Finite Group Databasebeta

← #32995413

Subgroups — #32995413

Order 18688.

330 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 69 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#22618560C211yesmaximal, characteristic
2#22611740C212yesmaximal, complemented
3#22607881C212yesmaximal, complemented
4#22607867C211yesmaximal, characteristic
5C73×#1320C211yesmaximal, characteristic
6C22×C4×Dic73C411yescharacteristic
7#17988641—22no—
8#17988637—22no—
9#17988610C411yescharacteristic
10#17988610C2211yescharacteristic
11#17988551C411yescharacteristic
12M16×Dic73C411yescharacteristic
13M16×Dic73C2211yescharacteristic
14#17988407—22no—
15#17988369C2212yes—
16#17988364—22no—
17#407×C73C2211yescharacteristic
18#349×C73C2212yes—
19C23×Dic73—21no—
20C2×#11924012C2×C411yescharacteristic
21C2×#11924012C2×C411yescharacteristic
22C2×C4×Dic73—21no—
23C2×C4×Dic73—21no—
24C2×C4×Dic73—21no—
25C2×C4×Dic73—21no—
26C2×C4×Dic73—21no—
27C2×C4×Dic73C2×C411yescharacteristic
28C2×C4×Dic73C2×C411yescharacteristic
29#14556531—22no—
30#14556520—22no—
31#14556520—22no—
32C22⋊#10596831—22no—
33#14556501—21no—
34#14556501D412yes—
35C8×Dic73—21no—
36C8×Dic73D412yes—
37C23×C4×C73C2×C411yescharacteristic
38C2×M16×C73C2×C411yescharacteristic
39C2×M16×C73C2311yescharacteristic
40M32×C73—22no—
41C22⋊C8×C73—22no—
42C22×Dic73—21no—
43C22×Dic73—21no—
44C22×Dic73—21no—
45C22×Dic73—21no—
46C22×Dic73—21no—
47C22×Dic73—21no—
48C22×Dic73—44no—
49#11924012—41no—
50#11924012—41no—
51C2×#10596831—21no—
52C2×#10596831C22⋊C412yes—
53C4×Dic73—21no—
54C4×Dic73—21no—
55C4×Dic73—21no—
56C4×Dic73—21no—
57C4×Dic73—21no—
58C4×Dic73—21no—
59C4×Dic73C22⋊C411yescharacteristic
60C4×Dic73C22⋊C411yescharacteristic
61C4×Dic73M1611yescharacteristic
62C4×Dic73M1611yescharacteristic
63#11924003—42no—
64C24×C73M1611yescharacteristic
65C22×C4×C73—21no—
66C22×C4×C73—21no—
67C22×C4×C73—41no—
68C22×C4×C73—41no—
69C22×C4×C73M1611yescharacteristic
70C22×C4×C73C22×C411yescharacteristic
71M16×C73—41no—
72M16×C73—41no—
73C2×C8×C73—21no—
74C2×C8×C73C2×D412yes—
75C16×C73—42no—
76C23×C73—21no—
77C23×C73—41no—
78C23×C73—42no—
79C23×C73C2×M1611yescharacteristic
80C2×C4×C73—21no—
81C2×C4×C73—21no—
82C2×C4×C73—21no—
83C2×C4×C73—42no—
84C2×C4×C73—41no—
85C2×C4×C73—41no—
86C2×C4×C73—41no—
87C2×C4×C73C2×C22⋊C411yescharacteristic
88C2×C4×C73C2×M1611yescharacteristic
89C2×Dic73—24no—
90C2×Dic73—21no—
91C2×Dic73—21no—
92C2×Dic73—21no—
93C2×Dic73—21no—
94C2×Dic73—42no—
95C2×Dic73—42no—
96C2×Dic73—42no—
97C2×Dic73—42no—
98C2×Dic73—42no—
99C8×C73—22no—
100C8×C73—41no—
101#10596831—22no—
102#10596831—41no—
103C22×C73—22no—
104C22×C73—21no—
105C22×C73—41no—
106C22×C73—41no—
107C22×C73—42no—
108C22×C73—42no—
109C22×C73—41no—
110C22×C73#40711yescharacteristic
111C4×C73—21no—
112C4×C73—41no—
113C4×C73#41011yescharacteristic
114C4×C73#41311yescharacteristic
115Dic73—22no—
116Dic73—22no—
117Dic73—41no—
118Dic73—41no—
119#11521—731nomaximal, Sylow
120C2×C73—21no—
121C2×C73—42no—
122C2×C73—41no—
123C2×C73#146411yescharacteristic
124#2920—731no—
125#2165—732no—
126#1327—732no—
127#1320—731no—
128#1320D7311yescharacteristic
129C73#1152111yescharacteristic, complemented, Sylow
130C22×C42—731no—
131#432—1462no—
132#431—1462no—
133#423—731no—
134#423—731no—
135#407—731no—
136#407C2×D7311yescharacteristic
137C4×M16—731no—
138C4×M16—731no—
139#364—1462no—
140#349—732no—
141#349C2×D7312yes—
142#347—1462no—
143C23×C4—1461no—
144C23×C4C4×D7311yescharacteristic
145C2×M16—731no—
146C2×M16—731no—
147C2×M16C4×D7311yescharacteristic
148C2×M16C22×D7311yescharacteristic
149C2×C42—731no—
150C2×C42—731no—
151C2×C42—1461no—
152C2×C42—1461no—
153C2×C42—1461no—
154C2×C42—1461no—
155C2×C42—1461no—
156M32—22no—
157M32—1462no—
158C4⋊C8—1462no—
159C4⋊C8—1462no—
160C22⋊C8—22no—
161C22⋊C8—1462no—
162#97—732no—
163#97—1461no—
164C4×C8—732no—
165C4×C8—1461no—
166C24#1192401111yescharacteristic
167C22×C4—21no—
168C22×C4—21no—
169C22×C4—41no—
170C22×C4—41no—
171C22×C4—2924no—
172C22×C4—1461no—
173C22×C4—1461no—
174C22×C4—1461no—
175C22×C4—1461no—
176C22×C4—1461no—
177C22×C4—1461no—
178C22×C4#1192401111yescharacteristic
179C22×C4C2×C4×D7311yescharacteristic
180M16—41no—
181M16—41no—
182M16—2921no—
183M16—2921no—
184C2×C8—21no—
185C2×C8—732no—
186C2×C8—1461no—
187C2×C8D4×D7312yes—
188C42—731no—
189C42—731no—
190C42—731no—
191C42—731no—
192C42—1461no—
193C42—1461no—
194C42—1461no—
195C42—1461no—
196C42—1461no—
197C42—1461no—
198C16—42no—
199C16—2922no—
200C23—21no—
201C23—41no—
202C23—42no—
203C23C2×#1192401111yescharacteristic
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—42no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—2922no—
212C2×C4—2922no—
213C2×C4—2922no—
214C2×C4—2922no—
215C2×C4—2922no—
216C2×C4—1461no—
217C2×C4—1461no—
218C2×C4—1464no—
219C2×C4—1461no—
220C2×C4—1461no—
221C2×C4C22⋊C4×D7311yescharacteristic
222C2×C4M16×D7311yescharacteristic
223C8—22no—
224C8—41no—
225C8—2921no—
226C8—1462no—
227C22—22no—
228C22—21no—
229C22—41no—
230C22—41no—
231C22—42no—
232C22—42no—
233C22—41no—
234C22#1798854911yescharacteristic
235C4—21no—
236C4—41no—
237C4—2921no—
238C4—2921no—
239C4—1462no—
240C4—1462no—
241C4#1798855911yescharacteristic
242C4#1798856811yescharacteristic
243C2—21no—
244C2—42no—
245C2—41no—
246C2#2260826211yescharacteristic
subgroupG/H
centerC4#17988559
commutatorC22×C4×C73C22×C4
FrattiniC2×M16C22×D73
FittingC73×#1320C2
socleC2×C73#1464
prime radicalC24×C73M16
cosocleC2×M16×C73C23
hypercenter#1320D73
hypocenterC73#11521
LCSG ▷ C22×C4×C73 ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #1320

Complements

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

NH ≅ G/Ntype
2. #22611740C2semidirect
3. #22607881C2semidirect
129. C73#11521semidirect

Maximal subgroups

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

subgroupindex
#226185602
#226117402
#226078812
#226078672
C73×#13202
#1152173