Finite Group Databasebeta

← #28375639

Subgroups — #28375639

Order 13952.

360 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 113 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#20295726C212yesmaximal, complemented
2#20295428C211yesmaximal, characteristic, complemented
3#20295348C212yesmaximal, complemented
4#20295338C212yesmaximal, complemented
5#20295326C212yesmaximal, complemented
6#20295276C212yesmaximal, complemented
7#20295105C211yesmaximal, characteristic, complemented
8#20295067C212yesmaximal, complemented
9C4×D8×C109C211yesmaximal, characteristic, complemented
10C2×#13182012C2212yes—
11#16812692—22no—
12#16812691C2212yes—
13#16812682—22no—
14#16812672—22no—
15#16812670C2212yes—
16#16812670C2212yes—
17C4×D436C2211yescharacteristic
18C4×C22⋊D109—22no—
19#16812657C2212yes—
20C4⋊C4×D109C2212yes—
21#16812633C2211yescharacteristic
22#16812633C2211yescharacteristic
23#16812632C2212yes—
24#16812631C2212yes—
25#16812630C2212yes—
26C4⋊#11724784C2211yescharacteristic
27#16812620C2212yes—
28#16812620C2212yes—
29#16812611C2212yes—
30C2×D8×C109C2211yescharacteristic
31C4×D4×C109C2212yes—
32#107×C109C2211yescharacteristic
33#102×C109C2212yes—
34C4×C8×C109C2211yescharacteristic
35C2×D436D411yescharacteristic
36C2×C22⋊D109—22no—
37C2×C22⋊D109—22no—
38C2×C4×D109—22no—
39C2×C4×D109C2312yes—
40#13182012—24no—
41C2×#11724784C2312yes—
42C4⋊Dic109D411yescharacteristic
43C4⋊Dic109C2312yes—
44C4⋊Dic109C2312yes—
45#13182008—22no—
46#13182008—22no—
47#13182008—22no—
48C22⋊Dic109—22no—
49C22⋊Dic109—22no—
50#13182006—22no—
51#13182006D412yes—
52C4×Dic109—22no—
53C2×D4×C109C2312yes—
54C22×C4×C109—22no—
55D8×C109—22no—
56C2×C8×C109C2311yescharacteristic
57C2×C8×C109C2311yescharacteristic
58C4⋊C4×C109C2312yes—
59C22⋊C4×C109—22no—
60C42×C109C2311yescharacteristic
61C23×C109—22no—
62C22×D109C2×D412yes—
63D4×C109—22no—
64D4×C109—22no—
65C2×C4×C109—22no—
66C2×C4×C109—82no—
67C2×C4×C109C2×D411yescharacteristic
68C2×C4×C109C2×D411yescharacteristic
69C2×C4×C109C2411yescharacteristic
70C22⋊D109—44no—
71C22⋊D109—82no—
72C2×Dic109—22no—
73C2×Dic109—22no—
74C2×Dic109C2×D412yes—
75D436—41no—
76C4×D109—22no—
77C4×D109—22no—
78C4×D109—82no—
79C8×C109—21no—
80C8×C109#4112yes—
81#11724784—22no—
82C22×C109—42no—
83C22×C109—42no—
84C22×C109—42no—
85C22×C109C22×D411yescharacteristic
86C2×D109—22no—
87C2×D109—22no—
88C2×D109—22no—
89C4×C109—21no—
90C4×C109—21no—
91C4×C109—42no—
92C4×C109C2×#4111yescharacteristic
93C4×C1092−1+411yescharacteristic
94Dic109—22no—
95Dic109—42no—
96Dic109—42no—
97C2×C109—82no—
98C2×C109#54711yescharacteristic
99C2×C109#57511yescharacteristic
100C2×C109#57611yescharacteristic
101D109—42no—
102#3355—1091nomaximal, Sylow
103C109#335511yescharacteristic, complemented, Sylow
104#553—1092no—
105#499—1091no—
106#482—1092no—
107#480—1092no—
108#478—1092no—
109#469—1092no—
110C4×D8D10911yescharacteristic, complemented
111#436—1091no—
112#428—1092no—
113C2×D8C2×D10911yescharacteristic
114C2×M16—1092no—
115#126—2182no—
116#125—1092no—
117#123—2182no—
118#121—1092no—
119#121—1092no—
120#121—2182no—
121C4×D4—1091no—
122C4×D4—2182no—
123C4×D4C2×D10912yes—
124#117—1092no—
125C2×C4⋊C4—1092no—
126#107—1091no—
127#107—1091no—
128#107—1092no—
129#107C2×D10911yescharacteristic
130#106—1092no—
131#106—1092no—
132C4⋊C8—1091no—
133#102—1092no—
134#102—1092no—
135#102C2×D10912yes—
136C22⋊C8—1092no—
137C4×C8C2×D10911yescharacteristic
138C2×D4—1091no—
139C2×D4—2182no—
140C2×D4—2182no—
141C2×D4C22×D10912yes—
142C22×C4—22no—
143C22×C4—1092no—
144C22×C4—2182no—
145D8—22no—
146M16—2184no—
147C2×C8—1092no—
148C2×C8C22×D10911yescharacteristic
149C2×C8C22×D10911yescharacteristic
150C4⋊C4—1091no—
151C4⋊C4—1092no—
152C4⋊C4—1092no—
153C4⋊C4—2182no—
154C4⋊C4—2182no—
155C4⋊C4—2182no—
156C4⋊C4C22×D10912yes—
157C22⋊C4—22no—
158C22⋊C4—1092no—
159C22⋊C4—2182no—
160C22⋊C4—2182no—
161C22⋊C4—2182no—
162C42—2182no—
163C42C22×D10911yescharacteristic
164C23—22no—
165C23—1092no—
166D4—22no—
167D4—22no—
168D4—8722no—
169D4—4361no—
170D4—4364no—
171C2×C4—22no—
172C2×C4—82no—
173C2×C4—8722no—
174C2×C4—1092no—
175C2×C4—2182no—
176C2×C4—2182no—
177C2×C4—2182no—
178C2×C4—2182no—
179C2×C4D4×D10911yescharacteristic
180C2×C4D4×D10911yescharacteristic
181C2×C4C23×D10911yescharacteristic
182C8—21no—
183C8—2182no—
184C8#1318202912yes—
185C22—42no—
186C22—42no—
187C22—42no—
188C22—2182no—
189C22—2182no—
190C22—2182no—
191C22C2×D4×D10911yescharacteristic
192C4—21no—
193C4—21no—
194C4—42no—
195C4—4362no—
196C4—4362no—
197C4—2182no—
198C4C2×#1318202911yescharacteristic
199C4#1681274611yescharacteristic
200C2—82no—
201C2—4362no—
202C2#2029568111yescharacteristic
203C2#2029582311yescharacteristic
204C2#2029582711yescharacteristic
subgroupG/H
centerC22C2×D4×D109
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
FittingC4×D8×C109C2
socleC22×C109C22×D4
hypercenterC4×D8D109
hypocenterC109#3355
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #20295726C2semidirect
2. #20295428C2semidirect
3. #20295348C2semidirect
4. #20295338C2semidirect
5. #20295326C2semidirect
6. #20295276C2semidirect
7. #20295105C2semidirect
8. #20295067C2semidirect
9. C4×D8×C109C2semidirect
103. C109#3355semidirect
110. C4×D8D109semidirect

Maximal subgroups

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

subgroupindex
#202957262
#202954282
#202953482
#202953382
#202953262
#202952762
#202951052
#202950672
C4×D8×C1092
#3355109