Finite Group Databasebeta

← #22614408

Subgroups — #22614408

Order 9344.

544 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 169 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×#14556567C211yesmaximal, characteristic
2C2×C4⋊C4×D73C211yesmaximal, characteristic
3#17988521C214yesmaximal, complemented
4#17988494C211yesmaximal, characteristic, complemented
5#17988461C214yesmaximal
6#17988457C211yesmaximal, characteristic, complemented
7#17988456C211yesmaximal, characteristic, complemented
8C4×#11924005C211yesmaximal, characteristic
9#391×C73C211yesmaximal, characteristic, complemented
10C22×C4×D73C2211yescharacteristic
11C22×C4×D73C2212yes—
12#14556567—24no—
13C2×C4⋊Dic73C2211yescharacteristic
14C2×C4⋊Dic73C2211yescharacteristic
15C2×C4⋊Dic73C2214yes—
16C2×#11924007C2212yes—
17C2×#11924007C2212yes—
18C2×#11924007C2214yes—
19C4⋊C4×D73—24no—
20C2×#11924005C2212yes—
21C2×#11924005C2212yes—
22C2×C4×Dic73C2211yescharacteristic
23#14556498C2212yes—
24#14556498C2214yes—
25C22×Q8×C73C2211yescharacteristic
26C2×C4⋊C4×C73C2211yescharacteristic
27C2×C42×C73C2211yescharacteristic
28#95×C73C2214yes—
29C23×D73C2311yescharacteristic
30C22×Dic73C2312yes—
31C22×Dic73C2312yes—
32C22×Dic73C2311yescharacteristic
33C22×Dic73C2312yes—
34C2×C4×D73—22no—
35C2×C4×D73—22no—
36C2×C4×D73—24no—
37C2×C4×D73—44no—
38C2×C4×D73D414yes—
39C4⋊Dic73—22no—
40C4⋊Dic73—22no—
41C4⋊Dic73—44no—
42#11924007—24no—
43#11924007—24no—
44#11924007—44no—
45#11924005—24no—
46#11924005Q818yescomplemented
47C4×Dic73—22no—
48C2×Q8×C73—22no—
49C2×Q8×C73—22no—
50C2×Q8×C73—22no—
51C22×C4×C73C2312yes—
52C22×C4×C73C2312yes—
53C22×C4×C73C2312yes—
54C22×C4×C73C2311yescharacteristic
55C4⋊C4×C73—22no—
56C42×C73—22no—
57C23×C73C2411yescharacteristic
58C22×D73—21no—
59C22×D73—21no—
60C22×D73—22no—
61C22×D73C2×D412yes—
62C22×D73C2×Q814yes—
63Q8×C73—44no—
64C2×C4×C73—22no—
65C2×C4×C73—22no—
66C2×C4×C73—22no—
67C2×C4×C73—22no—
68C2×C4×C73—22no—
69C2×C4×C73—22no—
70C2×C4×C73—24no—
71C2×C4×C73C2×D412yes—
72C2×C4×C73C2×Q814yes—
73C2×C4×C73#4112yes—
74C2×C4×C73#4112yes—
75C2×Dic73—22no—
76C2×Dic73—21no—
77C2×Dic73—21no—
78C2×Dic73—22no—
79C2×Dic73—22no—
80C2×Dic73—22no—
81C2×Dic73—24no—
82C2×Dic73—24no—
83C2×Dic73C2×D412yes—
84C2×Dic73C2×Q814yes—
85C4×D73—28no—
86C4×D73—48no—
87C22×C73C22×D411yescharacteristic
88C22×C73C22×Q812yes—
89C22×C73C2×#4111yescharacteristic
90C22×C73C2×#4111yescharacteristic
91C22×C73H(5,𝔽2)12yes—
92C2×D73—22no—
93C2×D73—22no—
94C2×D73—24no—
95C2×D73—24no—
96C2×D73C4⋊Q814yes—
97C4×C73—24no—
98C4×C73—42no—
99C4×C73—42no—
100C4×C73#12314yes—
101Dic73—22no—
102Dic73—24no—
103Dic73—42no—
104Dic73—42no—
105C2×C73C2×#12311yescharacteristic
106C2×C73C2×C4⋊Q811yescharacteristic
107C2×C73#53511yescharacteristic
108C2×C73#55412yes—
109C2×C73#55412yes—
110D73—24no—
111#2502—731nomaximal, Sylow
112C73#250211yescharacteristic, complemented, Sylow
113C2×C22⋊Q8—731no—
114C22×C4⋊C4—731no—
115#398—734no—
116#391—731no—
117#391D7311yescharacteristic, complemented
118#385—734no—
119#384—731no—
120#384—731no—
121C4×C22⋊C4—731no—
122C22×Q8C2×D7311yescharacteristic
123C23×C4—732no—
124C23×C4—731no—
125C22⋊Q8—1464no—
126C2×C4⋊C4—734no—
127C2×C4⋊C4—734no—
128C2×C4⋊C4—731no—
129C2×C4⋊C4—732no—
130C2×C4⋊C4—731no—
131C2×C4⋊C4—732no—
132C2×C4⋊C4—1464no—
133C2×C4⋊C4C2×D7311yescharacteristic
134C2×C22⋊C4—732no—
135C2×C22⋊C4—732no—
136C2×C42—731no—
137C2×C42C2×D7311yescharacteristic
138#95—732no—
139#95—734no—
140#95C2×D7314yes—
141C24—731no—
142C2×Q8—22no—
143C2×Q8—22no—
144C2×Q8—22no—
145C22×C4—2924no—
146C22×C4—732no—
147C22×C4—731no—
148C22×C4—734no—
149C22×C4—732no—
150C22×C4—732no—
151C22×C4—1464no—
152C22×C4—1462no—
153C22×C4—1462no—
154C22×C4C22×D7312yes—
155C22×C4C22×D7312yes—
156C22×C4C22×D7312yes—
157C22×C4C22×D7311yescharacteristic
158C4⋊C4—22no—
159C4⋊C4—2924no—
160C4⋊C4—2924no—
161C4⋊C4—1464no—
162C4⋊C4—1464no—
163C4⋊C4—1462no—
164C4⋊C4—1462no—
165C22⋊C4—738no—
166C22⋊C4—1464no—
167C42—22no—
168C42—1462no—
169C23—732no—
170C23—734no—
171C23—1461no—
172C23—1461no—
173C23—1462no—
174C23C23×D7311yescharacteristic
175Q8—44no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—24no—
183C2×C4—2928no—
184C2×C4—732no—
185C2×C4—734no—
186C2×C4—1462no—
187C2×C4—1462no—
188C2×C4—1464no—
189C2×C4—1464no—
190C2×C4—1461no—
191C2×C4—1462no—
192C2×C4—1461no—
193C2×C4—1462no—
194C2×C4—1468no—
195C2×C4D4×D7312yes—
196C2×C4Q8×D7314yes—
197C2×C4#1192402712yes—
198C2×C4#1192402812yes—
199C22—734no—
200C22—1462no—
201C22—1464no—
202C22—1464no—
203C22—1462no—
204C22C2×D4×D7311yescharacteristic
205C22C2×Q8×D7312yes—
206C22C2×#1192402711yescharacteristic
207C22C2×#1192402811yescharacteristic
208C22#1455663712yes—
209C4—24no—
210C4—42no—
211C4—42no—
212C4—2922no—
213C4—2922no—
214C4—1464no—
215C4—1462no—
216C4#1455657314yes—
217C2—1464no—
218C2C2×#1455657311yescharacteristic
219C2C4⋊Q8×D7311yescharacteristic
220C2#1798915511yescharacteristic
221C2#1798929512yes—
222C2#1798929712yes—
subgroupG/H
center, FrattiniC23C23×D73
commutator, socleC23×C73C24
Fitting#391×C73C2
hypercenter#391D73
hypocenterC73#2502
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
3. #17988521C2semidirect
4. #17988494C2semidirect
6. #17988457C2semidirect
7. #17988456C2semidirect
9. #391×C73C2semidirect
46. #11924005Q8semidirect
112. C73#2502semidirect
117. #391D73semidirect