Finite Group Databasebeta

← #16945492

Subgroups — #16945492

Order 4352.

388 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 99 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#14533989C211yesmaximal, characteristic
2#14528780C211yesmaximal, characteristic
3#14526815C214yesmaximal
4C17×#1461C211yesmaximal, characteristic
5C2×#10587555C411yescharacteristic
6#11762833—21no—
7C2×#10587507—21no—
8#11762729C412yes—
9#11762729C2212yes—
10#11762716—21no—
11#11762707—21no—
12#11762707—21no—
13#11762678—21no—
14C4×C4⋊Dic17C411yescharacteristic
15#11762578C2212yes—
16C2×C4×Q8×C17C2211yescharacteristic
17C17×#431—21no—
18C17×#324—21no—
19C17×#324C2212yes—
20C22×Q8×C17D411yescharacteristic
21C22×Dic34C2×C412yes—
22C4×Q8×C17—41no—
23C4×Q8×C17—41no—
24C2×C4⋊C4×C17C2×C411yescharacteristic
25C2×C4⋊C4×C17D411yescharacteristic
26C2×C4⋊C4×C17C2311yescharacteristic
27C2×C42×C17C2×C411yescharacteristic
28C2×C42×C17D411yescharacteristic
29C2×C42×C17D411yescharacteristic
30C2×C4⋊Dic17—21no—
31C2×C4⋊Dic17—21no—
32C2×C4⋊Dic17—21no—
33C2×#63225—22no—
34C2×#63225—22no—
35C2×C4×Dic17—21no—
36C2×#63223—22no—
37#10587555—41no—
38#10587555—41no—
39C17×C4⋊C8—41no—
40C17×C22⋊C8—22no—
41C4×C8×C17—41no—
42#10587507—42no—
43#10587502—22no—
44#10587502—22no—
45#10587502C2×C412yes—
46C4⋊#3622—41no—
47C4⋊#3622—41no—
48C2×Q8×C17—41no—
49C2×Q8×C17—41no—
50C2×Q8×C17SD1612yes—
51C2×Q8×C17Q1612yes—
52C22×C4×C17C22⋊C411yescharacteristic
53C22×C4×C17C22⋊C411yescharacteristic
54C22×C4×C17C22⋊C411yescharacteristic
55C22×C4×C17C22⋊C411yescharacteristic
56C22×C4×C17C22×C411yescharacteristic
57C22×C4×C17C2×D411yescharacteristic
58C22×C4×C17C2×D411yescharacteristic
59C22×Dic17—22no—
60C22×Dic17—22no—
61C2×Dic34—42no—
62C2×Dic34—82no—
63C2×C8×C17—42no—
64C4⋊C4×C17—41no—
65C4⋊C4×C17—41no—
66C4⋊C4×C17—41no—
67C42×C17—21no—
68C42×C17—21no—
69C42×C17—21no—
70C42×C17—21no—
71C42×C17—21no—
72C42×C17—21no—
73C4⋊Dic17—24no—
74C4⋊Dic17—42no—
75C4⋊Dic17—41no—
76C4⋊Dic17—41no—
77#63225—82no—
78#63225—82no—
79C4×Dic17—42no—
80#63223—42no—
81#63223—42no—
82C2×#3622—42no—
83#11908—171nomaximal, Sylow
84C23×C17C2×C22⋊C411yescharacteristic
85Q8×C17—42no—
86Q8×C17—42no—
87C2×C4×C17—21no—
88C2×C4×C17—21no—
89C2×C4×C17—21no—
90C2×C4×C17—21no—
91C2×C4×C17—21no—
92C2×C4×C17—21no—
93C2×C4×C17—22no—
94C2×C4×C17—21no—
95C2×C4×C17—21no—
96C2×C4×C17—21no—
97C2×C4×C17—41no—
98C2×C4×C17—41no—
99C2×C4×C17—41no—
100C2×C4×C17#9911yescharacteristic
101C2×C4×C17#9911yescharacteristic
102C2×C4×C17#10312yes—
103C2×C4×C17#10312yes—
104C2×C4×C17C2×SD1611yescharacteristic
105C2×C4×C17C2×Q1611yescharacteristic
106C2×Dic17—24no—
107C2×Dic17—42no—
108C2×Dic17—42no—
109C2×Dic17—42no—
110C2×Dic17—42no—
111C2×Dic17—42no—
112Dic34—84no—
113C8×C17—82no—
114#3622—82no—
115#2567—171no—
116#1801—171no—
117#1461D1711yescharacteristic
118#1354—174no—
119C22×C17—21no—
120C22×C17—21no—
121C22×C17C2×#9911yescharacteristic
122C22×C17C2×#10311yescharacteristic
123C22×C17#42111yescharacteristic
124C4×C17—21no—
125C4×C17—21no—
126C4×C17—22no—
127C4×C17—22no—
128C4×C17—21no—
129C4×C17—41no—
130C4×C17—41no—
131C4×C17—41no—
132C4×C17#35612yes—
133Dic17—44no—
134Dic17—82no—
135C2×C4⋊Q8—171no—
136C2×C4×Q8C2×D1711yescharacteristic
137#431—21no—
138#423—341no—
139C2×#101—341no—
140#395—172no—
141#395—172no—
142#391—341no—
143#389—341no—
144#389—341no—
145#384—341no—
146C4×C4⋊C4—171no—
147#343—172no—
148#324—21no—
149#324C2×D1712yes—
150C2×C17—21no—
151C2×C17—21no—
152C2×C17#152011yescharacteristic
153C2×C17#212211yescharacteristic
154C2×C17C2×#35611yescharacteristic
155C22×Q8—172no—
156C22×Q8D6811yescharacteristic
157C2×M16—342no—
158C4⋊Q8—681no—
159C4⋊Q8—681no—
160C4×Q8—41no—
161C4×Q8—41no—
162C2×C4⋊C4—341no—
163C2×C4⋊C4—341no—
164C2×C4⋊C4—341no—
165C2×C4⋊C4—342no—
166C2×C4⋊C4—342no—
167C2×C4⋊C4C4×D1711yescharacteristic
168C2×C4⋊C4C22⋊D1711yescharacteristic
169C2×C4⋊C4C22×D1711yescharacteristic
170C2×C42—341no—
171C2×C42C4×D1711yescharacteristic
172C2×C42D6811yescharacteristic
173C2×C42C22⋊D1711yescharacteristic
174C4⋊C8—41no—
175C4⋊C8—681no—
176C4⋊C8—681no—
177#101—682no—
178C22⋊C8—22no—
179C4×C8—41no—
180#95—172no—
181#95—342no—
182#95—342no—
183C17#1190811yescharacteristic, complemented, Sylow
184C2×Q8—41no—
185C2×Q8—41no—
186C2×Q8—682no—
187C2×Q8—1362no—
188C2×Q8#6321912yes—
189C2×Q8Dic6812yes—
190C22×C4—342no—
191C22×C4—342no—
192C22×C4#6322711yescharacteristic
193C22×C4#6322711yescharacteristic
194C22×C4#6322711yescharacteristic
195C22×C4#6322711yescharacteristic
196C22×C4C2×C4×D1711yescharacteristic
197C22×C4C2×D6811yescharacteristic
198C22×C4C2×C22⋊D1711yescharacteristic
199M16—682no—
200M16—682no—
201C2×C8—42no—
202C2×C8—682no—
203C4⋊C4—41no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—344no—
207C4⋊C4—682no—
208C4⋊C4—681no—
209C4⋊C4—681no—
210C4⋊C4—1362no—
211C4⋊C4—1362no—
212C42—21no—
213C42—21no—
214C42—21no—
215C42—21no—
216C42—21no—
217C42—21no—
218C42—682no—
219C23C2×#6322711yescharacteristic
220Q8—42no—
221Q8—42no—
222Q8—1364no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—22no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—344no—
237C2×C4—682no—
238C2×C4—682no—
239C2×C4—682no—
240C2×C4—682no—
241C2×C4—682no—
242C2×C4#1058747711yescharacteristic
243C2×C4#1058747711yescharacteristic
244C2×C4#1058748712yes—
245C2×C4#1058748712yes—
246C2×C4C2×#6321911yescharacteristic
247C2×C4C2×Dic6811yescharacteristic
248C8—82no—
249C8—1362no—
250C22—21no—
251C22—21no—
252C22C2×#1058747711yescharacteristic
253C22C2×#1058748711yescharacteristic
254C22#1176282511yescharacteristic
255C4—21no—
256C4—22no—
257C4—22no—
258C4—21no—
259C4—21no—
260C4—41no—
261C4—41no—
262C4—41no—
263C4—684no—
264C4—1362no—
265C4#1176260712yes—
266C2—21no—
267C2—21no—
268C2#1452735711yescharacteristic
269C2#1453043311yescharacteristic
270C2C2×#1176260711yescharacteristic
subgroupG/H
centerC22C2×#10587477
commutatorC22×C4×C17C22×C4
FrattiniC2×C4⋊C4C22×D17
FittingC17×#1461C2
socleC22×C17C2×#99
prime radicalC23×C17C2×C22⋊C4
cosocleC2×C4⋊C4×C17C23
hypercenter#1461D17
hypocenterC17#11908
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1461

Complements

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

NH ≅ G/Ntype
183. C17#11908semidirect

Maximal subgroups

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

subgroupindex
#145339892
#145287802
#145268152
C17×#14612
#1190817