Finite Group Databasebeta

← #34005247

Subgroups — #34005247

Order 18688.

526 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 100 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#22625657C212yesmaximal
2#22624807C212yesmaximal, complemented
3#22624807C212yesmaximal, complemented
4#22612334C211yesmaximal, characteristic
5C2×C22⋊#10596833—22no—
6C2×#14556646C2214yes—
7#17989453—22no—
8C2×#14556550C411yescharacteristic
9C22×C4×Dic73C2211yescharacteristic
10#17988456C411yescharacteristic
11#17988456C411yescharacteristic
12#17988452C2211yescharacteristic
13#17988452C2211yescharacteristic
14#17988445—22no—
15C4×#11924007—22no—
16C2×#117×C73C411yescharacteristic
17C22×#10596833—24no—
18C22⋊#10596833—28no—
19#14556646—28no—
20C23×Dic73D412yes—
21#14556550—42no—
22C2×C4⋊Dic73C2×C411yescharacteristic
23C2×C4⋊Dic73C2×C411yescharacteristic
24C2×#11924007—22no—
25C2×#11924007—22no—
26C2×C22⋊Dic73—21no—
27C2×C4×Dic73—24no—
28C2×C4×Dic73—21no—
29C2×C4×Dic73C2×C411yescharacteristic
30C2×C4×Dic73D412yes—
31C2×C4×Dic73C2311yescharacteristic
32#14556498—22no—
33#14556498—22no—
34C23×C4×C73C2×C411yescharacteristic
35#117×C73—42no—
36C2×C4⋊C4×C73C2×C411yescharacteristic
37C2×C4⋊C4×C73C2×C411yescharacteristic
38C2×C22⋊C4×C73—21no—
39C2×C42×C73—21no—
40C2×#10596833—28no—
41C2×#10596833—44no—
42C2×#10596833—44no—
43C22×Dic73—24no—
44C22×Dic73—24no—
45C22×Dic73—21no—
46C22×Dic73—21no—
47C22×Dic73—42no—
48C22×Dic73C22⋊C412yes—
49C22×Dic73C2×D412yes—
50C4⋊Dic73—41no—
51C4⋊Dic73—41no—
52#11924007—44no—
53#11924007—44no—
54C22⋊Dic73—42no—
55C4×Dic73—22no—
56C4×Dic73—24no—
57C4×Dic73—42no—
58C4×Dic73#4114yes—
59C24×C73C22⋊C411yescharacteristic
60C22×C4×C73—22no—
61C22×C4×C73—22no—
62C22×C4×C73—22no—
63C22×C4×C73—21no—
64C22×C4×C73—21no—
65C22×C4×C73C22⋊C411yescharacteristic
66C22×C4×C73C22×C411yescharacteristic
67C4⋊C4×C73—41no—
68C4⋊C4×C73—41no—
69C22⋊C4×C73—42no—
70C42×C73—42no—
71C23×C73—21no—
72C23×C73—21no—
73C23×C73—22no—
74C23×C73—22no—
75C23×C73#10112yes—
76C23×C73C2×C22⋊C411yescharacteristic
77C2×C4×C73—28no—
78C2×C4×C73—21no—
79C2×C4×C73—21no—
80C2×C4×C73—21no—
81C2×C4×C73—21no—
82C2×C4×C73—41no—
83C2×C4×C73—41no—
84C2×C4×C73—42no—
85C2×C4×C73—42no—
86C2×C4×C73#10012yes—
87C2×C4×C73#11712yes—
88C2×Dic73—22no—
89C2×Dic73—22no—
90C2×Dic73—22no—
91C2×Dic73—22no—
92C2×Dic73—48no—
93C2×Dic73—41no—
94C2×Dic73—41no—
95C2×Dic73—42no—
96C2×Dic73—42no—
97C2×Dic73#10414yes—
98C2×Dic73#12314yes—
99#10596833—48no—
100C22×C73—22no—
101C22×C73—24no—
102C22×C73—41no—
103C22×C73—42no—
104C22×C73—41no—
105C22×C73#38111yescharacteristic
106C22×C73C2×#10011yescharacteristic
107C22×C73C2×#10111yescharacteristic
108C22×C73C2×#10412yes—
109C22×C73#42112yes—
110C4×C73—22no—
111C4×C73—22no—
112C4×C73—81no—
113C4×C73—81no—
114Dic73—24no—
115Dic73—24no—
116Dic73—81no—
117Dic73—81no—
118#8721—731nomaximal, Sylow
119C2×C73—42no—
120C2×C73#152511yescharacteristic
121C2×C73#153112yes—
122C2×C73#153611yescharacteristic
123C2×C73#182111yescharacteristic
124C2×C73#182612yes—
125#2285—731no—
126#1749—732no—
127#1295—732no—
128#1295—732no—
129C73#872111yescharacteristic, complemented, Sylow
130C2×#117—731no—
131C2×#117#6440811yescharacteristic
132C22×C42—731no—
133C2×C22⋊C8—1462no—
134C2×#97—734no—
135#384—731no—
136#384—731no—
137#382—731no—
138#382—731no—
139#380—1462no—
140C4×C4⋊C4—1462no—
141#336—1462no—
142C23×C4—732no—
143C23×C4C2×#6440811yescharacteristic
144C22×C8—1464no—
145#117—42no—
146#117—2922no—
147C2×C4⋊C4—731no—
148C2×C4⋊C4—731no—
149C2×C4⋊C4—1462no—
150C2×C4⋊C4—1462no—
151C2×C4⋊C4C2×#6440811yescharacteristic
152C2×C4⋊C4C2×#6440811yescharacteristic
153C2×C22⋊C4—21no—
154C2×C22⋊C4—1461no—
155C2×C42—21no—
156C2×C42—731no—
157C2×C42—732no—
158C2×C42—731no—
159C2×C42—1461no—
160C2×C42—1464no—
161C22⋊C8—1468no—
162#97—1468no—
163#95—1462no—
164#95—1462no—
165C24C22⋊#6440811yescharacteristic
166C22×C4—22no—
167C22×C4—22no—
168C22×C4—22no—
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—2922no—
172C22×C4—732no—
173C22×C4—732no—
174C22×C4—1461no—
175C22×C4—1461no—
176C22×C4—1464no—
177C22×C4—1464no—
178C22×C4C22⋊#6440811yescharacteristic
179C22×C4C22×#6440811yescharacteristic
180C2×C8—2924no—
181C2×C8—2924no—
182C2×C8—1468no—
183C4⋊C4—41no—
184C4⋊C4—41no—
185C4⋊C4—2921no—
186C4⋊C4—2921no—
187C4⋊C4—2924no—
188C4⋊C4—2924no—
189C22⋊C4—42no—
190C22⋊C4—2922no—
191C42—42no—
192C42—2922no—
193C42—734no—
194C42—1464no—
195C42—1462no—
196C23—21no—
197C23—21no—
198C23—22no—
199C23—22no—
200C23#1455665212yes—
201C23C2×C22⋊#6440811yescharacteristic
202C2×C4—28no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—42no—
210C2×C4—42no—
211C2×C4—2921no—
212C2×C4—2921no—
213C2×C4—2922no—
214C2×C4—2922no—
215C2×C4—2928no—
216C2×C4—734no—
217C2×C4—734no—
218C2×C4—1462no—
219C2×C4—1462no—
220C2×C4—1462no—
221C2×C4—1462no—
222C2×C4#1455665112yes—
223C2×C4#1455667012yes—
224C8—2928no—
225C22—22no—
226C22—24no—
227C22—42no—
228C22—41no—
229C22—41no—
230C22#1798953011yescharacteristic
231C22C2×#1455665111yescharacteristic
232C22C2×#1455665211yescharacteristic
233C22D73⋊#10412yes—
234C22#1798958412yes—
235C4—22no—
236C4—22no—
237C4—81no—
238C4—81no—
239C4—5841no—
240C4—5841no—
241C4—1464no—
242C4—1464no—
243C2—42no—
244C2#2262538511yescharacteristic
245C2#2262540312yes—
246C2#2262541911yescharacteristic
247C2#2262583011yescharacteristic
248C2#2262583912yes—
subgroupG/H
centerC23C2×C22⋊#64408
commutatorC22×C4×C73C22×C4
FrattiniC22×C4C22×#64408
FittingC2×#117×C73C4
socleC23×C73C2×C22⋊C4
prime radicalC24×C73C22⋊C4
cosocleC2×C4×Dic73C23
hypercenterC2×#117#64408
hypocenterC73#8721
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #22624807C2semidirect
3. #22624807C2semidirect
129. C73#8721semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#226256572
#226248072
#226123342
#872173