Finite Group Databasebeta

← #14577813

Subgroups — #14577813

Order 2432.

1166 conjugacy classes of subgroups.

The subgroup lattice has 1082 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11927289C211yesmaximal, characteristic, complemented
2#11927289C211yesmaximal, characteristic, complemented
3#11927283C211yesmaximal, characteristic, complemented
4#11927281C211yesmaximal, characteristic, complemented
5#11927243C211yesmaximal, characteristic, complemented
6#11927237C211yesmaximal, characteristic, complemented
7#11927225C211yesmaximal, characteristic, complemented
8#11927223C211yesmaximal, characteristic, complemented
9#11927188C211yesmaximal, characteristic, complemented
10#11927188C211yesmaximal, characteristic, complemented
11#11927188C211yesmaximal, characteristic, complemented
12#11927183C211yesmaximal, characteristic, complemented
13#11927181C211yesmaximal, characteristic, complemented
14#11927181C211yesmaximal, characteristic, complemented
15D4×C22⋊D19C211yesmaximal, characteristic, complemented
16#11927148C211yesmaximal, characteristic, complemented
17#11927144C211yesmaximal, characteristic, complemented
18#11927139C211yesmaximal, characteristic, complemented
19#11927136C211yesmaximal, characteristic, complemented
20#11927136C211yesmaximal, characteristic, complemented
21#11927129C211yesmaximal, characteristic, complemented
22#11927129C211yesmaximal, characteristic, complemented
23#11927126C211yesmaximal, characteristic, complemented
24#11927121C211yesmaximal, characteristic, complemented
25#11927104C211yesmaximal, characteristic, complemented
26#11927103C211yesmaximal, characteristic, complemented
27#11927103C211yesmaximal, characteristic, complemented
28#11927050C211yesmaximal, characteristic, complemented
29C2×#10597381C211yesmaximal, characteristic, complemented
30C2×#10597385C211yesmaximal, characteristic, complemented
31D42×C19C211yesmaximal, characteristic, complemented
32C22×D4×C19C2211yescharacteristic
33C22×D4×C19C2211yescharacteristic, complemented
34C22×D4×C19C2211yescharacteristic, complemented
35C22×D4×C19C2211yescharacteristic, complemented
36C22×C22⋊D19C2211yescharacteristic, complemented
37C22×C22⋊D19C2211yescharacteristic, complemented
38C22×C22⋊D19C2211yescharacteristic, complemented
39C23×Dic19C2211yescharacteristic, complemented
40C2×#64543C2211yescharacteristic, complemented
41C2×#64543C2211yescharacteristic, complemented
42C2×#64543C2211yescharacteristic, complemented
43C2×D4×D19C2211yescharacteristic, complemented
44C19×#127C2211yescharacteristic, complemented
45C19×#121C2211yescharacteristic
46C19×#121C2211yescharacteristic, complemented
47C19×#121C2211yescharacteristic, complemented
48C19×#121C2211yescharacteristic, complemented
49C19×#120C2211yescharacteristic
50C19×#120C2211yescharacteristic, complemented
51C19×#120C2211yescharacteristic, complemented
52C19×#120C2211yescharacteristic, complemented
53C4×D4×C19C2211yescharacteristic, complemented
54C4×D4×C19C2211yescharacteristic, complemented
55#10597399C2211yescharacteristic, complemented
56#10597399C2211yescharacteristic, complemented
57#10597399C2211yescharacteristic, complemented
58#10597399C2211yescharacteristic, complemented
59#10597399C2211yescharacteristic, complemented
60#10597399C2211yescharacteristic, complemented
61C2×C22⋊Dic19C2211yescharacteristic, complemented
62C2×C22⋊Dic19C2211yescharacteristic, complemented
63C2×C22⋊Dic19C2211yescharacteristic, complemented
64C2×C22⋊Dic19C2211yescharacteristic, complemented
65C2×C22⋊Dic19C2211yescharacteristic, complemented
66C2×C22⋊Dic19C2211yescharacteristic, complemented
67#10597386C2211yescharacteristic, complemented
68#10597385C2211yescharacteristic
69#10597385C2211yescharacteristic
70#10597385C2211yescharacteristic, complemented
71#10597385C2211yescharacteristic, complemented
72#10597385C2211yescharacteristic, complemented
73#10597385C2211yescharacteristic, complemented
74#10597385C2211yescharacteristic, complemented
75#10597385C2211yescharacteristic, complemented
76#10597385C2211yescharacteristic, complemented
77#10597385C2211yescharacteristic, complemented
78#10597385C2211yescharacteristic, complemented
79#10597385C2211yescharacteristic, complemented
80#10597385C2211yescharacteristic, complemented
81#10597385C2211yescharacteristic, complemented
82#10597385C2211yescharacteristic, complemented
83#10597385C2211yescharacteristic, complemented
84#10597385C2211yescharacteristic, complemented
85#10597385C2211yescharacteristic, complemented
86#10597385C2211yescharacteristic, complemented
87#10597385C2211yescharacteristic, complemented
88#10597385C2211yescharacteristic, complemented
89#10597385C2211yescharacteristic, complemented
90#10597384C2211yescharacteristic, complemented
91#10597384C2211yescharacteristic, complemented
92#10597384C2211yescharacteristic, complemented
93#10597384C2211yescharacteristic, complemented
94#10597384C2211yescharacteristic, complemented
95#10597384C2211yescharacteristic, complemented
96#10597383C2211yescharacteristic
97#10597383C2211yescharacteristic, complemented
98#10597383C2211yescharacteristic, complemented
99#10597383C2211yescharacteristic, complemented
100#10597383C2211yescharacteristic, complemented
101#10597383C2211yescharacteristic, complemented
102#10597382C2211yescharacteristic, complemented
103#10597382C2211yescharacteristic, complemented
104#10597382C2211yescharacteristic, complemented
105#10597381C2211yescharacteristic, complemented
106#10597381C2211yescharacteristic, complemented
107#10597381C2211yescharacteristic, complemented
108#10597381C2211yescharacteristic, complemented
109#10597381C2211yescharacteristic, complemented
110#10597381C2211yescharacteristic, complemented
111#10597381C2211yescharacteristic, complemented
112#10597381C2211yescharacteristic, complemented
113#10597381C2211yescharacteristic, complemented
114#10597381C2211yescharacteristic, complemented
115#10597381C2211yescharacteristic, complemented
116#10597381C2211yescharacteristic, complemented
117#10597381C2211yescharacteristic, complemented
118#10597381C2211yescharacteristic, complemented
119#10597381C2211yescharacteristic, complemented
120#10597381C2211yescharacteristic, complemented
121D4×Dic19C2211yescharacteristic, complemented
122D4×Dic19C2211yescharacteristic, complemented
123D4×Dic19C2211yescharacteristic, complemented
124D4×Dic19C2211yescharacteristic, complemented
125D4×Dic19C2211yescharacteristic, complemented
126D4×Dic19C2211yescharacteristic, complemented
127#10597376C2211yescharacteristic, complemented
128#10597375C2211yescharacteristic, complemented
129#10597375C2211yescharacteristic, complemented
130#10597375C2211yescharacteristic, complemented
131#10597375C2211yescharacteristic, complemented
132C4×C22⋊D19C2211yescharacteristic, complemented
133C4×C22⋊D19C2211yescharacteristic, complemented
134C4×C22⋊D19C2211yescharacteristic, complemented
135C4×C22⋊D19C2211yescharacteristic, complemented
136C2×(C2×D19)⋊C4C2211yescharacteristic, complemented
137#10597370C2211yescharacteristic, complemented
138#10597370C2211yescharacteristic, complemented
139#10597370C2211yescharacteristic, complemented
140C2×Dic19⋊C4C2211yescharacteristic, complemented
141C2×Dic19⋊C4C2211yescharacteristic, complemented
142C2×Dic19⋊C4C2211yescharacteristic, complemented
143#10597344C2211yescharacteristic, complemented
144#10597342C2211yescharacteristic, complemented
145#10597342C2211yescharacteristic, complemented
146#10597342C2211yescharacteristic, complemented
147#10597340C2211yescharacteristic, complemented
148#10597335C2211yescharacteristic, complemented
149#10597335C2211yescharacteristic, complemented
150#10597335C2211yescharacteristic, complemented
151#10597332C2211yescharacteristic, complemented
152#10597332C2211yescharacteristic, complemented
153#10597331C2211yescharacteristic, complemented
154#10597331C2211yescharacteristic, complemented
155#10597331C2211yescharacteristic, complemented
156#10597330C2211yescharacteristic, complemented
157#10597330C2211yescharacteristic, complemented
158#10597330C2211yescharacteristic, complemented
159#10597329C2211yescharacteristic, complemented
160#10597329C2211yescharacteristic, complemented
161#10597329C2211yescharacteristic, complemented
162#10597329C2211yescharacteristic, complemented
163#10597329C2211yescharacteristic, complemented
164(C22⋊D19)⋊C4C2211yescharacteristic, complemented
165(C22⋊D19)⋊C4C2211yescharacteristic, complemented
166(C22⋊D19)⋊C4C2211yescharacteristic, complemented
167(C22⋊D19)⋊C4C2211yescharacteristic, complemented
168C22⋊C4×D19C2211yescharacteristic, complemented
169C22⋊C4×D19C2211yescharacteristic, complemented
170#10597325C2211yescharacteristic, complemented
171#10597325C2211yescharacteristic, complemented
172#10597325C2211yescharacteristic, complemented
173#10597325C2211yescharacteristic, complemented
174#10597325C2211yescharacteristic, complemented
175#10597324C2211yescharacteristic, complemented
176#10597324C2211yescharacteristic, complemented
177#10597324C2211yescharacteristic, complemented
178#10597324C2211yescharacteristic, complemented
179#10597324C2211yescharacteristic, complemented
180#10597324C2211yescharacteristic, complemented
181#10597323C2211yescharacteristic, complemented
182#10597323C2211yescharacteristic, complemented
183#10597322C2211yescharacteristic, complemented
184#10597322C2211yescharacteristic, complemented
185#10597318C2211yescharacteristic, complemented
186#10597316C2211yescharacteristic, complemented
187C24×C19C2311yescharacteristic
188C24×C19C2311yescharacteristic
189C24×C19C2311yescharacteristic
190C24×C19C2311yescharacteristic
191C23×D19C2311yescharacteristic
192C23×D19C2311yescharacteristic
193C2×D4×C19—42no—
194C2×D4×C19—42no—
195C2×D4×C19—42no—
196C2×D4×C19—42no—
197C2×D4×C19C2311yescharacteristic
198C2×D4×C19C2311yescharacteristic
199C2×D4×C19C2311yescharacteristic
200C2×D4×C19C2311yescharacteristic
201C2×D4×C19C2311yescharacteristic
202C2×D4×C19C2311yescharacteristic
203C2×D4×C19C2311yescharacteristic
204C2×D4×C19C2311yescharacteristic
205C2×D4×C19C2311yescharacteristic
206C2×D4×C19C2311yescharacteristic
207C2×D4×C19C2311yescharacteristic
208C2×D4×C19C2311yescharacteristic
209C2×D4×C19C2311yescharacteristic
210C2×D4×C19C2311yescharacteristic
211C2×D4×C19C2311yescharacteristic
212C2×D4×C19C2311yescharacteristic
213C22×C4×C19C2311yescharacteristic
214C22×C4×C19C2311yescharacteristic
215C22×C4×C19C2311yescharacteristic
216C22×C4×C19C2311yescharacteristic
217C2×C22⋊D19—42no—
218C2×C22⋊D19—42no—
219C2×C22⋊D19—42no—
220C2×C22⋊D19C2311yescharacteristic
221C2×C22⋊D19C2311yescharacteristic
222C2×C22⋊D19C2311yescharacteristic
223C2×C22⋊D19C2311yescharacteristic
224C2×C22⋊D19C2311yescharacteristic
225C2×C22⋊D19C2311yescharacteristic
226C2×C22⋊D19C2311yescharacteristic
227C2×C22⋊D19C2311yescharacteristic
228C2×C22⋊D19C2311yescharacteristic
229C2×C22⋊D19C2311yescharacteristic
230C2×C22⋊D19C2311yescharacteristic
231C2×C22⋊D19C2311yescharacteristic
232C2×C22⋊D19C2311yescharacteristic
233C2×C22⋊D19C2311yescharacteristic
234C2×C22⋊D19C2311yescharacteristic
235C2×C22⋊D19C2311yescharacteristic
236C2×C22⋊D19C2311yescharacteristic
237C2×C22⋊D19C2311yescharacteristic
238C2×C22⋊D19C2311yescharacteristic
239C2×C22⋊D19C2311yescharacteristic
240C22×Dic19—42no—
241C22×Dic19C2311yescharacteristic
242C22×Dic19C2311yescharacteristic
243C22×Dic19C2311yescharacteristic
244C22×Dic19C2311yescharacteristic
245C22×Dic19C2311yescharacteristic
246C22×Dic19C2311yescharacteristic
247C22×Dic19C2311yescharacteristic
248C22×Dic19C2311yescharacteristic
249C22×Dic19C2311yescharacteristic
250C22×Dic19C2311yescharacteristic
251C22×Dic19C2311yescharacteristic
252C22×Dic19C2311yescharacteristic
253C22×Dic19C2311yescharacteristic
254C22×Dic19C2311yescharacteristic
255#64543—42no—
256#64543—42no—
257#64543—42no—
258D4×D19—42no—
259C2×D76C2311yescharacteristic
260C2×C4×D19C2311yescharacteristic
261C2×C4×D19C2311yescharacteristic
262C2×C4×D19C2311yescharacteristic
263C2×C4×D19C2311yescharacteristic
264C2×C4×D19C2311yescharacteristic
265C2×Dic38C2311yescharacteristic
266C2×Dic38C2311yescharacteristic
267C2×Dic38C2311yescharacteristic
268C4⋊C4×C19C2311yescharacteristic
269C4⋊C4×C19C2311yescharacteristic
270C22⋊C4×C19C2311yescharacteristic
271C22⋊C4×C19C2311yescharacteristic
272C22⋊C4×C19C2311yescharacteristic
273C22⋊C4×C19C2311yescharacteristic
274C22⋊C4×C19C2311yescharacteristic
275C22⋊C4×C19C2311yescharacteristic
276C22⋊C4×C19C2311yescharacteristic
277C22⋊C4×C19C2311yescharacteristic
278C42×C19C2311yescharacteristic
279C22⋊Dic19C2311yescharacteristic
280C22⋊Dic19C2311yescharacteristic
281C22⋊Dic19C2311yescharacteristic
282C22⋊Dic19C2311yescharacteristic
283C22⋊Dic19C2311yescharacteristic
284C22⋊Dic19C2311yescharacteristic
285C22⋊Dic19C2311yescharacteristic
286C22⋊Dic19C2311yescharacteristic
287C22⋊Dic19C2311yescharacteristic
288C22⋊Dic19C2311yescharacteristic
289C22⋊Dic19C2311yescharacteristic
290C22⋊Dic19C2311yescharacteristic
291C22⋊Dic19C2311yescharacteristic
292C22⋊Dic19C2311yescharacteristic
293C22⋊Dic19C2311yescharacteristic
294C22⋊Dic19C2311yescharacteristic
295C22⋊Dic19C2311yescharacteristic
296C22⋊Dic19C2311yescharacteristic
297C22⋊Dic19C2311yescharacteristic
298C22⋊Dic19C2311yescharacteristic
299C22⋊Dic19C2311yescharacteristic
300C22⋊Dic19C2311yescharacteristic
301C22⋊Dic19C2311yescharacteristic
302C22⋊Dic19C2311yescharacteristic
303C22⋊Dic19C2311yescharacteristic
304C22⋊Dic19C2311yescharacteristic
305C22⋊Dic19C2311yescharacteristic
306C22⋊Dic19C2311yescharacteristic
307(C2×D19)⋊C4C2311yescharacteristic
308(C2×D19)⋊C4C2311yescharacteristic
309(C2×D19)⋊C4C2311yescharacteristic
310(C2×D19)⋊C4C2311yescharacteristic
311(C2×D19)⋊C4C2311yescharacteristic
312(C2×D19)⋊C4C2311yescharacteristic
313(C2×D19)⋊C4C2311yescharacteristic
314(C2×D19)⋊C4C2311yescharacteristic
315(C2×D19)⋊C4C2311yescharacteristic
316(C2×D19)⋊C4C2311yescharacteristic
317(C2×D19)⋊C4C2311yescharacteristic
318(C2×D19)⋊C4C2311yescharacteristic
319(C2×D19)⋊C4C2311yescharacteristic
320(C2×D19)⋊C4C2311yescharacteristic
321C4⋊Dic19C2311yescharacteristic
322C4⋊Dic19C2311yescharacteristic
323C4⋊Dic19C2311yescharacteristic
324C4⋊Dic19C2311yescharacteristic
325C4⋊Dic19C2311yescharacteristic
326C4⋊Dic19C2311yescharacteristic
327Dic19⋊C4C2311yescharacteristic
328Dic19⋊C4C2311yescharacteristic
329Dic19⋊C4C2311yescharacteristic
330Dic19⋊C4C2311yescharacteristic
331Dic19⋊C4C2311yescharacteristic
332Dic19⋊C4C2311yescharacteristic
333Dic19⋊C4C2311yescharacteristic
334Dic19⋊C4C2311yescharacteristic
335Dic19⋊C4C2311yescharacteristic
336Dic19⋊C4C2311yescharacteristic
337Dic19⋊C4C2311yescharacteristic
338Dic19⋊C4C2311yescharacteristic
339Dic19⋊C4C2311yescharacteristic
340Dic19⋊C4C2311yescharacteristic
341Dic19⋊C4C2311yescharacteristic
342Dic19⋊C4C2311yescharacteristic
343Dic19⋊C4C2311yescharacteristic
344Dic19⋊C4C2311yescharacteristic
345Dic19⋊C4C2311yescharacteristic
346Dic19⋊C4C2311yescharacteristic
347Dic19⋊C4C2311yescharacteristic
348Dic19⋊C4C2311yescharacteristic
349C4×Dic19C2311yescharacteristic
350C4×Dic19C2311yescharacteristic
351C4×Dic19C2311yescharacteristic
352C4×Dic19C2311yescharacteristic
353C4×Dic19C2311yescharacteristic
354C23×C19—22no—
355C23×C19—22no—
356C23×C19—22no—
357C23×C19—22no—
358C23×C19—41no—
359C23×C19—41no—
360C23×C19—41no—
361C23×C19—41no—
362C23×C19—41no—
363C23×C19—41no—
364C23×C19—41no—
365C23×C19—41no—
366C23×C19C2411yescharacteristic
367C23×C19C2411yescharacteristic
368C23×C19C2411yescharacteristic
369C23×C19C2411yescharacteristic
370C23×C19C2411yescharacteristic
371C23×C19C2411yescharacteristic
372C23×C19C2411yescharacteristic
373C23×C19C2411yescharacteristic
374C22×D19—22no—
375C22×D19—41no—
376C22×D19—41no—
377C22×D19—41no—
378C22×D19—41no—
379C22×D19—41no—
380C22×D19C2411yescharacteristic
381C22×D19C2411yescharacteristic
382C22×D19C2411yescharacteristic
383D4×C19—22no—
384D4×C19—22no—
385D4×C19—22no—
386D4×C19—22no—
387D4×C19—22no—
388D4×C19—22no—
389D4×C19—41no—
390D4×C19—41no—
391D4×C19—41no—
392D4×C19—41no—
393D4×C19—41no—
394D4×C19—41no—
395D4×C19—41no—
396D4×C19—41no—
397D4×C19—41no—
398D4×C19—41no—
399C2×C4×C19—41no—
400C2×C4×C19—41no—
401C2×C4×C19—41no—
402C2×C4×C19—41no—
403C2×C4×C19C2411yescharacteristic
404C2×C4×C19C2411yescharacteristic
405C2×C4×C19C2411yescharacteristic
406C2×C4×C19C2411yescharacteristic
407C2×C4×C19C2411yescharacteristic
408C2×C4×C19C2411yescharacteristic
409C2×C4×C19C2411yescharacteristic
410C22⋊D19—22no—
411C22⋊D19—22no—
412C22⋊D19—22no—
413C22⋊D19—22no—
414C22⋊D19—41no—
415C22⋊D19—41no—
416C22⋊D19—41no—
417C22⋊D19—41no—
418C22⋊D19—41no—
419C22⋊D19—41no—
420C22⋊D19—41no—
421C22⋊D19—41no—
422C22⋊D19—41no—
423C22⋊D19—41no—
424C22⋊D19—41no—
425C22⋊D19—41no—
426C22⋊D19—41no—
427C22⋊D19—41no—
428C22⋊D19—41no—
429C22⋊D19—41no—
430C2×Dic19—22no—
431C2×Dic19—22no—
432C2×Dic19—22no—
433C2×Dic19—41no—
434C2×Dic19—41no—
435C2×Dic19—41no—
436C2×Dic19—41no—
437C2×Dic19—41no—
438C2×Dic19—41no—
439C2×Dic19—41no—
440C2×Dic19—41no—
441C2×Dic19—41no—
442C2×Dic19—41no—
443C2×Dic19—41no—
444C2×Dic19C2411yescharacteristic
445C2×Dic19C2411yescharacteristic
446C2×Dic19C2411yescharacteristic
447C2×Dic19C2411yescharacteristic
448C2×Dic19C2411yescharacteristic
449C2×Dic19C2411yescharacteristic
450C2×Dic19C2411yescharacteristic
451C2×Dic19C2411yescharacteristic
452C2×Dic19C2411yescharacteristic
453C2×Dic19C2411yescharacteristic
454C2×Dic19C2411yescharacteristic
455C2×Dic19C2411yescharacteristic
456C2×Dic19C2411yescharacteristic
457D76—41no—
458C4×D19—41no—
459C4×D19—41no—
460C4×D19—41no—
461C4×D19—41no—
462C4×D19—41no—
463Dic38—41no—
464Dic38—41no—
465Dic38—41no—
466#3534—191nomaximal, Sylow
467C22×C19—21no—
468C22×C19—21no—
469C22×C19—21no—
470C22×C19—21no—
471C22×C19—21no—
472C22×C19—21no—
473C22×C19—21no—
474C22×C19—21no—
475C22×C19—21no—
476C22×C19—21no—
477C22×C19—21no—
478C22×C19—21no—
479C22×C19—21no—
480C22×C19—21no—
481C22×C19—21no—
482C22×C19—21no—
483C22×C19—21no—
484C22×C19—21no—
485C22×C19—21no—
486C22×C19—21no—
487C22×C19—21no—
488C22×C19—21no—
489C22×C19—44no—
490C22×C19—82no—
491C22×C19—82no—
492C22×C19—82no—
493C22×C19H(5,𝔽2)12yes—
494C22×C19H(5,𝔽2)12yes—
495C22×C19C2511yescharacteristic
496C2×D19—21no—
497C2×D19—21no—
498C2×D19—21no—
499C2×D19—21no—
500C2×D19—21no—
501C2×D19—21no—
502C2×D19—21no—
503C2×D19—21no—
504C2×D19—21no—
505C2×D19—82no—
506C2×D19—82no—
507C4×C19—21no—
508C4×C19—21no—
509C4×C19—21no—
510C4×C19—21no—
511C4×C19—21no—
512C4×C19—21no—
513C4×C19—21no—
514Dic19—21no—
515Dic19—21no—
516Dic19—21no—
517Dic19—21no—
518Dic19—21no—
519Dic19—21no—
520Dic19—21no—
521Dic19—21no—
522Dic19—21no—
523Dic19—21no—
524Dic19—21no—
525Dic19—21no—
526Dic19—21no—
527#562—191no—
528#562—191no—
529#560—191no—
530#560—191no—
531#553—191no—
532#553—191no—
533#551—191no—
534#551—191no—
535#546—191no—
536#546—191no—
537#546—191no—
538#546—191no—
539#546—191no—
540#546—191no—
541D42—191no—
542D42D1911yescharacteristic, complemented
543#540—191no—
544#540—191no—
545#539—191no—
546#539—191no—
547#539—191no—
548#538—191no—
549#538—191no—
550#538—191no—
551#537—191no—
552#534—191no—
553#534—191no—
554#534—191no—
555#525—191no—
556C2×#123—191no—
557C2×#121—191no—
558C2×C19—22no—
559C2×C19—22no—
560C2×C19—41no—
561C2×C19—41no—
562C2×C19—41no—
563C2×C19—41no—
564C2×C19—41no—
565C2×C19—41no—
566C2×C19C2×H(5,𝔽2)11yescharacteristic
567C2×C19C2×H(5,𝔽2)11yescharacteristic
568C2×C19#58511yescharacteristic
569D19—41no—
570D19—41no—
571D19—41no—
572C2×#41—191no—
573C2×#41—191no—
574C2×#41—191no—
575C22×D4—191no—
576C22×D4—191no—
577C22×D4—191no—
578C22×D4—191no—
579C22×D4C2×D1911yescharacteristic
580C22×D4C2×D1911yescharacteristic, complemented
581C22×D4C2×D1911yescharacteristic, complemented
582C22×D4C2×D1911yescharacteristic, complemented
583C23×C4—191no—
584#127—191no—
585#127C2×D1911yescharacteristic, complemented
586#126—191no—
587#126—191no—
588#126—191no—
589#126—191no—
590#126—191no—
591#126—191no—
592#126—191no—
593#126—191no—
594#125—191no—
595#125—191no—
596#125—191no—
597#125—191no—
598#124—191no—
599#124—191no—
600#124—191no—
601#124—191no—
602#124—191no—
603#124—191no—
604#123—191no—
605#123—191no—
606#123—191no—
607#123—191no—
608#123—191no—
609#123—191no—
610#123—191no—
611#123—191no—
612#123—191no—
613#123—191no—
614#123—191no—
615#123—191no—
616#123—191no—
617#123—191no—
618#123—191no—
619#123—191no—
620#123—191no—
621#123—191no—
622#123—191no—
623#123—191no—
624#123—191no—
625#123—191no—
626#123—191no—
627#123—191no—
628#123—191no—
629#123—191no—
630#123—191no—
631#123—191no—
632C22⋊Q8—191no—
633C22⋊Q8—191no—
634C22⋊Q8—191no—
635C22⋊Q8—191no—
636C22⋊Q8—191no—
637C22⋊Q8—191no—
638C22⋊Q8—191no—
639C22⋊Q8—191no—
640C22⋊Q8—191no—
641C22⋊Q8—191no—
642C22⋊Q8—191no—
643C22⋊Q8—191no—
644#121—191no—
645#121—191no—
646#121—191no—
647#121—191no—
648#121—191no—
649#121—191no—
650#121—191no—
651#121—191no—
652#121—191no—
653#121—191no—
654#121—191no—
655#121—191no—
656#121—191no—
657#121—191no—
658#121—191no—
659#121—191no—
660#121—191no—
661#121—191no—
662#121—191no—
663#121—191no—
664#121—191no—
665#121—191no—
666#121—191no—
667#121—191no—
668#121—191no—
669#121—191no—
670#121—191no—
671#121—191no—
672#121—191no—
673#121—191no—
674#121—191no—
675#121—191no—
676#121C2×D1911yescharacteristic
677#121C2×D1911yescharacteristic, complemented
678#121C2×D1911yescharacteristic, complemented
679#121C2×D1911yescharacteristic, complemented
680#120—191no—
681#120—191no—
682#120—191no—
683#120—191no—
684#120—191no—
685#120—191no—
686#120—191no—
687#120—191no—
688#120—191no—
689#120—191no—
690#120—191no—
691#120—191no—
692#120C2×D1911yescharacteristic
693#120C2×D1911yescharacteristic, complemented
694#120C2×D1911yescharacteristic, complemented
695#120C2×D1911yescharacteristic, complemented
696C4×D4—191no—
697C4×D4—191no—
698C4×D4—191no—
699C4×D4—191no—
700C4×D4—191no—
701C4×D4—191no—
702C4×D4—191no—
703C4×D4—191no—
704C4×D4—191no—
705C4×D4—191no—
706C4×D4—191no—
707C4×D4—191no—
708C4×D4—191no—
709C4×D4—191no—
710C4×D4C2×D1911yescharacteristic, complemented
711C4×D4C2×D1911yescharacteristic, complemented
712#117—191no—
713#117—191no—
714#117—191no—
715C2×C4⋊C4—191no—
716C2×C4⋊C4—191no—
717C2×C4⋊C4—191no—
718C2×C22⋊C4—191no—
719C2×C22⋊C4—191no—
720C2×C22⋊C4—191no—
721C2×C22⋊C4—191no—
722C2×C22⋊C4—191no—
723C2×C22⋊C4—191no—
724C2×C22⋊C4—191no—
725C2×C22⋊C4—191no—
726C2×C22⋊C4—191no—
727C19#353411yescharacteristic, complemented, Sylow
728C24—191no—
729C24—191no—
730C24C22×D1911yescharacteristic
731C24C22×D1911yescharacteristic
732C24C22×D1911yescharacteristic
733C24C22×D1911yescharacteristic
734#41—762no—
735#41—762no—
736#41—762no—
737C2×Q8—191no—
738C2×Q8—191no—
739C2×Q8—191no—
740C2×D4—42no—
741C2×D4—42no—
742C2×D4—42no—
743C2×D4—42no—
744C2×D4—191no—
745C2×D4—191no—
746C2×D4—191no—
747C2×D4—191no—
748C2×D4—191no—
749C2×D4—191no—
750C2×D4—191no—
751C2×D4—191no—
752C2×D4—191no—
753C2×D4—191no—
754C2×D4—191no—
755C2×D4—191no—
756C2×D4—191no—
757C2×D4—191no—
758C2×D4—191no—
759C2×D4—191no—
760C2×D4—191no—
761C2×D4—191no—
762C2×D4—191no—
763C2×D4—191no—
764C2×D4—191no—
765C2×D4—762no—
766C2×D4—762no—
767C2×D4—762no—
768C2×D4—762no—
769C2×D4C22×D1911yescharacteristic
770C2×D4C22×D1911yescharacteristic
771C2×D4C22×D1911yescharacteristic
772C2×D4C22×D1911yescharacteristic
773C2×D4C22×D1911yescharacteristic
774C2×D4C22×D1911yescharacteristic
775C2×D4C22×D1911yescharacteristic
776C2×D4C22×D1911yescharacteristic
777C2×D4C22×D1911yescharacteristic
778C2×D4C22×D1911yescharacteristic
779C2×D4C22×D1911yescharacteristic
780C2×D4C22×D1911yescharacteristic
781C2×D4C22×D1911yescharacteristic
782C2×D4C22×D1911yescharacteristic
783C2×D4C22×D1911yescharacteristic
784C2×D4C22×D1911yescharacteristic
785C22×C4—191no—
786C22×C4—191no—
787C22×C4—191no—
788C22×C4—191no—
789C22×C4—191no—
790C22×C4—191no—
791C22×C4—191no—
792C22×C4—191no—
793C22×C4—191no—
794C22×C4—191no—
795C22×C4—191no—
796C22×C4—191no—
797C22×C4—191no—
798C22×C4—191no—
799C22×C4—191no—
800C22×C4—191no—
801C22×C4—191no—
802C22×C4—191no—
803C22×C4—191no—
804C22×C4—762no—
805C22×C4C22×D1911yescharacteristic
806C22×C4C22×D1911yescharacteristic
807C22×C4C22×D1911yescharacteristic
808C22×C4C22×D1911yescharacteristic
809C4⋊C4—191no—
810C4⋊C4—191no—
811C4⋊C4—191no—
812C4⋊C4—191no—
813C4⋊C4—191no—
814C4⋊C4—191no—
815C4⋊C4—191no—
816C4⋊C4—191no—
817C4⋊C4—191no—
818C4⋊C4—191no—
819C4⋊C4—191no—
820C4⋊C4—191no—
821C4⋊C4—191no—
822C4⋊C4—191no—
823C4⋊C4—191no—
824C4⋊C4—191no—
825C4⋊C4—191no—
826C4⋊C4—191no—
827C4⋊C4—191no—
828C4⋊C4—191no—
829C4⋊C4—191no—
830C4⋊C4—191no—
831C4⋊C4—191no—
832C4⋊C4—191no—
833C4⋊C4—191no—
834C4⋊C4—191no—
835C4⋊C4—191no—
836C4⋊C4—191no—
837C4⋊C4C22×D1911yescharacteristic
838C4⋊C4C22×D1911yescharacteristic
839C22⋊C4—191no—
840C22⋊C4—191no—
841C22⋊C4—191no—
842C22⋊C4—191no—
843C22⋊C4—191no—
844C22⋊C4—191no—
845C22⋊C4—191no—
846C22⋊C4—191no—
847C22⋊C4—191no—
848C22⋊C4—191no—
849C22⋊C4—191no—
850C22⋊C4—191no—
851C22⋊C4—191no—
852C22⋊C4—191no—
853C22⋊C4—191no—
854C22⋊C4—191no—
855C22⋊C4—191no—
856C22⋊C4—191no—
857C22⋊C4—191no—
858C22⋊C4—191no—
859C22⋊C4—191no—
860C22⋊C4—191no—
861C22⋊C4—191no—
862C22⋊C4—191no—
863C22⋊C4—191no—
864C22⋊C4—191no—
865C22⋊C4—191no—
866C22⋊C4—191no—
867C22⋊C4—191no—
868C22⋊C4—191no—
869C22⋊C4—191no—
870C22⋊C4—191no—
871C22⋊C4—191no—
872C22⋊C4—191no—
873C22⋊C4—191no—
874C22⋊C4—191no—
875C22⋊C4—191no—
876C22⋊C4—191no—
877C22⋊C4—191no—
878C22⋊C4—191no—
879C22⋊C4—191no—
880C22⋊C4—191no—
881C22⋊C4C22×D1911yescharacteristic
882C22⋊C4C22×D1911yescharacteristic
883C22⋊C4C22×D1911yescharacteristic
884C22⋊C4C22×D1911yescharacteristic
885C22⋊C4C22×D1911yescharacteristic
886C22⋊C4C22×D1911yescharacteristic
887C22⋊C4C22×D1911yescharacteristic
888C22⋊C4C22×D1911yescharacteristic
889C42—191no—
890C42—191no—
891C42—191no—
892C42—191no—
893C42—191no—
894C42C22×D1911yescharacteristic
895C23—22no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—191no—
908C23—191no—
909C23—191no—
910C23—382no—
911C23—761no—
912C23—761no—
913C23—761no—
914C23—761no—
915C23—761no—
916C23C23×D1911yescharacteristic
917C23C23×D1911yescharacteristic
918C23C23×D1911yescharacteristic
919C23C23×D1911yescharacteristic
920C23C23×D1911yescharacteristic
921C23C23×D1911yescharacteristic
922C23C23×D1911yescharacteristic
923C23C23×D1911yescharacteristic
924Q8—761no—
925Q8—761no—
926Q8—761no—
927D4—22no—
928D4—22no—
929D4—22no—
930D4—22no—
931D4—22no—
932D4—22no—
933D4—41no—
934D4—41no—
935D4—41no—
936D4—41no—
937D4—41no—
938D4—41no—
939D4—41no—
940D4—41no—
941D4—41no—
942D4—41no—
943D4—382no—
944D4—382no—
945D4—382no—
946D4—382no—
947D4—761no—
948D4—761no—
949D4—761no—
950D4—761no—
951D4—761no—
952D4—761no—
953D4—761no—
954D4—761no—
955D4—761no—
956D4—761no—
957D4—761no—
958D4—761no—
959D4—761no—
960D4—761no—
961D4—761no—
962D4—761no—
963D4—761no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—191no—
969C2×C4—191no—
970C2×C4—191no—
971C2×C4—191no—
972C2×C4—191no—
973C2×C4—191no—
974C2×C4—191no—
975C2×C4—191no—
976C2×C4—191no—
977C2×C4—191no—
978C2×C4—191no—
979C2×C4—191no—
980C2×C4—191no—
981C2×C4—382no—
982C2×C4—382no—
983C2×C4—382no—
984C2×C4—761no—
985C2×C4—761no—
986C2×C4—761no—
987C2×C4—761no—
988C2×C4—761no—
989C2×C4—761no—
990C2×C4—761no—
991C2×C4—761no—
992C2×C4—761no—
993C2×C4—761no—
994C2×C4—761no—
995C2×C4—761no—
996C2×C4—761no—
997C2×C4—761no—
998C2×C4—761no—
999C2×C4—761no—
1000C2×C4C23×D1911yescharacteristic
1001C2×C4C23×D1911yescharacteristic
1002C2×C4C23×D1911yescharacteristic
1003C2×C4C23×D1911yescharacteristic
1004C2×C4C23×D1911yescharacteristic
1005C2×C4C23×D1911yescharacteristic
1006C2×C4C23×D1911yescharacteristic
1007C22—21no—
1008C22—21no—
1009C22—21no—
1010C22—21no—
1011C22—21no—
1012C22—21no—
1013C22—21no—
1014C22—21no—
1015C22—21no—
1016C22—21no—
1017C22—21no—
1018C22—21no—
1019C22—21no—
1020C22—21no—
1021C22—21no—
1022C22—21no—
1023C22—21no—
1024C22—21no—
1025C22—21no—
1026C22—21no—
1027C22—21no—
1028C22—21no—
1029C22—44no—
1030C22—82no—
1031C22—82no—
1032C22—82no—
1033C22—381no—
1034C22—381no—
1035C22—381no—
1036C22—381no—
1037C22—381no—
1038C22—381no—
1039C22—381no—
1040C22—381no—
1041C22—381no—
1042C22—1522no—
1043C22—1522no—
1044C22#1059743012yes—
1045C22#1059743012yes—
1046C22C24×D1911yescharacteristic
1047C4—21no—
1048C4—21no—
1049C4—21no—
1050C4—21no—
1051C4—21no—
1052C4—21no—
1053C4—21no—
1054C4—381no—
1055C4—381no—
1056C4—381no—
1057C4—381no—
1058C4—381no—
1059C4—381no—
1060C4—381no—
1061C4—381no—
1062C4—381no—
1063C4—381no—
1064C4—381no—
1065C4—381no—
1066C4—381no—
1067C2—22no—
1068C2—22no—
1069C2—41no—
1070C2—41no—
1071C2—41no—
1072C2—41no—
1073C2—41no—
1074C2—41no—
1075C2—761no—
1076C2—761no—
1077C2—761no—
1078C2C2×#1059743011yescharacteristic
1079C2C2×#1059743011yescharacteristic
1080C2#1192737911yescharacteristic
subgroupG/H
center, FrattiniC22C24×D19
commutator, socle, cosocleC22×C19C25
FittingD42×C19C2
hypercenterD42D19
hypocenterC19#3534
LCSG ▷ C22×C19 ▷ C19
UCSC1 ◁ C22 ◁ D42

Complements

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

NH ≅ G/Ntype
1. #11927289C2semidirect
2. #11927289C2semidirect
3. #11927283C2semidirect
4. #11927281C2semidirect
5. #11927243C2semidirect
6. #11927237C2semidirect
7. #11927225C2semidirect
8. #11927223C2semidirect
9. #11927188C2semidirect
10. #11927188C2semidirect
11. #11927188C2semidirect
12. #11927183C2semidirect
13. #11927181C2semidirect
14. #11927181C2semidirect
15. D4×C22⋊D19C2semidirect
16. #11927148C2semidirect
17. #11927144C2semidirect
18. #11927139C2semidirect
19. #11927136C2semidirect
20. #11927136C2semidirect
21. #11927129C2semidirect
22. #11927129C2semidirect
23. #11927126C2semidirect
24. #11927121C2semidirect
25. #11927104C2semidirect
26. #11927103C2semidirect
27. #11927103C2semidirect
28. #11927050C2semidirect
29. C2×#10597381C2semidirect
30. C2×#10597385C2semidirect
31. D42×C19C2semidirect
33. C22×D4×C19C22semidirect
34. C22×D4×C19C22semidirect
35. C22×D4×C19C22semidirect
36. C22×C22⋊D19C22semidirect
37. C22×C22⋊D19C22semidirect
38. C22×C22⋊D19C22semidirect
39. C23×Dic19C22semidirect
40. C2×#64543C22semidirect
41. C2×#64543C22semidirect
42. C2×#64543C22semidirect
43. C2×D4×D19C22semidirect
44. C19×#127C22semidirect
46. C19×#121C22semidirect
47. C19×#121C22semidirect
48. C19×#121C22semidirect
50. C19×#120C22semidirect
51. C19×#120C22semidirect
52. C19×#120C22semidirect
53. C4×D4×C19C22semidirect
54. C4×D4×C19C22semidirect
55. #10597399C22semidirect
56. #10597399C22semidirect
57. #10597399C22semidirect
58. #10597399C22semidirect
59. #10597399C22semidirect
60. #10597399C22semidirect
61. C2×C22⋊Dic19C22semidirect
62. C2×C22⋊Dic19C22semidirect
63. C2×C22⋊Dic19C22semidirect
64. C2×C22⋊Dic19C22semidirect
65. C2×C22⋊Dic19C22semidirect
66. C2×C22⋊Dic19C22semidirect
67. #10597386C22semidirect
70. #10597385C22semidirect
71. #10597385C22semidirect
72. #10597385C22semidirect
73. #10597385C22semidirect
74. #10597385C22semidirect
75. #10597385C22semidirect
76. #10597385C22semidirect
77. #10597385C22semidirect
78. #10597385C22semidirect
79. #10597385C22semidirect
80. #10597385C22semidirect
81. #10597385C22semidirect
82. #10597385C22semidirect
83. #10597385C22semidirect
84. #10597385C22semidirect
85. #10597385C22semidirect
86. #10597385C22semidirect
87. #10597385C22semidirect
88. #10597385C22semidirect
89. #10597385C22semidirect
90. #10597384C22semidirect
91. #10597384C22semidirect
92. #10597384C22semidirect
93. #10597384C22semidirect
94. #10597384C22semidirect
95. #10597384C22semidirect
97. #10597383C22semidirect
98. #10597383C22semidirect
99. #10597383C22semidirect
100. #10597383C22semidirect
101. #10597383C22semidirect
102. #10597382C22semidirect
103. #10597382C22semidirect
104. #10597382C22semidirect
105. #10597381C22semidirect
106. #10597381C22semidirect
107. #10597381C22semidirect
108. #10597381C22semidirect
109. #10597381C22semidirect
110. #10597381C22semidirect
111. #10597381C22semidirect
112. #10597381C22semidirect
113. #10597381C22semidirect
114. #10597381C22semidirect
115. #10597381C22semidirect
116. #10597381C22semidirect
117. #10597381C22semidirect
118. #10597381C22semidirect
119. #10597381C22semidirect
120. #10597381C22semidirect
121. D4×Dic19C22semidirect
122. D4×Dic19C22semidirect
123. D4×Dic19C22semidirect
124. D4×Dic19C22semidirect
125. D4×Dic19C22semidirect
126. D4×Dic19C22semidirect
127. #10597376C22semidirect
128. #10597375C22semidirect
129. #10597375C22semidirect
130. #10597375C22semidirect
131. #10597375C22semidirect
132. C4×C22⋊D19C22semidirect
133. C4×C22⋊D19C22semidirect
134. C4×C22⋊D19C22semidirect
135. C4×C22⋊D19C22semidirect
136. C2×(C2×D19)⋊C4C22semidirect
137. #10597370C22semidirect
138. #10597370C22semidirect
139. #10597370C22semidirect
140. C2×Dic19⋊C4C22semidirect
141. C2×Dic19⋊C4C22semidirect
142. C2×Dic19⋊C4C22semidirect
143. #10597344C22semidirect
144. #10597342C22semidirect
145. #10597342C22semidirect
146. #10597342C22semidirect
147. #10597340C22semidirect
148. #10597335C22semidirect
149. #10597335C22semidirect
150. #10597335C22semidirect
151. #10597332C22semidirect
152. #10597332C22semidirect
153. #10597331C22semidirect
154. #10597331C22semidirect
155. #10597331C22semidirect
156. #10597330C22semidirect
157. #10597330C22semidirect
158. #10597330C22semidirect
159. #10597329C22semidirect
160. #10597329C22semidirect
161. #10597329C22semidirect
162. #10597329C22semidirect
163. #10597329C22semidirect
164. (C22⋊D19)⋊C4C22semidirect
165. (C22⋊D19)⋊C4C22semidirect
166. (C22⋊D19)⋊C4C22semidirect
167. (C22⋊D19)⋊C4C22semidirect
168. C22⋊C4×D19C22semidirect
169. C22⋊C4×D19C22semidirect
170. #10597325C22semidirect
171. #10597325C22semidirect
172. #10597325C22semidirect
173. #10597325C22semidirect
174. #10597325C22semidirect
175. #10597324C22semidirect
176. #10597324C22semidirect
177. #10597324C22semidirect
178. #10597324C22semidirect
179. #10597324C22semidirect
180. #10597324C22semidirect
181. #10597323C22semidirect
182. #10597323C22semidirect
183. #10597322C22semidirect
184. #10597322C22semidirect
185. #10597318C22semidirect
186. #10597316C22semidirect
542. D42D19semidirect
580. C22×D4C2×D19semidirect
581. C22×D4C2×D19semidirect
582. C22×D4C2×D19semidirect
585. #127C2×D19semidirect
677. #121C2×D19semidirect
678. #121C2×D19semidirect
679. #121C2×D19semidirect
693. #120C2×D19semidirect
694. #120C2×D19semidirect
695. #120C2×D19semidirect
710. C4×D4C2×D19semidirect
711. C4×D4C2×D19semidirect
727. C19#3534semidirect

Maximal subgroups

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

subgroupindex
#119272892
#119272832
#119272812
#119272432
#119272372
#119272252
#119272232
#119271882
#119271832
#119271812
D4×C22⋊D192
#119271482
#119271442
#119271392
#119271362
#119271292
#119271262
#119271212
#119271042
#119271032
#119270502
C2×#105973812
C2×#105973852
D42×C192
#353419