Finite Group Databasebeta

← #16923637

Subgroups — #16923637

Order 4352.

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

normal subgroups only

This group has 322 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#14530346C211yesmaximal, characteristic
3#14530346C211yesmaximal, characteristic
4#14526608C211yesmaximal, characteristic
5#14526607C211yesmaximal, characteristic
6#14526606C211yesmaximal, characteristic
7C17×#2100C211yesmaximal, characteristic
8#11762749—21no—
9#11762748—21no—
10#11762747—21no—
11#11762707C2211yescharacteristic
12#11762707C2211yescharacteristic
13#11762696—21no—
14#11762695—21no—
15#11762690—21no—
16#11762571—21no—
17#11762571—21no—
18#11762571—21no—
19#11762571—21no—
20#11762564C2211yescharacteristic
21#11762564C2211yescharacteristic
22C17×#389C2211yescharacteristic
23C17×#384C2211yescharacteristic
24C17×#340—21no—
25C17×#340—21no—
26C17×#336C2211yescharacteristic
27C22×C8×C17—21no—
28C2×C4⋊C4×C17—21no—
29C2×C4⋊C4×C17—21no—
30C2×C4⋊C4×C17—21no—
31C2×C4⋊C4×C17—21no—
32C2×C4⋊C4×C17D411yescharacteristic
33C2×C4⋊C4×C17D411yescharacteristic
34C2×C42×C17C2311yescharacteristic
35C2×C4⋊Dic17D411yescharacteristic
36C2×C4⋊Dic17D411yescharacteristic
37C2×C4⋊Dic17D411yescharacteristic
38C2×C4⋊Dic17D411yescharacteristic
39C2×#63225—21no—
40C2×#63225—21no—
41C2×C4×Dic17—21no—
42C22×#3622—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—
54C22×C4×C17—21no—
55C22×C4×C17—21no—
56C22×C4×C17—41no—
57C22×C4×C17C2×D411yescharacteristic
58C22×C4×C17C2×D411yescharacteristic
59C22×C4×C17C2×D411yescharacteristic
60C22×Dic17—21no—
61C22×Dic17—21no—
62C22×Dic17—21no—
63C22×Dic17—21no—
64C2×C8×C17—41no—
65C2×C8×C17—41no—
66C2×C8×C17—41no—
67C4⋊C4×C17—21no—
68C4⋊C4×C17—21no—
69C4⋊C4×C17—41no—
70C4⋊C4×C17—42no—
71C4⋊C4×C17—42no—
72C4⋊C4×C17—42no—
73C4⋊C4×C17—41no—
74C4⋊C4×C17—41no—
75C42×C17—41no—
76C4⋊Dic17—21no—
77C4⋊Dic17—21no—
78C4⋊Dic17—21no—
79C4⋊Dic17—21no—
80C4⋊Dic17—41no—
81C4⋊Dic17—41no—
82#63225—41no—
83#63225—41no—
84#63225—41no—
85#63225—41no—
86C4×Dic17—81no—
87C2×#3622—41no—
88C2×#3622—41no—
89C2×#3622—41no—
90C2×#3622—41no—
91C2×#3622—41no—
92C2×#3622—41no—
93#7832—171nomaximal, Sylow
94C23×C17#12011yescharacteristic
95C2×C4×C17—21no—
96C2×C4×C17—21no—
97C2×C4×C17—21no—
98C2×C4×C17—21no—
99C2×C4×C17—21no—
100C2×C4×C17—21no—
101C2×C4×C17—41no—
102C2×C4×C17—41no—
103C2×C4×C17—41no—
104C2×C4×C17—41no—
105C2×C4×C17—41no—
106C2×C4×C17—41no—
107C2×C4×C17—81no—
108C2×C4×C17—81no—
109C2×C4×C17—81no—
110C2×C4×C17#13511yescharacteristic
111C2×C4×C17#13511yescharacteristic
112C2×C4×C17#13511yescharacteristic
113C2×C4×C17#13711yescharacteristic
114C2×C4×C17#13711yescharacteristic
115C2×C4×C17#13711yescharacteristic
116C2×Dic17—41no—
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—
128C8×C17—81no—
129#3622—81no—
130#3622—81no—
131#2810—171no—
132#2100—171no—
133#2100—171no—
134#2100D1711yescharacteristic
135#1271—171no—
136#1271—171no—
137#1271—171no—
138C22×C17#45211yescharacteristic
139C22×C17#45211yescharacteristic
140C22×C17#45211yescharacteristic
141C22×C17#45411yescharacteristic
142C22×C17#45411yescharacteristic
143C22×C17#45411yescharacteristic
144C22×C17#45811yescharacteristic
145C4×C17—21no—
146C4×C17—21no—
147C4×C17—21no—
148C4×C17—21no—
149C4×C17—21no—
150C4×C17—21no—
151C4×C17—81no—
152C4×C17—81no—
153C4×C17—161no—
154Dic17—81no—
155Dic17—81no—
156Dic17—81no—
157Dic17—81no—
158#400—341no—
159#400—341no—
160#400—341no—
161#389—171no—
162#389—171no—
163#389C2×D1711yescharacteristic
164#387—341no—
165#387—341no—
166#387—341no—
167#384C2×D1711yescharacteristic
168#340—21no—
169#340—21no—
170#340—341no—
171#340—341no—
172#340—341no—
173#340—341no—
174#336—171no—
175#336—171no—
176#336C2×D1711yescharacteristic
177C2×C17#161511yescharacteristic
178C2×C17#161511yescharacteristic
179C2×C17#161511yescharacteristic
180C2×C17#163811yescharacteristic
181C2×C17#163811yescharacteristic
182C2×C17#163811yescharacteristic
183C2×C17#165811yescharacteristic
184C22×C8—21no—
185C22×C8—341no—
186C22×C8—341no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—171no—
192C2×C4⋊C4—171no—
193C2×C4⋊C4—171no—
194C2×C4⋊C4—171no—
195C2×C4⋊C4—341no—
196C2×C4⋊C4—341no—
197C2×C4⋊C4C22⋊D1711yescharacteristic
198C2×C4⋊C4C22⋊D1711yescharacteristic
199C2×C42—341no—
200C2×C42C22×D1711yescharacteristic
201#95—21no—
202#95—341no—
203#95—341no—
204#95—341no—
205#95—341no—
206#95—341no—
207#95—341no—
208#95—341no—
209#95—341no—
210#95—341no—
211C17#783211yescharacteristic, complemented, Sylow
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—41no—
215C22×C4—341no—
216C22×C4—341no—
217C22×C4—341no—
218C22×C4—341no—
219C22×C4D4×D1711yescharacteristic
220C22×C4D4×D1711yescharacteristic
221C22×C4C2×C22⋊D1711yescharacteristic
222C2×C8—41no—
223C2×C8—41no—
224C2×C8—41no—
225C2×C8—681no—
226C2×C8—681no—
227C2×C8—681no—
228C2×C8—681no—
229C2×C8—681no—
230C2×C8—681no—
231C4⋊C4—21no—
232C4⋊C4—21no—
233C4⋊C4—41no—
234C4⋊C4—42no—
235C4⋊C4—42no—
236C4⋊C4—42no—
237C4⋊C4—41no—
238C4⋊C4—41no—
239C4⋊C4—341no—
240C4⋊C4—341no—
241C4⋊C4—341no—
242C4⋊C4—341no—
243C4⋊C4—681no—
244C4⋊C4—681no—
245C4⋊C4—681no—
246C4⋊C4—681no—
247C4⋊C4—681no—
248C4⋊C4—681no—
249C42—41no—
250C42—1361no—
251C23#1058762311yescharacteristic
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—81no—
265C2×C4—81no—
266C2×C4—81no—
267C2×C4—681no—
268C2×C4—681no—
269C2×C4—681no—
270C2×C4—681no—
271C2×C4—681no—
272C2×C4—681no—
273C2×C4—681no—
274C2×C4—681no—
275C2×C4—681no—
276C2×C4—681no—
277C2×C4—681no—
278C2×C4—681no—
279C2×C4#1058760111yescharacteristic
280C2×C4#1058760211yescharacteristic
281C2×C4#1058760411yescharacteristic
282C2×C4#1058760511yescharacteristic
283C2×C4#1058762811yescharacteristic
284C2×C4#1058763611yescharacteristic
285C8—81no—
286C8—1361no—
287C8—1361no—
288C22#1176296811yescharacteristic
289C22#1176296911yescharacteristic
290C22#1176297011yescharacteristic
291C22#1176298011yescharacteristic
292C22#1176298011yescharacteristic
293C22#1176298111yescharacteristic
294C22#1176299811yescharacteristic
295C4—21no—
296C4—21no—
297C4—21no—
298C4—21no—
299C4—21no—
300C4—21no—
301C4—81no—
302C4—81no—
303C4—161no—
304C4—1361no—
305C4—1361no—
306C4—1361no—
307C4—1361no—
308C2#1452781211yescharacteristic
309C2#1452781311yescharacteristic
310C2#1452781411yescharacteristic
311C2#1452795311yescharacteristic
312C2#1452795411yescharacteristic
313C2#1452795511yescharacteristic
314C2#1452808511yescharacteristic
subgroupG/H
centerC23#10587623
commutator, cosocleC2×C42×C17C23
FrattiniC2×C42C22×D17
FittingC17×#2100C2
socle, prime radicalC23×C17#120
hypercenter#2100D17
hypocenterC17#7832
LCSG ▷ C2×C42×C17 ▷ C23×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2100

Complements

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

NH ≅ G/Ntype
211. C17#7832semidirect

Maximal subgroups

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

subgroupindex
#145367752
#145303462
#145266082
#145266072
#145266062
C17×#21002
#783217