Finite Group Databasebeta

← #34043883

Subgroups — #34043883

Order 19072.

250 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 55 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#23750296C211yesmaximal, characteristic
2#23749973C211yesmaximal, characteristic, complemented
3#23749832C211yesmaximal, characteristic, complemented
4#23749368C211yesmaximal, characteristic, complemented
5#23749355C211yesmaximal, characteristic, complemented
6D4⋊#11924746C211yesmaximal, characteristic, complemented
7#474×C149C211yesmaximal, characteristic, complemented
8C2×#14558736—21no—
9C2×#14558726—21no—
10#18011908C2211yescharacteristic
11#18011907—21no—
12#18011885—21no—
13#18011884—22no—
14C4×Dic298C2211yescharacteristic
15#18011873—21no—
16C4⋊#11924746C2211yescharacteristic
17#18011835—21no—
18#18011831—22no—
19C4×#11924746C2211yescharacteristic
20C4⋊Q8×C149C2211yescharacteristic
21C4×D4×C149C2211yescharacteristic
22#107×C149—21no—
23C4⋊C8×C149C2211yescharacteristic
24#102×C149—21no—
25#14558736—42no—
26#14558736—42no—
27C2×Dic298D411yescharacteristic
28C2×D596—21no—
29C2×D596—21no—
30C2×D596D412yes—
31C2×C22⋊D149—22no—
32C2×C22⋊D149—22no—
33C2×C4×D149—22no—
34#14558726—42no—
35C2×#11924746—21no—
36C2×#11924746—21no—
37C4⋊Dic149D411yescharacteristic
38#14558715—21no—
39#14558713—22no—
40C4×Dic149—21no—
41C2×Q8×C149—21no—
42C2×D4×C149D411yescharacteristic
43C22×C4×C149—21no—
44C2×C8×C149—21no—
45C4⋊C4×C149—21no—
46C4⋊C4×C149—21no—
47C4⋊C4×C149D411yescharacteristic
48C22⋊C4×C149—21no—
49C42×C149C2311yescharacteristic
50C22×D149—22no—
51Dic298—21no—
52Dic298D812yes—
53D596—42no—
54D596—41no—
55D596—41no—
56D596—41no—
57D596—41no—
58C22⋊D149—44no—
59C22⋊D149—82no—
60C2×Dic149—21no—
61C2×Dic149—21no—
62C4×D149—44no—
63#11924746—41no—
64#11924746—41no—
65C23×C149—21no—
66Q8×C149—41no—
67Q8×C149—41no—
68D4×C149—21no—
69D4×C149—21no—
70C2×C4×C149—21no—
71C2×C4×C149—41no—
72C2×C4×C149—41no—
73C2×C4×C149—41no—
74C2×C4×C149C2×D411yescharacteristic
75C2×C4×C149C2×D411yescharacteristic
76C2×C4×C149C2×D411yescharacteristic
77C8×C149—41no—
78C22×C149—41no—
79C22×C149—41no—
80C22×C149—41no—
81C22×C149#12011yescharacteristic
82C2×D149—42no—
83C2×D149—42no—
84C2×D149—42no—
85C4×C149—21no—
86C4×C149—41no—
87C4×C149—81no—
88C4×C149C2×D811yescharacteristic
89C4×C149#13511yescharacteristic
90C4×C149AGL(1,ℤ/8)11yescharacteristic
91C4×C149#13711yescharacteristic
92Dic149—22no—
93Dic149—41no—
94C2×C149—81no—
95C2×C149#44711yescharacteristic
96C2×C149#45211yescharacteristic
97C2×C149#45511yescharacteristic
98D149—82no—
99C149#164111yescharacteristic, complemented, Sylow
100#1641—1491nomaximal, Sylow
101#550—1491no—
102#486—1491no—
103#474D14911yescharacteristic, complemented
104#462—1491no—
105#331—1491no—
106Q8⋊C8—1491no—
107D4⋊C8—1491no—
108C2×#41—2981no—
109C2×Q16—2981no—
110C4⋊Q8C2×D14911yescharacteristic
111#127—2981no—
112#127—1491no—
113#121—2982no—
114#121—2981no—
115C4×Q8—1491no—
116C4×D4—2981no—
117C4×D4C2×D14911yescharacteristic
118#107—21no—
119C4⋊C8—1491no—
120C4⋊C8C2×D14911yescharacteristic
121#103—2981no—
122#102—21no—
123#102—2982no—
124C4×C8—1491no—
125#41—5962no—
126#41—5962no—
127C2×Q8—21no—
128C2×Q8—1491no—
129C2×D4—2982no—
130C2×D4—2982no—
131C2×D4—2981no—
132C2×D4—2981no—
133C2×D4—1492no—
134C2×D4C22⋊D14911yescharacteristic
135C22×C4—21no—
136C22×C4—2982no—
137Q16—5962no—
138C2×C8—21no—
139C2×C8—2981no—
140C2×C8—2981no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—2981no—
144C4⋊C4—1491no—
145C4⋊C4C22⋊D14911yescharacteristic
146C22⋊C4—21no—
147C22⋊C4—2982no—
148C42—2981no—
149C42C22×D14911yescharacteristic
150C23—21no—
151C23—2982no—
152Q8—41no—
153Q8—41no—
154Q8—2981no—
155Q8—1492no—
156D4—21no—
157D4—21no—
158D4—5962no—
159D4—5964no—
160D4—5961no—
161D4—5961no—
162D4—5961no—
163D4—5961no—
164D4—11922no—
165C2×C4—21no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—2981no—
170C2×C4—2981no—
171C2×C4—5964no—
172C2×C4D4×D14911yescharacteristic
173C2×C4D4×D14911yescharacteristic
174C2×C4C2×C22⋊D14911yescharacteristic
175C8—41no—
176C8—5961no—
177C8—5961no—
178C22—41no—
179C22—41no—
180C22—41no—
181C22—5962no—
182C22—5962no—
183C22—5962no—
184C22#1801187911yescharacteristic
185C4—21no—
186C4—41no—
187C4—81no—
188C4—2982no—
189C4—5961no—
190C4D8×D14911yescharacteristic
191C4#1801193111yescharacteristic
192C4#1801193511yescharacteristic
193C4#1801194211yescharacteristic
194C2—81no—
195C2—11922no—
196C2#2374975711yescharacteristic
197C2#2374978511yescharacteristic
198C2#2374980111yescharacteristic
subgroupG/H
centerC22#18011879
commutator, cosocleC42×C149C23
FrattiniC42C22×D149
Fitting#474×C149C2
socleC22×C149#120
prime radical#23750296C2
hypercenter#474D149
hypocenterC149#1641
LCSG ▷ C42×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
2. #23749973C2semidirect
3. #23749832C2semidirect
4. #23749368C2semidirect
5. #23749355C2semidirect
6. D4⋊#11924746C2semidirect
7. #474×C149C2semidirect
99. C149#1641semidirect
103. #474D149semidirect

Maximal subgroups

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

subgroupindex
#237502962
#237499732
#237498322
#237493682
#237493552
D4⋊#119247462
#474×C1492
#1641149