Finite Group Databasebeta

← #36352857

Subgroups — #36352857

Order 22144.

230 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 45 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#26012235C211yesmaximal, characteristic, complemented
2#26011881C211yesmaximal, characteristic, complemented
3#26011880C211yesmaximal, characteristic, complemented
4#26011856C211yesmaximal, characteristic, complemented
5#26011232C211yesmaximal, characteristic, complemented
6#26011230C211yesmaximal, characteristic, complemented
7#329×C173C211yesmaximal, characteristic, complemented
8C2×#14583815—21no—
9C2×#14583813—21no—
10C2×D1384—21no—
11C2×#14583811—21no—
12#19149676C2211yescharacteristic
13#19149671C2211yescharacteristic
14#19149667C2211yescharacteristic
15#19149663—21no—
16#19149661—21no—
17#19149656—21no—
18#19149655—21no—
19#19149652—21no—
20#19149651—21no—
21#19149601—21no—
22#19149601—21no—
23#19149590C2211yescharacteristic
24#124×C173C2211yescharacteristic
25#97×C173C2211yescharacteristic
26#97×C173C2211yescharacteristic
27C2×Dic346D411yescharacteristic
28C2×D692—21no—
29C2×D692—21no—
30C2×D692—21no—
31C2×D692D411yescharacteristic
32C2×C22⋊D173—21no—
33C2×C22⋊D173—21no—
34C22×Dic173—21no—
35C2×C4×D173—21no—
36#14583815—42no—
37#14583813—42no—
38D1384—42no—
39#14583811—42no—
40C2×#13063436—21no—
41C4⋊Dic173—21no—
42C4⋊Dic173D411yescharacteristic
43C4⋊Dic173D411yescharacteristic
44#14583805—21no—
45#14583805—21no—
46#14583805—21no—
47C22⋊Dic173—21no—
48#14583803—21no—
49#14583803—21no—
50#14583803—21no—
51C2×Q8×C173D411yescharacteristic
52C2×D4×C173D411yescharacteristic
53C2×C8×C173—21no—
54C2×C8×C173—21no—
55C22⋊C4×C173—21no—
56C22⋊C4×C173—21no—
57C42×C173C2311yescharacteristic
58C22×D173—21no—
59C22×D173—41no—
60Dic346—41no—
61D692—41no—
62D692—41no—
63D692—41no—
64D692—41no—
65D692—41no—
66D692—42no—
67C22⋊D173—81no—
68C22⋊D173—81no—
69C2×Dic173—21no—
70C2×Dic173—21no—
71C2×Dic173—21no—
72C2×Dic173—81no—
73C4×D173—81no—
74#13063436—22no—
75C23×C173—21no—
76Q8×C173—41no—
77D4×C173—41no—
78C2×C4×C173—21no—
79C2×C4×C173C2×D411yescharacteristic
80C2×C4×C173C2×D411yescharacteristic
81C2×C4×C173C2×D411yescharacteristic
82C8×C173—22no—
83C8×C173—41no—
84C22×C173—41no—
85C22×C173—41no—
86C22×C173—41no—
87C22×C173#12011yescharacteristic
88C2×D173—41no—
89C2×D173—41no—
90C2×D173—41no—
91C2×D173—81no—
92C2×D173—81no—
93C2×D173—81no—
94C4×C173—21no—
95C4×C173—21no—
96C4×C173—21no—
97C4×C173—41no—
98Dic173—41no—
99Dic173—41no—
100Dic173—41no—
101C2×C173—81no—
102C2×C173#45311yescharacteristic
103C2×C173#45311yescharacteristic
104C2×C173#45411yescharacteristic
105D173—81no—
106D173—161no—
107C173#165611yescharacteristic, complemented, Sylow
108#1656—1731nomaximal, Sylow
109#562—1731no—
110#496—1731no—
111#496—1731no—
112#490—1731no—
113#330—1731no—
114#329—1731no—
115#329D17311yescharacteristic, complemented
116C2×SD16—3461no—
117C2×SD16—3461no—
118C2×D8—3461no—
119C2×D8—3461no—
120#127—1731no—
121#125—1731no—
122#124—1731no—
123#124C2×D17311yescharacteristic
124#123—3461no—
125#123—3461no—
126C22⋊Q8—3461no—
127C22⋊Q8—3461no—
128#121—3461no—
129#121—3461no—
130#102—3461no—
131#102—3461no—
132#97—1731no—
133#97C2×D17311yescharacteristic
134#97C2×D17311yescharacteristic
135C2×Q8—1731no—
136C2×Q8D69211yescharacteristic
137C2×D4—3461no—
138C2×D4—3461no—
139C2×D4—3461no—
140C2×D4—3461no—
141C2×D4—3461no—
142C2×D4—1731no—
143C2×D4D69211yescharacteristic
144C22×C4—3461no—
145C22×C4—3461no—
146SD16—6922no—
147SD16—6922no—
148D8—6922no—
149D8—6922no—
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—3461no—
153C4⋊C4—3461no—
154C4⋊C4—3461no—
155C4⋊C4—3461no—
156C4⋊C4—3461no—
157C4⋊C4—1731no—
158C4⋊C4—1731no—
159C22⋊C4—21no—
160C22⋊C4—21no—
161C22⋊C4—3461no—
162C22⋊C4—3461no—
163C22⋊C4—3461no—
164C22⋊C4—3461no—
165C42C22×D17311yescharacteristic
166C23—21no—
167C23—3461no—
168C23—6921no—
169Q8—41no—
170Q8—6921no—
171D4—41no—
172D4—13841no—
173D4—13841no—
174D4—6921no—
175D4—6921no—
176D4—6921no—
177D4—6921no—
178D4—6922no—
179D4—6921no—
180C2×C4—21no—
181C2×C4—3461no—
182C2×C4—3461no—
183C2×C4—3461no—
184C2×C4—13841no—
185C2×C4—13841no—
186C2×C4D4×D17311yescharacteristic
187C2×C4D4×D17311yescharacteristic
188C2×C4C2×D69211yescharacteristic
189C8—22no—
190C8—41no—
191C8—3462no—
192C22—41no—
193C22—41no—
194C22—41no—
195C22—13841no—
196C22—13841no—
197C22—13841no—
198C22—6921no—
199C22—6921no—
200C22—6921no—
201C22#1914964911yescharacteristic
202C4—21no—
203C4—21no—
204C4—21no—
205C4—41no—
206C4—6921no—
207C4—6921no—
208C4—6921no—
209C2—81no—
210C2—13841no—
211C2—27681no—
212C2#2601166011yescharacteristic
213C2#2601166111yescharacteristic
214C2#2601166511yescharacteristic
subgroupG/H
centerC22#19149649
commutator, cosocleC42×C173C23
FrattiniC42C22×D173
Fitting#329×C173C2
socleC22×C173#120
hypercenter#329D173
hypocenterC173#1656
LCSG ▷ C42×C173 ▷ C22×C173 ▷ C173
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
1. #26012235C2semidirect
2. #26011881C2semidirect
3. #26011880C2semidirect
4. #26011856C2semidirect
5. #26011232C2semidirect
6. #26011230C2semidirect
7. #329×C173C2semidirect
107. C173#1656semidirect
115. #329D173semidirect

Maximal subgroups

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

subgroupindex
#260122352
#260118812
#260118802
#260118562
#260112322
#260112302
#329×C1732
#1656173