Finite Group Databasebeta

← #16950326

Subgroups — #16950326

Order 4352.

468 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 95 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#14531353C211yesmaximal, characteristic
2C2×#11762607C212yesmaximal
3#14528778C212yesmaximal
4#14526911C211yesmaximal, characteristic
5C17×#1394C211yesmaximal, characteristic
6C2×#10587630C2211yescharacteristic
7C2×Q8×Dic17C2211yescharacteristic
8C2×#10587573C411yescharacteristic
9#11762832—22no—
10C2×#10587507C2212yes—
11#11762715C411yescharacteristic
12#11762706—22no—
13#11762678C411yescharacteristic
14#11762660—22no—
15C42×Dic17C411yescharacteristic
16#11762607—24no—
17#11762577—22no—
18C2×C17×#101C2212yes—
19C17×#391C2211yescharacteristic
20C22×Q8×C17C2311yescharacteristic
21C22×Dic34C2×C411yescharacteristic
22C2×M16×C17—22no—
23C2×C4⋊C4×C17C2×C411yescharacteristic
24C2×C42×C17C2×C411yescharacteristic
25Q8×Dic17—41no—
26Q8×Dic17—41no—
27#10587630—22no—
28#10587630D412yes—
29#10587630Q812yes—
30C2×C4⋊Dic17C2×C411yescharacteristic
31C2×C4⋊Dic17D412yes—
32C2×#63225—22no—
33C2×#63225—21no—
34C2×#63225—22no—
35C2×C4×Dic17—21no—
36C2×C4×Dic17—21no—
37C2×C4×Dic17—21no—
38C2×C4×Dic17C2×C411yescharacteristic
39C2×C4×Dic17C2×C411yescharacteristic
40C2×C4×Dic17D412yes—
41C2×#63223—22no—
42#10587573—41no—
43#10587573—41no—
44C17×#101—22no—
45C17×#101—22no—
46C17×#95—22no—
47#10587507—22no—
48#10587507—22no—
49#10587502—22no—
50#10587485—42no—
51#10587485—42no—
52C2×Q8×C17—41no—
53C2×Q8×C17—41no—
54C2×Q8×C17C2×D411yescharacteristic
55C2×Q8×C17C2×Q811yescharacteristic
56C2×Q8×C17#4112yes—
57C22×C4×C17—21no—
58C22×C4×C17—21no—
59C22×C4×C17C22×C411yescharacteristic
60C22×C4×C17C2×D412yes—
61C22×Dic17—21no—
62C22×Dic17—21no—
63C22×Dic17C22⋊C411yescharacteristic
64C22×Dic17C22⋊C412yes—
65C22×Dic17C22⋊C411yescharacteristic
66C2×Dic34—21no—
67C2×Dic34—41no—
68C2×Dic34—41no—
69C2×Dic34C4⋊C412yes—
70M16×C17—42no—
71M16×C17—42no—
72C2×C8×C17—42no—
73C4⋊C4×C17—41no—
74C42×C17—41no—
75C4⋊Dic17—41no—
76C4⋊Dic17—42no—
77#63225—24no—
78#63225—24no—
79#63225—42no—
80#63225—44no—
81C4×Dic17—24no—
82C4×Dic17—21no—
83C4×Dic17—22no—
84C4×Dic17—22no—
85C4×Dic17—21no—
86C4×Dic17—21no—
87C4×Dic17—42no—
88C4×Dic17—41no—
89C4×Dic17—41no—
90C4×Dic17C4⋊C412yes—
91#63223—42no—
92#63223—42no—
93C2×#3622—42no—
94#12802—171nomaximal, Sylow
95C23×C17C2×C22⋊C411yescharacteristic
96Q8×C17—41no—
97Q8×C17—41no—
98Q8×C17—42no—
99C2×C4×C17—21no—
100C2×C4×C17—22no—
101C2×C4×C17—21no—
102C2×C4×C17—22no—
103C2×C4×C17—22no—
104C2×C4×C17—41no—
105C2×C4×C17—41no—
106C2×C4×C17—42no—
107C2×C4×C17—41no—
108C2×C4×C17C2×C4⋊C411yescharacteristic
109C2×C4×C17#11711yescharacteristic
110C2×C4×C17#12112yes—
111C2×C4×C17C22⋊Q812yes—
112C2×Dic17—22no—
113C2×Dic17—22no—
114C2×Dic17—22no—
115C2×Dic17—22no—
116C2×Dic17—22no—
117C2×Dic17—21no—
118C2×Dic17—22no—
119C2×Dic17—41no—
120C2×Dic17—41no—
121C2×Dic17—41no—
122C2×Dic17—42no—
123C2×Dic17#9911yescharacteristic
124C2×Dic17#9911yescharacteristic
125Dic34—42no—
126Dic34—42no—
127C8×C17—82no—
128#3622—82no—
129C4×C4⋊Q8—171no—
130C2×#356—172no—
131#1801—172no—
132#1394—171no—
133#1394D1711yescharacteristic
134C22×C17—21no—
135C22×C17—21no—
136C22×C17#38011yescharacteristic
137C22×C17C2×#9911yescharacteristic
138C22×C17#41011yescharacteristic
139C4×C17—22no—
140C4×C17—21no—
141C4×C17—21no—
142C4×C17—22no—
143C4×C17—42no—
144C4×C17—81no—
145Dic17—24no—
146Dic17—21no—
147Dic17—42no—
148Dic17—41no—
149Dic17—42no—
150Dic17#35612yescomplemented
151C2×C4⋊Q8—171no—
152C2×C4×Q8—171no—
153C2×C4×Q8—171no—
154#423—342no—
155C2×#101—172no—
156C2×#101C2×D1712yes—
157#391—171no—
158#391C2×D1711yescharacteristic
159#389—342no—
160#384—171no—
161C4×C4⋊C4—342no—
162C43—171no—
163#356—344no—
164#343—342no—
165C2×C17—21no—
166C2×C17—21no—
167C2×C17#179911yescharacteristic
168C2×C17C2×#35611yescharacteristic
169C2×C17#213211yescharacteristic
170C22×Q8—171no—
171C22×Q8C22×D1711yescharacteristic
172C2×M16—22no—
173C2×M16—342no—
174C4⋊Q8—172no—
175C4⋊Q8—172no—
176C4⋊Q8—342no—
177C4×Q8—681no—
178C4×Q8—681no—
179C4×Q8—681no—
180C4×Q8—681no—
181C2×C4⋊C4—171no—
182C2×C4⋊C4—172no—
183C2×C4⋊C4—342no—
184C2×C4⋊C4—341no—
185C2×C4⋊C4—342no—
186C2×C4⋊C4C4×D1711yescharacteristic
187C2×C42—171no—
188C2×C42—171no—
189C2×C42—172no—
190C2×C42—341no—
191C2×C42—341no—
192C2×C42—341no—
193C2×C42C4×D1711yescharacteristic
194C4⋊C8—682no—
195C4⋊C8—682no—
196#101—22no—
197#101—22no—
198#101—342no—
199#101—342no—
200#95—22no—
201#95—342no—
202C17#1280211yescharacteristic, complemented, Sylow
203C2×Q8—41no—
204C2×Q8—41no—
205C2×Q8—172no—
206C2×Q8—341no—
207C2×Q8—681no—
208C2×Q8—681no—
209C2×Q8#6325212yes—
210C2×Q8D4×D1711yescharacteristic
211C2×Q8Q8×D1711yescharacteristic
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—171no—
215C22×C4—172no—
216C22×C4—171no—
217C22×C4—341no—
218C22×C4—341no—
219C22×C4C2×C4×D1711yescharacteristic
220C22×C4D4×D1712yes—
221M16—42no—
222M16—42no—
223M16—682no—
224M16—682no—
225C2×C8—42no—
226C2×C8—682no—
227C4⋊C4—41no—
228C4⋊C4—344no—
229C4⋊C4—344no—
230C4⋊C4—681no—
231C4⋊C4—682no—
232C4⋊C4—682no—
233C4⋊C4—684no—
234C42—41no—
235C42—172no—
236C42—342no—
237C42—342no—
238C42—341no—
239C42—341no—
240C42—344no—
241C42—341no—
242C42—681no—
243C42—681no—
244C42—682no—
245C23C22⋊C4×D1711yescharacteristic
246Q8—42no—
247Q8—41no—
248Q8—41no—
249Q8—682no—
250Q8—682no—
251C2×C4—21no—
252C2×C4—22no—
253C2×C4—21no—
254C2×C4—22no—
255C2×C4—22no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—42no—
259C2×C4—41no—
260C2×C4—171no—
261C2×C4—171no—
262C2×C4—342no—
263C2×C4—342no—
264C2×C4—342no—
265C2×C4—342no—
266C2×C4—341no—
267C2×C4—342no—
268C2×C4—342no—
269C2×C4—681no—
270C2×C4—681no—
271C2×C4—681no—
272C2×C4—682no—
273C2×C4#1058755811yescharacteristic
274C2×C4#1058757012yes—
275C2×C4C4⋊C4×D1711yescharacteristic
276C2×C4#1058758212yes—
277C8—82no—
278C8—1362no—
279C22—21no—
280C22—21no—
281C22#1176266811yescharacteristic
282C22#99×D1711yescharacteristic
283C22#1176278111yescharacteristic
284C4—22no—
285C4—21no—
286C4—21no—
287C4—22no—
288C4—42no—
289C4—81no—
290C4—172no—
291C4—344no—
292C4—341no—
293C4—682no—
294C4—681no—
295C4—682no—
296C2—21no—
297C2—21no—
298C2#1452877111yescharacteristic
299C2D17×#35611yescharacteristic
300C2#1453046611yescharacteristic
subgroupG/H
centerC22#99×D17
commutatorC22×C4×C17C22×C4
FrattiniC22×Q8C22×D17
FittingC17×#1394C2
socleC22×C17C2×#99
prime radicalC23×C17C2×C22⋊C4
cosocleC22×Q8×C17C23
hypercenter#1394D17
hypocenterC17#12802
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ #1394

Complements

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

NH ≅ G/Ntype
150. Dic17#356semidirect
202. C17#12802semidirect

Maximal subgroups

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

subgroupindex
#145313532
C2×#117626072
#145287782
#145269112
C17×#13942
#1280217