Finite Group Databasebeta

← D173⋊#354 #36369832

Subgroups — D173⋊#354 #36369832

Order 22144.

284 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 54 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
1D173⋊#99C212yesmaximal
2#26012398C212yesmaximal, complemented
3#26012397C212yesmaximal, complemented
4#124×D173C211yesmaximal, characteristic
5C2×C22⋊#10621924—22no—
6#19149738C2214yes—
7#19149737—22no—
8C2×Q8×D173C411yescharacteristic, complemented
9C2×D4×D173C2211yescharacteristic
10#19149668C2211yescharacteristic
11#19149667C2211yescharacteristic
12#19149666C411yescharacteristic, complemented
13#19149665—22no—
14C22⋊C4×D173—22no—
15C42×D173C411yescharacteristic, complemented
16#124×C173C411yescharacteristic, complemented
17C22×#10621924—42no—
18C22⋊#10621924—24no—
19C22⋊#10621924—42no—
20C23×D173D412yes—
21C2×Dic346—21no—
22C2×Dic346C2×C411yescharacteristic, complemented
23Q8×D173—41no—
24Q8×D173—41no—
25C2×D692C2311yescharacteristic
26C2×C22⋊D173D412yes—
27D4×D173—41no—
28D4×D173—41no—
29C2×C4×D173—21no—
30C2×C4×D173—21no—
31C2×C4×D173C2×C411yescharacteristic
32C22⋊Dic173—22no—
33#14583803—22no—
34#14583803—22no—
35C4×Dic173—21no—
36C4×Dic173C2×C411yescharacteristic, complemented
37C2×Q8×C173C2×C411yescharacteristic, complemented
38C2×D4×C173C2×C411yescharacteristic
39C22⋊C4×C173—22no—
40C42×C173C2×C411yescharacteristic, complemented
41C2×#10621924—44no—
42C2×#10621924—84no—
43C22×D173—22no—
44C22×D173—22no—
45C22×D173—44no—
46C22×D173C22⋊C411yescharacteristic
47C22×D173C2×D412yes—
48Dic346—42no—
49Dic346—41no—
50D692—41no—
51C22⋊D173—42no—
52C2×Dic173—21no—
53C2×Dic173—21no—
54C2×Dic173C22⋊C411yescharacteristic
55C4×D173—21no—
56C4×D173—21no—
57C4×D173—42no—
58C4×D173—41no—
59C4×D173—41no—
60C23×C173C22⋊C412yes—
61Q8×C173—41no—
62D4×C173—41no—
63C2×C4×C173—21no—
64C2×C4×C173—21no—
65C2×C4×C173C22×C411yescharacteristic
66C22×C173—22no—
67C22×C173—42no—
68C22×C173C2×C22⋊C411yescharacteristic
69C2×D173—22no—
70C2×D173—22no—
71C2×D173—44no—
72C2×D173—42no—
73C2×D173—82no—
74C2×D173#9911yescharacteristic
75C2×D173#9911yescharacteristic
76#10621924—84no—
77C4×C173—21no—
78C4×C173—41no—
79C4×C173—41no—
80Dic173—21no—
81Dic173—41no—
82Dic173—41no—
83C2×C173—21no—
84C2×C173—42no—
85C2×C173C2×#9911yescharacteristic
86D173—21no—
87D173—42no—
88D173#35412yescomplemented
89C173C2×#35411yescharacteristic, complemented, Sylow
90C2×#354—1731nomaximal, Sylow
91C2×#124—1731no—
92C2×#99—1732no—
93#354—1732no—
94#354—1732no—
95C22×Q8—1731no—
96C22×D4—1731no—
97#124—3462no—
98#124—1731no—
99#124—1731no—
100#124—1731no—
101#124#1062192411yescharacteristic, complemented
102C2×C22⋊C4—3462no—
103C2×C22⋊C4—3462no—
104C2×C42—1731no—
105#99—3462no—
106#99—1734no—
107C24—1732no—
108C2×Q8—3461no—
109C2×Q8—1731no—
110C2×Q8—6921no—
111C2×Q8—6921no—
112C2×Q8C2×#1062192411yescharacteristic, complemented
113C2×D4—1732no—
114C2×D4—1731no—
115C2×D4—6921no—
116C2×D4—6921no—
117C2×D4C2×#1062192411yescharacteristic
118C22×C4—3461no—
119C22×C4—3461no—
120C22×C4—1731no—
121C22×C4—6922no—
122C22⋊C4—22no—
123C22⋊C4—3462no—
124C22⋊C4—3462no—
125C22⋊C4—3462no—
126C22⋊C4—3464no—
127C22⋊C4—6922no—
128C42—3461no—
129C42—1731no—
130C42C2×#1062192411yescharacteristic, complemented
131C23—3462no—
132C23—3462no—
133C23—1731no—
134C23—1732no—
135C23—6924no—
136C23C22⋊#1062192412yes—
137Q8—41no—
138Q8—6921no—
139Q8—6922no—
140D4—41no—
141D4—6921no—
142D4—6922no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—3461no—
146C2×C4—3461no—
147C2×C4—3461no—
148C2×C4—3461no—
149C2×C4—13844no—
150C2×C4—1731no—
151C2×C4—6922no—
152C2×C4—6921no—
153C2×C4—6921no—
154C2×C4—6924no—
155C2×C4C22×#1062192411yescharacteristic
156C22—22no—
157C22—42no—
158C22—3462no—
159C22—3462no—
160C22—13842no—
161C22—1731no—
162C22—1731no—
163C22—6922no—
164C22—6924no—
165C22C2×C22⋊#1062192411yescharacteristic
166C4—21no—
167C4—41no—
168C4—41no—
169C4—3461no—
170C4—13844no—
171C4—6921no—
172C4—6921no—
173C2—21no—
174C2—42no—
175C2—3461no—
176C2—1732no—
177C2—6922no—
178C2D173⋊#9911yescharacteristic
subgroupG/H
centerC2D173⋊#99
commutatorC2×C4×C173C22×C4
FrattiniC2×C4C22×#10621924
Fitting#124×C173C4
socleC2×C173C2×#99
prime radicalC2×D4×D173C22
cosocleC2×D692C23
hypercenter#124#10621924
hypocenterC173C2×#354
LCSG ▷ C2×C4×C173 ▷ C22×C173 ▷ C2×C173 ▷ C173
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #124

Complements

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

NH ≅ G/Ntype
2. #26012398C2semidirect
3. #26012397C2semidirect
8. C2×Q8×D173C4semidirect
12. #19149666C4semidirect
15. C42×D173C4semidirect
16. #124×C173C4semidirect
22. C2×Dic346C2×C4semidirect
36. C4×Dic173C2×C4semidirect
37. C2×Q8×C173C2×C4semidirect
40. C42×C173C2×C4semidirect
88. D173#354semidirect
89. C173C2×#354semidirect
101. #124#10621924semidirect
112. C2×Q8C2×#10621924semidirect
130. C42C2×#10621924semidirect

Maximal subgroups

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

subgroupindex
D173⋊#992
#260123982
#260123972
#124×D1732
C2×#354173