Finite Group Databasebeta

← #29681273

Subgroups — #29681273

Order 15616.

1970 conjugacy classes of subgroups.

The subgroup lattice has 974 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840328C211yesmaximal, characteristic
2C2×#16840243C211yesmaximal, characteristic, complemented
3C2×#16839765C211yesmaximal, characteristic, complemented
4C2×#102×D61C211yesmaximal, characteristic, complemented
5C2×#16839727C211yesmaximal, characteristic, complemented
6#21446142C211yesmaximal, characteristic, complemented
7#21446140C211yesmaximal, characteristic, complemented
8#21446139C211yesmaximal, characteristic, complemented
9#21446138C211yesmaximal, characteristic, complemented
10#21446136C211yesmaximal, characteristic, complemented
11#21446135C211yesmaximal, characteristic, complemented
12#21446133C211yesmaximal, characteristic, complemented
13#21445537C211yesmaximal, characteristic, complemented
14#21445534C211yesmaximal, characteristic, complemented
15C61×#1874C211yesmaximal, characteristic, complemented
16C22×#11758222C2211yescharacteristic
17C22×D4×D61C2211yescharacteristic
18C22×#11758189C2211yescharacteristic
19C22×C8×D61C2211yescharacteristic
20#16840328—24no—
21#16840328C418yescomplemented
22C2×#14519773—21no—
23C2×#14519763—21no—
24C2×#14519752C2211yescharacteristic
25C2×#14519751C2211yescharacteristic
26C2×#14519748C2211yescharacteristic
27C2×#14519747—21no—
28C2×#14519745—21no—
29#16840243—24no—
30#16840243—24no—
31C2×#14519742—21no—
32C2×#14519739—21no—
33C2×C4×C22⋊D61—21no—
34C2×C4×C22⋊D61—21no—
35C2×#14519736C2211yescharacteristic, complemented
36C2×#14519735C2211yescharacteristic
37C2×#14519735C2211yescharacteristic
38C2×#14519735C2211yescharacteristic, complemented
39C2×C4⋊C4×D61C2211yescharacteristic
40C2×C4⋊C4×D61C2211yescharacteristic, complemented
41#16839765—24no—
42C2×#14519699C2211yescharacteristic
43C2×#14519699C2211yescharacteristic
44C2×#14519698C2211yescharacteristic
45C2×#14519698C2211yescharacteristic
46C2×#14519697C2211yescharacteristic
47C2×#14519697C2211yescharacteristic
48#102×D61—24no—
49#16839727—24no—
50C2×C22⋊#92418C2211yescharacteristic, complemented
51C2×#14519689C2211yescharacteristic, complemented
52C2×#14519689C2211yescharacteristic, complemented
53#16839525C2211yescharacteristic, complemented
54#16839525C2211yescharacteristic, complemented
55#16839524C2211yescharacteristic, complemented
56#16839524C2211yescharacteristic, complemented
57#16839524C2211yescharacteristic, complemented
58#16839524C2211yescharacteristic, complemented
59C2×#121×C61C2211yescharacteristic
60C22×C4⋊C4×C61C2211yescharacteristic, complemented
61C2×#102×C61C2211yescharacteristic
62C2×#102×C61C2211yescharacteristic
63C2×C22⋊C8×C61C2211yescharacteristic, complemented
64C61×#340C2211yescharacteristic, complemented
65C61×#340C2211yescharacteristic, complemented
66C24×D61—21no—
67C2×#11758222—22no—
68C2×#11758222—22no—
69C2×#11758222—22no—
70C2×#11758222—22no—
71C2×#11758222C2×C414yes—
72C2×#11758222D414yes—
73C22×Dic122D411yescharacteristic
74C22×D244—21no—
75C22×D244D411yescharacteristic
76C22×D244C2311yescharacteristic
77C22×C22⋊D61—21no—
78C22×C22⋊D61—21no—
79C22×C22⋊D61—21no—
80C22×C22⋊D61D411yescharacteristic
81C22×C22⋊D61D411yescharacteristic
82C2×D4×D61—22no—
83C2×D4×D61—22no—
84C2×D4×D61—22no—
85C2×D4×D61—22no—
86C2×D4×D61—22no—
87C2×D4×D61C2×C414yescomplemented
88C22×C4×D61—21no—
89C22×C4×D61—21no—
90C22×C4×D61C2311yescharacteristic
91C22×C4×D61C2311yescharacteristic
92C2×#11758189—22no—
93C2×#11758189—22no—
94C2×#11758189—22no—
95C22×#92418C2311yescharacteristic
96C22×#92418C2311yescharacteristic
97C2×C8×D61—22no—
98C2×C8×D61—22no—
99C2×C8×D61—22no—
100#14519773—28no—
101#14519763—28no—
102#14519752—22no—
103#14519752C2×C414yescomplemented
104#14519751—22no—
105#14519751C2×C414yescomplemented
106#14519748—22no—
107#14519748C2×C414yescomplemented
108#14519747—28no—
109#14519745—28no—
110#14519742—28no—
111#14519739—28no—
112C4×C22⋊D61—28no—
113C4×C22⋊D61—28no—
114#14519736—22no—
115#14519736—22no—
116#14519735—22no—
117#14519735—22no—
118#14519735—22no—
119#14519735—22no—
120#14519735C2×C414yescomplemented
121#14519735D414yescomplemented
122C2×C4⋊Dic61C2311yescharacteristic
123C2×C4⋊Dic61C2311yescharacteristic
124C2×C4⋊Dic61C2311yescharacteristic
125C2×#11758196—21no—
126C2×#11758196—21no—
127C4⋊C4×D61—22no—
128C4⋊C4×D61—22no—
129C4⋊C4×D61—22no—
130C4⋊C4×D61D414yescomplemented
131C2×C22⋊Dic61—21no—
132C2×C22⋊Dic61—21no—
133C2×#11758198—21no—
134C2×#11758198—21no—
135C2×#11758198—21no—
136C2×#11758198—21no—
137C2×#11758198—21no—
138C2×C4×Dic61—21no—
139C2×C4×Dic61—21no—
140C2×C4×Dic61—21no—
141C2×C4×Dic61—21no—
142#14519699—22no—
143#14519699—22no—
144#14519698—22no—
145#14519698—22no—
146#14519697—22no—
147#14519697—22no—
148C22⋊#92418—22no—
149#14519689—22no—
150#14519689—22no—
151C22×D4×C61—21no—
152C22×D4×C61C2311yescharacteristic
153C23×C4×C61—21no—
154C23×C4×C61C2311yescharacteristic
155C22×C8×C61C2311yescharacteristic
156C22×C8×C61C2311yescharacteristic
157#121×C61—22no—
158#121×C61C2×C414yescomplemented
159C2×C4⋊C4×C61—21no—
160C2×C4⋊C4×C61—22no—
161C2×C4⋊C4×C61—22no—
162C2×C4⋊C4×C61C2311yescharacteristic
163C2×C4⋊C4×C61C2311yescharacteristic
164C2×C4⋊C4×C61C2311yescharacteristic
165C2×C22⋊C4×C61—21no—
166#102×C61—22no—
167#102×C61—22no—
168C22⋊C8×C61—22no—
169C24×C61—21no—
170C24×C61C2×D411yescharacteristic
171C23×D61—21no—
172C23×D61—24no—
173C23×D61—42no—
174C23×D61—42no—
175C23×D61—81no—
176C23×D61—81no—
177C23×D61—81no—
178C23×D61—81no—
179C23×D61C2×D411yescharacteristic
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—81no—
188C2×D4×C61—81no—
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×C61—24no—
198C22×C4×C61—81no—
199C22×C4×C61—81no—
200C22×C4×C61C22×C412yes—
201C22×C4×C61C2×D411yescharacteristic
202C22×C4×C61C2×D412yes—
203C22×C4×C61C2411yescharacteristic
204C2×C22⋊D61—22no—
205C2×C22⋊D61—22no—
206C2×C22⋊D61—24no—
207C2×C22⋊D61—24no—
208C2×C22⋊D61—24no—
209C2×C22⋊D61—22no—
210C2×C22⋊D61—22no—
211C2×C22⋊D61—42no—
212C2×C22⋊D61—42no—
213C2×C22⋊D61—81no—
214C2×C22⋊D61—81no—
215C2×C22⋊D61—81no—
216C2×C22⋊D61—81no—
217C2×C22⋊D61C22⋊C414yes—
218C2×C22⋊D61C22⋊C414yes—
219C22×Dic61—21no—
220C22×Dic61—21no—
221C22×Dic61—21no—
222C22×Dic61C2×D411yescharacteristic
223C22×Dic61C2×D411yescharacteristic
224D4×D61—28no—
225D4×D61—28no—
226D4×D61—44no—
227D4×D61—44no—
228#11758222—28no—
229#11758222—28no—
230#11758222—28no—
231#11758222—28no—
232C2×D244—22no—
233C2×D244—22no—
234C2×D244—21no—
235C2×D244—21no—
236C2×D244—21no—
237C2×D244—21no—
238C2×D244—21no—
239C2×D244—24no—
240C2×D244—81no—
241C2×D244—81no—
242C2×D244C22⋊C414yes—
243C2×D244C22×C412yes—
244C2×C4×D61—21no—
245C2×C4×D61—21no—
246C2×C4×D61—21no—
247C2×C4×D61—21no—
248C2×C4×D61—24no—
249C2×C4×D61—24no—
250C2×C4×D61—81no—
251C2×C4×D61—81no—
252C2×C4×D61—81no—
253C2×C4×D61—81no—
254C2×C4×D61C22×C412yes—
255C2×C4×D61C22×C412yes—
256C2×C4×D61C2×D412yes—
257C2×C4×D61C2×D412yes—
258C2×C4×D61C2×D412yes—
259C2×C4×D61C2×D412yes—
260C2×C4×D61#4112yes—
261C2×C4×D61#4112yes—
262C2×Dic122—22no—
263C2×Dic122—22no—
264C2×Dic122C22⋊C414yes—
265C2×C8×C61—21no—
266C2×C8×C61—21no—
267C2×C8×C61—21no—
268C2×C8×C61—21no—
269C2×C8×C61—21no—
270C2×C8×C61—21no—
271C4⋊C4×C61—24no—
272C4⋊C4×C61—21no—
273C4⋊C4×C61—21no—
274C4⋊C4×C61—21no—
275C4⋊C4×C61C22×C412yes—
276C4⋊C4×C61C2×D412yes—
277C4⋊C4×C61C2×D412yes—
278C22⋊C4×C61—24no—
279C22⋊Dic61—24no—
280C22⋊Dic61—24no—
281#11758198—24no—
282#11758198—24no—
283#11758198—24no—
284#11758198—24no—
285#11758198—24no—
286C4⋊Dic61—21no—
287C4⋊Dic61—21no—
288C4⋊Dic61—21no—
289C4⋊Dic61C22×C412yes—
290C4⋊Dic61C2×D412yes—
291C4⋊Dic61C2×D412yes—
292#11758196—24no—
293#11758196—24no—
294C4×Dic61—24no—
295C4×Dic61—24no—
296C4×Dic61—24no—
297C4×Dic61—24no—
298C2×#92418—21no—
299C2×#92418—21no—
300C2×#92418—21no—
301C2×#92418—21no—
302C2×#92418—21no—
303C2×#92418—21no—
304#11758189—44no—
305C8×D61—44no—
306C23×C61—21no—
307C23×C61—21no—
308C23×C61—21no—
309C23×C61—21no—
310C23×C61—21no—
311C23×C61—21no—
312C23×C61—22no—
313C23×C61—41no—
314C23×C61—41no—
315C23×C61—41no—
316C23×C61—41no—
317C23×C61—41no—
318C23×C61—41no—
319C23×C61C2×C22⋊C412yes—
320C23×C61C22×D411yescharacteristic
321C22×D61—21no—
322C22×D61—21no—
323C22×D61—21no—
324C22×D61—21no—
325C22×D61—21no—
326C22×D61—21no—
327C22×D61—21no—
328C22×D61—21no—
329C22×D61—21no—
330C22×D61—21no—
331C22×D61—22no—
332C22×D61—41no—
333C22×D61—41no—
334C22×D61—41no—
335C22×D61—41no—
336C22×D61—41no—
337C22×D61—41no—
338C22×D61—48no—
339C22×D61—84no—
340C22×D61—84no—
341C22×D61—84no—
342C22×D61—84no—
343C22×D61—84no—
344C22×D61—84no—
345C22×D61C2×C22⋊C412yes—
346C22×D61C2×C22⋊C412yes—
347C22×D61#12012yes—
348C22×D61#12312yes—
349D4×C61—22no—
350D4×C61—22no—
351D4×C61—41no—
352D4×C61—41no—
353D4×C61—84no—
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—22no—
362C2×C4×C61—22no—
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×C61—84no—
370C2×C4×C61C2×C22⋊C412yes—
371C2×C4×C61C23×C411yescharacteristic
372C2×C4×C61C22×D411yescharacteristic
373C2×C4×C61C22×D411yescharacteristic
374C2×C4×C61C22×D411yescharacteristic
375C2×C4×C61C2×#4111yescharacteristic
376C2×C4×C61C2×#4111yescharacteristic
377C22⋊D61—28no—
378C22⋊D61—28no—
379C22⋊D61—48no—
380C22⋊D61—84no—
381C22⋊D61—84no—
382C2×Dic61—21no—
383C2×Dic61—21no—
384C2×Dic61—22no—
385C2×Dic61—22no—
386C2×Dic61—22no—
387C2×Dic61—41no—
388C2×Dic61—41no—
389C2×Dic61—41no—
390C2×Dic61—41no—
391C2×Dic61—41no—
392C2×Dic61—41no—
393C2×Dic61C2×C22⋊C412yes—
394C2×Dic61C2×C22⋊C412yes—
395C2×Dic61#12012yes—
396C2×Dic61#12312yes—
397D244—28no—
398D244—22no—
399D244—22no—
400D244—41no—
401D244—41no—
402D244—84no—
403C4×D61—22no—
404C4×D61—22no—
405C4×D61—22no—
406C4×D61—22no—
407C4×D61—84no—
408C4×D61—84no—
409C4×D61C4×D414yes—
410C4×D61C4×D414yes—
411C4×D61#12114yes—
412C4×D61#12114yes—
413Dic122—28no—
414C8×C61—41no—
415C8×C61—41no—
416#92418—41no—
417#92418—41no—
418#20914—611nomaximal, Sylow
419C22×C61—22no—
420C22×C61—22no—
421C22×C61—22no—
422C22×C61—41no—
423C22×C61—41no—
424C22×C61—41no—
425C22×C61—41no—
426C22×C61—42no—
427C22×C61—42no—
428C22×C61—42no—
429C22×C61—81no—
430C22×C61—81no—
431C22×C61—81no—
432C22×C61—81no—
433C22×C61C22×C22⋊C411yescharacteristic
434C22×C61C2×#12011yescharacteristic
435C22×C61C2×#12311yescharacteristic
436C22×C61#57611yescharacteristic
437C22×C61#57611yescharacteristic
438C22×C61#57711yescharacteristic
439C22×C61#57711yescharacteristic
440C2×D61—22no—
441C2×D61—22no—
442C2×D61—22no—
443C2×D61—22no—
444C2×D61—22no—
445C2×D61—22no—
446C2×D61—22no—
447C2×D61—22no—
448C2×D61—22no—
449C2×D61—41no—
450C2×D61—41no—
451C2×D61—41no—
452C2×D61—41no—
453C2×D61—42no—
454C2×D61—42no—
455C2×D61—42no—
456C2×D61—816no—
457C2×D61—81no—
458C2×D61—81no—
459C2×D61—81no—
460C2×D61—81no—
461C2×D61#38614yes—
462C4×C61—22no—
463C4×C61—42no—
464C4×C61—42no—
465C4×C61—42no—
466C4×C61C2×C4×D411yescharacteristic
467C4×C61C2×C4×D411yescharacteristic
468C4×C61C2×#12111yescharacteristic
469C4×C61C2×#12111yescharacteristic
470Dic61—22no—
471Dic61—42no—
472Dic61—42no—
473Dic61—42no—
474Dic61#38614yes—
475C2×#535—611no—
476C2×#520—611no—
477C2×#418—611no—
478C22×#102—611no—
479C2×#408—611no—
480#1875—611no—
481#1875—611no—
482#1875—611no—
483#1875—611no—
484#1874—611no—
485#1874—611no—
486#1874—611no—
487#1874D6111yescharacteristic, complemented
488#1736—611no—
489#1735—611no—
490C2×C61—42no—
491C2×C61—82no—
492C2×C61C2×#38611yescharacteristic
493C2×C61#289711yescharacteristic
494C2×C61#289711yescharacteristic
495C2×C61#300811yescharacteristic
496C2×C61#301011yescharacteristic
497C2×C61#309611yescharacteristic
498C2×C61#309611yescharacteristic
499D61—24no—
500D61—42no—
501D61—82no—
502C22×#41—611no—
503C23×D4—611no—
504C22×M16—611no—
505C23×C8—611no—
506#535—618no—
507#535—1224no—
508C2×#127—1221no—
509C2×#124—1221no—
510C2×#121—611no—
511C2×#121—611no—
512C2×#121—611no—
513C2×#121C2×D6111yescharacteristic
514C2×#120—1221no—
515C2×#120—1221no—
516#520—1224no—
517#520—1224no—
518C2×C4×Q8—1221no—
519C2×C4×D4—1221no—
520C2×C4×D4—1221no—
521C2×C4×D4—1221no—
522C2×#117—611no—
523C2×#117—611no—
524C2×#117—611no—
525C2×#117—611no—
526C22×C4⋊C4—611no—
527C22×C4⋊C4—611no—
528C22×C4⋊C4C2×D6111yescharacteristic, complemented
529#418—1224no—
530C2×#102—611no—
531C2×#102—611no—
532C2×#102—611no—
533C2×#102—611no—
534C2×#102—611no—
535C2×#102—611no—
536C2×#102—1224no—
537C2×#102C2×D6111yescharacteristic
538C2×#102C2×D6111yescharacteristic
539#408—1224no—
540C2×C22⋊C8—611no—
541C2×C22⋊C8—611no—
542C2×C22⋊C8—611no—
543C2×C22⋊C8C2×D6111yescharacteristic, complemented
544#340—611no—
545#340—611no—
546#340—611no—
547#340—611no—
548#340—611no—
549#340—611no—
550#340C2×D6111yescharacteristic, complemented
551#340C2×D6111yescharacteristic, complemented
552C61#2091411yescharacteristic, complemented, Sylow
553C25—1221no—
554C2×#41—614no—
555C2×#41—614no—
556C2×#41—1222no—
557C2×#41—1222no—
558C2×#41—1222no—
559C2×#41—1222no—
560C22×Q8—611no—
561C22×D4—21no—
562C22×D4—611no—
563C22×D4—611no—
564C22×D4—614no—
565C22×D4—611no—
566C22×D4—611no—
567C22×D4—1221no—
568C22×D4—1222no—
569C22×D4—1222no—
570C22×D4—1222no—
571C22×D4—1222no—
572C22×D4—1222no—
573C22×D4—1221no—
574C22×D4—1221no—
575C22×D4—1221no—
576C22×D4C22×D6111yescharacteristic
577C23×C4—21no—
578C23×C4—611no—
579C23×C4—611no—
580C23×C4—1221no—
581C23×C4—1221no—
582C23×C4C22×D6111yescharacteristic
583C2×M16—1222no—
584C2×M16—1222no—
585C2×M16—1222no—
586C22×C8—611no—
587C22×C8—611no—
588C22×C8—1222no—
589C22×C8—1222no—
590C22×C8—1222no—
591C22×C8C22×D6111yescharacteristic
592C22×C8C22×D6111yescharacteristic
593#127—1228no—
594#124—1228no—
595#121—22no—
596#121—614no—
597#121—614no—
598#121—614no—
599#121—1222no—
600#121—1222no—
601#121—1222no—
602#121C4×D6114yescomplemented
603#120—1228no—
604#120—1228no—
605C4×Q8—1228no—
606C4×D4—1228no—
607C4×D4—1228no—
608C4×D4—1228no—
609#117—614no—
610#117—614no—
611#117—1222no—
612#117—1222no—
613#117—1222no—
614#117—1222no—
615#117—1222no—
616#117—1222no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—22no—
619C2×C4⋊C4—22no—
620C2×C4⋊C4—611no—
621C2×C4⋊C4—611no—
622C2×C4⋊C4—611no—
623C2×C4⋊C4—614no—
624C2×C4⋊C4—1222no—
625C2×C4⋊C4—1222no—
626C2×C4⋊C4—1221no—
627C2×C4⋊C4—1221no—
628C2×C4⋊C4—1222no—
629C2×C4⋊C4C22×D6111yescharacteristic
630C2×C4⋊C4C22×D6111yescharacteristic
631C2×C4⋊C4C22×D6111yescharacteristic
632C2×C22⋊C4—21no—
633C2×C22⋊C4—1221no—
634C2×C22⋊C4—1221no—
635C2×C22⋊C4—1221no—
636C2×C22⋊C4—1221no—
637C2×C22⋊C4—1221no—
638C2×C22⋊C4—1221no—
639C2×C22⋊C4—1221no—
640C2×C42—1221no—
641C2×C42—1221no—
642C2×C42—1221no—
643C2×C42—1221no—
644#102—22no—
645#102—22no—
646#102—1222no—
647#102—1222no—
648#102—1222no—
649#102—1222no—
650#102—1222no—
651#102—1222no—
652C22⋊C8—22no—
653C22⋊C8—1222no—
654C22⋊C8—1222no—
655C22⋊C8—1222no—
656C24—21no—
657C24—611no—
658C24—611no—
659C24—1224no—
660C24—1221no—
661C24—4881no—
662C24—4881no—
663C24—4881no—
664C24—4881no—
665C24—2442no—
666C24—2442no—
667C24D4×D6111yescharacteristic
668#41—1228no—
669#41—1228no—
670#41—1228no—
671#41—1228no—
672C2×Q8—614no—
673C2×Q8—1222no—
674C2×Q8—1222no—
675C2×D4—24no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—81no—
682C2×D4—81no—
683C2×D4—614no—
684C2×D4—614no—
685C2×D4—612no—
686C2×D4—614no—
687C2×D4—1222no—
688C2×D4—1222no—
689C2×D4—1224no—
690C2×D4—1228no—
691C2×D4—1228no—
692C2×D4—1222no—
693C2×D4—1222no—
694C2×D4—1224no—
695C2×D4—1222no—
696C2×D4—1222no—
697C2×D4—1224no—
698C2×D4—1224no—
699C2×D4—1221no—
700C2×D4—1221no—
701C2×D4—1221no—
702C2×D4—1221no—
703C2×D4—1221no—
704C2×D4—4881no—
705C2×D4—4881no—
706C2×D4—4881no—
707C2×D4—4881no—
708C2×D4—4881no—
709C2×D4—4881no—
710C2×D4—2444no—
711C2×D4—2444no—
712C2×D4—2442no—
713C2×D4—2442no—
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—24no—
723C22×C4—81no—
724C22×C4—81no—
725C22×C4—611no—
726C22×C4—612no—
727C22×C4—612no—
728C22×C4—612no—
729C22×C4—612no—
730C22×C4—612no—
731C22×C4—612no—
732C22×C4—611no—
733C22×C4—612no—
734C22×C4—612no—
735C22×C4—1224no—
736C22×C4—1224no—
737C22×C4—1221no—
738C22×C4—1221no—
739C22×C4—1221no—
740C22×C4—1221no—
741C22×C4—1221no—
742C22×C4—1221no—
743C22×C4—1221no—
744C22×C4—4881no—
745C22×C4—4881no—
746C22×C4—4881no—
747C22×C4—4881no—
748C22×C4C2×C4×D6112yes—
749C22×C4D4×D6112yes—
750C22×C4D4×D6111yescharacteristic
751C22×C4C23×D6111yescharacteristic
752M16—2444no—
753C2×C8—21no—
754C2×C8—21no—
755C2×C8—21no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—1221no—
760C2×C8—1221no—
761C2×C8—1221no—
762C2×C8—1221no—
763C2×C8—1221no—
764C2×C8—1221no—
765C2×C8—2444no—
766C4⋊C4—24no—
767C4⋊C4—21no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—612no—
771C4⋊C4—612no—
772C4⋊C4—612no—
773C4⋊C4—1224no—
774C4⋊C4—1224no—
775C4⋊C4—1221no—
776C4⋊C4—1221no—
777C4⋊C4—1221no—
778C4⋊C4C2×C4×D6112yes—
779C4⋊C4D4×D6112yes—
780C4⋊C4D4×D6112yes—
781C22⋊C4—24no—
782C22⋊C4—1224no—
783C22⋊C4—1224no—
784C22⋊C4—1224no—
785C22⋊C4—1224no—
786C22⋊C4—1224no—
787C22⋊C4—1224no—
788C22⋊C4—1224no—
789C42—1224no—
790C42—1224no—
791C42—1224no—
792C42—1224no—
793C23—21no—
794C23—21no—
795C23—21no—
796C23—21no—
797C23—21no—
798C23—21no—
799C23—22no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—612no—
807C23—612no—
808C23—612no—
809C23—612no—
810C23—1221no—
811C23—1221no—
812C23—1221no—
813C23—1221no—
814C23—1221no—
815C23—1221no—
816C23—1221no—
817C23—1221no—
818C23—1221no—
819C23—1221no—
820C23—1222no—
821C23—4884no—
822C23—4884no—
823C23—4884no—
824C23—4884no—
825C23—4884no—
826C23—4884no—
827C23—2448no—
828C23—2441no—
829C23—2441no—
830C23—2441no—
831C23—2441no—
832C23—2441no—
833C23—2441no—
834C23C22⋊C4×D6112yes—
835C23C2×D4×D6111yescharacteristic
836Q8—1228no—
837D4—22no—
838D4—22no—
839D4—41no—
840D4—41no—
841D4—84no—
842D4—1228no—
843D4—1228no—
844D4—1228no—
845D4—1222no—
846D4—1222no—
847D4—4884no—
848D4—4884no—
849D4—4884no—
850D4—2448no—
851D4—2441no—
852D4—2441no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—84no—
869C2×C4—612no—
870C2×C4—612no—
871C2×C4—612no—
872C2×C4—614no—
873C2×C4—614no—
874C2×C4—614no—
875C2×C4—614no—
876C2×C4—612no—
877C2×C4—1221no—
878C2×C4—1221no—
879C2×C4—1222no—
880C2×C4—1222no—
881C2×C4—1222no—
882C2×C4—1222no—
883C2×C4—1222no—
884C2×C4—1222no—
885C2×C4—1222no—
886C2×C4—4884no—
887C2×C4—4884no—
888C2×C4—2441no—
889C2×C4—2441no—
890C2×C4—2441no—
891C2×C4—2441no—
892C2×C4—2441no—
893C2×C4—2441no—
894C2×C4C22⋊C4×D6112yes—
895C2×C4C22×C4×D6111yescharacteristic
896C2×C4C2×D4×D6111yescharacteristic
897C2×C4C2×D4×D6111yescharacteristic
898C2×C4C2×D4×D6111yescharacteristic
899C2×C4#41×D6111yescharacteristic
900C2×C4#41×D6111yescharacteristic
901C8—41no—
902C8—41no—
903C8—2441no—
904C8—2441no—
905C22—22no—
906C22—22no—
907C22—22no—
908C22—41no—
909C22—41no—
910C22—41no—
911C22—41no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—614no—
920C22—1222no—
921C22—1222no—
922C22—1222no—
923C22—1222no—
924C22—1222no—
925C22—1222no—
926C22—1222no—
927C22—1222no—
928C22—1222no—
929C22—48816no—
930C22—4881no—
931C22—4881no—
932C22—4881no—
933C22—4881no—
934C22—2442no—
935C22—2442no—
936C22—2442no—
937C22—2441no—
938C22—2441no—
939C22—2441no—
940C22—2441no—
941C22C2×C22⋊C4×D6111yescharacteristic
942C22#120×D6111yescharacteristic
943C22#123×D6111yescharacteristic
944C22#1684056311yescharacteristic
945C22#1684056611yescharacteristic
946C22#1684056811yescharacteristic
947C22#1684057111yescharacteristic
948C4—22no—
949C4—42no—
950C4—42no—
951C4—42no—
952C4—614no—
953C4—1222no—
954C4—2442no—
955C4—2442no—
956C4—2442no—
957C4C4×D4×D6111yescharacteristic
958C4C4×D4×D6111yescharacteristic
959C4#121×D6111yescharacteristic
960C4#121×D6111yescharacteristic
961C2—42no—
962C2—82no—
963C2—1224no—
964C2—4882no—
965C2—2442no—
966C2#386×D6111yescharacteristic
967C2#2145434011yescharacteristic
968C2#2145434311yescharacteristic
969C2#2145508211yescharacteristic
970C2#2145510011yescharacteristic
971C2#2145577011yescharacteristic
972C2#2145577611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1874C2
socleC23×C61C22×D4
prime radicalC2×#16840328C2
cosocleC22×C4×C61C24
hypercenter#1874D61
hypocenterC61#20914
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1874

Complements

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

NH ≅ G/Ntype
2. C2×#16840243C2semidirect
3. C2×#16839765C2semidirect
4. C2×#102×D61C2semidirect
5. C2×#16839727C2semidirect
6. #21446142C2semidirect
7. #21446140C2semidirect
8. #21446139C2semidirect
9. #21446138C2semidirect
10. #21446136C2semidirect
11. #21446135C2semidirect
12. #21446133C2semidirect
13. #21445537C2semidirect
14. #21445534C2semidirect
15. C61×#1874C2semidirect
21. #16840328C4semidirect
35. C2×#14519736C22semidirect
38. C2×#14519735C22semidirect
40. C2×C4⋊C4×D61C22semidirect
50. C2×C22⋊#92418C22semidirect
51. C2×#14519689C22semidirect
52. C2×#14519689C22semidirect
53. #16839525C22semidirect
54. #16839525C22semidirect
55. #16839524C22semidirect
56. #16839524C22semidirect
57. #16839524C22semidirect
58. #16839524C22semidirect
60. C22×C4⋊C4×C61C22semidirect
63. C2×C22⋊C8×C61C22semidirect
64. C61×#340C22semidirect
65. C61×#340C22semidirect
87. C2×D4×D61C2×C4semidirect
103. #14519752C2×C4semidirect
105. #14519751C2×C4semidirect
107. #14519748C2×C4semidirect
120. #14519735C2×C4semidirect
121. #14519735D4semidirect
130. C4⋊C4×D61D4semidirect
158. #121×C61C2×C4semidirect
487. #1874D61semidirect
528. C22×C4⋊C4C2×D61semidirect
543. C2×C22⋊C8C2×D61semidirect
550. #340C2×D61semidirect
551. #340C2×D61semidirect
552. C61#20914semidirect
602. #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×#168402432
C2×#168397652
C2×#102×D612
C2×#168397272
#214461422
#214461402
#214461392
#214461382
#214461362
#214461352
#214461332
#214455372
#214455342
C61×#18742
#2091461