Finite Group Databasebeta

← #22625959

Subgroups — #22625959

Order 9344.

338 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 72 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×D73⋊M16C211yesmaximal, characteristic
2C2×#14556652C212yesmaximal, complemented
3#17989559C211yesmaximal, characteristic
4#17989467C212yesmaximal, complemented
5C2×#14556569C211yesmaximal, characteristic
6C2×#11924038—21no—
7D73⋊M16—24no—
8C2×#11924037C2212yes—
9C2×#11924037C2212yes—
10C2×#11924036—21no—
11#14556652—24no—
12#14556648—21no—
13#14556648—21no—
14C22×Dic146C2211yescharacteristic
15C22×C4×D73C2211yescharacteristic
16#14556569—21no—
17#14556569—21no—
18#14556569—21no—
19#14556569—21no—
20C2×#11924007C411yescharacteristic
21C2×#11924007C2211yescharacteristic
22C2×#11924005C411yescharacteristic
23C2×#11924005C411yescharacteristic
24C2×C4⋊C4×C73C411yescharacteristic
25#11924038—24no—
26#11924037—22no—
27#11924037—22no—
28#11924037—22no—
29#11924037D414yes—
30#11924036—24no—
31C2×#10596833—22no—
32C2×#10596833—22no—
33C23×D73C2×C411yescharacteristic
34C2×Dic146—21no—
35C2×Dic146—21no—
36C2×Dic146—22no—
37C2×Dic146—22no—
38C22×Dic73C2×C411yescharacteristic
39C22×Dic73C2×C411yescharacteristic
40C22×Dic73C2311yescharacteristic
41C2×C4×D73—22no—
42C2×C4×D73—22no—
43C2×C4×D73D411yescharacteristic
44C2×C4×D73D411yescharacteristic
45C2×C4×D73D411yescharacteristic
46C2×C4×D73D411yescharacteristic
47#11924007—21no—
48#11924007—21no—
49#11924007—21no—
50#11924007—21no—
51#11924005—21no—
52#11924005—21no—
53#11924005—21no—
54#11924005—21no—
55C22×C4×C73C2×C411yescharacteristic
56C22×C4×C73C2×C411yescharacteristic
57C22×C4×C73C2×C411yescharacteristic
58C4⋊C4×C73—21no—
59C4⋊C4×C73—21no—
60C23×C73C22×C411yescharacteristic
61C22×D73—22no—
62C22×D73—22no—
63C22×D73—41no—
64C22×D73C22⋊C411yescharacteristic
65C22×D73C22⋊C411yescharacteristic
66C2×C4×C73—22no—
67C2×C4×C73—21no—
68C2×C4×C73—21no—
69C2×C4×C73—22no—
70C2×C4×C73—41no—
71C2×C4×C73C22⋊C411yescharacteristic
72C2×C4×C73C22⋊C411yescharacteristic
73C2×Dic73—21no—
74C2×Dic73—21no—
75C2×Dic73—22no—
76C2×Dic73—41no—
77C2×Dic73C2×D412yes—
78C2×Dic73C2×D411yescharacteristic
79C2×Dic73C2×D411yescharacteristic
80C2×Dic73#4112yes—
81C4×D73—21no—
82C4×D73—21no—
83C4×D73—22no—
84C4×D73—22no—
85C4×D73—21no—
86C4×D73—21no—
87Dic146—41no—
88Dic146—42no—
89Dic146—41no—
90#10596833—24no—
91#10596833—42no—
92C22×C73—21no—
93C22×C73—21no—
94C22×C73C2×C22⋊C411yescharacteristic
95C22×C73C4×D412yes—
96C2×D73—21no—
97C2×D73—21no—
98C2×D73—21no—
99C2×D73—21no—
100C2×D73—21no—
101C2×D73—44no—
102C2×D73#10112yescomplemented
103C4×C73—21no—
104C4×C73—21no—
105C4×C73—41no—
106C4×C73—41no—
107Dic73—41no—
108Dic73—41no—
109Dic73#12011yescharacteristic
110Dic73#12112yes—
111Dic73#12311yescharacteristic
112C2×C73—22no—
113C2×C73#38611yescharacteristic
114C2×C73C2×#10111yescharacteristic
115C2×C73#41311yescharacteristic
116D73—22no—
117D73—41no—
118#1901—731nomaximal, Sylow
119C73#190111yescharacteristic, complemented, Sylow
120C22×M16—731no—
121C2×C22⋊Q8—731no—
122C2×#101—732no—
123#407—731no—
124#343—732no—
125C22×Q8—731no—
126C23×C4—731no—
127C2×M16—732no—
128C2×M16—732no—
129C2×M16—1464no—
130C2×M16—1461no—
131C22×C8—1461no—
132C22⋊Q8—1461no—
133C22⋊Q8—1461no—
134C22⋊Q8—1461no—
135C22⋊Q8—1461no—
136C2×C4⋊C4—731no—
137C2×C4⋊C4—731no—
138C2×C4⋊C4#6440811yescharacteristic
139C2×C22⋊C4—731no—
140C2×C22⋊C4—731no—
141#101—1464no—
142C22⋊C8—1461no—
143C22⋊C8—1461no—
144C24—731no—
145C2×Q8—1462no—
146C2×Q8—1461no—
147C2×Q8—1461no—
148C2×Q8—1462no—
149C22×C4—731no—
150C22×C4—731no—
151C22×C4—731no—
152C22×C4—731no—
153C22×C4—731no—
154C22×C4—731no—
155C22×C4—731no—
156C22×C4—1462no—
157C22×C4—1462no—
158C22×C4C2×#6440811yescharacteristic
159C22×C4C2×#6440811yescharacteristic
160C22×C4C2×#6440811yescharacteristic
161M16—734no—
162M16—1462no—
163M16—1462no—
164M16—1462no—
165M16—1464no—
166C2×C8—1462no—
167C2×C8—1462no—
168C2×C8—1464no—
169C4⋊C4—21no—
170C4⋊C4—21no—
171C4⋊C4—1461no—
172C4⋊C4—1461no—
173C4⋊C4—1461no—
174C4⋊C4—1461no—
175C22⋊C4—1461no—
176C22⋊C4—1461no—
177C22⋊C4—1461no—
178C22⋊C4—1461no—
179C23—2921no—
180C23—731no—
181C23—731no—
182C23—1462no—
183C23—1462no—
184C23C22×#6440811yescharacteristic
185Q8—2922no—
186Q8—2921no—
187Q8—2921no—
188C2×C4—22no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—22no—
192C2×C4—41no—
193C2×C4—2921no—
194C2×C4—731no—
195C2×C4—731no—
196C2×C4—732no—
197C2×C4—732no—
198C2×C4—1461no—
199C2×C4—1461no—
200C2×C4—1462no—
201C2×C4—1462no—
202C2×C4—1461no—
203C2×C4—1461no—
204C2×C4—1461no—
205C2×C4—1461no—
206C2×C4—1462no—
207C2×C4C22⋊#6440811yescharacteristic
208C2×C4C22⋊#6440811yescharacteristic
209C8—2922no—
210C8—1464no—
211C22—21no—
212C22—21no—
213C22—2924no—
214C22—732no—
215C22—1461no—
216C22—1461no—
217C22—1461no—
218C22—1461no—
219C22—1461no—
220C22C2×C22⋊#6440811yescharacteristic
221C22D4×#6440812yes—
222C4—21no—
223C4—21no—
224C4—41no—
225C4—41no—
226C4—2921no—
227C4—2921no—
228C4—732no—
229C4—731no—
230C4—731no—
231C2—22no—
232C2—2921no—
233C2—1462no—
234C2#1798953511yescharacteristic
235C2D73⋊#10111yescharacteristic
236C2#1798957311yescharacteristic
subgroupG/H
centerC22C2×C22⋊#64408
commutatorC23×C73C22×C4
FrattiniC23C22×#64408
FittingC2×C4⋊C4×C73C4
socleC22×C73C2×C22⋊C4
hypercenterC2×C4⋊C4#64408
hypocenterC73#1901
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#14556652C2semidirect
4. #17989467C2semidirect
102. C2×D73#101semidirect
119. C73#1901semidirect