Finite Group Databasebeta

← #29717619

Subgroups — #29717619

Order 15616.

1500 conjugacy classes of subgroups.

The subgroup lattice has 912 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×#16839924C211yesmaximal, characteristic, complemented
4C2×#16839758C211yesmaximal, characteristic, complemented
5#21449248C211yesmaximal, characteristic, complemented
6#21447050C211yesmaximal, characteristic, complemented
7#21447005C211yesmaximal, characteristic, complemented
8#21446907C211yesmaximal, characteristic, complemented
9#21446822C211yesmaximal, characteristic, complemented
10#21446160C211yesmaximal, characteristic, complemented
11#21446142C211yesmaximal, characteristic, complemented
12#21446112C211yesmaximal, characteristic, complemented
13#21446087C211yesmaximal, characteristic, complemented
14#21445759C211yesmaximal, characteristic, complemented
15C2×C61×#550C211yesmaximal, characteristic
16C22×#11758202C2211yescharacteristic
17C22×#11758200C2211yescharacteristic
18C22×#11758200C2211yescharacteristic
19C23×#92418C2211yescharacteristic
20C2×#14519756C2211yescharacteristic
21C2×#14519756C2211yescharacteristic
22C2×#14519736C2211yescharacteristic
23#16839989—24no—
24#16839924—24no—
25#16839924—24no—
26C2×#14519708C2211yescharacteristic
27#16839758—24no—
28C2×#14519701C2211yescharacteristic
29C2×#14519701C2211yescharacteristic
30C2×#14519701C2211yescharacteristic
31C2×#14519700C2211yescharacteristic
32C2×#14519698C2211yescharacteristic
33C2×#14519698C2211yescharacteristic
34C2×#14519698C2211yescharacteristic
35C2×#14519698C2211yescharacteristic
36C2×#14519698C2211yescharacteristic
37C2×#14519698C2211yescharacteristic
38C2×C22⋊#92418C2211yescharacteristic
39C2×C22⋊#92418C2211yescharacteristic
40C2×C22⋊#92418C2211yescharacteristic
41#16839690—21no—
42#16839676—21no—
43#16839668C2211yescharacteristic
44#16839660C2211yescharacteristic
45#16839657—21no—
46#16839656—21no—
47#16839622C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839517C2211yescharacteristic
51#16839517C2211yescharacteristic
52C22×#41×C61C2211yescharacteristic
53C22×#41×C61C2211yescharacteristic
54C61×#550—24no—
55C61×#550—24no—
56C2×#127×C61—21no—
57C2×#127×C61C2211yescharacteristic
58C2×#121×C61—21no—
59C2×#121×C61—21no—
60C2×#121×C61C2211yescharacteristic
61C2×#121×C61C2211yescharacteristic
62C2×C4×Q8×C61C2211yescharacteristic
63C2×C4×D4×C61—21no—
64C2×C4×D4×C61C2211yescharacteristic
65C22×Dic122C2311yescharacteristic
66C2×#11758202—22no—
67C2×#11758202—22no—
68C2×#11758202—22no—
69C2×#11758200—22no—
70C2×#11758200—22no—
71C2×#11758200—22no—
72C2×#11758200—41no—
73C2×#11758200—41no—
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#14519701D414yescomplemented
103#14519700—22no—
104#14519698—22no—
105#14519698—22no—
106#14519698—22no—
107#14519698—22no—
108#14519698—22no—
109#14519698—41no—
110C22⋊#92418—22no—
111C22⋊#92418—22no—
112C22⋊#92418—41no—
113#14519684—21no—
114#14519684—21no—
115#14519684—21no—
116#14519684—21no—
117C2×#41×C61—22no—
118C2×#41×C61—22no—
119C2×#41×C61—22no—
120C2×#41×C61—22no—
121C2×#41×C61—22no—
122C2×#41×C61—22no—
123C2×#41×C61—22no—
124C2×#41×C61—41no—
125C2×#41×C61—41no—
126C2×#41×C61—41no—
127C2×#41×C61—41no—
128C2×#41×C61D414yes—
129C22×Q8×C61C2311yescharacteristic
130C22×D4×C61—21no—
131C22×D4×C61—21no—
132C22×D4×C61—21no—
133C22×D4×C61—21no—
134C22×D4×C61—21no—
135C22×D4×C61—21no—
136C22×D4×C61D411yescharacteristic
137C22×D4×C61C2311yescharacteristic
138C22×D4×C61C2311yescharacteristic
139C23×C4×C61—21no—
140C23×C4×C61—21no—
141C23×C4×C61C2311yescharacteristic
142C23×C4×C61C2311yescharacteristic
143#127×C61—28no—
144#127×C61—22no—
145#127×C61—22no—
146#121×C61—28no—
147#121×C61—28no—
148#121×C61—22no—
149#121×C61—22no—
150#121×C61—22no—
151#121×C61D414yes—
152C4×Q8×C61—22no—
153C4×Q8×C61—22no—
154C4×D4×C61—28no—
155C4×D4×C61—22no—
156C4×D4×C61—22no—
157C2×C4⋊C4×C61—21no—
158C2×C4⋊C4×C61D411yescharacteristic
159C2×C4⋊C4×C61C2311yescharacteristic
160C2×C22⋊C4×C61—21no—
161C2×C22⋊C4×C61—21no—
162C2×C22⋊C4×C61D411yescharacteristic
163C2×C22⋊C4×C61D411yescharacteristic
164C2×C42×C61—21no—
165C2×C42×C61C2311yescharacteristic
166C24×C61—21no—
167C24×C61—21no—
168C24×C61C2×D411yescharacteristic
169C24×C61C2×D411yescharacteristic
170#41×C61—28no—
171#41×C61—44no—
172#41×C61—44no—
173#41×C61—44no—
174#41×C61—44no—
175#41×C61—44no—
176#41×C61—44no—
177#41×C61—44no—
178C2×Q8×C61—21no—
179C2×Q8×C61—21no—
180C2×Q8×C61—21no—
181C2×Q8×C61C2×D412yes—
182C2×Q8×C61C2×D412yes—
183C2×Q8×C61#4112yes—
184C2×D4×C61—24no—
185C2×D4×C61—24no—
186C2×D4×C61—22no—
187C2×D4×C61—24no—
188C2×D4×C61—24no—
189C2×D4×C61—24no—
190C2×D4×C61—24no—
191C2×D4×C61—22no—
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—21no—
201C2×D4×C61—21no—
202C2×D4×C61—41no—
203C2×D4×C61—42no—
204C2×D4×C61—42no—
205C2×D4×C61—42no—
206C2×D4×C61—42no—
207C2×D4×C61—42no—
208C2×D4×C61—42no—
209C2×D4×C61—81no—
210C2×D4×C61—81no—
211C2×D4×C61—81no—
212C2×D4×C61—81no—
213C2×D4×C61—81no—
214C2×D4×C61—81no—
215C2×D4×C61C2×D412yes—
216C2×D4×C61C2×D412yes—
217C22×C4×C61—21no—
218C22×C4×C61—21no—
219C22×C4×C61—21no—
220C22×C4×C61—21no—
221C22×C4×C61—21no—
222C22×C4×C61—24no—
223C22×C4×C61—21no—
224C22×C4×C61—24no—
225C22×C4×C61—21no—
226C22×C4×C61—21no—
227C22×C4×C61—21no—
228C22×C4×C61—21no—
229C22×C4×C61—21no—
230C22×C4×C61—21no—
231C22×C4×C61—42no—
232C22×C4×C61—42no—
233C22×C4×C61—42no—
234C22×C4×C61—42no—
235C22×C4×C61C2×D411yescharacteristic
236C22×C4×C61C2×D411yescharacteristic
237C22×C4×C61C2×D411yescharacteristic
238C22×C4×C61C2×D412yes—
239C22×C4×C61C2×D412yes—
240C22×C4×C61C2×D411yescharacteristic
241C22×C4×C61C2411yescharacteristic
242C22×Dic61—21no—
243C22×Dic61—21no—
244C22×Dic61—21no—
245C22×Dic61—21no—
246C2×Dic122—21no—
247C2×Dic122—21no—
248C2×Dic122—21no—
249C2×Dic122—21no—
250C2×Dic122—21no—
251C2×Dic122—21no—
252C4⋊C4×C61—24no—
253C4⋊C4×C61—22no—
254C4⋊C4×C61—21no—
255C4⋊C4×C61C2×D412yes—
256C22⋊C4×C61—24no—
257C22⋊C4×C61—22no—
258C22⋊C4×C61—24no—
259C22⋊C4×C61—22no—
260C42×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—21no—
295C23×C61—21no—
296C23×C61—21no—
297C23×C61—21no—
298C23×C61—21no—
299C23×C61—21no—
300C23×C61—22no—
301C23×C61—22no—
302C23×C61—21no—
303C23×C61—21no—
304C23×C61—21no—
305C23×C61—21no—
306C23×C61—21no—
307C23×C61—21no—
308C23×C61—41no—
309C23×C61—41no—
310C23×C61—41no—
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#12012yes—
321C23×C61C22×D411yescharacteristic
322Q8×C61—22no—
323Q8×C61—22no—
324Q8×C61—22no—
325Q8×C61#12114yes—
326D4×C61—22no—
327D4×C61—22no—
328D4×C61—22no—
329D4×C61—22no—
330D4×C61—44no—
331D4×C61—48no—
332D4×C61—48no—
333D4×C61—48no—
334D4×C61—41no—
335D4×C61—41no—
336D4×C61—41no—
337D4×C61—41no—
338D4×C61—84no—
339D4×C61—84no—
340D4×C61—84no—
341C2×C4×C61—21no—
342C2×C4×C61—22no—
343C2×C4×C61—21no—
344C2×C4×C61—22no—
345C2×C4×C61—21no—
346C2×C4×C61—22no—
347C2×C4×C61—21no—
348C2×C4×C61—22no—
349C2×C4×C61—22no—
350C2×C4×C61—22no—
351C2×C4×C61—22no—
352C2×C4×C61—21no—
353C2×C4×C61—22no—
354C2×C4×C61—21no—
355C2×C4×C61—21no—
356C2×C4×C61—21no—
357C2×C4×C61—21no—
358C2×C4×C61—21no—
359C2×C4×C61—48no—
360C2×C4×C61—48no—
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#12012yes—
368C2×C4×C61#13512yes—
369C2×C4×C61C22×D411yescharacteristic
370C2×C4×C61C22×D411yescharacteristic
371C2×C4×C61C22×D411yescharacteristic
372C2×C4×C61C2×#4111yescharacteristic
373C2×C4×C61H(5,𝔽2)11yescharacteristic
374C2×C4×C61H(5,𝔽2)11yescharacteristic
375C2×Dic61—22no—
376C2×Dic61—41no—
377C2×Dic61—41no—
378C2×Dic61—41no—
379C2×Dic61—41no—
380C2×Dic61—41no—
381C2×Dic61—41no—
382C2×Dic61—41no—
383C2×Dic61—41no—
384C2×Dic61—41no—
385C2×Dic61—41no—
386C2×Dic61—41no—
387Dic122—41no—
388Dic122—41no—
389Dic122—41no—
390Dic122—41no—
391#92418—22no—
392#92418—41no—
393#92418—41no—
394#92418—41no—
395#24427—611nomaximal, Sylow
396C22×C61—22no—
397C22×C61—22no—
398C22×C61—22no—
399C22×C61—41no—
400C22×C61—41no—
401C22×C61—41no—
402C22×C61—41no—
403C22×C61—42no—
404C22×C61—42no—
405C22×C61—41no—
406C22×C61—41no—
407C22×C61—42no—
408C22×C61—42no—
409C22×C61—41no—
410C22×C61—42no—
411C22×C61—42no—
412C22×C61—41no—
413C22×C61—41no—
414C22×C61—41no—
415C22×C61—41no—
416C22×C61—81no—
417C22×C61—81no—
418C22×C61—81no—
419C22×C61—81no—
420C22×C61—81no—
421C22×C61—81no—
422C22×C61—81no—
423C22×C61—81no—
424C22×C61C2×#12011yescharacteristic
425C22×C61D4211yescharacteristic
426C22×C61#54611yescharacteristic
427C22×C61C2×#13511yescharacteristic
428C22×C61#57511yescharacteristic
429C22×C61#57711yescharacteristic
430C22×C61#57711yescharacteristic
431C4×C61—22no—
432C4×C61—24no—
433C4×C61—22no—
434C4×C61—41no—
435C4×C61—41no—
436C4×C61—42no—
437C4×C61C2×#12111yescharacteristic
438C4×C61#53411yescharacteristic
439C4×C61D4211yescharacteristic
440C4×C61#54611yescharacteristic
441Dic61—42no—
442Dic61—81no—
443Dic61—81no—
444Dic61—81no—
445C2×#550D6111yescharacteristic
446C2×#465—611no—
447C2×#452—611no—
448C2×#452—611no—
449C2×#416—611no—
450#2415—611no—
451#2041—611no—
452#2034—611no—
453#2014—611no—
454#2000—611no—
455#1878—611no—
456#1875—611no—
457#1869—611no—
458#1865—611no—
459#1788—611no—
460C2×C61—42no—
461C2×C61—81no—
462C2×C61—82no—
463C2×C61—82no—
464C2×C61#241011yescharacteristic
465C2×C61#300211yescharacteristic
466C2×C61#300911yescharacteristic
467C2×C61#327111yescharacteristic
468C2×C61#328411yescharacteristic
469C2×C61#330411yescharacteristic
470C2×C61#331711yescharacteristic
471C22×#41C2×D6111yescharacteristic
472C22×#41C2×D6111yescharacteristic
473C22×Q16—611no—
474C22×SD16—611no—
475C22×SD16—611no—
476C23×C8—611no—
477#550—24no—
478#550—24no—
479C2×#127—21no—
480C2×#127C2×D6111yescharacteristic
481C2×C22⋊Q8—611no—
482C2×C22⋊Q8—611no—
483C2×#121—21no—
484C2×#121—21no—
485C2×#121C2×D6111yescharacteristic
486C2×#121C2×D6111yescharacteristic
487C2×C4×Q8C2×D6111yescharacteristic
488C2×C4×D4—21no—
489C2×C4×D4C2×D6111yescharacteristic
490C2×#117—611no—
491#465—1224no—
492#452—1224no—
493#452—1224no—
494C2×#106—611no—
495#416—1224no—
496C2×#103—611no—
497C2×#103—611no—
498C2×#103—611no—
499C2×#103—611no—
500C2×#102—611no—
501C2×#102—611no—
502C2×#102—611no—
503C2×#102—611no—
504C2×#102—611no—
505C2×#102—611no—
506C2×C22⋊C8—611no—
507C2×C22⋊C8—611no—
508C2×C22⋊C8—611no—
509#397—1221no—
510#394—1221no—
511#391—611no—
512#389—611no—
513#389—1221no—
514#388—1221no—
515#380—611no—
516#340—611no—
517#340—611no—
518#336—611no—
519#336—611no—
520C61#2442711yescharacteristic, complemented, Sylow
521C2×#41—22no—
522C2×#41—22no—
523C2×#41—22no—
524C2×#41—22no—
525C2×#41—22no—
526C2×#41—22no—
527C2×#41—22no—
528C2×#41—41no—
529C2×#41—41no—
530C2×#41—41no—
531C2×#41—41no—
532C2×#41C22⋊D6114yes—
533C22×Q8—611no—
534C22×Q8C22×D6111yescharacteristic
535C22×D4—21no—
536C22×D4—21no—
537C22×D4—21no—
538C22×D4—21no—
539C22×D4—21no—
540C22×D4—21no—
541C22×D4C22⋊D6111yescharacteristic
542C22×D4C22×D6111yescharacteristic
543C22×D4C22×D6111yescharacteristic
544C23×C4—21no—
545C23×C4—21no—
546C23×C4C22×D6111yescharacteristic
547C23×C4C22×D6111yescharacteristic
548C2×Q16—1222no—
549C2×Q16—1222no—
550C2×Q16—1222no—
551C2×SD16—1222no—
552C2×SD16—1222no—
553C2×SD16—1222no—
554C2×SD16—2441no—
555C2×SD16—2441no—
556C2×SD16—2441no—
557C22×C8—611no—
558C22×C8—611no—
559C22×C8—611no—
560C22×C8—611no—
561C22×C8—1222no—
562C22×C8—1222no—
563C22×C8—2441no—
564#127—28no—
565#127—22no—
566#127—22no—
567C22⋊Q8—1222no—
568C22⋊Q8—1222no—
569C22⋊Q8—1222no—
570C22⋊Q8—2441no—
571#121—28no—
572#121—28no—
573#121—22no—
574#121—22no—
575#121—22no—
576#121C22⋊D6114yes—
577C4×Q8—22no—
578C4×Q8—22no—
579C4×D4—28no—
580C4×D4—22no—
581C4×D4—22no—
582#117—1222no—
583#117—2441no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—611no—
586C2×C4⋊C4—611no—
587C2×C4⋊C4—611no—
588C2×C4⋊C4—1221no—
589C2×C4⋊C4—1221no—
590C2×C4⋊C4—1221no—
591C2×C4⋊C4C22⋊D6111yescharacteristic
592C2×C4⋊C4C22×D6111yescharacteristic
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—1221no—
596C2×C22⋊C4—1221no—
597C2×C22⋊C4—1221no—
598C2×C22⋊C4—1221no—
599C2×C22⋊C4C22⋊D6111yescharacteristic
600C2×C22⋊C4C22⋊D6111yescharacteristic
601C2×C42—21no—
602C2×C42—1221no—
603C2×C42C22×D6111yescharacteristic
604#106—1222no—
605#103—614no—
606#103—1222no—
607#103—1222no—
608#103—1222no—
609#102—1222no—
610#102—1222no—
611#102—1222no—
612#102—1222no—
613#102—1222no—
614#102—2441no—
615C22⋊C8—1222no—
616C22⋊C8—1222no—
617C22⋊C8—2441no—
618#95—1221no—
619#95—1221no—
620#95—1221no—
621#95—1221no—
622C24—21no—
623C24—21no—
624C24C2×C22⋊D6111yescharacteristic
625C24C2×C22⋊D6111yescharacteristic
626#41—28no—
627#41—44no—
628#41—44no—
629#41—44no—
630#41—44no—
631#41—44no—
632#41—44no—
633#41—44no—
634C2×Q8—21no—
635C2×Q8—21no—
636C2×Q8—21no—
637C2×Q8—1221no—
638C2×Q8—1221no—
639C2×Q8—1221no—
640C2×Q8—1221no—
641C2×Q8—1221no—
642C2×Q8—1221no—
643C2×Q8D4×D6112yes—
644C2×Q8#1175822412yes—
645C2×Q8C2×C22⋊D6112yes—
646C2×D4—24no—
647C2×D4—24no—
648C2×D4—22no—
649C2×D4—24no—
650C2×D4—24no—
651C2×D4—24no—
652C2×D4—24no—
653C2×D4—21no—
654C2×D4—21no—
655C2×D4—21no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—22no—
664C2×D4—41no—
665C2×D4—42no—
666C2×D4—42no—
667C2×D4—42no—
668C2×D4—42no—
669C2×D4—42no—
670C2×D4—42no—
671C2×D4—81no—
672C2×D4—81no—
673C2×D4—81no—
674C2×D4—81no—
675C2×D4—81no—
676C2×D4—81no—
677C2×D4C2×C22⋊D6112yes—
678C2×D4C2×C22⋊D6112yes—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—24no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—24no—
693C22×C4—42no—
694C22×C4—42no—
695C22×C4—42no—
696C22×C4—42no—
697C22×C4—1221no—
698C22×C4—1221no—
699C22×C4—1221no—
700C22×C4—1221no—
701C22×C4C2×C22⋊D6111yescharacteristic
702C22×C4C2×C22⋊D6111yescharacteristic
703C22×C4C2×C22⋊D6112yes—
704C22×C4C2×C22⋊D6112yes—
705C22×C4C2×C22⋊D6111yescharacteristic
706C22×C4C2×C22⋊D6111yescharacteristic
707C22×C4C23×D6111yescharacteristic
708Q16—2444no—
709SD16—2444no—
710SD16—2444no—
711C2×C8—612no—
712C2×C8—1221no—
713C2×C8—1221no—
714C2×C8—1221no—
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—2444no—
724C4⋊C4—24no—
725C4⋊C4—21no—
726C4⋊C4—22no—
727C4⋊C4—612no—
728C4⋊C4—1221no—
729C4⋊C4—1221no—
730C4⋊C4—1221no—
731C4⋊C4—1221no—
732C4⋊C4—1221no—
733C4⋊C4—2442no—
734C4⋊C4—2442no—
735C4⋊C4—2442no—
736C4⋊C4C2×C22⋊D6112yes—
737C22⋊C4—24no—
738C22⋊C4—22no—
739C22⋊C4—24no—
740C22⋊C4—22no—
741C22⋊C4—2442no—
742C22⋊C4—2442no—
743C22⋊C4—2442no—
744C22⋊C4—2442no—
745C42—24no—
746C42—21no—
747C42—21no—
748C42—2442no—
749C23—21no—
750C23—21no—
751C23—21no—
752C23—21no—
753C23—21no—
754C23—21no—
755C23—21no—
756C23—22no—
757C23—22no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—21no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23#1451974612yes—
777C23C22×C22⋊D6111yescharacteristic
778Q8—22no—
779Q8—22no—
780Q8—22no—
781Q8—2441no—
782Q8—2441no—
783Q8—2441no—
784Q8—2441no—
785Q8#1451974914yes—
786D4—22no—
787D4—22no—
788D4—22no—
789D4—22no—
790D4—44no—
791D4—48no—
792D4—48no—
793D4—48no—
794D4—41no—
795D4—41no—
796D4—41no—
797D4—41no—
798D4—84no—
799D4—84no—
800D4—84no—
801C2×C4—21no—
802C2×C4—22no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—22no—
806C2×C4—21no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—21no—
813C2×C4—22no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—48no—
820C2×C4—48no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—1222no—
828C2×C4—2441no—
829C2×C4—2441no—
830C2×C4—2441no—
831C2×C4—2441no—
832C2×C4—2441no—
833C2×C4—2441no—
834C2×C4—2441no—
835C2×C4—2441no—
836C2×C4—2441no—
837C2×C4—2441no—
838C2×C4—2441no—
839C2×C4#1451974612yes—
840C2×C4#1451979712yes—
841C2×C4C2×D4×D6111yescharacteristic
842C2×C4C22×C22⋊D6111yescharacteristic
843C2×C4C22×C22⋊D6111yescharacteristic
844C2×C4C2×#1175822411yescharacteristic
845C2×C4#1451982211yescharacteristic
846C2×C4#1451982211yescharacteristic
847C8—1222no—
848C8—2441no—
849C8—2441no—
850C8—2441no—
851C22—22no—
852C22—22no—
853C22—22no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—42no—
863C22—42no—
864C22—42no—
865C22—42no—
866C22—41no—
867C22—41no—
868C22—42no—
869C22—42no—
870C22—41no—
871C22—81no—
872C22—81no—
873C22—81no—
874C22—81no—
875C22—81no—
876C22—81no—
877C22—81no—
878C22—81no—
879C22C2×#1451974611yescharacteristic
880C22D4×C22⋊D6111yescharacteristic
881C22#1684040611yescharacteristic
882C22C2×#1451979711yescharacteristic
883C22#1684056011yescharacteristic
884C22#1684057311yescharacteristic
885C22#1684057311yescharacteristic
886C4—22no—
887C4—22no—
888C4—24no—
889C4—41no—
890C4—41no—
891C4—42no—
892C4—4881no—
893C4—4881no—
894C4—4881no—
895C4—2442no—
896C4C2×#1451974911yescharacteristic
897C4#1684032111yescharacteristic
898C4D4×C22⋊D6111yescharacteristic
899C4#1684040611yescharacteristic
900C2—42no—
901C2—81no—
902C2—82no—
903C2—82no—
904C2#2144919311yescharacteristic
905C2#2145503711yescharacteristic
906C2#2145509611yescharacteristic
907C2#2145740011yescharacteristic
908C2#2145754911yescharacteristic
909C2#2145775811yescharacteristic
910C2#2145794511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
Fitting, prime radicalC2×C61×#550C2
socleC23×C61C22×D4
hypercenterC2×#550D61
hypocenterC61#24427
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. C2×#16839989C2semidirect
2. C2×#16839924C2semidirect
3. C2×#16839924C2semidirect
4. C2×#16839758C2semidirect
5. #21449248C2semidirect
6. #21447050C2semidirect
7. #21447005C2semidirect
8. #21446907C2semidirect
9. #21446822C2semidirect
10. #21446160C2semidirect
11. #21446142C2semidirect
12. #21446112C2semidirect
13. #21446087C2semidirect
14. #21445759C2semidirect
102. #14519701D4semidirect
520. C61#24427semidirect

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×#168397582
#214492482
#214470502
#214470052
#214469072
#214468222
#214461602
#214461422
#214461122
#214460872
#214457592
C2×C61×#5502
#2442761