Finite Group Databasebeta

← #22608923

Subgroups — #22608923

Order 9344.

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

normal subgroups only

This group has 228 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#17989212C211yesmaximal, characteristic
2#17988918C211yesmaximal, characteristic, complemented
3#17988915C211yesmaximal, characteristic, complemented
4#17988514C211yesmaximal, characteristic
5#17988323C211yesmaximal, characteristic, complemented
6#17988310C211yesmaximal, characteristic
7#328×C73C211yesmaximal, characteristic, complemented
8#14556571—21no—
9#14556570C2211yescharacteristic
10#14556569—21no—
11#14556569—21no—
12#14556568—21no—
13#14556567—21no—
14C2×C4⋊Dic73C2211yescharacteristic
15C2×#11924005—21no—
16C2×#11924005C2211yescharacteristic
17C22⋊C4×D73—21no—
18#14556523—21no—
19#14556522—21no—
20#14556516—21no—
21#14556515—21no—
22C22⋊#10596831C2211yescharacteristic
23#14556498—21no—
24C22⋊Q8×C73C2211yescharacteristic
25C22⋊C8×C73C2211yescharacteristic
26#95×C73C2211yescharacteristic
27C23×D73D411yescharacteristic
28C2×Dic146—21no—
29C2×Dic146D411yescharacteristic
30C22×Dic73—21no—
31C22×Dic73D411yescharacteristic
32C2×C4×D73—21no—
33C2×C4×D73—21no—
34C2×#10596831—21no—
35C4⋊Dic73—21no—
36C4⋊Dic73—21no—
37C4⋊Dic73—21no—
38C4⋊Dic73D411yescharacteristic
39#11924007—21no—
40#11924007—21no—
41#11924007—21no—
42C22⋊Dic73—21no—
43#11924005—21no—
44#11924005—21no—
45#11924005—21no—
46#11924005—21no—
47#11924005—42no—
48C2×Q8×C73D411yescharacteristic
49C22×C4×C73—21no—
50C22×C4×C73C2311yescharacteristic
51C2×C8×C73—21no—
52C4⋊C4×C73—21no—
53C4⋊C4×C73D411yescharacteristic
54C22⋊C4×C73—21no—
55C23×C73C2×D411yescharacteristic
56C22×D73—21no—
57C22×D73—21no—
58C22×D73—41no—
59C22×D73—41no—
60C22×D73SD1612yes—
61Q8×C73—41no—
62C2×C4×C73—21no—
63C2×C4×C73—21no—
64C2×C4×C73—41no—
65C2×C4×C73—41no—
66C2×C4×C73—41no—
67C2×C4×C73—41no—
68C2×C4×C73C2×D411yescharacteristic
69C2×C4×C73C2×D411yescharacteristic
70C2×Dic73—21no—
71C2×Dic73—21no—
72C2×Dic73—21no—
73C2×Dic73—41no—
74C2×Dic73—41no—
75C2×Dic73—41no—
76C2×Dic73—41no—
77C4×D73—81no—
78C4×D73—81no—
79Dic146—41no—
80Dic146—81no—
81C8×C73—41no—
82#10596831—41no—
83C22×C73—21no—
84C22×C73—21no—
85C22×C73#12011yescharacteristic
86C22×C73C2×SD1611yescharacteristic
87C22×C73#13711yescharacteristic
88C2×D73—22no—
89C2×D73—41no—
90C2×D73—41no—
91C2×D73—42no—
92C2×D73—81no—
93C4×C73—21no—
94C4×C73—21no—
95C4×C73—41no—
96C4×C73—41no—
97C4×C73—81no—
98Dic73—41no—
99Dic73—41no—
100Dic73—41no—
101Dic73—81no—
102C2×C73—21no—
103C2×C73—21no—
104C2×C73#44811yescharacteristic
105C2×C73#45511yescharacteristic
106C2×C73#45811yescharacteristic
107D73—42no—
108#1608—731nomaximal, Sylow
109C73#160811yescharacteristic, complemented, Sylow
110#543—731no—
111#483—731no—
112#483—731no—
113#397—731no—
114#328—731no—
115#328D7311yescharacteristic, complemented
116#323—731no—
117C22⋊Q8—731no—
118C22⋊Q8—1461no—
119C22⋊Q8—1461no—
120C22⋊Q8—1461no—
121C22⋊Q8—1461no—
122C22⋊Q8—1461no—
123C22⋊Q8C2×D7311yescharacteristic
124C2×C4⋊C4—731no—
125C2×C22⋊C4—731no—
126C2×C22⋊C4—1461no—
127C2×C22⋊C4—1461no—
128#106—1461no—
129#106—1461no—
130#103—1461no—
131#103—1461no—
132C22⋊C8—731no—
133C22⋊C8C2×D7311yescharacteristic
134#95—1461no—
135#95C2×D7311yescharacteristic
136C24—731no—
137C2×Q8—731no—
138C2×Q8—1461no—
139C2×Q8D29211yescharacteristic
140C22×C4—21no—
141C22×C4—731no—
142C22×C4—1461no—
143C22×C4—1461no—
144C22×C4—1461no—
145C22×C4C22×D7311yescharacteristic
146C2×C8—21no—
147C2×C8—1461no—
148C4⋊C4—21no—
149C4⋊C4—731no—
150C4⋊C4—1461no—
151C4⋊C4—1461no—
152C4⋊C4—1461no—
153C4⋊C4—1461no—
154C4⋊C4—1461no—
155C4⋊C4—1461no—
156C4⋊C4D29211yescharacteristic
157C22⋊C4—21no—
158C22⋊C4—2922no—
159C22⋊C4—1461no—
160C22⋊C4—1461no—
161C22⋊C4—1461no—
162C22⋊C4—1461no—
163C22⋊C4—1461no—
164C23—2921no—
165C23—2921no—
166C23—732no—
167C23—1461no—
168C23—1461no—
169C23D4×D7311yescharacteristic
170Q8—41no—
171Q8—2921no—
172Q8—5841no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—2921no—
180C2×C4—2921no—
181C2×C4—2921no—
182C2×C4—2921no—
183C2×C4—5841no—
184C2×C4—5841no—
185C2×C4—1461no—
186C2×C4—1461no—
187C2×C4—1461no—
188C2×C4D4×D7311yescharacteristic
189C2×C4C2×D29211yescharacteristic
190C8—41no—
191C8—2921no—
192C22—21no—
193C22—21no—
194C22—2922no—
195C22—2921no—
196C22—2921no—
197C22—5841no—
198C22—1462no—
199C22#1455656111yescharacteristic
200C22SD16×D7311yescharacteristic
201C22#1455662311yescharacteristic
202C4—21no—
203C4—21no—
204C4—41no—
205C4—41no—
206C4—81no—
207C4—2921no—
208C4—2921no—
209C4—2921no—
210C4—5841no—
211C2—21no—
212C2—21no—
213C2—2922no—
214C2#1798872711yescharacteristic
215C2#1798876611yescharacteristic
216C2#1798877811yescharacteristic
subgroupG/H
centerC22#14556561
commutatorC22×C4×C73C23
FrattiniC22×C4C22×D73
Fitting#328×C73C2
socleC22×C73#120
hypercenter#328D73
hypocenterC73#1608
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #17988918C2semidirect
3. #17988915C2semidirect
5. #17988323C2semidirect
7. #328×C73C2semidirect
109. C73#1608semidirect
115. #328D73semidirect