Finite Group Databasebeta

← #14577866

Subgroups — #14577866

Order 2432.

1270 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11927283C212yesmaximal, complemented
2#11927282C212yesmaximal, complemented
3#11927246C211yesmaximal, characteristic, complemented
4#11927244C211yesmaximal, characteristic, complemented
5#11927241C211yesmaximal, characteristic, complemented
6#11927240C211yesmaximal, characteristic, complemented
7#11927179C211yesmaximal, characteristic, complemented
8D4×C22⋊D19C211yesmaximal, characteristic, complemented
9D4×C22⋊D19C212yesmaximal, complemented
10D4×C22⋊D19C211yesmaximal, characteristic, complemented
11#11927176C212yesmaximal, complemented
12#11927148C211yesmaximal, characteristic, complemented
13#11927145C211yesmaximal, characteristic, complemented
14#11927129C212yesmaximal, complemented
15#11927126C212yesmaximal, complemented
16#11927111C211yesmaximal, characteristic, complemented
17#11927110C211yesmaximal, characteristic, complemented
18#11927104C212yesmaximal, complemented
19#11927103C212yesmaximal, complemented
20#11927053C211yesmaximal, characteristic, complemented
21C2×#10597384C211yesmaximal, characteristic, complemented
22#121×D19C211yesmaximal, characteristic, complemented
23D42×C19C211yesmaximal, characteristic, complemented
24C22×D4×C19C2212yescomplemented
25C22×D4×C19C2211yescharacteristic, complemented
26C22×D4×C19C2211yescharacteristic, complemented
27C22×C22⋊D19C2212yescomplemented
28C22×C22⋊D19C2212yescomplemented
29C22×C22⋊D19C2212yescomplemented
30C2×D4×D19C2212yescomplemented
31C2×D4×D19C2211yescharacteristic, complemented
32C2×D4×D19C2212yescomplemented
33C2×D4×D19C2211yescharacteristic, complemented
34C2×#64541C2211yescharacteristic, complemented
35C22×C4×D19C2211yescharacteristic, complemented
36C19×#127C2211yescharacteristic, complemented
37C19×#121C2211yescharacteristic, complemented
38C19×#121C2212yescomplemented
39C19×#121C2211yescharacteristic, complemented
40C19×#120C2212yescomplemented
41C19×#120C2212yescomplemented
42C4×D4×C19C2211yescharacteristic, complemented
43C4×D4×C19C2211yescharacteristic, complemented
44#10597399C2212yescomplemented
45#10597399C2212yescomplemented
46#10597399C2212yescomplemented
47#10597399C2212yescomplemented
48C2×C22⋊Dic19C2212yescomplemented
49#10597386C2212yescomplemented
50#10597386C2212yescomplemented
51#10597386C2211yescharacteristic, complemented
52#10597385C2211yescharacteristic, complemented
53#10597385C2212yescomplemented
54#10597385C2212yescomplemented
55#10597385C2212yescomplemented
56#10597385C2212yescomplemented
57#10597385C2212yescomplemented
58#10597385C2212yescomplemented
59#10597385C2212yescomplemented
60#10597384C2212yescomplemented
61#10597384C2212yescomplemented
62#10597384C2211yescharacteristic, complemented
63#10597384C2211yescharacteristic, complemented
64#10597384C2211yescharacteristic, complemented
65#10597384C2211yescharacteristic, complemented
66#10597384C2211yescharacteristic, complemented
67#10597384C2212yescomplemented
68#10597384C2211yescharacteristic, complemented
69#10597384C2211yescharacteristic, complemented
70#10597384C2212yescomplemented
71#10597383C2211yescharacteristic, complemented
72#10597383C2212yescomplemented
73#10597383C2212yescomplemented
74#10597383C2212yescomplemented
75#10597383C2212yescomplemented
76#10597383C2212yescomplemented
77#10597382C2212yescomplemented
78#10597381C2212yescomplemented
79#10597381C2212yescomplemented
80#10597381C2212yescomplemented
81D4×Dic19C2212yescomplemented
82D4×Dic19C2211yescharacteristic, complemented
83D4×Dic19C2211yescharacteristic, complemented
84#10597376C2211yescharacteristic, complemented
85#10597376C2212yescomplemented
86#10597376C2211yescharacteristic, complemented
87#10597375C2212yescomplemented
88#10597375C2212yescomplemented
89C4×C22⋊D19C2211yescharacteristic, complemented
90C4×C22⋊D19C2211yescharacteristic, complemented
91C4×C22⋊D19C2212yescomplemented
92#10597372C2211yescharacteristic, complemented
93C2×C4⋊Dic19C2211yescharacteristic, complemented
94#10597344C2212yescomplemented
95#10597342C2211yescharacteristic, complemented
96#10597341C2211yescharacteristic, complemented
97#10597340C2211yescharacteristic, complemented
98#10597338C2211yescharacteristic, complemented
99C4⋊C4×D19C2211yescharacteristic, complemented
100#10597336C2211yescharacteristic, complemented
101#10597332C2212yescomplemented
102#10597331C2212yescomplemented
103#10597330C2211yescharacteristic, complemented
104#10597330C2212yescomplemented
105#10597330C2212yescomplemented
106#10597330C2212yescomplemented
107#10597329C2211yescharacteristic, complemented
108#10597329C2212yescomplemented
109#10597329C2212yescomplemented
110#10597328C2211yescharacteristic, complemented
111#10597328C2212yescomplemented
112(C22⋊D19)⋊C4C2212yescomplemented
113(C22⋊D19)⋊C4C2212yescomplemented
114C22⋊C4×D19C2212yescomplemented
115#10597325C2212yescomplemented
116#10597325C2212yescomplemented
117#10597325C2212yescomplemented
118#10597324C2211yescharacteristic, complemented
119C4×D76C2211yescharacteristic, complemented
120C4×D76C2211yescharacteristic, complemented
121#10597318C2211yescharacteristic, complemented
122#10597316C2211yescharacteristic, complemented
123C24×C19C2312yes—
124C24×C19C2312yes—
125C23×D19C2311yescharacteristic
126C23×D19C2312yes—
127C23×D19C2312yes—
128C2×D4×C19—42no—
129C2×D4×C19—42no—
130C2×D4×C19—44no—
131C2×D4×C19C2311yescharacteristic
132C2×D4×C19C2311yescharacteristic
133C2×D4×C19C2312yes—
134C2×D4×C19C2311yescharacteristic
135C2×D4×C19C2311yescharacteristic
136C2×D4×C19C2312yes—
137C2×D4×C19C2312yes—
138C2×D4×C19C2312yes—
139C2×D4×C19C2312yes—
140C2×D4×C19C2312yes—
141C22×C4×C19C2311yescharacteristic
142C22×C4×C19C2311yescharacteristic
143C22×C4×C19C2312yes—
144C2×C22⋊D19—44no—
145C2×C22⋊D19—44no—
146C2×C22⋊D19—44no—
147C2×C22⋊D19C2312yes—
148C2×C22⋊D19C2312yes—
149C2×C22⋊D19C2311yescharacteristic
150C2×C22⋊D19C2312yes—
151C2×C22⋊D19C2311yescharacteristic
152C2×C22⋊D19C2312yes—
153C2×C22⋊D19C2312yes—
154C2×C22⋊D19C2312yes—
155C2×C22⋊D19C2311yescharacteristic
156C2×C22⋊D19C2312yes—
157C2×C22⋊D19C2312yes—
158C2×C22⋊D19C2312yes—
159C2×C22⋊D19C2312yes—
160C2×C22⋊D19C2312yes—
161C2×C22⋊D19C2311yescharacteristic
162C2×C22⋊D19C2312yes—
163C2×C22⋊D19C2312yes—
164C22×Dic19C2312yes—
165C22×Dic19C2312yes—
166C22×Dic19C2312yes—
167C22×Dic19C2311yescharacteristic
168D4×D19—42no—
169D4×D19—42no—
170D4×D19—44no—
171D4×D19—44no—
172#64541—42no—
173C2×D76C2311yescharacteristic
174C2×D76C2311yescharacteristic
175C2×D76C2312yes—
176C2×D76C2311yescharacteristic
177C2×C4×D19—42no—
178C2×C4×D19C2311yescharacteristic
179C2×C4×D19C2311yescharacteristic
180C2×C4×D19C2311yescharacteristic
181C2×C4×D19C2311yescharacteristic
182C2×C4×D19C2311yescharacteristic
183C2×C4×D19C2312yes—
184C2×C4×D19C2312yes—
185C2×Dic38C2311yescharacteristic
186C4⋊C4×C19C2311yescharacteristic
187C4⋊C4×C19C2311yescharacteristic
188C22⋊C4×C19C2311yescharacteristic
189C22⋊C4×C19C2312yes—
190C22⋊C4×C19C2311yescharacteristic
191C22⋊C4×C19C2312yes—
192C22⋊C4×C19C2312yes—
193C42×C19C2311yescharacteristic
194C22⋊Dic19C2311yescharacteristic
195C22⋊Dic19C2312yes—
196C22⋊Dic19C2312yes—
197C22⋊Dic19C2312yes—
198C22⋊Dic19C2312yes—
199C22⋊Dic19C2312yes—
200C22⋊Dic19C2311yescharacteristic
201C22⋊Dic19C2312yes—
202C22⋊Dic19C2312yes—
203C22⋊Dic19C2312yes—
204C22⋊Dic19C2312yes—
205C22⋊Dic19C2312yes—
206(C2×D19)⋊C4C2311yescharacteristic
207(C2×D19)⋊C4C2312yes—
208(C2×D19)⋊C4C2312yes—
209(C2×D19)⋊C4C2312yes—
210(C2×D19)⋊C4C2311yescharacteristic
211(C2×D19)⋊C4C2311yescharacteristic
212(C2×D19)⋊C4C2311yescharacteristic
213(C2×D19)⋊C4C2311yescharacteristic
214(C2×D19)⋊C4C2312yes—
215(C2×D19)⋊C4C2312yes—
216(C2×D19)⋊C4C2311yescharacteristic
217C4⋊Dic19C2311yescharacteristic
218C4⋊Dic19C2311yescharacteristic
219C4⋊Dic19C2312yes—
220C4⋊Dic19C2311yescharacteristic
221C4⋊Dic19C2311yescharacteristic
222C4⋊Dic19C2312yes—
223Dic19⋊C4C2311yescharacteristic
224Dic19⋊C4C2311yescharacteristic
225Dic19⋊C4C2312yes—
226Dic19⋊C4C2312yes—
227Dic19⋊C4C2312yes—
228Dic19⋊C4C2312yes—
229Dic19⋊C4C2311yescharacteristic
230Dic19⋊C4C2311yescharacteristic
231C4×Dic19C2311yescharacteristic
232C4×Dic19C2312yes—
233C4×Dic19C2312yes—
234C23×C19—24no—
235C23×C19—42no—
236C23×C19—42no—
237C23×C19—42no—
238C23×C19—42no—
239C23×C19—42no—
240C23×C19C2412yes—
241C23×C19C2412yes—
242C23×C19C2411yescharacteristic
243C23×C19C2412yes—
244C23×C19C2411yescharacteristic
245C22×D19—22no—
246C22×D19—22no—
247C22×D19—24no—
248C22×D19—41no—
249C22×D19—42no—
250C22×D19—42no—
251C22×D19—42no—
252C22×D19—42no—
253C22×D19—42no—
254C22×D19C2411yescharacteristic
255C22×D19C2412yes—
256C22×D19C2411yescharacteristic
257C22×D19C2411yescharacteristic
258D4×C19—24no—
259D4×C19—22no—
260D4×C19—22no—
261D4×C19—22no—
262D4×C19—22no—
263D4×C19—42no—
264D4×C19—42no—
265D4×C19—42no—
266D4×C19—42no—
267D4×C19—42no—
268C2×C4×C19—22no—
269C2×C4×C19—22no—
270C2×C4×C19—42no—
271C2×C4×C19C2411yescharacteristic
272C2×C4×C19C2412yes—
273C2×C4×C19C2411yescharacteristic
274C2×C4×C19C2411yescharacteristic
275C2×C4×C19C2411yescharacteristic
276C2×C4×C19C2411yescharacteristic
277C22⋊D19—24no—
278C22⋊D19—22no—
279C22⋊D19—24no—
280C22⋊D19—24no—
281C22⋊D19—22no—
282C22⋊D19—41no—
283C22⋊D19—41no—
284C22⋊D19—42no—
285C22⋊D19—42no—
286C22⋊D19—42no—
287C22⋊D19—42no—
288C22⋊D19—42no—
289C22⋊D19—42no—
290C22⋊D19—42no—
291C22⋊D19—42no—
292C22⋊D19—42no—
293C22⋊D19—42no—
294C2×Dic19—41no—
295C2×Dic19—42no—
296C2×Dic19—42no—
297C2×Dic19—42no—
298C2×Dic19C2411yescharacteristic
299C2×Dic19C2411yescharacteristic
300C2×Dic19C2412yes—
301C2×Dic19C2411yescharacteristic
302C2×Dic19C2412yes—
303C2×Dic19C2412yes—
304C2×Dic19C2411yescharacteristic
305C2×Dic19C2411yescharacteristic
306D76—22no—
307D76—22no—
308D76—41no—
309D76—42no—
310C4×D19—22no—
311C4×D19—22no—
312C4×D19—22no—
313C4×D19—41no—
314C4×D19—41no—
315C4×D19—42no—
316C4×D19—42no—
317Dic38—41no—
318#3537—191nomaximal, Sylow
319C22×C19—21no—
320C22×C19—21no—
321C22×C19—22no—
322C22×C19—22no—
323C22×C19—21no—
324C22×C19—22no—
325C22×C19—22no—
326C22×C19—21no—
327C22×C19—22no—
328C22×C19—22no—
329C22×C19—22no—
330C22×C19—22no—
331C22×C19—21no—
332C22×C19—22no—
333C22×C19—84no—
334C22×C19—84no—
335C22×C19H(5,𝔽2)12yes—
336C22×C19C2511yescharacteristic
337C2×D19—21no—
338C2×D19—21no—
339C2×D19—21no—
340C2×D19—21no—
341C2×D19—22no—
342C2×D19—21no—
343C2×D19—22no—
344C2×D19—21no—
345C2×D19—22no—
346C2×D19—21no—
347C2×D19—21no—
348C2×D19—44no—
349C2×D19—84no—
350C2×D19—84no—
351C2×D19H(5,𝔽2)12yes—
352C4×C19—21no—
353C4×C19—21no—
354C4×C19—21no—
355C4×C19—22no—
356C4×C19—21no—
357C4×C19H(5,𝔽2)12yes—
358Dic19—21no—
359Dic19—21no—
360Dic19—21no—
361Dic19—22no—
362Dic19—22no—
363Dic19—22no—
364Dic19—21no—
365Dic19—21no—
366#560—192no—
367#560—192no—
368#553—191no—
369#553—191no—
370#553—191no—
371#553—191no—
372D42—192no—
373D42—191no—
374D42—191no—
375D42—191no—
376D42—192no—
377D42D1911yescharacteristic, complemented
378#540—191no—
379#540—191no—
380#538—192no—
381#538—192no—
382#535—191no—
383#535—191no—
384#534—192no—
385#534—192no—
386#525—191no—
387C2×#121—191no—
388C2×#121—191no—
389C2×C19—22no—
390C2×C19—42no—
391C2×C19—42no—
392C2×C19—41no—
393C2×C19—42no—
394C2×C19C2×H(5,𝔽2)11yescharacteristic
395C2×C19C2×H(5,𝔽2)11yescharacteristic
396C2×C19C2×H(5,𝔽2)11yescharacteristic
397D19—22no—
398D19—41no—
399D19—41no—
400D19—42no—
401C2×#41—191no—
402C22×D4—192no—
403C22×D4—192no—
404C22×D4—192no—
405C22×D4—191no—
406C22×D4—192no—
407C22×D4—192no—
408C22×D4—191no—
409C22×D4C2×D1911yescharacteristic, complemented
410C22×D4C2×D1912yescomplemented
411C22×D4C2×D1911yescharacteristic, complemented
412C23×C4—191no—
413#127—192no—
414#127—192no—
415#127—191no—
416#127C2×D1911yescharacteristic, complemented
417#126—192no—
418#126—192no—
419#126—192no—
420#126—192no—
421#125—191no—
422#125—191no—
423#124—192no—
424#124—192no—
425#123—192no—
426#123—192no—
427#123—192no—
428#123—192no—
429#123—192no—
430#123—191no—
431#123—191no—
432#123—192no—
433#123—192no—
434#123—192no—
435C22⋊Q8—191no—
436C22⋊Q8—191no—
437#121—192no—
438#121—191no—
439#121—191no—
440#121—191no—
441#121—191no—
442#121—191no—
443#121—192no—
444#121—192no—
445#121—191no—
446#121—191no—
447#121—192no—
448#121—192no—
449#121—191no—
450#121—192no—
451#121—192no—
452#121—192no—
453#121—192no—
454#121—192no—
455#121—192no—
456#121—191no—
457#121—191no—
458#121—192no—
459#121—191no—
460#121—192no—
461#121—191no—
462#121—192no—
463#121—192no—
464#121C2×D1911yescharacteristic, complemented
465#121C2×D1911yescharacteristic, complemented
466#121C2×D1912yescomplemented
467#120—192no—
468#120—192no—
469#120—192no—
470#120—192no—
471#120—191no—
472#120—192no—
473#120—192no—
474#120—192no—
475#120—192no—
476#120—192no—
477#120—191no—
478#120—192no—
479#120C2×D1912yescomplemented
480#120C2×D1912yescomplemented
481C4×D4—192no—
482C4×D4—191no—
483C4×D4—191no—
484C4×D4—191no—
485C4×D4—191no—
486C4×D4—192no—
487C4×D4—192no—
488C4×D4—192no—
489C4×D4—191no—
490C4×D4—191no—
491C4×D4C2×D1911yescharacteristic, complemented
492C4×D4C2×D1911yescharacteristic, complemented
493#117—191no—
494#117—191no—
495#117—191no—
496C2×C4⋊C4—191no—
497C2×C4⋊C4—191no—
498C2×C22⋊C4—192no—
499C2×C22⋊C4—192no—
500C19#353711yescharacteristic, complemented, Sylow
501C24—191no—
502C24—192no—
503C24—192no—
504C24C22×D1912yes—
505C24C22×D1912yes—
506#41—762no—
507C2×Q8—191no—
508C2×D4—42no—
509C2×D4—42no—
510C2×D4—44no—
511C2×D4—192no—
512C2×D4—191no—
513C2×D4—192no—
514C2×D4—192no—
515C2×D4—191no—
516C2×D4—191no—
517C2×D4—191no—
518C2×D4—192no—
519C2×D4—192no—
520C2×D4—192no—
521C2×D4—192no—
522C2×D4—192no—
523C2×D4—192no—
524C2×D4—192no—
525C2×D4—192no—
526C2×D4—192no—
527C2×D4—192no—
528C2×D4—191no—
529C2×D4—191no—
530C2×D4—191no—
531C2×D4—192no—
532C2×D4—762no—
533C2×D4—762no—
534C2×D4—764no—
535C2×D4—764no—
536C2×D4—764no—
537C2×D4—764no—
538C2×D4—764no—
539C2×D4C22×D1912yes—
540C2×D4C22×D1911yescharacteristic
541C2×D4C22×D1911yescharacteristic
542C2×D4C22×D1911yescharacteristic
543C2×D4C22×D1911yescharacteristic
544C2×D4C22×D1912yes—
545C2×D4C22×D1912yes—
546C2×D4C22×D1912yes—
547C2×D4C22×D1912yes—
548C2×D4C22×D1912yes—
549C22×C4—191no—
550C22×C4—192no—
551C22×C4—192no—
552C22×C4—192no—
553C22×C4—191no—
554C22×C4—191no—
555C22×C4—191no—
556C22×C4—191no—
557C22×C4—192no—
558C22×C4—192no—
559C22×C4—191no—
560C22×C4—762no—
561C22×C4C22×D1911yescharacteristic
562C22×C4C22×D1911yescharacteristic
563C22×C4C22×D1912yes—
564C4⋊C4—192no—
565C4⋊C4—191no—
566C4⋊C4—191no—
567C4⋊C4—191no—
568C4⋊C4—191no—
569C4⋊C4—192no—
570C4⋊C4—192no—
571C4⋊C4—192no—
572C4⋊C4—191no—
573C4⋊C4—191no—
574C4⋊C4—191no—
575C4⋊C4—192no—
576C4⋊C4—191no—
577C4⋊C4—192no—
578C4⋊C4C22×D1911yescharacteristic
579C4⋊C4C22×D1911yescharacteristic
580C22⋊C4—192no—
581C22⋊C4—192no—
582C22⋊C4—192no—
583C22⋊C4—192no—
584C22⋊C4—192no—
585C22⋊C4—192no—
586C22⋊C4—191no—
587C22⋊C4—192no—
588C22⋊C4—192no—
589C22⋊C4—192no—
590C22⋊C4—192no—
591C22⋊C4—191no—
592C22⋊C4—192no—
593C22⋊C4—192no—
594C22⋊C4—192no—
595C22⋊C4—191no—
596C22⋊C4—191no—
597C22⋊C4—191no—
598C22⋊C4—191no—
599C22⋊C4—192no—
600C22⋊C4—192no—
601C22⋊C4—191no—
602C22⋊C4—191no—
603C22⋊C4C22×D1912yes—
604C22⋊C4C22×D1911yescharacteristic
605C22⋊C4C22×D1912yes—
606C22⋊C4C22×D1912yes—
607C22⋊C4C22×D1911yescharacteristic
608C42—191no—
609C42—192no—
610C42—192no—
611C42C22×D1911yescharacteristic
612C23—24no—
613C23—42no—
614C23—42no—
615C23—42no—
616C23—42no—
617C23—42no—
618C23—191no—
619C23—192no—
620C23—191no—
621C23—191no—
622C23—382no—
623C23—384no—
624C23—382no—
625C23—761no—
626C23—762no—
627C23—762no—
628C23—762no—
629C23—762no—
630C23—762no—
631C23C23×D1912yes—
632C23C23×D1912yes—
633C23C23×D1911yescharacteristic
634C23C23×D1912yes—
635C23C23×D1911yescharacteristic
636Q8—761no—
637D4—22no—
638D4—24no—
639D4—22no—
640D4—22no—
641D4—22no—
642D4—42no—
643D4—42no—
644D4—42no—
645D4—42no—
646D4—42no—
647D4—382no—
648D4—384no—
649D4—382no—
650D4—384no—
651D4—384no—
652D4—382no—
653D4—382no—
654D4—762no—
655D4—761no—
656D4—762no—
657D4—762no—
658D4—762no—
659D4—762no—
660D4—762no—
661D4—762no—
662D4—762no—
663D4—762no—
664D4—762no—
665D4—762no—
666D4—761no—
667D4—761no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—42no—
671C2×C4—191no—
672C2×C4—191no—
673C2×C4—192no—
674C2×C4—192no—
675C2×C4—191no—
676C2×C4—192no—
677C2×C4—191no—
678C2×C4—191no—
679C2×C4—382no—
680C2×C4—382no—
681C2×C4—382no—
682C2×C4—761no—
683C2×C4—761no—
684C2×C4—762no—
685C2×C4—762no—
686C2×C4—761no—
687C2×C4—762no—
688C2×C4—762no—
689C2×C4—762no—
690C2×C4C23×D1911yescharacteristic
691C2×C4C23×D1912yes—
692C2×C4C23×D1911yescharacteristic
693C2×C4C23×D1911yescharacteristic
694C2×C4C23×D1911yescharacteristic
695C2×C4C23×D1911yescharacteristic
696C22—21no—
697C22—21no—
698C22—22no—
699C22—22no—
700C22—21no—
701C22—22no—
702C22—21no—
703C22—22no—
704C22—22no—
705C22—21no—
706C22—22no—
707C22—22no—
708C22—22no—
709C22—22no—
710C22—84no—
711C22—84no—
712C22—192no—
713C22—381no—
714C22—381no—
715C22—382no—
716C22—381no—
717C22—381no—
718C22—381no—
719C22—381no—
720C22—382no—
721C22—381no—
722C22—382no—
723C22—381no—
724C22—764no—
725C22—1524no—
726C22—1524no—
727C22#1059743012yes—
728C22C24×D1911yescharacteristic
729C4—21no—
730C4—21no—
731C4—21no—
732C4—21no—
733C4—22no—
734C4—382no—
735C4—381no—
736C4—382no—
737C4—381no—
738C4—381no—
739C4—381no—
740C4—382no—
741C4—381no—
742C4#1059743012yes—
743C2—22no—
744C2—41no—
745C2—42no—
746C2—42no—
747C2—42no—
748C2—382no—
749C2—761no—
750C2—762no—
751C2—761no—
752C2H(5,𝔽2)×D1911yescharacteristic
753C2C2×#1059743011yescharacteristic
754C2C2×#1059743011yescharacteristic
subgroupG/H
center, FrattiniC22C24×D19
commutator, socle, cosocleC22×C19C25
FittingD42×C19C2
hypercenterD42D19
hypocenterC19#3537
LCSG ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ D42

Complements

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

NH ≅ G/Ntype
1. #11927283C2semidirect
2. #11927282C2semidirect
3. #11927246C2semidirect
4. #11927244C2semidirect
5. #11927241C2semidirect
6. #11927240C2semidirect
7. #11927179C2semidirect
8. D4×C22⋊D19C2semidirect
9. D4×C22⋊D19C2semidirect
10. D4×C22⋊D19C2semidirect
11. #11927176C2semidirect
12. #11927148C2semidirect
13. #11927145C2semidirect
14. #11927129C2semidirect
15. #11927126C2semidirect
16. #11927111C2semidirect
17. #11927110C2semidirect
18. #11927104C2semidirect
19. #11927103C2semidirect
20. #11927053C2semidirect
21. C2×#10597384C2semidirect
22. #121×D19C2semidirect
23. D42×C19C2semidirect
24. C22×D4×C19C22semidirect
25. C22×D4×C19C22semidirect
26. C22×D4×C19C22semidirect
27. C22×C22⋊D19C22semidirect
28. C22×C22⋊D19C22semidirect
29. C22×C22⋊D19C22semidirect
30. C2×D4×D19C22semidirect
31. C2×D4×D19C22semidirect
32. C2×D4×D19C22semidirect
33. C2×D4×D19C22semidirect
34. C2×#64541C22semidirect
35. C22×C4×D19C22semidirect
36. C19×#127C22semidirect
37. C19×#121C22semidirect
38. C19×#121C22semidirect
39. C19×#121C22semidirect
40. C19×#120C22semidirect
41. C19×#120C22semidirect
42. C4×D4×C19C22semidirect
43. C4×D4×C19C22semidirect
44. #10597399C22semidirect
45. #10597399C22semidirect
46. #10597399C22semidirect
47. #10597399C22semidirect
48. C2×C22⋊Dic19C22semidirect
49. #10597386C22semidirect
50. #10597386C22semidirect
51. #10597386C22semidirect
52. #10597385C22semidirect
53. #10597385C22semidirect
54. #10597385C22semidirect
55. #10597385C22semidirect
56. #10597385C22semidirect
57. #10597385C22semidirect
58. #10597385C22semidirect
59. #10597385C22semidirect
60. #10597384C22semidirect
61. #10597384C22semidirect
62. #10597384C22semidirect
63. #10597384C22semidirect
64. #10597384C22semidirect
65. #10597384C22semidirect
66. #10597384C22semidirect
67. #10597384C22semidirect
68. #10597384C22semidirect
69. #10597384C22semidirect
70. #10597384C22semidirect
71. #10597383C22semidirect
72. #10597383C22semidirect
73. #10597383C22semidirect
74. #10597383C22semidirect
75. #10597383C22semidirect
76. #10597383C22semidirect
77. #10597382C22semidirect
78. #10597381C22semidirect
79. #10597381C22semidirect
80. #10597381C22semidirect
81. D4×Dic19C22semidirect
82. D4×Dic19C22semidirect
83. D4×Dic19C22semidirect
84. #10597376C22semidirect
85. #10597376C22semidirect
86. #10597376C22semidirect
87. #10597375C22semidirect
88. #10597375C22semidirect
89. C4×C22⋊D19C22semidirect
90. C4×C22⋊D19C22semidirect
91. C4×C22⋊D19C22semidirect
92. #10597372C22semidirect
93. C2×C4⋊Dic19C22semidirect
94. #10597344C22semidirect
95. #10597342C22semidirect
96. #10597341C22semidirect
97. #10597340C22semidirect
98. #10597338C22semidirect
99. C4⋊C4×D19C22semidirect
100. #10597336C22semidirect
101. #10597332C22semidirect
102. #10597331C22semidirect
103. #10597330C22semidirect
104. #10597330C22semidirect
105. #10597330C22semidirect
106. #10597330C22semidirect
107. #10597329C22semidirect
108. #10597329C22semidirect
109. #10597329C22semidirect
110. #10597328C22semidirect
111. #10597328C22semidirect
112. (C22⋊D19)⋊C4C22semidirect
113. (C22⋊D19)⋊C4C22semidirect
114. C22⋊C4×D19C22semidirect
115. #10597325C22semidirect
116. #10597325C22semidirect
117. #10597325C22semidirect
118. #10597324C22semidirect
119. C4×D76C22semidirect
120. C4×D76C22semidirect
121. #10597318C22semidirect
122. #10597316C22semidirect
377. D42D19semidirect
409. C22×D4C2×D19semidirect
410. C22×D4C2×D19semidirect
411. C22×D4C2×D19semidirect
416. #127C2×D19semidirect
464. #121C2×D19semidirect
465. #121C2×D19semidirect
466. #121C2×D19semidirect
479. #120C2×D19semidirect
480. #120C2×D19semidirect
491. C4×D4C2×D19semidirect
492. C4×D4C2×D19semidirect
500. C19#3537semidirect

Maximal subgroups

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

subgroupindex
#119272832
#119272822
#119272462
#119272442
#119272412
#119272402
#119271792
D4×C22⋊D192
#119271762
#119271482
#119271452
#119271292
#119271262
#119271112
#119271102
#119271042
#119271032
#119270532
C2×#105973842
#121×D192
D42×C192
#353719