Finite Group Databasebeta

← #353×D149 #34046347

Subgroups — #353×D149 #34046347

Order 19072.

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

normal subgroups only

This group has 368 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#127×D149C211yesmaximal, characteristic
2#99×D149C212yesmaximal, complemented
3#23749418C211yesmaximal, characteristic, complemented
4#23749417C212yesmaximal, complemented
5#353×C149C211yesmaximal, characteristic, complemented
6C2×D4×D149—22no—
7C2×D4×D149C411yescharacteristic, complemented
8C2×D4×D149C2211yescharacteristic
9#18011908C411yescharacteristic, complemented
10#18011907—22no—
11#18011907C411yescharacteristic, complemented
12#18011907C2211yescharacteristic
13C22⋊C4×D149—22no—
14C42×D149C411yescharacteristic, complemented
15#18011826C2212yescomplemented
16#18011825—22no—
17#127×C149C2211yescharacteristic
18#99×C149C2212yescomplemented
19C23×D149—21no—
20C23×D149D412yes—
21C2×D596—22no—
22C2×D596C2×C411yescharacteristic
23C2×D596C2×C411yescharacteristic, complemented
24C2×C22⋊D149—22no—
25C2×C22⋊D149—21no—
26C2×C22⋊D149—22no—
27C2×C22⋊D149D412yes—
28D4×D149—41no—
29D4×D149—41no—
30D4×D149—48no—
31D4×D149—41no—
32D4×D149—41no—
33C2×C4×D149—21no—
34C2×C4×D149—42no—
35C2×C4×D149C2×C411yescharacteristic
36C22⋊Dic149—22no—
37#14558713—42no—
38C4×Dic149—21no—
39C4×Dic149C2×C411yescharacteristic, complemented
40C2×D4×C149—22no—
41C2×D4×C149C2×C411yescharacteristic, complemented
42C2×D4×C149C2311yescharacteristic
43C22⋊C4×C149—22no—
44C42×C149C2×C411yescharacteristic, complemented
45C22×D149—22no—
46C22×D149—22no—
47C22×D149—21no—
48C22×D149—44no—
49C22×D149—44no—
50C22×D149—41no—
51C22×D149—41no—
52C22×D149C22⋊C411yescharacteristic
53C22×D149C22⋊C412yes—
54D596—41no—
55D596—41no—
56D596—44no—
57C22⋊D149—42no—
58C22⋊D149—44no—
59C22⋊D149—44no—
60C22⋊D149—42no—
61C2×Dic149—21no—
62C2×Dic149—42no—
63C2×Dic149C22⋊C411yescharacteristic
64C4×D149—24no—
65C4×D149—21no—
66C4×D149—21no—
67C4×D149—84no—
68C23×C149—21no—
69C23×C149C2×D412yes—
70D4×C149—41no—
71D4×C149—41no—
72D4×C149—44no—
73C2×C4×C149—21no—
74C2×C4×C149—42no—
75C2×C4×C149C22×C411yescharacteristic
76C22×C149—22no—
77C22×C149—42no—
78C22×C149—42no—
79C22×C149—41no—
80C22×C149C2×C22⋊C411yescharacteristic
81C2×D149—22no—
82C2×D149—22no—
83C2×D149—44no—
84C2×D149—42no—
85C2×D149—42no—
86C2×D149—41no—
87C2×D149—82no—
88C2×D149—82no—
89C2×D149—82no—
90C2×D149#9911yescharacteristic
91C2×D149#9911yescharacteristic
92C4×C149—22no—
93C4×C149—21no—
94C4×C149—82no—
95Dic149—22no—
96Dic149—21no—
97Dic149—82no—
98C2×C149—21no—
99C2×C149—42no—
100C2×C149—81no—
101C2×C149C2×#9911yescharacteristic
102D149—21no—
103D149—42no—
104D149—81no—
105D149#35312yesdirect product factor
106C149C2×#35311yescharacteristic, complemented, Sylow
107C2×#353—1491nomaximal, Sylow
108C2×#127—1491no—
109C2×#99—1492no—
110#353—1491no—
111#353—1492no—
112#353D14911yescharacteristic, direct product factor
113C22×D4—2982no—
114C22×D4—1491no—
115C22×D4—1491no—
116#127—2982no—
117#127—1491no—
118#127—1491no—
119#127—1491no—
120#127C2×D14911yescharacteristic
121C2×C22⋊C4—2982no—
122C2×C42—1491no—
123#99—2982no—
124#99—1492no—
125#99C2×D14912yescomplemented
126C24—2981no—
127C24—1492no—
128C2×D4—22no—
129C2×D4—2982no—
130C2×D4—2982no—
131C2×D4—2982no—
132C2×D4—2981no—
133C2×D4—5961no—
134C2×D4—5961no—
135C2×D4—5961no—
136C2×D4—5961no—
137C2×D4—5968no—
138C2×D4—1492no—
139C2×D4—1491no—
140C2×D4—1491no—
141C2×D4C4×D14911yescharacteristic, complemented
142C2×D4C22×D14911yescharacteristic
143C22×C4—2981no—
144C22×C4—5962no—
145C22×C4—1491no—
146C22⋊C4—22no—
147C22⋊C4—2982no—
148C22⋊C4—5962no—
149C42—2981no—
150C42—1491no—
151C42C4×D14911yescharacteristic, complemented
152C23—21no—
153C23—2982no—
154C23—2982no—
155C23—2981no—
156C23—5964no—
157C23—5964no—
158C23—5961no—
159C23—5961no—
160C23—1491no—
161C23—1492no—
162C23D4×D14912yes—
163D4—41no—
164D4—41no—
165D4—44no—
166D4—5961no—
167D4—5961no—
168D4—5964no—
169D4—5962no—
170D4—5964no—
171D4—5964no—
172D4—5962no—
173C2×C4—21no—
174C2×C4—42no—
175C2×C4—2984no—
176C2×C4—2981no—
177C2×C4—2981no—
178C2×C4—2981no—
179C2×C4—5962no—
180C2×C4—1491no—
181C2×C4—11924no—
182C2×C4C2×C4×D14911yescharacteristic
183C22—22no—
184C22—42no—
185C22—42no—
186C22—41no—
187C22—2982no—
188C22—2982no—
189C22—5962no—
190C22—5962no—
191C22—5964no—
192C22—5961no—
193C22—1491no—
194C22—1491no—
195C22—11922no—
196C22—11922no—
197C22—11922no—
198C22C22⋊C4×D14911yescharacteristic
199C4—22no—
200C4—21no—
201C4—82no—
202C4—2982no—
203C4—2981no—
204C4—11922no—
205C2—21no—
206C2—42no—
207C2—81no—
208C2—2981no—
209C2—5962no—
210C2—1492no—
211C2—11921no—
212C2#99×D14911yescharacteristic
subgroupG/H
centerC2#99×D149
commutatorC2×C4×C149C22×C4
FrattiniC2×D4C22×D149
Fitting#353×C149C2
socleC2×C149C2×#99
prime radical#127×D149C2
cosocleC2×D4×C149C23
hypercenter#353D149
hypocenterC149C2×#353
LCSG ▷ C2×C4×C149 ▷ C22×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #353

Complements

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

NH ≅ G/Ntype
2. #99×D149C2semidirect
3. #23749418C2semidirect
4. #23749417C2semidirect
5. #353×C149C2semidirect
7. C2×D4×D149C4semidirect
9. #18011908C4semidirect
11. #18011907C4semidirect
14. C42×D149C4semidirect
15. #18011826C22semidirect
18. #99×C149C22semidirect
23. C2×D596C2×C4semidirect
39. C4×Dic149C2×C4semidirect
41. C2×D4×C149C2×C4semidirect
44. C42×C149C2×C4semidirect
105. D149#353direct (N × H)
106. C149C2×#353semidirect
112. #353D149direct (N × H)
125. #99C2×D149semidirect
141. C2×D4C4×D149semidirect
151. C42C4×D149semidirect

Maximal subgroups

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

subgroupindex
#127×D1492
#99×D1492
#237494182
#237494172
#353×C1492
C2×#353149