Finite Group Databasebeta

← #34061557

Subgroups — #34061557

Order 19072.

412 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750660C211yesmaximal, characteristic, complemented
2#23750658C211yesmaximal, characteristic, complemented
3#23750657C211yesmaximal, characteristic, complemented
4#23750656C211yesmaximal, characteristic, complemented
5#23750656C211yesmaximal, characteristic, complemented
6#23750654C211yesmaximal, characteristic, complemented
7#23750652C211yesmaximal, characteristic, complemented
8D4×#11924753C211yesmaximal, characteristic, complemented
9#23750649C211yesmaximal, characteristic, complemented
10#23750649C211yesmaximal, characteristic, complemented
11#23750599C211yesmaximal, characteristic, complemented
12#23750598C211yesmaximal, characteristic, complemented
13#23750595C211yesmaximal, characteristic, complemented
14C2×C22⋊#11924753C211yesmaximal, characteristic, complemented
15#23750131C211yesmaximal, characteristic
16C2×#14558746C2211yescharacteristic, complemented
17C2×#14558745C2211yescharacteristic
18C2×#14558745C2211yescharacteristic
19C2×#14558745C2211yescharacteristic, complemented
20C2×D149⋊C8C2211yescharacteristic, complemented
21C22×#11924753C2211yescharacteristic
22C22×#11924753C2211yescharacteristic
23C22×#11924753C2211yescharacteristic, complemented
24#18011978C2211yescharacteristic, complemented
25#18011978C2211yescharacteristic, complemented
26C4⋊#11924753C2211yescharacteristic, complemented
27C4⋊#11924753C2211yescharacteristic, complemented
28#18011968C2211yescharacteristic, complemented
29#18011968C2211yescharacteristic, complemented
30C22⋊#11924753C2211yescharacteristic
31C22⋊#11924753C2211yescharacteristic
32C22⋊#11924753C2211yescharacteristic
33C22⋊#11924753C2211yescharacteristic
34C22⋊#11924753C2211yescharacteristic
35C22⋊#11924753C2211yescharacteristic
36C22⋊#11924753C2211yescharacteristic
37C22⋊#11924753C2211yescharacteristic
38C22⋊#11924753C2211yescharacteristic, complemented
39C22⋊#11924753C2211yescharacteristic, complemented
40#18011966C2211yescharacteristic, complemented
41#18011966C2211yescharacteristic, complemented
42C4×#11924753C2211yescharacteristic, complemented
43C4×#11924753C2211yescharacteristic, complemented
44C2×#14558735C2211yescharacteristic
45C23×Dic149C2211yescharacteristic
46#18011895C411yescharacteristic
47#18011892C411yescharacteristic
48#18011888C411yescharacteristic
49#18011888C411yescharacteristic
50#18011883C411yescharacteristic
51#18011883C411yescharacteristic
52#18011880C411yescharacteristic
53D4×Dic149C2211yescharacteristic
54D4×Dic149C2211yescharacteristic
55#18011871C2211yescharacteristic
56#18011871C2211yescharacteristic
57#18011867C2211yescharacteristic
58#120×C149C411yescharacteristic
59#14558746—41no—
60#14558745—41no—
61#14558745—41no—
62#14558745—41no—
63D149⋊C8—41no—
64C2×#11924753—41no—
65C2×#11924753—41no—
66C2×#11924753—41no—
67C2×#11924753C2311yescharacteristic
68C2×#11924753C2311yescharacteristic
69C2×#11924753C2311yescharacteristic
70C2×#11924753C2311yescharacteristic
71C2×#11924753C2311yescharacteristic
72C2×#11924753C2311yescharacteristic
73C2×#11924753C2311yescharacteristic
74C2×#11924753C2311yescharacteristic
75#14558735—41no—
76#14558735—41no—
77C2×Dic298C2×C411yescharacteristic
78C2×C22⋊D149C2×C411yescharacteristic
79C2×C22⋊D149C2×C411yescharacteristic
80C2×C22⋊D149C2×C411yescharacteristic
81C2×C22⋊D149C2×C411yescharacteristic
82C22×Dic149—41no—
83C22×Dic149—41no—
84C22×Dic149C2×C411yescharacteristic
85C22×Dic149C2×C411yescharacteristic
86C22×Dic149C2×C411yescharacteristic
87C22×Dic149C2311yescharacteristic
88C22×Dic149C2311yescharacteristic
89C22×Dic149C2311yescharacteristic
90C22×Dic149C2311yescharacteristic
91C2×C4×D149C2311yescharacteristic
92C4⋊Dic149C2×C411yescharacteristic
93C4⋊Dic149C2×C411yescharacteristic
94#14558715C2×C411yescharacteristic
95#14558715C2×C411yescharacteristic
96#14558715C2×C411yescharacteristic
97#14558715C2×C411yescharacteristic
98C22⋊Dic149C2×C411yescharacteristic
99C22⋊Dic149C2×C411yescharacteristic
100C22⋊Dic149C2×C411yescharacteristic
101C22⋊Dic149C2×C411yescharacteristic
102C22⋊Dic149C2×C411yescharacteristic
103#14558713C2×C411yescharacteristic
104#14558713C2×C411yescharacteristic
105C4×Dic149C2311yescharacteristic
106C4×Dic149C2311yescharacteristic
107C24×C149C2×C411yescharacteristic
108C2×D4×C149C2×C411yescharacteristic
109C2×D4×C149C2×C411yescharacteristic
110C2×D4×C149C2×C411yescharacteristic
111C22⋊C4×C149C2×C411yescharacteristic
112C22⋊C4×C149C2×C411yescharacteristic
113C22⋊C4×C149C2×C411yescharacteristic
114#11924753—21no—
115#11924753—21no—
116#11924753—21no—
117#11924753—21no—
118#11924753—21no—
119#11924753—21no—
120#11924753—21no—
121#11924753—21no—
122C22×D149C22×C411yescharacteristic
123Dic298—41no—
124C22⋊D149—22no—
125C22⋊D149—41no—
126C22⋊D149—41no—
127C22⋊D149—41no—
128C2×Dic149—21no—
129C2×Dic149—21no—
130C2×Dic149—21no—
131C2×Dic149—21no—
132C2×Dic149—21no—
133C2×Dic149—21no—
134C2×Dic149—21no—
135C2×Dic149—21no—
136C2×Dic149—41no—
137C2×Dic149—41no—
138C2×Dic149—41no—
139C2×Dic149C22×C411yescharacteristic
140C2×Dic149C22×C411yescharacteristic
141C2×Dic149C22×C411yescharacteristic
142C2×Dic149C22×C411yescharacteristic
143C2×Dic149C22×C411yescharacteristic
144C2×Dic149C22×C411yescharacteristic
145C2×Dic149C2411yescharacteristic
146C4×D149—21no—
147C4×D149—21no—
148C23×C149—22no—
149C23×C149—41no—
150C23×C149—41no—
151C23×C149C22×C411yescharacteristic
152C23×C149C22×C411yescharacteristic
153C23×C149C22×C411yescharacteristic
154C23×C149C22×C411yescharacteristic
155D4×C149—22no—
156D4×C149—41no—
157D4×C149—41no—
158C2×C4×C149C22×C411yescharacteristic
159C2×C4×C149C22×C411yescharacteristic
160C2×C4×C149C22×C411yescharacteristic
161C22×C149—21no—
162C22×C149—21no—
163C22×C149—21no—
164C22×C149—21no—
165C22×C149—21no—
166C22×C149—21no—
167C22×C149—21no—
168C22×C149—21no—
169C22×C149—21no—
170C22×C149—21no—
171C22×C149—21no—
172C22×C149—44no—
173C22×C149#13112yes—
174C22×C149C23×C411yescharacteristic
175C2×D149—21no—
176C2×D149—21no—
177C2×D149—21no—
178C4×C149—21no—
179C4×C149—21no—
180C4×C149—21no—
181Dic149—21no—
182Dic149—21no—
183Dic149—21no—
184Dic149—21no—
185Dic149—21no—
186Dic149—21no—
187Dic149H(5,𝔽2)11yescharacteristic
188Dic149H(5,𝔽2)11yescharacteristic
189C2×C149—22no—
190C2×C149—41no—
191C2×C149—41no—
192C2×C149—41no—
193C2×C149#51811yescharacteristic
194C2×C149C2×#13111yescharacteristic
195C2×C149#56811yescharacteristic
196D149—41no—
197C149#297611yescharacteristic, complemented, Sylow
198#2976—1491nomaximal, Sylow
199#525—1491no—
200#436—1491no—
201#436—1491no—
202#435—1491no—
203#435—1491no—
204#435—1491no—
205#435—1491no—
206C8×D4—1491no—
207C8×D4—1491no—
208#433—1491no—
209#433—1491no—
210#408—1491no—
211#408—1491no—
212#407—1491no—
213C2×C22⋊C8—1491no—
214C2×#41—1491no—
215C23×C4—1491no—
216C2×M16—1491no—
217C2×M16—1491no—
218C2×M16—1491no—
219C2×M16—1491no—
220C22×C8—1491no—
221C22×C8—1491no—
222C22×C8—1491no—
223C22×C8—1491no—
224#123—1491no—
225#123—1491no—
226C22⋊Q8—1491no—
227C22⋊Q8—1491no—
228#121—1491no—
229#121—1491no—
230#120—1491no—
231#120#1059701011yescharacteristic
232C4×D4—1491no—
233C4×D4—1491no—
234C4×D4—1491no—
235C4×D4—1491no—
236#117—1491no—
237C4⋊C8—1491no—
238C4⋊C8—1491no—
239C4⋊C8—1491no—
240C4⋊C8—1491no—
241C22⋊C8—1491no—
242C22⋊C8—1491no—
243C22⋊C8—1491no—
244C22⋊C8—1491no—
245C22⋊C8—1491no—
246C22⋊C8—1491no—
247C22⋊C8—1491no—
248C22⋊C8—1491no—
249C22⋊C8—1491no—
250C22⋊C8—1491no—
251C22⋊C8—1491no—
252C22⋊C8—1491no—
253#97—1491no—
254#97—1491no—
255C4×C8—1491no—
256C4×C8—1491no—
257C24C2×#1059701011yescharacteristic
258#41—5961no—
259#41—5961no—
260C2×Q8—1491no—
261C2×D4—1491no—
262C2×D4—1491no—
263C2×D4—1491no—
264C2×D4—1491no—
265C2×D4C2×#1059701011yescharacteristic
266C2×D4C2×#1059701011yescharacteristic
267C2×D4C2×#1059701011yescharacteristic
268C22×C4—5961no—
269C22×C4—5961no—
270C22×C4—1491no—
271C22×C4—1491no—
272C22×C4—1491no—
273C22×C4—1491no—
274C22×C4—1491no—
275C22×C4—1491no—
276C22×C4—1491no—
277C22×C4—1491no—
278M16—5961no—
279M16—5961no—
280M16—5961no—
281M16—5961no—
282C2×C8—5961no—
283C2×C8—5961no—
284C2×C8—5961no—
285C2×C8—5961no—
286C2×C8—1491no—
287C2×C8—1491no—
288C2×C8—1491no—
289C2×C8—1491no—
290C2×C8—1491no—
291C2×C8—1491no—
292C2×C8—1491no—
293C2×C8—1491no—
294C4⋊C4—1491no—
295C4⋊C4—1491no—
296C4⋊C4—1491no—
297C4⋊C4—1491no—
298C4⋊C4—1491no—
299C4⋊C4—1491no—
300C22⋊C4—1491no—
301C22⋊C4—1491no—
302C22⋊C4—1491no—
303C22⋊C4—1491no—
304C22⋊C4—1491no—
305C22⋊C4—1491no—
306C22⋊C4—1491no—
307C22⋊C4C2×#1059701011yescharacteristic
308C22⋊C4C2×#1059701011yescharacteristic
309C22⋊C4C2×#1059701011yescharacteristic
310C42—1491no—
311C42—1491no—
312C23—22no—
313C23—41no—
314C23—41no—
315C23—1491no—
316C23C22×#1059701011yescharacteristic
317C23C22×#1059701011yescharacteristic
318C23C22×#1059701011yescharacteristic
319C23C22×#1059701011yescharacteristic
320Q8—5961no—
321D4—22no—
322D4—41no—
323D4—41no—
324D4—2982no—
325D4—5961no—
326D4—5961no—
327D4—5961no—
328C2×C4—2981no—
329C2×C4—2981no—
330C2×C4—2981no—
331C2×C4—2981no—
332C2×C4—2981no—
333C2×C4—2981no—
334C2×C4—2981no—
335C2×C4—2981no—
336C2×C4—2981no—
337C2×C4—2981no—
338C2×C4—5961no—
339C2×C4—5961no—
340C2×C4—5961no—
341C2×C4—1491no—
342C2×C4—1491no—
343C2×C4—1491no—
344C2×C4—1491no—
345C2×C4—1491no—
346C2×C4—1491no—
347C2×C4—1491no—
348C2×C4C22×#1059701011yescharacteristic
349C2×C4C22×#1059701011yescharacteristic
350C2×C4C22×#1059701011yescharacteristic
351C8—2981no—
352C8—2981no—
353C8—2981no—
354C8—2981no—
355C8—2981no—
356C8—2981no—
357C8—2981no—
358C8—2981no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—44no—
371C22—2981no—
372C22—2981no—
373C22—2981no—
374C22#1801199812yes—
375C22C23×#1059701011yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—2981no—
380C4—2981no—
381C4—2981no—
382C4—2981no—
383C4—2981no—
384C4—2981no—
385C4—1491no—
386C4—1491no—
387C2—22no—
388C2—41no—
389C2—41no—
390C2—41no—
391C2—5961no—
392C2#2375069211yescharacteristic
393C2C2×#1801199811yescharacteristic
394C2#2375070311yescharacteristic
subgroupG/H
center, FrattiniC22C23×#10597010
commutator, socleC22×C149C23×C4
Fitting#120×C149C4
prime radical#23750131C2
cosocleC2×Dic149C24
hypercenter#120#10597010
hypocenterC149#2976
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ #120

Complements

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

NH ≅ G/Ntype
1. #23750660C2semidirect
2. #23750658C2semidirect
3. #23750657C2semidirect
4. #23750656C2semidirect
5. #23750656C2semidirect
6. #23750654C2semidirect
7. #23750652C2semidirect
8. D4×#11924753C2semidirect
9. #23750649C2semidirect
10. #23750649C2semidirect
11. #23750599C2semidirect
12. #23750598C2semidirect
13. #23750595C2semidirect
14. C2×C22⋊#11924753C2semidirect
16. C2×#14558746C22semidirect
19. C2×#14558745C22semidirect
20. C2×D149⋊C8C22semidirect
23. C22×#11924753C22semidirect
24. #18011978C22semidirect
25. #18011978C22semidirect
26. C4⋊#11924753C22semidirect
27. C4⋊#11924753C22semidirect
28. #18011968C22semidirect
29. #18011968C22semidirect
38. C22⋊#11924753C22semidirect
39. C22⋊#11924753C22semidirect
40. #18011966C22semidirect
41. #18011966C22semidirect
42. C4×#11924753C22semidirect
43. C4×#11924753C22semidirect
197. C149#2976semidirect

Maximal subgroups

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

subgroupindex
#237506602
#237506582
#237506572
#237506562
#237506542
#237506522
D4×#119247532
#237506492
#237505992
#237505982
#237505952
C2×C22⋊#119247532
#237501312
#2976149