Finite Group Databasebeta

← #34000415

Subgroups — #34000415

Order 18688.

276 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 52 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#22625832C211yesmaximal, characteristic
2#22625184C211yesmaximal, characteristic
3#22609700C211yesmaximal, characteristic
4#17989607—21no—
5#17989559—21no—
6#17989467—21no—
7#17989467C412yes—
8#17989433—21no—
9#17989431C412yes—
10C2×#14556548C2211yescharacteristic
11C2×#14556503—21no—
12C2×C4×#10596831C411yescharacteristic
13#17988341—21no—
14C2×#97×C73C411yescharacteristic
15C2×#11924037—22no—
16#14556658—41no—
17#14556648—41no—
18#14556648—41no—
19C22⋊#10596833—22no—
20#14556646—41no—
21C22×C4×D73D411yescharacteristic
22C22×#10596831—21no—
23#14556548—41no—
24#14556548—41no—
25C2×#11924007C2×C411yescharacteristic
26C2×#11924007D411yescharacteristic
27C2×#11924005C2×C411yescharacteristic
28C2×#11924005Q811yescharacteristic
29C2×C4×Dic73D411yescharacteristic
30#14556503—24no—
31C4×#10596831—41no—
32C22×C8×C73—21no—
33C2×C42×C73C2×C411yescharacteristic
34#97×C73—41no—
35#11924037—42no—
36#11924037—42no—
37C2×#10596833—42no—
38C2×#10596833—42no—
39C23×D73C4⋊C411yescharacteristic
40C22×Dic73C22⋊C411yescharacteristic
41C22×Dic73C22⋊C411yescharacteristic
42C22×Dic73C4⋊C411yescharacteristic
43C2×C4×D73—21no—
44C2×C4×D73—21no—
45C2×C4×D73—22no—
46C2×C4×D73—41no—
47C2×#10596831—22no—
48C2×#10596831—41no—
49C2×#10596831—41no—
50#11924007—41no—
51#11924007—41no—
52#11924005—41no—
53#11924005—41no—
54C4×Dic73—21no—
55C4×Dic73—21no—
56C22×C4×C73C4211yescharacteristic
57C22×C4×C73C22⋊C411yescharacteristic
58C22×C4×C73C4⋊C411yescharacteristic
59C2×C8×C73—22no—
60C2×C8×C73—41no—
61C2×C8×C73—41no—
62C42×C73—21no—
63C42×C73—21no—
64C23×C73#9511yescharacteristic
65C22×D73—21no—
66C22×D73—21no—
67C22×D73—21no—
68C22×D73—41no—
69C22×D73—41no—
70C2×C4×C73—21no—
71C2×C4×C73—21no—
72C2×C4×C73—21no—
73C2×C4×C73—21no—
74C2×C4×C73—41no—
75C2×C4×C73—41no—
76C2×C4×C73#9911yescharacteristic
77C2×C4×C73#9911yescharacteristic
78C2×Dic73—21no—
79C2×Dic73—21no—
80C2×Dic73—21no—
81C2×Dic73—21no—
82C2×Dic73—41no—
83C2×Dic73—41no—
84C2×Dic73#10412yes—
85C4×D73—42no—
86C4×D73—42no—
87#10596833—82no—
88#10596833—82no—
89C8×C73—42no—
90#10596831—42no—
91C22×C73—21no—
92C22×C73—21no—
93C22×C73H(3,ℤ/4)11yescharacteristic
94C22×C73#33911yescharacteristic
95C22×C73#34211yescharacteristic
96C2×D73—42no—
97C2×D73—41no—
98C2×D73—41no—
99C2×D73—41no—
100C2×D73—81no—
101C4×C73—21no—
102C4×C73—21no—
103C4×C73—41no—
104C4×C73—41no—
105Dic73—22no—
106Dic73—41no—
107Dic73—41no—
108#7216—731nomaximal, Sylow
109C2×C73—21no—
110C2×C73—21no—
111C2×C73#128411yescharacteristic
112C2×C73#139211yescharacteristic
113C2×C73#139511yescharacteristic
114D73—81no—
115#1822—731no—
116#1750—731no—
117#1464—731no—
118C73#721611yescharacteristic, complemented, Sylow
119C2×#117—731no—
120#432—1461no—
121#407—1461no—
122C2×C22⋊C8—1461no—
123C2×#97#6440811yescharacteristic
124C2×C4×C8—731no—
125#343—732no—
126#343—1461no—
127#336—1461no—
128#324—1461no—
129#323—732no—
130C23×C4—731no—
131C2×M16—1462no—
132C22×C8—21no—
133C22×C8—1461no—
134#117—2921no—
135#117—2921no—
136C2×C4⋊C4—731no—
137C2×C4⋊C4—731no—
138C2×C22⋊C4—731no—
139C2×C22⋊C4—731no—
140C2×C42—731no—
141C2×C42C2×#6440811yescharacteristic
142C4⋊C8—2921no—
143C22⋊C8—2921no—
144C22⋊C8—2921no—
145C22⋊C8—1464no—
146C22⋊C8—1462no—
147#97—41no—
148#97—2921no—
149C4×C8—2921no—
150C24—731no—
151C22×C4—2921no—
152C22×C4—731no—
153C22×C4—731no—
154C22×C4—731no—
155C22×C4—1462no—
156C22×C4—1461no—
157C22×C4—1461no—
158C22×C4C4×#6440811yescharacteristic
159C22×C4C22⋊#6440811yescharacteristic
160C22×C4C4⋊#6440811yescharacteristic
161M16—2922no—
162M16—2922no—
163C2×C8—22no—
164C2×C8—41no—
165C2×C8—41no—
166C2×C8—2921no—
167C2×C8—2921no—
168C2×C8—2922no—
169C2×C8—2922no—
170C2×C8—1462no—
171C4⋊C4—2921no—
172C4⋊C4—2921no—
173C22⋊C4—2921no—
174C22⋊C4—2921no—
175C42—21no—
176C42—21no—
177C42—1461no—
178C42—1461no—
179C23—2921no—
180C23—2921no—
181C23—1461no—
182C23—1461no—
183C23—1461no—
184C23(C2×#64408)⋊C411yescharacteristic
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—2922no—
192C2×C4—2922no—
193C2×C4—2921no—
194C2×C4—2921no—
195C2×C4—732no—
196C2×C4—1461no—
197C2×C4—1461no—
198C2×C4—1461no—
199C2×C4—1461no—
200C2×C4#1455664911yescharacteristic
201C2×C4#1455665011yescharacteristic
202C8—42no—
203C8—2922no—
204C8—5842no—
205C8—5842no—
206C22—21no—
207C22—21no—
208C22—2922no—
209C22—2921no—
210C22—2921no—
211C22—2921no—
212C22—5841no—
213C22#1798945411yescharacteristic
214C22#1798945811yescharacteristic
215C22#1798946511yescharacteristic
216C4—21no—
217C4—21no—
218C4—41no—
219C4—41no—
220C4—2921no—
221C4—2921no—
222C4—1462no—
223C2—21no—
224C2—21no—
225C2—5841no—
226C2#2262477911yescharacteristic
227C2#2262502311yescharacteristic
228C2#2262503211yescharacteristic
subgroupG/H
centerC22#17989465
commutatorC22×C4×C73C42
FrattiniC2×C42C2×#64408
FittingC2×#97×C73C4
socleC22×C73#342
prime radicalC23×D73C4⋊C4
cosocleC2×#14556548C22
hypercenterC2×#97#64408
hypocenterC73#7216
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C2×#97

Complements

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

NH ≅ G/Ntype
118. C73#7216semidirect

Maximal subgroups

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

subgroupindex
#226258322
#226251842
#226097002
#721673