Finite Group Databasebeta

← #16923464

Subgroups — #16923464

Order 4352.

338 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 79 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#14536775C211yesmaximal, characteristic
2#14530342C211yesmaximal, characteristic
3#14530262C211yesmaximal, characteristic
4#14530257C211yesmaximal, characteristic
5#14526608C211yesmaximal, characteristic
6#14526606C211yesmaximal, characteristic
7C17×#1271C211yesmaximal, characteristic
8C2×#10587489—21no—
9C2×#10587488—21no—
10#11762749—21no—
11#11762748—21no—
12#11762747—21no—
13#11762707C2211yescharacteristic
14#11762707C2211yescharacteristic
15#11762696—21no—
16#11762695—21no—
17#11762690—21no—
18#11762679C2211yescharacteristic
19#11762572—21no—
20#11762572—21no—
21#11762571—21no—
22#11762571—21no—
23#11762564C2211yescharacteristic
24C17×#389C2211yescharacteristic
25C17×#336C2211yescharacteristic
26C17×#336C2211yescharacteristic
27C22×C8×C17—21no—
28C22×C8×C17—21no—
29C2×C4⋊C4×C17—21no—
30C2×C4⋊C4×C17D411yescharacteristic
31C2×C4⋊C4×C17D411yescharacteristic
32C2×C42×C17C2311yescharacteristic
33C2×C4⋊Dic17—21no—
34C2×C4⋊Dic17—21no—
35C2×C4⋊Dic17—21no—
36C2×C4⋊Dic17D411yescharacteristic
37C2×C4⋊Dic17D411yescharacteristic
38C2×C4⋊Dic17D411yescharacteristic
39C2×C4⋊Dic17D411yescharacteristic
40C2×#63225—21no—
41C2×#63225—21no—
42C2×C4×Dic17—21no—
43C22×#3622—21no—
44C17×#95—21no—
45#10587502—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#10587489—42no—
55#10587488—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×C8×C17—22no—
67C2×C8×C17—22no—
68C2×C8×C17—41no—
69C2×C8×C17—41no—
70C2×C8×C17—41no—
71C2×C8×C17—41no—
72C4⋊C4×C17—21no—
73C4⋊C4×C17—21no—
74C4⋊C4×C17—41no—
75C4⋊C4×C17—41no—
76C4⋊C4×C17—41no—
77C42×C17—41no—
78C4⋊Dic17—21no—
79C4⋊Dic17—21no—
80C4⋊Dic17—21no—
81C4⋊Dic17—21no—
82C4⋊Dic17—41no—
83C4⋊Dic17—41no—
84C4⋊Dic17—42no—
85C4⋊Dic17—41no—
86C4⋊Dic17—41no—
87C4⋊Dic17—41no—
88C4⋊Dic17—41no—
89#63225—41no—
90#63225—41no—
91#63225—41no—
92#63225—41no—
93C4×Dic17—81no—
94C2×#3622—41no—
95C2×#3622—41no—
96C2×#3622—41no—
97#7803—171nomaximal, Sylow
98C23×C17#12011yescharacteristic
99C2×C4×C17—21no—
100C2×C4×C17—21no—
101C2×C4×C17—21no—
102C2×C4×C17—21no—
103C2×C4×C17—21no—
104C2×C4×C17—21no—
105C2×C4×C17—41no—
106C2×C4×C17—41no—
107C2×C4×C17—41no—
108C2×C4×C17—41no—
109C2×C4×C17—41no—
110C2×C4×C17—41no—
111C2×C4×C17#13511yescharacteristic
112C2×C4×C17#13511yescharacteristic
113C2×C4×C17#13511yescharacteristic
114C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
115C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
116C2×C4×C17#13711yescharacteristic
117C2×Dic17—41no—
118C2×Dic17—41no—
119C2×Dic17—41no—
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—81no—
130C2×Dic17—81no—
131C2×Dic17—81no—
132C8×C17—42no—
133C8×C17—42no—
134#3622—81no—
135#2810—171no—
136#2099—171no—
137#2084—171no—
138#2083—171no—
139#1271—171no—
140#1271—171no—
141#1271D1711yescharacteristic
142C22×C17#44911yescharacteristic
143C22×C17#44911yescharacteristic
144C22×C17#45211yescharacteristic
145C22×C17#45411yescharacteristic
146C22×C17#45611yescharacteristic
147C22×C17#45611yescharacteristic
148C22×C17#45811yescharacteristic
149C4×C17—21no—
150C4×C17—21no—
151C4×C17—21no—
152C4×C17—21no—
153C4×C17—21no—
154C4×C17—21no—
155C4×C17—81no—
156C4×C17—81no—
157Dic17—81no—
158Dic17—81no—
159Dic17—81no—
160Dic17—81no—
161Dic17—161no—
162C2×#107—341no—
163C2×#106—341no—
164#400—341no—
165#400—341no—
166#400—341no—
167#389—171no—
168#389—171no—
169#389C2×D1711yescharacteristic
170#387—341no—
171#387—341no—
172#387—341no—
173#384—171no—
174#340—341no—
175#340—341no—
176#340—341no—
177#340—341no—
178#336—171no—
179#336C2×D1711yescharacteristic
180#336C2×D1711yescharacteristic
181C2×C17#160911yescharacteristic
182C2×C17#160911yescharacteristic
183C2×C17#161511yescharacteristic
184C2×C17#162811yescharacteristic
185C2×C17#165011yescharacteristic
186C2×C17#165211yescharacteristic
187C2×C17#166311yescharacteristic
188C22×C8—21no—
189C22×C8—21no—
190C22×C8—341no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—171no—
193C2×C4⋊C4—171no—
194C2×C4⋊C4—171no—
195C2×C4⋊C4—171no—
196C2×C4⋊C4—341no—
197C2×C4⋊C4—341no—
198C2×C4⋊C4—341no—
199C2×C4⋊C4—341no—
200C2×C4⋊C4—341no—
201C2×C4⋊C4D6811yescharacteristic
202C2×C4⋊C4D6811yescharacteristic
203C2×C42—341no—
204C2×C42C22×D1711yescharacteristic
205#107—682no—
206#106—682no—
207#95—21no—
208#95—341no—
209#95—341no—
210#95—341no—
211#95—341no—
212#95—341no—
213#95—341no—
214#95—341no—
215#95—341no—
216#95—341no—
217C17#780311yescharacteristic, complemented, Sylow
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—341no—
221C22×C4—341no—
222C22×C4—341no—
223C22×C4—341no—
224C22×C4—681no—
225C22×C4C2×D6811yescharacteristic
226C22×C4D4×D1711yescharacteristic
227C22×C4D4×D1711yescharacteristic
228C2×C8—22no—
229C2×C8—22no—
230C2×C8—41no—
231C2×C8—41no—
232C2×C8—41no—
233C2×C8—41no—
234C2×C8—681no—
235C2×C8—681no—
236C2×C8—681no—
237C4⋊C4—21no—
238C4⋊C4—21no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C4⋊C4—341no—
243C4⋊C4—341no—
244C4⋊C4—341no—
245C4⋊C4—341no—
246C4⋊C4—681no—
247C4⋊C4—681no—
248C4⋊C4—682no—
249C4⋊C4—681no—
250C4⋊C4—681no—
251C4⋊C4—681no—
252C4⋊C4—681no—
253C4⋊C4—681no—
254C4⋊C4—681no—
255C4⋊C4—681no—
256C4⋊C4—681no—
257C42—41no—
258C42—1361no—
259C23#1058756811yescharacteristic
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—681no—
273C2×C4—681no—
274C2×C4—681no—
275C2×C4—681no—
276C2×C4—681no—
277C2×C4—681no—
278C2×C4—681no—
279C2×C4—681no—
280C2×C4—681no—
281C2×C4—681no—
282C2×C4—681no—
283C2×C4—681no—
284C2×C4—1361no—
285C2×C4—1361no—
286C2×C4—1361no—
287C2×C4#1058759011yescharacteristic
288C2×C4#1058759511yescharacteristic
289C2×C4#1058759711yescharacteristic
290C2×C4#1058760011yescharacteristic
291C2×C4#1058760211yescharacteristic
292C2×C4#1058760511yescharacteristic
293C8—42no—
294C8—42no—
295C8—1361no—
296C22#1176295511yescharacteristic
297C22#1176295711yescharacteristic
298C22#1176297311yescharacteristic
299C22#1176298411yescharacteristic
300C22#1176299311yescharacteristic
301C22#1176299311yescharacteristic
302C22#1176300011yescharacteristic
303C4—21no—
304C4—21no—
305C4—21no—
306C4—21no—
307C4—21no—
308C4—21no—
309C4—81no—
310C4—81no—
311C4—2721no—
312C4—1361no—
313C4—1361no—
314C4—1361no—
315C4—1361no—
316C2#1452778211yescharacteristic
317C2#1452778411yescharacteristic
318C2#1452781711yescharacteristic
319C2#1452789511yescharacteristic
320C2#1452804311yescharacteristic
321C2#1452805711yescharacteristic
322C2#1452811311yescharacteristic
subgroupG/H
centerC23#10587568
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#1271C2
socle, prime radicalC23×C17#120
hypercenter#1271D17
hypocenterC17#7803
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
217. C17#7803semidirect

Maximal subgroups

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

subgroupindex
#145367752
#145303422
#145302622
#145302572
#145266082
#145266062
C17×#12712
#780317