Finite Group Databasebeta

← #16939215

Subgroups — #16939215

Order 4352.

236 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 67 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#14527558C211yesmaximal, characteristic
2#14527515C211yesmaximal, characteristic
3#14527482C211yesmaximal, characteristic
4#14527256C211yesmaximal, characteristic
5#14526694C211yesmaximal, characteristic
6#14526647C211yesmaximal, characteristic
7C17×#1290C211yesmaximal, characteristic
8#11763366C2211yescharacteristic
9#11762866C2211yescharacteristic
10#11762862C2211yescharacteristic
11#11762833C2211yescharacteristic
12#11762561—22no—
13#11762557—21no—
14#11762556—21no—
15#11762554—21no—
16#11762554—21no—
17#11762539—22no—
18C17×#432C2211yescharacteristic
19C17×#432C2211yescharacteristic
20C2×C17×C4⋊C8C2211yescharacteristic
21C22×C8×C17—21no—
22C2×C42×C17C2311yescharacteristic
23#10587612—21no—
24#10587610—21no—
25#10587610—21no—
26C2×#63223—21no—
27#10587556—21no—
28#10587555D411yescharacteristic
29#10587555D411yescharacteristic
30C4×Dic34—21no—
31C4×Dic34—21no—
32C17×C4⋊C8—21no—
33C17×C4⋊C8—21no—
34C17×C4⋊C8—21no—
35C17×C4⋊C8—21no—
36C17×C22⋊C8—21no—
37C17×C22⋊C8—21no—
38C17×#97—21no—
39C17×#97—21no—
40C22⋊#3622—21no—
41C22⋊#3622—21no—
42C4⋊#3622—21no—
43C4⋊#3622—21no—
44C4⋊#3622—21no—
45C4⋊#3622—21no—
46#10587474—21no—
47C4×#3622D412yes—
48C22×C4×C17#4111yescharacteristic
49C22×C4×C17#4111yescharacteristic
50C22×C4×C17#4111yescharacteristic
51C2×Dic34—21no—
52C2×Dic34—21no—
53C2×C8×C17—41no—
54C2×C8×C17—41no—
55C2×C8×C17—41no—
56C2×C8×C17—81no—
57C42×C17C2×D411yescharacteristic
58C42×C17C2×D411yescharacteristic
59C42×C17#4111yescharacteristic
60C42×C17#4111yescharacteristic
61C22⋊Dic17—41no—
62C4⋊Dic17—21no—
63C4⋊Dic17—21no—
64C4⋊Dic17—21no—
65C4⋊Dic17—21no—
66#63225—41no—
67#63225—41no—
68C4×Dic17—41no—
69#63223—81no—
70C2×#3622—22no—
71C2×#3622—41no—
72C2×#3622—41no—
73#10646—171nomaximal, Sylow
74C23×C17#12611yescharacteristic
75C2×C4×C17—21no—
76C2×C4×C17—21no—
77C2×C4×C17—41no—
78C2×C4×C17—41no—
79C2×C4×C17#12111yescharacteristic
80C2×C4×C17#12311yescharacteristic
81C2×C4×C17#12311yescharacteristic
82C2×C4×C17#12311yescharacteristic
83C2×C4×C17#12411yescharacteristic
84C2×C4×C17#12611yescharacteristic
85C2×Dic17—41no—
86C2×Dic17—41no—
87Dic34—41no—
88Dic34—41no—
89Dic34—81no—
90C8×C17—81no—
91C8×C17—81no—
92C8×C17—81no—
93#3622—42no—
94#3622—81no—
95#3622—81no—
96#1571—171no—
97#1559—171no—
98#1552—171no—
99#1497—171no—
100#1307—171no—
101#1290D1711yescharacteristic
102#1287—171no—
103C22×C17—21no—
104C22×C17—21no—
105C22×C17—21no—
106C22×C17#39711yescharacteristic
107C4×C17—21no—
108C4×C17—21no—
109C4×C17—21no—
110C4×C17—21no—
111C4×C17—21no—
112C4×C17#47211yescharacteristic
113C4×C17#47311yescharacteristic
114Dic17—81no—
115Dic17—81no—
116#533—171no—
117#432—171no—
118#432C2×D1711yescharacteristic
119#432C2×D1711yescharacteristic
120#431—171no—
121#423—171no—
122C2×C4⋊C8C2×D1711yescharacteristic
123#335—342no—
124#333—341no—
125#332—341no—
126#332—341no—
127#332—341no—
128Q8⋊C8—342no—
129C2×C17—41no—
130C2×C17#207811yescharacteristic
131C2×C17#208011yescharacteristic
132C2×C17#208211yescharacteristic
133C2×M16—341no—
134C22×C8—21no—
135C4⋊Q8—171no—
136C4⋊Q8—171no—
137#125—341no—
138C22⋊Q8—341no—
139C22⋊Q8—341no—
140C4×Q8—341no—
141C4×Q8—341no—
142#117—341no—
143C2×C42C22×D1711yescharacteristic
144C4⋊C8—21no—
145C4⋊C8—21no—
146C4⋊C8—21no—
147C4⋊C8—21no—
148C4⋊C8—341no—
149C4⋊C8—341no—
150C4⋊C8—341no—
151C4⋊C8—341no—
152C22⋊C8—21no—
153C22⋊C8—21no—
154C22⋊C8—341no—
155C22⋊C8—341no—
156#97—21no—
157#97—21no—
158#97—341no—
159C4×C8—172no—
160C17#1064611yescharacteristic, complemented, Sylow
161C2×Q8—341no—
162C2×Q8—341no—
163C22×C4#6325211yescharacteristic
164C22×C4#6325411yescharacteristic
165C22×C4#6325611yescharacteristic
166M16—1361no—
167C2×C8—41no—
168C2×C8—41no—
169C2×C8—41no—
170C2×C8—81no—
171C2×C8—342no—
172C2×C8—681no—
173C2×C8—681no—
174C4⋊C4—341no—
175C4⋊C4—341no—
176C4⋊C4—341no—
177C4⋊C4—341no—
178C4⋊C4—681no—
179C4⋊C4—681no—
180C22⋊C4—681no—
181C42—681no—
182C42#6325211yescharacteristic
183C42#6325211yescharacteristic
184C42D4×D1711yescharacteristic
185C42D4×D1711yescharacteristic
186C23#1058758411yescharacteristic
187Q8—681no—
188Q8—681no—
189Q8—1361no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—681no—
195C2×C4—681no—
196C2×C4#1058756211yescharacteristic
197C2×C4#1058756911yescharacteristic
198C2×C4#1058757011yescharacteristic
199C2×C4#1058757111yescharacteristic
200C2×C4#1058758011yescharacteristic
201C2×C4#1058758011yescharacteristic
202C8—81no—
203C8—81no—
204C8—81no—
205C8—682no—
206C8—1361no—
207C8—1361no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22#1176273811yescharacteristic
212C4—21no—
213C4—21no—
214C4—21no—
215C4—21no—
216C4—21no—
217C4—1361no—
218C4—1361no—
219C4#1176307811yescharacteristic
220C4#1176308311yescharacteristic
221C2—41no—
222C2#1453022811yescharacteristic
223C2#1453024011yescharacteristic
224C2#1453025311yescharacteristic
subgroupG/H
centerC22#11762738
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#1290C2
socleC22×C17#397
prime radicalC23×C17#126
hypercenter#1290D17
hypocenterC17#10646
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1290

Complements

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

NH ≅ G/Ntype
160. C17#10646semidirect

Maximal subgroups

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

subgroupindex
#145275582
#145275152
#145274822
#145272562
#145266942
#145266472
C17×#12902
#1064617