Finite Group Databasebeta

← #28362058

Subgroups — #28362058

Order 13952.

236 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 51 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#20295651C211yesmaximal, characteristic
2#20295362C211yesmaximal, characteristic, complemented
3#20295359C211yesmaximal, characteristic, complemented
4#20294963C211yesmaximal, characteristic
5#20294762C211yesmaximal, characteristic, complemented
6#20294749C211yesmaximal, characteristic
7#328×C109C211yesmaximal, characteristic, complemented
8#16812679—21no—
9#16812678C2211yescharacteristic
10#16812677—21no—
11#16812677—21no—
12#16812676—21no—
13#16812675—21no—
14C2×C4⋊Dic109—21no—
15C2×C4⋊Dic109C2211yescharacteristic
16C2×#13182006—21no—
17C2×#13182006C2211yescharacteristic
18C22⋊C4×D109—21no—
19#16812633—21no—
20#16812632—21no—
21#16812624—21no—
22#16812623—21no—
23C22⋊#11724784C2211yescharacteristic
24C22⋊Q8×C109C2211yescharacteristic
25C22⋊C8×C109C2211yescharacteristic
26#95×C109C2211yescharacteristic
27C23×D109D411yescharacteristic
28C2×Dic218—21no—
29C2×Dic218D411yescharacteristic
30C22×Dic109—21no—
31C22×Dic109D411yescharacteristic
32C2×C4×D109—21no—
33C2×C4×D109—21no—
34C2×#11724784—21no—
35C4⋊Dic109—21no—
36C4⋊Dic109—21no—
37C4⋊Dic109—21no—
38C4⋊Dic109—42no—
39C4⋊Dic109D411yescharacteristic
40#13182008—21no—
41#13182008—21no—
42#13182008—21no—
43C22⋊Dic109—21no—
44#13182006—21no—
45#13182006—21no—
46#13182006—21no—
47#13182006—21no—
48#13182006—42no—
49C2×Q8×C109D411yescharacteristic
50C22×C4×C109—21no—
51C22×C4×C109C2311yescharacteristic
52C2×C8×C109—21no—
53C4⋊C4×C109—21no—
54C4⋊C4×C109D411yescharacteristic
55C22⋊C4×C109—21no—
56C23×C109C2×D411yescharacteristic
57C22×D109—21no—
58C22×D109—21no—
59C22×D109—41no—
60C22×D109—41no—
61C22×D109Q1612yes—
62Q8×C109—41no—
63C2×C4×C109—22no—
64C2×C4×C109—21no—
65C2×C4×C109—21no—
66C2×C4×C109—41no—
67C2×C4×C109—41no—
68C2×C4×C109—41no—
69C2×C4×C109C2×D411yescharacteristic
70C2×C4×C109C2×D411yescharacteristic
71C2×Dic109—21no—
72C2×Dic109—21no—
73C2×Dic109—21no—
74C2×Dic109—41no—
75C2×Dic109—41no—
76C2×Dic109—41no—
77C2×Dic109—41no—
78C4×D109—81no—
79C4×D109—81no—
80Dic218—41no—
81Dic218—81no—
82C8×C109—41no—
83#11724784—41no—
84C22×C109—21no—
85C22×C109—21no—
86C22×C109#12011yescharacteristic
87C22×C109C2×Q1611yescharacteristic
88C22×C109#13711yescharacteristic
89C2×D109—22no—
90C2×D109—41no—
91C2×D109—41no—
92C2×D109—42no—
93C2×D109—81no—
94C4×C109—21no—
95C4×C109—21no—
96C4×C109—42no—
97C4×C109—41no—
98C4×C109—41no—
99Dic109—41no—
100Dic109—41no—
101Dic109—41no—
102Dic109—81no—
103C2×C109—21no—
104C2×C109—21no—
105C2×C109#45111yescharacteristic
106C2×C109#45311yescharacteristic
107C2×C109#45811yescharacteristic
108D109—42no—
109#1614—1091nomaximal, Sylow
110C109#161411yescharacteristic, complemented, Sylow
111#543—1091no—
112#484—1091no—
113#484—1091no—
114#399—1091no—
115#328—1091no—
116#328D10911yescharacteristic, complemented
117#323—1091no—
118C22⋊Q8—1091no—
119C22⋊Q8—2181no—
120C22⋊Q8—2181no—
121C22⋊Q8—2181no—
122C22⋊Q8—2181no—
123C22⋊Q8—2181no—
124C22⋊Q8C2×D10911yescharacteristic
125C2×C4⋊C4—1091no—
126C2×C4⋊C4—2181no—
127C2×C22⋊C4—1091no—
128C2×C22⋊C4—2181no—
129C2×C22⋊C4—2181no—
130#107—2181no—
131#107—2181no—
132#103—2181no—
133#103—2181no—
134C22⋊C8—1091no—
135C22⋊C8C2×D10911yescharacteristic
136#95C2×D10911yescharacteristic
137C24—1091no—
138C2×Q8—1091no—
139C2×Q8—2181no—
140C2×Q8D43611yescharacteristic
141C22×C4—21no—
142C22×C4—1091no—
143C22×C4—2181no—
144C22×C4—2181no—
145C22×C4—2181no—
146C22×C4C22×D10911yescharacteristic
147C2×C8—21no—
148C2×C8—2181no—
149C4⋊C4—21no—
150C4⋊C4—1091no—
151C4⋊C4—4362no—
152C4⋊C4—2181no—
153C4⋊C4—2181no—
154C4⋊C4—2181no—
155C4⋊C4—2181no—
156C4⋊C4—2181no—
157C4⋊C4—2181no—
158C4⋊C4D43611yescharacteristic
159C22⋊C4—21no—
160C22⋊C4—4362no—
161C22⋊C4—2181no—
162C22⋊C4—2181no—
163C22⋊C4—2181no—
164C22⋊C4—2181no—
165C22⋊C4—2181no—
166C23—1092no—
167C23—4361no—
168C23—4361no—
169C23—2181no—
170C23—2181no—
171C23D4×D10911yescharacteristic
172Q8—41no—
173Q8—8721no—
174Q8—4361no—
175C2×C4—22no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—8721no—
182C2×C4—8721no—
183C2×C4—4361no—
184C2×C4—4361no—
185C2×C4—4361no—
186C2×C4—4361no—
187C2×C4—2181no—
188C2×C4—2181no—
189C2×C4—2181no—
190C2×C4D4×D10911yescharacteristic
191C2×C4C2×D43611yescharacteristic
192C8—41no—
193C8—4361no—
194C22—21no—
195C22—21no—
196C22—8721no—
197C22—4362no—
198C22—4361no—
199C22—4361no—
200C22—2182no—
201C22#1681266911yescharacteristic
202C22Q16×D10911yescharacteristic
203C22#1681272811yescharacteristic
204C4—21no—
205C4—21no—
206C4—42no—
207C4—41no—
208C4—41no—
209C4—8721no—
210C4—4361no—
211C4—4361no—
212C4—4361no—
213C2—21no—
214C2—21no—
215C2—4362no—
216C2#2029518311yescharacteristic
217C2#2029519511yescharacteristic
218C2#2029521711yescharacteristic
subgroupG/H
centerC22#16812669
commutator, cosocleC22×C4×C109C23
FrattiniC22×C4C22×D109
Fitting#328×C109C2
socleC22×C109#120
prime radicalC23×D109D4
hypercenter#328D109
hypocenterC109#1614
LCSG ▷ C22×C4×C109 ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #20295362C2semidirect
3. #20295359C2semidirect
5. #20294762C2semidirect
7. #328×C109C2semidirect
110. C109#1614semidirect
116. #328D109semidirect

Maximal subgroups

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

subgroupindex
#202956512
#202953622
#202953592
#202949632
#202947622
#202947492
#328×C1092
#1614109