×C4semidirect
142. C2×C4⋊C4×C61C2×C4semidirect
143. C2×C4⋊C4×C61C2×C4semidirect
383. C22×C61#410semidirect
408. C2×D61#410semidirect
456. C2×C22⋊Q8#6923semidirect
481. C61#20983semidirect
489. C22×Q8C2×#6923semidirect
561. C2×C4⋊C4C2×#6923semidirect
562. C2×C4⋊C4C2×#6923semidirect
845. C22#16840743semidirect

Maximal subgroups

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

subgroupindex
C22×#145198562
C2×#168407432
#214622632
#214618432
#214618412
#214615192
C2×#168402752
#2098361