Finite Group Databasebeta

← #22625992

Subgroups — #22625992

Order 9344.

230 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 70 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#17989538C211yesmaximal, characteristic
2C4⋊C4×#64408C211yesmaximal, characteristic
3#17989461C211yesmaximal, characteristic
4#17989460C211yesmaximal, characteristic
5#17989460C211yesmaximal, characteristic
6#17989452C211yesmaximal, characteristic
7#107×D73C211yesmaximal, characteristic
8C2×#11924036C2211yescharacteristic
9C2×C4⋊#64408—21no—
10C2×C4⋊#64408C2211yescharacteristic
11C2×C4⋊#64408C2211yescharacteristic
12C2×C4×#64408—21no—
13C2×C4×#64408C2211yescharacteristic
14(C2×#64408)⋊C4—21no—
15(C2×#64408)⋊C4—21no—
16C2×C8×D73C2211yescharacteristic
17C4⋊C4×D73C2211yescharacteristic
18C4⋊C4×D73C2211yescharacteristic
19#14556525C411yescharacteristic, complemented
20#14556524C411yescharacteristic, complemented
21#14556524C411yescharacteristic, complemented
22#107×C73C411yescharacteristic, complemented
23C22×#64408—21no—
24C22×#64408—21no—
25C22×#64408D411yescharacteristic
26C22×#64408D411yescharacteristic
27#11924036—21no—
28#11924036—21no—
29C2×#10596833—21no—
30C4⋊#64408—21no—
31C4⋊#64408—21no—
32C4⋊#64408—21no—
33C4⋊#64408—42no—
34C4⋊#64408Q812yes—
35C4×#64408—21no—
36C4×#64408—21no—
37C4×#64408—42no—
38C2×C4×D73—21no—
39C2×C4×D73—21no—
40C2×C4×D73C2311yescharacteristic
41C2×#10596831C2×C411yescharacteristic
42C8×D73—21no—
43C8×D73—21no—
44C4⋊Dic73C2×C411yescharacteristic
45C4⋊Dic73C2×C411yescharacteristic
46#11924007—21no—
47#11924007—21no—
48C2×C8×C73C2×C411yescharacteristic
49C4⋊C4×C73C2×C411yescharacteristic
50C4⋊C4×C73C2×C411yescharacteristic
51C22×D73C2×D411yescharacteristic
52C2×#64408—21no—
53C2×#64408—21no—
54C2×#64408—22no—
55C2×#64408—21no—
56C2×#64408—21no—
57C2×#64408—21no—
58C2×#64408—41no—
59C2×#64408—41no—
60C2×#64408—41no—
61C2×#64408—41no—
62C2×#64408—41no—
63C2×#64408D812yes—
64C2×C4×C73—21no—
65C2×C4×C73—21no—
66C2×C4×C73C22×C411yescharacteristic
67C2×Dic73—21no—
68C2×Dic73—21no—
69C2×Dic73#4111yescharacteristic
70C4×D73—41no—
71C4×D73—41no—
72C4×D73—41no—
73C4×D73—41no—
74C4×D73C2×Q811yescharacteristic
75C4×D73#4111yescharacteristic
76C4×D73#4111yescharacteristic
77C4×D73#4111yescharacteristic
78#10596833—41no—
79C8×C73—21no—
80#10596831—21no—
81C22×C73C4×D411yescharacteristic
82C2×D73C22⋊Q811yescharacteristic
83C2×D73#12311yescharacteristic
84C2×D73C2×D811yescharacteristic
85C2×D73#13511yescharacteristic
86C2×D73#13711yescharacteristic
87C2×D73#13711yescharacteristic
88#64408—22no—
89#64408—42no—
90#64408—41no—
91#64408—81no—
92C4×C73—41no—
93C4×C73—41no—
94C4×C73#11711yescharacteristic
95C4×C73C4×Q811yescharacteristic
96Dic73—41no—
97Dic73—41no—
98Dic73#12511yescharacteristic
99Dic73#12611yescharacteristic
100C2×C73#38711yescharacteristic
101C2×C73C4×D811yescharacteristic
102C2×C73#44111yescharacteristic
103D73#47411yescharacteristic
104D73#47911yescharacteristic
105D73#48011yescharacteristic
106D73#48511yescharacteristic
107#1918—731nomaximal, Sylow
108C73#191811yescharacteristic, complemented, Sylow
109C2×#107—731no—
110#389—731no—
111C4×C4⋊C4—731no—
112#340—731no—
113#340—731no—
114#340—731no—
115#336—731no—
116C22×C8—731no—
117C22×C8—731no—
118C2×C4⋊C4—731no—
119C2×C4⋊C4—731no—
120C2×C4⋊C4—731no—
121C2×C4⋊C4—731no—
122C2×C4⋊C4—1461no—
123C2×C42—731no—
124C2×C42—1461no—
125#107—731no—
126#107—731no—
127#107—731no—
128#107#6440811yescharacteristic, complemented
129#95—1461no—
130#95—1461no—
131C22×C4—731no—
132C22×C4—731no—
133C22×C4—731no—
134C22×C4—1461no—
135C22×C4—1461no—
136C22×C4—1461no—
137C22×C4—1461no—
138C2×C8—731no—
139C2×C8—1461no—
140C2×C8—1461no—
141C2×C8—1461no—
142C2×C8—1461no—
143C2×C8—1461no—
144C2×C8C2×#6440811yescharacteristic
145C4⋊C4—2922no—
146C4⋊C4—732no—
147C4⋊C4—731no—
148C4⋊C4—731no—
149C4⋊C4—1461no—
150C4⋊C4—1461no—
151C4⋊C4—1461no—
152C4⋊C4—1461no—
153C4⋊C4—1461no—
154C4⋊C4C2×#6440811yescharacteristic
155C4⋊C4C2×#6440811yescharacteristic
156C42—2922no—
157C42—1461no—
158C42—1461no—
159C23—731no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—2921no—
163C2×C4—2921no—
164C2×C4—2921no—
165C2×C4—2921no—
166C2×C4—2921no—
167C2×C4—2921no—
168C2×C4—2921no—
169C2×C4—2921no—
170C2×C4—2921no—
171C2×C4—731no—
172C2×C4—731no—
173C2×C4—731no—
174C2×C4—731no—
175C2×C4—731no—
176C2×C4—732no—
177C2×C4—1461no—
178C2×C4—1462no—
179C2×C4—1461no—
180C2×C4—1461no—
181C2×C4—1461no—
182C2×C4—1461no—
183C2×C4—1461no—
184C2×C4—1461no—
185C2×C4C22×#6440811yescharacteristic
186C8—21no—
187C8—2921no—
188C8—1461no—
189C22—731no—
190C22—731no—
191C22—731no—
192C22—731no—
193C22—731no—
194C22—731no—
195C22D4×#6440811yescharacteristic
196C4—41no—
197C4—41no—
198C4—2922no—
199C4—2921no—
200C4—2921no—
201C4—2921no—
202C4—5841no—
203C4—731no—
204C4—731no—
205C4—1462no—
206C4#1455667011yescharacteristic
207C4Q8×#6440811yescharacteristic
208C2—731no—
209C2—731no—
210C2—731no—
211C2—731no—
212C2#1798953611yescharacteristic
213C2D8×#6440811yescharacteristic
214C2#1798962711yescharacteristic
subgroupG/H
centerC22D4×#64408
commutatorC2×C4×C73C22×C4
FrattiniC2×C4C22×#64408
Fitting#107×C73C4
socleC22×C73C4×D4
hypercenter#107#64408
hypocenterC73#1918
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
19. #14556525C4semidirect
20. #14556524C4semidirect
21. #14556524C4semidirect
22. #107×C73C4semidirect
108. C73#1918semidirect
128. #107#64408semidirect