Finite Group Databasebeta

← #34061559

Subgroups — #34061559

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#23750659C211yesmaximal, characteristic, complemented
2#23750658C211yesmaximal, characteristic, complemented
3#23750657C211yesmaximal, characteristic, complemented
4#23750655C211yesmaximal, characteristic, complemented
5#23750655C211yesmaximal, characteristic, complemented
6#23750654C211yesmaximal, characteristic, complemented
7#23750653C211yesmaximal, characteristic, complemented
8#23750652C211yesmaximal, characteristic, complemented
9#23750649C211yesmaximal, characteristic, complemented
10#23750649C211yesmaximal, characteristic, complemented
11#23750599C211yesmaximal, characteristic, complemented
12#23750598C211yesmaximal, characteristic, complemented
13#23750596C211yesmaximal, characteristic, complemented
14D149⋊(C22⋊C8)C211yesmaximal, characteristic, complemented
15#23750133C211yesmaximal, characteristic
16C2×#14558746C2211yescharacteristic
17C2×#14558746C2211yescharacteristic
18C2×#14558746C2211yescharacteristic, complemented
19C2×#14558745C2211yescharacteristic, complemented
20C2×D149⋊C8C2211yescharacteristic
21C2×D149⋊C8C2211yescharacteristic
22C2×D149⋊C8C2211yescharacteristic, complemented
23C22×#11924753C2211yescharacteristic, complemented
24#18011978C2211yescharacteristic, complemented
25#18011978C2211yescharacteristic, complemented
26C4⋊#11924753C2211yescharacteristic, complemented
27C4⋊#11924753C2211yescharacteristic, complemented
28#18011968C2211yescharacteristic
29#18011968C2211yescharacteristic
30#18011968C2211yescharacteristic
31#18011968C2211yescharacteristic
32#18011968C2211yescharacteristic, complemented
33#18011968C2211yescharacteristic, complemented
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
45C22×C4×D149C2211yescharacteristic
46#18011894C411yescharacteristic
47#18011889C411yescharacteristic
48#18011889C411yescharacteristic
49#18011884C411yescharacteristic
50#18011884C411yescharacteristic
51#18011881C411yescharacteristic
52#18011879C411yescharacteristic
53#18011873C2211yescharacteristic
54#18011873C2211yescharacteristic
55#18011871C2211yescharacteristic
56#18011871C2211yescharacteristic
57#18011867C2211yescharacteristic
58#123×C149C411yescharacteristic
59#14558746—41no—
60#14558746—41no—
61#14558746—41no—
62#14558745—41no—
63D149⋊C8—41no—
64D149⋊C8—41no—
65D149⋊C8—41no—
66C2×#11924753—41no—
67C2×#11924753C2311yescharacteristic
68C2×#11924753C2311yescharacteristic
69C2×#11924753C2311yescharacteristic
70C2×#11924753C2311yescharacteristic
71C2×#11924753C2311yescharacteristic
72C2×#11924753C2311yescharacteristic
73C2×#11924753C2311yescharacteristic
74C2×#11924753C2311yescharacteristic
75C23×D149C2×C411yescharacteristic
76#14558735—41no—
77#14558735—41no—
78C2×Dic298C2×C411yescharacteristic
79C2×D596C2×C411yescharacteristic
80C2×D596C2×C411yescharacteristic
81C2×C22⋊D149C2×C411yescharacteristic
82C2×C22⋊D149C2×C411yescharacteristic
83C2×C22⋊D149C2×C411yescharacteristic
84C2×C22⋊D149C2×C411yescharacteristic
85C22×Dic149C2311yescharacteristic
86C22×Dic149C2311yescharacteristic
87C2×C4×D149—41no—
88C2×C4×D149—41no—
89C2×C4×D149C2×C411yescharacteristic
90C2×C4×D149C2×C411yescharacteristic
91C2×C4×D149C2311yescharacteristic
92C2×C4×D149C2311yescharacteristic
93C2×C4×D149C2311yescharacteristic
94#14558715C2×C411yescharacteristic
95#14558715C2×C411yescharacteristic
96#14558715C2×C411yescharacteristic
97#14558715C2×C411yescharacteristic
98C22⋊Dic149C2×C411yescharacteristic
99#14558713C2×C411yescharacteristic
100#14558713C2×C411yescharacteristic
101#14558713C2×C411yescharacteristic
102#14558713C2×C411yescharacteristic
103#14558713C2×C411yescharacteristic
104#14558713C2×C411yescharacteristic
105C4×Dic149C2311yescharacteristic
106C4×Dic149C2311yescharacteristic
107C2×D4×C149C2×C411yescharacteristic
108C22×C4×C149C2×C411yescharacteristic
109C4⋊C4×C149C2×C411yescharacteristic
110C4⋊C4×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×D149—22no—
123C22×D149—41no—
124C22×D149—41no—
125C22×D149C22×C411yescharacteristic
126C22×D149C22×C411yescharacteristic
127C22×D149C22×C411yescharacteristic
128Dic298—41no—
129D596—22no—
130D596—41no—
131C22⋊D149—22no—
132C22⋊D149—41no—
133C22⋊D149—41no—
134C22⋊D149—41no—
135C2×Dic149—21no—
136C2×Dic149—21no—
137C2×Dic149—21no—
138C2×Dic149—21no—
139C2×Dic149C22×C411yescharacteristic
140C2×Dic149C22×C411yescharacteristic
141C2×Dic149C22×C411yescharacteristic
142C2×Dic149C22×C411yescharacteristic
143C2×Dic149C2411yescharacteristic
144C4×D149—21no—
145C4×D149—21no—
146C4×D149—21no—
147C4×D149—21no—
148C4×D149—21no—
149C4×D149—21no—
150C4×D149—41no—
151C4×D149—41no—
152C23×C149C22×C411yescharacteristic
153C23×C149C22×C411yescharacteristic
154D4×C149—41no—
155C2×C4×C149—41no—
156C2×C4×C149C22×C411yescharacteristic
157C2×C4×C149C22×C411yescharacteristic
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×C149C23×C411yescharacteristic
168C2×D149—21no—
169C2×D149—21no—
170C2×D149—21no—
171C2×D149—21no—
172C2×D149—21no—
173C2×D149—21no—
174C2×D149—21no—
175C2×D149—21no—
176C2×D149—44no—
177C2×D149#13112yes—
178C4×C149—21no—
179C4×C149—21no—
180C4×C149—21no—
181C4×C149—21no—
182C4×C149—21no—
183Dic149—21no—
184Dic149—21no—
185Dic149—21no—
186Dic149—21no—
187Dic149H(5,𝔽2)11yescharacteristic
188Dic149H(5,𝔽2)11yescharacteristic
189C2×C149—41no—
190C2×C149—41no—
191C2×C149#51811yescharacteristic
192C2×C149C2×#13111yescharacteristic
193C2×C149#56811yescharacteristic
194D149—22no—
195D149—41no—
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#1059701011yescharacteristic
226C22⋊Q8—1491no—
227C22⋊Q8—1491no—
228#121—1491no—
229#121—1491no—
230#120—1491no—
231#120—1491no—
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—
257C24—1491no—
258#41—5961no—
259#41—5961no—
260C2×Q8—1491no—
261C2×D4—1491no—
262C2×D4—1491no—
263C2×D4—1491no—
264C2×D4—1491no—
265C2×D4—1491no—
266C2×D4—1491no—
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×C4C2×#1059701011yescharacteristic
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⋊C4C2×#1059701011yescharacteristic
299C4⋊C4C2×#1059701011yescharacteristic
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—2982no—
313C23—5961no—
314C23—5961no—
315C23—1491no—
316C23—1491no—
317C23—1491no—
318C23C22×#1059701011yescharacteristic
319C23C22×#1059701011yescharacteristic
320Q8—5961no—
321D4—41no—
322D4—2982no—
323D4—2982no—
324D4—5961no—
325D4—5961no—
326D4—5961no—
327D4—5961no—
328C2×C4—41no—
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—2981no—
339C2×C4—5961no—
340C2×C4—5961no—
341C2×C4—1491no—
342C2×C4—1491no—
343C2×C4—1491no—
344C2×C4—1491no—
345C2×C4—1491no—
346C2×C4C22×#1059701011yescharacteristic
347C2×C4C22×#1059701011yescharacteristic
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—2981no—
366C22—2981no—
367C22—2981no—
368C22—2981no—
369C22—2981no—
370C22—2981no—
371C22—2981no—
372C22—2981no—
373C22—5964no—
374C22—1492no—
375C22C23×#1059701011yescharacteristic
376C4—21no—
377C4—21no—
378C4—21no—
379C4—21no—
380C4—21no—
381C4—2981no—
382C4—2981no—
383C4—2981no—
384C4—2981no—
385C4—1491no—
386C4—1491no—
387C2—41no—
388C2—41no—
389C2—2982no—
390C2—5961no—
391C2—5961no—
392C2#2375069211yescharacteristic
393C2D149⋊#13111yescharacteristic
394C2#2375070411yescharacteristic
subgroupG/H
center, FrattiniC22C23×#10597010
commutator, socleC22×C149C23×C4
Fitting#123×C149C4
prime radical#23750133C2
cosocleC2×Dic149C24
hypercenter#123#10597010
hypocenterC149#2976
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
1. #23750659C2semidirect
2. #23750658C2semidirect
3. #23750657C2semidirect
4. #23750655C2semidirect
5. #23750655C2semidirect
6. #23750654C2semidirect
7. #23750653C2semidirect
8. #23750652C2semidirect
9. #23750649C2semidirect
10. #23750649C2semidirect
11. #23750599C2semidirect
12. #23750598C2semidirect
13. #23750596C2semidirect
14. D149⋊(C22⋊C8)C2semidirect
18. C2×#14558746C22semidirect
19. C2×#14558745C22semidirect
22. C2×D149⋊C8C22semidirect
23. C22×#11924753C22semidirect
24. #18011978C22semidirect
25. #18011978C22semidirect
26. C4⋊#11924753C22semidirect
27. C4⋊#11924753C22semidirect
32. #18011968C22semidirect
33. #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
#237506592
#237506582
#237506572
#237506552
#237506542
#237506532
#237506522
#237506492
#237505992
#237505982
#237505962
D149⋊(C22⋊C8)2
#237501332
#2976149