Finite Group Databasebeta

← #34055765

Subgroups — #34055765

Order 19072.

396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750237C211yesmaximal, characteristic, complemented
2#23750194C211yesmaximal, characteristic
3#23750019C211yesmaximal, characteristic, complemented
4#23749998C211yesmaximal, characteristic, complemented
5#23749990C211yesmaximal, characteristic, complemented
6#23749980C211yesmaximal, characteristic, complemented
7#23749848C212yesmaximal, complemented
8#23749826C212yesmaximal, complemented
9#23749789C212yesmaximal, complemented
10#23749778C212yesmaximal, complemented
11#433×C149C211yesmaximal, characteristic, complemented
12C2×#14558736C2211yescharacteristic
13C22×D596C2211yescharacteristic
14C2×Dic596C2212yescomplemented
15C2×#14558725C2212yes—
16C2×#14558725C2212yes—
17C2×#14558725C2212yescomplemented
18#18011911C2211yescharacteristic, complemented
19#18011908C2211yescharacteristic
20#18011908C2211yescharacteristic
21#18011904—22no—
22#18011903C2211yescharacteristic, complemented
23#18011901—22no—
24#18011899C2211yescharacteristic
25#18011899C2211yescharacteristic
26#18011890C2212yes—
27#18011886—22no—
28#18011881—22no—
29C4×Dic298C2212yescomplemented
30#18011836C2212yescomplemented
31#18011833C2212yes—
32#18011833C2212yes—
33#18011833C2212yescomplemented
34#117×C149C2211yescharacteristic
35C4⋊C8×C149C2212yescomplemented
36C22⋊C8×C149C2212yes—
37#97×C149C2211yescharacteristic, complemented
38C4×C8×C149C2211yescharacteristic, complemented
39C23×D149—21no—
40#14558736—42no—
41C2×Dic298C2312yes—
42C2×Dic298C2311yescharacteristic
43C2×D596—21no—
44C2×D596—22no—
45C2×D596—22no—
46C2×D596—42no—
47C2×D596C2311yescharacteristic
48C2×D596C2311yescharacteristic
49C2×D596C2311yescharacteristic
50C2×C22⋊D149—21no—
51C2×C4×D149—21no—
52Dic596—42no—
53#14558725—42no—
54#14558725—42no—
55#14558725—42no—
56C4⋊Dic149—22no—
57C4⋊Dic149C2312yes—
58#14558715—22no—
59#14558715—22no—
60#14558715—22no—
61C22⋊Dic149—22no—
62#14558713—22no—
63#14558713—22no—
64C4×Dic149—22no—
65C22×C4×C149C2311yescharacteristic
66C2×C8×C149C2312yes—
67C2×C8×C149C2312yes—
68C4⋊C4×C149D412yes—
69C22⋊C4×C149D412yes—
70C42×C149C2311yescharacteristic
71C42×C149C2311yescharacteristic
72C22×D149—21no—
73C22×D149—21no—
74C22×D149—21no—
75C22×D149—42no—
76C22×D149—82no—
77Dic298—22no—
78Dic298—22no—
79Dic298—22no—
80D596—22no—
81D596—22no—
82D596—22no—
83D596—42no—
84D596—82no—
85D596—82no—
86C22⋊D149—42no—
87C2×Dic149—21no—
88C2×Dic149—22no—
89C2×Dic149—22no—
90C4×D149—42no—
91C23×C149C2×D411yescharacteristic
92C2×C4×C149—22no—
93C2×C4×C149C2×D411yescharacteristic
94C2×C4×C149C2×D412yes—
95C2×C4×C149C2×D412yes—
96C2×C4×C149C2411yescharacteristic
97C8×C149—22no—
98C8×C149—22no—
99C22×C149—21no—
100C22×C149—22no—
101C22×C149C22×D411yescharacteristic
102C2×D149—41no—
103C2×D149—41no—
104C2×D149—41no—
105C2×D149—42no—
106C2×D149—42no—
107C2×D149—42no—
108C2×D149—84no—
109C4×C149—21no—
110C4×C149—22no—
111C4×C149—22no—
112C4×C149H(5,𝔽2)12yes—
113Dic149—41no—
114Dic149—42no—
115Dic149—42no—
116C2×C149—41no—
117C2×C149#53511yescharacteristic
118C2×C149#57712yes—
119D149—81no—
120D149—81no—
121D149—81no—
122C149#322211yescharacteristic, complemented, Sylow
123#3222—1491nomaximal, Sylow
124#541—1491no—
125#535—1491no—
126#497—1491no—
127#492—1491no—
128#490—1491no—
129#488—1491no—
130#464—1492no—
131#460—1492no—
132#452—1492no—
133#450—1492no—
134#433D14911yescharacteristic, complemented
135C2×#41—1491no—
136C22×D4—1491no—
137C2×Q16—1492no—
138C2×SD16—1492no—
139C2×SD16—1492no—
140C2×SD16—1492no—
141C4⋊Q8—1491no—
142#127—1491no—
143#127—1491no—
144#126—2982no—
145#125—2982no—
146#125—1491no—
147#124—1491no—
148#124—1491no—
149C22⋊Q8—1492no—
150#121—2982no—
151#120—2982no—
152C4×Q8—1492no—
153#117C2×D14911yescharacteristic
154C4⋊C8C2×D14912yescomplemented
155#103—1492no—
156#102—1492no—
157#102—1492no—
158#102—1492no—
159C22⋊C8C2×D14912yes—
160#97C2×D14911yescharacteristic, complemented
161C4×C8C2×D14911yescharacteristic, complemented
162C24—2981no—
163#41—5962no—
164C2×Q8—1491no—
165C2×Q8—1492no—
166C2×D4—2981no—
167C2×D4—2981no—
168C2×D4—2982no—
169C2×D4—2982no—
170C2×D4—5962no—
171C2×D4—1491no—
172C2×D4—1491no—
173C2×D4—1491no—
174C22×C4—2981no—
175C22×C4C22×D14911yescharacteristic
176Q16—5962no—
177SD16—5962no—
178SD16—5962no—
179SD16—5962no—
180C2×C8C22×D14912yes—
181C2×C8C22×D14912yes—
182C4⋊C4—2982no—
183C4⋊C4—2982no—
184C4⋊C4—2982no—
185C4⋊C4—2982no—
186C4⋊C4—1492no—
187C4⋊C4D59612yes—
188C22⋊C4—2982no—
189C22⋊C4—2982no—
190C22⋊C4—2982no—
191C22⋊C4D59612yes—
192C42—2982no—
193C42C22×D14911yescharacteristic
194C42C22×D14911yescharacteristic
195C23—2981no—
196C23—2981no—
197C23—2981no—
198C23—5962no—
199C23—11922no—
200C23C2×D59611yescharacteristic
201Q8—2982no—
202Q8—2982no—
203Q8—2982no—
204D4—2982no—
205D4—2982no—
206D4—2982no—
207D4—5962no—
208D4—5962no—
209D4—11922no—
210D4—11922no—
211C2×C4—22no—
212C2×C4—2982no—
213C2×C4—2982no—
214C2×C4—2981no—
215C2×C4—5962no—
216C2×C4C2×D59612yes—
217C2×C4C2×D59612yes—
218C2×C4C2×D59611yescharacteristic
219C2×C4C23×D14911yescharacteristic
220C8—22no—
221C8—22no—
222C22—22no—
223C22—21no—
224C22—5962no—
225C22—5962no—
226C22—5962no—
227C22—5961no—
228C22—5961no—
229C22—5961no—
230C22—11924no—
231C22C22×D59611yescharacteristic
232C4—22no—
233C4—22no—
234C4—21no—
235C4—5962no—
236C4—5961no—
237C4—5962no—
238C4#1801195712yes—
239C2—41no—
240C2—11921no—
241C2—11921no—
242C2—11921no—
243C2#2375019411yescharacteristic
244C2#2375043712yes—
subgroupG/H
centerC22C22×D596
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#433×C149C2
socleC22×C149C22×D4
prime radical#23750194C2
hypercenter#433D149
hypocenterC149#3222
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #23750237C2semidirect
3. #23750019C2semidirect
4. #23749998C2semidirect
5. #23749990C2semidirect
6. #23749980C2semidirect
7. #23749848C2semidirect
8. #23749826C2semidirect
9. #23749789C2semidirect
10. #23749778C2semidirect
11. #433×C149C2semidirect
14. C2×Dic596C22semidirect
17. C2×#14558725C22semidirect
18. #18011911C22semidirect
22. #18011903C22semidirect
29. C4×Dic298C22semidirect
30. #18011836C22semidirect
33. #18011833C22semidirect
35. C4⋊C8×C149C22semidirect
37. #97×C149C22semidirect
38. C4×C8×C149C22semidirect
122. C149#3222semidirect
134. #433D149semidirect
154. C4⋊C8C2×D149semidirect
160. #97C2×D149semidirect
161. C4×C8C2×D149semidirect

Maximal subgroups

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

subgroupindex
#237502372
#237501942
#237500192
#237499982
#237499902
#237499802
#237498482
#237498262
#237497892
#237497782
#433×C1492
#3222149