Finite Group Databasebeta

← #16954743

Subgroups — #16954743

Order 4352.

304 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 67 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#14539867C211yesmaximal, characteristic
2#14530479C211yesmaximal, characteristic
3#14526956C212yesmaximal, complemented
4#14526952C212yesmaximal, complemented
5C17×#2133C211yesmaximal, characteristic
6#11763421C411yescharacteristic
7#11763204C411yescharacteristic
8#11763188C2211yescharacteristic
9#11763177C2211yescharacteristic
10#11763163C411yescharacteristic
11#11763028—21no—
12#11763016—21no—
13#11762971—21no—
14#11762965—21no—
15#11762870C411yescharacteristic
16#11762793—21no—
17#11762608—21no—
18#11762608C2212yes—
19C17×#536C2211yescharacteristic
20C2×C17×#101—21no—
21C17×#356C2212yes—
22C17×#355—21no—
23C2×#41×C17D411yescharacteristic
24C22×Q8×C17D411yescharacteristic
25C2×M16×C17—41no—
26C17×C4⋊Q8D411yescharacteristic
27C17×C4⋊Q8C2311yescharacteristic
28C17×#124C2×C411yescharacteristic
29C17×#124D411yescharacteristic
30C17×#123—41no—
31C17×C22⋊Q8—41no—
32C17×#117C2×C411yescharacteristic
33C2×#63231—21no—
34C2×#63231—21no—
35C2×#63231—21no—
36C2×#63229—21no—
37#10587610—21no—
38C2×#63223—41no—
39#10587575—41no—
40#10587565—41no—
41#10587556C2×C411yescharacteristic
42#10587555C2×C411yescharacteristic
43C4×Dic34—21no—
44C17×#101—22no—
45C17×#101—41no—
46#10587507—22no—
47#10587506—21no—
48#10587506—21no—
49#10587506—21no—
50#10587504—41no—
51#10587503—21no—
52C22⋊#3622—21no—
53C4⋊#3622—21no—
54#10587474C2×C411yescharacteristic
55C4×#3622C2×C411yescharacteristic
56#41×C17—81no—
57C2×Q8×C17—21no—
58C2×Q8×C17—81no—
59C2×Q8×C17C22⋊C411yescharacteristic
60C2×Q8×C17C2×D411yescharacteristic
61C2×Q8×C17C2×D411yescharacteristic
62C2×D4×C17—21no—
63C2×D4×C17C22⋊C411yescharacteristic
64C22×C4×C17—21no—
65C22×C4×C17—21no—
66C22×C4×C17C22⋊C411yescharacteristic
67C2×Dic34—21no—
68M16×C17—42no—
69M16×C17—81no—
70C2×C8×C17—81no—
71C4⋊C4×C17—21no—
72C4⋊C4×C17—41no—
73C4⋊C4×C17—41no—
74C22⋊C4×C17—21no—
75C22⋊C4×C17—41no—
76C22⋊C4×C17—41no—
77C42×C17C22⋊C411yescharacteristic
78C42×C17C22×C411yescharacteristic
79C22⋊Dic17—41no—
80#63231—81no—
81#63231—81no—
82#63231—81no—
83#63229—81no—
84C4⋊Dic17—21no—
85C4⋊Dic17—41no—
86#63225—41no—
87#63225—41no—
88#63225—41no—
89C4×Dic17—41no—
90#63223—42no—
91#63223—81no—
92C2×#3622—21no—
93C2×#3622—21no—
94C2×#3622—81no—
95#13612—171nomaximal, Sylow
96C23×C17—21no—
97C23×C17#9911yescharacteristic
98Q8×C17—41no—
99Q8×C17—41no—
100Q8×C17—41no—
101Q8×C17—81no—
102D4×C17—41no—
103D4×C17—81no—
104C2×C4×C17—21no—
105C2×C4×C17—21no—
106C2×C4×C17—21no—
107C2×C4×C17—21no—
108C2×C4×C17—21no—
109C2×C4×C17—41no—
110C2×C4×C17—41no—
111C2×C4×C17—41no—
112C2×C4×C17—41no—
113C2×C4×C17—41no—
114C2×C4×C17#9911yescharacteristic
115C2×C4×C17C2×C22⋊C411yescharacteristic
116C2×Dic17—41no—
117C2×Dic17—41no—
118Dic34—41no—
119Dic34—41no—
120C8×C17—82no—
121#3622—41no—
122#3622—41no—
123#3622—82no—
124#3223—171no—
125#2135—171no—
126#2133D1711yescharacteristic
127#1413—172no—
128#1411—172no—
129C22×C17—21no—
130C22×C17—41no—
131C22×C17—41no—
132C22×C17—81no—
133C22×C17C2×#9911yescharacteristic
134C4×C17—21no—
135C4×C17—21no—
136C4×C17—41no—
137C4×C17—41no—
138C4×C17—41no—
139C4×C17—41no—
140C4×C17—41no—
141Dic17—81no—
142Dic17—81no—
143#541—171no—
144#536C2×D1711yescharacteristic
145#497—171no—
146#494—171no—
147#491—171no—
148#488—171no—
149#464—341no—
150#462—341no—
151#452—341no—
152#451—341no—
153#433—171no—
154#413—341no—
155C2×#101—21no—
156#356—172no—
157#356—341no—
158#356C2×D1712yes—
159#355—21no—
160C2×C17—21no—
161C2×C17—41no—
162C2×C17—81no—
163C2×C17#212711yescharacteristic
164C2×#41D6811yescharacteristic
165C22×Q8C22⋊D1711yescharacteristic
166C2×Q16—341no—
167C2×Q16—341no—
168C2×Q16—341no—
169C2×SD16—341no—
170C2×M16—41no—
171C2×M16—681no—
172C4⋊Q8—171no—
173C4⋊Q8D6811yescharacteristic
174C4⋊Q8C22×D1711yescharacteristic
175#126—681no—
176#125—171no—
177#125—681no—
178#124C4×D1711yescharacteristic
179#124C22⋊D1711yescharacteristic
180#123—41no—
181C22⋊Q8—41no—
182C22⋊Q8—341no—
183C4×Q8—341no—
184#117C4×D1711yescharacteristic
185C4⋊C8—341no—
186#103—341no—
187#103—341no—
188#103—341no—
189#102—341no—
190#101—22no—
191#101—41no—
192#101—342no—
193#100—681no—
194C22⋊C8—341no—
195#97—171no—
196C4×C8—171no—
197C17#1361211yescharacteristic, complemented, Sylow
198#41—81no—
199C2×Q8—21no—
200C2×Q8—81no—
201C2×Q8—341no—
202C2×Q8#6322711yescharacteristic
203C2×Q8C2×D6811yescharacteristic
204C2×Q8C2×C22⋊D1711yescharacteristic
205C2×D4—21no—
206C2×D4#6322711yescharacteristic
207C22×C4—21no—
208C22×C4—21no—
209C22×C4#6322711yescharacteristic
210Q16—1361no—
211Q16—1361no—
212Q16—1361no—
213SD16—1361no—
214M16—42no—
215M16—81no—
216M16—682no—
217M16—1361no—
218C2×C8—81no—
219C2×C8—341no—
220C2×C8—341no—
221C2×C8—1361no—
222C4⋊C4—21no—
223C4⋊C4—41no—
224C4⋊C4—41no—
225C4⋊C4—341no—
226C4⋊C4—681no—
227C4⋊C4—681no—
228C4⋊C4—681no—
229C4⋊C4—681no—
230C22⋊C4—21no—
231C22⋊C4—41no—
232C22⋊C4—41no—
233C22⋊C4—681no—
234C42—681no—
235C42#6322711yescharacteristic
236C42C2×C4×D1711yescharacteristic
237C23—21no—
238C23#1058747711yescharacteristic
239Q8—41no—
240Q8—41no—
241Q8—41no—
242Q8—81no—
243Q8—681no—
244Q8—681no—
245D4—41no—
246D4—81no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—681no—
258C2×C4—681no—
259C2×C4#1058747711yescharacteristic
260C2×C4C2×#6322711yescharacteristic
261C8—82no—
262C8—681no—
263C8—681no—
264C8—1362no—
265C22—21no—
266C22—41no—
267C22—41no—
268C22—81no—
269C22C2×#1058747711yescharacteristic
270C4—21no—
271C4—21no—
272C4—41no—
273C4—41no—
274C4—41no—
275C4—41no—
276C4—41no—
277C4—1361no—
278C4—1361no—
279C2—21no—
280C2—41no—
281C2—81no—
282C2#1453045111yescharacteristic
subgroupG/H
centerC2#14530451
commutatorC42×C17C22×C4
FrattiniC4⋊Q8C22×D17
FittingC17×#2133C2
socleC2×C17#2127
prime radicalC2×#41×C17D4
cosocleC17×C4⋊Q8C23
hypercenter#2133D17
hypocenterC17#13612
LCSG ▷ C42×C17 ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C22 ◁ C22×C4 ◁ #536 ◁ #2133

Complements

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

NH ≅ G/Ntype
3. #14526956C2semidirect
4. #14526952C2semidirect
197. C17#13612semidirect

Maximal subgroups

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

subgroupindex
#145398672
#145304792
#145269562
#145269522
C17×#21332
#1361217