Finite Group Databasebeta

← #29695428

Subgroups — #29695428

Order 15616.

1638 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840403C211yesmaximal, characteristic
2C2×#16839825C211yesmaximal, characteristic, complemented
3C2×#16839757C211yesmaximal, characteristic, complemented
4C22×#14519697C211yesmaximal, characteristic, complemented
5#21448744C211yesmaximal, characteristic, complemented
6#21446748C211yesmaximal, characteristic, complemented
7#21446627C211yesmaximal, characteristic, complemented
8#21446246C211yesmaximal, characteristic, complemented
9#21446243C211yesmaximal, characteristic, complemented
10#21446140C211yesmaximal, characteristic, complemented
11#21445828C211yesmaximal, characteristic, complemented
12#21445758C211yesmaximal, characteristic, complemented
13#21445751C211yesmaximal, characteristic, complemented
14#21445633C211yesmaximal, characteristic, complemented
15C61×#1872C211yesmaximal, characteristic, complemented
16C22×#11758226C2211yescharacteristic
17C23×D244C2211yescharacteristic
18C23×#92418C2211yescharacteristic
19C22×C8×D61C2211yescharacteristic, complemented
20#16840403—24no—
21#16840403C418yescomplemented
22C2×#14519766C2211yescharacteristic
23C2×#14519762—21no—
24C2×#14519752—21no—
25C2×#14519752C2211yescharacteristic
26C2×#14519747—21no—
27C2×#14519739C2211yescharacteristic
28C2×C4×C22⋊D61C2211yescharacteristic
29C2×#14519735C2211yescharacteristic, complemented
30C2×C22⋊C4×D61—21no—
31#16839825—24no—
32C2×#14519706C2211yescharacteristic, complemented
33#16839757—24no—
34C2×#14519701C2211yescharacteristic, complemented
35C2×#14519701C2211yescharacteristic, complemented
36C2×#14519699C2211yescharacteristic
37C2×#14519699C2211yescharacteristic
38C2×#14519699C2211yescharacteristic
39C2×#14519699C2211yescharacteristic
40C2×#14519697—24no—
41C2×#14519697C2211yescharacteristic
42C2×#14519697C2211yescharacteristic
43C2×#14519697C2211yescharacteristic
44C2×#14519697C2211yescharacteristic
45C2×#14519689C2211yescharacteristic, complemented
46C2×C8×Dic61C2211yescharacteristic, complemented
47#16839652—21no—
48#16839643—21no—
49#16839641—21no—
50#16839627C2211yescharacteristic, complemented
51#16839622C2211yescharacteristic
52#16839619C2211yescharacteristic, complemented
53C4⋊C4×Dic61C2211yescharacteristic, complemented
54C4×C22⋊Dic61—21no—
55#16839524C2211yescharacteristic, complemented
56#16839524C2211yescharacteristic, complemented
57C2×C22⋊Q8×C61C2211yescharacteristic
58C22×C4⋊C4×C61C2211yescharacteristic
59C2×#103×C61C2211yescharacteristic, complemented
60C2×#103×C61C2211yescharacteristic, complemented
61C2×C22⋊C8×C61C2211yescharacteristic
62C61×#340C2211yescharacteristic, complemented
63C61×#340C2211yescharacteristic, complemented
64C24×D61—21no—
65C2×#11758226—22no—
66C2×#11758226—22no—
67C2×#11758226—22no—
68C2×#11758226—41no—
69C2×#11758226—41no—
70C2×#11758226C2×C414yescomplemented
71C22×D244—22no—
72C22×D244—22no—
73C22×D244—21no—
74C22×D244—21no—
75C22×D244—22no—
76C22×D244—21no—
77C22×D244—41no—
78C22×D244—41no—
79C22×D244C2×C414yes—
80C22×D244C2311yescharacteristic
81C22×D244C2311yescharacteristic
82C22×C22⋊D61D411yescharacteristic
83C22×C4×D61—21no—
84C22×C4×D61—21no—
85C22×C4×D61C2311yescharacteristic
86C22×#92418—22no—
87C22×#92418—22no—
88C22×#92418—41no—
89C22×#92418C2311yescharacteristic
90C22×#92418C2311yescharacteristic
91C2×C8×D61—22no—
92C2×C8×D61—22no—
93C2×C8×D61—41no—
94#14519766—22no—
95#14519766C2×C414yescomplemented
96#14519762—28no—
97#14519752—22no—
98#14519752—28no—
99#14519752C2×C414yescomplemented
100#14519747—28no—
101#14519739—22no—
102#14519739C2×C414yescomplemented
103C4×C22⋊D61C2×C414yes—
104C4×C22⋊D61D414yes—
105#14519735—22no—
106#14519735—41no—
107C2×C4⋊Dic61C2311yescharacteristic
108C2×C4⋊Dic61C2311yescharacteristic
109C2×#11758196D411yescharacteristic
110C2×C22⋊Dic61—21no—
111C2×C22⋊Dic61D411yescharacteristic
112C2×#11758198—21no—
113C2×#11758198—21no—
114C2×#11758198—21no—
115C2×#11758198—21no—
116C2×#11758198—21no—
117C2×#11758198—21no—
118C2×#11758198D411yescharacteristic
119C22⋊C4×D61—28no—
120C2×C4×Dic61—21no—
121C2×C4×Dic61—21no—
122C2×C4×Dic61C2311yescharacteristic
123#14519706—22no—
124#14519701—22no—
125#14519701—41no—
126#14519699—22no—
127#14519699—22no—
128#14519699—41no—
129#14519699—41no—
130#14519697—22no—
131#14519697—22no—
132#14519697—22no—
133#14519697D414yescomplemented
134#14519689—22no—
135C8×Dic61—22no—
136#14519684—21no—
137#14519684—21no—
138#14519684—21no—
139#14519684—21no—
140#14519684—21no—
141C22×Q8×C61C2311yescharacteristic
142C23×C4×C61—21no—
143C23×C4×C61C2311yescharacteristic
144C22×C8×C61C2311yescharacteristic
145C22×C8×C61C2311yescharacteristic
146C22⋊Q8×C61—22no—
147C22⋊Q8×C61C2×C414yes—
148C2×C4⋊C4×C61—21no—
149C2×C4⋊C4×C61—22no—
150C2×C4⋊C4×C61—21no—
151C2×C4⋊C4×C61—41no—
152C2×C4⋊C4×C61C2311yescharacteristic
153C2×C4⋊C4×C61C2311yescharacteristic
154C2×C4⋊C4×C61C2311yescharacteristic
155C2×C22⋊C4×C61—21no—
156#103×C61—22no—
157#103×C61—41no—
158C22⋊C8×C61—22no—
159C24×C61C2×D411yescharacteristic
160C23×D61—21no—
161C23×D61—21no—
162C23×D61—24no—
163C23×D61—42no—
164C23×D61—42no—
165C23×D61—42no—
166C23×D61—42no—
167C23×D61—81no—
168C23×D61—81no—
169C23×D61C2×D411yescharacteristic
170C2×Q8×C61—21no—
171C2×Q8×C61—21no—
172C2×Q8×C61—21no—
173C2×Q8×C61—21no—
174C2×Q8×C61—21no—
175C2×Q8×C61C22×C412yes—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61—42no—
185C22×C4×C61—42no—
186C22×C4×C61—81no—
187C22×C4×C61C22×C412yes—
188C22×C4×C61C2×D411yescharacteristic
189C22×C4×C61C2×D412yes—
190C22×C4×C61C2411yescharacteristic
191C2×C22⋊D61—22no—
192C2×C22⋊D61—22no—
193C2×C22⋊D61C22⋊C414yes—
194C22×Dic61—21no—
195C22×Dic61—21no—
196C22×Dic61C2×D411yescharacteristic
197C22×Dic61C2×D411yescharacteristic
198C22×Dic61C2×D411yescharacteristic
199#11758226—28no—
200#11758226—44no—
201#11758226—44no—
202#11758226—44no—
203C2×D244—21no—
204C2×D244—21no—
205C2×D244—21no—
206C2×D244—21no—
207C2×D244—21no—
208C2×D244—21no—
209C2×D244—21no—
210C2×D244—28no—
211C2×D244—24no—
212C2×D244—24no—
213C2×D244—21no—
214C2×D244—24no—
215C2×D244—44no—
216C2×D244—44no—
217C2×D244—44no—
218C2×D244—42no—
219C2×D244—42no—
220C2×D244—42no—
221C2×D244—42no—
222C2×D244—81no—
223C2×D244—81no—
224C2×D244C22×C412yes—
225C2×D244C22×C412yes—
226C2×D244C2×D412yes—
227C2×D244#4112yes—
228C2×C4×D61—21no—
229C2×C4×D61—21no—
230C2×C4×D61—21no—
231C2×C4×D61—21no—
232C2×C4×D61—24no—
233C2×C4×D61—24no—
234C2×C4×D61—42no—
235C2×C4×D61—42no—
236C2×C4×D61—81no—
237C2×C4×D61—81no—
238C2×C4×D61C22×C412yes—
239C2×C4×D61C2×D412yes—
240C2×C8×C61—21no—
241C2×C8×C61—21no—
242C2×C8×C61—21no—
243C2×C8×C61—21no—
244C2×C8×C61—21no—
245C2×C8×C61—21no—
246C4⋊C4×C61—24no—
247C4⋊C4×C61—21no—
248C4⋊C4×C61—21no—
249C4⋊C4×C61—21no—
250C4⋊C4×C61—21no—
251C4⋊C4×C61—42no—
252C4⋊C4×C61C22×C412yes—
253C4⋊C4×C61C2×D412yes—
254C22⋊C4×C61—24no—
255C22⋊Dic61—42no—
256C22⋊Dic61C22⋊C414yes—
257#11758198—24no—
258#11758198—24no—
259#11758198—24no—
260#11758198—24no—
261#11758198—42no—
262#11758198—81no—
263#11758198C22⋊C414yes—
264C4⋊Dic61—21no—
265C4⋊Dic61—21no—
266C4⋊Dic61—21no—
267C4⋊Dic61—21no—
268#11758196C22⋊C414yes—
269C4×Dic61—42no—
270C4×Dic61—81no—
271C4×Dic61C22×C412yes—
272C4×Dic61C2×D412yes—
273C2×#92418—21no—
274C2×#92418—21no—
275C2×#92418—21no—
276C2×#92418—21no—
277C2×#92418—21no—
278C2×#92418—44no—
279C2×#92418C2×D412yes—
280C8×D61—44no—
281C23×C61—21no—
282C23×C61—21no—
283C23×C61—21no—
284C23×C61—21no—
285C23×C61C2×C22⋊C412yes—
286C23×C61#13512yes—
287C23×C61#13512yes—
288C23×C61C22×D411yescharacteristic
289C22×D61—22no—
290C22×D61—21no—
291C22×D61—22no—
292C22×D61—21no—
293C22×D61—22no—
294C22×D61—21no—
295C22×D61—21no—
296C22×D61—21no—
297C22×D61—21no—
298C22×D61—22no—
299C22×D61—48no—
300C22×D61—41no—
301C22×D61—41no—
302C22×D61—41no—
303C22×D61—41no—
304C22×D61—41no—
305C22×D61—41no—
306C22×D61—41no—
307C22×D61—41no—
308C22×D61—41no—
309C22×D61—41no—
310C22×D61—48no—
311C22×D61—84no—
312C22×D61—84no—
313C22×D61—84no—
314C22×D61—84no—
315C22×D61—84no—
316C22×D61C2×C22⋊C412yes—
317Q8×C61—22no—
318Q8×C61—22no—
319Q8×C61—41no—
320Q8×C61—41no—
321C2×C4×C61—21no—
322C2×C4×C61—21no—
323C2×C4×C61—22no—
324C2×C4×C61—22no—
325C2×C4×C61—22no—
326C2×C4×C61—22no—
327C2×C4×C61—22no—
328C2×C4×C61—22no—
329C2×C4×C61—22no—
330C2×C4×C61—41no—
331C2×C4×C61—41no—
332C2×C4×C61—41no—
333C2×C4×C61—41no—
334C2×C4×C61—41no—
335C2×C4×C61—41no—
336C2×C4×C61—41no—
337C2×C4×C61—41no—
338C2×C4×C61—41no—
339C2×C4×C61—84no—
340C2×C4×C61C2×C22⋊C412yes—
341C2×C4×C61C23×C411yescharacteristic
342C2×C4×C61C22×D411yescharacteristic
343C2×C4×C61C22×D411yescharacteristic
344C2×C4×C61C2×#4111yescharacteristic
345C2×C4×C61H(5,𝔽2)11yescharacteristic
346C2×C4×C61H(5,𝔽2)11yescharacteristic
347C22⋊D61—28no—
348C2×Dic61—21no—
349C2×Dic61—21no—
350C2×Dic61—21no—
351C2×Dic61—21no—
352C2×Dic61—21no—
353C2×Dic61—21no—
354C2×Dic61—41no—
355C2×Dic61—41no—
356C2×Dic61—41no—
357C2×Dic61—41no—
358C2×Dic61—41no—
359C2×Dic61—41no—
360C2×Dic61C2×C22⋊C412yes—
361C2×Dic61C2×C22⋊C412yes—
362C2×Dic61C2×C22⋊C412yes—
363D244—22no—
364D244—22no—
365D244—22no—
366D244—22no—
367D244—22no—
368D244—48no—
369D244—48no—
370D244—41no—
371D244—41no—
372D244—84no—
373D244C4×D414yes—
374C4×D61—22no—
375C4×D61—22no—
376C4×D61—22no—
377C4×D61—22no—
378C4×D61—48no—
379C4×D61—84no—
380C8×C61—41no—
381C8×C61—41no—
382#92418—22no—
383#92418—41no—
384#22414—611nomaximal, Sylow
385C22×C61—22no—
386C22×C61—22no—
387C22×C61—22no—
388C22×C61—22no—
389C22×C61—22no—
390C22×C61—22no—
391C22×C61#41614yescomplemented
392C22×C61C22×C22⋊C411yescharacteristic
393C22×C61D4211yescharacteristic
394C22×C61#54611yescharacteristic
395C22×C61C2×#13511yescharacteristic
396C22×C61C2×#13511yescharacteristic
397C22×C61#57611yescharacteristic
398C22×C61#57711yescharacteristic
399C2×D61—22no—
400C2×D61—24no—
401C2×D61—22no—
402C2×D61—22no—
403C2×D61—42no—
404C2×D61—42no—
405C2×D61—41no—
406C2×D61—42no—
407C2×D61—41no—
408C2×D61—42no—
409C2×D61—41no—
410C2×D61—42no—
411C2×D61—41no—
412C2×D61—42no—
413C2×D61—42no—
414C2×D61—42no—
415C2×D61—42no—
416C2×D61—816no—
417C2×D61—81no—
418C2×D61—81no—
419C2×D61—81no—
420C2×D61—81no—
421C4×C61—22no—
422C4×C61—42no—
423C4×C61—42no—
424C4×C61—42no—
425C4×C61—81no—
426C4×C61C2×C4×D411yescharacteristic
427C4×C61#51811yescharacteristic
428C4×C61D4211yescharacteristic
429C4×C61#54611yescharacteristic
430Dic61—22no—
431Dic61—22no—
432Dic61—22no—
433Dic61—81no—
434Dic61—81no—
435C2×#546—611no—
436C2×C8×D4—611no—
437C2×#416—611no—
438C22×#102—611no—
439#2352—611no—
440#1983—611no—
441#1958—611no—
442#1893—611no—
443#1892—611no—
444#1875—611no—
445#1872D6111yescharacteristic, complemented
446#1804—611no—
447#1788—611no—
448#1786—611no—
449C4×#102—611no—
450C2×C61—24no—
451C2×C61D4×C22⋊C411yescharacteristic
452C2×C61C2×#41611yescharacteristic
453C2×C61#289711yescharacteristic
454C2×C61#328011yescharacteristic
455C2×C61#328211yescharacteristic
456C2×C61#329611yescharacteristic
457C2×C61#329711yescharacteristic
458D61—42no—
459D61—44no—
460D61—82no—
461C22×#41—611no—
462C23×D4—611no—
463C23×C8—611no—
464C23×C8—611no—
465#546—618no—
466#546—1224no—
467C2×#124—611no—
468C2×#123—1221no—
469C2×C22⋊Q8C2×D6111yescharacteristic
470C2×#121—611no—
471C2×#121—1221no—
472C2×#120—1221no—
473C2×C4×D4—611no—
474C2×C4×D4—611no—
475C2×#117—611no—
476C22×C4⋊C4C2×D6111yescharacteristic
477C22×C22⋊C4—1221no—
478C8×D4—1224no—
479C2×C4⋊C8—611no—
480#416—1224no—
481C2×#103—611no—
482C2×#103—611no—
483C2×#103C2×D6111yescharacteristic, complemented
484C2×#103C2×D6111yescharacteristic, complemented
485C2×#102—611no—
486C2×#102—611no—
487C2×#102—611no—
488C2×#102—611no—
489C2×#102—611no—
490C2×#102—611no—
491C2×#102—611no—
492C2×#102—611no—
493C2×#102—1224no—
494C2×C22⋊C8—611no—
495C2×C22⋊C8C2×D6111yescharacteristic
496C2×C4×C8—611no—
497#388—1221no—
498#387—1221no—
499#386—1221no—
500#382—611no—
501#380—611no—
502#380—611no—
503C4×C4⋊C4—611no—
504C4×C22⋊C4—1221no—
505#340—611no—
506#340—611no—
507#340C2×D6111yescharacteristic, complemented
508#340C2×D6111yescharacteristic, complemented
509C61#2241411yescharacteristic, complemented, Sylow
510C25—1221no—
511C2×#41—614no—
512C2×#41—1222no—
513C2×#41—1222no—
514C2×#41—1222no—
515C2×#41—2441no—
516C2×#41—2441no—
517C22×Q8C22×D6111yescharacteristic
518C22×D4—611no—
519C22×D4—614no—
520C22×D4—611no—
521C22×D4—611no—
522C22×D4—1222no—
523C22×D4—1222no—
524C22×D4—1221no—
525C22×D4—1221no—
526C22×D4—1221no—
527C22×D4—1222no—
528C22×D4—2441no—
529C22×D4—2441no—
530C23×C4—21no—
531C23×C4—611no—
532C23×C4—1221no—
533C23×C4—1221no—
534C23×C4C22×D6111yescharacteristic
535C22×C8—611no—
536C22×C8—611no—
537C22×C8—1222no—
538C22×C8—1222no—
539C22×C8—1222no—
540C22×C8—1222no—
541C22×C8—2441no—
542C22×C8—2441no—
543C22×C8C22×D6111yescharacteristic
544C22×C8C22×D6111yescharacteristic
545#124—614no—
546#124—1222no—
547#123—1228no—
548C22⋊Q8—22no—
549C22⋊Q8C4×D6114yes—
550#121—614no—
551#121—1228no—
552#121—1222no—
553#120—1228no—
554C4×D4—614no—
555C4×D4—614no—
556C4×D4—614no—
557C4×D4—1222no—
558#117—1222no—
559#117—2441no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—22no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—41no—
564C2×C4⋊C4—611no—
565C2×C4⋊C4—611no—
566C2×C4⋊C4—611no—
567C2×C4⋊C4C22×D6111yescharacteristic
568C2×C4⋊C4C22×D6111yescharacteristic
569C2×C4⋊C4C22×D6111yescharacteristic
570C2×C22⋊C4—21no—
571C2×C22⋊C4—611no—
572C2×C22⋊C4—611no—
573C2×C22⋊C4—1228no—
574C2×C22⋊C4—1221no—
575C2×C22⋊C4—1221no—
576C2×C22⋊C4—1221no—
577C2×C22⋊C4—1221no—
578C2×C22⋊C4—1221no—
579C2×C22⋊C4—1221no—
580C2×C22⋊C4—1221no—
581C2×C42—611no—
582C2×C42—1221no—
583C2×C42—1221no—
584C4⋊C8—1222no—
585#103—22no—
586#103—41no—
587#103—1222no—
588#103—2441no—
589#102—614no—
590#102—1222no—
591#102—1222no—
592#102—1222no—
593#102—1222no—
594#102—1222no—
595#102—2441no—
596#102—2441no—
597C22⋊C8—22no—
598C22⋊C8—1222no—
599C4×C8—1222no—
600#95—1221no—
601#95—1221no—
602#95—1221no—
603#95—1221no—
604#95—1221no—
605C24—611no—
606C24—1221no—
607C24—1224no—
608C24—1221no—
609C24—4881no—
610C24—4881no—
611C24—2442no—
612C24—2442no—
613C24—2442no—
614C24—2442no—
615C24D4×D6111yescharacteristic
616#41—1228no—
617#41—2444no—
618#41—2444no—
619#41—2444no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8—21no—
625C2×Q8C2×C4×D6112yes—
626C2×D4—614no—
627C2×D4—612no—
628C2×D4—612no—
629C2×D4—612no—
630C2×D4—612no—
631C2×D4—1228no—
632C2×D4—1224no—
633C2×D4—1224no—
634C2×D4—1222no—
635C2×D4—1222no—
636C2×D4—1221no—
637C2×D4—1221no—
638C2×D4—1221no—
639C2×D4—1221no—
640C2×D4—1221no—
641C2×D4—1221no—
642C2×D4—1221no—
643C2×D4—1221no—
644C2×D4—1224no—
645C2×D4—4881no—
646C2×D4—4881no—
647C2×D4—2444no—
648C2×D4—2444no—
649C2×D4—2444no—
650C2×D4—2442no—
651C2×D4—2442no—
652C2×D4—2442no—
653C2×D4—2442no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—42no—
663C22×C4—42no—
664C22×C4—81no—
665C22×C4—611no—
666C22×C4—611no—
667C22×C4—611no—
668C22×C4—612no—
669C22×C4—612no—
670C22×C4—1224no—
671C22×C4—1224no—
672C22×C4—1221no—
673C22×C4—1221no—
674C22×C4—1221no—
675C22×C4—1221no—
676C22×C4—1221no—
677C22×C4—1221no—
678C22×C4—4881no—
679C22×C4—4881no—
680C22×C4—2442no—
681C22×C4—2442no—
682C22×C4C2×C4×D6112yes—
683C22×C4D4×D6112yes—
684C22×C4D4×D6111yescharacteristic
685C22×C4C23×D6111yescharacteristic
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—612no—
693C2×C8—1221no—
694C2×C8—1221no—
695C2×C8—1221no—
696C2×C8—1221no—
697C2×C8—1221no—
698C2×C8—2444no—
699C2×C8—2444no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—24no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—42no—
706C4⋊C4—614no—
707C4⋊C4—1221no—
708C4⋊C4—1221no—
709C4⋊C4—1221no—
710C4⋊C4—1221no—
711C4⋊C4C2×C4×D6112yes—
712C4⋊C4D4×D6112yes—
713C22⋊C4—24no—
714C22⋊C4—614no—
715C22⋊C4—614no—
716C22⋊C4—1224no—
717C22⋊C4—1224no—
718C22⋊C4—1224no—
719C22⋊C4—1224no—
720C22⋊C4—4881no—
721C22⋊C4—2442no—
722C22⋊C4—2442no—
723C42—612no—
724C42—612no—
725C42—4881no—
726C42—2442no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—612no—
732C23—1222no—
733C23—1221no—
734C23—1221no—
735C23—1221no—
736C23—1221no—
737C23—1221no—
738C23—1222no—
739C23—1221no—
740C23—1222no—
741C23—1222no—
742C23—4884no—
743C23—4884no—
744C23—4884no—
745C23—4884no—
746C23—4884no—
747C23—2448no—
748C23—2448no—
749C23—2441no—
750C23—2441no—
751C23—2441no—
752C23—2441no—
753C23—2441no—
754C23—2441no—
755C23—2441no—
756C23—2441no—
757C23—2441no—
758C23—2441no—
759C23C22⋊C4×D6112yes—
760C23#1451979812yes—
761C23#1451980012yes—
762C23C2×D4×D6111yescharacteristic
763Q8—22no—
764Q8—22no—
765Q8—41no—
766Q8—41no—
767D4—614no—
768D4—1228no—
769D4—1222no—
770D4—1222no—
771D4—1222no—
772D4—1222no—
773D4—1222no—
774D4—4884no—
775D4—2448no—
776D4—2448no—
777D4—2441no—
778D4—2441no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—84no—
798C2×C4—612no—
799C2×C4—612no—
800C2×C4—612no—
801C2×C4—1221no—
802C2×C4—1221no—
803C2×C4—1221no—
804C2×C4—1221no—
805C2×C4—1221no—
806C2×C4—1221no—
807C2×C4—1222no—
808C2×C4—1222no—
809C2×C4—1222no—
810C2×C4—1222no—
811C2×C4—4884no—
812C2×C4—2448no—
813C2×C4—2441no—
814C2×C4—2441no—
815C2×C4—2441no—
816C2×C4—2441no—
817C2×C4—2441no—
818C2×C4—2441no—
819C2×C4C22⋊C4×D6112yes—
820C2×C4C22×C4×D6111yescharacteristic
821C2×C4C2×D4×D6111yescharacteristic
822C2×C4C2×D4×D6111yescharacteristic
823C2×C4#41×D6111yescharacteristic
824C2×C4#1451982211yescharacteristic
825C2×C4#1451982311yescharacteristic
826C8—41no—
827C8—41no—
828C8—1222no—
829C8—2441no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—1222no—
837C22—1222no—
838C22—1224no—
839C22—1222no—
840C22—48816no—
841C22—4881no—
842C22—4881no—
843C22—4881no—
844C22—4881no—
845C22—2442no—
846C22—2442no—
847C22—2442no—
848C22—2441no—
849C22—2442no—
850C22—2442no—
851C22—2441no—
852C22—2442no—
853C22—2441no—
854C22—2442no—
855C22—2442no—
856C22—2441no—
857C22—2442no—
858C22#1683975714yescomplemented
859C22C2×C22⋊C4×D6111yescharacteristic
860C22#1684039411yescharacteristic
861C22#1684040411yescharacteristic
862C22C2×#1451979811yescharacteristic
863C22C2×#1451980011yescharacteristic
864C22#1684056611yescharacteristic
865C22#1684057111yescharacteristic
866C4—22no—
867C4—42no—
868C4—42no—
869C4—42no—
870C4—81no—
871C4—1222no—
872C4—1222no—
873C4—1222no—
874C4—4881no—
875C4—4881no—
876C4C4×D4×D6111yescharacteristic
877C4#1684023411yescharacteristic
878C4#1684039611yescharacteristic
879C4#1684040111yescharacteristic
880C2—24no—
881C2—4882no—
882C2—2442no—
883C2—2444no—
884C2#2144863711yescharacteristic
885C2C2×#1683975711yescharacteristic
886C2#2145434311yescharacteristic
887C2#2145749711yescharacteristic
888C2#2145751911yescharacteristic
889C2#2145765211yescharacteristic
890C2#2145766711yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1872C2
socleC23×C61C22×D4
prime radicalC2×#16840403C2
cosocleC22×C4×C61C24
hypercenter#1872D61
hypocenterC61#22414
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1872

Complements

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

NH ≅ G/Ntype
2. C2×#16839825C2semidirect
3. C2×#16839757C2semidirect
4. C22×#14519697C2semidirect
5. #21448744C2semidirect
6. #21446748C2semidirect
7. #21446627C2semidirect
8. #21446246C2semidirect
9. #21446243C2semidirect
10. #21446140C2semidirect
11. #21445828C2semidirect
12. #21445758C2semidirect
13. #21445751C2semidirect
14. #21445633C2semidirect
15. C61×#1872C2semidirect
19. C22×C8×D61C22semidirect
21. #16840403C4semidirect
29. C2×#14519735C22semidirect
32. C2×#14519706C22semidirect
34. C2×#14519701C22semidirect
35. C2×#14519701C22semidirect
45. C2×#14519689C22semidirect
46. C2×C8×Dic61C22semidirect
50. #16839627C22semidirect
52. #16839619C22semidirect
53. C4⋊C4×Dic61C22semidirect
55. #16839524C22semidirect
56. #16839524C22semidirect
59. C2×#103×C61C22semidirect
60. C2×#103×C61C22semidirect
62. C61×#340C22semidirect
63. C61×#340C22semidirect
70. C2×#11758226C2×C4semidirect
95. #14519766C2×C4semidirect
99. #14519752C2×C4semidirect
102. #14519739C2×C4semidirect
133. #14519697D4semidirect
391. C22×C61#416semidirect
445. #1872D61semidirect
483. C2×#103C2×D61semidirect
484. C2×#103C2×D61semidirect
507. #340C2×D61semidirect
508. #340C2×D61semidirect
509. C61#22414semidirect
858. C22#16839757semidirect

Maximal subgroups

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

subgroupindex
C2×#168404032
C2×#168398252
C2×#168397572
C22×#145196972
#214487442
#214467482
#214466272
#214462462
#214462432
#214461402
#214458282
#214457582
#214457512
#214456332
C61×#18722
#2241461