Finite Group Databasebeta

← #34001461

Subgroups — #34001461

Order 18688.

440 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 106 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#22625859C212yesmaximal
2#22624752C212yesmaximal
3#22624751C212yesmaximal
4C4×#14556589C211yesmaximal, characteristic
5#17989453—22no—
6#17989453—22no—
7#17989453C2214yes—
8C2×#14556589C411yescharacteristic
9C2×C4×Dic146C411yescharacteristic
10#17988494C2211yescharacteristic
11#17988492C2211yescharacteristic
12#17988482—22no—
13#17988456C411yescharacteristic
14C4×#11924007—22no—
15C42×Dic73C2211yescharacteristic
16C2×C4×Q8×C73C411yescharacteristic
17C22×#10596833—24no—
18C22×Dic146C2×C411yescharacteristic
19#14556589—22no—
20#14556589C814yescomplemented
21C4×Dic146—42no—
22C2×C4⋊Dic73C2×C411yescharacteristic
23C2×#11924007—22no—
24C2×#11924007—22no—
25C2×#11924007—21no—
26C2×C4×Dic73—21no—
27C2×C4×Dic73C2×C411yescharacteristic
28C2×C4×Dic73D412yes—
29C2×C4×Dic73D412yes—
30C2×C4×Dic73C2311yescharacteristic
31#14556498—22no—
32#14556498—22no—
33C22×Q8×C73C2×C411yescharacteristic
34C4×Q8×C73—42no—
35C2×C4⋊C4×C73—21no—
36C2×C4⋊C4×C73C2×C411yescharacteristic
37C2×C42×C73—21no—
38C2×C42×C73C2×C411yescharacteristic
39C2×#10596833—44no—
40C2×#10596833—44no—
41C2×#10596833—44no—
42C2×Dic146—21no—
43C2×Dic146—41no—
44C2×Dic146—41no—
45C2×Dic146C2×C812yes—
46C22×Dic73—21no—
47C22×Dic73—21no—
48C22×Dic73C22⋊C412yes—
49C22×Dic73C2×D412yes—
50C4⋊Dic73—41no—
51#11924007—28no—
52#11924007—44no—
53#11924007—42no—
54C4×Dic73—24no—
55C4×Dic73—42no—
56C4×Dic73—41no—
57C4×Dic73—42no—
58C4×Dic73C2×C812yes—
59C4×Dic73M1612yes—
60C2×Q8×C73—21no—
61C2×Q8×C73—41no—
62C2×Q8×C73—41no—
63C2×Q8×C73C2×C812yes—
64C22×C4×C73—21no—
65C22×C4×C73—21no—
66C22×C4×C73C22⋊C411yescharacteristic
67C22×C4×C73C22⋊C411yescharacteristic
68C22×C4×C73C22×C411yescharacteristic
69C4⋊C4×C73—41no—
70C4⋊C4×C73—42no—
71C42×C73—22no—
72C42×C73—42no—
73C23×C73C2×C22⋊C411yescharacteristic
74Q8×C73—42no—
75Q8×C73—42no—
76C2×C4×C73—21no—
77C2×C4×C73—21no—
78C2×C4×C73—22no—
79C2×C4×C73—22no—
80C2×C4×C73—21no—
81C2×C4×C73—22no—
82C2×C4×C73—41no—
83C2×C4×C73—41no—
84C2×C4×C73—41no—
85C2×C4×C73—42no—
86C2×C4×C73#10012yes—
87C2×C4×C73C22×C811yescharacteristic
88C2×C4×C73C2×M1611yescharacteristic
89C2×Dic73—22no—
90C2×Dic73—22no—
91C2×Dic73—22no—
92C2×Dic73—22no—
93C2×Dic73—22no—
94C2×Dic73—41no—
95C2×Dic73—41no—
96C2×Dic73—41no—
97C2×Dic73—42no—
98C2×Dic73C22⋊C814yes—
99C2×Dic73#13714yes—
100Dic146—42no—
101Dic146—42no—
102#10596833—84no—
103C22×C73C2×C22⋊C811yescharacteristic
104C22×C73#41011yescharacteristic
105C22×C73C2×#10011yescharacteristic
106C22×C73#41912yes—
107C22×C73#42112yes—
108C4×C73—22no—
109C4×C73—21no—
110C4×C73—21no—
111C4×C73—41no—
112C4×C73—42no—
113C4×C73—81no—
114Dic73—24no—
115Dic73—24no—
116Dic73—42no—
117Dic73—81no—
118#7605—731nomaximal, Sylow
119C2×C73#146011yescharacteristic
120C2×C73#147912yes—
121C2×C73#151512yes—
122C2×C73#153611yescharacteristic
123C2×C73#155811yescharacteristic
124C4×C4⋊Q8—731no—
125#1839—732no—
126#1272—732no—
127#1272—732no—
128C73#760511yescharacteristic, complemented, Sylow
129C2×C4⋊Q8—731no—
130C2×C4×Q8—731no—
131C2×C4×Q8#6440811yescharacteristic
132#391—731no—
133#391—731no—
134#389—1462no—
135#384—731no—
136C4×C4⋊C4—1462no—
137C43—731no—
138#336—734no—
139#336—1462no—
140#336—1462no—
141C22×Q8—731no—
142C22×Q8C2×#6440811yescharacteristic
143C22×C8—1464no—
144C4⋊Q8—734no—
145C4⋊Q8—1462no—
146C4×Q8—42no—
147C4×Q8—2922no—
148C2×C4⋊C4—21no—
149C2×C4⋊C4—731no—
150C2×C4⋊C4—1462no—
151C2×C4⋊C4—1461no—
152C2×C4⋊C4—1462no—
153C2×C4⋊C4C2×#6440811yescharacteristic
154C2×C42—21no—
155C2×C42—732no—
156C2×C42—731no—
157C2×C42—731no—
158C2×C42—732no—
159C2×C42—1461no—
160C2×C42C2×#6440811yescharacteristic
161#95—1462no—
162#95—1462no—
163C2×Q8—21no—
164C2×Q8—41no—
165C2×Q8—41no—
166C2×Q8—2921no—
167C2×Q8—2921no—
168C2×Q8—732no—
169C2×Q8—1461no—
170C2×Q8#1192403612yes—
171C22×C4—21no—
172C22×C4—21no—
173C22×C4—732no—
174C22×C4—732no—
175C22×C4—1461no—
176C22×C4—1461no—
177C22×C4C22⋊#6440811yescharacteristic
178C22×C4C22⋊#6440811yescharacteristic
179C22×C4C22×#6440811yescharacteristic
180C2×C8—2924no—
181C2×C8—2924no—
182C2×C8—2924no—
183C4⋊C4—41no—
184C4⋊C4—42no—
185C4⋊C4—2921no—
186C4⋊C4—2922no—
187C4⋊C4—2924no—
188C4⋊C4—1468no—
189C42—22no—
190C42—42no—
191C42—2921no—
192C42—2922no—
193C42—2922no—
194C42—732no—
195C42—732no—
196C42—1464no—
197C23C2×C22⋊#6440811yescharacteristic
198Q8—42no—
199Q8—42no—
200Q8—2922no—
201Q8—2922no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—42no—
212C2×C4—2921no—
213C2×C4—2921no—
214C2×C4—2921no—
215C2×C4—2922no—
216C2×C4—734no—
217C2×C4—734no—
218C2×C4—1462no—
219C2×C4—1462no—
220C2×C4—1462no—
221C2×C4—1462no—
222C2×C4—1462no—
223C2×C4#1455665112yes—
224C2×C4C2×#1192403611yescharacteristic
225C2×C4D73⋊M1611yescharacteristic
226C8—5844no—
227C22#1798955511yescharacteristic
228C22#1798956611yescharacteristic
229C22C2×#1455665111yescharacteristic
230C22#1798958012yes—
231C22#1798958412yes—
232C4—21no—
233C4—21no—
234C4—22no—
235C4—41no—
236C4—42no—
237C4—81no—
238C4—2922no—
239C4—5841no—
240C4—1464no—
241C4—1464no—
242C2#2262517011yescharacteristic
243C2#2262523412yes—
244C2#2262535312yes—
245C2#2262541911yescharacteristic
246C2#2262546411yescharacteristic
subgroupG/H
centerC23C2×C22⋊#64408
commutatorC2×C4×C73C22×C8
FrattiniC22×C4C22×#64408
FittingC2×C4×Q8×C73C4
socle, prime radicalC23×C73C2×C22⋊C4
cosocleC2×C4×Dic73C23
hypercenterC2×C4×Q8#64408
hypocenterC73#7605
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
20. #14556589C8semidirect
128. C73#7605semidirect

Maximal subgroups

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

subgroupindex
#226258592
#226247522
#226247512
C4×#145565892
#760573