Finite Group Databasebeta

← #16946244

Subgroups — #16946244

Order 4352.

240 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 75 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
1C4×#10587497C211yesmaximal, characteristic
2#14527668C211yesmaximal, characteristic, complemented
3D8×#3622C211yesmaximal, characteristic, complemented
4#14526857C211yesmaximal, characteristic, complemented
5#14526746C211yesmaximal, characteristic, complemented
6#14526703C211yesmaximal, characteristic, complemented
7C17×#1331C211yesmaximal, characteristic, complemented
8C2×#10587497C411yescharacteristic
9C4×D136C2211yescharacteristic
10#11762886—21no—
11D4×#3622—21no—
12#11762634C411yescharacteristic
13#11762610C411yescharacteristic
14#11762609C411yescharacteristic
15C4×#63214C2211yescharacteristic
16#11762562C2211yescharacteristic
17D4⋊#3622—21no—
18#11762536—21no—
19C8×#3622C2211yescharacteristic
20C4×D8×C17C2211yescharacteristic
21C4×C16×C17C2211yescharacteristic
22C17×#335C2211yescharacteristic
23C2×D8×C17C2×C411yescharacteristic
24C4×D4×C17—21no—
25C22×#3622—41no—
26C2×D136C2×C411yescharacteristic
27C2×#63218—41no—
28C4×D68—21no—
29C2×C16×C17—21no—
30C17×#107C2×C411yescharacteristic
31C17×C4⋊C8—21no—
32C17×#102—21no—
33C4×C8×C17C2311yescharacteristic
34C22⋊#3622—41no—
35#10587497—22no—
36#10587492—21no—
37#10587491—41no—
38#10587489C2×C411yescharacteristic
39C2×#63214C2×C411yescharacteristic
40C2×#63214C2×C411yescharacteristic
41C4⋊#3622—21no—
42C4×#3622D411yescharacteristic
43C4×#3622D411yescharacteristic
44C2×D4×C17—21no—
45C22×C4×C17—41no—
46C2×D68—21no—
47C2×C4×D17—41no—
48D8×C17—21no—
49D8×C17M1612yescomplemented
50C2×C8×C17—41no—
51C2×C8×C17C22×C411yescharacteristic
52C2×C8×C17#4111yescharacteristic
53C4⋊C4×C17—21no—
54C22⋊C4×C17—41no—
55C42×C17C2×D411yescharacteristic
56#63227—41no—
57C4⋊Dic17—21no—
58C2×#3622—21no—
59C2×#3622—41no—
60C2×#3622—82no—
61C2×#3622D811yescharacteristic
62C2×#3622D811yescharacteristic
63D136—21no—
64D136—21no—
65#63218—82no—
66C16×C17—41no—
67#63214—21no—
68#63214—21no—
69#12073—171nomaximal, Sylow
70C23×C17—41no—
71C22×D17—41no—
72D4×C17—22no—
73D4×C17—41no—
74C2×C4×C17—41no—
75C2×C4×C17—81no—
76C2×C4×C17—81no—
77C2×C4×C17C4×D411yescharacteristic
78C2×C4×C17C2×D811yescharacteristic
79C2×C4×C17#13511yescharacteristic
80C2×Dic17—41no—
81D68—41no—
82D68—41no—
83C4×D17—81no—
84C4×D17—81no—
85C8×C17—21no—
86C8×C17—81no—
87C8×C17C2×M1611yescharacteristic
88C8×C17#13111yescharacteristic
89#3622—22no—
90#3622—21no—
91#3622—21no—
92#3622—81no—
93C4×D16—171no—
94#1589—171no—
95C8×D8—171no—
96#1372—171no—
97#1331—171no—
98#1331D1711yescharacteristic, complemented
99#1312—171no—
100C22×C17—42no—
101C22×C17—81no—
102C22×C17—81no—
103C22×C17C4×D811yescharacteristic
104C2×D17—81no—
105C2×D17—81no—
106C2×D17—81no—
107C4×C17—21no—
108C4×C17—81no—
109C4×C17#43511yescharacteristic
110C4×C17#44411yescharacteristic
111C4×C17#50911yescharacteristic
112C4×C17#50911yescharacteristic
113Dic17—81no—
114C2×D16—171no—
115C4×D8—171no—
116C4×D8C2×D1711yescharacteristic
117#436—341no—
118C8×D4—341no—
119#366—171no—
120#357—171no—
121#357—171no—
122C4×C16—171no—
123C4×C16C2×D1711yescharacteristic
124#335—171no—
125#335C2×D1711yescharacteristic
126D4⋊C8—341no—
127D4⋊C8—341no—
128C82—171no—
129C2×C17—82no—
130C2×C17#158111yescharacteristic
131C2×C17#217711yescharacteristic
132C2×C17#217811yescharacteristic
133D17—161no—
134C2×D8—171no—
135C2×D8C4×D1711yescharacteristic
136C2×M16—681no—
137C22×C8—681no—
138C4×D4—21no—
139C4×D4—341no—
140D16—342no—
141C2×C16—21no—
142C2×C16—171no—
143C2×C16—171no—
144#107—171no—
145#107C4×D1711yescharacteristic
146C4⋊C8—21no—
147C4⋊C8—341no—
148#102—21no—
149#102—341no—
150C22⋊C8—681no—
151C22⋊C8—681no—
152C4×C8—171no—
153C4×C8—171no—
154C4×C8C22×D1711yescharacteristic
155C17#1207311yescharacteristic, complemented, Sylow
156C2×D4—21no—
157C2×D4—341no—
158C22×C4—41no—
159C22×C4—681no—
160D8—21no—
161D8—341no—
162D8—341no—
163D8#6321812yescomplemented
164M16—1362no—
165C2×C8—41no—
166C2×C8—171no—
167C2×C8—171no—
168C2×C8—341no—
169C2×C8—681no—
170C2×C8—1362no—
171C2×C8C2×C4×D1711yescharacteristic
172C2×C8#6325411yescharacteristic
173C4⋊C4—21no—
174C4⋊C4—341no—
175C22⋊C4—41no—
176C22⋊C4—681no—
177C42D4×D1711yescharacteristic
178C16—41no—
179C16—341no—
180C16—341no—
181C23—41no—
182C23—681no—
183D4—22no—
184D4—41no—
185D4—681no—
186D4—681no—
187C2×C4—41no—
188C2×C4—81no—
189C2×C4—81no—
190C2×C4—681no—
191C2×C4—1361no—
192C2×C4—1361no—
193C2×C4#1058756711yescharacteristic
194C2×C4D8×D1711yescharacteristic
195C2×C4#1058760211yescharacteristic
196C8—21no—
197C8—81no—
198C8—342no—
199C8—341no—
200C8—341no—
201C8—1361no—
202C8C2×#6321811yescharacteristic
203C8#1058759311yescharacteristic
204C22—42no—
205C22—81no—
206C22—81no—
207C22—1361no—
208C22—1361no—
209C22—1361no—
210C22#1176288911yescharacteristic
211C4—21no—
212C4—81no—
213C4—1361no—
214C4#1176287711yescharacteristic
215C4#1176292811yescharacteristic
216C4#1176324311yescharacteristic
217C4#1176324611yescharacteristic
218C2—82no—
219C2—2721no—
220C2#1452761011yescharacteristic
221C2#1453065711yescharacteristic
222C2#1453066211yescharacteristic
subgroupG/H
centerC2×C4D8×D17
commutatorC2×C8×C17C22×C4
FrattiniC4×C8C22×D17
FittingC17×#1331C2
socleC22×C17C4×D8
prime radicalC2×#10587497C4
cosocleC4×C8×C17C23
hypercenter#1331D17
hypocenterC17#12073
LCSG ▷ C2×C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8 ◁ #1331

Complements

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

NH ≅ G/Ntype
2. #14527668C2semidirect
3. D8×#3622C2semidirect
4. #14526857C2semidirect
5. #14526746C2semidirect
6. #14526703C2semidirect
7. C17×#1331C2semidirect
49. D8×C17M16semidirect
98. #1331D17semidirect
155. C17#12073semidirect
163. D8#63218semidirect

Maximal subgroups

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

subgroupindex
C4×#105874972
#145276682
D8×#36222
#145268572
#145267462
#145267032
C17×#13312
#1207317