Finite Group Databasebeta

← #16947276

Subgroups — #16947276

Order 4352.

350 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 59 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#14530129C211yesmaximal, characteristic
2#14527791C211yesmaximal, characteristic
3#14527757C211yesmaximal, characteristic
4#14526814C211yesmaximal, characteristic
5#14526790C211yesmaximal, characteristic
6#14526730C211yesmaximal, characteristic
7C17×#2792C211yesmaximal, characteristic
8#11763440C2211yescharacteristic
9#11763139—21no—
10#11762965—21no—
11#11762849—21no—
12#11762578C2211yescharacteristic
13#11762569—21no—
14#11762545—21no—
15#11762545—21no—
16#11762535C2211yescharacteristic
17#11762535C2211yescharacteristic
18C17×#398—21no—
19C17×#398C2211yescharacteristic
20C17×#395—21no—
21C17×#395C2211yescharacteristic
22C17×#389—21no—
23C17×#389—21no—
24C17×#387—21no—
25C17×#387—21no—
26C17×#384C2211yescharacteristic
27C22×Q8×C17D411yescharacteristic
28C2×C4⋊C4×C17—21no—
29C2×C4⋊C4×C17—21no—
30C2×C4⋊C4×C17—21no—
31C2×C4⋊C4×C17—21no—
32C2×C4⋊C4×C17—21no—
33C2×C4⋊C4×C17—21no—
34C2×C4⋊C4×C17—21no—
35C2×C4⋊C4×C17D411yescharacteristic
36C2×C4⋊C4×C17D411yescharacteristic
37C2×C4⋊C4×C17C2311yescharacteristic
38C2×C42×C17—21no—
39C2×C42×C17D411yescharacteristic
40C2×#63231—41no—
41#10587612—21no—
42#10587610—21no—
43#10587610—21no—
44C2×#63223—21no—
45#10587576—41no—
46#10587574—41no—
47C17×#95—21no—
48C17×#95—21no—
49C17×#95—21no—
50C17×#95—21no—
51C17×#95—21no—
52C17×#95—21no—
53C17×#95D411yescharacteristic
54C17×#95D411yescharacteristic
55#10587506—41no—
56C22⋊#3622—21no—
57C22⋊#3622—21no—
58#10587481—41no—
59#10587479—41no—
60#10587479—41no—
61#10587478—41no—
62C2×Q8×C17—41no—
63C2×Q8×C17—81no—
64C22×C4×C17—21no—
65C22×C4×C17—21no—
66C22×C4×C17—21no—
67C22×C4×C17—21no—
68C22×C4×C17—21no—
69C22×C4×C17—21no—
70C22×C4×C17C2×D411yescharacteristic
71C22×C4×C17C2×D411yescharacteristic
72C22×C4×C17C2×D411yescharacteristic
73C2×Dic34—21no—
74C2×Dic34—21no—
75C4⋊C4×C17—24no—
76C4⋊C4×C17—41no—
77C4⋊C4×C17—41no—
78C4⋊C4×C17—41no—
79C4⋊C4×C17—41no—
80C4⋊C4×C17—41no—
81C4⋊C4×C17—81no—
82C4⋊C4×C17—81no—
83C4⋊C4×C17—81no—
84C4⋊C4×C17—81no—
85C4⋊C4×C17—81no—
86C42×C17—21no—
87C42×C17—21no—
88C42×C17—81no—
89C22⋊Dic17—41no—
90#63231—82no—
91C4⋊Dic17—21no—
92C4⋊Dic17—21no—
93C4⋊Dic17—21no—
94C4⋊Dic17—21no—
95#63225—41no—
96#63225—41no—
97C4×Dic17—41no—
98#63223—22no—
99#63223—41no—
100C2×#3622—41no—
101C2×#3622—41no—
102C2×#3622—41no—
103#12240—171nomaximal, Sylow
104C23×C17#12011yescharacteristic
105Q8×C17—42no—
106Q8×C17—81no—
107C2×C4×C17—21no—
108C2×C4×C17—21no—
109C2×C4×C17—22no—
110C2×C4×C17—22no—
111C2×C4×C17—22no—
112C2×C4×C17—21no—
113C2×C4×C17—21no—
114C2×C4×C17—41no—
115C2×C4×C17—41no—
116C2×C4×C17—41no—
117C2×C4×C17—41no—
118C2×C4×C17—41no—
119C2×C4×C17—41no—
120C2×C4×C17—41no—
121C2×C4×C17—41no—
122C2×C4×C17—41no—
123C2×C4×C17—41no—
124C2×C4×C17—41no—
125C2×C4×C17—41no—
126C2×C4×C17—41no—
127C2×C4×C17—41no—
128C2×C4×C17—41no—
129C2×C4×C17—41no—
130C2×C4×C17—41no—
131C2×C4×C17#13511yescharacteristic
132C2×C4×C17#13711yescharacteristic
133C2×Dic17—41no—
134C2×Dic17—41no—
135Dic34—81no—
136Dic34—81no—
137#3622—42no—
138#3622—81no—
139#3622—81no—
140#2792D1711yescharacteristic
141#2060—171no—
142#1611—171no—
143#1605—171no—
144#1354—171no—
145#1346—171no—
146#1325—171no—
147C22×C17—21no—
148C22×C17—21no—
149C22×C17#45211yescharacteristic
150C22×C17#45611yescharacteristic
151C22×C17B(4,𝔽2)11yescharacteristic
152C4×C17—21no—
153C4×C17—21no—
154C4×C17—42no—
155C4×C17—42no—
156C4×C17—42no—
157C4×C17—41no—
158C4×C17—41no—
159C4×C17—81no—
160C4×C17—81no—
161C4×C17—81no—
162Dic17—81no—
163Dic17—81no—
164#544—171no—
165#483—341no—
166#451—341no—
167#428—341no—
168#398—21no—
169#398C2×D1711yescharacteristic
170#395—21no—
171#395C2×D1711yescharacteristic
172#389—21no—
173#389—21no—
174#387—21no—
175#387—21no—
176#384C2×D1711yescharacteristic
177#343—171no—
178#339—341no—
179#328—341no—
180#328—341no—
181#324—171no—
182#324—171no—
183C2×C17—21no—
184C2×C17—21no—
185C2×C17#160311yescharacteristic
186C2×C17#220011yescharacteristic
187C2×C17#220511yescharacteristic
188C22×Q8C22⋊D1711yescharacteristic
189C2×Q16—681no—
190C2×M16—341no—
191C4⋊Q8—681no—
192#125—681no—
193C22⋊Q8—341no—
194C22⋊Q8—341no—
195#117—341no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4C22⋊D1711yescharacteristic
204C2×C4⋊C4C22⋊D1711yescharacteristic
205C2×C4⋊C4C22×D1711yescharacteristic
206C2×C42—21no—
207C2×C42C22⋊D1711yescharacteristic
208#107—681no—
209#106—681no—
210#106—681no—
211#103—681no—
212#103—681no—
213C22⋊C8—341no—
214C22⋊C8—341no—
215#95—21no—
216#95—21no—
217#95—21no—
218#95—21no—
219#95—21no—
220#95—21no—
221#95C22⋊D1711yescharacteristic
222#95C22⋊D1711yescharacteristic
223C17#1224011yescharacteristic, complemented, Sylow
224C2×Q8—41no—
225C2×Q8—81no—
226C2×Q8—341no—
227C2×Q8—341no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4C2×C22⋊D1711yescharacteristic
235C22×C4C2×C22⋊D1711yescharacteristic
236C22×C4C2×C22⋊D1711yescharacteristic
237Q16—1362no—
238M16—342no—
239M16—681no—
240C2×C8—681no—
241C2×C8—681no—
242C2×C8—681no—
243C4⋊C4—24no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—81no—
250C4⋊C4—81no—
251C4⋊C4—81no—
252C4⋊C4—81no—
253C4⋊C4—81no—
254C4⋊C4—341no—
255C4⋊C4—341no—
256C4⋊C4—341no—
257C4⋊C4—341no—
258C4⋊C4—681no—
259C4⋊C4—681no—
260C22⋊C4—681no—
261C42—21no—
262C42—21no—
263C42—81no—
264C42—681no—
265C23#1058763911yescharacteristic
266Q8—42no—
267Q8—81no—
268Q8—1361no—
269Q8—1361no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—681no—
295C2×C4—681no—
296C2×C4#1058763611yescharacteristic
297C2×C4#1058763711yescharacteristic
298C8—682no—
299C8—1361no—
300C8—1361no—
301C22—21no—
302C22—21no—
303C22#1176297111yescharacteristic
304C22#1176299211yescharacteristic
305C22#1176299611yescharacteristic
306C4—21no—
307C4—21no—
308C4—42no—
309C4—42no—
310C4—42no—
311C4—41no—
312C4—41no—
313C4—81no—
314C4—81no—
315C4—81no—
316C4—1361no—
317C4—1361no—
318C2—21no—
319C2—21no—
320C2#1452774711yescharacteristic
321C2#1453079111yescharacteristic
322C2#1453081411yescharacteristic
subgroupG/H
centerC22#11762996
commutator, cosocleC2×C4⋊C4×C17C23
FrattiniC2×C4⋊C4C22×D17
FittingC17×#2792C2
socleC22×C17B(4,𝔽2)
prime radicalC23×C17#120
hypercenter#2792D17
hypocenterC17#12240
LCSG ▷ C2×C4⋊C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #2792

Complements

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

NH ≅ G/Ntype
223. C17#12240semidirect

Maximal subgroups

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

subgroupindex
#145301292
#145277912
#145277572
#145268142
#145267902
#145267302
C17×#27922
#1224017