Finite Group Databasebeta

← #33006763

Subgroups — #33006763

Order 18688.

232 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 57 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×D2336C211yesmaximal, characteristic, complemented
2C2×#17988422C211yesmaximal, characteristic, complemented
3#22612179C211yesmaximal, characteristic, complemented
4#22611777C211yesmaximal, characteristic, complemented
5#22608126C211yesmaximal, characteristic, complemented
6#22608108C211yesmaximal, characteristic, complemented
7C73×#1415C211yesmaximal, characteristic, complemented
8C2×D1168C2211yescharacteristic
9C2×D1168C2211yescharacteristic
10C2×#14556532—21no—
11#17988962—21no—
12#17988669—21no—
13D2336—22no—
14#17988422—22no—
15C2×#14556497C2211yescharacteristic
16#17988387—21no—
17C16×Dic73C2211yescharacteristic
18C2×D16×C73C2211yescharacteristic
19C2×C32×C73C2211yescharacteristic
20#366×C73C2211yescharacteristic
21C2×D584—21no—
22C2×D584—21no—
23C2×#11924013—41no—
24#14556587—41no—
25#14556553—41no—
26D1168—21no—
27D1168—21no—
28D1168—21no—
29D1168D412yescomplemented
30#14556532—42no—
31C2×#11924003D411yescharacteristic
32#14556511—41no—
33C8×Dic73D411yescharacteristic
34#14556497—21no—
35C2×D8×C73—21no—
36D16×C73—21no—
37D16×C73—21no—
38C2×C16×C73C2311yescharacteristic
39#107×C73—21no—
40C32×C73—21no—
41C2×D292—41no—
42C2×D292—41no—
43C2×C22⋊D73—81no—
44C2×C22⋊D73—81no—
45C2×C4×D73—81no—
46D584—22no—
47D584—41no—
48D584—41no—
49D584—41no—
50#11924013—82no—
51C2×#10596831D811yescharacteristic
52#11924005—81no—
53C4×Dic73D811yescharacteristic
54#11924003—21no—
55C2×D4×C73—41no—
56D8×C73—41no—
57D8×C73—41no—
58C2×C8×C73C2×D411yescharacteristic
59C4⋊C4×C73—41no—
60C16×C73C2×D411yescharacteristic
61C16×C73#4111yescharacteristic
62C23×C73—81no—
63C22×D73—81no—
64C22×D73—81no—
65D4×C73—81no—
66D4×C73—81no—
67C2×C4×C73—81no—
68C2×C4×C73C2×D811yescharacteristic
69C22⋊D73—162no—
70C22⋊D73—162no—
71C2×Dic73D1611yescharacteristic
72C2×Dic73D1611yescharacteristic
73D292—42no—
74D292—81no—
75D292—81no—
76D292—81no—
77C4×D73—162no—
78C8×C73#12111yescharacteristic
79C8×C73AGL(1,ℤ/8)11yescharacteristic
80#10596831—21no—
81C22×C73—161no—
82C22×C73—161no—
83C22×C73—161no—
84C22×C73C2×D1611yescharacteristic
85C2×D73—82no—
86C2×D73—161no—
87C2×D73—161no—
88C2×D73—161no—
89C2×D73—161no—
90C2×D73—161no—
91C4×C73—161no—
92C4×C73#45911yescharacteristic
93C4×C73#50911yescharacteristic
94Dic73—21no—
95Dic73D3212yescomplemented
96#13685—731nomaximal, Sylow
97C2×C73—321no—
98C2×C73#220611yescharacteristic
99C2×C73C2×D3211yescharacteristic
100C2×C73#226311yescharacteristic
101D73—162no—
102D73—321no—
103C2×D32—731no—
104C2×D32—731no—
105#2246—731no—
106C4×D16—731no—
107C4⋊C32—731no—
108#1415—731no—
109#1415D7311yescharacteristic, complemented
110C73#1368511yescharacteristic, complemented, Sylow
111C2×D16—731no—
112C2×D16—731no—
113C2×D16—1461no—
114C2×D16C2×D7311yescharacteristic
115#493—1461no—
116C4×D8—1461no—
117D32—1462no—
118D32—1462no—
119C2×C32—731no—
120C2×C32C2×D7311yescharacteristic
121#366C2×D7311yescharacteristic
122#357—1461no—
123C4×C16—731no—
124C2×D8—21no—
125C2×D8—2921no—
126C2×D8—1461no—
127C2×D8—1461no—
128#127—2921no—
129C4×D4—2921no—
130D16—21no—
131D16—21no—
132D16—2922no—
133D16—732no—
134D16—1461no—
135D16—1461no—
136D16—1461no—
137C2×C16—731no—
138C2×C16C22×D7311yescharacteristic
139#107—21no—
140#102—2921no—
141C4×C8—731no—
142C32—21no—
143C32—1461no—
144C2×D4—41no—
145C2×D4—2921no—
146C2×D4—2921no—
147C2×D4—5841no—
148C2×D4—5841no—
149C22×C4—5841no—
150D8—41no—
151D8—41no—
152D8—2921no—
153D8—2921no—
154D8—2921no—
155D8—5842no—
156D8—1462no—
157C2×C8—731no—
158C2×C8D4×D7311yescharacteristic
159C4⋊C4—41no—
160C22⋊C4—5841no—
161C42—731no—
162C16—1461no—
163C16D4×D7311yescharacteristic
164C16#1192402811yescharacteristic
165C23—81no—
166C23—5841no—
167C23—5841no—
168D4—81no—
169D4—81no—
170D4—2922no—
171D4—5841no—
172D4—5841no—
173D4—5841no—
174D4—11682no—
175D4—11682no—
176C2×C4—81no—
177C2×C4—731no—
178C2×C4—731no—
179C2×C4—11682no—
180C2×C4D8×D7311yescharacteristic
181C8—1461no—
182C8#1455656411yescharacteristic
183C8#1455661811yescharacteristic
184C22—161no—
185C22—161no—
186C22—161no—
187C22—5842no—
188C22—11681no—
189C22—11681no—
190C22—11681no—
191C22—11681no—
192C22—11681no—
193C22D16×D7311yescharacteristic
194C4—161no—
195C4—732no—
196C4—1461no—
197C4#1798878111yescharacteristic
198C4#1798902411yescharacteristic
199C2—321no—
200C2—23361no—
201C2—11682no—
202C2#2261196511yescharacteristic
203C2D32×D7311yescharacteristic
204C2#2261224511yescharacteristic
subgroupG/H
centerC22D16×D73
commutator, cosocleC2×C16×C73C23
FrattiniC2×C16C22×D73
FittingC73×#1415C2
socleC22×C73C2×D16
hypercenter#1415D73
hypocenterC73#13685
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×D2336C2semidirect
2. C2×#17988422C2semidirect
3. #22612179C2semidirect
4. #22611777C2semidirect
5. #22608126C2semidirect
6. #22608108C2semidirect
7. C73×#1415C2semidirect
29. D1168D4semidirect
95. Dic73D32semidirect
109. #1415D73semidirect
110. C73#13685semidirect

Maximal subgroups

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

subgroupindex
C2×D23362
C2×#179884222
#226121792
#226117772
#226081262
#226081082
C73×#14152
#1368573