Finite Group Databasebeta

← #28379034

Subgroups — #28379034

Order 13952.

332 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 66 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#20296106C211yesmaximal, characteristic, complemented
2#20296025C212yesmaximal, complemented
3#20296007C211yesmaximal, characteristic, complemented
4#20295897C212yesmaximal, complemented
5#20295577C211yesmaximal, characteristic
6#16812787—24no—
7D109⋊M16—22no—
8D109⋊M16C2212yes—
9#16812778C2212yes—
10#16812764—24no—
11#16812758—22no—
12C2×#13182030C2211yescharacteristic
13C2×#13182030C2211yescharacteristic
14#16812696C411yescharacteristic, complemented
15#16812688C411yescharacteristic, complemented
16#16812688C411yescharacteristic, complemented
17#16812674—22no—
18#16812661—22no—
19C42×D109C2211yescharacteristic
20C4⋊Q8×C109C411yescharacteristic, complemented
21#13182039—24no—
22#13182039D414yescomplemented
23#13182038—22no—
24D109⋊C8—24no—
25D109⋊C8—22no—
26C4⋊#89137—22no—
27C22⋊#89137—22no—
28C4×#89137—22no—
29#13182030—22no—
30#13182030—22no—
31#13182030—22no—
32#13182030—22no—
33C2×D436—22no—
34C2×D436—21no—
35C2×D436C2×C411yescharacteristic
36C2×D436C2×C411yescharacteristic
37C2×D436D412yes—
38C2×C4×D109—21no—
39C2×C4×D109—21no—
40C2×C4×D109D412yes—
41C2×C4×D109C2311yescharacteristic
42#13182006—22no—
43#13182006—22no—
44C4×Dic109—21no—
45C4×Dic109C2×C411yescharacteristic
46C2×Q8×C109C2×C411yescharacteristic
47C2×Q8×C109C2×C411yescharacteristic
48C4⋊C4×C109—22no—
49C42×C109C2×C411yescharacteristic
50C22×D109—21no—
51C22×D109C22⋊C412yes—
52C22×D109C2×D411yescharacteristic
53C2×#89137—42no—
54Q8×C109—22no—
55Q8×C109—22no—
56C2×C4×C109—21no—
57C2×C4×C109—21no—
58C2×C4×C109C22⋊C412yes—
59C2×C4×C109C22×C411yescharacteristic
60C2×Dic109—21no—
61C2×Dic109C2×D411yescharacteristic
62D436—24no—
63D436—22no—
64D436—22no—
65D436—44no—
66D436—42no—
67C4×D109—22no—
68C4×D109—22no—
69C4×D109—42no—
70C4×D109—41no—
71C4×D109—41no—
72C4×D109C2×D412yes—
73C4×D109#4112yes—
74#11724786—24no—
75C22×C109C2×C22⋊C411yescharacteristic
76C2×D109—22no—
77C2×D109—41no—
78C2×D109—42no—
79C2×D109—42no—
80C2×D109—41no—
81C2×D109#12112yes—
82#89137—82no—
83C4×C109—22no—
84C4×C109—22no—
85C4×C109—41no—
86C4×C109C4×D412yes—
87Dic109—41no—
88Dic109#12011yescharacteristic
89Dic109#12311yescharacteristic
90C2×C109—21no—
91C2×C109#38611yescharacteristic
92D109—22no—
93D109—42no—
94D109—81no—
95#1884—1091nomaximal, Sylow
96C109#188411yescharacteristic, complemented, Sylow
97#568—1091no—
98#532—1091no—
99#421—1092no—
100#410—1091no—
101#339—1092no—
102C2×#41—1091no—
103C2×#41—1091no—
104#131—2184no—
105C2×M16—1092no—
106C2×M16—2182no—
107C4⋊Q8#8913711yescharacteristic, complemented
108#127—1091no—
109#124—1091no—
110#124—1091no—
111#121—2182no—
112C4×D4—2182no—
113#117—1092no—
114C2×C42—1091no—
115#104—2184no—
116#99—2182no—
117#41—2182no—
118#41—2182no—
119#41—2182no—
120#41—2182no—
121C2×Q8C2×#8913711yescharacteristic
122C2×Q8C2×#8913711yescharacteristic
123C2×D4—1092no—
124C2×D4—1091no—
125C2×D4—1091no—
126C2×D4—2182no—
127C2×D4—2181no—
128C22×C4—1091no—
129C22×C4—1092no—
130C22×C4—2181no—
131C22×C4—2181no—
132M16—1094no—
133M16—2182no—
134M16—2184no—
135C2×C8—2182no—
136C2×C8—2184no—
137C4⋊C4—22no—
138C4⋊C4—2182no—
139C22⋊C4—2182no—
140C22⋊C4—2182no—
141C22⋊C4—2182no—
142C42—1091no—
143C42—2181no—
144C42—2182no—
145C42C2×#8913711yescharacteristic
146C23—1091no—
147C23—1092no—
148C23—2181no—
149Q8—22no—
150Q8—22no—
151D4—4364no—
152D4—4362no—
153D4—2184no—
154D4—2182no—
155D4—2182no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—1091no—
159C2×C4—1092no—
160C2×C4—1092no—
161C2×C4—4362no—
162C2×C4—4361no—
163C2×C4—4361no—
164C2×C4—4362no—
165C2×C4—2182no—
166C2×C4—2182no—
167C2×C4—2181no—
168C2×C4C22⋊#8913712yes—
169C2×C4C22×#8913711yescharacteristic
170C8—2184no—
171C22—1092no—
172C22—4362no—
173C22—4362no—
174C22—4361no—
175C22—4361no—
176C22—2182no—
177C22C2×C22⋊#8913711yescharacteristic
178C4—22no—
179C4—22no—
180C4—41no—
181C4—8722no—
182C4—1091no—
183C4—1091no—
184C4—4361no—
185C4D4×#8913712yes—
186C2—21no—
187C2—8721no—
188C2—4362no—
189C2—2182no—
190C2#2029597411yescharacteristic
subgroupG/H
centerC2#20295974
commutatorC2×C4×C109C22×C4
FrattiniC2×C4C22×#89137
FittingC4⋊Q8×C109C4
socleC2×C109#386
prime radical#20295577C2
cosocleC2×C4×D109C23
hypercenterC4⋊Q8#89137
hypocenterC109#1884
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #20296106C2semidirect
2. #20296025C2semidirect
3. #20296007C2semidirect
4. #20295897C2semidirect
14. #16812696C4semidirect
15. #16812688C4semidirect
16. #16812688C4semidirect
20. C4⋊Q8×C109C4semidirect
22. #13182039D4semidirect
96. C109#1884semidirect
107. C4⋊Q8#89137semidirect

Maximal subgroups

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

subgroupindex
#202961062
#202960252
#202960072
#202958972
#202955772
#1884109