Finite Group Databasebeta

← #33006635

Subgroups — #33006635

Order 18688.

298 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 59 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
1C2×#17989016C211yesmaximal, characteristic, complemented
2C2×#17988426C211yesmaximal, characteristic, complemented
3C2×#17988422C211yesmaximal, characteristic, complemented
4#22612018C211yesmaximal, characteristic, complemented
5#22608111C211yesmaximal, characteristic, complemented
6#22608068C211yesmaximal, characteristic, complemented
7C73×#1415C211yesmaximal, characteristic, complemented
8C2×#14556610—21no—
9#17989016—22no—
10#17989016—22no—
11C2×Dic584C2211yescharacteristic
12C2×#14556535—21no—
13C2×D1168C2211yescharacteristic
14C2×C16×D73C2211yescharacteristic
15#17988824—21no—
16#17988426—22no—
17#17988422—22no—
18C2×#14556497C2211yescharacteristic
19#17988387—21no—
20C2×D16×C73C2211yescharacteristic
21C2×C32×C73C2211yescharacteristic
22#366×C73C2211yescharacteristic
23C2×#11924027—41no—
24#14556610—24no—
25#14556610—42no—
26C2×Dic292—21no—
27C2×#11924016—41no—
28C2×D584—21no—
29C2×C8×D73D411yescharacteristic
30#14556566—41no—
31Dic584—21no—
32Dic584D412yescomplemented
33#14556535—24no—
34D1168—21no—
35D1168—21no—
36C2×#11924003D411yescharacteristic
37C16×D73—21no—
38C16×D73—21no—
39#14556511—41no—
40#14556497—21no—
41C2×D8×C73—21no—
42D16×C73—21no—
43D16×C73D412yescomplemented
44C2×C16×C73C2311yescharacteristic
45#107×C73—21no—
46C32×C73—21no—
47#11924027—44no—
48#11924027—82no—
49C2×Dic146—41no—
50C2×D292—41no—
51C2×D292—81no—
52C2×C22⋊D73—81no—
53C22×Dic73—81no—
54C2×C4×D73D811yescharacteristic
55Dic292—22no—
56Dic292—41no—
57#11924016—44no—
58D584—41no—
59D584—41no—
60C2×#10596831D811yescharacteristic
61C8×D73—21no—
62C8×D73—21no—
63#11924005—81no—
64#11924003—21no—
65C2×D4×C73—41no—
66D8×C73—22no—
67D8×C73—41no—
68C2×C8×C73C2×D411yescharacteristic
69C4⋊C4×C73—41no—
70C16×C73C2×D411yescharacteristic
71C16×C73C2×D411yescharacteristic
72C23×C73—81no—
73C22×D73—81no—
74C22×D73D1611yescharacteristic
75D4×C73—42no—
76D4×C73—81no—
77C2×C4×C73—81no—
78C2×C4×C73C2×D811yescharacteristic
79C22⋊D73—84no—
80C2×Dic73—84no—
81C2×Dic73—81no—
82C2×Dic73D1611yescharacteristic
83D292—81no—
84D292—81no—
85D292—162no—
86C4×D73—21no—
87C4×D73—21no—
88Dic146—42no—
89Dic146—81no—
90C8×C73#12011yescharacteristic
91C8×C73AGL(1,ℤ/8)11yescharacteristic
92#10596831—21no—
93C22×C73—82no—
94C22×C73—161no—
95C22×C73—161no—
96C22×C73C2×D1611yescharacteristic
97C2×D73—21no—
98C2×D73—21no—
99C2×D73—21no—
100C2×D73—161no—
101C2×D73—161no—
102C2×D73—161no—
103C4×C73—161no—
104C4×C73#44711yescharacteristic
105C4×C73#50911yescharacteristic
106Dic73—21no—
107Dic73—82no—
108#13663—731nomaximal, Sylow
109C2×C73—162no—
110C2×C73#218411yescharacteristic
111C2×C73#226211yescharacteristic
112C2×C73#226311yescharacteristic
113D73—41no—
114D73—321no—
115C2×#508—731no—
116C2×SD64—731no—
117C2×D32—731no—
118#2215—731no—
119#1416—731no—
120#1415D7311yescharacteristic, complemented
121C22⋊C32—731no—
122C73#1366311yescharacteristic, complemented, Sylow
123C2×#135—1461no—
124#508—1462no—
125#508—1462no—
126C2×Q32—731no—
127C2×SD32—1461no—
128C2×D16—731no—
129C2×D16C2×D7311yescharacteristic
130C22×C16—731no—
131#466—1461no—
132SD64—1462no—
133D32—1462no—
134C2×C32—731no—
135C2×C32C2×D7311yescharacteristic
136#366C2×D7311yescharacteristic
137#357—1461no—
138C2×#41—2921no—
139#135—2922no—
140#135—1464no—
141C2×Q16—1461no—
142C2×SD16—2921no—
143C2×D8—21no—
144C2×D8—1461no—
145C22×C8—731no—
146#121—2921no—
147Q32—732no—
148Q32—1461no—
149SD32—1464no—
150D16—21no—
151D16—1461no—
152D16—1461no—
153D16D29212yescomplemented
154C2×C16—731no—
155C2×C16—1461no—
156C2×C16—1461no—
157C2×C16C22×D7311yescharacteristic
158#107—21no—
159#102—2921no—
160C32—21no—
161C32—1461no—
162#41—2924no—
163#41—5842no—
164C2×Q8—2921no—
165C2×D4—41no—
166C2×D4—2921no—
167C2×D4—5841no—
168C2×D4—5841no—
169C22×C4—5841no—
170C22×C4—731no—
171Q16—2921no—
172Q16—1462no—
173SD16—2924no—
174D8—22no—
175D8—41no—
176D8—2921no—
177D8—2921no—
178C2×C8—731no—
179C2×C8—1461no—
180C2×C8—1461no—
181C2×C8D4×D7311yescharacteristic
182C4⋊C4—41no—
183C22⋊C4—5841no—
184C16—1461no—
185C16D4×D7311yescharacteristic
186C16C2×D29211yescharacteristic
187C23—81no—
188C23—5841no—
189C23—731no—
190Q8—2922no—
191Q8—5841no—
192D4—42no—
193D4—81no—
194D4—5844no—
195D4—5841no—
196D4—5841no—
197D4—11682no—
198C2×C4—81no—
199C2×C4—5841no—
200C2×C4—5844no—
201C2×C4—731no—
202C2×C4—1461no—
203C2×C4—1461no—
204C2×C4D8×D7311yescharacteristic
205C8—1461no—
206C8#1455656111yescharacteristic
207C8#1455661811yescharacteristic
208C22—82no—
209C22—161no—
210C22—161no—
211C22—11681no—
212C22—11681no—
213C22—11681no—
214C22—1461no—
215C22—1461no—
216C22—1461no—
217C22D16×D7311yescharacteristic
218C4—161no—
219C4—5842no—
220C4—1461no—
221C4#1798872211yescharacteristic
222C4#1798902411yescharacteristic
223C2—162no—
224C2—23361no—
225C2—2921no—
226C2#2261184411yescharacteristic
227C2#2261223911yescharacteristic
228C2#2261224211yescharacteristic
subgroupG/H
centerC22D16×D73
commutator, cosocleC2×C16×C73C23
FrattiniC2×C16C22×D73
FittingC73×#1415C2
socleC22×C73C2×D16
hypercenter#1415D73
hypocenterC73#13663
LCSG ▷ C2×C16×C73 ▷ C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #1415

Complements

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

NH ≅ G/Ntype
1. C2×#17989016C2semidirect
2. C2×#17988426C2semidirect
3. C2×#17988422C2semidirect
4. #22612018C2semidirect
5. #22608111C2semidirect
6. #22608068C2semidirect
7. C73×#1415C2semidirect
32. Dic584D4semidirect
43. D16×C73D4semidirect
120. #1415D73semidirect
122. C73#13663semidirect
153. D16D292semidirect

Maximal subgroups

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

subgroupindex
C2×#179890162
C2×#179884262
C2×#179884222
#226120182
#226081112
#226080682
C73×#14152
#1366373