Finite Group Databasebeta

← #34055581

Subgroups — #34055581

Order 19072.

378 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 109 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#23750198C212yesmaximal
2#23749968C212yesmaximal, complemented
3#23749965C212yesmaximal, complemented
4#23749881C212yesmaximal, complemented
5#23749866C211yesmaximal, characteristic, complemented
6#23749782C212yesmaximal, complemented
7#23749779C212yesmaximal, complemented
8#23749591C211yesmaximal, characteristic
9#467×C149C211yesmaximal, characteristic, complemented
10C2×#14558736C2211yescharacteristic
11C2×Q8×D149C2212yes—
12C2×Dic596C2211yescharacteristic
13C2×#14558726C2212yes—
14C2×#14558720C2211yescharacteristic
15#18011910—22no—
16#18011897—22no—
17#18011896—22no—
18#18011893—22no—
19#18011891C2212yes—
20#18011890C2212yes—
21#18011887C2212yes—
22#18011869C2212yes—
23#18011845C2211yescharacteristic
24#18011842C2212yes—
25#18011836C2212yes—
26#18011835C2212yes—
27#18011834C2212yes—
28#18011823C2212yes—
29#18011823C2212yes—
30C2×Q16×C149C2211yescharacteristic
31C22×C8×C149C2211yescharacteristic
32C22⋊Q8×C149C2212yes—
33#107×C149C2211yescharacteristic
34#103×C149C2212yes—
35#14558736—41no—
36#14558736—41no—
37C2×Dic298—22no—
38C2×Dic298D411yescharacteristic
39C2×Dic298C2312yes—
40Q8×D149—42no—
41Q8×D149—42no—
42C2×D596D411yescharacteristic
43C2×C22⋊D149D412yes—
44C2×C4×D149—22no—
45C2×C4×D149C2312yes—
46Dic596—41no—
47#14558726—42no—
48#14558720—41no—
49C2×#11924746C2312yes—
50C4⋊Dic149—22no—
51C4⋊Dic149C2312yes—
52#14558715—22no—
53#14558715—22no—
54C22⋊Dic149—22no—
55#14558713—22no—
56#14558713—22no—
57#14558713—22no—
58C4×Dic149—22no—
59C2×Q8×C149C2312yes—
60C22×C4×C149C2311yescharacteristic
61Q16×C149—41no—
62C2×C8×C149—41no—
63C2×C8×C149C2311yescharacteristic
64C2×C8×C149C2311yescharacteristic
65C4⋊C4×C149—22no—
66C4⋊C4×C149C2312yes—
67C22⋊C4×C149—22no—
68C22×D149C2×D412yes—
69Dic298—22no—
70Dic298—22no—
71Dic298—41no—
72Dic298—44no—
73D596—41no—
74C22⋊D149—42no—
75C2×Dic149—22no—
76C2×Dic149—22no—
77C2×Dic149C2×D412yes—
78C4×D149—22no—
79C4×D149—22no—
80C4×D149—44no—
81#11924746—22no—
82C23×C149C2×D411yescharacteristic
83Q8×C149—22no—
84Q8×C149—22no—
85C2×C4×C149—21no—
86C2×C4×C149—21no—
87C2×C4×C149—22no—
88C2×C4×C149—22no—
89C2×C4×C149C2×D411yescharacteristic
90C2×C4×C149C2411yescharacteristic
91C8×C149—21no—
92C8×C149—21no—
93C22×C149—21no—
94C22×C149—21no—
95C22×C149—21no—
96C22×C149C22×D411yescharacteristic
97C2×D149—22no—
98C2×D149—22no—
99C2×D149—22no—
100C4×C149—21no—
101C4×C149—42no—
102C4×C149—42no—
103C4×C149H(5,𝔽2)11yescharacteristic
104C4×C149H(5,𝔽2)11yescharacteristic
105Dic149—22no—
106Dic149—42no—
107Dic149—42no—
108C2×C149—41no—
109C2×C149#53411yescharacteristic
110C2×C149#57811yescharacteristic
111C2×C149#57811yescharacteristic
112D149—42no—
113C149#320211yescharacteristic, complemented, Sylow
114#3202—1491nomaximal, Sylow
115#536—1492no—
116#485—1492no—
117#485—1492no—
118#470—1492no—
119#467—1491no—
120#467D14911yescharacteristic, complemented
121#451—1492no—
122#451—1492no—
123#408—1491no—
124C2×#41—1491no—
125C22×Q8—1492no—
126C2×Q16—1492no—
127C2×Q16—1491no—
128C2×Q16C2×D14911yescharacteristic
129C2×M16—1491no—
130C22×C8C2×D14911yescharacteristic
131C4⋊Q8—2982no—
132#124—2982no—
133#123—2982no—
134#123—2982no—
135C22⋊Q8—1492no—
136C22⋊Q8—1492no—
137C22⋊Q8—1492no—
138C22⋊Q8C2×D14912yes—
139#117—1492no—
140#107—1491no—
141#107C2×D14911yescharacteristic
142#106—1492no—
143#103—1492no—
144#103—1492no—
145#103—1492no—
146#103C2×D14912yes—
147C22⋊C8—1492no—
148C22⋊C8—1492no—
149#41—5961no—
150#41—5961no—
151C2×Q8—2982no—
152C2×Q8—5962no—
153C2×Q8—5962no—
154C2×Q8—1492no—
155C2×Q8—1491no—
156C2×Q8C22×D14912yes—
157C2×D4—1492no—
158C2×D4—1491no—
159C22×C4—2982no—
160C22×C4—1492no—
161C22×C4C22×D14911yescharacteristic
162Q16—41no—
163Q16—5961no—
164Q16—5962no—
165M16—5961no—
166C2×C8—41no—
167C2×C8—1492no—
168C2×C8C22×D14911yescharacteristic
169C2×C8C22×D14911yescharacteristic
170C4⋊C4—22no—
171C4⋊C4—2982no—
172C4⋊C4—2982no—
173C4⋊C4—2982no—
174C4⋊C4—1492no—
175C4⋊C4C22×D14912yes—
176C22⋊C4—22no—
177C22⋊C4—2982no—
178C22⋊C4—2982no—
179C22⋊C4—2982no—
180C22⋊C4—2982no—
181C42—2982no—
182C23—1492no—
183C23D4×D14911yescharacteristic
184Q8—22no—
185Q8—22no—
186Q8—2982no—
187Q8—2982no—
188Q8—5961no—
189Q8—5964no—
190D4—5961no—
191D4—5962no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—2982no—
197C2×C4—2982no—
198C2×C4—2982no—
199C2×C4—2982no—
200C2×C4—5964no—
201C2×C4—1492no—
202C2×C4D4×D14911yescharacteristic
203C2×C4C23×D14911yescharacteristic
204C8—21no—
205C8—21no—
206C8—2982no—
207C22—21no—
208C22—21no—
209C22—21no—
210C22—2982no—
211C22—2982no—
212C22—2982no—
213C22C2×D4×D14911yescharacteristic
214C4—21no—
215C4—42no—
216C4—42no—
217C4—2982no—
218C4—5962no—
219C4—5962no—
220C4#1801195611yescharacteristic
221C4#1801195711yescharacteristic
222C2—41no—
223C2—5962no—
224C2#2375018311yescharacteristic
225C2#2375043811yescharacteristic
226C2#2375043911yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#467×C149C2
socleC22×C149C22×D4
prime radicalC2×#14558736C22
hypercenter#467D149
hypocenterC149#3202
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
2. #23749968C2semidirect
3. #23749965C2semidirect
4. #23749881C2semidirect
5. #23749866C2semidirect
6. #23749782C2semidirect
7. #23749779C2semidirect
9. #467×C149C2semidirect
113. C149#3202semidirect
120. #467D149semidirect

Maximal subgroups

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

subgroupindex
#237501982
#237499682
#237499652
#237498812
#237498662
#237497822
#237497792
#237495912
#467×C1492
#3202149