Finite Group Databasebeta

← #34057693

Subgroups — #34057693

Order 19072.

348 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 123 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#23750353C211yesmaximal, characteristic
2#23750350C211yesmaximal, characteristic
3#23750004C211yesmaximal, characteristic
4#23750003C212yesmaximal
5#23749836C211yesmaximal, characteristic
6#23749834C212yesmaximal
7#23749833C212yesmaximal
8#23749749C211yesmaximal, characteristic
9C4×#14558726C211yesmaximal, characteristic
10#23749717C212yesmaximal
11#462×C149C211yesmaximal, characteristic
12C2×Dic596C2212yes—
13C2×#14558726C2212yes—
14C2×#14558726C2211yescharacteristic
15C2×#14558726C2212yes—
16#18011911C2211yescharacteristic
17#18011909C2212yes—
18#18011909C2212yes—
19#18011903—21no—
20#18011902—21no—
21#18011901—22no—
22#18011901—22no—
23Q8×Dic149C2212yes—
24C4×Dic298—21no—
25C4×Dic298C2211yescharacteristic
26C4×Dic298C2211yescharacteristic
27#18011876—21no—
28#18011876C2212yes—
29#18011844C2211yescharacteristic
30#18011840C2212yes—
31#18011836C2212yes—
32#18011835C2211yescharacteristic
33#18011834C2211yescharacteristic
34C4×#11924746C2211yescharacteristic
35C8×Dic149C2212yes—
36C2×Q16×C149C2212yes—
37C4⋊Q8×C149C2211yescharacteristic
38C4×Q8×C149C2211yescharacteristic
39C4⋊C8×C149C2211yescharacteristic
40#103×C149C2212yes—
41C2×Dic298D411yescharacteristic
42C2×Dic298C2311yescharacteristic
43C2×Dic298C2312yes—
44Dic596—42no—
45#14558726—24no—
46#14558726—22no—
47#14558726—42no—
48C2×#11924746C2311yescharacteristic
49C2×#11924746C2311yescharacteristic
50C4⋊Dic149—22no—
51C4⋊Dic149—21no—
52C4⋊Dic149—21no—
53C4⋊Dic149D411yescharacteristic
54C4⋊Dic149C2311yescharacteristic
55#14558715—22no—
56#14558715—22no—
57#14558715—22no—
58#14558715—22no—
59#14558715—22no—
60#14558715—21no—
61#14558715D412yes—
62C4×Dic149—22no—
63C4×Dic149—22no—
64C4×Dic149—21no—
65C4×Dic149C2312yes—
66C2×Q8×C149C2311yescharacteristic
67C2×Q8×C149C2312yes—
68Q16×C149—42no—
69C2×C8×C149C2312yes—
70C4⋊C4×C149—21no—
71C4⋊C4×C149—21no—
72C4⋊C4×C149—21no—
73C4⋊C4×C149C2311yescharacteristic
74C42×C149—21no—
75C42×C149C2311yescharacteristic
76Dic298—21no—
77Dic298—22no—
78Dic298—22no—
79Dic298—21no—
80Dic298Q1614yescomplemented
81C2×Dic149—21no—
82C2×Dic149—22no—
83C2×Dic149—21no—
84C2×Dic149C2×D412yes—
85C2×Dic149C2×D412yes—
86#11924746—21no—
87#11924746#4112yes—
88Q8×C149—21no—
89Q8×C149—22no—
90Q8×C149—22no—
91Q8×C149—21no—
92C2×C4×C149—21no—
93C2×C4×C149—21no—
94C2×C4×C149—22no—
95C2×C4×C149C2×D411yescharacteristic
96C2×C4×C149C2×D411yescharacteristic
97C2×C4×C149C2411yescharacteristic
98C8×C149—22no—
99C22×C149C22×D411yescharacteristic
100C4×C149—21no—
101C4×C149—41no—
102C4×C149—42no—
103C4×C149—41no—
104C4×C149C2×Q1612yes—
105C4×C149C2×#4111yescharacteristic
106C4×C149H(5,𝔽2)11yescharacteristic
107Dic149—22no—
108Dic149—41no—
109Dic149—42no—
110Dic149—41no—
111Dic149C2×Q1614yes—
112C2×C149#55011yescharacteristic
113C2×C149C22×Q1611yescharacteristic
114C2×C149#57811yescharacteristic
115C149#339511yescharacteristic, complemented, Sylow
116#3395—1491nomaximal, Sylow
117#557—1491no—
118#557—1491no—
119#494—1492no—
120#494—1491no—
121#462—1492no—
122#462—1491no—
123#462—1492no—
124#462D14911yescharacteristic
125C8×Q8—1491no—
126C4×Q16—1491no—
127C4×Q16—1492no—
128C2×Q16—1491no—
129C2×Q16—1492no—
130C2×Q16—1492no—
131C2×Q16—1492no—
132C2×Q16C2×D14912yes—
133C4⋊Q8—1492no—
134C4⋊Q8—1492no—
135C4⋊Q8—1491no—
136C4⋊Q8C2×D14911yescharacteristic
137#125—2981no—
138#125—2982no—
139#125—2982no—
140#125—2981no—
141C4×Q8—2981no—
142C4×Q8—2981no—
143C4×Q8—1492no—
144C4×Q8—1492no—
145C4×Q8—1491no—
146C4×Q8—1491no—
147C4×Q8C2×D14911yescharacteristic
148#107—1491no—
149C4⋊C8—1492no—
150C4⋊C8C2×D14911yescharacteristic
151#103—1491no—
152#103—1492no—
153#103—1491no—
154#103C2×D14912yes—
155C4×C8—1492no—
156C4×C8—1491no—
157C2×Q8—1491no—
158C2×Q8—1492no—
159C2×Q8—1491no—
160C2×Q8C22×D14911yescharacteristic
161C2×Q8C22×D14912yes—
162Q16—42no—
163Q16—2982no—
164Q16—2984no—
165Q16—5962no—
166Q16—5962no—
167C2×C8—1491no—
168C2×C8—1491no—
169C2×C8C22×D14912yes—
170C4⋊C4—21no—
171C4⋊C4—21no—
172C4⋊C4—21no—
173C4⋊C4—2982no—
174C4⋊C4—2982no—
175C4⋊C4—2982no—
176C4⋊C4—2982no—
177C4⋊C4—2982no—
178C4⋊C4—2982no—
179C4⋊C4—2981no—
180C4⋊C4—2981no—
181C4⋊C4—2981no—
182C4⋊C4—1491no—
183C4⋊C4—1492no—
184C4⋊C4—1491no—
185C4⋊C4C22×D14911yescharacteristic
186C42—21no—
187C42—2982no—
188C42—2982no—
189C42—2981no—
190C42—1492no—
191C42C22×D14911yescharacteristic
192Q8—21no—
193Q8—22no—
194Q8—21no—
195Q8—22no—
196Q8—2981no—
197Q8—2982no—
198Q8—2982no—
199Q8—2981no—
200Q8—1494no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—2981no—
205C2×C4—2981no—
206C2×C4—2982no—
207C2×C4—1492no—
208C2×C4—1492no—
209C2×C4D4×D14911yescharacteristic
210C2×C4D4×D14911yescharacteristic
211C2×C4C23×D14911yescharacteristic
212C8—22no—
213C8—2981no—
214C8—1492no—
215C22C2×D4×D14911yescharacteristic
216C4—21no—
217C4—41no—
218C4—41no—
219C4—42no—
220C4—2982no—
221C4—5961no—
222C4—5961no—
223C4—5962no—
224C4—1494no—
225C4Q16×D14912yes—
226C4#41×D14911yescharacteristic
227C4#1801195611yescharacteristic
228C2#2375029311yescharacteristic
229C2C2×Q16×D14911yescharacteristic
230C2#2375044111yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#462×C149C2
socle, prime radicalC22×C149C22×D4
hypercenter#462D149
hypocenterC149#3395
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
80. Dic298Q16semidirect
115. C149#3395semidirect

Maximal subgroups

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

subgroupindex
#237503532
#237503502
#237500042
#237500032
#237498362
#237498342
#237498332
#237497492
C4×#145587262
#237497172
#462×C1492
#3395149