Finite Group Databasebeta

← #29717754

Subgroups — #29717754

Order 15616.

1582 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×#16839989C211yesmaximal, characteristic, complemented
2C2×#16839924C211yesmaximal, characteristic, complemented
3C2×#16839913C211yesmaximal, characteristic, complemented
4C2×#16839758C211yesmaximal, characteristic, complemented
5#21449248C211yesmaximal, characteristic, complemented
6#21447055C211yesmaximal, characteristic, complemented
7#21447012C211yesmaximal, characteristic, complemented
8#21446913C211yesmaximal, characteristic, complemented
9#21446827C211yesmaximal, characteristic, complemented
10#21446153C211yesmaximal, characteristic, complemented
11#21446142C211yesmaximal, characteristic, complemented
12#21446112C211yesmaximal, characteristic, complemented
13#21446080C211yesmaximal, characteristic, complemented
14#21445750C211yesmaximal, characteristic, complemented
15C2×C61×#546C211yesmaximal, characteristic
16C22×#11758202C2211yescharacteristic, complemented
17C22×#11758200C2211yescharacteristic
18C22×#11758200C2211yescharacteristic
19C23×#92418C2211yescharacteristic, complemented
20C2×#14519756C2211yescharacteristic
21C2×#14519756C2211yescharacteristic, complemented
22C2×#14519736C2211yescharacteristic, complemented
23#16839989—24no—
24#16839924—24no—
25#16839913—24no—
26C2×#14519708C2211yescharacteristic, complemented
27#16839758—24no—
28C2×#14519701C2211yescharacteristic, complemented
29C2×#14519701C2211yescharacteristic, complemented
30C2×#14519701C2211yescharacteristic, complemented
31C2×#14519700C2211yescharacteristic, complemented
32C2×#14519698C2211yescharacteristic
33C2×#14519698C2211yescharacteristic
34C2×#14519698C2211yescharacteristic
35C2×#14519698C2211yescharacteristic
36C2×#14519698C2211yescharacteristic
37C2×#14519698C2211yescharacteristic
38C2×C22⋊#92418C2211yescharacteristic
39C2×C22⋊#92418C2211yescharacteristic
40C2×C22⋊#92418C2211yescharacteristic, complemented
41#16839690—21no—
42#16839676—21no—
43#16839668C2211yescharacteristic, complemented
44#16839660C2211yescharacteristic, complemented
45#16839657—21no—
46#16839656—21no—
47#16839622C2211yescharacteristic
48#16839524C2211yescharacteristic, complemented
49#16839524C2211yescharacteristic, complemented
50#16839517C2211yescharacteristic, complemented
51#16839517C2211yescharacteristic, complemented
52C22×#41×C61C2211yescharacteristic
53C23×D4×C61C2211yescharacteristic
54C61×#546—24no—
55C61×#546—24no—
56C2×#124×C61C2211yescharacteristic
57C2×#123×C61—21no—
58C2×C22⋊Q8×C61C2211yescharacteristic
59C2×#121×C61—21no—
60C2×#121×C61C2211yescharacteristic
61C2×#120×C61—21no—
62C2×C4×D4×C61C2211yescharacteristic
63C2×C4×D4×C61C2211yescharacteristic
64C22×C22⋊C4×C61—21no—
65C22×Dic122C2311yescharacteristic
66C2×#11758202—22no—
67C2×#11758202—41no—
68C2×#11758202—41no—
69C2×#11758200—22no—
70C2×#11758200—22no—
71C2×#11758200—22no—
72C2×#11758200—22no—
73C2×#11758200—22no—
74C2×#11758200—41no—
75C22×#92418—22no—
76C22×#92418—22no—
77C22×#92418—41no—
78C22×#92418C2311yescharacteristic
79C22×#92418C2311yescharacteristic
80C22×#92418C2311yescharacteristic
81C22×#92418C2311yescharacteristic
82#14519756—22no—
83#14519756—22no—
84#14519756—22no—
85#14519756—41no—
86#14519736—22no—
87#14519736—41no—
88C2×C4⋊Dic61C2311yescharacteristic
89C2×C4⋊Dic61C2311yescharacteristic
90C2×C4⋊Dic61C2311yescharacteristic
91C2×#11758196—21no—
92C2×#11758196—21no—
93C2×#11758196—21no—
94C2×C22⋊Dic61—21no—
95C2×C22⋊Dic61—21no—
96C2×C22⋊Dic61—21no—
97C2×C22⋊Dic61—21no—
98C2×C4×Dic61—21no—
99#14519708—22no—
100#14519701—22no—
101#14519701—22no—
102#14519701—22no—
103#14519700—22no—
104#14519698—22no—
105#14519698—22no—
106#14519698—22no—
107#14519698—22no—
108#14519698—41no—
109#14519698D414yescomplemented
110C22⋊#92418—22no—
111C22⋊#92418—22no—
112C22⋊#92418—41no—
113#14519684—21no—
114#14519684—21no—
115#14519684—21no—
116#14519684—21no—
117C25×C61—21no—
118C2×#41×C61—22no—
119C2×#41×C61—22no—
120C2×#41×C61—22no—
121C2×#41×C61—41no—
122C2×#41×C61—41no—
123C2×#41×C61D414yes—
124C22×Q8×C61C2311yescharacteristic
125C22×D4×C61—21no—
126C22×D4×C61—21no—
127C22×D4×C61—22no—
128C22×D4×C61—22no—
129C22×D4×C61—22no—
130C22×D4×C61—22no—
131C22×D4×C61—21no—
132C22×D4×C61—41no—
133C22×D4×C61—41no—
134C22×D4×C61D411yescharacteristic
135C22×D4×C61C2311yescharacteristic
136C22×D4×C61C2311yescharacteristic
137C23×C4×C61—21no—
138C23×C4×C61—21no—
139C23×C4×C61C2311yescharacteristic
140C23×C4×C61C2311yescharacteristic
141#124×C61—22no—
142#124×C61—22no—
143#123×C61—28no—
144C22⋊Q8×C61—22no—
145C22⋊Q8×C61—22no—
146#121×C61—28no—
147#121×C61—22no—
148#121×C61D414yes—
149#120×C61—28no—
150C4×D4×C61—22no—
151C4×D4×C61—22no—
152C4×D4×C61—22no—
153C4×D4×C61—22no—
154C2×C4⋊C4×C61—21no—
155C2×C4⋊C4×C61D411yescharacteristic
156C2×C4⋊C4×C61C2311yescharacteristic
157C2×C22⋊C4×C61—28no—
158C2×C22⋊C4×C61—21no—
159C2×C22⋊C4×C61—21no—
160C2×C22⋊C4×C61—21no—
161C2×C22⋊C4×C61—21no—
162C2×C22⋊C4×C61—21no—
163C2×C22⋊C4×C61D411yescharacteristic
164C2×C22⋊C4×C61D411yescharacteristic
165C2×C42×C61C2311yescharacteristic
166C24×C61—21no—
167C24×C61—24no—
168C24×C61—21no—
169C24×C61—42no—
170C24×C61—42no—
171C24×C61—42no—
172C24×C61—42no—
173C24×C61—81no—
174C24×C61—81no—
175C24×C61C2×D411yescharacteristic
176C24×C61C2×D411yescharacteristic
177#41×C61—28no—
178#41×C61—44no—
179#41×C61—44no—
180#41×C61—44no—
181C2×Q8×C61—21no—
182C2×Q8×C61—21no—
183C2×Q8×C61—21no—
184C2×Q8×C61—21no—
185C2×Q8×C61—21no—
186C2×Q8×C61C2×D412yes—
187C2×D4×C61—24no—
188C2×D4×C61—22no—
189C2×D4×C61—24no—
190C2×D4×C61—22no—
191C2×D4×C61—24no—
192C2×D4×C61—21no—
193C2×D4×C61—21no—
194C2×D4×C61—21no—
195C2×D4×C61—21no—
196C2×D4×C61—21no—
197C2×D4×C61—21no—
198C2×D4×C61—21no—
199C2×D4×C61—21no—
200C2×D4×C61—41no—
201C2×D4×C61—42no—
202C2×D4×C61—42no—
203C2×D4×C61—44no—
204C2×D4×C61—44no—
205C2×D4×C61—44no—
206C2×D4×C61—42no—
207C2×D4×C61—42no—
208C2×D4×C61—44no—
209C2×D4×C61—81no—
210C2×D4×C61—81no—
211C2×D4×C61C2×D412yes—
212C2×D4×C61C2×D412yes—
213C2×D4×C61C2×D412yes—
214C2×D4×C61#4112yes—
215C22×C4×C61—21no—
216C22×C4×C61—21no—
217C22×C4×C61—21no—
218C22×C4×C61—21no—
219C22×C4×C61—21no—
220C22×C4×C61—21no—
221C22×C4×C61—24no—
222C22×C4×C61—24no—
223C22×C4×C61—21no—
224C22×C4×C61—21no—
225C22×C4×C61—21no—
226C22×C4×C61—21no—
227C22×C4×C61—21no—
228C22×C4×C61—21no—
229C22×C4×C61—42no—
230C22×C4×C61—42no—
231C22×C4×C61—81no—
232C22×C4×C61—81no—
233C22×C4×C61C2×D411yescharacteristic
234C22×C4×C61C2×D411yescharacteristic
235C22×C4×C61C2×D411yescharacteristic
236C22×C4×C61C2×D411yescharacteristic
237C22×C4×C61C2×D412yes—
238C22×C4×C61C2×D412yes—
239C22×C4×C61C2411yescharacteristic
240C22×Dic61—21no—
241C22×Dic61—21no—
242C22×Dic61—21no—
243C22×Dic61—21no—
244C2×Dic122—21no—
245C2×Dic122—21no—
246C2×Dic122—21no—
247C2×Dic122—21no—
248C2×Dic122—21no—
249C2×Dic122—21no—
250C4⋊C4×C61—24no—
251C4⋊C4×C61—22no—
252C4⋊C4×C61—21no—
253C4⋊C4×C61C2×D412yes—
254C22⋊C4×C61—24no—
255C22⋊C4×C61—24no—
256C22⋊C4×C61—24no—
257C22⋊C4×C61—24no—
258C22⋊C4×C61—22no—
259C22⋊C4×C61—22no—
260C22⋊C4×C61—24no—
261C42×C61—21no—
262C42×C61—21no—
263C22⋊Dic61—42no—
264C22⋊Dic61—42no—
265C22⋊Dic61—42no—
266C22⋊Dic61—42no—
267#11758202—44no—
268#11758200—44no—
269#11758200—44no—
270C4⋊Dic61—21no—
271C4⋊Dic61—21no—
272C4⋊Dic61—21no—
273C4⋊Dic61—21no—
274C4⋊Dic61—21no—
275C4⋊Dic61C2×D412yes—
276#11758196—42no—
277#11758196—42no—
278#11758196—42no—
279C4×Dic61—42no—
280C2×#92418—21no—
281C2×#92418—21no—
282C2×#92418—21no—
283C2×#92418—21no—
284C2×#92418—21no—
285C2×#92418—21no—
286C2×#92418—21no—
287C2×#92418—21no—
288C2×#92418—21no—
289C2×#92418—21no—
290C2×#92418—21no—
291C2×#92418—44no—
292C2×#92418C2×D412yes—
293C23×C61—21no—
294C23×C61—22no—
295C23×C61—21no—
296C23×C61—21no—
297C23×C61—22no—
298C23×C61—21no—
299C23×C61—21no—
300C23×C61—22no—
301C23×C61—21no—
302C23×C61—21no—
303C23×C61—21no—
304C23×C61—21no—
305C23×C61—21no—
306C23×C61—21no—
307C23×C61—21no—
308C23×C61—22no—
309C23×C61—48no—
310C23×C61—48no—
311C23×C61—41no—
312C23×C61—41no—
313C23×C61—41no—
314C23×C61—41no—
315C23×C61—41no—
316C23×C61—41no—
317C23×C61—41no—
318C23×C61—41no—
319C23×C61—41no—
320C23×C61—41no—
321C23×C61—84no—
322C23×C61—84no—
323C23×C61—84no—
324C23×C61—84no—
325C23×C61—84no—
326C23×C61#12012yes—
327C23×C61#13512yes—
328C23×C61C22×D411yescharacteristic
329Q8×C61—22no—
330Q8×C61—22no—
331Q8×C61—41no—
332Q8×C61—41no—
333D4×C61—22no—
334D4×C61—22no—
335D4×C61—22no—
336D4×C61—22no—
337D4×C61—22no—
338D4×C61—44no—
339D4×C61—48no—
340D4×C61—48no—
341D4×C61—41no—
342D4×C61—41no—
343D4×C61—84no—
344D4×C61#12114yes—
345C2×C4×C61—21no—
346C2×C4×C61—21no—
347C2×C4×C61—22no—
348C2×C4×C61—22no—
349C2×C4×C61—22no—
350C2×C4×C61—22no—
351C2×C4×C61—21no—
352C2×C4×C61—21no—
353C2×C4×C61—22no—
354C2×C4×C61—22no—
355C2×C4×C61—21no—
356C2×C4×C61—21no—
357C2×C4×C61—21no—
358C2×C4×C61—21no—
359C2×C4×C61—21no—
360C2×C4×C61—21no—
361C2×C4×C61—21no—
362C2×C4×C61—48no—
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—41no—
370C2×C4×C61—41no—
371C2×C4×C61—84no—
372C2×C4×C61#12012yes—
373C2×C4×C61C22×D411yescharacteristic
374C2×C4×C61C22×D411yescharacteristic
375C2×C4×C61C22×D411yescharacteristic
376C2×C4×C61C2×#4111yescharacteristic
377C2×C4×C61H(5,𝔽2)11yescharacteristic
378C2×C4×C61H(5,𝔽2)11yescharacteristic
379C2×Dic61—22no—
380C2×Dic61—41no—
381C2×Dic61—41no—
382C2×Dic61—41no—
383C2×Dic61—41no—
384C2×Dic61—41no—
385C2×Dic61—41no—
386C2×Dic61—41no—
387C2×Dic61—41no—
388C2×Dic61—41no—
389C2×Dic61—41no—
390C2×Dic61—41no—
391Dic122—41no—
392Dic122—41no—
393Dic122—41no—
394Dic122—41no—
395#92418—22no—
396#92418—41no—
397#92418—41no—
398#92418—41no—
399#24436—611nomaximal, Sylow
400C22×C61—22no—
401C22×C61—24no—
402C22×C61—22no—
403C22×C61—22no—
404C22×C61—22no—
405C22×C61—22no—
406C22×C61—22no—
407C22×C61—41no—
408C22×C61—42no—
409C22×C61—42no—
410C22×C61—41no—
411C22×C61—41no—
412C22×C61—41no—
413C22×C61—42no—
414C22×C61—41no—
415C22×C61—42no—
416C22×C61—41no—
417C22×C61—42no—
418C22×C61—41no—
419C22×C61—41no—
420C22×C61—42no—
421C22×C61—42no—
422C22×C61—42no—
423C22×C61—42no—
424C22×C61—816no—
425C22×C61—81no—
426C22×C61—81no—
427C22×C61—81no—
428C22×C61—81no—
429C22×C61C2×#12011yescharacteristic
430C22×C61D4211yescharacteristic
431C22×C61#54611yescharacteristic
432C22×C61C2×#13511yescharacteristic
433C22×C61#57511yescharacteristic
434C22×C61#57711yescharacteristic
435C22×C61#57711yescharacteristic
436C4×C61—22no—
437C4×C61—41no—
438C4×C61—42no—
439C4×C61—41no—
440C4×C61—41no—
441C4×C61—42no—
442C4×C61C2×#12111yescharacteristic
443C4×C61#53411yescharacteristic
444C4×C61D4211yescharacteristic
445C4×C61#54611yescharacteristic
446Dic61—42no—
447Dic61—81no—
448Dic61—81no—
449Dic61—81no—
450C2×#546D6111yescharacteristic
451C2×#465—611no—
452C2×#452—611no—
453C2×#450—611no—
454C2×#416—611no—
455#2415—611no—
456#2042—611no—
457#2035—611no—
458#2015—611no—
459#2001—611no—
460#1877—611no—
461#1875—611no—
462#1869—611no—
463#1864—611no—
464#1786—611no—
465C2×C61—42no—
466C2×C61—42no—
467C2×C61—44no—
468C2×C61—82no—
469C2×C61#241011yescharacteristic
470C2×C61#300211yescharacteristic
471C2×C61#300911yescharacteristic
472C2×C61#326711yescharacteristic
473C2×C61#328211yescharacteristic
474C2×C61#329611yescharacteristic
475C2×C61#331111yescharacteristic
476C22×#41C2×D6111yescharacteristic
477C23×D4C2×D6111yescharacteristic
478C22×Q16—611no—
479C22×SD16—611no—
480C22×SD16—611no—
481C23×C8—611no—
482#546—24no—
483#546—24no—
484C2×#124C2×D6111yescharacteristic
485C2×#123—21no—
486C2×C22⋊Q8—611no—
487C2×C22⋊Q8—611no—
488C2×C22⋊Q8C2×D6111yescharacteristic
489C2×#121—21no—
490C2×#121C2×D6111yescharacteristic
491C2×#120—21no—
492C2×C4×D4C2×D6111yescharacteristic
493C2×C4×D4C2×D6111yescharacteristic
494C2×#117—611no—
495C22×C22⋊C4—21no—
496#465—1224no—
497#452—1224no—
498#450—1224no—
499C2×#106—611no—
500#416—1224no—
501C2×#103—611no—
502C2×#103—611no—
503C2×#103—611no—
504C2×#103—611no—
505C2×#102—611no—
506C2×#102—611no—
507C2×#102—611no—
508C2×#102—611no—
509C2×#102—611no—
510C2×#102—611no—
511C2×C22⋊C8—611no—
512C2×C22⋊C8—611no—
513C2×C22⋊C8—611no—
514#397—1221no—
515#394—1221no—
516#391—611no—
517#389—611no—
518#389—1221no—
519#388—1221no—
520#380—611no—
521#340—611no—
522#340—611no—
523#336—611no—
524#336—611no—
525C61#2443611yescharacteristic, complemented, Sylow
526C25—21no—
527C2×#41—22no—
528C2×#41—22no—
529C2×#41—22no—
530C2×#41—41no—
531C2×#41—41no—
532C2×#41C22⋊D6114yes—
533C22×Q8—611no—
534C22×Q8C22×D6111yescharacteristic
535C22×D4—21no—
536C22×D4—21no—
537C22×D4—22no—
538C22×D4—22no—
539C22×D4—22no—
540C22×D4—22no—
541C22×D4—21no—
542C22×D4—41no—
543C22×D4—41no—
544C22×D4C22⋊D6111yescharacteristic
545C22×D4C22×D6111yescharacteristic
546C22×D4C22×D6111yescharacteristic
547C23×C4—21no—
548C23×C4—21no—
549C23×C4C22×D6111yescharacteristic
550C23×C4C22×D6111yescharacteristic
551C2×Q16—1222no—
552C2×Q16—2441no—
553C2×Q16—2441no—
554C2×SD16—1222no—
555C2×SD16—1222no—
556C2×SD16—1222no—
557C2×SD16—1222no—
558C2×SD16—1222no—
559C2×SD16—2441no—
560C22×C8—611no—
561C22×C8—611no—
562C22×C8—611no—
563C22×C8—611no—
564C22×C8—1222no—
565C22×C8—1222no—
566C22×C8—2441no—
567#124—22no—
568#124—22no—
569#123—28no—
570C22⋊Q8—22no—
571C22⋊Q8—22no—
572C22⋊Q8—1222no—
573C22⋊Q8—1222no—
574C22⋊Q8—1222no—
575C22⋊Q8—2441no—
576#121—28no—
577#121—22no—
578#121C22⋊D6114yes—
579#120—28no—
580C4×D4—22no—
581C4×D4—22no—
582C4×D4—22no—
583C4×D4—22no—
584#117—1222no—
585#117—2441no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—611no—
588C2×C4⋊C4—611no—
589C2×C4⋊C4—611no—
590C2×C4⋊C4—1221no—
591C2×C4⋊C4—1221no—
592C2×C4⋊C4—1221no—
593C2×C4⋊C4C22⋊D6111yescharacteristic
594C2×C4⋊C4C22×D6111yescharacteristic
595C2×C22⋊C4—28no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—1221no—
602C2×C22⋊C4—1221no—
603C2×C22⋊C4—1221no—
604C2×C22⋊C4—1221no—
605C2×C22⋊C4C22⋊D6111yescharacteristic
606C2×C22⋊C4C22⋊D6111yescharacteristic
607C2×C42—1221no—
608C2×C42C22×D6111yescharacteristic
609#106—1222no—
610#103—1222no—
611#103—1222no—
612#103—1222no—
613#103—1222no—
614#102—614no—
615#102—1222no—
616#102—1222no—
617#102—1222no—
618#102—1222no—
619#102—2441no—
620C22⋊C8—1222no—
621C22⋊C8—1222no—
622C22⋊C8—2441no—
623#95—1221no—
624#95—1221no—
625#95—1221no—
626#95—1221no—
627C24—21no—
628C24—24no—
629C24—21no—
630C24—42no—
631C24—42no—
632C24—42no—
633C24—42no—
634C24—81no—
635C24—81no—
636C24C2×C22⋊D6111yescharacteristic
637C24C2×C22⋊D6111yescharacteristic
638#41—28no—
639#41—44no—
640#41—44no—
641#41—44no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8—21no—
645C2×Q8—21no—
646C2×Q8—21no—
647C2×Q8—1221no—
648C2×Q8—1221no—
649C2×Q8—1221no—
650C2×Q8—1221no—
651C2×Q8—1221no—
652C2×Q8—1221no—
653C2×Q8C2×C22⋊D6112yes—
654C2×D4—24no—
655C2×D4—22no—
656C2×D4—24no—
657C2×D4—22no—
658C2×D4—24no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—41no—
668C2×D4—42no—
669C2×D4—42no—
670C2×D4—44no—
671C2×D4—44no—
672C2×D4—44no—
673C2×D4—42no—
674C2×D4—42no—
675C2×D4—44no—
676C2×D4—81no—
677C2×D4—81no—
678C2×D4D4×D6112yes—
679C2×D4#1175822412yes—
680C2×D4C2×C22⋊D6112yes—
681C2×D4C2×C22⋊D6112yes—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—24no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—24no—
696C22×C4—42no—
697C22×C4—42no—
698C22×C4—81no—
699C22×C4—81no—
700C22×C4—1221no—
701C22×C4—1221no—
702C22×C4—1221no—
703C22×C4—1221no—
704C22×C4C2×C22⋊D6111yescharacteristic
705C22×C4C2×C22⋊D6111yescharacteristic
706C22×C4C2×C22⋊D6111yescharacteristic
707C22×C4C2×C22⋊D6112yes—
708C22×C4C2×C22⋊D6112yes—
709C22×C4C2×C22⋊D6111yescharacteristic
710C22×C4C23×D6111yescharacteristic
711Q16—2444no—
712SD16—2444no—
713SD16—2444no—
714C2×C8—612no—
715C2×C8—1221no—
716C2×C8—1221no—
717C2×C8—1221no—
718C2×C8—1221no—
719C2×C8—1221no—
720C2×C8—1221no—
721C2×C8—1221no—
722C2×C8—1221no—
723C2×C8—1221no—
724C2×C8—1221no—
725C2×C8—1221no—
726C2×C8—2444no—
727C4⋊C4—24no—
728C4⋊C4—21no—
729C4⋊C4—22no—
730C4⋊C4—612no—
731C4⋊C4—1221no—
732C4⋊C4—1221no—
733C4⋊C4—1221no—
734C4⋊C4—1221no—
735C4⋊C4—1221no—
736C4⋊C4—2442no—
737C4⋊C4—2442no—
738C4⋊C4—2442no—
739C4⋊C4C2×C22⋊D6112yes—
740C22⋊C4—24no—
741C22⋊C4—24no—
742C22⋊C4—24no—
743C22⋊C4—24no—
744C22⋊C4—22no—
745C22⋊C4—22no—
746C22⋊C4—24no—
747C22⋊C4—2442no—
748C22⋊C4—2442no—
749C22⋊C4—2442no—
750C22⋊C4—2442no—
751C42—21no—
752C42—21no—
753C42—2442no—
754C23—21no—
755C23—22no—
756C23—21no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—22no—
766C23—21no—
767C23—21no—
768C23—22no—
769C23—22no—
770C23—48no—
771C23—48no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—84no—
783C23—84no—
784C23—84no—
785C23—84no—
786C23—84no—
787C23#1451974612yes—
788C23#1451979712yes—
789C23C22×C22⋊D6111yescharacteristic
790Q8—22no—
791Q8—22no—
792Q8—41no—
793Q8—41no—
794Q8—2441no—
795Q8—2441no—
796Q8—2441no—
797Q8—2441no—
798D4—22no—
799D4—22no—
800D4—22no—
801D4—22no—
802D4—22no—
803D4—44no—
804D4—48no—
805D4—48no—
806D4—41no—
807D4—41no—
808D4—84no—
809D4#1451974914yes—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—48no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—84no—
837C2×C4—1222no—
838C2×C4—2441no—
839C2×C4—2441no—
840C2×C4—2441no—
841C2×C4—2441no—
842C2×C4—2441no—
843C2×C4—2441no—
844C2×C4—2441no—
845C2×C4—2441no—
846C2×C4—2441no—
847C2×C4—2441no—
848C2×C4—2441no—
849C2×C4#1451974612yes—
850C2×C4C2×D4×D6111yescharacteristic
851C2×C4C22×C22⋊D6111yescharacteristic
852C2×C4C22×C22⋊D6111yescharacteristic
853C2×C4C2×#1175822411yescharacteristic
854C2×C4#1451982211yescharacteristic
855C2×C4#1451982211yescharacteristic
856C8—1222no—
857C8—2441no—
858C8—2441no—
859C8—2441no—
860C22—22no—
861C22—22no—
862C22—22no—
863C22—22no—
864C22—24no—
865C22—22no—
866C22—22no—
867C22—41no—
868C22—42no—
869C22—41no—
870C22—41no—
871C22—42no—
872C22—42no—
873C22—41no—
874C22—41no—
875C22—42no—
876C22—41no—
877C22—41no—
878C22—42no—
879C22—42no—
880C22—41no—
881C22—42no—
882C22—42no—
883C22—42no—
884C22—816no—
885C22—81no—
886C22—81no—
887C22—81no—
888C22—81no—
889C22C2×#1451974611yescharacteristic
890C22D4×C22⋊D6111yescharacteristic
891C22#1684040611yescharacteristic
892C22C2×#1451979711yescharacteristic
893C22#1684056011yescharacteristic
894C22#1684057311yescharacteristic
895C22#1684057311yescharacteristic
896C4—22no—
897C4—41no—
898C4—41no—
899C4—42no—
900C4—41no—
901C4—42no—
902C4—4881no—
903C4—4881no—
904C4—4881no—
905C4—2442no—
906C4C2×#1451974911yescharacteristic
907C4#1684032111yescharacteristic
908C4D4×C22⋊D6111yescharacteristic
909C4#1684040611yescharacteristic
910C2—42no—
911C2—42no—
912C2—44no—
913C2—82no—
914C2#2144919311yescharacteristic
915C2#2145503711yescharacteristic
916C2#2145509611yescharacteristic
917C2#2145734011yescharacteristic
918C2#2145752211yescharacteristic
919C2#2145765411yescharacteristic
920C2#2145785511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
Fitting, prime radicalC2×C61×#546C2
socleC23×C61C22×D4
hypercenterC2×#546D61
hypocenterC61#24436
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#546

Complements

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

NH ≅ G/Ntype
1. C2×#16839989C2semidirect
2. C2×#16839924C2semidirect
3. C2×#16839913C2semidirect
4. C2×#16839758C2semidirect
5. #21449248C2semidirect
6. #21447055C2semidirect
7. #21447012C2semidirect
8. #21446913C2semidirect
9. #21446827C2semidirect
10. #21446153C2semidirect
11. #21446142C2semidirect
12. #21446112C2semidirect
13. #21446080C2semidirect
14. #21445750C2semidirect
16. C22×#11758202C22semidirect
19. C23×#92418C22semidirect
21. C2×#14519756C22semidirect
22. C2×#14519736C22semidirect
26. C2×#14519708C22semidirect
28. C2×#14519701C22semidirect
29. C2×#14519701C22semidirect
30. C2×#14519701C22semidirect
31. C2×#14519700C22semidirect
40. C2×C22⋊#92418C22semidirect
43. #16839668C22semidirect
44. #16839660C22semidirect
48. #16839524C22semidirect
49. #16839524C22semidirect
50. #16839517C22semidirect
51. #16839517C22semidirect
109. #14519698D4semidirect
525. C61#24436semidirect

Maximal subgroups

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

subgroupindex
C2×#168399892
C2×#168399242
C2×#168399132
C2×#168397582
#214492482
#214470552
#214470122
#214469132
#214468272
#214461532
#214461422
#214461122
#214460802
#214457502
C2×C61×#5462
#2443661