Finite Group Databasebeta

← #16938271

Subgroups — #16938271

Order 4352.

344 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 81 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#14539930C211yesmaximal, characteristic
2#14529773C211yesmaximal, characteristic
3#14527572C211yesmaximal, characteristic
4#14527521C211yesmaximal, characteristic
5#14527470C211yesmaximal, characteristic
6#14527206C211yesmaximal, characteristic
7C17×#1299C211yesmaximal, characteristic
8#11763366C2211yescharacteristic
9C2×#10587555C2211yescharacteristic
10#11763207—21no—
11#11763160—21no—
12#11763140—22no—
13#11763095—21no—
14#11763095—21no—
15#11762862C2211yescharacteristic
16#11762833C2211yescharacteristic
17#11762577—22no—
18#11762561—21no—
19#11762559—21no—
20#11762556—21no—
21#11762554—21no—
22#11762554—22no—
23#11762541—22no—
24C17×#431C2211yescharacteristic
25C17×#423C2211yescharacteristic
26C4×M16×C17C2211yescharacteristic
27C22×Dic34—21no—
28C2×M16×C17—21no—
29C2×M16×C17—21no—
30C2×C42×C17C2311yescharacteristic
31#10587612—21no—
32C2×C4⋊Dic17—21no—
33C2×C4⋊Dic17D412yes—
34#10587610—21no—
35#10587610—21no—
36C2×#63223—21no—
37#10587556—21no—
38#10587555—21no—
39#10587555—21no—
40#10587555—21no—
41#10587555—21no—
42#10587555D411yescharacteristic
43#10587555D411yescharacteristic
44C4×Dic34—21no—
45C4×Dic34—21no—
46C17×C4⋊C8—21no—
47C17×C4⋊C8—21no—
48C17×C4⋊C8D411yescharacteristic
49C17×C4⋊C8D411yescharacteristic
50C17×C22⋊C8—21no—
51C17×#97—21no—
52C4×C8×C17—21no—
53C4×C8×C17—21no—
54C22⋊#3622—21no—
55#10587488—22no—
56#10587488—22no—
57#10587487—22no—
58#10587487—22no—
59C4⋊#3622—21no—
60C4⋊#3622—21no—
61C4⋊#3622D412yes—
62C4×#3622—21no—
63C22×C4×C17C2×D411yescharacteristic
64C22×C4×C17#4111yescharacteristic
65C22×C4×C17#4111yescharacteristic
66C22×Dic17—22no—
67C2×Dic34—21no—
68C2×Dic34—21no—
69C2×Dic34—41no—
70C2×Dic34—41no—
71C2×Dic34—82no—
72M16×C17—22no—
73M16×C17—41no—
74M16×C17—81no—
75C2×C8×C17—21no—
76C2×C8×C17—21no—
77C2×C8×C17—41no—
78C2×C8×C17—41no—
79C42×C17C2×D411yescharacteristic
80C42×C17C2×D411yescharacteristic
81C42×C17C2×D411yescharacteristic
82C42×C17#4111yescharacteristic
83C22⋊Dic17—41no—
84C4⋊Dic17—22no—
85C4⋊Dic17—21no—
86C4⋊Dic17—21no—
87C4⋊Dic17—22no—
88C4⋊Dic17—21no—
89C4⋊Dic17—21no—
90C4⋊Dic17—41no—
91C4⋊Dic17—41no—
92#63225—41no—
93#63225—41no—
94C4×Dic17—41no—
95#63223—42no—
96C2×#3622—22no—
97C2×#3622—41no—
98#10494—171nomaximal, Sylow
99C23×C17#12311yescharacteristic
100C2×C4×C17—21no—
101C2×C4×C17—21no—
102C2×C4×C17—21no—
103C2×C4×C17—22no—
104C2×C4×C17—21no—
105C2×C4×C17#12011yescharacteristic
106C2×C4×C17#12111yescharacteristic
107C2×C4×C17#12111yescharacteristic
108C2×C4×C17#12111yescharacteristic
109C2×C4×C17#12311yescharacteristic
110C2×C4×C17#12411yescharacteristic
111C2×Dic17—41no—
112C2×Dic17—41no—
113C2×Dic17—42no—
114C2×Dic17—82no—
115Dic34—41no—
116Dic34—41no—
117Dic34—41no—
118Dic34—41no—
119Dic34—82no—
120Dic34—82no—
121C8×C17—42no—
122C8×C17—41no—
123C8×C17—41no—
124C8×C17—81no—
125#3622—42no—
126#3622—81no—
127#3229—171no—
128#1997—171no—
129#1574—171no—
130#1561—171no—
131#1549—171no—
132#1485—171no—
133#1299D1711yescharacteristic
134C22×C17—21no—
135C22×C17—21no—
136C22×C17—21no—
137C22×C17#39411yescharacteristic
138C4×C17—21no—
139C4×C17—21no—
140C4×C17—21no—
141C4×C17#45411yescharacteristic
142C4×C17#45611yescharacteristic
143C4×C17#47111yescharacteristic
144C4×C17#47112yes—
145C4×C17#47311yescharacteristic
146Dic17—81no—
147Dic17—81no—
148Dic17—82no—
149#533—171no—
150C2×C4⋊Q8—171no—
151#498—341no—
152#487—341no—
153#483—342no—
154#475—341no—
155#475—341no—
156#431—171no—
157#431C2×D1711yescharacteristic
158#423—171no—
159#423C2×D1711yescharacteristic
160C4×M16C2×D1711yescharacteristic
161#343—342no—
162#335—341no—
163#334—341no—
164#332—342no—
165#332—341no—
166#332—341no—
167Q8⋊C8—342no—
168C2×C17—41no—
169C2×C17#203811yescharacteristic
170C2×C17#204611yescharacteristic
171C2×C17#205211yescharacteristic
172C22×Q8—341no—
173C2×M16—21no—
174C2×M16—21no—
175C2×M16—341no—
176C4⋊Q8—171no—
177C4⋊Q8—171no—
178C4⋊Q8—341no—
179C4⋊Q8—341no—
180C4⋊Q8—341no—
181C4⋊Q8—341no—
182#125—341no—
183C22⋊Q8—341no—
184C22⋊Q8—341no—
185C4×Q8—341no—
186C4×Q8—341no—
187#117—341no—
188C2×C4⋊C4—172no—
189C2×C4⋊C4—341no—
190C2×C42C22×D1711yescharacteristic
191#106—342no—
192#106—342no—
193C4⋊C8—21no—
194C4⋊C8—21no—
195C4⋊C8—172no—
196C4⋊C8—341no—
197C4⋊C8—341no—
198C4⋊C8D6811yescharacteristic
199C4⋊C8D6811yescharacteristic
200#103—342no—
201#103—342no—
202C22⋊C8—21no—
203C22⋊C8—341no—
204#97—21no—
205C4×C8—21no—
206C4×C8—21no—
207C4×C8—341no—
208C17#1049411yescharacteristic, complemented, Sylow
209C2×Q8—341no—
210C2×Q8—341no—
211C2×Q8—681no—
212C2×Q8—681no—
213C2×Q8—1362no—
214C22×C4—342no—
215C22×C4#6325211yescharacteristic
216C22×C4D4×D1711yescharacteristic
217C22×C4#6325611yescharacteristic
218M16—22no—
219M16—41no—
220M16—81no—
221M16—682no—
222C2×C8—21no—
223C2×C8—21no—
224C2×C8—41no—
225C2×C8—41no—
226C2×C8—342no—
227C2×C8—681no—
228C4⋊C4—342no—
229C4⋊C4—341no—
230C4⋊C4—342no—
231C4⋊C4—341no—
232C4⋊C4—341no—
233C4⋊C4—341no—
234C4⋊C4—681no—
235C4⋊C4—681no—
236C4⋊C4—681no—
237C4⋊C4—681no—
238C22⋊C4—681no—
239C42—681no—
240C42C2×D6811yescharacteristic
241C42#6325211yescharacteristic
242C42D4×D1711yescharacteristic
243C42D4×D1711yescharacteristic
244C23#1058758011yescharacteristic
245Q8—681no—
246Q8—681no—
247Q8—681no—
248Q8—681no—
249Q8—1362no—
250Q8—1362no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—22no—
255C2×C4—21no—
256C2×C4—681no—
257C2×C4—681no—
258C2×C4—682no—
259C2×C4—1362no—
260C2×C4#1058756111yescharacteristic
261C2×C4#1058756811yescharacteristic
262C2×C4#1058757011yescharacteristic
263C2×C4#1058757011yescharacteristic
264C2×C4#1058758011yescharacteristic
265C2×C4#1058758111yescharacteristic
266C8—42no—
267C8—41no—
268C8—41no—
269C8—81no—
270C8—682no—
271C8—1361no—
272C22—21no—
273C22—21no—
274C22—21no—
275C22#1176272711yescharacteristic
276C4—21no—
277C4—21no—
278C4—21no—
279C4—1362no—
280C4—1361no—
281C4—1361no—
282C4#1176298311yescharacteristic
283C4#1176299311yescharacteristic
284C4#1176307111yescharacteristic
285C4#1176307312yes—
286C4#1176308311yescharacteristic
287C2—41no—
288C2#1453000411yescharacteristic
289C2#1453004811yescharacteristic
290C2#1453008611yescharacteristic
subgroupG/H
centerC22#11762727
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#1299C2
socleC22×C17#394
prime radicalC23×C17#123
hypercenter#1299D17
hypocenterC17#10494
LCSG ▷ C2×C42×C17 ▷ C22×C17 ▷ C17
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1299

Complements

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

NH ≅ G/Ntype
208. C17#10494semidirect

Maximal subgroups

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

subgroupindex
#145399302
#145297732
#145275722
#145275212
#145274702
#145272062
C17×#12992
#1049417