Finite Group Databasebeta

← #16954745

Subgroups — #16954745

Order 4352.

304 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 75 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#14530479C211yesmaximal, characteristic
2#14530473C211yesmaximal, characteristic
3#14526957C212yesmaximal, complemented
4#14526953C212yesmaximal, complemented
5C17×#3223C211yesmaximal, characteristic
6#11762793—21no—
7C2×#10587507—21no—
8#11762608—21no—
9#11762608C2212yes—
10#11762608C2212yes—
11#11762606—21no—
12C17×#541C411yescharacteristic
13C17×#536C2211yescharacteristic
14C17×#497C411yescharacteristic
15C17×#494C2211yescharacteristic
16C17×#491C2211yescharacteristic
17C17×#488C411yescharacteristic
18C17×#464—21no—
19C17×#462—21no—
20C17×#452—21no—
21C17×#451—21no—
22C17×#433C411yescharacteristic
23C2×#41×C17D411yescharacteristic
24C22×Q8×C17D411yescharacteristic
25C2×Q16×C17—21no—
26C2×Q16×C17—21no—
27C2×Q16×C17—21no—
28C2×SD16×C17—21no—
29C17×C4⋊Q8C2×C411yescharacteristic
30C17×C4⋊Q8D411yescharacteristic
31C17×C4⋊Q8C2311yescharacteristic
32C17×#126—41no—
33C17×#125—41no—
34C17×#125C2×C411yescharacteristic
35C17×#124C2×C411yescharacteristic
36C17×#124D411yescharacteristic
37C17×#123—41no—
38C17×C22⋊Q8—21no—
39C17×C22⋊Q8—41no—
40C4×Q8×C17—21no—
41C17×#117C2×C411yescharacteristic
42C2×#63223—41no—
43C2×#63223—41no—
44C17×C4⋊C8—21no—
45C17×#103—21no—
46C17×#103—21no—
47C17×#103—21no—
48C17×#102—21no—
49C17×C22⋊C8—21no—
50C17×#97C2×C411yescharacteristic
51C4×C8×C17C2×C411yescharacteristic
52#10587507—22no—
53#10587507—22no—
54#10587507—41no—
55#10587504—41no—
56#41×C17—81no—
57C2×Q8×C17—21no—
58C2×Q8×C17—21no—
59C2×Q8×C17—81no—
60C2×Q8×C17C22⋊C411yescharacteristic
61C2×Q8×C17C2×D411yescharacteristic
62C2×Q8×C17C2×D411yescharacteristic
63C2×D4×C17—21no—
64C2×D4×C17C22⋊C411yescharacteristic
65C22×C4×C17—21no—
66C22×C4×C17—21no—
67C22×C4×C17C22⋊C411yescharacteristic
68Q16×C17—81no—
69Q16×C17—81no—
70Q16×C17—81no—
71SD16×C17—81no—
72C2×C8×C17—21no—
73C2×C8×C17—21no—
74C4⋊C4×C17—21no—
75C4⋊C4×C17—21no—
76C4⋊C4×C17—41no—
77C4⋊C4×C17—41no—
78C4⋊C4×C17—41no—
79C4⋊C4×C17—41no—
80C4⋊C4×C17—41no—
81C4⋊C4×C17—41no—
82C22⋊C4×C17—21no—
83C22⋊C4×C17—41no—
84C22⋊C4×C17—41no—
85C22⋊C4×C17—41no—
86C42×C17—41no—
87C42×C17C22⋊C411yescharacteristic
88C42×C17C22×C411yescharacteristic
89#63223—42no—
90#63223—42no—
91#63223—81no—
92#63223—81no—
93C2×#3622—81no—
94C2×#3622—81no—
95#13612—171nomaximal, Sylow
96C23×C17—21no—
97C23×C17#9911yescharacteristic
98Q8×C17—41no—
99Q8×C17—41no—
100Q8×C17—41no—
101Q8×C17—41no—
102Q8×C17—41no—
103Q8×C17—81no—
104D4×C17—41no—
105D4×C17—81no—
106C2×C4×C17—21no—
107C2×C4×C17—21no—
108C2×C4×C17—21no—
109C2×C4×C17—21no—
110C2×C4×C17—21no—
111C2×C4×C17—41no—
112C2×C4×C17—41no—
113C2×C4×C17—41no—
114C2×C4×C17—41no—
115C2×C4×C17—41no—
116C2×C4×C17—41no—
117C2×C4×C17—41no—
118C2×C4×C17#9911yescharacteristic
119C2×C4×C17C2×C22⋊C411yescharacteristic
120C8×C17—41no—
121C8×C17—41no—
122#3622—82no—
123#3622—82no—
124#3223D1711yescharacteristic
125#2135—171no—
126#2133—171no—
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—
141C4×C17—81no—
142C4×C17—81no—
143#541Dic1711yescharacteristic
144#536C2×D1711yescharacteristic
145#497Dic1711yescharacteristic
146#494C2×D1711yescharacteristic
147#491C2×D1711yescharacteristic
148#488Dic1711yescharacteristic
149#464—21no—
150#462—21no—
151#452—21no—
152#451—21no—
153#433Dic1711yescharacteristic
154#413—341no—
155C2×#101—341no—
156#356—172no—
157#356—172no—
158#356—341no—
159#355—341no—
160C2×C17—21no—
161C2×C17—41no—
162C2×C17—81no—
163C2×C17#212711yescharacteristic
164C2×#41C22⋊D1711yescharacteristic
165C22×Q8C22⋊D1711yescharacteristic
166C2×Q16—21no—
167C2×Q16—21no—
168C2×Q16—21no—
169C2×SD16—21no—
170C2×M16—681no—
171C2×M16—681no—
172C4⋊Q8C2×Dic1711yescharacteristic
173C4⋊Q8C22⋊D1711yescharacteristic
174C4⋊Q8C22×D1711yescharacteristic
175#126—41no—
176#125—41no—
177#125C2×Dic1711yescharacteristic
178#124C2×Dic1711yescharacteristic
179#124C22⋊D1711yescharacteristic
180#123—41no—
181C22⋊Q8—21no—
182C22⋊Q8—41no—
183C4×Q8—21no—
184#117C2×Dic1711yescharacteristic
185C4⋊C8—21no—
186#103—21no—
187#103—21no—
188#103—21no—
189#102—21no—
190#101—342no—
191#101—342no—
192#101—681no—
193#100—681no—
194C22⋊C8—21no—
195#97C2×Dic1711yescharacteristic
196C4×C8C2×Dic1711yescharacteristic
197C17#1361211yescharacteristic, complemented, Sylow
198#41—81no—
199C2×Q8—21no—
200C2×Q8—21no—
201C2×Q8—81no—
202C2×Q8C22⋊Dic1711yescharacteristic
203C2×Q8C2×C22⋊D1711yescharacteristic
204C2×Q8C2×C22⋊D1711yescharacteristic
205C2×D4—21no—
206C2×D4C22⋊Dic1711yescharacteristic
207C22×C4—21no—
208C22×C4—21no—
209C22×C4C22⋊Dic1711yescharacteristic
210Q16—81no—
211Q16—81no—
212Q16—81no—
213SD16—81no—
214M16—682no—
215M16—682no—
216M16—1361no—
217M16—1361no—
218C2×C8—21no—
219C2×C8—21no—
220C2×C8—1361no—
221C2×C8—1361no—
222C4⋊C4—21no—
223C4⋊C4—21no—
224C4⋊C4—41no—
225C4⋊C4—41no—
226C4⋊C4—41no—
227C4⋊C4—41no—
228C4⋊C4—41no—
229C4⋊C4—41no—
230C22⋊C4—21no—
231C22⋊C4—41no—
232C22⋊C4—41no—
233C22⋊C4—41no—
234C42—41no—
235C42C22⋊Dic1711yescharacteristic
236C42C22×Dic1711yescharacteristic
237C23—21no—
238C23#1058750511yescharacteristic
239Q8—41no—
240Q8—41no—
241Q8—41no—
242Q8—41no—
243Q8—41no—
244Q8—81no—
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—41no—
258C2×C4—41no—
259C2×C4#1058750511yescharacteristic
260C2×C4C2×C22⋊Dic1711yescharacteristic
261C8—41no—
262C8—41no—
263C8—1362no—
264C8—1362no—
265C22—21no—
266C22—41no—
267C22—41no—
268C22—81no—
269C22C2×#1058750511yescharacteristic
270C4—21no—
271C4—21no—
272C4—41no—
273C4—41no—
274C4—41no—
275C4—41no—
276C4—41no—
277C4—81no—
278C4—81no—
279C2—21no—
280C2—41no—
281C2—81no—
282C2#1453045311yescharacteristic
subgroupG/H
centerC2#14530453
commutatorC42×C17C22×C4
FrattiniC4⋊Q8C22×D17
FittingC17×#3223C2
socleC2×C17#2127
prime radicalC2×#41×C17D4
cosocleC17×C4⋊Q8C23
hypercenter#3223D17
hypocenterC17#13612
LCSG ▷ C42×C17 ▷ C2×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2 ◁ C22 ◁ C22×C4 ◁ #536 ◁ #3223

Complements

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

NH ≅ G/Ntype
3. #14526957C2semidirect
4. #14526953C2semidirect
197. C17#13612semidirect

Maximal subgroups

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

subgroupindex
#145304792
#145304732
#145269572
#145269532
C17×#32232
#1361217