Finite Group Databasebeta

← #16955154

Subgroups — #16955154

Order 4352.

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

normal subgroups only

This group has 214 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×#11762644C211yesmaximal, characteristic, complemented
2C2×C32×D17C211yesmaximal, characteristic, complemented
3#14530871C211yesmaximal, characteristic, complemented
4#14530867C211yesmaximal, characteristic, complemented
5#14526983C211yesmaximal, characteristic, complemented
6#14526963C211yesmaximal, characteristic, complemented
7C17×#1415C211yesmaximal, characteristic, complemented
8C2×D272C2211yescharacteristic
9C2×C16×D17C2211yescharacteristic
10#11763046—21no—
11#11763042—21no—
12#11762644—22no—
13C2×#10587465C2211yescharacteristic
14C32×D17—22no—
15#11762635C2211yescharacteristic
16#11762610—21no—
17#11762609—21no—
18C2×C17×D16C2211yescharacteristic
19C2×C17×C32C2211yescharacteristic
20C17×#366C2211yescharacteristic
21C2×D8×C17—21no—
22#10587624—41no—
23C2×D136—21no—
24C2×C8×D17D411yescharacteristic
25#10587581—41no—
26C17×D16—21no—
27C17×D16—21no—
28C2×C16×C17C2311yescharacteristic
29C17×#107—21no—
30#10587503—41no—
31#10587489—21no—
32C2×#63214D411yescharacteristic
33#10587480—41no—
34D272—21no—
35D272—21no—
36C16×D17—21no—
37C16×D17—21no—
38C17×C32—21no—
39#10587465D412yescomplemented
40C2×D4×C17—41no—
41C2×C22⋊D17—81no—
42C2×D68—41no—
43C2×D68—81no—
44C2×C4×D17D811yescharacteristic
45D8×C17—41no—
46D8×C17—41no—
47C2×C8×C17C2×D411yescharacteristic
48C4⋊C4×C17—41no—
49C22⋊Dic17—81no—
50#63227—81no—
51C4⋊Dic17—41no—
52C2×#3622D811yescharacteristic
53D136—41no—
54D136—41no—
55C8×D17—21no—
56C8×D17—21no—
57C16×C17C2×D411yescharacteristic
58C16×C17#4111yescharacteristic
59#63214—21no—
60#13694—171nomaximal, Sylow
61C23×C17—81no—
62C22×D17—81no—
63C22×D17D1611yescharacteristic
64D4×C17—81no—
65D4×C17—81no—
66C2×C4×C17—81no—
67C2×C4×C17C2×D811yescharacteristic
68C22⋊D17—162no—
69C2×Dic17—81no—
70C2×Dic17D1611yescharacteristic
71D68—81no—
72D68—81no—
73D68—162no—
74C4×D17—21no—
75C4×D17—21no—
76C8×C17#12111yescharacteristic
77C8×C17#13511yescharacteristic
78#3622—21no—
79C2×D32—171no—
80C22×C32—171no—
81#2215—171no—
82#2215—171no—
83#1423—171no—
84#1415—171no—
85#1415D1711yescharacteristic, complemented
86C22×C17—161no—
87C22×C17—161no—
88C22×C17—161no—
89C22×C17C2×D1611yescharacteristic
90C2×D17—21no—
91C2×D17—21no—
92C2×D17—161no—
93C2×D17—161no—
94C2×D17—161no—
95C2×D17D3212yescomplemented
96C4×C17—161no—
97C4×C17#46611yescharacteristic
98C4×C17#50811yescharacteristic
99Dic17—21no—
100Dic17—161no—
101C2×D16—171no—
102C2×D16C2×D1711yescharacteristic
103C22×C16—171no—
104#466—341no—
105#466—341no—
106D32—342no—
107C2×C32—171no—
108C2×C32—342no—
109C2×C32C2×D1711yescharacteristic
110#366—171no—
111#366C2×D1711yescharacteristic
112#357—341no—
113#357—341no—
114C2×C17—321no—
115C2×C17#221511yescharacteristic
116C2×C17C2×D3211yescharacteristic
117C2×C17#226211yescharacteristic
118D17—22no—
119D17—321no—
120C2×D8—21no—
121C2×D8—341no—
122C22×C8—171no—
123#121—681no—
124#121—681no—
125D16—21no—
126D16—21no—
127D16—341no—
128D16—341no—
129C2×C16—171no—
130C2×C16—341no—
131C2×C16—341no—
132C2×C16C22×D1711yescharacteristic
133#107—21no—
134#107—341no—
135#102—681no—
136#102—681no—
137C32—21no—
138C32—172no—
139C17#1369411yescharacteristic, complemented, Sylow
140C2×D4—41no—
141C2×D4—681no—
142C2×D4—1361no—
143C2×D4—1361no—
144C22×C4—171no—
145D8—41no—
146D8—41no—
147D8—681no—
148D8—681no—
149C2×C8—171no—
150C2×C8—341no—
151C2×C8—341no—
152C2×C8D4×D1711yescharacteristic
153C4⋊C4—41no—
154C4⋊C4—681no—
155C22⋊C4—1361no—
156C22⋊C4—1361no—
157C16—341no—
158C16#6325211yescharacteristic
159C16D4×D1711yescharacteristic
160C23—81no—
161C23—171no—
162C23—1361no—
163D4—81no—
164D4—81no—
165D4—2722no—
166D4—2722no—
167D4—1361no—
168D4—1361no—
169C2×C4—81no—
170C2×C4—171no—
171C2×C4—341no—
172C2×C4—341no—
173C2×C4—1361no—
174C2×C4D8×D1711yescharacteristic
175C8—341no—
176C8#1058757011yescharacteristic
177C8#1058760211yescharacteristic
178C22—161no—
179C22—161no—
180C22—161no—
181C22—2721no—
182C22—2721no—
183C22—2721no—
184C22—172no—
185C22—341no—
186C22—341no—
187C22D16×D1711yescharacteristic
188C4—161no—
189C4—2721no—
190C4—341no—
191C4#1176304411yescharacteristic
192C4#1176324011yescharacteristic
193C2—321no—
194C2—5441no—
195C2—342no—
196C2#1453086911yescharacteristic
197C2D17×D3211yescharacteristic
198C2#1453109211yescharacteristic
subgroupG/H
centerC22D16×D17
commutator, cosocleC2×C16×C17C23
FrattiniC2×C16C22×D17
FittingC17×#1415C2
socleC22×C17C2×D16
hypercenter#1415D17
hypocenterC17#13694
LCSG ▷ C2×C16×C17 ▷ C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
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×#11762644C2semidirect
2. C2×C32×D17C2semidirect
3. #14530871C2semidirect
4. #14530867C2semidirect
5. #14526983C2semidirect
6. #14526963C2semidirect
7. C17×#1415C2semidirect
39. #10587465D4semidirect
85. #1415D17semidirect
95. C2×D17D32semidirect
139. C17#13694semidirect

Maximal subgroups

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

subgroupindex
C2×#117626442
C2×C32×D172
#145308712
#145308672
#145269832
#145269632
C17×#14152
#1369417