Finite Group Databasebeta

← #16938264

Subgroups — #16938264

Order 4352.

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

normal subgroups only

This group has 372 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#14539734C211yesmaximal, characteristic
2#14529628C211yesmaximal, characteristic
3#14527572C211yesmaximal, characteristic
4#14527521C211yesmaximal, characteristic
5#14527466C211yesmaximal, characteristic
6#14527206C211yesmaximal, characteristic
7C17×#1299C211yesmaximal, characteristic
8#11763366C2211yescharacteristic
9C2×#10587555C2211yescharacteristic
10#11763189—21no—
11#11763160—21no—
12#11763020—21no—
13#11763020—21no—
14#11762967—22no—
15#11762862C2211yescharacteristic
16#11762833C2211yescharacteristic
17C2×#10587495—22no—
18#11762561—21no—
19#11762559—21no—
20#11762557—22no—
21#11762556—21no—
22#11762554—21no—
23#11762541—22no—
24C17×#431C2211yescharacteristic
25C17×#423C2211yescharacteristic
26C4×M16×C17C2211yescharacteristic
27C22×Dic34D412yes—
28C2×M16×C17—21no—
29C2×M16×C17—21no—
30C2×C42×C17C2311yescharacteristic
31#10587612—21no—
32C2×C4⋊Dic17—21no—
33C2×C4⋊Dic17—21no—
34#10587610—21no—
35#10587610—21no—
36C2×#63223—21no—
37C2×Dic68—22no—
38C2×Dic68—22no—
39#10587556—21no—
40#10587555—21no—
41#10587555—21no—
42#10587555—21no—
43#10587555—21no—
44#10587555D411yescharacteristic
45#10587555D411yescharacteristic
46C4×Dic34—21no—
47C4×Dic34—21no—
48C17×C4⋊C8—21no—
49C17×C4⋊C8—21no—
50C17×C4⋊C8D411yescharacteristic
51C17×C4⋊C8D411yescharacteristic
52C17×C22⋊C8—21no—
53C17×#97—21no—
54C4×C8×C17—21no—
55C4×C8×C17—21no—
56C22⋊#3622—21no—
57#10587495—44no—
58#10587487—22no—
59#10587487—22no—
60C4⋊#3622—21no—
61C4⋊#3622—21no—
62C4⋊#3622D412yes—
63C4×#3622—21no—
64C22×C4×C17C2×D411yescharacteristic
65C22×C4×C17#4111yescharacteristic
66C22×C4×C17#4111yescharacteristic
67C22×Dic17—22no—
68C2×Dic34—22no—
69C2×Dic34—21no—
70C2×Dic34—21no—
71C2×Dic34—22no—
72C2×Dic34—42no—
73C2×Dic34—42no—
74M16×C17—22no—
75M16×C17—41no—
76M16×C17—81no—
77C2×C8×C17—21no—
78C2×C8×C17—21no—
79C2×C8×C17—41no—
80C2×C8×C17—41no—
81C42×C17C2×D411yescharacteristic
82C42×C17C2×D411yescharacteristic
83C42×C17C2×D411yescharacteristic
84C42×C17#4111yescharacteristic
85C22⋊Dic17—41no—
86C4⋊Dic17—21no—
87C4⋊Dic17—21no—
88C4⋊Dic17—21no—
89C4⋊Dic17—21no—
90C4⋊Dic17—41no—
91C4⋊Dic17—41no—
92C4⋊Dic17—41no—
93C4⋊Dic17—41no—
94#63225—41no—
95#63225—41no—
96C4×Dic17—41no—
97#63223—42no—
98C2×#3622—22no—
99C2×#3622—41no—
100Dic68—82no—
101Dic68—82no—
102#10493—171nomaximal, Sylow
103C23×C17#12311yescharacteristic
104C2×C4×C17—21no—
105C2×C4×C17—21no—
106C2×C4×C17—21no—
107C2×C4×C17—21no—
108C2×C4×C17—22no—
109C2×C4×C17#12011yescharacteristic
110C2×C4×C17#12111yescharacteristic
111C2×C4×C17#12111yescharacteristic
112C2×C4×C17#12111yescharacteristic
113C2×C4×C17#12311yescharacteristic
114C2×C4×C17#12411yescharacteristic
115C2×Dic17—44no—
116C2×Dic17—41no—
117C2×Dic17—41no—
118C2×Dic17—42no—
119Dic34—42no—
120Dic34—41no—
121Dic34—42no—
122Dic34—41no—
123Dic34—41no—
124Dic34—41no—
125Dic34—82no—
126C8×C17—42no—
127C8×C17—41no—
128C8×C17—41no—
129C8×C17—81no—
130#3622—42no—
131#3622—81no—
132#3209—171no—
133#1966—171no—
134#1574—171no—
135#1561—171no—
136#1548—171no—
137#1485—171no—
138#1299D1711yescharacteristic
139C22×C17—21no—
140C22×C17—21no—
141C22×C17—21no—
142C22×C17#39411yescharacteristic
143C4×C17—21no—
144C4×C17—21no—
145C4×C17—21no—
146C4×C17#45311yescharacteristic
147C4×C17#45511yescharacteristic
148C4×C17#47111yescharacteristic
149C4×C17#47311yescharacteristic
150C4×C17#47312yes—
151Dic17—81no—
152Dic17—82no—
153Dic17—81no—
154#533—171no—
155C2×C4⋊Q8—171no—
156#494—341no—
157#487—341no—
158#462—341no—
159#462—341no—
160#451—342no—
161#431—171no—
162#431C2×D1711yescharacteristic
163#423—171no—
164#423C2×D1711yescharacteristic
165C2×#101—342no—
166C4×M16C2×D1711yescharacteristic
167#335—341no—
168#334—341no—
169#333—342no—
170#332—341no—
171#332—341no—
172Q8⋊C8—342no—
173C2×C17—41no—
174C2×C17#203711yescharacteristic
175C2×C17#204711yescharacteristic
176C2×C17#205211yescharacteristic
177C22×Q8—172no—
178C2×Q16—342no—
179C2×Q16—342no—
180C2×M16—21no—
181C2×M16—21no—
182C2×M16—341no—
183C4⋊Q8—171no—
184C4⋊Q8—171no—
185C4⋊Q8—341no—
186C4⋊Q8—341no—
187C4⋊Q8—341no—
188C4⋊Q8—341no—
189#125—341no—
190C22⋊Q8—341no—
191C22⋊Q8—341no—
192C4×Q8—341no—
193C4×Q8—341no—
194#117—341no—
195C2×C4⋊C4—341no—
196C2×C4⋊C4—341no—
197C2×C42C22×D1711yescharacteristic
198C4⋊C8—21no—
199C4⋊C8—21no—
200C4⋊C8—172no—
201C4⋊C8—341no—
202C4⋊C8—341no—
203C4⋊C8D6811yescharacteristic
204C4⋊C8D6811yescharacteristic
205#103—342no—
206#103—342no—
207#101—684no—
208C22⋊C8—21no—
209C22⋊C8—341no—
210#97—21no—
211C4×C8—21no—
212C4×C8—21no—
213C4×C8—341no—
214C17#1049311yescharacteristic, complemented, Sylow
215C2×Q8—342no—
216C2×Q8—341no—
217C2×Q8—341no—
218C2×Q8—342no—
219C2×Q8—682no—
220C2×Q8—682no—
221C22×C4—342no—
222C22×C4#6325211yescharacteristic
223C22×C4D4×D1711yescharacteristic
224C22×C4#6325611yescharacteristic
225Q16—1362no—
226Q16—1362no—
227M16—22no—
228M16—41no—
229M16—81no—
230M16—682no—
231C2×C8—21no—
232C2×C8—21no—
233C2×C8—41no—
234C2×C8—41no—
235C2×C8—342no—
236C2×C8—681no—
237C4⋊C4—341no—
238C4⋊C4—341no—
239C4⋊C4—341no—
240C4⋊C4—341no—
241C4⋊C4—681no—
242C4⋊C4—681no—
243C4⋊C4—681no—
244C4⋊C4—681no—
245C4⋊C4—681no—
246C4⋊C4—681no—
247C22⋊C4—681no—
248C42—681no—
249C42C2×D6811yescharacteristic
250C42#6325211yescharacteristic
251C42D4×D1711yescharacteristic
252C42D4×D1711yescharacteristic
253C23#1058758011yescharacteristic
254Q8—681no—
255Q8—682no—
256Q8—681no—
257Q8—682no—
258Q8—681no—
259Q8—681no—
260Q8—1362no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—22no—
266C2×C4—684no—
267C2×C4—681no—
268C2×C4—681no—
269C2×C4—682no—
270C2×C4#1058756111yescharacteristic
271C2×C4#1058756811yescharacteristic
272C2×C4#1058757011yescharacteristic
273C2×C4#1058757011yescharacteristic
274C2×C4#1058758011yescharacteristic
275C2×C4#1058758111yescharacteristic
276C8—42no—
277C8—41no—
278C8—41no—
279C8—81no—
280C8—682no—
281C8—1361no—
282C22—21no—
283C22—21no—
284C22—21no—
285C22#1176272711yescharacteristic
286C4—21no—
287C4—21no—
288C4—21no—
289C4—1361no—
290C4—1362no—
291C4—1361no—
292C4#1176297811yescharacteristic
293C4#1176298811yescharacteristic
294C4#1176307111yescharacteristic
295C4#1176308311yescharacteristic
296C4#1176308512yes—
297C2—41no—
298C2#1452999711yescharacteristic
299C2#1453005311yescharacteristic
300C2#1453008611yescharacteristic
subgroupG/H
centerC22#11762727
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#1299C2
socleC22×C17#394
prime radicalC23×C17#123
hypercenter#1299D17
hypocenterC17#10493
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
214. C17#10493semidirect

Maximal subgroups

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

subgroupindex
#145397342
#145296282
#145275722
#145275212
#145274662
#145272062
C17×#12992
#1049317