Finite Group Databasebeta

← #17960378

Subgroups — #17960378

Order 4352.

224 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 68 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#14544423C211yesmaximal, characteristic, complemented
2#14544416C211yesmaximal, characteristic
3#14543817C211yesmaximal, characteristic, complemented
4#14543741C211yesmaximal, characteristic, complemented
5#14543739C211yesmaximal, characteristic
6C16×#3624C211yesmaximal, characteristic, complemented
7#14530635C211yesmaximal, characteristic
8#11763859—21no—
9#11763843—21no—
10#11763695C2211yescharacteristic
11#11763672C2211yescharacteristic
12#11763672C2211yescharacteristic
13#11763659—21no—
14#11763657—21no—
15C8×#3624C2211yescharacteristic
16C2×#10587471C411yescharacteristic
17#11762903C2211yescharacteristic
18#11762891C2211yescharacteristic
19#11762612C411yescharacteristic
20#11762609C411yescharacteristic
21C16×Dic17C2211yescharacteristic
22C17×#367C411yescharacteristic
23C2×#63243—41no—
24C2×Dic68C2×C411yescharacteristic
25C2×D136C2×C411yescharacteristic
26#10587579—21no—
27#10587573—21no—
28#10587543—41no—
29#10587542—41no—
30C4⋊#3624—21no—
31C4⋊#3624—21no—
32C4⋊#3624—41no—
33C4×#3624D411yescharacteristic
34C4×#3624D411yescharacteristic
35C2×#63216—21no—
36C2×C16×C17C2×C411yescharacteristic
37C17×#107C2×C411yescharacteristic
38C17×#107C2×C411yescharacteristic
39C8×Dic17C2311yescharacteristic
40C2×#63214C2×C411yescharacteristic
41#10587481—21no—
42#10587480—21no—
43#10587471—22no—
44C2×D68—21no—
45C2×C4×D17—41no—
46C2×Dic34—21no—
47C2×#3624—21no—
48C2×#3624—41no—
49C2×#3624—41no—
50C2×#3624D811yescharacteristic
51C2×#3624D811yescharacteristic
52#63243—82no—
53C2×C8×C17C22×C411yescharacteristic
54C4⋊C4×C17—21no—
55C4⋊C4×C17—21no—
56#63227—41no—
57#63225—41no—
58C4×Dic17—41no—
59C4×Dic17C2×D411yescharacteristic
60C2×#3622#4111yescharacteristic
61Dic68—21no—
62Dic68—21no—
63D136—21no—
64D136—21no—
65#63216—22no—
66C16×C17M1612yescomplemented
67#63214—21no—
68#12082—171nomaximal, Sylow
69C22×D17—41no—
70C2×C4×C17—41no—
71C2×C4×C17—41no—
72C2×C4×C17C4×D411yescharacteristic
73C2×Dic17—41no—
74C2×Dic17C2×D811yescharacteristic
75C2×Dic17#13511yescharacteristic
76D68—41no—
77D68—41no—
78C4×D17—81no—
79C4×D17—81no—
80Dic34—41no—
81Dic34—41no—
82#3624—22no—
83#3624—21no—
84#3624—81no—
85#3624—81no—
86#3624SD3212yescomplemented
87C8×C17C2×M1611yescharacteristic
88C8×C17#13111yescharacteristic
89#3622—21no—
90C4×SD32—171no—
91#1591—171no—
92#1589—171no—
93#1372—171no—
94#1332—171no—
95#1331—171no—
96C8×C16—171no—
97C22×C17C4×D811yescharacteristic
98C2×D17—81no—
99C2×D17—81no—
100C2×D17—81no—
101C4×C17—81no—
102C4×C17—81no—
103C4×C17#43611yescharacteristic
104C4×C17#44311yescharacteristic
105Dic17—21no—
106Dic17—81no—
107Dic17C2×SD3211yescharacteristic
108Dic17#50811yescharacteristic
109C2×SD32—171no—
110#446—341no—
111C4×Q16—171no—
112C4×D8—171no—
113#436—341no—
114#367#59511yescharacteristic
115#358—171no—
116#357—171no—
117C4×C16—171no—
118C4×C16—171no—
119#335—171no—
120#335—171no—
121Q8⋊C8—341no—
122D4⋊C8—341no—
123C82—171no—
124C2×C17#158911yescharacteristic
125C2×C17C4×SD3211yescharacteristic
126C2×C17#217811yescharacteristic
127D17—161no—
128C2×Q16—171no—
129C2×D8—171no—
130C2×M16—681no—
131C4×Q8—341no—
132C4×D4—341no—
133SD32—342no—
134C2×C16—171no—
135C2×C16—341no—
136C2×C16C2×#59511yescharacteristic
137#107C2×#59511yescharacteristic
138#107C2×#59511yescharacteristic
139C4⋊C8—341no—
140C4⋊C8—341no—
141C4⋊C8—681no—
142#103—341no—
143#102—341no—
144C22⋊C8—681no—
145#97—681no—
146C4×C8—171no—
147C4×C8—171no—
148C4×C8—171no—
149C17#1208211yescharacteristic, complemented, Sylow
150C2×Q8—341no—
151C2×D4—341no—
152C22×C4—681no—
153Q16—341no—
154Q16—341no—
155D8—341no—
156D8—341no—
157M16—1362no—
158C2×C8—171no—
159C2×C8—171no—
160C2×C8—171no—
161C2×C8—341no—
162C2×C8—681no—
163C2×C8—681no—
164C2×C8C22×#59511yescharacteristic
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—681no—
168C22⋊C4—681no—
169C42—171no—
170C42—681no—
171C16—342no—
172C16—341no—
173C16#6324312yescomplemented
174C23—681no—
175Q8—681no—
176Q8—681no—
177D4—681no—
178D4—681no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—171no—
182C2×C4—171no—
183C2×C4—681no—
184C2×C4—1361no—
185C2×C4—1361no—
186C2×C4D4×#59511yescharacteristic
187C8—172no—
188C8—341no—
189C8—342no—
190C8—341no—
191C8—1361no—
192C8—1361no—
193C8C2×#6324311yescharacteristic
194C8#1058768011yescharacteristic
195C22—1361no—
196C22—1361no—
197C22—1361no—
198C22D8×#59511yescharacteristic
199C4—81no—
200C4—81no—
201C4—171no—
202C4—171no—
203C4—341no—
204C4—1361no—
205C4#1176384311yescharacteristic
206C4#1176385311yescharacteristic
207C2—2721no—
208C2#1454441611yescharacteristic
209C2SD32×#59511yescharacteristic
210C2#1454518411yescharacteristic
subgroupG/H
centerC22D8×#595
commutatorC2×C8×C17C22×C4
FrattiniC2×C8C22×#595
FittingC17×#367C4
socleC22×C17C4×D8
prime radicalC2×D136C2×C4
cosocleC8×Dic17C23
hypercenter#367#595
hypocenterC17#12082
LCSG ▷ C2×C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #367

Complements

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

NH ≅ G/Ntype
1. #14544423C2semidirect
3. #14543817C2semidirect
4. #14543741C2semidirect
6. C16×#3624C2semidirect
66. C16×C17M16semidirect
86. #3624SD32semidirect
149. C17#12082semidirect
173. C16#63243semidirect

Maximal subgroups

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

subgroupindex
#145444232
#145444162
#145438172
#145437412
#145437392
C16×#36242
#145306352
#1208217