Finite Group Databasebeta

← #32990055

Subgroups — #32990055

Order 18688.

408 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 77 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#22621241C211yesmaximal, characteristic
2#22610084C211yesmaximal, characteristic, complemented
3#22608627C212yesmaximal, complemented
4#22608440C212yesmaximal, complemented
5C73×#1290C211yesmaximal, characteristic, complemented
6#17989137C2212yes—
7#17988868—22no—
8#17988823—22no—
9#17988783—22no—
10C2×C4⋊#10596831C2211yescharacteristic
11C2×#14556520—22no—
12#17988433C2211yescharacteristic
13#17988335—22no—
14#17988330—22no—
15#17988322—24no—
16#432×C73C2212yes—
17C2×C4⋊C8×C73C2211yescharacteristic
18C2×#11924028—22no—
19C2×D584—22no—
20C22×#10596831—21no—
21#14556591D412yes—
22#14556588D412yes—
23#14556579—22no—
24#14556565—22no—
25#14556565—22no—
26C4×D292—22no—
27C4×D292—22no—
28C2×C4×Dic73—21no—
29#14556525—22no—
30C4⋊#10596831—22no—
31#14556520—44no—
32#14556513—24no—
33#14556498—21no—
34#14556498D412yes—
35C22×C8×C73D412yes—
36C2×C42×C73C2311yescharacteristic
37C4⋊C8×C73—22no—
38C4⋊C8×C73—22no—
39C22⋊C8×C73—22no—
40#97×C73—22no—
41#11924028—84no—
42C2×Dic146—22no—
43C2×D292—22no—
44C2×D292—22no—
45C2×D292—22no—
46C2×C22⋊D73—42no—
47C22×Dic73—22no—
48C2×C4×D73—42no—
49D584—82no—
50C2×#10596831—42no—
51C2×#10596831—41no—
52C4⋊Dic73—22no—
53C4⋊Dic73—22no—
54#11924005—42no—
55#11924005—42no—
56C4×Dic73—22no—
57C4×Dic73—22no—
58C22×C4×C73C2×D411yescharacteristic
59C22×C4×C73C2×D411yescharacteristic
60C22×C4×C73#4111yescharacteristic
61C2×C8×C73—22no—
62C2×C8×C73—42no—
63C2×C8×C73—42no—
64C42×C73C2×D412yes—
65C42×C73#4112yes—
66C23×C73#12111yescharacteristic
67C22×D73—42no—
68C2×C4×C73—22no—
69C2×C4×C73—21no—
70C2×C4×C73—21no—
71C2×C4×C73—41no—
72C2×C4×C73#12011yescharacteristic
73C2×C4×C73#12112yes—
74C2×C4×C73#12312yes—
75C2×C4×C73#12411yescharacteristic
76C22⋊D73—84no—
77C2×Dic73—24no—
78C2×Dic73—42no—
79C2×Dic73—42no—
80C2×Dic73—42no—
81D292—42no—
82D292—42no—
83D292—82no—
84D292—82no—
85C4×D73—84no—
86Dic146—82no—
87C8×C73—42no—
88C8×C73—82no—
89#10596831—81no—
90C22×C73—21no—
91C22×C73—21no—
92C22×C73#39411yescharacteristic
93C22×C73#47212yes—
94C2×D73—82no—
95C2×D73—82no—
96C2×D73—82no—
97C4×C73—22no—
98C4×C73—21no—
99C4×C73—22no—
100C4×C73#45311yescharacteristic
101C4×C73#45611yescharacteristic
102Dic73—44no—
103Dic73—82no—
104#10512—731nomaximal, Sylow
105C2×C73—22no—
106C2×C73#203911yescharacteristic
107C2×C73#204511yescharacteristic
108C2×C73#205311yescharacteristic
109D73—162no—
110#3245—731no—
111#1843—731no—
112#1551—732no—
113#1505—732no—
114#1290D7311yescharacteristic, complemented
115C73#1051211yescharacteristic, complemented, Sylow
116#532—732no—
117#474—1462no—
118#466—1462no—
119#459—1462no—
120#432C2×D7312yes—
121C2×C4⋊C8—731no—
122C2×C4⋊C8—1462no—
123C2×C4⋊C8C2×D7311yescharacteristic
124#376—731no—
125#333—1462no—
126#331—1462no—
127#327—1464no—
128C2×#41—1462no—
129C2×D8—1462no—
130C22×C8—1461no—
131C22×C8D29212yes—
132C4⋊Q8—732no—
133#127—732no—
134#124—1462no—
135#121—1462no—
136#121—1462no—
137C4×D4—1462no—
138C4×D4—1462no—
139C2×C42—1461no—
140C2×C42C22×D7311yescharacteristic
141#107—1462no—
142C4⋊C8—22no—
143C4⋊C8—22no—
144C4⋊C8—2924no—
145C4⋊C8—1462no—
146#102—1464no—
147C22⋊C8—22no—
148#97—22no—
149#95—732no—
150#95—1461no—
151#41—5844no—
152C2×Q8—1462no—
153C2×D4—2922no—
154C2×D4—1462no—
155C2×D4—1462no—
156C2×D4—1462no—
157C22×C4—2922no—
158C22×C4—1462no—
159C22×C4D4×D7311yescharacteristic
160C22×C4C2×D29211yescharacteristic
161C22×C4#1192402911yescharacteristic
162D8—5842no—
163C2×C8—22no—
164C2×C8—42no—
165C2×C8—42no—
166C2×C8—2922no—
167C2×C8—2921no—
168C4⋊C4—1462no—
169C4⋊C4—1462no—
170C22⋊C4—2922no—
171C22⋊C4—2922no—
172C42—1462no—
173C42—1462no—
174C42D4×D7312yes—
175C42#1192402812yes—
176C23—2922no—
177C23#1455656611yescharacteristic
178Q8—5842no—
179D4—2922no—
180D4—2922no—
181D4—5842no—
182D4—5842no—
183D4—5844no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—41no—
188C2×C4—2922no—
189C2×C4—2922no—
190C2×C4—2922no—
191C2×C4—5844no—
192C2×C4—1464no—
193C2×C4#1455656111yescharacteristic
194C2×C4#1455656412yes—
195C2×C4#1455657612yes—
196C2×C4#1455657911yescharacteristic
197C8—42no—
198C8—82no—
199C8—5841no—
200C22—21no—
201C22—21no—
202C22—5842no—
203C22—5842no—
204C22—5842no—
205C22#1798850511yescharacteristic
206C22#1798885812yes—
207C4—22no—
208C4—21no—
209C4—22no—
210C4—2924no—
211C4—5842no—
212C4#1798875711yescharacteristic
213C4#1798877211yescharacteristic
214C2—22no—
215C2—11682no—
216C2#2261115611yescharacteristic
217C2#2261118811yescharacteristic
218C2#2261123811yescharacteristic
subgroupG/H
centerC22#17988505
commutator, cosocleC2×C42×C73C23
FrattiniC2×C42C22×D73
FittingC73×#1290C2
socleC22×C73#394
prime radical#22621241C2
hypercenter#1290D73
hypocenterC73#10512
LCSG ▷ C2×C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1290

Complements

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

NH ≅ G/Ntype
2. #22610084C2semidirect
3. #22608627C2semidirect
4. #22608440C2semidirect
5. C73×#1290C2semidirect
114. #1290D73semidirect
115. C73#10512semidirect

Maximal subgroups

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

subgroupindex
#226212412
#226100842
#226086272
#226084402
C73×#12902
#1051273