Finite Group Databasebeta

← #29689105

Subgroups — #29689105

Order 15616.

1518 conjugacy classes of subgroups.

The subgroup lattice has 922 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840328C211yesmaximal, characteristic
2C2×#16839728C211yesmaximal, characteristic, complemented
3#21448408C211yesmaximal, characteristic, complemented
4#21446258C211yesmaximal, characteristic, complemented
5#21446255C211yesmaximal, characteristic, complemented
6#21446247C211yesmaximal, characteristic, complemented
7#21446140C211yesmaximal, characteristic, complemented
8#21446138C211yesmaximal, characteristic, complemented
9#21446135C211yesmaximal, characteristic, complemented
10#21446133C211yesmaximal, characteristic, complemented
11#21445913C211yesmaximal, characteristic, complemented
12#21445912C211yesmaximal, characteristic, complemented
13#21445748C211yesmaximal, characteristic, complemented
14#21445748C211yesmaximal, characteristic, complemented
15C61×#1893C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C22×D4×D61C2211yescharacteristic
18C22×#11758194C2211yescharacteristic, complemented
19#16840328—24no—
20#16840328C418yescomplemented
21C2×#14519773—21no—
22C2×#14519763—21no—
23C2×#14519752C2211yescharacteristic
24C2×#14519751C2211yescharacteristic
25C2×#14519748C2211yescharacteristic
26C2×#14519747—21no—
27C2×#14519745—21no—
28C2×#14519735C2211yescharacteristic
29C2×#14519735C2211yescharacteristic, complemented
30C2×C4⋊C4×D61C2211yescharacteristic, complemented
31C2×#14519699C2211yescharacteristic
32C2×#14519699C2211yescharacteristic
33C2×#14519698C2211yescharacteristic
34C2×#14519698C2211yescharacteristic
35C2×#14519697C2211yescharacteristic
36C2×#14519697C2211yescharacteristic
37#16839728—24no—
38C2×#14519689C2211yescharacteristic
39C2×#14519689C2211yescharacteristic
40C2×#14519689C2211yescharacteristic, complemented
41C2×#14519689C2211yescharacteristic, complemented
42#16839666—21no—
43#16839662—21no—
44#16839640—21no—
45#16839638—21no—
46#16839622C2211yescharacteristic, complemented
47#16839619C2211yescharacteristic
48#16839619C2211yescharacteristic
49#16839525C2211yescharacteristic, complemented
50#16839525C2211yescharacteristic, complemented
51#16839524C2211yescharacteristic, complemented
52#16839524C2211yescharacteristic, complemented
53#16839524C2211yescharacteristic, complemented
54#16839524C2211yescharacteristic, complemented
55C23×C8×C61C2211yescharacteristic, complemented
56C2×#121×C61C2211yescharacteristic
57C2×#102×C61C2211yescharacteristic
58C2×#102×C61C2211yescharacteristic
59C61×#380C2211yescharacteristic, complemented
60C61×#340C2211yescharacteristic, complemented
61C61×#340C2211yescharacteristic, complemented
62C24×D61—21no—
63C2×#11758222—41no—
64C2×#11758222—41no—
65C2×#11758222—41no—
66C2×#11758222—41no—
67C2×#11758222C2×C414yes—
68C2×#11758222D414yes—
69C22×Dic122D411yescharacteristic
70C22×D244—21no—
71C22×D244D411yescharacteristic
72C22×D244C2311yescharacteristic
73C22×C22⋊D61—21no—
74C22×C22⋊D61—21no—
75C22×C22⋊D61—21no—
76C22×C22⋊D61D411yescharacteristic
77C22×C22⋊D61D411yescharacteristic
78C2×D4×D61—22no—
79C2×D4×D61—41no—
80C2×D4×D61—41no—
81C2×D4×D61—41no—
82C2×D4×D61—41no—
83C2×D4×D61C2×C414yescomplemented
84C22×C4×D61—21no—
85C22×C4×D61C2311yescharacteristic
86C22×C4×D61C2311yescharacteristic
87C2×#11758194—22no—
88C2×#11758194—41no—
89C2×#11758194—41no—
90C22×#92418C2311yescharacteristic
91C22×#92418C2311yescharacteristic
92#14519773—28no—
93#14519763—28no—
94#14519752—22no—
95#14519752C2×C414yes—
96#14519751—22no—
97#14519751C2×C414yescomplemented
98#14519748—22no—
99#14519748C2×C414yes—
100#14519747—28no—
101#14519745—28no—
102#14519735—22no—
103#14519735—41no—
104#14519735—41no—
105#14519735C2×C414yescomplemented
106C2×C4⋊Dic61C2311yescharacteristic
107C2×C4⋊Dic61C2311yescharacteristic
108C2×C4⋊Dic61C2311yescharacteristic
109C2×#11758196—21no—
110C4⋊C4×D61—41no—
111C4⋊C4×D61—41no—
112C2×C22⋊Dic61—21no—
113C2×C22⋊Dic61—21no—
114C2×#11758198—21no—
115C2×#11758198—21no—
116C2×#11758198—21no—
117C2×#11758198—21no—
118C2×#11758198—21no—
119C2×#11758198—21no—
120C2×C4×Dic61—21no—
121C2×C4×Dic61—21no—
122#14519699—41no—
123#14519699—41no—
124#14519698—41no—
125#14519698—41no—
126#14519697—41no—
127#14519697—41no—
128#14519689—22no—
129#14519689—22no—
130#14519689—22no—
131#14519689—22no—
132#14519684—21no—
133#14519684—21no—
134#14519684—21no—
135C22×D4×C61—21no—
136C22×D4×C61C2311yescharacteristic
137C23×C4×C61C2311yescharacteristic
138C22×C8×C61—22no—
139C22×C8×C61—41no—
140C22×C8×C61—41no—
141C22×C8×C61C2311yescharacteristic
142C22×C8×C61C2311yescharacteristic
143#121×C61—22no—
144#121×C61C2×C414yescomplemented
145C2×C4⋊C4×C61C2311yescharacteristic
146C2×C4⋊C4×C61C2311yescharacteristic
147C2×C4⋊C4×C61C2311yescharacteristic
148C2×C22⋊C4×C61—21no—
149C2×C22⋊C4×C61—21no—
150#102×C61—41no—
151#102×C61—41no—
152#95×C61—21no—
153C24×C61—21no—
154C24×C61C2×D411yescharacteristic
155C23×D61—21no—
156C23×D61—24no—
157C23×D61—42no—
158C23×D61—42no—
159C23×D61—81no—
160C23×D61—81no—
161C23×D61—81no—
162C23×D61—81no—
163C23×D61C2×D411yescharacteristic
164C23×D61C2×D411yescharacteristic
165C2×D4×C61—24no—
166C2×D4×C61—21no—
167C2×D4×C61—21no—
168C2×D4×C61—21no—
169C2×D4×C61—21no—
170C2×D4×C61—21no—
171C2×D4×C61—81no—
172C2×D4×C61—81no—
173C2×D4×C61C22×C412yes—
174C22×C4×C61—21no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61C22×C412yes—
182C22×C4×C61C2×D411yescharacteristic
183C22×C4×C61C2×D412yes—
184C22×C4×C61C2411yescharacteristic
185C2×C22⋊D61—24no—
186C2×C22⋊D61—24no—
187C2×C22⋊D61—24no—
188C2×C22⋊D61—41no—
189C2×C22⋊D61—41no—
190C2×C22⋊D61—41no—
191C2×C22⋊D61—41no—
192C2×C22⋊D61—42no—
193C2×C22⋊D61—42no—
194C2×C22⋊D61—81no—
195C2×C22⋊D61—81no—
196C2×C22⋊D61—81no—
197C2×C22⋊D61—81no—
198C2×C22⋊D61C22⋊C414yes—
199C2×C22⋊D61C22⋊C414yes—
200C22×Dic61—21no—
201C22×Dic61—21no—
202C22×Dic61—21no—
203C22×Dic61C2×D411yescharacteristic
204C22×Dic61C2×D411yescharacteristic
205D4×D61—44no—
206D4×D61—44no—
207D4×D61—44no—
208D4×D61—44no—
209#11758222—44no—
210#11758222—44no—
211#11758222—44no—
212#11758222—44no—
213C2×D244—21no—
214C2×D244—21no—
215C2×D244—21no—
216C2×D244—21no—
217C2×D244—21no—
218C2×D244—24no—
219C2×D244—41no—
220C2×D244—41no—
221C2×D244—81no—
222C2×D244—81no—
223C2×D244C22⋊C414yes—
224C2×D244C22×C412yes—
225C2×C4×D61—21no—
226C2×C4×D61—21no—
227C2×C4×D61—21no—
228C2×C4×D61—21no—
229C2×C4×D61—21no—
230C2×C4×D61—21no—
231C2×C4×D61—21no—
232C2×C4×D61—21no—
233C2×C4×D61—42no—
234C2×C4×D61—81no—
235C2×C4×D61—81no—
236C2×C4×D61C22×C412yes—
237C2×C4×D61C22×C412yes—
238C2×C4×D61C2×D412yes—
239C2×C4×D61C2×D412yes—
240C2×Dic122—41no—
241C2×Dic122—41no—
242C2×Dic122C22⋊C414yes—
243C2×C8×C61—21no—
244C2×C8×C61—21no—
245C2×C8×C61—21no—
246C2×C8×C61—21no—
247C2×C8×C61—21no—
248C2×C8×C61—21no—
249C2×C8×C61—44no—
250C4⋊C4×C61—21no—
251C4⋊C4×C61—21no—
252C4⋊C4×C61—21no—
253C4⋊C4×C61—21no—
254C4⋊C4×C61—21no—
255C4⋊C4×C61C22×C412yes—
256C22⋊C4×C61—24no—
257C22⋊C4×C61—81no—
258C22⋊Dic61—24no—
259C22⋊Dic61—81no—
260#11758198—24no—
261#11758198—24no—
262#11758198—24no—
263#11758198—42no—
264#11758198—81no—
265#11758198—81no—
266C4⋊Dic61—21no—
267C4⋊Dic61—21no—
268C4⋊Dic61—21no—
269C4⋊Dic61—21no—
270C4⋊Dic61—21no—
271C4⋊Dic61C22×C412yes—
272#11758196—42no—
273C4×Dic61—24no—
274C4×Dic61—42no—
275#11758194—44no—
276C2×#92418—21no—
277C2×#92418—21no—
278C2×#92418—21no—
279C2×#92418—21no—
280C2×#92418—21no—
281C2×#92418—21no—
282C23×C61—21no—
283C23×C61—21no—
284C23×C61—21no—
285C23×C61—21no—
286C23×C61—21no—
287C23×C61—21no—
288C23×C61—22no—
289C23×C61—41no—
290C23×C61—41no—
291C23×C61—41no—
292C23×C61—41no—
293C23×C61—41no—
294C23×C61—41no—
295C23×C61C2×C22⋊C412yes—
296C23×C61C22×D411yescharacteristic
297C22×D61—21no—
298C22×D61—21no—
299C22×D61—21no—
300C22×D61—21no—
301C22×D61—21no—
302C22×D61—21no—
303C22×D61—21no—
304C22×D61—21no—
305C22×D61—21no—
306C22×D61—21no—
307C22×D61—21no—
308C22×D61—21no—
309C22×D61—22no—
310C22×D61—48no—
311C22×D61—41no—
312C22×D61—41no—
313C22×D61—41no—
314C22×D61—41no—
315C22×D61—41no—
316C22×D61—41no—
317C22×D61—84no—
318C22×D61—84no—
319C22×D61—84no—
320C22×D61—84no—
321C22×D61—84no—
322C22×D61—84no—
323C22×D61C2×C22⋊C412yes—
324C22×D61C2×C22⋊C412yes—
325D4×C61—22no—
326D4×C61—22no—
327D4×C61—41no—
328D4×C61—41no—
329D4×C61—84no—
330C2×C4×C61—21no—
331C2×C4×C61—21no—
332C2×C4×C61—22no—
333C2×C4×C61—22no—
334C2×C4×C61—22no—
335C2×C4×C61—22no—
336C2×C4×C61—22no—
337C2×C4×C61—41no—
338C2×C4×C61—41no—
339C2×C4×C61—41no—
340C2×C4×C61—41no—
341C2×C4×C61—41no—
342C2×C4×C61—41no—
343C2×C4×C61—41no—
344C2×C4×C61—41no—
345C2×C4×C61C2×C22⋊C412yes—
346C2×C4×C61C23×C411yescharacteristic
347C2×C4×C61C22×D411yescharacteristic
348C2×C4×C61H(5,𝔽2)11yescharacteristic
349C2×C4×C61H(5,𝔽2)11yescharacteristic
350C2×C4×C61H(5,𝔽2)11yescharacteristic
351C2×C4×C61H(5,𝔽2)11yescharacteristic
352C22⋊D61—44no—
353C22⋊D61—44no—
354C22⋊D61—48no—
355C22⋊D61—84no—
356C22⋊D61—84no—
357C2×Dic61—21no—
358C2×Dic61—21no—
359C2×Dic61—21no—
360C2×Dic61—21no—
361C2×Dic61—22no—
362C2×Dic61—41no—
363C2×Dic61—41no—
364C2×Dic61—41no—
365C2×Dic61—41no—
366C2×Dic61—41no—
367C2×Dic61—41no—
368C2×Dic61—41no—
369C2×Dic61—41no—
370C2×Dic61C2×C22⋊C412yes—
371C2×Dic61C2×C22⋊C412yes—
372D244—22no—
373D244—22no—
374D244—44no—
375D244—41no—
376D244—41no—
377D244—84no—
378C4×D61—22no—
379C4×D61—22no—
380C4×D61—22no—
381C4×D61—22no—
382C4×D61—22no—
383C4×D61—22no—
384C4×D61—22no—
385C4×D61—22no—
386C4×D61—84no—
387Dic122—44no—
388C8×C61—41no—
389C8×C61—41no—
390#92418—41no—
391#92418—41no—
392#21770—611nomaximal, Sylow
393C22×C61—22no—
394C22×C61—22no—
395C22×C61—22no—
396C22×C61—41no—
397C22×C61—41no—
398C22×C61—41no—
399C22×C61—41no—
400C22×C61—42no—
401C22×C61—42no—
402C22×C61—42no—
403C22×C61—81no—
404C22×C61—81no—
405C22×C61—81no—
406C22×C61—81no—
407C22×C61C22×C22⋊C411yescharacteristic
408C22×C61#53411yescharacteristic
409C22×C61#53411yescharacteristic
410C22×C61#57611yescharacteristic
411C22×C61#57611yescharacteristic
412C22×C61#57711yescharacteristic
413C22×C61#57711yescharacteristic
414C2×D61—22no—
415C2×D61—22no—
416C2×D61—22no—
417C2×D61—22no—
418C2×D61—22no—
419C2×D61—22no—
420C2×D61—41no—
421C2×D61—41no—
422C2×D61—41no—
423C2×D61—41no—
424C2×D61—41no—
425C2×D61—41no—
426C2×D61—41no—
427C2×D61—41no—
428C2×D61—42no—
429C2×D61—42no—
430C2×D61—42no—
431C2×D61—816no—
432C2×D61—81no—
433C2×D61—81no—
434C2×D61—81no—
435C2×D61—81no—
436C4×C61—22no—
437C4×C61—42no—
438C4×C61—81no—
439C4×C61—81no—
440C4×C61#51811yescharacteristic
441C4×C61#51811yescharacteristic
442C4×C61#53411yescharacteristic
443C4×C61#53411yescharacteristic
444Dic61—22no—
445Dic61—22no—
446Dic61—42no—
447Dic61—81no—
448Dic61—81no—
449C2×#535—611no—
450C2×#408—611no—
451#2311—611no—
452#1895—611no—
453#1895—611no—
454#1893—611no—
455#1893D6111yescharacteristic, complemented
456#1875—611no—
457#1875—611no—
458#1874—611no—
459#1874—611no—
460#1825—611no—
461#1825—611no—
462#1786—611no—
463#1786—611no—
464C2×C61—42no—
465C2×C61—82no—
466C2×C61#230811yescharacteristic
467C2×C61#289711yescharacteristic
468C2×C61#289711yescharacteristic
469C2×C61#319811yescharacteristic
470C2×C61#319811yescharacteristic
471C2×C61#319911yescharacteristic
472C2×C61#320011yescharacteristic
473D61—42no—
474D61—42no—
475D61—82no—
476C22×#41—611no—
477C23×D4—611no—
478C22×M16—611no—
479C23×C8C2×D6111yescharacteristic, complemented
480#535—618no—
481#535—1224no—
482C2×#127—1221no—
483C2×#124—1221no—
484C2×#121—611no—
485C2×#121—611no—
486C2×#121—611no—
487C2×#121C2×D6111yescharacteristic
488C2×#120—1221no—
489C2×#120—1221no—
490C2×#117—611no—
491C2×#117—611no—
492C22×C4⋊C4—611no—
493C2×#102—611no—
494C2×#102—611no—
495C2×#102—611no—
496C2×#102—611no—
497C2×#102—611no—
498C2×#102—611no—
499C2×#102C2×D6111yescharacteristic
500C2×#102C2×D6111yescharacteristic
501#408—1224no—
502C2×C22⋊C8—611no—
503C2×C22⋊C8—611no—
504C2×C22⋊C8—611no—
505C2×C22⋊C8—611no—
506#391—1221no—
507#390—1221no—
508#386—1221no—
509#386—1221no—
510#380—611no—
511#380—611no—
512#380—611no—
513#380C2×D6111yescharacteristic, complemented
514#340—611no—
515#340—611no—
516#340—611no—
517#340—611no—
518#340—611no—
519#340—611no—
520#340C2×D6111yescharacteristic, complemented
521#340C2×D6111yescharacteristic, complemented
522C61#2177011yescharacteristic, complemented, Sylow
523C25—1221no—
524C2×#41—614no—
525C2×#41—614no—
526C2×#41—2441no—
527C2×#41—2441no—
528C2×#41—2441no—
529C2×#41—2441no—
530C22×Q8—611no—
531C22×D4—21no—
532C22×D4—611no—
533C22×D4—611no—
534C22×D4—614no—
535C22×D4—611no—
536C22×D4—611no—
537C22×D4—1221no—
538C22×D4—1222no—
539C22×D4—1221no—
540C22×D4—1221no—
541C22×D4—1221no—
542C22×D4—2441no—
543C22×D4—2441no—
544C22×D4—2441no—
545C22×D4—2441no—
546C22×D4C22×D6111yescharacteristic
547C23×C4—611no—
548C23×C4—611no—
549C23×C4—1221no—
550C23×C4C22×D6111yescharacteristic
551C2×M16—1222no—
552C2×M16—2441no—
553C2×M16—2441no—
554C22×C8—22no—
555C22×C8—41no—
556C22×C8—41no—
557C22×C8—611no—
558C22×C8—611no—
559C22×C8C22×D6111yescharacteristic
560C22×C8C22×D6111yescharacteristic
561#127—1228no—
562#124—1228no—
563#121—22no—
564#121—614no—
565#121—614no—
566#121—614no—
567#121—1222no—
568#121—1222no—
569#121—1222no—
570#121C4×D6114yescomplemented
571#120—1228no—
572#120—1228no—
573#117—614no—
574#117—1222no—
575#117—2441no—
576#117—2441no—
577C2×C4⋊C4—611no—
578C2×C4⋊C4—611no—
579C2×C4⋊C4—611no—
580C2×C4⋊C4—1221no—
581C2×C4⋊C4—2441no—
582C2×C4⋊C4—2441no—
583C2×C4⋊C4C22×D6111yescharacteristic
584C2×C4⋊C4C22×D6111yescharacteristic
585C2×C4⋊C4C22×D6111yescharacteristic
586C2×C22⋊C4—21no—
587C2×C22⋊C4—21no—
588C2×C22⋊C4—1221no—
589C2×C22⋊C4—1221no—
590C2×C22⋊C4—1221no—
591C2×C22⋊C4—1221no—
592C2×C22⋊C4—1221no—
593C2×C22⋊C4—1221no—
594C2×C22⋊C4—1221no—
595C2×C22⋊C4—1221no—
596C2×C42—1221no—
597C2×C42—1221no—
598#102—41no—
599#102—41no—
600#102—2441no—
601#102—2441no—
602#102—2441no—
603#102—2441no—
604#102—2441no—
605#102—2441no—
606C22⋊C8—1222no—
607C22⋊C8—1222no—
608C22⋊C8—1222no—
609C22⋊C8—1222no—
610#95—21no—
611#95—1221no—
612#95—1221no—
613#95—1221no—
614C24—21no—
615C24—611no—
616C24—611no—
617C24—1224no—
618C24—1221no—
619C24—4881no—
620C24—4881no—
621C24—4881no—
622C24—4881no—
623C24—2442no—
624C24—2442no—
625C24D4×D6111yescharacteristic
626#41—2444no—
627#41—2444no—
628#41—2444no—
629#41—2444no—
630C2×Q8—614no—
631C2×Q8—2441no—
632C2×Q8—2441no—
633C2×D4—24no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—81no—
640C2×D4—81no—
641C2×D4—614no—
642C2×D4—614no—
643C2×D4—612no—
644C2×D4—614no—
645C2×D4—1224no—
646C2×D4—1224no—
647C2×D4—1224no—
648C2×D4—1224no—
649C2×D4—1221no—
650C2×D4—1221no—
651C2×D4—1221no—
652C2×D4—1221no—
653C2×D4—1221no—
654C2×D4—4881no—
655C2×D4—4881no—
656C2×D4—4881no—
657C2×D4—4881no—
658C2×D4—4881no—
659C2×D4—4881no—
660C2×D4—2441no—
661C2×D4—2441no—
662C2×D4—2444no—
663C2×D4—2444no—
664C2×D4—2444no—
665C2×D4—2444no—
666C2×D4—2441no—
667C2×D4—2441no—
668C2×D4—2441no—
669C2×D4—2441no—
670C2×D4—2442no—
671C2×D4—2442no—
672C2×D4C2×C4×D6112yes—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—611no—
681C22×C4—611no—
682C22×C4—612no—
683C22×C4—612no—
684C22×C4—612no—
685C22×C4—612no—
686C22×C4—1221no—
687C22×C4—1221no—
688C22×C4—1221no—
689C22×C4—1221no—
690C22×C4—1221no—
691C22×C4—1221no—
692C22×C4—1221no—
693C22×C4—1221no—
694C22×C4—1221no—
695C22×C4—1221no—
696C22×C4—1221no—
697C22×C4—4881no—
698C22×C4—4881no—
699C22×C4—2442no—
700C22×C4C2×C4×D6112yes—
701C22×C4D4×D6112yes—
702C22×C4D4×D6111yescharacteristic
703C22×C4C23×D6111yescharacteristic
704M16—2444no—
705C2×C8—21no—
706C2×C8—21no—
707C2×C8—21no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—44no—
712C2×C8—1221no—
713C2×C8—1221no—
714C2×C8—1221no—
715C2×C8—1221no—
716C2×C8—1221no—
717C2×C8—1221no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—612no—
724C4⋊C4—1221no—
725C4⋊C4—1221no—
726C4⋊C4—1221no—
727C4⋊C4—1221no—
728C4⋊C4—1221no—
729C4⋊C4—2442no—
730C4⋊C4C2×C4×D6112yes—
731C22⋊C4—24no—
732C22⋊C4—81no—
733C22⋊C4—1224no—
734C22⋊C4—1224no—
735C22⋊C4—1224no—
736C22⋊C4—1224no—
737C22⋊C4—4881no—
738C22⋊C4—4881no—
739C22⋊C4—4881no—
740C22⋊C4—2442no—
741C42—1224no—
742C42—2442no—
743C23—21no—
744C23—21no—
745C23—21no—
746C23—21no—
747C23—21no—
748C23—21no—
749C23—22no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—612no—
757C23—612no—
758C23—1221no—
759C23—1221no—
760C23—1221no—
761C23—1221no—
762C23—1221no—
763C23—1221no—
764C23—1221no—
765C23—1221no—
766C23—1221no—
767C23—1221no—
768C23—1221no—
769C23—1221no—
770C23—1222no—
771C23—4884no—
772C23—4884no—
773C23—4884no—
774C23—4884no—
775C23—4884no—
776C23—4884no—
777C23—2448no—
778C23—2441no—
779C23—2441no—
780C23—2441no—
781C23—2441no—
782C23—2441no—
783C23—2441no—
784C23C22⋊C4×D6112yes—
785C23C2×D4×D6111yescharacteristic
786Q8—2444no—
787D4—22no—
788D4—22no—
789D4—41no—
790D4—41no—
791D4—84no—
792D4—1222no—
793D4—1222no—
794D4—4884no—
795D4—4884no—
796D4—4884no—
797D4—2444no—
798D4—2444no—
799D4—2444no—
800D4—2448no—
801D4—2441no—
802D4—2441no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—612no—
819C2×C4—612no—
820C2×C4—1221no—
821C2×C4—1221no—
822C2×C4—1221no—
823C2×C4—1221no—
824C2×C4—1222no—
825C2×C4—1222no—
826C2×C4—1222no—
827C2×C4—1222no—
828C2×C4—1222no—
829C2×C4—1222no—
830C2×C4—1222no—
831C2×C4—1222no—
832C2×C4—1222no—
833C2×C4—4884no—
834C2×C4—2441no—
835C2×C4—2441no—
836C2×C4—2441no—
837C2×C4—2441no—
838C2×C4—2441no—
839C2×C4—2441no—
840C2×C4—2441no—
841C2×C4—2441no—
842C2×C4C22⋊C4×D6112yes—
843C2×C4C22×C4×D6111yescharacteristic
844C2×C4C2×D4×D6111yescharacteristic
845C2×C4#1451982211yescharacteristic
846C2×C4#1451982211yescharacteristic
847C2×C4#1451982311yescharacteristic
848C2×C4#1451982311yescharacteristic
849C8—41no—
850C8—41no—
851C8—2441no—
852C8—2441no—
853C22—22no—
854C22—22no—
855C22—22no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—42no—
861C22—42no—
862C22—42no—
863C22—81no—
864C22—81no—
865C22—81no—
866C22—81no—
867C22—1222no—
868C22—1222no—
869C22—1222no—
870C22—1222no—
871C22—1222no—
872C22—1222no—
873C22—48816no—
874C22—4881no—
875C22—4881no—
876C22—4881no—
877C22—4881no—
878C22—2442no—
879C22—2442no—
880C22—2442no—
881C22—2441no—
882C22—2441no—
883C22—2441no—
884C22—2441no—
885C22—2441no—
886C22—2441no—
887C22—2441no—
888C22—2441no—
889C22C2×C22⋊C4×D6111yescharacteristic
890C22#1684032011yescharacteristic
891C22#1684032011yescharacteristic
892C22#1684056311yescharacteristic
893C22#1684056411yescharacteristic
894C22#1684056811yescharacteristic
895C22#1684056911yescharacteristic
896C4—22no—
897C4—42no—
898C4—81no—
899C4—81no—
900C4—1222no—
901C4—1222no—
902C4—4881no—
903C4—4881no—
904C4—2442no—
905C4#1684023411yescharacteristic
906C4#1684023411yescharacteristic
907C4#1684032211yescharacteristic
908C4#1684032311yescharacteristic
909C2—42no—
910C2—82no—
911C2—4882no—
912C2—2442no—
913C2—2442no—
914C2#2144839311yescharacteristic
915C2#2145434011yescharacteristic
916C2#2145434111yescharacteristic
917C2#2145666411yescharacteristic
918C2#2145667411yescharacteristic
919C2#2145667911yescharacteristic
920C2#2145668511yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1893C2
socleC23×C61C22×D4
prime radicalC2×#16840328C2
cosocleC22×C4×C61C24
hypercenter#1893D61
hypocenterC61#21770
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1893

Complements

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

NH ≅ G/Ntype
2. C2×#16839728C2semidirect
3. #21448408C2semidirect
4. #21446258C2semidirect
5. #21446255C2semidirect
6. #21446247C2semidirect
7. #21446140C2semidirect
8. #21446138C2semidirect
9. #21446135C2semidirect
10. #21446133C2semidirect
11. #21445913C2semidirect
12. #21445912C2semidirect
13. #21445748C2semidirect
14. #21445748C2semidirect
15. C61×#1893C2semidirect
18. C22×#11758194C22semidirect
20. #16840328C4semidirect
29. C2×#14519735C22semidirect
30. C2×C4⋊C4×D61C22semidirect
40. C2×#14519689C22semidirect
41. C2×#14519689C22semidirect
46. #16839622C22semidirect
49. #16839525C22semidirect
50. #16839525C22semidirect
51. #16839524C22semidirect
52. #16839524C22semidirect
53. #16839524C22semidirect
54. #16839524C22semidirect
55. C23×C8×C61C22semidirect
59. C61×#380C22semidirect
60. C61×#340C22semidirect
61. C61×#340C22semidirect
83. C2×D4×D61C2×C4semidirect
97. #14519751C2×C4semidirect
105. #14519735C2×C4semidirect
144. #121×C61C2×C4semidirect
455. #1893D61semidirect
479. C23×C8C2×D61semidirect
513. #380C2×D61semidirect
520. #340C2×D61semidirect
521. #340C2×D61semidirect
522. C61#21770semidirect
570. #121C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168403282
C2×#168397282
#214484082
#214462582
#214462552
#214462472
#214461402
#214461382
#214461352
#214461332
#214459132
#214459122
#214457482
C61×#18932
#2177061