Finite Group Databasebeta

← #34052761

Subgroups — #34052761

Order 19072.

380 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 125 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
1C2×#18011902C211yesmaximal, characteristic
2C2×#18011901C211yesmaximal, characteristic
3#23749567C212yesmaximal
4#23749565C211yesmaximal, characteristic
5#23749564C211yesmaximal, characteristic
6#23749559C212yesmaximal
7#23749558C212yesmaximal
8#23749556C211yesmaximal, characteristic
9#23749556C212yesmaximal
10#23749489C211yesmaximal, characteristic
11#398×C149C211yesmaximal, characteristic
12#18011902—24no—
13#18011901—24no—
14C2×C4⋊Dic149C2211yescharacteristic
15C2×C4⋊Dic149C2212yes—
16C2×C4⋊Dic149C2211yescharacteristic
17C2×#14558715C2211yescharacteristic
18C2×#14558715C2211yescharacteristic
19C2×#14558715C2211yescharacteristic
20C2×#14558715C2211yescharacteristic
21C2×#14558715C2212yes—
22C2×#14558715C2212yes—
23C2×#14558715C2212yes—
24C2×C4×Dic149C2211yescharacteristic
25#18011818C2211yescharacteristic
26#18011818C2212yes—
27#18011818C2212yes—
28#18011818C2212yes—
29#18011818C2212yes—
30#18011818C2212yes—
31#18011818C2212yes—
32C2×C4⋊C4×C149C2211yescharacteristic
33C2×C4⋊C4×C149C2211yescharacteristic
34C2×C4⋊C4×C149C2212yes—
35#95×C149C2211yescharacteristic
36#95×C149C2212yes—
37C22×Dic149C2312yes—
38C22×Dic149C2311yescharacteristic
39C22×Dic149C2312yes—
40C22×Dic149C2311yescharacteristic
41C22×Dic149C2311yescharacteristic
42C22×Dic149C2311yescharacteristic
43C4⋊Dic149—22no—
44C4⋊Dic149—24no—
45C4⋊Dic149—22no—
46#14558715—22no—
47#14558715—22no—
48#14558715—22no—
49#14558715—24no—
50#14558715—22no—
51#14558715—42no—
52#14558715—42no—
53C4×Dic149D414yes—
54C22×C4×C149C2312yes—
55C22×C4×C149C2311yescharacteristic
56C22×C4×C149C2312yes—
57C22×C4×C149C2311yescharacteristic
58C22×C4×C149C2311yescharacteristic
59C4⋊C4×C149—22no—
60C4⋊C4×C149—22no—
61C4⋊C4×C149—42no—
62C2×Dic149—21no—
63C2×Dic149—21no—
64C2×Dic149—22no—
65C2×Dic149—21no—
66C2×Dic149—21no—
67C2×Dic149—22no—
68C2×Dic149—21no—
69C2×Dic149—22no—
70C2×Dic149—22no—
71C2×Dic149—21no—
72C2×Dic149—22no—
73C2×Dic149—24no—
74C2×Dic149—22no—
75C2×Dic149C2×D412yes—
76C2×Dic149C2×D412yes—
77C23×C149C2411yescharacteristic
78C2×C4×C149—22no—
79C2×C4×C149—21no—
80C2×C4×C149—21no—
81C2×C4×C149—22no—
82C2×C4×C149—21no—
83C2×C4×C149—22no—
84C2×C4×C149—22no—
85C2×C4×C149—22no—
86C2×C4×C149—22no—
87C2×C4×C149—21no—
88C2×C4×C149—22no—
89C2×C4×C149—22no—
90C2×C4×C149C2×D412yes—
91C22×C149C22×D411yescharacteristic
92C22×C149H(5,𝔽2)11yescharacteristic
93C22×C1492−1+412yes—
94C22×C1492−1+411yescharacteristic
95C22×C1492−1+412yes—
96C4×C149—22no—
97C4×C149—41no—
98C4×C149—41no—
99C4×C149—42no—
100C4×C149—42no—
101Dic149—22no—
102Dic149—22no—
103Dic149—41no—
104Dic149—42no—
105Dic149—41no—
106Dic149—42no—
107C2×C149#53611yescharacteristic
108C2×C149#53611yescharacteristic
109C2×C149#53711yescharacteristic
110C2×C149#56312yes—
111C2×C149#56412yes—
112C149#282211yescharacteristic, complemented, Sylow
113#2822—1491nomaximal, Sylow
114C2×#125—1491no—
115C2×#125—1491no—
116#400—1491no—
117#400—1491no—
118#400—1492no—
119#398—1491no—
120#398—1492no—
121#398—1492no—
122#398—1492no—
123#398D14911yescharacteristic
124#382—1491no—
125#125—2984no—
126#125—2984no—
127C2×C4⋊C4—1491no—
128C2×C4⋊C4—1492no—
129C2×C4⋊C4—1491no—
130C2×C4⋊C4—1491no—
131C2×C4⋊C4—1491no—
132C2×C4⋊C4—1492no—
133C2×C4⋊C4—1491no—
134C2×C4⋊C4—1491no—
135C2×C4⋊C4—1492no—
136C2×C4⋊C4—1492no—
137C2×C4⋊C4C2×D14911yescharacteristic
138C2×C4⋊C4C2×D14911yescharacteristic
139C2×C4⋊C4C2×D14912yes—
140C2×C42—1491no—
141#95—1491no—
142#95—1492no—
143#95—1492no—
144#95—1492no—
145#95—1492no—
146#95—1492no—
147#95—1492no—
148#95C2×D14911yescharacteristic
149#95C2×D14912yes—
150C22×C4—1492no—
151C22×C4—1491no—
152C22×C4—1492no—
153C22×C4—1491no—
154C22×C4—1491no—
155C22×C4—1491no—
156C22×C4C22×D14912yes—
157C22×C4C22×D14911yescharacteristic
158C22×C4C22×D14911yescharacteristic
159C22×C4C22×D14912yes—
160C22×C4C22×D14911yescharacteristic
161C4⋊C4—22no—
162C4⋊C4—22no—
163C4⋊C4—42no—
164C4⋊C4—2982no—
165C4⋊C4—2982no—
166C4⋊C4—2984no—
167C4⋊C4—2982no—
168C4⋊C4—2982no—
169C4⋊C4—2984no—
170C4⋊C4—2982no—
171C4⋊C4—2982no—
172C4⋊C4—5962no—
173C4⋊C4—5962no—
174C42—1494no—
175C23C23×D14911yescharacteristic
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—22no—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—21no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—2981no—
189C2×C4—2981no—
190C2×C4—2982no—
191C2×C4—2981no—
192C2×C4—2982no—
193C2×C4—2981no—
194C2×C4—2981no—
195C2×C4—2982no—
196C2×C4—2982no—
197C2×C4—2981no—
198C2×C4—2982no—
199C2×C4—2984no—
200C2×C4—2982no—
201C2×C4—1492no—
202C2×C4—1492no—
203C2×C4D4×D14912yes—
204C22C2×D4×D14911yescharacteristic
205C22#1801195611yescharacteristic
206C22#1801195812yes—
207C22#1801195811yescharacteristic
208C22#1801195912yes—
209C4—22no—
210C4—41no—
211C4—41no—
212C4—42no—
213C4—42no—
214C4—2982no—
215C4—2982no—
216C4—5961no—
217C4—5962no—
218C4—5961no—
219C4—5962no—
220C2#2375019711yescharacteristic
221C2#2375020011yescharacteristic
222C2#2375020411yescharacteristic
223C2#2375037612yes—
224C2C149⋊#56412yes—
subgroupG/H
center, FrattiniC23C23×D149
commutator, socle, prime radical, cosocleC23×C149C24
Fitting#398×C149C2
hypercenter#398D149
hypocenterC149#2822
LCSG ▷ C23×C149 ▷ C149
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
112. C149#2822semidirect

Maximal subgroups

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

subgroupindex
C2×#180119022
C2×#180119012
#237495672
#237495652
#237495642
#237495592
#237495582
#237495562
#237494892
#398×C1492
#2822149