Finite Group Databasebeta

← #34061645

Subgroups — #34061645

Order 19072.

346 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750677C211yesmaximal, characteristic, complemented
2#23750675C211yesmaximal, characteristic, complemented
3#23750660C211yesmaximal, characteristic, complemented
4#23750658C211yesmaximal, characteristic, complemented
5#23750657C211yesmaximal, characteristic, complemented
6#23750657C211yesmaximal, characteristic, complemented
7#23750656C211yesmaximal, characteristic, complemented
8#23750654C211yesmaximal, characteristic, complemented
9#23750650C211yesmaximal, characteristic, complemented
10#23750649C211yesmaximal, characteristic, complemented
11#23750646C211yesmaximal, characteristic, complemented
12#23750632C211yesmaximal, characteristic, complemented
13#23750631C211yesmaximal, characteristic, complemented
14#23750628C211yesmaximal, characteristic, complemented
15#23750152C211yesmaximal, characteristic
16C2×#14558746C2211yescharacteristic
17C2×#14558745C2211yescharacteristic
18C2×#14558745C2211yescharacteristic
19C2×#14558745C2211yescharacteristic
20C2×D149⋊C8C2211yescharacteristic
21C22×#11924753C2211yescharacteristic
22#18011978C2211yescharacteristic
23#18011978C2211yescharacteristic
24#18011978C2211yescharacteristic
25#18011978C2211yescharacteristic
26C4⋊#11924753C2211yescharacteristic
27C4⋊#11924753C2211yescharacteristic
28C4⋊#11924753C2211yescharacteristic
29C4⋊#11924753C2211yescharacteristic
30C4⋊#11924753C2211yescharacteristic
31C4⋊#11924753C2211yescharacteristic
32#18011968C2211yescharacteristic
33#18011968C2211yescharacteristic
34C22⋊#11924753C2211yescharacteristic
35C22⋊#11924753C2211yescharacteristic
36C22⋊#11924753C2211yescharacteristic
37C22⋊#11924753C2211yescharacteristic
38#18011966C2211yescharacteristic
39#18011966C2211yescharacteristic
40#18011966C2211yescharacteristic
41#18011966C2211yescharacteristic
42C4×#11924753C2211yescharacteristic
43C4×#11924753C2211yescharacteristic
44#18011906C411yescharacteristic
45#18011904C411yescharacteristic
46#18011901C411yescharacteristic
47#18011897C411yescharacteristic
48#18011894C411yescharacteristic
49#18011888C411yescharacteristic
50#18011883C411yescharacteristic
51#18011876C2211yescharacteristic
52D4×Dic149C2211yescharacteristic
53#18011871C2211yescharacteristic
54#18011871C2211yescharacteristic
55#18011869C2211yescharacteristic
56#18011867C2211yescharacteristic
57C2×C4×Dic149C2211yescharacteristic
58#123×C149C411yescharacteristic
59#14558746—41no—
60#14558745—41no—
61#14558745—41no—
62#14558745—41no—
63D149⋊C8—41no—
64C2×#11924753—41no—
65C2×#11924753C2311yescharacteristic
66C2×#11924753C2311yescharacteristic
67C2×#11924753C2311yescharacteristic
68C2×#11924753C2311yescharacteristic
69C2×#11924753C2311yescharacteristic
70C2×#11924753C2311yescharacteristic
71C2×#11924753C2311yescharacteristic
72C2×#11924753C2311yescharacteristic
73C2×Dic298C2×C411yescharacteristic
74C2×C22⋊D149C2×C411yescharacteristic
75C2×C22⋊D149C2×C411yescharacteristic
76C22×Dic149C2×C411yescharacteristic
77C22×Dic149C2311yescharacteristic
78C22×Dic149C2311yescharacteristic
79C2×C4×D149C2311yescharacteristic
80C4⋊Dic149C2×C411yescharacteristic
81C4⋊Dic149C2×C411yescharacteristic
82#14558715C2×C411yescharacteristic
83#14558715C2×C411yescharacteristic
84#14558715C2×C411yescharacteristic
85#14558715C2×C411yescharacteristic
86#14558715C2×C411yescharacteristic
87#14558715C2×C411yescharacteristic
88C22⋊Dic149C2×C411yescharacteristic
89C22⋊Dic149C2×C411yescharacteristic
90C22⋊Dic149C2×C411yescharacteristic
91#14558713C2×C411yescharacteristic
92#14558713C2×C411yescharacteristic
93#14558713C2×C411yescharacteristic
94#14558713C2×C411yescharacteristic
95C4×Dic149C2×C411yescharacteristic
96C4×Dic149C2×C411yescharacteristic
97C4×Dic149C2311yescharacteristic
98C4×Dic149C2311yescharacteristic
99C4×Dic149C2311yescharacteristic
100C4×Dic149C2311yescharacteristic
101C2×D4×C149C2×C411yescharacteristic
102C22×C4×C149C2×C411yescharacteristic
103C4⋊C4×C149C2×C411yescharacteristic
104C4⋊C4×C149C2×C411yescharacteristic
105C22⋊C4×C149C2×C411yescharacteristic
106C22⋊C4×C149C2×C411yescharacteristic
107C22⋊C4×C149C2×C411yescharacteristic
108#11924753—21no—
109#11924753—21no—
110#11924753—21no—
111#11924753—21no—
112#11924753—21no—
113#11924753—21no—
114#11924753—21no—
115#11924753—21no—
116C22×D149C22×C411yescharacteristic
117Dic298—41no—
118C22⋊D149—41no—
119C22⋊D149—41no—
120C2×Dic149—21no—
121C2×Dic149—21no—
122C2×Dic149—21no—
123C2×Dic149—21no—
124C2×Dic149—41no—
125C2×Dic149C22×C411yescharacteristic
126C2×Dic149C22×C411yescharacteristic
127C2×Dic149C22×C411yescharacteristic
128C2×Dic149C22×C411yescharacteristic
129C2×Dic149C22×C411yescharacteristic
130C2×Dic149C22×C411yescharacteristic
131C2×Dic149C2411yescharacteristic
132C4×D149—21no—
133C4×D149—21no—
134C23×C149C22×C411yescharacteristic
135C23×C149C22×C411yescharacteristic
136D4×C149—41no—
137C2×C4×C149—41no—
138C2×C4×C149C22×C411yescharacteristic
139C2×C4×C149C22×C411yescharacteristic
140C2×C4×C149C22×C411yescharacteristic
141C2×C4×C149C22×C411yescharacteristic
142C2×C4×C149C22×C411yescharacteristic
143C22×C149—21no—
144C22×C149—21no—
145C22×C149—21no—
146C22×C149—21no—
147C22×C149—21no—
148C22×C149—21no—
149C22×C149C23×C411yescharacteristic
150C2×D149—21no—
151C2×D149—21no—
152C2×D149—21no—
153C4×C149—21no—
154C4×C149—21no—
155C4×C149—21no—
156C4×C149—21no—
157C4×C149—21no—
158Dic149—21no—
159Dic149—21no—
160Dic149—21no—
161Dic149—21no—
162Dic149—21no—
163Dic149—21no—
164Dic149H(5,𝔽2)11yescharacteristic
165Dic1492−1+411yescharacteristic
166C2×C149—41no—
167C2×C149—41no—
168C2×C149#52011yescharacteristic
169C2×C149#56811yescharacteristic
170C2×C149#56811yescharacteristic
171D149—41no—
172C149#299511yescharacteristic, complemented, Sylow
173#2995—1491nomaximal, Sylow
174#529—1491no—
175#446—1491no—
176#446—1491no—
177#436—1491no—
178#436—1491no—
179#435—1491no—
180#435—1491no—
181#435—1491no—
182#435—1491no—
183#433—1491no—
184#433—1491no—
185#432—1491no—
186#424—1491no—
187#424—1491no—
188#423—1491no—
189C2×M16—1491no—
190C2×M16—1491no—
191C2×M16—1491no—
192C2×M16—1491no—
193C22×C8—1491no—
194C22×C8—1491no—
195#126—1491no—
196#126—1491no—
197#125—1491no—
198#124—1491no—
199#123—1491no—
200#123#1059701011yescharacteristic
201C22⋊Q8—1491no—
202#121—1491no—
203C4×Q8—1491no—
204C4×D4—1491no—
205C4×D4—1491no—
206C4×D4—1491no—
207#117—1491no—
208#117—1491no—
209C2×C42—1491no—
210C4⋊C8—1491no—
211C4⋊C8—1491no—
212C4⋊C8—1491no—
213C4⋊C8—1491no—
214C4⋊C8—1491no—
215C4⋊C8—1491no—
216C4⋊C8—1491no—
217C4⋊C8—1491no—
218C4⋊C8—1491no—
219C4⋊C8—1491no—
220C22⋊C8—1491no—
221C22⋊C8—1491no—
222C22⋊C8—1491no—
223C22⋊C8—1491no—
224C22⋊C8—1491no—
225C22⋊C8—1491no—
226#97—1491no—
227#97—1491no—
228#97—1491no—
229#97—1491no—
230C4×C8—1491no—
231C4×C8—1491no—
232C2×Q8—1491no—
233C2×D4—1491no—
234C2×D4—1491no—
235C2×D4C2×#1059701011yescharacteristic
236C22×C4—1491no—
237C22×C4—1491no—
238C22×C4—1491no—
239C22×C4—1491no—
240C22×C4C2×#1059701011yescharacteristic
241M16—5961no—
242M16—5961no—
243M16—5961no—
244M16—5961no—
245C2×C8—5961no—
246C2×C8—5961no—
247C2×C8—1491no—
248C2×C8—1491no—
249C2×C8—1491no—
250C2×C8—1491no—
251C2×C8—1491no—
252C2×C8—1491no—
253C2×C8—1491no—
254C2×C8—1491no—
255C4⋊C4—1491no—
256C4⋊C4—1491no—
257C4⋊C4—1491no—
258C4⋊C4—1491no—
259C4⋊C4—1491no—
260C4⋊C4—1491no—
261C4⋊C4—1491no—
262C4⋊C4—1491no—
263C4⋊C4C2×#1059701011yescharacteristic
264C4⋊C4C2×#1059701011yescharacteristic
265C22⋊C4—1491no—
266C22⋊C4—1491no—
267C22⋊C4—1491no—
268C22⋊C4—1491no—
269C22⋊C4—1491no—
270C22⋊C4—1491no—
271C22⋊C4—1491no—
272C22⋊C4C2×#1059701011yescharacteristic
273C22⋊C4C2×#1059701011yescharacteristic
274C22⋊C4C2×#1059701011yescharacteristic
275C42—1491no—
276C42—1491no—
277C42—1491no—
278C42—1491no—
279C42—1491no—
280C42—1491no—
281C23—1491no—
282C23C22×#1059701011yescharacteristic
283C23C22×#1059701011yescharacteristic
284Q8—5961no—
285D4—41no—
286D4—5961no—
287D4—5961no—
288C2×C4—41no—
289C2×C4—2981no—
290C2×C4—2981no—
291C2×C4—2981no—
292C2×C4—2981no—
293C2×C4—2981no—
294C2×C4—2981no—
295C2×C4—5961no—
296C2×C4—1491no—
297C2×C4—1491no—
298C2×C4—1491no—
299C2×C4—1491no—
300C2×C4—1491no—
301C2×C4—1491no—
302C2×C4—1491no—
303C2×C4C22×#1059701011yescharacteristic
304C2×C4C22×#1059701011yescharacteristic
305C2×C4C22×#1059701011yescharacteristic
306C2×C4C22×#1059701011yescharacteristic
307C2×C4C22×#1059701011yescharacteristic
308C8—2981no—
309C8—2981no—
310C8—2981no—
311C8—2981no—
312C8—2981no—
313C8—2981no—
314C8—2981no—
315C8—2981no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22—21no—
322C22—2981no—
323C22—2981no—
324C22—2981no—
325C22C23×#1059701011yescharacteristic
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—2981no—
332C4—2981no—
333C4—2981no—
334C4—2981no—
335C4—2981no—
336C4—2981no—
337C4—1491no—
338C4—1491no—
339C2—41no—
340C2—41no—
341C2—5961no—
342C2#2375069411yescharacteristic
343C2#2375070311yescharacteristic
344C2#2375070411yescharacteristic
subgroupG/H
center, FrattiniC22C23×#10597010
commutator, socleC22×C149C23×C4
Fitting#123×C149C4
prime radical#18011883C4
cosocleC2×Dic149C24
hypercenter#123#10597010
hypocenterC149#2995
LCSG ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
1. #23750677C2semidirect
2. #23750675C2semidirect
3. #23750660C2semidirect
4. #23750658C2semidirect
5. #23750657C2semidirect
6. #23750657C2semidirect
7. #23750656C2semidirect
8. #23750654C2semidirect
9. #23750650C2semidirect
10. #23750649C2semidirect
11. #23750646C2semidirect
12. #23750632C2semidirect
13. #23750631C2semidirect
14. #23750628C2semidirect
172. C149#2995semidirect

Maximal subgroups

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

subgroupindex
#237506772
#237506752
#237506602
#237506582
#237506572
#237506562
#237506542
#237506502
#237506492
#237506462
#237506322
#237506312
#237506282
#237501522
#2995149