Finite Group Databasebeta

← #16923484

Subgroups — #16923484

Order 4352.

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

normal subgroups only

This group has 350 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#14536734C211yesmaximal, characteristic
2#14530343C211yesmaximal, characteristic
3#14530255C211yesmaximal, characteristic
4#14530194C211yesmaximal, characteristic
5#14526609C211yesmaximal, characteristic
6#14526606C211yesmaximal, characteristic
7C17×#1271C211yesmaximal, characteristic
8C2×#10587478—21no—
9C2×#10587487—21no—
10#11762751—21no—
11#11762747—21no—
12#11762729—21no—
13#11762715C2211yescharacteristic
14#11762707C2211yescharacteristic
15#11762704—21no—
16#11762695—21no—
17#11762694—21no—
18#11762679C2211yescharacteristic
19#11762572—21no—
20#11762572—21no—
21#11762572—21no—
22#11762571—21no—
23#11762564C2211yescharacteristic
24C17×#389C2211yescharacteristic
25C17×#336C2211yescharacteristic
26C17×#336C2211yescharacteristic
27C22×Dic34D411yescharacteristic
28C22×C8×C17—21no—
29C22×C8×C17—21no—
30C2×C4⋊C4×C17—21no—
31C2×C4⋊C4×C17D411yescharacteristic
32C2×C4⋊C4×C17D411yescharacteristic
33C2×C42×C17C2311yescharacteristic
34C2×C4⋊Dic17—21no—
35C2×C4⋊Dic17—21no—
36C2×C4⋊Dic17—21no—
37C2×C4⋊Dic17D411yescharacteristic
38C2×C4⋊Dic17D411yescharacteristic
39C2×C4⋊Dic17D411yescharacteristic
40C2×#63225—21no—
41C2×#63225—21no—
42C2×#63225—21no—
43C2×C4×Dic17—21no—
44C22×#3622—21no—
45C17×#95—21no—
46#10587502—21no—
47#10587502—21no—
48#10587502—21no—
49#10587502—21no—
50#10587502—21no—
51#10587502—21no—
52#10587502—21no—
53#10587502—21no—
54#10587487—42no—
55#10587478—42no—
56C22×C4×C17—21no—
57C22×C4×C17—21no—
58C22×C4×C17C2×D411yescharacteristic
59C22×C4×C17C2×D411yescharacteristic
60C22×C4×C17C2×D411yescharacteristic
61C22×Dic17—21no—
62C22×Dic17—21no—
63C22×Dic17—21no—
64C22×Dic17—21no—
65C22×Dic17—41no—
66C2×Dic34—21no—
67C2×Dic34—21no—
68C2×Dic34—41no—
69C2×Dic34—41no—
70C2×C8×C17—41no—
71C2×C8×C17—41no—
72C2×C8×C17—41no—
73C2×C8×C17—41no—
74C2×C8×C17—41no—
75C2×C8×C17—41no—
76C4⋊C4×C17—21no—
77C4⋊C4×C17—21no—
78C4⋊C4×C17—41no—
79C4⋊C4×C17—41no—
80C4⋊C4×C17—41no—
81C42×C17—41no—
82C4⋊Dic17—21no—
83C4⋊Dic17—41no—
84C4⋊Dic17—41no—
85C4⋊Dic17—42no—
86C4⋊Dic17—41no—
87C4⋊Dic17—41no—
88C4⋊Dic17—41no—
89C4⋊Dic17—41no—
90C4⋊Dic17Q1612yes—
91#63225—41no—
92#63225—41no—
93#63225—81no—
94#63225—81no—
95C4×Dic17—81no—
96C2×#3622—22no—
97C2×#3622—41no—
98C2×#3622—41no—
99#7806—171nomaximal, Sylow
100C23×C17#12011yescharacteristic
101C2×C4×C17—21no—
102C2×C4×C17—21no—
103C2×C4×C17—21no—
104C2×C4×C17—21no—
105C2×C4×C17—21no—
106C2×C4×C17—21no—
107C2×C4×C17—41no—
108C2×C4×C17—41no—
109C2×C4×C17—41no—
110C2×C4×C17—41no—
111C2×C4×C17—41no—
112C2×C4×C17—41no—
113C2×C4×C17C2×Q1611yescharacteristic
114C2×C4×C17#13511yescharacteristic
115C2×C4×C17#13511yescharacteristic
116C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
117C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
118C2×C4×C17#13711yescharacteristic
119C2×Dic17—22no—
120C2×Dic17—41no—
121C2×Dic17—41no—
122C2×Dic17—41no—
123C2×Dic17—41no—
124C2×Dic17—41no—
125C2×Dic17—41no—
126C2×Dic17—41no—
127C2×Dic17—41no—
128C2×Dic17—41no—
129C2×Dic17—41no—
130C2×Dic17—41no—
131C2×Dic17—81no—
132C2×Dic17—81no—
133C2×Dic17—81no—
134Dic34—42no—
135Dic34—81no—
136C8×C17—81no—
137C8×C17—81no—
138#3622—42no—
139#2805—171no—
140#2099—171no—
141#2083—171no—
142#2072—171no—
143#1272—171no—
144#1271—171no—
145#1271D1711yescharacteristic
146C22×C17#44911yescharacteristic
147C22×C17#44911yescharacteristic
148C22×C17#45111yescharacteristic
149C22×C17#45411yescharacteristic
150C22×C17#45511yescharacteristic
151C22×C17#45611yescharacteristic
152C22×C17#45811yescharacteristic
153C4×C17—21no—
154C4×C17—21no—
155C4×C17—21no—
156C4×C17—21no—
157C4×C17—21no—
158C4×C17—21no—
159C4×C17—81no—
160C4×C17—81no—
161Dic17—42no—
162Dic17—81no—
163Dic17—81no—
164Dic17—81no—
165Dic17—161no—
166C2×#107—341no—
167C2×#103—341no—
168#400—341no—
169#400—341no—
170#395—341no—
171#391—171no—
172#389—171no—
173#389—341no—
174#389C2×D1711yescharacteristic
175#387—341no—
176#387—341no—
177#384—171no—
178#340—341no—
179#340—341no—
180#340—341no—
181#340—341no—
182#336—171no—
183#336C2×D1711yescharacteristic
184#336C2×D1711yescharacteristic
185C2×C17#160911yescharacteristic
186C2×C17#161211yescharacteristic
187C2×C17#161711yescharacteristic
188C2×C17#162811yescharacteristic
189C2×C17#164411yescharacteristic
190C2×C17#164811yescharacteristic
191C2×C17#166411yescharacteristic
192C22×Q8—171no—
193C22×C8—21no—
194C22×C8—21no—
195C22×C8—341no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—171no—
198C2×C4⋊C4—171no—
199C2×C4⋊C4—171no—
200C2×C4⋊C4—341no—
201C2×C4⋊C4—341no—
202C2×C4⋊C4—341no—
203C2×C4⋊C4—341no—
204C2×C4⋊C4—341no—
205C2×C4⋊C4—341no—
206C2×C4⋊C4D6811yescharacteristic
207C2×C4⋊C4D6811yescharacteristic
208C2×C42—341no—
209C2×C42C22×D1711yescharacteristic
210#107—682no—
211#103—682no—
212#95—21no—
213#95—341no—
214#95—341no—
215#95—341no—
216#95—341no—
217#95—341no—
218#95—341no—
219#95—341no—
220#95—341no—
221C17#780611yescharacteristic, complemented, Sylow
222C2×Q8—341no—
223C2×Q8—341no—
224C2×Q8—681no—
225C2×Q8—681no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—341no—
229C22×C4—341no—
230C22×C4—341no—
231C22×C4—341no—
232C22×C4—681no—
233C22×C4C2×D6811yescharacteristic
234C22×C4D4×D1711yescharacteristic
235C22×C4D4×D1711yescharacteristic
236C2×C8—41no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—41no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—342no—
243C2×C8—681no—
244C2×C8—681no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—172no—
251C4⋊C4—341no—
252C4⋊C4—681no—
253C4⋊C4—681no—
254C4⋊C4—682no—
255C4⋊C4—681no—
256C4⋊C4—681no—
257C4⋊C4—681no—
258C4⋊C4—681no—
259C4⋊C4—681no—
260C4⋊C4—681no—
261C4⋊C4—1361no—
262C4⋊C4—1361no—
263C42—41no—
264C42—1361no—
265C23#1058756811yescharacteristic
266Q8—682no—
267Q8—1361no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—342no—
281C2×C4—681no—
282C2×C4—681no—
283C2×C4—681no—
284C2×C4—681no—
285C2×C4—681no—
286C2×C4—681no—
287C2×C4—681no—
288C2×C4—681no—
289C2×C4—681no—
290C2×C4—681no—
291C2×C4—681no—
292C2×C4—1361no—
293C2×C4—1361no—
294C2×C4—1361no—
295C2×C4#1058759011yescharacteristic
296C2×C4#1058759411yescharacteristic
297C2×C4#1058759711yescharacteristic
298C2×C4#1058760111yescharacteristic
299C2×C4#1058760211yescharacteristic
300C2×C4Q16×D1711yescharacteristic
301C8—81no—
302C8—81no—
303C8—682no—
304C22#1176295511yescharacteristic
305C22#1176295611yescharacteristic
306C22#1176296611yescharacteristic
307C22#1176298311yescharacteristic
308C22#1176298811yescharacteristic
309C22#1176299411yescharacteristic
310C22#1176300011yescharacteristic
311C4—21no—
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—21no—
317C4—81no—
318C4—81no—
319C4—2721no—
320C4—682no—
321C4—1361no—
322C4—1361no—
323C4—1361no—
324C2#1452778311yescharacteristic
325C2#1452779911yescharacteristic
326C2#1452782711yescharacteristic
327C2#1452789611yescharacteristic
328C2#1452800011yescharacteristic
329C2#1452802711yescharacteristic
330C2#1452812011yescharacteristic
subgroupG/H
centerC23#10587568
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#1271C2
socle, prime radicalC23×C17#120
hypercenter#1271D17
hypocenterC17#7806
LCSG ▷ C2×C42×C17 ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
221. C17#7806semidirect

Maximal subgroups

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

subgroupindex
#145367342
#145303432
#145302552
#145301942
#145266092
#145266062
C17×#12712
#780617