Finite Group Databasebeta

← #17959931

Subgroups — #17959931

Order 4352.

310 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 86 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#14545143C211yesmaximal, characteristic
2#14544329C211yesmaximal, characteristic
3#14543803C212yesmaximal, complemented
4#14543799C212yesmaximal, complemented
5#14539367C211yesmaximal, characteristic
6#11763810—21no—
7#11763730C2212yes—
8#11763704—21no—
9C4×#63216—21no—
10#11763673C2212yes—
11#11763672—21no—
12#11763363—21no—
13#11763213C2211yescharacteristic
14#11763187C2211yescharacteristic
15#11763158—21no—
16#11763051C411yescharacteristic
17#11763049—21no—
18#11763047C411yescharacteristic
19C4×Dic68C411yescharacteristic
20C4×#63231—21no—
21C4×C8×D17C2211yescharacteristic
22C4×Q16×C17C411yescharacteristic
23C2×#63242—41no—
24C2×Q16×C17C2×C411yescharacteristic
25C4×Q8×C17—21no—
26#10587632—21no—
27#10587630—21no—
28C2×#63231—21no—
29C2×Dic68C2×C411yescharacteristic
30C2×C8×D17C2×C411yescharacteristic
31C2×C8×D17D411yescharacteristic
32#10587583—21no—
33#10587582—41no—
34#10587575—41no—
35#10587574—21no—
36#10587558—41no—
37C42×D17D411yescharacteristic
38C4×Dic34—21no—
39C4×Dic34—41no—
40#10587544—41no—
41C4⋊#3624—22no—
42C2×#63216—22no—
43C17×#107C2×C411yescharacteristic
44C17×#103—21no—
45C4×C8×C17C2×C411yescharacteristic
46#10587506—21no—
47#10587489C2×C411yescharacteristic
48#10587487—21no—
49C8×Dic17D411yescharacteristic
50C8×Dic17C2311yescharacteristic
51#10587481—21no—
52#10587478—21no—
53C4×#3622D411yescharacteristic
54C2×Q8×C17—21no—
55C2×C4×D17C22⋊C411yescharacteristic
56C2×C4×D17D811yescharacteristic
57C2×C4×D17SD1611yescharacteristic
58C2×Dic34—21no—
59C2×Dic34—41no—
60C2×#3624—42no—
61#63242—82no—
62Q16×C17—41no—
63C2×C8×C17C22⋊C411yescharacteristic
64C2×C8×C17C22×C411yescharacteristic
65C4⋊C4×C17—21no—
66C4⋊C4×C17—41no—
67C42×C17—41no—
68C42×C17C22⋊C411yescharacteristic
69#63231—42no—
70#63227—41no—
71#63227—41no—
72C4⋊Dic17—21no—
73C4⋊Dic17—41no—
74#63225—41no—
75#63225—41no—
76#63225—41no—
77#63225—41no—
78#63225—41no—
79C4×Dic17—41no—
80C4×Dic17D811yescharacteristic
81C4×Dic17SD1611yescharacteristic
82C4×Dic17C2×D411yescharacteristic
83C2×#3622C22⋊C411yescharacteristic
84C2×#3622C2×D411yescharacteristic
85Dic68—41no—
86C8×D17—22no—
87C8×D17—41no—
88#63216—42no—
89#11949—171nomaximal, Sylow
90C22×D17#10211yescharacteristic
91Q8×C17—41no—
92Q8×C17—41no—
93C2×C4×C17—41no—
94C2×C4×C17—41no—
95C2×C4×C17#10211yescharacteristic
96C2×C4×C17#10211yescharacteristic
97C2×C4×C17C2×C22⋊C411yescharacteristic
98C2×Dic17—41no—
99C2×Dic17—41no—
100C2×Dic17#10211yescharacteristic
101C2×Dic17C2×D811yescharacteristic
102C2×Dic17C2×SD1611yescharacteristic
103C4×D17—21no—
104C4×D17—21no—
105C4×D17—41no—
106C4×D17SD3212yes—
107C4×D17Q3212yes—
108Dic34—41no—
109Dic34—41no—
110Dic34—82no—
111#3624—82no—
112C8×C17—21no—
113C8×C17—21no—
114#3622—21no—
115#3622#13512yes—
116#3170—171no—
117#2162—171no—
118C2×#335—171no—
119#1365—172no—
120#1362—172no—
121C22×C17C2×#10211yescharacteristic
122C2×D17—21no—
123C2×D17—21no—
124C2×D17#35812yes—
125C4×C17—21no—
126C4×C17—81no—
127C4×C17—81no—
128C4×C17#35812yes—
129C4×C17#41311yescharacteristic
130C4×C17#41611yescharacteristic
131Dic17—21no—
132Dic17—21no—
133Dic17—81no—
134Dic17—81no—
135Dic17C2×SD3211yescharacteristic
136Dic17C2×Q3211yescharacteristic
137#533—341no—
138#500—171no—
139#494—171no—
140#487—341no—
141#467—171no—
142#467—171no—
143#467—341no—
144C4×Q16—171no—
145C4×Q16—341no—
146C4×Q16#59511yescharacteristic
147C2×C4⋊C8—341no—
148C2×C4×C8—171no—
149C4⋊C16—172no—
150C22⋊C16—341no—
151C4×C16—341no—
152#335—172no—
153#335—341no—
154C2×C17#154011yescharacteristic
155C2×C17C2×#35811yescharacteristic
156C2×C17#214811yescharacteristic
157D17—22no—
158C2×Q16—171no—
159C2×Q16—341no—
160C2×Q16C2×#59511yescharacteristic
161C22×C8—171no—
162C22×C8—171no—
163C22×C8—681no—
164C4⋊Q8—341no—
165C4⋊Q8—341no—
166#125—681no—
167C22⋊Q8—341no—
168C22⋊Q8—341no—
169C22⋊Q8—681no—
170C4×Q8—21no—
171C4×Q8—341no—
172C4×Q8—681no—
173#117—681no—
174C2×C42—171no—
175C2×C16—342no—
176#107—171no—
177#107—341no—
178#107C2×#59511yescharacteristic
179C4⋊C8—342no—
180C4⋊C8—681no—
181#103—21no—
182#103—341no—
183#103—341no—
184#103—341no—
185C4×C8—171no—
186C4×C8—171no—
187C4×C8—171no—
188C4×C8C2×#59511yescharacteristic
189C17#1194911yescharacteristic, complemented, Sylow
190C2×Q8—21no—
191C2×Q8—341no—
192C2×Q8—681no—
193C22×C4—171no—
194C22×C4—171no—
195C22×C4—171no—
196Q16—41no—
197Q16—681no—
198Q16—682no—
199C2×C8—171no—
200C2×C8—171no—
201C2×C8—342no—
202C2×C8—681no—
203C2×C8—682no—
204C2×C8—1362no—
205C2×C8C22⋊#59511yescharacteristic
206C2×C8C22×#59511yescharacteristic
207C4⋊C4—21no—
208C4⋊C4—41no—
209C4⋊C4—341no—
210C4⋊C4—681no—
211C4⋊C4—681no—
212C4⋊C4—681no—
213C4⋊C4—681no—
214C4⋊C4—681no—
215C4⋊C4—681no—
216C22⋊C4—681no—
217C22⋊C4—681no—
218C42—41no—
219C42—171no—
220C42—171no—
221C42—171no—
222C42—681no—
223C42C22⋊#59511yescharacteristic
224C16—682no—
225C23—171no—
226Q8—41no—
227Q8—41no—
228Q8—681no—
229Q8—681no—
230Q8—1362no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—171no—
234C2×C4—172no—
235C2×C4—172no—
236C2×C4—171no—
237C2×C4—171no—
238C2×C4—341no—
239C2×C4—341no—
240C2×C4—681no—
241C2×C4—681no—
242C2×C4—681no—
243C2×C4#1058754711yescharacteristic
244C2×C4#1058754711yescharacteristic
245C2×C4C2×C22⋊#59511yescharacteristic
246C8—21no—
247C8—21no—
248C8—172no—
249C8—341no—
250C8—1362no—
251C22—172no—
252C22—341no—
253C22—341no—
254C22C2×#1058754711yescharacteristic
255C4—21no—
256C4—81no—
257C4—81no—
258C4—171no—
259C4—171no—
260C4—341no—
261C4—341no—
262C4—1361no—
263C4—1361no—
264C4#1176372212yes—
265C4#1176379511yescharacteristic
266C4#1176379911yescharacteristic
267C2—342no—
268C2#1454428111yescharacteristic
269C2C2×#1176372211yescharacteristic
270C2#1454511111yescharacteristic
subgroupG/H
centerC2×C4#10587547
commutatorC2×C8×C17C22×C4
FrattiniC2×C8C22×#595
FittingC4×Q16×C17C4
socleC22×C17C2×#102
prime radicalC22×D17#102
cosocleC8×Dic17C23
hypercenterC4×Q16#595
hypocenterC17#11949
LCSG ▷ C2×C8×C17 ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
3. #14543803C2semidirect
4. #14543799C2semidirect
189. C17#11949semidirect

Maximal subgroups

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

subgroupindex
#145451432
#145443292
#145438032
#145437992
#145393672
#1194917