Finite Group Databasebeta

← #34009869

Subgroups — #34009869

Order 18688.

434 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 90 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#22625165C212yesmaximal
2#22624874C212yesmaximal, complemented
3#22624873C212yesmaximal, complemented
4#22612556C211yesmaximal, characteristic
5#17989604—22no—
6#17989432C2214yes—
7#17989431—22no—
8C2×#14556549C2211yescharacteristic
9C2×#14556548C411yescharacteristic
10C2×C4⋊C4×D73C411yescharacteristic
11#17988484—22no—
12#17988461—22no—
13#17988457C2211yescharacteristic
14#17988456C2211yescharacteristic
15#17988452C411yescharacteristic
16#382×C73C411yescharacteristic
17#14556658—42no—
18C22⋊#10596833—24no—
19C4×#10596833—42no—
20C22×C4×D73—21no—
21C22×C4×D73C2×C411yescharacteristic
22#14556549—42no—
23#14556548—22no—
24#14556548C814yescomplemented
25C2×C4⋊Dic73—22no—
26C2×C4⋊Dic73C2×C411yescharacteristic
27C2×C4⋊Dic73C2311yescharacteristic
28C2×#11924007—21no—
29C2×#11924007—21no—
30C2×#11924007—22no—
31C4⋊C4×D73—42no—
32C2×#11924005—21no—
33C2×#11924005D412yes—
34C2×C4×Dic73C2×C411yescharacteristic
35C2×C4×Dic73D412yes—
36#14556498—22no—
37C2×C4⋊C4×C73C2×C411yescharacteristic
38C2×C4⋊C4×C73C2×C411yescharacteristic
39C2×C42×C73C2×C411yescharacteristic
40#95×C73—22no—
41C2×#10596833—44no—
42C23×D73C22⋊C411yescharacteristic
43C22×Dic73—21no—
44C22×Dic73—21no—
45C22×Dic73C22⋊C411yescharacteristic
46C22×Dic73C2×D412yes—
47C2×C4×D73—22no—
48C2×C4×D73—22no—
49C2×C4×D73—42no—
50C2×C4×D73—82no—
51C2×C4×D73C2×C812yes—
52C2×C4×D73M1612yes—
53C4⋊Dic73—41no—
54C4⋊Dic73—41no—
55C4⋊Dic73—82no—
56#11924007—24no—
57#11924007—42no—
58#11924007—82no—
59#11924005—24no—
60#11924005—42no—
61C4×Dic73—21no—
62C4×Dic73—22no—
63C4×Dic73—22no—
64C4×Dic73C2×C812yes—
65C22×C4×C73—21no—
66C22×C4×C73—21no—
67C22×C4×C73C22⋊C412yes—
68C22×C4×C73C22×C411yescharacteristic
69C4⋊C4×C73—41no—
70C4⋊C4×C73—41no—
71C42×C73—21no—
72C42×C73C2×C812yes—
73C23×C73C2×C22⋊C411yescharacteristic
74C22×D73—21no—
75C22×D73—21no—
76C22×D73—41no—
77C22×D73—41no—
78C22×D73C22⋊C812yes—
79C2×C4×C73—21no—
80C2×C4×C73—21no—
81C2×C4×C73—22no—
82C2×C4×C73—22no—
83C2×C4×C73—41no—
84C2×C4×C73—41no—
85C2×C4×C73—42no—
86C2×C4×C73—42no—
87C2×C4×C73—41no—
88C2×C4×C73C22×C811yescharacteristic
89C2×C4×C73C2×M1611yescharacteristic
90C2×Dic73—22no—
91C2×Dic73—22no—
92C2×Dic73—41no—
93C2×Dic73—41no—
94C2×Dic73—42no—
95C2×Dic73—42no—
96C2×Dic73—41no—
97C2×Dic73C22⋊C812yes—
98C2×Dic73#9912yes—
99C2×Dic73#10112yes—
100C4×D73—24no—
101C4×D73—24no—
102C4×D73—84no—
103#10596833—84no—
104C22×C73—21no—
105C22×C73—21no—
106C22×C73C2×C22⋊C811yescharacteristic
107C22×C73C2×#9911yescharacteristic
108C22×C73C2×#10111yescharacteristic
109C2×D73—22no—
110C2×D73—42no—
111C2×D73—41no—
112C2×D73—41no—
113C2×D73—42no—
114C4×C73—21no—
115C4×C73—21no—
116C4×C73—42no—
117C4×C73—42no—
118C4×C73—81no—
119Dic73—42no—
120Dic73—42no—
121Dic73—81no—
122Dic73#32414yes—
123#11450—731nomaximal, Sylow
124C2×C73—21no—
125C2×C73—21no—
126C2×C73C2×#32411yescharacteristic
127C2×C73#212811yescharacteristic
128C2×C73#213511yescharacteristic
129D73—42no—
130#2317—731no—
131#1458—732no—
132#1325—732no—
133#1325—732no—
134C73#1145011yescharacteristic, complemented, Sylow
135C2×#117—731no—
136C2×#117—731no—
137C22×C4⋊C4—731no—
138#431—1462no—
139#389—1462no—
140#385—1462no—
141#384—731no—
142#384—731no—
143#382—731no—
144#382#6440811yescharacteristic
145#324—734no—
146#323—1462no—
147C23×C4—731no—
148C23×C4—1461no—
149#117—2922no—
150#117—734no—
151#117—1462no—
152C2×C4⋊C4—2922no—
153C2×C4⋊C4—731no—
154C2×C4⋊C4—731no—
155C2×C4⋊C4—1461no—
156C2×C4⋊C4—1462no—
157C2×C4⋊C4—1462no—
158C2×C4⋊C4—1461no—
159C2×C4⋊C4C2×#6440811yescharacteristic
160C2×C4⋊C4C2×#6440811yescharacteristic
161C2×C22⋊C4—732no—
162C2×C22⋊C4—1461no—
163C2×C42—731no—
164C2×C42—732no—
165C2×C42C2×#6440811yescharacteristic
166C4⋊C8—2922no—
167C22⋊C8—1464no—
168C4×C8—2922no—
169#95—22no—
170#95—1462no—
171C24—731no—
172C22×C4—21no—
173C22×C4—21no—
174C22×C4—2922no—
175C22×C4—5842no—
176C22×C4—732no—
177C22×C4—731no—
178C22×C4—732no—
179C22×C4—732no—
180C22×C4—1462no—
181C22×C4—1462no—
182C22×C4—1461no—
183C22×C4—1461no—
184C22×C4C22⋊#6440812yes—
185C22×C4C22×#6440811yescharacteristic
186C2×C8—2924no—
187C4⋊C4—41no—
188C4⋊C4—41no—
189C4⋊C4—2921no—
190C4⋊C4—2921no—
191C4⋊C4—2922no—
192C4⋊C4—5842no—
193C4⋊C4—5842no—
194C4⋊C4—1464no—
195C22⋊C4—2922no—
196C22⋊C4—1464no—
197C42—21no—
198C42—732no—
199C42—1462no—
200C42—1462no—
201C42—1461no—
202C42#1192403612yes—
203C23—2921no—
204C23—2921no—
205C23—732no—
206C23—1461no—
207C23—1461no—
208C23C2×C22⋊#6440811yescharacteristic
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—41no—
214C2×C4—41no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—41no—
218C2×C4—2921no—
219C2×C4—2921no—
220C2×C4—2922no—
221C2×C4—2922no—
222C2×C4—2921no—
223C2×C4—5844no—
224C2×C4—732no—
225C2×C4—732no—
226C2×C4—732no—
227C2×C4—1464no—
228C2×C4—1464no—
229C2×C4—1462no—
230C2×C4—1462no—
231C2×C4C2×#1192403611yescharacteristic
232C2×C4D73⋊M1611yescharacteristic
233C8—5844no—
234C22—21no—
235C22—21no—
236C22—2922no—
237C22—2922no—
238C22—2921no—
239C22—2921no—
240C22—1462no—
241C22#1798955511yescharacteristic
242C22D73⋊#9911yescharacteristic
243C22D73⋊#10111yescharacteristic
244C4—21no—
245C4—21no—
246C4—42no—
247C4—42no—
248C4—81no—
249C4—2922no—
250C4—2922no—
251C4—5841no—
252C4—734no—
253C2—21no—
254C2—21no—
255C2—2922no—
256C2#2262516011yescharacteristic
257C2#2262621111yescharacteristic
258C2#2262623411yescharacteristic
subgroupG/H
centerC22D73⋊#99
commutatorC2×C4×C73C22×C8
FrattiniC22×C4C22×#64408
Fitting#382×C73C4
socleC22×C73C2×#99
prime radicalC23×D73C22⋊C4
cosocleC2×C4⋊Dic73C23
hypercenter#382#64408
hypocenterC73#11450
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #382

Complements

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

NH ≅ G/Ntype
2. #22624874C2semidirect
3. #22624873C2semidirect
24. #14556548C8semidirect
134. C73#11450semidirect

Maximal subgroups

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

subgroupindex
#226251652
#226248742
#226248732
#226125562
#1145073