Finite Group Databasebeta

← #34055583

Subgroups — #34055583

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#23749969C212yesmaximal, complemented
3#23749964C212yesmaximal, complemented
4#23749883C211yesmaximal, characteristic, complemented
5#23749864C212yesmaximal, complemented
6#23749782C212yesmaximal, complemented
7#23749779C212yesmaximal, complemented
8#23749593C211yesmaximal, characteristic
9#470×C149C211yesmaximal, characteristic, complemented
10C2×#14558736C2211yescharacteristic
11C2×Q8×D149C2212yes—
12C2×Dic596C2211yescharacteristic
13C2×#14558726C2212yes—
14C22×#11924746C2211yescharacteristic
15#18011910—22no—
16#18011897—22no—
17#18011896—22no—
18#18011893—22no—
19#18011891C2212yes—
20#18011890C2212yes—
21#18011887C2212yes—
22#18011869C2212yes—
23#18011844C2212yes—
24#18011843C2211yescharacteristic
25#18011836C2212yes—
26#18011835C2212yes—
27#18011834C2212yes—
28#18011823C2212yes—
29#18011823C2212yes—
30C2×Q16×C149C2211yescharacteristic
31C2×M16×C149C2211yescharacteristic
32C22⋊Q8×C149C2212yes—
33#106×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—
48C2×#11924746—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—
62M16×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—22no—
95C22×C149C22×D411yescharacteristic
96C2×D149—22no—
97C2×D149—24no—
98C4×C149—21no—
99C4×C149—42no—
100C4×C149—42no—
101C4×C149H(5,𝔽2)11yescharacteristic
102C4×C149H(5,𝔽2)11yescharacteristic
103Dic149—22no—
104Dic149—42no—
105Dic149—42no—
106C2×C149—41no—
107C2×C149#53411yescharacteristic
108C2×C149#57812yes—
109D149—42no—
110C149#320211yescharacteristic, complemented, Sylow
111#3202—1491nomaximal, Sylow
112#536—1492no—
113#485—1492no—
114#485—1492no—
115#470—1491no—
116#470D14911yescharacteristic, complemented
117#467—1492no—
118#451—1492no—
119#451—1492no—
120#408—1491no—
121C2×#41—1491no—
122C22×Q8—1492no—
123C2×Q16—1492no—
124C2×Q16—1491no—
125C2×Q16C2×D14911yescharacteristic
126C2×M16C2×D14911yescharacteristic
127C22×C8—1491no—
128C4⋊Q8—2982no—
129#124—2982no—
130#123—2982no—
131#123—2982no—
132C22⋊Q8—1492no—
133C22⋊Q8—1492no—
134C22⋊Q8—1492no—
135C22⋊Q8C2×D14912yes—
136#117—1492no—
137#107—1492no—
138#106—1491no—
139#106C2×D14911yescharacteristic
140#103—1492no—
141#103—1492no—
142#103—1492no—
143#103C2×D14912yes—
144C22⋊C8—1492no—
145C22⋊C8—1492no—
146#41—5961no—
147#41—5961no—
148C2×Q8—2982no—
149C2×Q8—5962no—
150C2×Q8—5962no—
151C2×Q8—1492no—
152C2×Q8—1491no—
153C2×Q8C22×D14912yes—
154C2×D4—1492no—
155C2×D4—1491no—
156C22×C4—2982no—
157C22×C4—1492no—
158C22×C4C22×D14911yescharacteristic
159Q16—41no—
160Q16—5961no—
161Q16—5962no—
162M16—41no—
163C2×C8—5961no—
164C2×C8—1492no—
165C2×C8C22×D14911yescharacteristic
166C2×C8C22×D14911yescharacteristic
167C4⋊C4—22no—
168C4⋊C4—2982no—
169C4⋊C4—2982no—
170C4⋊C4—2982no—
171C4⋊C4—1492no—
172C4⋊C4C22×D14912yes—
173C22⋊C4—22no—
174C22⋊C4—2982no—
175C22⋊C4—2982no—
176C22⋊C4—2982no—
177C22⋊C4—2982no—
178C42—2982no—
179C23—1492no—
180C23D4×D14911yescharacteristic
181Q8—22no—
182Q8—22no—
183Q8—2982no—
184Q8—2982no—
185Q8—5961no—
186Q8—5964no—
187D4—5961no—
188D4—5962no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—2982no—
194C2×C4—2982no—
195C2×C4—2982no—
196C2×C4—2982no—
197C2×C4—5964no—
198C2×C4—1492no—
199C2×C4D4×D14911yescharacteristic
200C2×C4C23×D14911yescharacteristic
201C8—21no—
202C8—21no—
203C8—2982no—
204C22—21no—
205C22—22no—
206C22—2982no—
207C22—2984no—
208C22C2×D4×D14911yescharacteristic
209C4—21no—
210C4—42no—
211C4—42no—
212C4—2982no—
213C4—5962no—
214C4—5962no—
215C4#1801195611yescharacteristic
216C4#1801195711yescharacteristic
217C2—41no—
218C2—5962no—
219C2#2375018311yescharacteristic
220C2#2375044112yes—
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#470×C149C2
socleC22×C149C22×D4
prime radicalC2×#14558736C22
hypercenter#470D149
hypocenterC149#3202
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
2. #23749969C2semidirect
3. #23749964C2semidirect
4. #23749883C2semidirect
5. #23749864C2semidirect
6. #23749782C2semidirect
7. #23749779C2semidirect
9. #470×C149C2semidirect
110. C149#3202semidirect
116. #470D149semidirect

Maximal subgroups

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

subgroupindex
#237501982
#237499692
#237499642
#237498832
#237498642
#237497822
#237497792
#237495932
#470×C1492
#3202149