Finite Group Databasebeta

← #355×D149 #34046367

Subgroups — #355×D149 #34046367

Order 19072.

260 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 57 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#124×D149C211yesmaximal, characteristic
2#101×D149C212yesmaximal, complemented
3#23749422C211yesmaximal, characteristic, complemented
4#23749421C212yesmaximal, complemented
5#355×C149C211yesmaximal, characteristic, complemented
6C2×Q8×D149C2211yescharacteristic
7C2×D4×D149C411yescharacteristic
8M16×D149—22no—
9#18011900C2211yescharacteristic
10#18011899C411yescharacteristic
11#18011898C411yescharacteristic
12#18011897—22no—
13C22⋊C4×D149—22no—
14C42×D149C411yescharacteristic
15#18011830C2212yescomplemented
16#18011829—22no—
17#124×C149C2211yescharacteristic
18#101×C149C2212yescomplemented
19C23×D149—21no—
20C2×Dic298C2×C411yescharacteristic
21C2×Dic298D412yes—
22Q8×D149—41no—
23Q8×D149—41no—
24C2×D596C2×C411yescharacteristic
25C2×C22⋊D149—21no—
26D4×D149—41no—
27D4×D149—41no—
28C2×C4×D149—21no—
29C2×C4×D149C2×C411yescharacteristic
30C2×C4×D149D412yes—
31#14558720—22no—
32#14558719—42no—
33C8×D149—42no—
34C22⋊Dic149—22no—
35#14558713—22no—
36#14558713—22no—
37C4×Dic149—21no—
38C4×Dic149C2×C411yescharacteristic
39C2×Q8×C149C2311yescharacteristic
40C2×D4×C149C2×C411yescharacteristic
41M16×C149—22no—
42C22⋊C4×C149—22no—
43C42×C149C2×C411yescharacteristic
44C22×D149—21no—
45C22×D149—44no—
46C22×D149—41no—
47C22×D149—41no—
48C22×D149C22⋊C411yescharacteristic
49Dic298—41no—
50Dic298—42no—
51D596—41no—
52C22⋊D149—42no—
53C2×Dic149—21no—
54C2×Dic149C22⋊C411yescharacteristic
55C2×Dic149C22⋊C412yes—
56C4×D149—21no—
57C4×D149—21no—
58C4×D149—22no—
59C4×D149—22no—
60C4×D149—42no—
61#11924746—42no—
62C23×C149—21no—
63Q8×C149—41no—
64D4×C149—41no—
65C2×C4×C149—21no—
66C2×C4×C149C22×C411yescharacteristic
67C2×C4×C149C2×D412yes—
68C8×C149—42no—
69C22×C149—42no—
70C22×C149—41no—
71C22×C149C2×C22⋊C411yescharacteristic
72C2×D149—22no—
73C2×D149—42no—
74C2×D149—41no—
75C2×D149—82no—
76C2×D149—82no—
77C2×D149#9911yescharacteristic
78C2×D149#9911yescharacteristic
79C4×C149—22no—
80C4×C149—21no—
81C4×C149—41no—
82Dic149—21no—
83Dic149—22no—
84Dic149—41no—
85C2×C149—21no—
86C2×C149—81no—
87C2×C149C2×#9911yescharacteristic
88D149—21no—
89D149—81no—
90D149#35512yesdirect product factor
91C149C2×#35511yescharacteristic, complemented, Sylow
92C2×#355—1491nomaximal, Sylow
93C2×#124—1491no—
94C2×#101—1492no—
95#355—1491no—
96#355—1492no—
97#355D14911yescharacteristic, direct product factor
98C22×Q8—1491no—
99C22×D4—1491no—
100C2×M16—2982no—
101#124—2982no—
102#124—1491no—
103#124—1491no—
104#124—1491no—
105#124C2×D14911yescharacteristic
106C2×C22⋊C4—2982no—
107C2×C42—1491no—
108#101—2982no—
109#101—1492no—
110#101C2×D14912yescomplemented
111C24—2981no—
112C2×Q8—5961no—
113C2×Q8—5961no—
114C2×Q8—1491no—
115C2×Q8—1492no—
116C2×Q8C22×D14911yescharacteristic
117C2×D4—2981no—
118C2×D4—5961no—
119C2×D4—5961no—
120C2×D4—1491no—
121C2×D4C4×D14911yescharacteristic
122C22×C4—2981no—
123C22×C4—1491no—
124C22×C4—1492no—
125M16—22no—
126M16—2982no—
127M16—5962no—
128C2×C8—5962no—
129C22⋊C4—22no—
130C22⋊C4—2982no—
131C22⋊C4—2982no—
132C22⋊C4—2982no—
133C42—2981no—
134C42—1491no—
135C42C4×D14911yescharacteristic
136C23—21no—
137C23—2981no—
138C23—5964no—
139C23—5961no—
140C23—5961no—
141C23—1491no—
142Q8—41no—
143Q8—5962no—
144Q8—5961no—
145D4—41no—
146D4—5961no—
147D4—5962no—
148C2×C4—21no—
149C2×C4—2982no—
150C2×C4—2982no—
151C2×C4—2981no—
152C2×C4—2981no—
153C2×C4—2981no—
154C2×C4—5962no—
155C2×C4—1491no—
156C2×C4—1492no—
157C2×C4C2×C4×D14911yescharacteristic
158C2×C4D4×D14912yes—
159C8—42no—
160C8—5962no—
161C22—42no—
162C22—41no—
163C22—2982no—
164C22—5962no—
165C22—5961no—
166C22—1491no—
167C22—1491no—
168C22—11922no—
169C22—11922no—
170C22C22⋊C4×D14911yescharacteristic
171C4—22no—
172C4—21no—
173C4—41no—
174C4—2981no—
175C4—2982no—
176C4—5961no—
177C2—21no—
178C2—81no—
179C2—2981no—
180C2—1492no—
181C2—11921no—
182C2#99×D14911yescharacteristic
subgroupG/H
centerC2#99×D149
commutatorC2×C4×C149C22×C4
FrattiniC2×Q8C22×D149
Fitting#355×C149C2
socleC2×C149C2×#99
prime radicalC2×D4×D149C4
cosocleC2×Q8×C149C23
hypercenter#355D149
hypocenterC149C2×#355
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #355

Complements

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

NH ≅ G/Ntype
2. #101×D149C2semidirect
3. #23749422C2semidirect
4. #23749421C2semidirect
5. #355×C149C2semidirect
15. #18011830C22semidirect
18. #101×C149C22semidirect
90. D149#355direct (N × H)
91. C149C2×#355semidirect
97. #355D149direct (N × H)
110. #101C2×D149semidirect

Maximal subgroups

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

subgroupindex
#124×D1492
#101×D1492
#237494222
#237494212
#355×C1492
C2×#355149