Finite Group Databasebeta

← #22610631

Subgroups — #22610631

Order 9344.

284 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 91 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
1C2×#14556512C211yesmaximal, characteristic
2C2×#14556512C211yesmaximal, characteristic
3C2×#14556502C211yesmaximal, characteristic, complemented
4#17988485C211yesmaximal, characteristic, complemented
5#17988349C211yesmaximal, characteristic, complemented
6#17988349C211yesmaximal, characteristic, complemented
7#390×C73C211yesmaximal, characteristic
8C22×#10596831C2211yescharacteristic
9C22×#10596831C2211yescharacteristic
10C2×C4⋊Dic73C2211yescharacteristic
11C2×C4⋊Dic73C2211yescharacteristic
12C2×#11924007—21no—
13#14556512—22no—
14#14556512C414yescomplemented
15#14556502—22no—
16#14556498—21no—
17C22×D4×C73C2211yescharacteristic
18C2×C4⋊C4×C73C2211yescharacteristic
19C2×C22⋊C4×C73—21no—
20C2×C22⋊C4×C73—21no—
21C2×C42×C73C2211yescharacteristic
22C22×Dic73—21no—
23C22×Dic73—21no—
24C2×#10596831—21no—
25C2×#10596831—21no—
26C2×#10596831—21no—
27C2×#10596831—21no—
28C2×#10596831C2×C412yes—
29C2×#10596831D412yes—
30C4⋊Dic73—21no—
31C4⋊Dic73—21no—
32C4⋊Dic73—21no—
33C4⋊Dic73C2×C412yes—
34#11924007—42no—
35C24×C73—21no—
36C2×D4×C73—21no—
37C2×D4×C73—21no—
38C2×D4×C73—21no—
39C2×D4×C73—21no—
40C2×D4×C73—21no—
41C2×D4×C73C2×C412yes—
42C22×C4×C73—21no—
43C22×C4×C73D411yescharacteristic
44C22×C4×C73D411yescharacteristic
45C22×C4×C73C2311yescharacteristic
46C4⋊C4×C73—21no—
47C4⋊C4×C73—21no—
48C22⋊C4×C73—42no—
49C22⋊C4×C73—42no—
50C42×C73—21no—
51C42×C73—21no—
52C23×C73—22no—
53C23×C73—41no—
54C23×C73—41no—
55C23×C73—41no—
56C23×C73—41no—
57C23×C73—41no—
58C23×C73—41no—
59C23×C73C2×D411yescharacteristic
60D4×C73—22no—
61D4×C73—22no—
62D4×C73—41no—
63D4×C73—41no—
64C2×C4×C73—21no—
65C2×C4×C73—21no—
66C2×C4×C73—21no—
67C2×C4×C73—21no—
68C2×C4×C73—21no—
69C2×C4×C73—21no—
70C2×C4×C73—41no—
71C2×C4×C73—41no—
72C2×C4×C73—41no—
73C2×C4×C73C22×C411yescharacteristic
74C2×C4×C73C2×D411yescharacteristic
75C2×C4×C73#4111yescharacteristic
76C2×C4×C73#4111yescharacteristic
77C2×C4×C73#4111yescharacteristic
78C2×C4×C73#4111yescharacteristic
79C2×Dic73—22no—
80C2×Dic73—41no—
81C2×Dic73—41no—
82C2×Dic73—41no—
83C2×Dic73—41no—
84C2×Dic73—41no—
85#10596831—22no—
86#10596831—22no—
87C22×C73—42no—
88C22×C73—42no—
89C22×C73—42no—
90C22×C73—81no—
91C22×C73—81no—
92C22×C73—81no—
93C22×C73—81no—
94C22×C73C4×D411yescharacteristic
95C22×C73#12111yescharacteristic
96C22×C73#12411yescharacteristic
97C22×C73AGL(1,ℤ/8)11yescharacteristic
98C22×C73AGL(1,ℤ/8)11yescharacteristic
99C22×C73AGL(1,ℤ/8)11yescharacteristic
100C22×C73#13711yescharacteristic
101C4×C73—41no—
102C4×C73—41no—
103C4×C73—81no—
104C4×C73#11711yescharacteristic
105C4×C73C4×D411yescharacteristic
106C4×C73#12311yescharacteristic
107C4×C73#12611yescharacteristic
108Dic73—42no—
109Dic73—81no—
110C2×C73—82no—
111C2×C73#38811yescharacteristic
112C2×C73#44011yescharacteristic
113C2×C73#44211yescharacteristic
114C2×C73#46811yescharacteristic
115C2×C73#46911yescharacteristic
116C2×C73#48911yescharacteristic
117C2×C73#49011yescharacteristic
118#1936—731nomaximal, Sylow
119C73#193611yescharacteristic, complemented, Sylow
120C2×#102—731no—
121C2×#102—731no—
122C2×#97—731no—
123#390D7311yescharacteristic
124#389—731no—
125#340—731no—
126#340—731no—
127C22×D4C2×D7311yescharacteristic
128C22×C8—731no—
129C22×C8—731no—
130C2×C4⋊C4—731no—
131C2×C4⋊C4—731no—
132C2×C4⋊C4—1461no—
133C2×C4⋊C4C2×D7311yescharacteristic
134C2×C22⋊C4—21no—
135C2×C22⋊C4—21no—
136C2×C42C2×D7311yescharacteristic
137#102—734no—
138#102—1462no—
139#97—1462no—
140#95—1461no—
141C24—21no—
142C2×D4—21no—
143C2×D4—21no—
144C2×D4—21no—
145C2×D4—21no—
146C2×D4—21no—
147C2×D4C4×D7312yes—
148C22×C4—21no—
149C22×C4—1461no—
150C22×C4—1461no—
151C22×C4C22⋊D7311yescharacteristic
152C22×C4C22⋊D7311yescharacteristic
153C22×C4C22×D7311yescharacteristic
154C2×C8—732no—
155C2×C8—732no—
156C2×C8—1461no—
157C2×C8—1461no—
158C2×C8—1461no—
159C2×C8—1461no—
160C4⋊C4—21no—
161C4⋊C4—21no—
162C4⋊C4—2922no—
163C4⋊C4—732no—
164C4⋊C4—1461no—
165C4⋊C4—1461no—
166C4⋊C4—1461no—
167C22⋊C4—42no—
168C22⋊C4—42no—
169C42—21no—
170C42—21no—
171C23—22no—
172C23—41no—
173C23—41no—
174C23—41no—
175C23—41no—
176C23—41no—
177C23—41no—
178C23C2×C22⋊D7311yescharacteristic
179D4—22no—
180D4—22no—
181D4—41no—
182D4—41no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—2921no—
193C2×C4—2921no—
194C2×C4—2921no—
195C2×C4—2921no—
196C2×C4—2921no—
197C2×C4—1462no—
198C2×C4C2×C4×D7311yescharacteristic
199C2×C4D4×D7311yescharacteristic
200C2×C4#1192402711yescharacteristic
201C2×C4#1192402711yescharacteristic
202C2×C4#1192402711yescharacteristic
203C2×C4#1192402811yescharacteristic
204C8—1462no—
205C8—1462no—
206C22—42no—
207C22—42no—
208C22—42no—
209C22—81no—
210C22—81no—
211C22—81no—
212C22—81no—
213C22C4×C22⋊D7311yescharacteristic
214C22#1455656311yescharacteristic
215C22#1455657811yescharacteristic
216C22#1455661611yescharacteristic
217C22#1455661711yescharacteristic
218C22#1455661711yescharacteristic
219C22#1455662111yescharacteristic
220C4—41no—
221C4—41no—
222C4—81no—
223C4—2922no—
224C4—5841no—
225C4#1455654711yescharacteristic
226C4#1455655111yescharacteristic
227C4#1455657311yescharacteristic
228C4#1455658411yescharacteristic
229C2—82no—
230C2#1798848111yescharacteristic
231C2#1798868711yescharacteristic
232C2#1798869711yescharacteristic
233C2#1798883111yescharacteristic
234C2#1798883811yescharacteristic
235C2#1798894611yescharacteristic
236C2#1798895111yescharacteristic
subgroupG/H
centerC23C2×C22⋊D73
commutatorC2×C4×C73C22×C4
FrattiniC22×C4C22×D73
Fitting#390×C73C2
socleC23×C73C2×D4
hypercenter#390D73
hypocenterC73#1936
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #390

Complements

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

NH ≅ G/Ntype
3. C2×#14556502C2semidirect
4. #17988485C2semidirect
5. #17988349C2semidirect
6. #17988349C2semidirect
14. #14556512C4semidirect
119. C73#1936semidirect