Finite Group Databasebeta

← #32990754

Subgroups — #32990754

Order 18688.

330 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 93 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#22610763C211yesmaximal, characteristic
2#22610085C211yesmaximal, characteristic, complemented
3#22608578C212yesmaximal
4#22607827C212yesmaximal, complemented
5C73×#1274C211yesmaximal, characteristic, complemented
6#17989137C2211yescharacteristic
7#17988611C2211yescharacteristic
8C2×C4⋊#10596831—21no—
9C2×C4⋊#10596831—21no—
10C2×C4⋊#10596831C2212yes—
11C2×#14556519—21no—
12C2×#14556519—21no—
13#17988332—22no—
14#17988330—22no—
15#431×C73C2212yes—
16#376×C73C2211yescharacteristic
17C2×#11924028—21no—
18C2×#11924012—21no—
19C22×#10596831—22no—
20#14556591D411yescharacteristic
21#14556588D411yescharacteristic
22#14556579—21no—
23#14556565—22no—
24C4×D292—22no—
25C4⋊#10596831—22no—
26C4⋊#10596831—22no—
27C4⋊#10596831—22no—
28C4⋊#10596831—42no—
29C4⋊#10596831—42no—
30#14556519—42no—
31#14556519—42no—
32C2×C42×C73D411yescharacteristic
33C2×C42×C73D411yescharacteristic
34C2×C42×C73C2311yescharacteristic
35C4⋊C8×C73—22no—
36C22⋊C8×C73—22no—
37C4×C8×C73—22no—
38#95×C73—22no—
39#11924028—41no—
40#11924028—41no—
41#11924028—41no—
42#11924028—41no—
43C2×Dic146—21no—
44C2×D292—21no—
45C2×D292—22no—
46C2×C22⋊D73—41no—
47C2×C4×D73—41no—
48#11924012—41no—
49#11924012—41no—
50C2×#10596831—42no—
51C2×#10596831—41no—
52C2×#10596831—42no—
53C2×#10596831—42no—
54C4⋊Dic73—22no—
55#11924005—42no—
56C22×C4×C73—21no—
57C22×C4×C73—21no—
58C22×C4×C73C2×D411yescharacteristic
59C22×C4×C73#4112yes—
60C2×C8×C73—42no—
61C42×C73—21no—
62C42×C73—21no—
63C42×C73D812yes—
64C42×C73SD1612yes—
65C42×C73C2×D411yescharacteristic
66C42×C73#4112yes—
67C42×C73#4111yescharacteristic
68C23×C73#12311yescharacteristic
69C22×D73—41no—
70C2×C4×C73—22no—
71C2×C4×C73—22no—
72C2×C4×C73—42no—
73C2×C4×C73—42no—
74C2×C4×C73—42no—
75C2×C4×C73#12111yescharacteristic
76C2×C4×C73#12312yes—
77C2×C4×C73#12411yescharacteristic
78C2×C4×C73#12612yes—
79C2×C4×C73C2×D811yescharacteristic
80C2×C4×C73C2×SD1611yescharacteristic
81C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
82C2×C4×C73#13711yescharacteristic
83C22⋊D73—81no—
84C22⋊D73—81no—
85C2×Dic73—41no—
86D292—41no—
87D292—41no—
88D292—82no—
89C4×D73—81no—
90C4×D73—81no—
91Dic146—41no—
92Dic146—41no—
93C8×C73—82no—
94#10596831—82no—
95#10596831—81no—
96C22×C73—22no—
97C22×C73#39711yescharacteristic
98C22×C73#48011yescharacteristic
99C22×C73#48111yescharacteristic
100C2×D73—81no—
101C2×D73—82no—
102C4×C73—22no—
103C4×C73—22no—
104C4×C73—42no—
105C4×C73—42no—
106C4×C73#45911yescharacteristic
107C4×C73#46111yescharacteristic
108C4×C73#48611yescharacteristic
109C4×C73#48911yescharacteristic
110Dic73—81no—
111#10627—731nomaximal, Sylow
112C2×C73—21no—
113C2×C73—21no—
114C2×C73#207111yescharacteristic
115C2×C73#208012yes—
116D73—161no—
117#1963—731no—
118#1843—731no—
119#1540—732no—
120#1301—732no—
121#1274D7311yescharacteristic, complemented
122C73#1062711yescharacteristic, complemented, Sylow
123#532—731no—
124#431C2×D7312yes—
125#423—731no—
126C2×C4⋊C8—732no—
127C2×C4⋊C8—1461no—
128C2×C4⋊C8—1461no—
129C2×#104—1461no—
130C2×#104—1461no—
131#376C2×D7311yescharacteristic
132#332—1462no—
133#331—1462no—
134C2×#41—1461no—
135C2×M16—1461no—
136C22×C8—1462no—
137C4⋊Q8—731no—
138#127—731no—
139#124—1461no—
140#121—1462no—
141C4×D4—1462no—
142C2×C42D29211yescharacteristic
143C2×C42D29211yescharacteristic
144C2×C42C22×D7311yescharacteristic
145C4⋊C8—22no—
146C4⋊C8—2922no—
147C4⋊C8—2922no—
148C4⋊C8—1462no—
149C4⋊C8—1462no—
150C4⋊C8—1462no—
151#104—2922no—
152#104—2922no—
153C22⋊C8—22no—
154C4×C8—22no—
155#95—22no—
156#41—2921no—
157#41—2921no—
158#41—2921no—
159#41—2921no—
160C2×Q8—1461no—
161C2×D4—2921no—
162C2×D4—1461no—
163C2×D4—1462no—
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—2921no—
167C22×C4C2×D29211yescharacteristic
168C22×C4#1192402712yes—
169M16—2921no—
170M16—2921no—
171C2×C8—42no—
172C2×C8—2922no—
173C2×C8—2921no—
174C2×C8—2922no—
175C2×C8—2922no—
176C4⋊C4—1462no—
177C22⋊C4—2922no—
178C42—21no—
179C42—21no—
180C42D58412yes—
181C42#1192401712yes—
182C42D4×D7311yescharacteristic
183C42#1192402812yes—
184C42#1192402911yescharacteristic
185C23—2921no—
186C23#1455657511yescharacteristic
187Q8—2921no—
188Q8—2921no—
189D4—2921no—
190D4—2921no—
191D4—5842no—
192D4—5841no—
193D4—5841no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—42no—
197C2×C4—42no—
198C2×C4—42no—
199C2×C4—2921no—
200C2×C4—5841no—
201C2×C4—5841no—
202C2×C4#1455656611yescharacteristic
203C2×C4#1455657312yes—
204C2×C4#1455657911yescharacteristic
205C2×C4#1455658612yes—
206C2×C4C2×D58411yescharacteristic
207C2×C4C2×#1192401711yescharacteristic
208C2×C4#1455661911yescharacteristic
209C2×C4#1455662411yescharacteristic
210C8—82no—
211C8—5841no—
212C8—5842no—
213C22—22no—
214C22—5841no—
215C22—5842no—
216C22#1798851411yescharacteristic
217C22#1798890111yescharacteristic
218C22#1798890611yescharacteristic
219C4—22no—
220C4—22no—
221C4—42no—
222C4—42no—
223C4—5841no—
224C4#1798878311yescharacteristic
225C4#1798879311yescharacteristic
226C4#1798893411yescharacteristic
227C4#1798894711yescharacteristic
228C2—21no—
229C2—21no—
230C2—11681no—
231C2#2261133611yescharacteristic
232C2#2261138312yes—
subgroupG/H
centerC2×C4#14556579
commutator, cosocleC2×C42×C73C23
FrattiniC2×C42C22×D73
FittingC73×#1274C2
socleC22×C73#397
prime radical#17989137C22
hypercenter#1274D73
hypocenterC73#10627
LCSG ▷ C2×C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1274

Complements

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

NH ≅ G/Ntype
2. #22610085C2semidirect
4. #22607827C2semidirect
5. C73×#1274C2semidirect
121. #1274D73semidirect
122. C73#10627semidirect

Maximal subgroups

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

subgroupindex
#226107632
#226100852
#226085782
#226078272
C73×#12742
#1062773