Finite Group Databasebeta

← #17949084

Subgroups — #17949084

Order 4352.

244 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 48 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#14544678C211yesmaximal, characteristic
2#14544038C211yesmaximal, characteristic
3#14527117C211yesmaximal, characteristic
4#11763830—21no—
5C2×#10587543C411yescharacteristic
6C2×#10587543C411yescharacteristic
7#11763675—21no—
8#11763675—21no—
9#11763654C412yes—
10#11763653—21no—
11C2×#10587578C2211yescharacteristic
12#11762863—21no—
13#11762535C411yescharacteristic
14#11762532—21no—
15C17×#324C411yescharacteristic
16C22×C4×D17C2×C411yescharacteristic
17C22×#3624—21no—
18C22×#3624—21no—
19C2×C4⋊C4×C17C2×C411yescharacteristic
20C2×#63227D411yescharacteristic
21C2×#63227Q811yescharacteristic
22C2×C4⋊Dic17C2×C411yescharacteristic
23C2×C4×Dic17D411yescharacteristic
24C2×C4×Dic17D411yescharacteristic
25#10587578—41no—
26#10587578—41no—
27C22⋊#3624—22no—
28#10587543—41no—
29#10587543—41no—
30#10587542—41no—
31C4⋊#3624—41no—
32C17×C22⋊C8—21no—
33C22⋊#3622—21no—
34#10587486—41no—
35#10587485—41no—
36C23×D17C4⋊C411yescharacteristic
37C22×C4×C17C4211yescharacteristic
38C22×C4×C17C22⋊C411yescharacteristic
39C22×C4×C17C4⋊C411yescharacteristic
40C22×Dic17C22⋊C411yescharacteristic
41C22×Dic17C22⋊C411yescharacteristic
42C22×Dic17C4⋊C411yescharacteristic
43C2×C4×D17—21no—
44C2×C4×D17—21no—
45C2×C4×D17—41no—
46C2×C4×D17—41no—
47C2×#3624—41no—
48C2×#3624—41no—
49C2×#3624—41no—
50C2×#3624—41no—
51C2×#3624—42no—
52C2×#3624—41no—
53C2×#3624—41no—
54C2×C8×C17—41no—
55C4⋊C4×C17—41no—
56#63227—41no—
57#63227—41no—
58C4⋊Dic17—41no—
59C4×Dic17—21no—
60C4×Dic17—21no—
61C4×Dic17—21no—
62C4×Dic17—21no—
63C2×#3622—41no—
64#7327—171nomaximal, Sylow
65C23×C17#9511yescharacteristic
66C22×D17—21no—
67C22×D17—21no—
68C22×D17—21no—
69C22×D17—41no—
70C22×D17—41no—
71C2×C4×C17—21no—
72C2×C4×C17—21no—
73C2×C4×C17—21no—
74C2×C4×C17—21no—
75C2×C4×C17—21no—
76C2×C4×C17—41no—
77C2×C4×C17—41no—
78C2×Dic17—21no—
79C2×Dic17—21no—
80C2×Dic17—21no—
81C2×Dic17—21no—
82C2×Dic17—41no—
83C2×Dic17—41no—
84C2×Dic17#9911yescharacteristic
85C2×Dic17#9911yescharacteristic
86C4×D17—42no—
87C4×D17—42no—
88#3624—81no—
89#3624—81no—
90#3624—82no—
91C8×C17—81no—
92#3622—81no—
93#1818—171no—
94#1464—171no—
95#1464—171no—
96C22×C17—21no—
97C22×C17—21no—
98C22×C17#34211yescharacteristic
99C22×C17#34411yescharacteristic
100C22×C17#34411yescharacteristic
101C2×D17—41no—
102C2×D17—41no—
103C2×D17—41no—
104C2×D17—81no—
105C2×D17—81no—
106C4×C17—41no—
107C4×C17—41no—
108C4×C17—41no—
109Dic17—21no—
110Dic17—21no—
111Dic17—41no—
112Dic17—41no—
113C2×#117—171no—
114#432—341no—
115#432—341no—
116C2×C22⋊C8—171no—
117C2×C22⋊C8—171no—
118#336—341no—
119#336—341no—
120#324—172no—
121#324—171no—
122#324#59511yescharacteristic
123#323—341no—
124#323—341no—
125C2×C17—21no—
126C2×C17—21no—
127C2×C17#130611yescharacteristic
128C2×C17#139511yescharacteristic
129C2×C17#139511yescharacteristic
130D17—81no—
131C23×C4—171no—
132C22×C8—341no—
133C22×C8—341no—
134#117—681no—
135#117—681no—
136C2×C4⋊C4—171no—
137C2×C4⋊C4C2×#59511yescharacteristic
138C2×C22⋊C4—171no—
139C2×C22⋊C4—171no—
140C2×C42—171no—
141C2×C42—171no—
142C4⋊C8—681no—
143C4⋊C8—681no—
144C22⋊C8—21no—
145C22⋊C8—342no—
146C22⋊C8—341no—
147C22⋊C8—681no—
148C22⋊C8—681no—
149#97—681no—
150#97—681no—
151C17#732711yescharacteristic, complemented, Sylow
152C24—171no—
153C22×C4—171no—
154C22×C4—171no—
155C22×C4—171no—
156C22×C4—341no—
157C22×C4—341no—
158C22×C4—681no—
159C22×C4—681no—
160C22×C4C4×#59511yescharacteristic
161C22×C4C4⋊#59511yescharacteristic
162C22×C4C22⋊#59511yescharacteristic
163C2×C8—41no—
164C2×C8—681no—
165C2×C8—681no—
166C2×C8—681no—
167C2×C8—682no—
168C2×C8—681no—
169C2×C8—681no—
170C2×C8—681no—
171C2×C8—681no—
172C4⋊C4—41no—
173C4⋊C4—681no—
174C22⋊C4—681no—
175C22⋊C4—681no—
176C42—341no—
177C42—341no—
178C42—341no—
179C42—341no—
180C23—341no—
181C23—341no—
182C23—341no—
183C23—681no—
184C23—681no—
185C23(C2×#595)⋊C411yescharacteristic
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—171no—
194C2×C4—171no—
195C2×C4—341no—
196C2×C4—341no—
197C2×C4—341no—
198C2×C4—341no—
199C2×C4—682no—
200C2×C4—682no—
201C2×C4—681no—
202C2×C4—681no—
203C8—81no—
204C8—1361no—
205C8—1361no—
206C8—1361no—
207C8—1362no—
208C22—21no—
209C22—21no—
210C22—681no—
211C22—681no—
212C22—681no—
213C22—1361no—
214C22—1361no—
215C22#1176368611yescharacteristic
216C22#1176369111yescharacteristic
217C22#1176369211yescharacteristic
218C4—41no—
219C4—41no—
220C4—41no—
221C4—341no—
222C4—341no—
223C4—681no—
224C4—681no—
225C2—21no—
226C2—21no—
227C2—1361no—
228C2#1454368811yescharacteristic
229C2#1454388311yescharacteristic
230C2#1454388611yescharacteristic
subgroupG/H
centerC22#11763686
commutatorC22×C4×C17C42
FrattiniC2×C4⋊C4C2×#595
FittingC17×#324C4
socleC22×C17#342
prime radicalC23×D17C4⋊C4
cosocleC2×#10587578C22
hypercenter#324#595
hypocenterC17#7327
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #324

Complements

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

NH ≅ G/Ntype
151. C17#7327semidirect

Maximal subgroups

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

subgroupindex
#145446782
#145440382
#145271172
#732717