Finite Group Databasebeta

← #28379077

Subgroups — #28379077

Order 13952.

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

normal subgroups only

This group has 362 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#20296093C211yesmaximal, characteristic, complemented
2#20296025C212yesmaximal, complemented
3D109⋊#100C211yesmaximal, characteristic, complemented
4#20295893C212yesmaximal, complemented
5#20295594C211yesmaximal, characteristic
6D109⋊M16C2212yes—
7D4×#89137—24no—
8#16812778C2212yes—
9C2×C22⋊#89137—22no—
10#16812764—24no—
11#16812759—22no—
12C2×#13182030C2211yescharacteristic
13C2×D4×D109C2211yescharacteristic
14#16812696C411yescharacteristic, complemented
15#16812695C411yescharacteristic, complemented
16#16812688C411yescharacteristic, complemented
17#16812672—22no—
18#16812669—22no—
19#16812656C2211yescharacteristic
20#124×C109C411yescharacteristic, complemented
21C22×#89137—24no—
22#13182039—22no—
23#13182038—22no—
24D109⋊C8—22no—
25C4⋊#89137—22no—
26C22⋊#89137—24no—
27C22⋊#89137—22no—
28C4×#89137D414yescomplemented
29C23×D109D412yes—
30#13182030—22no—
31#13182030—22no—
32C2×D436—21no—
33C2×D436—22no—
34C2×D436C2×C411yescharacteristic
35C2×D436C2×C411yescharacteristic, complemented
36C2×C22⋊D109—22no—
37C2×C22⋊D109D412yes—
38D4×D109—22no—
39D4×D109—22no—
40C2×C4×D109—21no—
41C2×C4×D109C2311yescharacteristic
42#13182008—21no—
43#13182006—22no—
44#13182006—21no—
45C4×Dic109C2×C411yescharacteristic, complemented
46C2×Q8×C109C2×C411yescharacteristic, complemented
47C2×D4×C109C2×C411yescharacteristic
48C22⋊C4×C109—22no—
49C42×C109C2×C411yescharacteristic, complemented
50C23×C109C22⋊C412yes—
51C22×D109—22no—
52C22×D109—22no—
53C22×D109—21no—
54C22×D109—82no—
55C22×D109C22⋊C412yes—
56C22×D109C2×D411yescharacteristic
57C2×#89137—24no—
58C2×#89137—84no—
59Q8×C109—22no—
60D4×C109—22no—
61C2×C4×C109—21no—
62C2×C4×C109—21no—
63C2×C4×C109C22×C411yescharacteristic
64C22⋊D109—24no—
65C22⋊D109—82no—
66C2×Dic109—21no—
67C2×Dic109C2×D411yescharacteristic
68D436—22no—
69D436—22no—
70D436—41no—
71D436—41no—
72D436—82no—
73C4×D109—42no—
74C4×D109C2×D412yes—
75C4×D109#4112yes—
76#11724786—42no—
77C22×C109—22no—
78C22×C109—42no—
79C22×C109C2×C22⋊C411yescharacteristic
80C2×D109—22no—
81C2×D109—41no—
82C2×D109—44no—
83C2×D109—42no—
84C2×D109—42no—
85C2×D109—41no—
86C2×D109—82no—
87C2×D109#12011yescharacteristic
88C2×D109#12311yescharacteristic
89#89137—44no—
90C4×C109—41no—
91C4×C109—41no—
92C4×C109C4×D412yes—
93Dic109—41no—
94Dic109#12112yes—
95C2×C109—21no—
96C2×C109—42no—
97C2×C109#38611yescharacteristic
98D109—21no—
99D109—21no—
100D109—42no—
101D109—81no—
102#1911—1091nomaximal, Sylow
103C109#191111yescharacteristic, complemented, Sylow
104#535—1091no—
105#518—1091no—
106#421—1092no—
107C2×#100—1091no—
108H(3,ℤ/4)—1092no—
109C2×#41—1091no—
110C22×D4—1091no—
111C2×M16—1092no—
112#127—1091no—
113#127—1091no—
114#124—1091no—
115#124#8913711yescharacteristic, complemented
116#121—2182no—
117#120—2182no—
118C4×D4—2184no—
119#117—1092no—
120#117—1091no—
121C2×C22⋊C4—2182no—
122#104—2184no—
123#100—2182no—
124C24—1092no—
125#41—2182no—
126#41—2182no—
127C2×Q8C2×#8913711yescharacteristic, complemented
128C2×D4—1092no—
129C2×D4—1091no—
130C2×D4—1091no—
131C2×D4—2182no—
132C2×D4—2181no—
133C2×D4—2182no—
134C2×D4—2182no—
135C2×D4—2182no—
136C2×D4C2×#8913711yescharacteristic
137C22×C4—1091no—
138C22×C4—2181no—
139C22×C4—2184no—
140M16—2182no—
141M16—2182no—
142C2×C8—2182no—
143C4⋊C4—2181no—
144C4⋊C4—2182no—
145C22⋊C4—22no—
146C22⋊C4—2181no—
147C22⋊C4—2182no—
148C22⋊C4—2182no—
149C22⋊C4—2184no—
150C42—1094no—
151C42—1091no—
152C42C2×#8913711yescharacteristic, complemented
153C23—8722no—
154C23—1091no—
155C23—1092no—
156C23—2182no—
157C23—2182no—
158C23—2181no—
159C23C22⋊#8913712yes—
160Q8—22no—
161D4—22no—
162D4—8722no—
163D4—8722no—
164D4—4361no—
165D4—4361no—
166D4—2184no—
167D4—2182no—
168D4—2182no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—8724no—
172C2×C4—1091no—
173C2×C4—1092no—
174C2×C4—1092no—
175C2×C4—4362no—
176C2×C4—2184no—
177C2×C4—2181no—
178C2×C4C22×#8913711yescharacteristic
179C8—4362no—
180C22—22no—
181C22—42no—
182C22—8722no—
183C22—1091no—
184C22—1091no—
185C22—4362no—
186C22—4362no—
187C22—4361no—
188C22—4364no—
189C22—4361no—
190C22—2182no—
191C22C2×C22⋊#8913711yescharacteristic
192C4—41no—
193C4—41no—
194C4—1092no—
195C4—4361no—
196C4—4364no—
197C4D4×#8913712yes—
198C2—21no—
199C2—42no—
200C2—8721no—
201C2—4362no—
202C2—2181no—
203C2—2181no—
204C2#2029597411yescharacteristic
subgroupG/H
centerC2#20295974
commutatorC2×C4×C109C22×C4
FrattiniC2×C4C22×#89137
Fitting#124×C109C4
socleC2×C109#386
prime radical#20295594C2
cosocleC2×C4×D109C23
hypercenter#124#89137
hypocenterC109#1911
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C2 ◁ C2×C4 ◁ #124

Complements

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

NH ≅ G/Ntype
1. #20296093C2semidirect
2. #20296025C2semidirect
3. D109⋊#100C2semidirect
4. #20295893C2semidirect
14. #16812696C4semidirect
15. #16812695C4semidirect
16. #16812688C4semidirect
20. #124×C109C4semidirect
28. C4×#89137D4semidirect
35. C2×D436C2×C4semidirect
45. C4×Dic109C2×C4semidirect
46. C2×Q8×C109C2×C4semidirect
49. C42×C109C2×C4semidirect
103. C109#1911semidirect
115. #124#89137semidirect
127. C2×Q8C2×#89137semidirect
152. C42C2×#89137semidirect

Maximal subgroups

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

subgroupindex
#202960932
#202960252
D109⋊#1002
#202958932
#202955942
#1911109