Finite Group Databasebeta

← #34000629

Subgroups — #34000629

Order 18688.

324 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 58 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#22625170C211yesmaximal, characteristic
2#22625166C211yesmaximal, characteristic
3#22610226C211yesmaximal, characteristic
4#17989604—21no—
5#17989555—21no—
6#17989433C412yes—
7#17989431C412yes—
8#17989430—21no—
9#17989430—21no—
10C22×#11924012C411yescharacteristic
11C2×C4×C22⋊D73C2211yescharacteristic
12C2×#14556503—21no—
13#17988341—21no—
14C2×C22⋊C8×C73C411yescharacteristic
15C2×#11924036—41no—
16#14556658—41no—
17#14556648—41no—
18C22⋊#10596833—22no—
19C22⋊#10596833—22no—
20C4×#10596833—41no—
21C22×C22⋊D73Q811yescharacteristic
22C22×C4×D73D411yescharacteristic
23C2×#11924012—41no—
24C2×#11924012—42no—
25C22×#10596831—21no—
26C4×C22⋊D73—41no—
27C4×C22⋊D73—41no—
28C2×#11924007C2×C411yescharacteristic
29C2×C22⋊Dic73D411yescharacteristic
30C2×#11924005C2×C411yescharacteristic
31C2×C4×Dic73D411yescharacteristic
32#14556503—42no—
33C23×C4×C73C2×C411yescharacteristic
34C22×C8×C73—21no—
35C22⋊C8×C73—41no—
36#11924036—81no—
37#11924036—81no—
38C2×#10596833—42no—
39C2×#10596833—42no—
40C23×D73C4⋊C411yescharacteristic
41C2×C22⋊D73—22no—
42C2×C22⋊D73—22no—
43C2×C22⋊D73—41no—
44C22×Dic73C22⋊C411yescharacteristic
45C22×Dic73C22⋊C411yescharacteristic
46C22×Dic73C4⋊C411yescharacteristic
47C2×C4×D73—21no—
48C2×C4×D73—21no—
49C2×C4×D73—41no—
50C2×C4×D73—41no—
51#11924012—42no—
52#11924012—42no—
53C2×#10596831—22no—
54C2×#10596831—41no—
55C2×#10596831—41no—
56#11924007—41no—
57C22⋊Dic73—41no—
58#11924005—41no—
59C4×Dic73—21no—
60C4×Dic73—21no—
61C24×C73C4⋊C411yescharacteristic
62C22×C4×C73—21no—
63C22×C4×C73—21no—
64C22×C4×C73—41no—
65C22×C4×C73—41no—
66C22×C4×C73C4211yescharacteristic
67C22×C4×C73C22⋊C411yescharacteristic
68C2×C8×C73—41no—
69C2×C8×C73—41no—
70C2×C8×C73—41no—
71C23×C73—21no—
72C23×C73—21no—
73C23×C73—21no—
74C23×C73—41no—
75C23×C73—41no—
76C23×C73#9511yescharacteristic
77C22×D73—21no—
78C22×D73—21no—
79C22×D73—41no—
80C22×D73—41no—
81C22×D73#10812yes—
82C2×C4×C73—21no—
83C2×C4×C73—21no—
84C2×C4×C73—21no—
85C2×C4×C73—42no—
86C2×C4×C73—41no—
87C2×C4×C73—41no—
88C2×C4×C73—41no—
89C2×C4×C73#9911yescharacteristic
90C2×C4×C73#9911yescharacteristic
91C22⋊D73—44no—
92C2×Dic73—21no—
93C2×Dic73—21no—
94C2×Dic73—21no—
95C2×Dic73—21no—
96C2×Dic73—41no—
97C2×Dic73—41no—
98C2×Dic73#10812yes—
99C4×D73—41no—
100C4×D73—41no—
101C4×D73—81no—
102#10596833—82no—
103#10596833—82no—
104C8×C73—81no—
105#10596831—42no—
106C22×C73—21no—
107C22×C73—21no—
108C22×C73—41no—
109C22×C73—41no—
110C22×C73—41no—
111C22×C73—81no—
112C22×C73—81no—
113C22×C73#34111yescharacteristic
114C22×C73#34111yescharacteristic
115C22×C73#34211yescharacteristic
116C2×D73—22no—
117C2×D73—41no—
118C2×D73—41no—
119C2×D73—42no—
120C2×D73—81no—
121C4×C73—21no—
122C4×C73—41no—
123C4×C73AΣL(1,𝔽16)11yescharacteristic
124C4×C73#35211yescharacteristic
125Dic73—22no—
126Dic73—41no—
127Dic73—41no—
128#7285—731nomaximal, Sylow
129C2×C73—21no—
130C2×C73—21no—
131C2×C73—81no—
132C2×C73#129811yescharacteristic
133C2×C73#139011yescharacteristic
134C2×C73#139511yescharacteristic
135D73—42no—
136#1870—731no—
137#1460—731no—
138#1459—731no—
139C73#728511yescharacteristic, complemented, Sylow
140C22×M16—731no—
141C2×C4×D4—731no—
142#431—1461no—
143C2×C22⋊C8—1461no—
144C2×C22⋊C8—1461no—
145C2×C22⋊C8#6440811yescharacteristic
146#336—1461no—
147#324—732no—
148#323—732no—
149#323—1461no—
150#323—1461no—
151C22×D4—731no—
152C23×C4—731no—
153C23×C4C2×#6440811yescharacteristic
154C2×M16—2922no—
155C2×M16—2921no—
156C22×C8—21no—
157C22×C8—2921no—
158C22×C8—1461no—
159C4×D4—2921no—
160C4×D4—2921no—
161C2×C4⋊C4—731no—
162C2×C22⋊C4—731no—
163C2×C22⋊C4—731no—
164C2×C42—731no—
165C4⋊C8—2921no—
166C22⋊C8—41no—
167C22⋊C8—2922no—
168C22⋊C8—2921no—
169C22⋊C8—1462no—
170C22⋊C8—1462no—
171C4×C8—2921no—
172C24—731no—
173C24C4⋊#6440811yescharacteristic
174C2×D4—2921no—
175C2×D4—1462no—
176C2×D4—1462no—
177C22×C4—21no—
178C22×C4—21no—
179C22×C4—41no—
180C22×C4—41no—
181C22×C4—2921no—
182C22×C4—2921no—
183C22×C4—731no—
184C22×C4—731no—
185C22×C4—731no—
186C22×C4—1461no—
187C22×C4—1461no—
188C22×C4C4×#6440811yescharacteristic
189C22×C4C22⋊#6440811yescharacteristic
190M16—2922no—
191M16—2922no—
192C2×C8—41no—
193C2×C8—41no—
194C2×C8—41no—
195C2×C8—2921no—
196C2×C8—2921no—
197C2×C8—2922no—
198C2×C8—2922no—
199C2×C8—5841no—
200C2×C8—5841no—
201C2×C8—1462no—
202C4⋊C4—2921no—
203C22⋊C4—2921no—
204C22⋊C4—2921no—
205C42—1461no—
206C42—1461no—
207C23—21no—
208C23—21no—
209C23—21no—
210C23—41no—
211C23—41no—
212C23—2921no—
213C23—2921no—
214C23—732no—
215C23—1461no—
216C23—1461no—
217C23(C2×#64408)⋊C411yescharacteristic
218D4—2924no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—42no—
223C2×C4—41no—
224C2×C4—41no—
225C2×C4—41no—
226C2×C4—2921no—
227C2×C4—2921no—
228C2×C4—2921no—
229C2×C4—2921no—
230C2×C4—5841no—
231C2×C4—732no—
232C2×C4—1461no—
233C2×C4—1461no—
234C2×C4—1461no—
235C2×C4—1461no—
236C2×C4#1455664911yescharacteristic
237C2×C4#1455665011yescharacteristic
238C8—81no—
239C8—2922no—
240C8—5842no—
241C8—5842no—
242C22—21no—
243C22—21no—
244C22—41no—
245C22—41no—
246C22—41no—
247C22—81no—
248C22—81no—
249C22—2922no—
250C22—2921no—
251C22—2921no—
252C22—5841no—
253C22—1462no—
254C22#1798946211yescharacteristic
255C22#1798946211yescharacteristic
256C22#1798946511yescharacteristic
257C4—21no—
258C4—41no—
259C4—2921no—
260C4—2921no—
261C4—1462no—
262C4#1798948811yescharacteristic
263C4#1798949011yescharacteristic
264C2—21no—
265C2—21no—
266C2—81no—
267C2—2922no—
268C2#2262481311yescharacteristic
269C2#2262501611yescharacteristic
270C2#2262503111yescharacteristic
subgroupG/H
centerC2×C4#14556650
commutatorC22×C4×C73C42
FrattiniC23×C4C2×#64408
FittingC2×C22⋊C8×C73C4
socleC22×C73#342
prime radicalC22×C22⋊D73Q8
cosocleC2×C4×C22⋊D73C22
hypercenterC2×C22⋊C8#64408
hypocenterC73#7285
LCSG ▷ C22×C4×C73 ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
139. C73#7285semidirect

Maximal subgroups

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

subgroupindex
#226251702
#226251662
#226102262
#728573