Finite Group Databasebeta

← #14577660

Subgroups — #14577660

Order 2432.

1252 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11927257C211yesmaximal, characteristic, complemented
2#11927249C211yesmaximal, characteristic, complemented
3#11927247C211yesmaximal, characteristic, complemented
4#11927245C212yesmaximal, complemented
5#11927212C211yesmaximal, characteristic, complemented
6#11927190C212yesmaximal, complemented
7#11927190C211yesmaximal, characteristic, complemented
8#11927189C211yesmaximal, characteristic, complemented
9#11927186C212yesmaximal, complemented
10#11927178C212yesmaximal, complemented
11#11927178C211yesmaximal, characteristic, complemented
12#11927146C212yesmaximal, complemented
13#11927133C212yesmaximal, complemented
14#11927131C212yesmaximal, complemented
15#11927091C211yesmaximal, characteristic, complemented
16#11927079C211yesmaximal, characteristic, complemented
17#11927056C211yesmaximal, characteristic, complemented
18#11927054C211yesmaximal, characteristic, complemented
19C2×#10597341C211yesmaximal, characteristic, complemented
20#121×D19C211yesmaximal, characteristic, complemented
21#11927016C212yesmaximal, complemented
22C4×D4×D19C211yesmaximal, characteristic, complemented
23C19×#553C211yesmaximal, characteristic, complemented
24C2×#64543C2211yescharacteristic, complemented
25C2×D4×D19C2211yescharacteristic
26C2×D4×D19C2212yes—
27C2×D4×D19C2212yescomplemented
28C2×D4×D19C2211yescharacteristic, complemented
29C2×#64541C2211yescharacteristic, complemented
30C2×#64541C2212yescomplemented
31C22×D76C2211yescharacteristic, complemented
32C22×D76C2212yescomplemented
33C22×C4×D19C2211yescharacteristic, complemented
34C22×C4×D19C2211yescharacteristic, complemented
35C19×#126C2212yescomplemented
36C19×#125C2211yescharacteristic, complemented
37C19×#123C2212yescomplemented
38C19×#121C2211yescharacteristic, complemented
39C19×#121C2212yescomplemented
40C19×#121C2211yescharacteristic, complemented
41C4×D4×C19C2211yescharacteristic, complemented
42C4×D4×C19C2211yescharacteristic, complemented
43C4×D4×C19C2212yescomplemented
44C19×#117C2211yescharacteristic, complemented
45C2×C4⋊C4×C19C2211yescharacteristic, complemented
46#10597386C2211yescharacteristic, complemented
47#10597386C2212yescomplemented
48#10597385C2212yescomplemented
49#10597385C2212yescomplemented
50#10597384C2211yescharacteristic, complemented
51#10597383C2212yescomplemented
52#10597383C2212yescomplemented
53#10597383C2212yescomplemented
54D4×Dic19C2212yescomplemented
55D4×Dic19C2211yescharacteristic, complemented
56#10597376C2212yescomplemented
57#10597376C2211yescharacteristic, complemented
58C4×C22⋊D19C2211yescharacteristic
59C4×C22⋊D19C2212yes—
60C4×C22⋊D19C2212yescomplemented
61C4×C22⋊D19C2211yescharacteristic, complemented
62C2×(C2×D19)⋊C4C2212yescomplemented
63C2×(C2×D19)⋊C4C2212yescomplemented
64#10597370C2211yescharacteristic, complemented
65#10597370C2212yescomplemented
66#10597344C2212yescomplemented
67#10597344C2212yescomplemented
68#10597343C2211yescharacteristic, complemented
69#10597343C2211yescharacteristic, complemented
70#10597342C2212yescomplemented
71#10597341C2211yescharacteristic
72#10597341C2211yescharacteristic, complemented
73#10597341C2211yescharacteristic, complemented
74#10597341C2212yescomplemented
75#10597341C2212yescomplemented
76#10597341C2212yescomplemented
77#10597341C2211yescharacteristic, complemented
78#10597341C2211yescharacteristic, complemented
79#10597340C2212yescomplemented
80#10597340C2212yescomplemented
81#10597340C2212yescomplemented
82#10597339C2212yescomplemented
83#10597339C2211yescharacteristic, complemented
84#10597339C2211yescharacteristic, complemented
85#10597339C2212yescomplemented
86#10597338C2211yescharacteristic, complemented
87#10597338C2212yescomplemented
88C4⋊C4×D19C2211yescharacteristic, complemented
89C4⋊C4×D19C2211yescharacteristic, complemented
90#10597335C2212yescomplemented
91#10597334C2211yescharacteristic, complemented
92#10597333C2211yescharacteristic, complemented
93#10597332C2212yescomplemented
94#10597332C2212yescomplemented
95#10597331C2212yescomplemented
96#10597331C2212yescomplemented
97#10597330C2212yescomplemented
98#10597330C2212yescomplemented
99#10597330C2212yescomplemented
100#10597330C2212yescomplemented
101#10597330C2212yescomplemented
102#10597330C2212yescomplemented
103#10597329C2212yescomplemented
104#10597328C2212yescomplemented
105#10597328C2212yescomplemented
106#10597328C2212yescomplemented
107(C22⋊D19)⋊C4C2211yescharacteristic
108(C22⋊D19)⋊C4C2212yescomplemented
109(C22⋊D19)⋊C4C2211yescharacteristic, complemented
110(C22⋊D19)⋊C4C2212yescomplemented
111C22⋊C4×D19C2212yescomplemented
112C22⋊C4×D19C2211yescharacteristic, complemented
113C22⋊C4×D19C2211yescharacteristic, complemented
114C22⋊C4×D19C2212yescomplemented
115#10597321C2211yescharacteristic, complemented
116#10597321C2212yescomplemented
117C4×D76C2212yescomplemented
118C4×D76C2212yescomplemented
119C4×D76C2211yescharacteristic, complemented
120C4×D76C2211yescharacteristic, complemented
121#10597318C2212yescomplemented
122C42×D19C2211yescharacteristic, complemented
123C23×D19C2311yescharacteristic
124C23×D19C2311yescharacteristic
125C23×D19C2312yes—
126C23×D19C2312yes—
127C2×D4×C19C2312yes—
128C2×D4×C19C2311yescharacteristic
129C2×D4×C19C2311yescharacteristic
130C2×D4×C19C2312yes—
131C22×C4×C19C2311yescharacteristic
132C22×C4×C19C2311yescharacteristic
133C22×C4×C19C2312yes—
134C22×C4×C19C2312yes—
135C2×C22⋊D19C2312yes—
136C2×C22⋊D19C2312yes—
137C2×C22⋊D19C2311yescharacteristic
138C2×C22⋊D19C2312yes—
139C2×C22⋊D19C2312yes—
140C2×C22⋊D19C2312yes—
141C2×C22⋊D19C2312yes—
142C2×C22⋊D19C2312yes—
143C2×C22⋊D19C2311yescharacteristic
144C22×Dic19C2311yescharacteristic
145C22×Dic19C2311yescharacteristic
146C22×Dic19C2312yes—
147#64543—42no—
148D4×D19—24no—
149D4×D19—28no—
150D4×D19—42no—
151D4×D19—44no—
152#64541—42no—
153#64541—44no—
154C2×D76—42no—
155C2×D76—44no—
156C2×D76C2311yescharacteristic
157C2×D76C2311yescharacteristic
158C2×D76C2312yes—
159C2×D76C2312yes—
160C2×D76C2311yescharacteristic
161C2×D76C2312yes—
162C2×D76C2312yes—
163C2×D76C2312yes—
164C2×D76C2312yes—
165C2×C4×D19—42no—
166C2×C4×D19—42no—
167C2×C4×D19C2311yescharacteristic
168C2×C4×D19C2311yescharacteristic
169C2×C4×D19C2311yescharacteristic
170C2×C4×D19C2311yescharacteristic
171C2×C4×D19C2311yescharacteristic
172C2×C4×D19C2312yes—
173C2×C4×D19C2311yescharacteristic
174C2×C4×D19C2311yescharacteristic
175C2×C4×D19C2311yescharacteristic
176C2×C4×D19C2311yescharacteristic
177C2×C4×D19C2312yes—
178C2×C4×D19C2312yes—
179C2×C4×D19C2312yes—
180C2×Dic38C2311yescharacteristic
181C2×Dic38C2312yes—
182C4⋊C4×C19C2311yescharacteristic
183C4⋊C4×C19C2311yescharacteristic
184C4⋊C4×C19C2312yes—
185C4⋊C4×C19C2311yescharacteristic
186C4⋊C4×C19C2312yes—
187C4⋊C4×C19C2311yescharacteristic
188C4⋊C4×C19C2312yes—
189C22⋊C4×C19C2312yes—
190C22⋊C4×C19C2311yescharacteristic
191C22⋊C4×C19C2312yes—
192C22⋊C4×C19C2312yes—
193C22⋊C4×C19C2311yescharacteristic
194C22⋊C4×C19C2312yes—
195C42×C19C2312yes—
196C42×C19C2311yescharacteristic
197C22⋊Dic19C2311yescharacteristic
198C22⋊Dic19C2312yes—
199C22⋊Dic19C2312yes—
200C22⋊Dic19C2311yescharacteristic
201(C2×D19)⋊C4C2311yescharacteristic
202(C2×D19)⋊C4C2312yes—
203(C2×D19)⋊C4C2312yes—
204(C2×D19)⋊C4C2312yes—
205(C2×D19)⋊C4C2312yes—
206(C2×D19)⋊C4C2312yes—
207(C2×D19)⋊C4C2312yes—
208(C2×D19)⋊C4C2312yes—
209(C2×D19)⋊C4C2312yes—
210(C2×D19)⋊C4C2312yes—
211(C2×D19)⋊C4C2312yes—
212(C2×D19)⋊C4C2312yes—
213(C2×D19)⋊C4C2311yescharacteristic
214(C2×D19)⋊C4C2312yes—
215(C2×D19)⋊C4C2312yes—
216(C2×D19)⋊C4C2311yescharacteristic
217(C2×D19)⋊C4C2311yescharacteristic
218C4⋊Dic19C2311yescharacteristic
219C4⋊Dic19C2312yes—
220C4⋊Dic19C2312yes—
221C4⋊Dic19C2311yescharacteristic
222Dic19⋊C4C2312yes—
223Dic19⋊C4C2312yes—
224Dic19⋊C4C2311yescharacteristic
225Dic19⋊C4C2312yes—
226Dic19⋊C4C2312yes—
227Dic19⋊C4C2311yescharacteristic
228C4×Dic19C2311yescharacteristic
229C4×Dic19C2312yes—
230C4×Dic19C2311yescharacteristic
231C4×Dic19C2312yes—
232C4×Dic19C2311yescharacteristic
233C23×C19C2411yescharacteristic
234C23×C19C2412yes—
235C23×C19C2411yescharacteristic
236C22×D19—22no—
237C22×D19—24no—
238C22×D19—22no—
239C22×D19—22no—
240C22×D19—22no—
241C22×D19—24no—
242C22×D19—41no—
243C22×D19—41no—
244C22×D19—42no—
245C22×D19—42no—
246C22×D19—42no—
247C22×D19—42no—
248C22×D19C2412yes—
249C22×D19C2411yescharacteristic
250C22×D19C2412yes—
251C22×D19C2411yescharacteristic
252C22×D19C2411yescharacteristic
253D4×C19—22no—
254D4×C19—24no—
255D4×C19—22no—
256D4×C19—42no—
257C2×C4×C19—22no—
258C2×C4×C19—22no—
259C2×C4×C19—42no—
260C2×C4×C19—42no—
261C2×C4×C19C2412yes—
262C2×C4×C19C2411yescharacteristic
263C2×C4×C19C2412yes—
264C2×C4×C19C2411yescharacteristic
265C2×C4×C19C2411yescharacteristic
266C2×C4×C19C2412yes—
267C2×C4×C19C2411yescharacteristic
268C2×C4×C19C2411yescharacteristic
269C22⋊D19—24no—
270C22⋊D19—22no—
271C22⋊D19—24no—
272C22⋊D19—42no—
273C22⋊D19—42no—
274C22⋊D19—42no—
275C22⋊D19—42no—
276C22⋊D19—42no—
277C22⋊D19#4114yescomplemented
278C2×Dic19—41no—
279C2×Dic19—41no—
280C2×Dic19—42no—
281C2×Dic19C2411yescharacteristic
282C2×Dic19C2411yescharacteristic
283C2×Dic19C2411yescharacteristic
284C2×Dic19C2412yes—
285C2×Dic19C2412yes—
286C2×Dic19C2411yescharacteristic
287C2×Dic19C2411yescharacteristic
288D76—22no—
289D76—24no—
290D76—24no—
291D76—24no—
292D76—22no—
293D76—22no—
294D76—42no—
295D76—42no—
296D76—42no—
297C4×D19—22no—
298C4×D19—22no—
299C4×D19—22no—
300C4×D19—22no—
301C4×D19—22no—
302C4×D19—24no—
303C4×D19—41no—
304C4×D19—41no—
305C4×D19—41no—
306C4×D19—41no—
307C4×D19—42no—
308C4×D19—42no—
309C4×D19—42no—
310Dic38—22no—
311Dic38—42no—
312#3519—191nomaximal, Sylow
313C22×C19—21no—
314C22×C19—21no—
315C22×C19—21no—
316C22×C19—22no—
317C22×C19—21no—
318C22×C19—22no—
319C22×C19—22no—
320C22×C19—21no—
321C22×C19C2×#4112yes—
322C22×C19C2511yescharacteristic
323C2×D19—21no—
324C2×D19—21no—
325C2×D19—21no—
326C2×D19—21no—
327C2×D19—22no—
328C2×D19—21no—
329C2×D19—22no—
330C2×D19—21no—
331C2×D19—22no—
332C2×D19—22no—
333C2×D19—22no—
334C2×D19—22no—
335C2×D19—21no—
336C2×D19—44no—
337C2×D19—44no—
338C2×D19—84no—
339C2×D19—84no—
340C2×D19C2×#4112yes—
341C2×D19H(5,𝔽2)12yes—
342C4×C19—21no—
343C4×C19—22no—
344C4×C19—22no—
345C4×C19—21no—
346C4×C19—21no—
347C4×C19—21no—
348C4×C19—22no—
349C4×C19H(5,𝔽2)12yes—
350Dic19—22no—
351Dic19—21no—
352Dic19—22no—
353Dic19—21no—
354Dic19—21no—
355Dic19—21no—
356Dic19C2×#4112yes—
357#555—191no—
358#554—191no—
359#553—192no—
360#553—191no—
361#553D1911yescharacteristic, complemented
362#550—191no—
363#546—192no—
364#546—191no—
365#546—192no—
366#546—191no—
367D42—191no—
368D42—192no—
369#540—192no—
370#538—192no—
371#538—192no—
372#532—191no—
373#529—191no—
374#525—191no—
375#525—191no—
376C2×#121—191no—
377C2×#121—191no—
378#518—192no—
379C2×C4×D4—191no—
380C2×C19—22no—
381C2×C19—41no—
382C2×C19—42no—
383C2×C19C22×#4111yescharacteristic
384C2×C19C2×H(5,𝔽2)11yescharacteristic
385C2×C19C2×H(5,𝔽2)11yescharacteristic
386D19—22no—
387D19—22no—
388D19—41no—
389D19—42no—
390D19—42no—
391C2×#41—191no—
392C2×#41—191no—
393C2×#41—192no—
394C22×D4—191no—
395C22×D4—192no—
396C22×D4—191no—
397C22×D4—192no—
398C22×D4—191no—
399C22×D4—192no—
400C23×C4—191no—
401C23×C4—191no—
402C4⋊Q8—191no—
403#127—191no—
404#127—192no—
405#126—192no—
406#126—192no—
407#126C2×D1912yescomplemented
408#125—192no—
409#125C2×D1911yescharacteristic, complemented
410#124—192no—
411#124—192no—
412#124—191no—
413#124—192no—
414#123—192no—
415#123—192no—
416#123—192no—
417#123—192no—
418#123—192no—
419#123—192no—
420#123C2×D1912yescomplemented
421C22⋊Q8—191no—
422C22⋊Q8—192no—
423C22⋊Q8—191no—
424C22⋊Q8—191no—
425C22⋊Q8—192no—
426#121—191no—
427#121—192no—
428#121—192no—
429#121—191no—
430#121—192no—
431#121—191no—
432#121—191no—
433#121—192no—
434#121—192no—
435#121—191no—
436#121—191no—
437#121—191no—
438#121—192no—
439#121—192no—
440#121—192no—
441#121—192no—
442#121—192no—
443#121—192no—
444#121—192no—
445#121C2×D1911yescharacteristic, complemented
446#121C2×D1911yescharacteristic, complemented
447#121C2×D1912yescomplemented
448#120—192no—
449#120—192no—
450#120—192no—
451#120—192no—
452#120—192no—
453#120—192no—
454C4×Q8—191no—
455C4×D4—191no—
456C4×D4—192no—
457C4×D4—191no—
458C4×D4—191no—
459C4×D4—192no—
460C4×D4—192no—
461C4×D4—191no—
462C4×D4—192no—
463C4×D4—192no—
464C4×D4—191no—
465C4×D4—191no—
466C4×D4—191no—
467C4×D4—192no—
468C4×D4—192no—
469C4×D4—191no—
470C4×D4—192no—
471C4×D4—192no—
472C4×D4—191no—
473C4×D4C2×D1911yescharacteristic, complemented
474C4×D4C2×D1912yescomplemented
475C4×D4C2×D1911yescharacteristic, complemented
476#117—192no—
477#117—191no—
478#117—192no—
479#117C2×D1911yescharacteristic, complemented
480C2×C4⋊C4—191no—
481C2×C4⋊C4—191no—
482C2×C4⋊C4C2×D1911yescharacteristic, complemented
483C2×C22⋊C4—192no—
484C2×C22⋊C4—192no—
485C2×C22⋊C4—191no—
486C2×C22⋊C4—191no—
487C2×C22⋊C4—192no—
488C2×C22⋊C4—192no—
489C2×C42—191no—
490C19#351911yescharacteristic, complemented, Sylow
491C24—191no—
492C24—191no—
493C24—192no—
494C24—192no—
495#41—762no—
496#41—764no—
497#41—762no—
498C2×Q8—191no—
499C2×Q8—192no—
500C2×D4—191no—
501C2×D4—191no—
502C2×D4—192no—
503C2×D4—192no—
504C2×D4—192no—
505C2×D4—192no—
506C2×D4—192no—
507C2×D4—192no—
508C2×D4—192no—
509C2×D4—191no—
510C2×D4—192no—
511C2×D4—192no—
512C2×D4—192no—
513C2×D4—191no—
514C2×D4—191no—
515C2×D4—192no—
516C2×D4—192no—
517C2×D4—192no—
518C2×D4—384no—
519C2×D4—388no—
520C2×D4—762no—
521C2×D4—764no—
522C2×D4—762no—
523C2×D4—764no—
524C2×D4C22×D1911yescharacteristic
525C2×D4C22×D1912yes—
526C2×D4C22×D1911yescharacteristic
527C2×D4C22×D1912yes—
528C22×C4—191no—
529C22×C4—192no—
530C22×C4—191no—
531C22×C4—191no—
532C22×C4—191no—
533C22×C4—191no—
534C22×C4—191no—
535C22×C4—192no—
536C22×C4—191no—
537C22×C4—191no—
538C22×C4—191no—
539C22×C4—191no—
540C22×C4—192no—
541C22×C4—192no—
542C22×C4—192no—
543C22×C4—191no—
544C22×C4—762no—
545C22×C4—762no—
546C22×C4C22×D1911yescharacteristic
547C22×C4C22×D1911yescharacteristic
548C22×C4C22×D1912yes—
549C22×C4C22×D1912yes—
550C4⋊C4—191no—
551C4⋊C4—191no—
552C4⋊C4—192no—
553C4⋊C4—192no—
554C4⋊C4—192no—
555C4⋊C4—192no—
556C4⋊C4—191no—
557C4⋊C4—191no—
558C4⋊C4—192no—
559C4⋊C4—192no—
560C4⋊C4C22×D1911yescharacteristic
561C4⋊C4C22×D1911yescharacteristic
562C4⋊C4C22×D1911yescharacteristic
563C4⋊C4C22×D1912yes—
564C4⋊C4C22×D1911yescharacteristic
565C4⋊C4C22×D1912yes—
566C4⋊C4C22×D1912yes—
567C22⋊C4—191no—
568C22⋊C4—192no—
569C22⋊C4—192no—
570C22⋊C4—191no—
571C22⋊C4—191no—
572C22⋊C4—192no—
573C22⋊C4—192no—
574C22⋊C4—192no—
575C22⋊C4—192no—
576C22⋊C4—191no—
577C22⋊C4—192no—
578C22⋊C4—192no—
579C22⋊C4—191no—
580C22⋊C4—192no—
581C22⋊C4—191no—
582C22⋊C4—192no—
583C22⋊C4—192no—
584C22⋊C4—192no—
585C22⋊C4—192no—
586C22⋊C4—192no—
587C22⋊C4—192no—
588C22⋊C4C22×D1911yescharacteristic
589C22⋊C4C22×D1912yes—
590C22⋊C4C22×D1911yescharacteristic
591C22⋊C4C22×D1912yes—
592C22⋊C4C22×D1912yes—
593C22⋊C4C22×D1912yes—
594C42—191no—
595C42—191no—
596C42—191no—
597C42—192no—
598C42—192no—
599C42C22×D1911yescharacteristic
600C42C22×D1912yes—
601C23—191no—
602C23—191no—
603C23—192no—
604C23—192no—
605C23—191no—
606C23—382no—
607C23—382no—
608C23—382no—
609C23—384no—
610C23—382no—
611C23—384no—
612C23—761no—
613C23—761no—
614C23—762no—
615C23—762no—
616C23—762no—
617C23—762no—
618C23C23×D1912yes—
619C23C23×D1911yescharacteristic
620C23C23×D1911yescharacteristic
621Q8—382no—
622Q8—762no—
623D4—22no—
624D4—24no—
625D4—22no—
626D4—42no—
627D4—194no—
628D4—382no—
629D4—384no—
630D4—384no—
631D4—384no—
632D4—382no—
633D4—384no—
634D4—384no—
635D4—382no—
636D4—382no—
637D4—762no—
638D4—762no—
639D4—762no—
640D4—762no—
641D4—762no—
642D4—762no—
643D4—762no—
644D4—762no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—191no—
650C2×C4—191no—
651C2×C4—191no—
652C2×C4—191no—
653C2×C4—192no—
654C2×C4—192no—
655C2×C4—191no—
656C2×C4—382no—
657C2×C4—384no—
658C2×C4—382no—
659C2×C4—382no—
660C2×C4—382no—
661C2×C4—382no—
662C2×C4—761no—
663C2×C4—761no—
664C2×C4—761no—
665C2×C4—761no—
666C2×C4—762no—
667C2×C4—762no—
668C2×C4—762no—
669C2×C4—761no—
670C2×C4—761no—
671C2×C4—762no—
672C2×C4C23×D1911yescharacteristic
673C2×C4C23×D1912yes—
674C2×C4C23×D1911yescharacteristic
675C2×C4C23×D1912yes—
676C2×C4C23×D1911yescharacteristic
677C2×C4C23×D1912yes—
678C2×C4C23×D1911yescharacteristic
679C2×C4C23×D1911yescharacteristic
680C22—21no—
681C22—21no—
682C22—21no—
683C22—22no—
684C22—22no—
685C22—21no—
686C22—21no—
687C22—22no—
688C22—192no—
689C22—192no—
690C22—381no—
691C22—381no—
692C22—381no—
693C22—381no—
694C22—382no—
695C22—381no—
696C22—382no—
697C22—382no—
698C22—382no—
699C22—381no—
700C22—381no—
701C22—382no—
702C22—382no—
703C22—764no—
704C22—764no—
705C22—1524no—
706C22—1524no—
707C22#41×D1912yes—
708C22C24×D1911yescharacteristic
709C4—21no—
710C4—22no—
711C4—21no—
712C4—22no—
713C4—22no—
714C4—21no—
715C4—21no—
716C4—192no—
717C4—381no—
718C4—382no—
719C4—381no—
720C4—381no—
721C4—381no—
722C4—382no—
723C4#1059743512yes—
724C2—22no—
725C2—41no—
726C2—42no—
727C2—382no—
728C2—382no—
729C2—761no—
730C2—762no—
731C2—762no—
732C2C2×#41×D1911yescharacteristic
733C2H(5,𝔽2)×D1911yescharacteristic
734C2C2×#1059743511yescharacteristic
subgroupG/H
center, FrattiniC22C24×D19
commutator, socle, cosocleC22×C19C25
FittingC19×#553C2
hypercenter#553D19
hypocenterC19#3519
LCSG ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ #553

Complements

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

NH ≅ G/Ntype
1. #11927257C2semidirect
2. #11927249C2semidirect
3. #11927247C2semidirect
4. #11927245C2semidirect
5. #11927212C2semidirect
6. #11927190C2semidirect
7. #11927190C2semidirect
8. #11927189C2semidirect
9. #11927186C2semidirect
10. #11927178C2semidirect
11. #11927178C2semidirect
12. #11927146C2semidirect
13. #11927133C2semidirect
14. #11927131C2semidirect
15. #11927091C2semidirect
16. #11927079C2semidirect
17. #11927056C2semidirect
18. #11927054C2semidirect
19. C2×#10597341C2semidirect
20. #121×D19C2semidirect
21. #11927016C2semidirect
22. C4×D4×D19C2semidirect
23. C19×#553C2semidirect
24. C2×#64543C22semidirect
27. C2×D4×D19C22semidirect
28. C2×D4×D19C22semidirect
29. C2×#64541C22semidirect
30. C2×#64541C22semidirect
31. C22×D76C22semidirect
32. C22×D76C22semidirect
33. C22×C4×D19C22semidirect
34. C22×C4×D19C22semidirect
35. C19×#126C22semidirect
36. C19×#125C22semidirect
37. C19×#123C22semidirect
38. C19×#121C22semidirect
39. C19×#121C22semidirect
40. C19×#121C22semidirect
41. C4×D4×C19C22semidirect
42. C4×D4×C19C22semidirect
43. C4×D4×C19C22semidirect
44. C19×#117C22semidirect
45. C2×C4⋊C4×C19C22semidirect
46. #10597386C22semidirect
47. #10597386C22semidirect
48. #10597385C22semidirect
49. #10597385C22semidirect
50. #10597384C22semidirect
51. #10597383C22semidirect
52. #10597383C22semidirect
53. #10597383C22semidirect
54. D4×Dic19C22semidirect
55. D4×Dic19C22semidirect
56. #10597376C22semidirect
57. #10597376C22semidirect
60. C4×C22⋊D19C22semidirect
61. C4×C22⋊D19C22semidirect
62. C2×(C2×D19)⋊C4C22semidirect
63. C2×(C2×D19)⋊C4C22semidirect
64. #10597370C22semidirect
65. #10597370C22semidirect
66. #10597344C22semidirect
67. #10597344C22semidirect
68. #10597343C22semidirect
69. #10597343C22semidirect
70. #10597342C22semidirect
72. #10597341C22semidirect
73. #10597341C22semidirect
74. #10597341C22semidirect
75. #10597341C22semidirect
76. #10597341C22semidirect
77. #10597341C22semidirect
78. #10597341C22semidirect
79. #10597340C22semidirect
80. #10597340C22semidirect
81. #10597340C22semidirect
82. #10597339C22semidirect
83. #10597339C22semidirect
84. #10597339C22semidirect
85. #10597339C22semidirect
86. #10597338C22semidirect
87. #10597338C22semidirect
88. C4⋊C4×D19C22semidirect
89. C4⋊C4×D19C22semidirect
90. #10597335C22semidirect
91. #10597334C22semidirect
92. #10597333C22semidirect
93. #10597332C22semidirect
94. #10597332C22semidirect
95. #10597331C22semidirect
96. #10597331C22semidirect
97. #10597330C22semidirect
98. #10597330C22semidirect
99. #10597330C22semidirect
100. #10597330C22semidirect
101. #10597330C22semidirect
102. #10597330C22semidirect
103. #10597329C22semidirect
104. #10597328C22semidirect
105. #10597328C22semidirect
106. #10597328C22semidirect
108. (C22⋊D19)⋊C4C22semidirect
109. (C22⋊D19)⋊C4C22semidirect
110. (C22⋊D19)⋊C4C22semidirect
111. C22⋊C4×D19C22semidirect
112. C22⋊C4×D19C22semidirect
113. C22⋊C4×D19C22semidirect
114. C22⋊C4×D19C22semidirect
115. #10597321C22semidirect
116. #10597321C22semidirect
117. C4×D76C22semidirect
118. C4×D76C22semidirect
119. C4×D76C22semidirect
120. C4×D76C22semidirect
121. #10597318C22semidirect
122. C42×D19C22semidirect
277. C22⋊D19#41semidirect
361. #553D19semidirect
407. #126C2×D19semidirect
409. #125C2×D19semidirect
420. #123C2×D19semidirect
445. #121C2×D19semidirect
446. #121C2×D19semidirect
447. #121C2×D19semidirect
473. C4×D4C2×D19semidirect
474. C4×D4C2×D19semidirect
475. C4×D4C2×D19semidirect
479. #117C2×D19semidirect
482. C2×C4⋊C4C2×D19semidirect
490. C19#3519semidirect

Maximal subgroups

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

subgroupindex
#119272572
#119272492
#119272472
#119272452
#119272122
#119271902
#119271892
#119271862
#119271782
#119271462
#119271332
#119271312
#119270912
#119270792
#119270562
#119270542
C2×#105973412
#121×D192
#119270162
C4×D4×D192
C19×#5532
#351919