Finite Group Databasebeta

← #29695414

Subgroups — #29695414

Order 15616.

2014 conjugacy classes of subgroups.

The subgroup lattice has 972 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840396C211yesmaximal, characteristic
2C2×C8×C22⋊D61C211yesmaximal, characteristic, complemented
3C22×#14519699C211yesmaximal, characteristic, complemented
4C2×#102×D61C211yesmaximal, characteristic, complemented
5#21448715C211yesmaximal, characteristic, complemented
6#21446744C211yesmaximal, characteristic, complemented
7#21446623C211yesmaximal, characteristic, complemented
8#21446246C211yesmaximal, characteristic, complemented
9#21446137C211yesmaximal, characteristic, complemented
10#21446135C211yesmaximal, characteristic, complemented
11#21445818C211yesmaximal, characteristic, complemented
12#21445749C211yesmaximal, characteristic, complemented
13#21445748C211yesmaximal, characteristic, complemented
14#21445633C211yesmaximal, characteristic, complemented
15C61×#1893C211yesmaximal, characteristic, complemented
16C23×D244C2211yescharacteristic
17C22×D4×D61—21no—
18C22×D4×D61C2211yescharacteristic
19C22×C8×D61C2211yescharacteristic, complemented
20#16840396—24no—
21#16840396C418yescomplemented
22C2×#14519773C2211yescharacteristic
23C2×#14519752C2211yescharacteristic
24C2×#14519750—21no—
25C2×#14519747—21no—
26C2×#14519745—21no—
27C2×#14519739C2211yescharacteristic
28C2×C4×C22⋊D61C2211yescharacteristic
29C2×#14519737—21no—
30C22×C4⋊Dic61C2211yescharacteristic, complemented
31C2×C4⋊C4×D61C2211yescharacteristic, complemented
32C8×C22⋊D61—24no—
33C2×#14519706C2211yescharacteristic, complemented
34C2×#14519699—24no—
35C2×#14519699C2211yescharacteristic
36C2×#14519699C2211yescharacteristic
37C2×#14519699C2211yescharacteristic, complemented
38C2×#14519699C2211yescharacteristic, complemented
39C2×#14519698C2211yescharacteristic, complemented
40C2×#14519698C2211yescharacteristic, complemented
41C2×#14519697C2211yescharacteristic
42C2×#14519697C2211yescharacteristic
43C2×#14519697C2211yescharacteristic, complemented
44C2×#14519697C2211yescharacteristic, complemented
45#102×D61—24no—
46C2×C22⋊#92418C2211yescharacteristic, complemented
47C2×#14519689C2211yescharacteristic, complemented
48C2×C8×Dic61C2211yescharacteristic, complemented
49#16839659—21no—
50#16839636—21no—
51#16839634—21no—
52#16839631C2211yescharacteristic, complemented
53#16839619C2211yescharacteristic, complemented
54C4⋊C4×Dic61C2211yescharacteristic, complemented
55#16839524C2211yescharacteristic, complemented
56#16839524C2211yescharacteristic, complemented
57C23×C8×C61C2211yescharacteristic, complemented
58C2×#121×C61C2211yescharacteristic
59C2×#102×C61C2211yescharacteristic, complemented
60C2×#102×C61C2211yescharacteristic, complemented
61C61×#380C2211yescharacteristic, complemented
62C61×#340C2211yescharacteristic, complemented
63C61×#340C2211yescharacteristic, complemented
64C24×D61—21no—
65C24×D61—21no—
66C22×D244—22no—
67C22×D244—22no—
68C22×D244—21no—
69C22×D244—21no—
70C22×D244—22no—
71C22×D244—41no—
72C22×D244—41no—
73C22×D244C2×C414yescomplemented
74C22×D244C2311yescharacteristic
75C22×D244C2311yescharacteristic
76C22×C22⋊D61—21no—
77C22×C22⋊D61—21no—
78C22×C22⋊D61—21no—
79C22×C22⋊D61D411yescharacteristic
80C2×D4×D61—28no—
81C2×D4×D61—22no—
82C2×D4×D61—22no—
83C2×D4×D61—22no—
84C2×D4×D61—41no—
85C2×D4×D61—41no—
86C2×D4×D61—44no—
87C2×D4×D61—44no—
88C2×D4×D61C2×C414yescomplemented
89C23×Dic61—21no—
90C22×C4×D61—21no—
91C22×C4×D61—21no—
92C22×C4×D61C2311yescharacteristic
93C22×#92418C2311yescharacteristic
94C22×#92418C2311yescharacteristic
95C2×C8×D61—22no—
96C2×C8×D61—22no—
97C2×C8×D61—41no—
98#14519773—22no—
99#14519773C2×C414yescomplemented
100#14519752—22no—
101#14519752C2×C414yescomplemented
102#14519750—28no—
103#14519747—28no—
104#14519745—28no—
105#14519739—22no—
106#14519739C2×C414yescomplemented
107C4×C22⋊D61C2×C414yes—
108C4×C22⋊D61D414yes—
109#14519737—44no—
110C2×C4⋊Dic61—22no—
111C2×C4⋊Dic61—21no—
112C2×C4⋊Dic61—41no—
113C2×C4⋊Dic61C2311yescharacteristic
114C2×C4⋊Dic61C2311yescharacteristic
115C2×#11758196—21no—
116C2×#11758196—21no—
117C2×#11758196—21no—
118C2×#11758196D411yescharacteristic
119C4⋊C4×D61—22no—
120C4⋊C4×D61—41no—
121C2×C22⋊Dic61D411yescharacteristic
122C2×#11758198—21no—
123C2×#11758198—21no—
124C2×#11758198—21no—
125C2×#11758198D411yescharacteristic
126C2×C4×Dic61—21no—
127C2×C4×Dic61C2311yescharacteristic
128#14519706—22no—
129#14519699—22no—
130#14519699—22no—
131#14519699—22no—
132#14519699D414yescomplemented
133#14519698—22no—
134#14519698—41no—
135#14519697—22no—
136#14519697—22no—
137#14519697—41no—
138#14519697—41no—
139C22⋊#92418—22no—
140#14519689—22no—
141C8×Dic61—22no—
142#14519684—21no—
143#14519684—21no—
144C22×D4×C61—21no—
145C22×D4×C61C2311yescharacteristic
146C23×C4×C61C2311yescharacteristic
147C22×C8×C61—22no—
148C22×C8×C61—22no—
149C22×C8×C61—41no—
150C22×C8×C61C2311yescharacteristic
151C22×C8×C61C2311yescharacteristic
152#121×C61—22no—
153#121×C61C2×C414yescomplemented
154C2×C4⋊C4×C61C2311yescharacteristic
155C2×C4⋊C4×C61C2311yescharacteristic
156C2×C4⋊C4×C61C2311yescharacteristic
157C2×C22⋊C4×C61—21no—
158C2×C22⋊C4×C61—21no—
159#102×C61—22no—
160#102×C61—41no—
161#95×C61—21no—
162C24×C61—21no—
163C24×C61C2×D411yescharacteristic
164C23×D61—21no—
165C23×D61—21no—
166C23×D61—24no—
167C23×D61—24no—
168C23×D61—42no—
169C23×D61—42no—
170C23×D61—42no—
171C23×D61—42no—
172C23×D61—42no—
173C23×D61—42no—
174C23×D61—42no—
175C23×D61—42no—
176C23×D61—81no—
177C23×D61—81no—
178C23×D61—81no—
179C23×D61—81no—
180C23×D61C2×D411yescharacteristic
181C2×D4×C61—24no—
182C2×D4×C61—21no—
183C2×D4×C61—21no—
184C2×D4×C61—21no—
185C2×D4×C61—21no—
186C2×D4×C61—21no—
187C2×D4×C61—42no—
188C2×D4×C61—42no—
189C2×D4×C61C22×C412yes—
190C22×C4×C61—21no—
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61—21no—
197C22×C4×C61C22×C412yes—
198C22×C4×C61C2×D411yescharacteristic
199C22×C4×C61C2×D412yes—
200C22×C4×C61C2411yescharacteristic
201C2×C22⋊D61—24no—
202C2×C22⋊D61—24no—
203C2×C22⋊D61—24no—
204C2×C22⋊D61—42no—
205C2×C22⋊D61—42no—
206C2×C22⋊D61—42no—
207C2×C22⋊D61—42no—
208C2×C22⋊D61—81no—
209C2×C22⋊D61—81no—
210C2×C22⋊D61C22⋊C414yes—
211C2×C22⋊D61D814yes—
212C2×C22⋊D61SD1614yes—
213C22×Dic61—21no—
214C22×Dic61—21no—
215C22×Dic61—42no—
216C22×Dic61—42no—
217C22×Dic61—81no—
218C22×Dic61C2×D411yescharacteristic
219C22×Dic61C2×D411yescharacteristic
220C22×Dic61C2×D411yescharacteristic
221D4×D61—28no—
222D4×D61—44no—
223D4×D61—44no—
224D4×D61—44no—
225D4×D61—432no—
226C2×D244—21no—
227C2×D244—21no—
228C2×D244—21no—
229C2×D244—21no—
230C2×D244—21no—
231C2×D244—21no—
232C2×D244—21no—
233C2×D244—28no—
234C2×D244—24no—
235C2×D244—24no—
236C2×D244—21no—
237C2×D244—44no—
238C2×D244—44no—
239C2×D244—44no—
240C2×D244—42no—
241C2×D244—42no—
242C2×D244—42no—
243C2×D244—42no—
244C2×D244C22×C412yes—
245C2×D244C22×C412yes—
246C2×D244C2×D412yes—
247C2×D244#4112yes—
248C2×C4×D61—21no—
249C2×C4×D61—21no—
250C2×C4×D61—21no—
251C2×C4×D61—21no—
252C2×C4×D61—24no—
253C2×C4×D61—42no—
254C2×C4×D61—42no—
255C2×C4×D61—42no—
256C2×C4×D61—42no—
257C2×C4×D61—81no—
258C2×C4×D61C22×C412yes—
259C2×C4×D61C2×D412yes—
260C2×C8×C61—21no—
261C2×C8×C61—21no—
262C2×C8×C61—21no—
263C2×C8×C61—21no—
264C2×C8×C61—21no—
265C2×C8×C61—44no—
266C2×C8×C61C2×D412yescomplemented
267C4⋊C4×C61—21no—
268C4⋊C4×C61—21no—
269C4⋊C4×C61—21no—
270C4⋊C4×C61—21no—
271C4⋊C4×C61—21no—
272C4⋊C4×C61C22×C412yes—
273C22⋊C4×C61—24no—
274C22⋊C4×C61—42no—
275C22⋊Dic61C22⋊C414yes—
276#11758198—24no—
277#11758198—24no—
278#11758198—42no—
279#11758198C22⋊C414yes—
280C4⋊Dic61—21no—
281C4⋊Dic61—21no—
282C4⋊Dic61—21no—
283C4⋊Dic61—42no—
284C4⋊Dic61C2×D412yescomplemented
285#11758196—42no—
286#11758196—42no—
287#11758196—81no—
288#11758196C22⋊C414yes—
289C4×Dic61—42no—
290C4×Dic61C22×C412yes—
291C4×Dic61C2×D412yes—
292C2×#92418—21no—
293C2×#92418—21no—
294C2×#92418—21no—
295C2×#92418—21no—
296C2×#92418—21no—
297C2×#92418—21no—
298C8×D61—44no—
299C23×C61—21no—
300C23×C61—21no—
301C23×C61—21no—
302C23×C61—21no—
303C23×C61—22no—
304C23×C61—41no—
305C23×C61—41no—
306C23×C61—41no—
307C23×C61—41no—
308C23×C61—41no—
309C23×C61—41no—
310C23×C61C2×C22⋊C412yes—
311C23×C61C2×D812yes—
312C23×C61C2×SD1612yes—
313C23×C61C22×D411yescharacteristic
314C22×D61—21no—
315C22×D61—21no—
316C22×D61—21no—
317C22×D61—21no—
318C22×D61—22no—
319C22×D61—22no—
320C22×D61—22no—
321C22×D61—22no—
322C22×D61—48no—
323C22×D61—48no—
324C22×D61—41no—
325C22×D61—41no—
326C22×D61—41no—
327C22×D61—41no—
328C22×D61—41no—
329C22×D61—41no—
330C22×D61—41no—
331C22×D61—41no—
332C22×D61—41no—
333C22×D61—41no—
334C22×D61—48no—
335C22×D61—48no—
336C22×D61—84no—
337C22×D61—84no—
338C22×D61—84no—
339C22×D61—84no—
340C22×D61—84no—
341C22×D61—84no—
342C22×D61—84no—
343C22×D61—84no—
344C22×D61—84no—
345C22×D61—84no—
346C22×D61C2×C22⋊C412yes—
347C22×D61C2×D812yes—
348C22×D61C2×SD1612yes—
349D4×C61—22no—
350D4×C61—22no—
351D4×C61—48no—
352D4×C61—41no—
353D4×C61—41no—
354C2×C4×C61—21no—
355C2×C4×C61—21no—
356C2×C4×C61—22no—
357C2×C4×C61—22no—
358C2×C4×C61—22no—
359C2×C4×C61—22no—
360C2×C4×C61—22no—
361C2×C4×C61—41no—
362C2×C4×C61—41no—
363C2×C4×C61—41no—
364C2×C4×C61—41no—
365C2×C4×C61—41no—
366C2×C4×C61—41no—
367C2×C4×C61—41no—
368C2×C4×C61—41no—
369C2×C4×C61C2×C22⋊C412yes—
370C2×C4×C61C23×C411yescharacteristic
371C2×C4×C61C22×D411yescharacteristic
372C2×C4×C61C22×D411yescharacteristic
373C2×C4×C61C2×#4111yescharacteristic
374C2×C4×C61H(5,𝔽2)11yescharacteristic
375C2×C4×C61H(5,𝔽2)11yescharacteristic
376C22⋊D61—48no—
377C22⋊D61—48no—
378C22⋊D61—84no—
379C22⋊D61#102116yescomplemented
380C2×Dic61—21no—
381C2×Dic61—21no—
382C2×Dic61—21no—
383C2×Dic61—21no—
384C2×Dic61—22no—
385C2×Dic61—41no—
386C2×Dic61—41no—
387C2×Dic61—41no—
388C2×Dic61—41no—
389C2×Dic61—41no—
390C2×Dic61—84no—
391C2×Dic61C2×C22⋊C412yes—
392C2×Dic61C2×C22⋊C412yes—
393C2×Dic61C2×C22⋊C412yes—
394C2×Dic61C2×D812yes—
395C2×Dic61C2×SD1612yes—
396D244—22no—
397D244—22no—
398D244—22no—
399D244—22no—
400D244—22no—
401D244—48no—
402D244—48no—
403D244—41no—
404D244—41no—
405D244C4×D414yescomplemented
406C4×D61—22no—
407C4×D61—22no—
408C4×D61—22no—
409C4×D61—22no—
410C4×D61—48no—
411C4×D61—84no—
412C8×C61—22no—
413C8×C61—41no—
414#92418—41no—
415#92418—41no—
416D4×#102—611nomaximal, Sylow
417C22×C61—22no—
418C22×C61—22no—
419C22×C61—22no—
420C22×C61—22no—
421C22×C61—22no—
422C22×C61—22no—
423C22×C61—42no—
424C22×C61—42no—
425C22×C61—42no—
426C22×C61—81no—
427C22×C61—81no—
428C22×C61—81no—
429C22×C61—81no—
430C22×C61C2×#10214yescomplemented
431C22×C61C22×C22⋊C411yescharacteristic
432C22×C61D4211yescharacteristic
433C22×C61#54611yescharacteristic
434C22×C61C22×D811yescharacteristic
435C22×C61C22×SD1611yescharacteristic
436C22×C61#57611yescharacteristic
437C22×C61#57711yescharacteristic
438C2×D61—22no—
439C2×D61—22no—
440C2×D61—22no—
441C2×D61—22no—
442C2×D61—22no—
443C2×D61—22no—
444C2×D61—24no—
445C2×D61—42no—
446C2×D61—42no—
447C2×D61—42no—
448C2×D61—42no—
449C2×D61—42no—
450C2×D61—42no—
451C2×D61—42no—
452C2×D61—42no—
453C2×D61—42no—
454C2×D61—816no—
455C2×D61—816no—
456C2×D61—81no—
457C2×D61—81no—
458C2×D61—81no—
459C2×D61—81no—
460C2×D61C2×#10214yescomplemented
461C4×C61—22no—
462C4×C61—42no—
463C4×C61—81no—
464C4×C61—81no—
465C4×C61C2×C4×D411yescharacteristic
466C4×C61#51811yescharacteristic
467C4×C61D4211yescharacteristic
468C4×C61#54611yescharacteristic
469Dic61—22no—
470Dic61—22no—
471Dic61—42no—
472Dic61—81no—
473Dic61C2×#10214yescomplemented
474C2×D42—611no—
475C2×C8×D4—611no—
476C22×#102—611no—
477C22×#102—611no—
478D4×C4⋊C4—611no—
479#1982—611no—
480#1957—611no—
481#1893—611no—
482#1893D6111yescharacteristic, complemented
483#1874—611no—
484#1874—611no—
485#1802—611no—
486#1786—611no—
487#1786—611no—
488C4×#102—611no—
489C2×C61—24no—
490C2×C61—82no—
491C2×C61D4×C22⋊C411yescharacteristic
492C2×C61C22×#10211yescharacteristic
493C2×C61#289711yescharacteristic
494C2×C61D4×D811yescharacteristic
495C2×C61D4×SD1611yescharacteristic
496C2×C61#329411yescharacteristic
497C2×C61#329511yescharacteristic
498D61—24no—
499D61—44no—
500D61—82no—
501C23×D4—611no—
502C23×D4—611no—
503C23×D4—1221no—
504C23×C8—611no—
505C23×C8C2×D6111yescharacteristic, complemented
506D42—618no—
507D42—1224no—
508C2×#127—611no—
509C2×#121—611no—
510C2×#121—1221no—
511C2×#121C2×D6111yescharacteristic
512C2×#120—1221no—
513C2×#120—1221no—
514C2×C4×D4—611no—
515C2×C4×D4—611no—
516C2×C4×D4—1221no—
517C22×C4⋊C4—611no—
518C22×C4⋊C4—611no—
519C8×D4—1224no—
520C2×C4⋊C8—611no—
521C2×#102—611no—
522C2×#102—611no—
523C2×#102—611no—
524C2×#102—611no—
525C2×#102—611no—
526C2×#102—611no—
527C2×#102—611no—
528C2×#102—611no—
529C2×#102—611no—
530C2×#102—611no—
531C2×#102—1224no—
532C2×#102—1224no—
533C2×#102C2×D6111yescharacteristic, complemented
534C2×#102C2×D6111yescharacteristic, complemented
535C2×C22⋊C8—611no—
536C2×C22⋊C8—611no—
537C2×C4×C8—611no—
538#389—1221no—
539#385—1221no—
540#385—1221no—
541#384—611no—
542#380—611no—
543#380C2×D6111yescharacteristic, complemented
544C4×C4⋊C4—611no—
545#340—611no—
546#340—611no—
547#340C2×D6111yescharacteristic, complemented
548#340C2×D6111yescharacteristic, complemented
549C61D4×#10211yescharacteristic, complemented, Sylow
550C25—1221no—
551C25—1221no—
552C22×D4—21no—
553C22×D4—611no—
554C22×D4—614no—
555C22×D4—614no—
556C22×D4—611no—
557C22×D4—611no—
558C22×D4—1222no—
559C22×D4—1222no—
560C22×D4—1221no—
561C22×D4—1222no—
562C22×D4—1221no—
563C22×D4—1221no—
564C22×D4—1221no—
565C22×D4—1222no—
566C22×D4—1222no—
567C22×D4—1228no—
568C22×D4—1221no—
569C22×D4—1222no—
570C22×D4—2441no—
571C22×D4—2441no—
572C22×D4—2441no—
573C22×D4—2441no—
574C22×D4—2444no—
575C22×D4—2444no—
576C22×D4C22×D6111yescharacteristic
577C23×C4—611no—
578C23×C4—1221no—
579C23×C4—1221no—
580C23×C4—1221no—
581C23×C4C22×D6111yescharacteristic
582C22×C8—22no—
583C22×C8—22no—
584C22×C8—41no—
585C22×C8—611no—
586C22×C8—611no—
587C22×C8—1222no—
588C22×C8—1222no—
589C22×C8—2441no—
590C22×C8C22×D6111yescharacteristic
591C22×C8C22×D6111yescharacteristic
592#127—614no—
593#127—1222no—
594#121—22no—
595#121—614no—
596#121—1228no—
597#121—1222no—
598#121C4×D6114yescomplemented
599#120—1228no—
600#120—1228no—
601C4×D4—614no—
602C4×D4—614no—
603C4×D4—614no—
604C4×D4—1222no—
605C4×D4—2444no—
606C2×C4⋊C4—611no—
607C2×C4⋊C4—611no—
608C2×C4⋊C4—611no—
609C2×C4⋊C4—1222no—
610C2×C4⋊C4—1222no—
611C2×C4⋊C4—1221no—
612C2×C4⋊C4—1221no—
613C2×C4⋊C4—1221no—
614C2×C4⋊C4—1221no—
615C2×C4⋊C4—2441no—
616C2×C4⋊C4—2441no—
617C2×C4⋊C4C22×D6111yescharacteristic
618C2×C4⋊C4C22×D6111yescharacteristic
619C2×C4⋊C4C22×D6111yescharacteristic
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—611no—
623C2×C22⋊C4—611no—
624C2×C22⋊C4—1221no—
625C2×C22⋊C4—1221no—
626C2×C22⋊C4—1221no—
627C2×C42—611no—
628C2×C42—1221no—
629C4⋊C8—1222no—
630#102—22no—
631#102—41no—
632#102—614no—
633#102—1222no—
634#102—1222no—
635#102—1222no—
636#102—1222no—
637#102—1222no—
638#102—1222no—
639#102—2441no—
640#102—2441no—
641#102—2441no—
642C22⋊C8—1222no—
643C22⋊C8—1222no—
644C4×C8—1222no—
645#95—21no—
646#95—1221no—
647#95—1221no—
648C24—21no—
649C24—611no—
650C24—1224no—
651C24—1221no—
652C24—1224no—
653C24—1221no—
654C24—4881no—
655C24—4881no—
656C24—4881no—
657C24—4881no—
658C24—2442no—
659C24—2442no—
660C24—2442no—
661C24—2442no—
662C24—2442no—
663C24—2442no—
664C24—2442no—
665C24—2442no—
666C24D4×D6111yescharacteristic
667C2×D4—24no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—42no—
674C2×D4—42no—
675C2×D4—614no—
676C2×D4—614no—
677C2×D4—614no—
678C2×D4—612no—
679C2×D4—612no—
680C2×D4—612no—
681C2×D4—612no—
682C2×D4—1228no—
683C2×D4—1224no—
684C2×D4—1224no—
685C2×D4—1224no—
686C2×D4—1224no—
687C2×D4—1228no—
688C2×D4—1221no—
689C2×D4—1221no—
690C2×D4—1221no—
691C2×D4—1221no—
692C2×D4—1221no—
693C2×D4—1221no—
694C2×D4—1221no—
695C2×D4—1221no—
696C2×D4—1224no—
697C2×D4—4881no—
698C2×D4—4881no—
699C2×D4—2444no—
700C2×D4—2444no—
701C2×D4—2444no—
702C2×D4—2442no—
703C2×D4—2442no—
704C2×D4—2442no—
705C2×D4—2442no—
706C2×D4—2442no—
707C2×D4—2442no—
708C2×D4—2444no—
709C2×D4—2444no—
710C2×D4—2444no—
711C2×D4—2442no—
712C2×D4—2442no—
713C2×D4—24432no—
714C2×D4C2×C4×D6112yes—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—611no—
723C22×C4—611no—
724C22×C4—611no—
725C22×C4—612no—
726C22×C4—612no—
727C22×C4—1224no—
728C22×C4—1221no—
729C22×C4—1221no—
730C22×C4—1221no—
731C22×C4—1221no—
732C22×C4—1221no—
733C22×C4—1221no—
734C22×C4—4881no—
735C22×C4—4881no—
736C22×C4—2442no—
737C22×C4—2442no—
738C22×C4—2442no—
739C22×C4—2442no—
740C22×C4—2442no—
741C22×C4—2442no—
742C22×C4C2×C4×D6112yes—
743C22×C4D4×D6112yes—
744C22×C4D4×D6111yescharacteristic
745C22×C4C23×D6111yescharacteristic
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—44no—
752C2×C8—1221no—
753C2×C8—1221no—
754C2×C8—1221no—
755C2×C8—1221no—
756C2×C8—1221no—
757C2×C8—1221no—
758C2×C8—2444no—
759C2×C8D4×D6112yescomplemented
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—614no—
766C4⋊C4—612no—
767C4⋊C4—1221no—
768C4⋊C4—1221no—
769C4⋊C4—1221no—
770C4⋊C4—4881no—
771C4⋊C4—2442no—
772C4⋊C4—2442no—
773C4⋊C4—2442no—
774C4⋊C4C2×C4×D6112yes—
775C22⋊C4—24no—
776C22⋊C4—42no—
777C22⋊C4—614no—
778C22⋊C4—614no—
779C22⋊C4—1224no—
780C22⋊C4—1224no—
781C22⋊C4—2442no—
782C42—612no—
783C42—612no—
784C42—2442no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—21no—
789C23—22no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—612no—
797C23—612no—
798C23—612no—
799C23—1221no—
800C23—1221no—
801C23—1221no—
802C23—1221no—
803C23—1222no—
804C23—1222no—
805C23—1222no—
806C23—1222no—
807C23—4884no—
808C23—4884no—
809C23—4884no—
810C23—4884no—
811C23—4884no—
812C23—4884no—
813C23—4884no—
814C23—4884no—
815C23—4884no—
816C23—4884no—
817C23—2448no—
818C23—2448no—
819C23—2448no—
820C23—2448no—
821C23—2441no—
822C23—2441no—
823C23—2441no—
824C23—2441no—
825C23—2441no—
826C23—2441no—
827C23—2441no—
828C23—2441no—
829C23—2441no—
830C23—2441no—
831C23C22⋊C4×D6112yes—
832C23D8×D6112yes—
833C23SD16×D6112yes—
834C23C2×D4×D6111yescharacteristic
835D4—22no—
836D4—22no—
837D4—48no—
838D4—41no—
839D4—41no—
840D4—6116no—
841D4—614no—
842D4—1222no—
843D4—1222no—
844D4—1222no—
845D4—1222no—
846D4—1222no—
847D4—4884no—
848D4—2448no—
849D4—2448no—
850D4—2448no—
851D4—2448no—
852D4—2441no—
853D4—2441no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—612no—
870C2×C4—612no—
871C2×C4—612no—
872C2×C4—612no—
873C2×C4—612no—
874C2×C4—1221no—
875C2×C4—1221no—
876C2×C4—1221no—
877C2×C4—1221no—
878C2×C4—1222no—
879C2×C4—1222no—
880C2×C4—1222no—
881C2×C4—1222no—
882C2×C4—1222no—
883C2×C4—4884no—
884C2×C4—4884no—
885C2×C4—2448no—
886C2×C4—2441no—
887C2×C4—2441no—
888C2×C4—2441no—
889C2×C4—2441no—
890C2×C4—2441no—
891C2×C4C22⋊C4×D6112yes—
892C2×C4C22×C4×D6111yescharacteristic
893C2×C4C2×D4×D6111yescharacteristic
894C2×C4C2×D4×D6111yescharacteristic
895C2×C4#41×D6111yescharacteristic
896C2×C4#1451982211yescharacteristic
897C2×C4#1451982311yescharacteristic
898C8—22no—
899C8—41no—
900C8—2441no—
901C8—2441no—
902C22—22no—
903C22—22no—
904C22—22no—
905C22—22no—
906C22—22no—
907C22—22no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—614no—
916C22—1222no—
917C22—1222no—
918C22—1222no—
919C22—1222no—
920C22—1222no—
921C22—1222no—
922C22—1224no—
923C22—48816no—
924C22—48816no—
925C22—4881no—
926C22—4881no—
927C22—4881no—
928C22—4881no—
929C22—2442no—
930C22—2442no—
931C22—2442no—
932C22—2442no—
933C22—2442no—
934C22—2442no—
935C22—2442no—
936C22—2442no—
937C22—2442no—
938C22#102×D6114yescomplemented
939C22C2×C22⋊C4×D6111yescharacteristic
940C22#1684039611yescharacteristic
941C22#1684040111yescharacteristic
942C22C2×D8×D6111yescharacteristic
943C22C2×SD16×D6111yescharacteristic
944C22#1684056411yescharacteristic
945C22#1684056911yescharacteristic
946C4—22no—
947C4—42no—
948C4—81no—
949C4—81no—
950C4—614no—
951C4—1222no—
952C4—1222no—
953C4—4881no—
954C4—2442no—
955C4C4×D4×D6111yescharacteristic
956C4#1684023411yescharacteristic
957C4#1684039411yescharacteristic
958C4#1684040411yescharacteristic
959C2—24no—
960C2—82no—
961C2—1224no—
962C2—4882no—
963C2—2444no—
964C2#2144863711yescharacteristic
965C2C2×#102×D6111yescharacteristic
966C2#2145434111yescharacteristic
967C2#2145749311yescharacteristic
968C2#2145751211yescharacteristic
969C2#2145762711yescharacteristic
970C2#2145763811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1893C2
socleC23×C61C22×D4
prime radicalC2×#16840396C2
cosocleC22×C4×C61C24
hypercenter#1893D61
hypocenterC61D4×#102
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×C8×C22⋊D61C2semidirect
3. C22×#14519699C2semidirect
4. C2×#102×D61C2semidirect
5. #21448715C2semidirect
6. #21446744C2semidirect
7. #21446623C2semidirect
8. #21446246C2semidirect
9. #21446137C2semidirect
10. #21446135C2semidirect
11. #21445818C2semidirect
12. #21445749C2semidirect
13. #21445748C2semidirect
14. #21445633C2semidirect
15. C61×#1893C2semidirect
19. C22×C8×D61C22semidirect
21. #16840396C4semidirect
30. C22×C4⋊Dic61C22semidirect
31. C2×C4⋊C4×D61C22semidirect
33. C2×#14519706C22semidirect
37. C2×#14519699C22semidirect
38. C2×#14519699C22semidirect
39. C2×#14519698C22semidirect
40. C2×#14519698C22semidirect
43. C2×#14519697C22semidirect
44. C2×#14519697C22semidirect
46. C2×C22⋊#92418C22semidirect
47. C2×#14519689C22semidirect
48. C2×C8×Dic61C22semidirect
52. #16839631C22semidirect
53. #16839619C22semidirect
54. C4⋊C4×Dic61C22semidirect
55. #16839524C22semidirect
56. #16839524C22semidirect
57. C23×C8×C61C22semidirect
59. C2×#102×C61C22semidirect
60. C2×#102×C61C22semidirect
61. C61×#380C22semidirect
62. C61×#340C22semidirect
63. C61×#340C22semidirect
73. C22×D244C2×C4semidirect
88. C2×D4×D61C2×C4semidirect
99. #14519773C2×C4semidirect
101. #14519752C2×C4semidirect
106. #14519739C2×C4semidirect
132. #14519699D4semidirect
153. #121×C61C2×C4semidirect
266. C2×C8×C61C2×D4semidirect
284. C4⋊Dic61C2×D4semidirect
379. C22⋊D61#102semidirect
405. D244C4×D4semidirect
430. C22×C61C2×#102semidirect
460. C2×D61C2×#102semidirect
473. Dic61C2×#102semidirect
482. #1893D61semidirect
505. C23×C8C2×D61semidirect
533. C2×#102C2×D61semidirect
534. C2×#102C2×D61semidirect
543. #380C2×D61semidirect
547. #340C2×D61semidirect
548. #340C2×D61semidirect
549. C61D4×#102semidirect
598. #121C4×D61semidirect
759. C2×C8D4×D61semidirect
938. C22#102×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168403962
C2×C8×C22⋊D612
C22×#145196992
C2×#102×D612
#214487152
#214467442
#214466232
#214462462
#214461372
#214461352
#214458182
#214457492
#214457482
#214456332
C61×#18932
D4×#10261