Finite Group Databasebeta

← #22608993

Subgroups — #22608993

Order 9344.

278 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 55 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#17989257C211yesmaximal, characteristic, complemented
2#17988784C211yesmaximal, characteristic, complemented
3#17988779C211yesmaximal, characteristic, complemented
4#17988331C211yesmaximal, characteristic, complemented
5#17988319C211yesmaximal, characteristic, complemented
6#17988316C211yesmaximal, characteristic, complemented
7#493×C73C211yesmaximal, characteristic, complemented
8C2×#11924027—21no—
9C2×#11924016—21no—
10C2×#11924013—21no—
11#14556587—21no—
12#14556563—22no—
13#14556562—21no—
14C4×Dic146C2211yescharacteristic
15C4×D292C2211yescharacteristic
16D4×Dic73—21no—
17C4⋊#10596831C2211yescharacteristic
18C4⋊#10596831C2211yescharacteristic
19#14556512—21no—
20#14556512—21no—
21C2×D8×C73—22no—
22#127×C73C2211yescharacteristic
23#127×C73C2211yescharacteristic
24C4×C8×C73C2211yescharacteristic
25#11924027—42no—
26#11924027—42no—
27C2×Dic146D411yescharacteristic
28C2×D292D411yescharacteristic
29C2×C22⋊D73—22no—
30C2×C22⋊D73—22no—
31C22×Dic73—22no—
32C2×C4×D73—21no—
33#11924016—42no—
34#11924013—42no—
35C2×#10596831—21no—
36C2×#10596831—21no—
37C4⋊Dic73D411yescharacteristic
38C4⋊Dic73D411yescharacteristic
39#11924007—21no—
40C22⋊Dic73—22no—
41#11924005—21no—
42C4×Dic73—21no—
43C2×D4×C73—21no—
44C2×D4×C73—21no—
45C2×D4×C73—21no—
46C2×D4×C73—21no—
47C2×D4×C73—21no—
48C2×D4×C73D412yes—
49D8×C73—44no—
50C2×C8×C73—21no—
51C42×C73C2311yescharacteristic
52C23×C73—22no—
53C23×C73—41no—
54C22×D73—21no—
55D4×C73—42no—
56D4×C73—42no—
57D4×C73—41no—
58D4×C73—41no—
59D4×C73—41no—
60D4×C73—41no—
61D4×C73—41no—
62D4×C73—41no—
63D4×C73—41no—
64D4×C73—41no—
65C2×C4×C73C2×D411yescharacteristic
66C2×C4×C73C2×D411yescharacteristic
67C2×C4×C73C2×D411yescharacteristic
68C22⋊D73—44no—
69C22⋊D73—82no—
70C2×Dic73—21no—
71C2×Dic73—21no—
72C2×Dic73—21no—
73C2×Dic73—44no—
74D292—21no—
75D292—21no—
76C4×D73—41no—
77C4×D73—41no—
78Dic146—21no—
79Dic146D812yescomplemented
80C8×C73—22no—
81#10596831—41no—
82#10596831—41no—
83C22×C73—42no—
84C22×C73—42no—
85C22×C73—42no—
86C22×C73—81no—
87C22×C73—81no—
88C22×C73—81no—
89C22×C73#12011yescharacteristic
90C2×D73—41no—
91C2×D73—41no—
92C2×D73—41no—
93C4×C73—21no—
94C4×C73C2×D811yescharacteristic
95C4×C73#13511yescharacteristic
96C4×C73AGL(1,ℤ/8)11yescharacteristic
97C4×C73AGL(1,ℤ/8)11yescharacteristic
98Dic73—22no—
99Dic73—41no—
100Dic73—41no—
101C2×C73—82no—
102C2×C73—161no—
103C2×C73#44711yescharacteristic
104C2×C73#44911yescharacteristic
105C2×C73#45311yescharacteristic
106D73—81no—
107#1621—731nomaximal, Sylow
108C73#162111yescharacteristic, complemented, Sylow
109#550—731no—
110#493D7311yescharacteristic, complemented
111#460—731no—
112#459—731no—
113#331—731no—
114Q8⋊C8—731no—
115D4⋊C8—731no—
116C2×#41—1461no—
117C2×SD16—1461no—
118C2×D8—22no—
119C2×D8—1461no—
120#127—1461no—
121#127C2×D7311yescharacteristic
122#127C2×D7311yescharacteristic
123#121—1461no—
124#121—1462no—
125C4×Q8—731no—
126C4×D4—731no—
127C4×D4—1461no—
128C4⋊C8—731no—
129C4⋊C8—731no—
130#102—1461no—
131#102—1461no—
132C4×C8C2×D7311yescharacteristic
133#41—2922no—
134#41—2922no—
135C2×Q8—731no—
136C2×D4—21no—
137C2×D4—21no—
138C2×D4—21no—
139C2×D4—21no—
140C2×D4—21no—
141C2×D4—731no—
142C2×D4—1462no—
143C2×D4—1462no—
144C2×D4C22⋊D7312yes—
145C22×C4—1462no—
146C22×C4—1461no—
147SD16—2922no—
148D8—44no—
149D8—2922no—
150C2×C8—21no—
151C2×C8—1461no—
152C2×C8—1461no—
153C4⋊C4—731no—
154C4⋊C4—731no—
155C4⋊C4—1461no—
156C22⋊C4—1462no—
157C22⋊C4—1461no—
158C42—1461no—
159C42C22×D7311yescharacteristic
160C23—22no—
161C23—41no—
162C23—1461no—
163Q8—732no—
164Q8—1461no—
165D4—42no—
166D4—42no—
167D4—41no—
168D4—41no—
169D4—41no—
170D4—41no—
171D4—41no—
172D4—41no—
173D4—41no—
174D4—41no—
175D4—2924no—
176D4—5842no—
177D4—1461no—
178D4—1461no—
179C2×C4—2924no—
180C2×C4—2921no—
181C2×C4—2921no—
182C2×C4—1461no—
183C2×C4—1461no—
184C2×C4—1461no—
185C2×C4D4×D7311yescharacteristic
186C2×C4D4×D7311yescharacteristic
187C2×C4C2×C22⋊D7311yescharacteristic
188C8—22no—
189C8—2921no—
190C8—2921no—
191C22—42no—
192C22—42no—
193C22—42no—
194C22—81no—
195C22—81no—
196C22—81no—
197C22—2921no—
198C22—2921no—
199C22—2921no—
200C22#1455655911yescharacteristic
201C4—21no—
202C4—2921no—
203C4—2921no—
204C4—1462no—
205C4D8×D7311yescharacteristic
206C4#1455661011yescharacteristic
207C4#1455661511yescharacteristic
208C4#1455661511yescharacteristic
209C2—82no—
210C2—161no—
211C2—5841no—
212C2#1798871911yescharacteristic
213C2#1798872911yescharacteristic
214C2#1798875411yescharacteristic
subgroupG/H
centerC22#14556559
commutatorC42×C73C23
FrattiniC42C22×D73
Fitting#493×C73C2
socleC22×C73#120
hypercenter#493D73
hypocenterC73#1621
LCSG ▷ C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #493

Complements

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

NH ≅ G/Ntype
1. #17989257C2semidirect
2. #17988784C2semidirect
3. #17988779C2semidirect
4. #17988331C2semidirect
5. #17988319C2semidirect
6. #17988316C2semidirect
7. #493×C73C2semidirect
79. Dic146D8semidirect
108. C73#1621semidirect
110. #493D73semidirect