Finite Group Databasebeta

← #34057578

Subgroups — #34057578

Order 19072.

324 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 133 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#23750353C211yesmaximal, characteristic
2#23750028C211yesmaximal, characteristic
3#23750024C212yesmaximal
4#23749932C212yesmaximal
5#23749929C212yesmaximal
6#23749910C211yesmaximal, characteristic
7#23749907C211yesmaximal, characteristic
8Q8×#11924746C211yesmaximal, characteristic
9C4×#14558726C211yesmaximal, characteristic
10C4×#14558726C212yesmaximal
11#557×C149C211yesmaximal, characteristic
12C2×#14558726C2211yescharacteristic
13#18011911C2211yescharacteristic
14#18011909—21no—
15#18011903C2212yes—
16#18011901—22no—
17C4×Dic298C2211yescharacteristic
18C4×Dic298C2212yes—
19#18011876—21no—
20#18011844C2212yes—
21#18011844C2211yescharacteristic
22#18011844C2212yes—
23#18011842C2212yes—
24#18011842C2212yes—
25C4⋊#11924746C2211yescharacteristic
26C4⋊#11924746C2212yes—
27#18011835C2212yes—
28#18011835C2211yescharacteristic
29#18011834C2212yes—
30#18011834C2211yescharacteristic
31C4×#11924746C2212yes—
32C4×#11924746C2211yescharacteristic
33C4⋊Q8×C149—21no—
34C4⋊Q8×C149C2211yescharacteristic
35#125×C149—22no—
36#125×C149C2212yes—
37C4×Q8×C149—21no—
38C4×Q8×C149C2211yescharacteristic
39C4×Q8×C149C2212yes—
40C4×Q8×C149C2211yescharacteristic
41C2×Dic298—21no—
42C2×Dic298C2311yescharacteristic
43#14558726Q814yescomplemented
44C2×#11924746C2312yes—
45C2×#11924746C2311yescharacteristic
46C2×#11924746C2311yescharacteristic
47C4⋊Dic149—21no—
48C4⋊Dic149C2312yes—
49C4⋊Dic149C2311yescharacteristic
50#14558715—22no—
51#14558715—22no—
52#14558715—22no—
53#14558715—21no—
54C4×Dic149—21no—
55C4×Dic149—22no—
56C2×Q8×C149—21no—
57C2×Q8×C149D411yescharacteristic
58C2×Q8×C149C2311yescharacteristic
59C4⋊C4×C149—22no—
60C4⋊C4×C149—21no—
61C4⋊C4×C149—22no—
62C4⋊C4×C149—21no—
63C4⋊C4×C149—22no—
64C4⋊C4×C149D411yescharacteristic
65C4⋊C4×C149D412yes—
66C4⋊C4×C149C2311yescharacteristic
67C4⋊C4×C149C2312yes—
68C42×C149—22no—
69C42×C149—21no—
70C42×C149C2311yescharacteristic
71C42×C149C2312yes—
72Dic298—21no—
73Dic298—42no—
74Dic298C2×Q812yes—
75C2×Dic149—21no—
76C2×Dic149—22no—
77C2×Dic149—21no—
78#11924746—22no—
79#11924746—21no—
80#11924746C2×Q812yes—
81Q8×C149—22no—
82Q8×C149—21no—
83Q8×C149—42no—
84Q8×C149C2×Q812yes—
85C2×C4×C149—21no—
86C2×C4×C149—21no—
87C2×C4×C149—22no—
88C2×C4×C149C2×D412yes—
89C2×C4×C149C2×D411yescharacteristic
90C2×C4×C149C2×D412yes—
91C2×C4×C149C2×D411yescharacteristic
92C2×C4×C149C2411yescharacteristic
93C22×C149C22×D411yescharacteristic
94C4×C149—22no—
95C4×C149—22no—
96C4×C149—22no—
97C4×C149—21no—
98C4×C149—42no—
99C4×C149—41no—
100C4×C149#13512yes—
101C4×C149C22×Q811yescharacteristic
102C4×C1492−1+411yescharacteristic
103Dic149—22no—
104Dic149—42no—
105Dic149—41no—
106C2×C149D4×Q811yescharacteristic
107C2×C149C2×#13511yescharacteristic
108C2×C149#57811yescharacteristic
109C149#338311yescharacteristic, complemented, Sylow
110#3383—1491nomaximal, Sylow
111#557—1491no—
112#557D14911yescharacteristic
113#500—1491no—
114#499—1492no—
115#479—1492no—
116#479—1492no—
117#475—1491no—
118#475—1491no—
119C8×Q8—1491no—
120C4×Q16—1492no—
121C4×Q16—1491no—
122C2×Q16—1491no—
123C4⋊Q8—21no—
124C4⋊Q8—2981no—
125C4⋊Q8—1491no—
126C4⋊Q8C2×D14911yescharacteristic
127#125—22no—
128#125—2982no—
129#125—1492no—
130#125C2×D14912yes—
131C4×Q8—21no—
132C4×Q8—2981no—
133C4×Q8—1491no—
134C4×Q8—1492no—
135C4×Q8C2×D14911yescharacteristic
136C4×Q8C2×D14912yes—
137C4×Q8C2×D14911yescharacteristic
138#107—1491no—
139#107—1492no—
140#107—1492no—
141#106—1492no—
142#106—1492no—
143C4⋊C8—1491no—
144C4⋊C8—1492no—
145#103—1492no—
146#103—1491no—
147#103—1492no—
148#103—1491no—
149C4×C8—1492no—
150C4×C8—1491no—
151C2×Q8—21no—
152C2×Q8—2981no—
153C2×Q8—1491no—
154C2×Q8C22⋊D14911yescharacteristic
155C2×Q8C22×D14911yescharacteristic
156Q16—1494no—
157C2×C8—1492no—
158C2×C8—1491no—
159C2×C8—1491no—
160C4⋊C4—22no—
161C4⋊C4—21no—
162C4⋊C4—22no—
163C4⋊C4—21no—
164C4⋊C4—22no—
165C4⋊C4—2982no—
166C4⋊C4—2981no—
167C4⋊C4—2982no—
168C4⋊C4—2981no—
169C4⋊C4—2982no—
170C4⋊C4—1491no—
171C4⋊C4—1492no—
172C4⋊C4C22⋊D14911yescharacteristic
173C4⋊C4C22⋊D14912yes—
174C4⋊C4C22×D14911yescharacteristic
175C4⋊C4C22×D14912yes—
176C42—22no—
177C42—21no—
178C42—2982no—
179C42—2981no—
180C42C22×D14912yes—
181C42C22×D14911yescharacteristic
182Q8—22no—
183Q8—21no—
184Q8—42no—
185Q8—2981no—
186Q8—5962no—
187Q8—1492no—
188Q8Q8×D14912yes—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—22no—
192C2×C4—2981no—
193C2×C4—2981no—
194C2×C4—2982no—
195C2×C4C2×C22⋊D14912yes—
196C2×C4C2×C22⋊D14911yescharacteristic
197C2×C4C2×C22⋊D14912yes—
198C2×C4C2×C22⋊D14911yescharacteristic
199C2×C4C23×D14911yescharacteristic
200C8—2982no—
201C8—2981no—
202C8—1492no—
203C22C22×C22⋊D14911yescharacteristic
204C4—22no—
205C4—22no—
206C4—21no—
207C4—22no—
208C4—42no—
209C4—41no—
210C4—2982no—
211C4—5962no—
212C4—5961no—
213C4#1801193112yes—
214C4C2×Q8×D14911yescharacteristic
215C4#1801195911yescharacteristic
216C2Q8×C22⋊D14911yescharacteristic
217C2C2×#1801193111yescharacteristic
218C2#2375044011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#557×C149C2
socle, prime radicalC22×C149C22×D4
hypercenter#557D149
hypocenterC149#3383
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #557

Complements

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

NH ≅ G/Ntype
43. #14558726Q8semidirect
109. C149#3383semidirect

Maximal subgroups

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

subgroupindex
#237503532
#237500282
#237500242
#237499322
#237499292
#237499102
#237499072
Q8×#119247462
C4×#145587262
#557×C1492
#3383149