Finite Group Databasebeta

← #34005240

Subgroups — #34005240

Order 18688.

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

normal subgroups only

This group has 554 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#22625658C212yesmaximal
2#22624807C212yesmaximal, complemented
3#22624807C212yesmaximal, complemented
4#382×D73C211yesmaximal, characteristic
5C2×#14556648—22no—
6C2×#14556646C2214yes—
7#17989453—22no—
8C2×C4⋊C4×D73C411yescharacteristic
9C2×C4⋊C4×D73C411yescharacteristic
10C2×C42×D73C2211yescharacteristic
11#17988453C411yescharacteristic
12#17988452C2211yescharacteristic
13#17988452C2211yescharacteristic
14#17988451—22no—
15#95×D73—22no—
16#382×C73C411yescharacteristic
17C22×#10596833—24no—
18#14556648—28no—
19#14556646—28no—
20C22×C4×D73—21no—
21C22×C4×D73—21no—
22C22×C4×D73C2×C411yescharacteristic
23C22×C4×D73D412yes—
24C2×C4⋊Dic73C2×C411yescharacteristic
25C2×C4⋊Dic73C2×C411yescharacteristic
26C2×#11924007—21no—
27C2×#11924007—21no—
28C4⋊C4×D73—42no—
29C4⋊C4×D73—42no—
30C2×C4×Dic73D412yes—
31C2×C4×Dic73C2311yescharacteristic
32C42×D73—24no—
33#14556498—22no—
34#14556498—22no—
35#14556498—22no—
36C2×C4⋊C4×C73C2×C411yescharacteristic
37C2×C4⋊C4×C73C2×C411yescharacteristic
38C2×C42×C73C2×C411yescharacteristic
39#95×C73—22no—
40C2×#10596833—28no—
41C2×#10596833—44no—
42C2×#10596833—44no—
43C23×D73C22⋊C411yescharacteristic
44C22×Dic73—21no—
45C22×Dic73—21no—
46C22×Dic73C22⋊C411yescharacteristic
47C22×Dic73C2×D412yes—
48C2×C4×D73—22no—
49C2×C4×D73—22no—
50C2×C4×D73—22no—
51C2×C4×D73—24no—
52C2×C4×D73—24no—
53C2×C4×D73—42no—
54C2×C4×D73—44no—
55C2×C4×D73—42no—
56C2×C4×D73—42no—
57C2×C4×D73—44no—
58C4⋊Dic73—41no—
59C4⋊Dic73—41no—
60#11924007—42no—
61#11924007—42no—
62C4×Dic73—24no—
63C4×Dic73#4114yes—
64C22×C4×C73—21no—
65C22×C4×C73—21no—
66C22×C4×C73C22⋊C412yes—
67C22×C4×C73C22×C411yescharacteristic
68C4⋊C4×C73—41no—
69C4⋊C4×C73—41no—
70C42×C73—22no—
71C23×C73C2×C22⋊C411yescharacteristic
72C22×D73—21no—
73C22×D73—21no—
74C22×D73—22no—
75C22×D73#10012yes—
76C22×D73#10414yes—
77C2×C4×C73—21no—
78C2×C4×C73—21no—
79C2×C4×C73—22no—
80C2×C4×C73—22no—
81C2×C4×C73—22no—
82C2×C4×C73—41no—
83C2×C4×C73—41no—
84C2×C4×C73—42no—
85C2×C4×C73—42no—
86C2×C4×C73#11712yes—
87C2×Dic73—21no—
88C2×Dic73—21no—
89C2×Dic73—22no—
90C2×Dic73—22no—
91C2×Dic73—41no—
92C2×Dic73—41no—
93C2×Dic73—42no—
94C2×Dic73—42no—
95C2×Dic73#10112yes—
96C2×Dic73#12314yes—
97C4×D73—28no—
98C4×D73—48no—
99C4×D73—84no—
100C4×D73—84no—
101#10596833—48no—
102C22×C73#38111yescharacteristic
103C22×C73C2×#10011yescharacteristic
104C22×C73C2×#10111yescharacteristic
105C22×C73C2×#10412yes—
106C22×C73#42112yes—
107C2×D73—22no—
108C2×D73—24no—
109C2×D73—24no—
110C2×D73—22no—
111C2×D73#32914yes—
112C4×C73—22no—
113C4×C73—42no—
114C4×C73—81no—
115C4×C73—81no—
116Dic73—22no—
117Dic73—24no—
118Dic73—81no—
119Dic73—81no—
120#8718—731nomaximal, Sylow
121C2×C73C2×#32911yescharacteristic
122C2×C73#152812yes—
123C2×C73#153311yescharacteristic
124C2×C73#182111yescharacteristic
125C2×C73#182612yes—
126D73—24no—
127C2×#382—731no—
128#1749—732no—
129#1295—732no—
130#1295—732no—
131C73#871811yescharacteristic, complemented, Sylow
132C22×C4⋊C4—731no—
133C22×C4⋊C4—731no—
134C22×C42—731no—
135C2×C22⋊C8—1462no—
136C2×#97—734no—
137#382—731no—
138#382—731no—
139#382—731no—
140#382—1462no—
141#382#6440811yescharacteristic
142C2×#95—1462no—
143#336—1462no—
144C23×C4—732no—
145C23×C4—731no—
146C23×C4—1461no—
147C23×C4—1461no—
148C22×C8—1464no—
149C2×C4⋊C4—2922no—
150C2×C4⋊C4—2922no—
151C2×C4⋊C4—731no—
152C2×C4⋊C4—731no—
153C2×C4⋊C4—1461no—
154C2×C4⋊C4—1461no—
155C2×C4⋊C4C2×#6440811yescharacteristic
156C2×C4⋊C4C2×#6440811yescharacteristic
157C2×C42—731no—
158C2×C42—732no—
159C2×C42—1464no—
160C2×C42C2×#6440811yescharacteristic
161C22⋊C8—1468no—
162#97—1468no—
163#95—22no—
164#95—1462no—
165#95—1462no—
166#95—1462no—
167C24—731no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—2922no—
171C22×C4—2922no—
172C22×C4—2922no—
173C22×C4—2924no—
174C22×C4—2924no—
175C22×C4—731no—
176C22×C4—732no—
177C22×C4—1464no—
178C22×C4—1464no—
179C22×C4—1462no—
180C22×C4—1462no—
181C22×C4—1461no—
182C22×C4—1461no—
183C22×C4—1462no—
184C22×C4C22⋊#6440812yes—
185C22×C4C22×#6440811yescharacteristic
186C2×C8—2924no—
187C2×C8—2924no—
188C2×C8—1468no—
189C4⋊C4—41no—
190C4⋊C4—41no—
191C4⋊C4—2921no—
192C4⋊C4—2921no—
193C4⋊C4—2922no—
194C4⋊C4—2922no—
195C42—22no—
196C42—734no—
197C42—1464no—
198C23—732no—
199C23—734no—
200C23—1461no—
201C23—1461no—
202C23—1462no—
203C23C2×C22⋊#6440811yescharacteristic
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—42no—
212C2×C4—42no—
213C2×C4—2928no—
214C2×C4—2921no—
215C2×C4—2921no—
216C2×C4—2922no—
217C2×C4—2922no—
218C2×C4—5844no—
219C2×C4—5844no—
220C2×C4—734no—
221C2×C4—732no—
222C2×C4—1468no—
223C2×C4—1461no—
224C2×C4—1461no—
225C2×C4—1462no—
226C2×C4—1462no—
227C2×C4#1455667012yes—
228C8—2928no—
229C22—734no—
230C22—1462no—
231C22—1464no—
232C22—1464no—
233C22—1462no—
234C22#1798953011yescharacteristic
235C22D73⋊#10011yescharacteristic
236C22D73⋊#10111yescharacteristic
237C22D73⋊#10412yes—
238C22#1798958412yes—
239C4—22no—
240C4—42no—
241C4—81no—
242C4—81no—
243C4—5841no—
244C4—5841no—
245C4—1462no—
246C4—1464no—
247C2—1464no—
248C2D73⋊#32911yescharacteristic
249C2#2262539412yes—
250C2#2262541111yescharacteristic
251C2#2262583111yescharacteristic
252C2#2262583912yes—
subgroupG/H
centerC23C2×C22⋊#64408
commutatorC22×C4×C73C22×C4
FrattiniC22×C4C22×#64408
Fitting#382×C73C4
socleC23×C73C2×C22⋊C4
prime radicalC23×D73C22⋊C4
cosocleC2×C4×Dic73C23
hypercenter#382#64408
hypocenterC73#8718
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #382

Complements

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

NH ≅ G/Ntype
2. #22624807C2semidirect
3. #22624807C2semidirect
131. C73#8718semidirect

Maximal subgroups

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

subgroupindex
#226256582
#226248072
#382×D732
#871873