Finite Group Databasebeta

← #17959795

Subgroups — #17959795

Order 4352.

440 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 80 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#14544648C211yesmaximal, characteristic
2#14544019C211yesmaximal, characteristic
3#14543783C214yesmaximal, complemented
4#14533095C211yesmaximal, characteristic
5#11763812—21no—
6C2×#10587553—21no—
7#11763777—21no—
8#11763689C2212yes—
9#11763655C2212yes—
10#11763652—21no—
11C2×C4×C22⋊D17C2211yescharacteristic
12#11762747C2212yes—
13#11762744C412yes—
14#11762705—21no—
15#11762688—21no—
16#11762682—21no—
17#11762669C411yescharacteristic
18#11762666—21no—
19C22×C4⋊C4×C17C411yescharacteristic
20C23×C4×C17—21no—
21C23×C4×C17C2×C411yescharacteristic
22C22×C22⋊D17D411yescharacteristic
23C22×C4×D17D411yescharacteristic
24C2×#63247—22no—
25C2×#63242—41no—
26C2×C4⋊C4×C17—21no—
27C2×C4⋊C4×C17—41no—
28C2×C4⋊C4×C17—41no—
29C2×C4⋊C4×C17C2×C412yes—
30C2×C22⋊Dic17—21no—
31C2×C22⋊Dic17D411yescharacteristic
32C4×C22⋊D17—41no—
33C4×C22⋊D17—41no—
34C2×#63227—22no—
35C2×#63227C2×C411yescharacteristic
36C2×C4⋊Dic17—21no—
37C2×#63225—22no—
38C2×#63225C2311yescharacteristic
39C2×C4×Dic17D411yescharacteristic
40#10587553—42no—
41C22⋊#3624—22no—
42#10587544—41no—
43#10587543—41no—
44C4⋊#3624—41no—
45#10587502—22no—
46#10587502—22no—
47#10587502C2×C412yes—
48C24×C17C22⋊C411yescharacteristic
49C23×D17C22⋊C411yescharacteristic
50C22×C4×C17—21no—
51C22×C4×C17—21no—
52C22×C4×C17—22no—
53C22×C4×C17—42no—
54C22×C4×C17—42no—
55C22×C4×C17—82no—
56C22×C4×C17C22⋊C411yescharacteristic
57C22×C4×C17C22×C411yescharacteristic
58C2×C22⋊D17—41no—
59C2×C22⋊D17—41no—
60C2×C22⋊D17SD1612yes—
61C2×C22⋊D17Q1612yes—
62C22×Dic17—22no—
63C22×Dic17C22⋊C411yescharacteristic
64C22×Dic17C2×D411yescharacteristic
65C22×Dic17C2×D411yescharacteristic
66C2×C4×D17—21no—
67C2×C4×D17—21no—
68C2×C4×D17—42no—
69#63247—42no—
70#63247—42no—
71C2×#3624—42no—
72C2×#3624—42no—
73#63242—82no—
74C4⋊C4×C17—42no—
75C4⋊C4×C17—41no—
76C4⋊C4×C17—41no—
77C22⋊Dic17—41no—
78C22⋊Dic17—42no—
79#63227—41no—
80#63227—82no—
81C4⋊Dic17—42no—
82#63225—41no—
83#63225—82no—
84C4×Dic17—21no—
85C4×Dic17—21no—
86#11903—171nomaximal, Sylow
87C23×C17—21no—
88C23×C17—21no—
89C23×C17—41no—
90C23×C17—41no—
91C23×C17#10312yes—
92C23×C17C2×C22⋊C411yescharacteristic
93C22×D17—21no—
94C22×D17—21no—
95C22×D17—41no—
96C22×D17—41no—
97C22×D17#10312yes—
98C2×C4×C17—22no—
99C2×C4×C17—21no—
100C2×C4×C17—42no—
101C2×C4×C17—42no—
102C2×C4×C17—41no—
103C2×C4×C17—42no—
104C2×C4×C17—42no—
105C2×C4×C17—42no—
106C2×C4×C17—84no—
107C2×C4×C17#9911yescharacteristic
108C2×C4×C17#9911yescharacteristic
109C22⋊D17—42no—
110C22⋊D17—42no—
111C2×Dic17—21no—
112C2×Dic17—21no—
113C2×Dic17—21no—
114C2×Dic17—21no—
115C2×Dic17—41no—
116C2×Dic17—41no—
117C2×Dic17—42no—
118C2×Dic17—42no—
119C2×Dic17—42no—
120C2×Dic17C2×SD1611yescharacteristic
121C2×Dic17C2×Q1611yescharacteristic
122C4×D17—42no—
123C4×D17—81no—
124#3624—82no—
125#3624—82no—
126#2487—171no—
127#1800—171no—
128#1459—171no—
129#1353—174no—
130C22×C17—21no—
131C22×C17—21no—
132C22×C17—22no—
133C22×C17—42no—
134C22×C17—42no—
135C22×C17—41no—
136C22×C17—41no—
137C22×C17C2×#9911yescharacteristic
138C22×C17C2×#10311yescharacteristic
139C22×C17#42111yescharacteristic
140C2×D17—22no—
141C2×D17—41no—
142C2×D17—41no—
143C2×D17—42no—
144C2×D17—81no—
145C4×C17—21no—
146C4×C17—41no—
147C4×C17—82no—
148C4×C17#35212yes—
149Dic17—21no—
150Dic17—21no—
151Dic17—41no—
152Dic17—41no—
153Dic17—82no—
154C2×C4×D4—171no—
155C22×C4⋊C4#59511yescharacteristic
156#423—341no—
157C2×#100—341no—
158C2×C22⋊C8—341no—
159#400—172no—
160#399—172no—
161#389—341no—
162#386—341no—
163#385—341no—
164#380—171no—
165#380—341no—
166#343—172no—
167#324—172no—
168#323—341no—
169C2×C17—21no—
170C2×C17—21no—
171C2×C17—42no—
172C2×C17#152011yescharacteristic
173C2×C17C2×#35211yescharacteristic
174C2×C17#213411yescharacteristic
175D17—42no—
176C22×D4—171no—
177C23×C4—21no—
178C23×C4—171no—
179C23×C4C2×#59511yescharacteristic
180C2×M16—342no—
181C22×C8—681no—
182C4×D4—681no—
183C4×D4—681no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—41no—
186C2×C4⋊C4—41no—
187C2×C4⋊C4—171no—
188C2×C4⋊C4—341no—
189C2×C4⋊C4—342no—
190C2×C4⋊C4C2×#59512yes—
191C2×C22⋊C4—171no—
192C2×C22⋊C4—171no—
193C2×C22⋊C4—341no—
194C2×C22⋊C4—342no—
195C2×C42—171no—
196C4⋊C8—681no—
197C4⋊C8—681no—
198#100—682no—
199C22⋊C8—342no—
200C22⋊C8—681no—
201#95—172no—
202#95—342no—
203#95—342no—
204C17#1190311yescharacteristic, complemented, Sylow
205C24—171no—
206C24C22⋊#59511yescharacteristic
207C2×D4—172no—
208C2×D4—172no—
209C2×D4—681no—
210C2×D4—681no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—22no—
214C22×C4—42no—
215C22×C4—42no—
216C22×C4—82no—
217C22×C4—171no—
218C22×C4—171no—
219C22×C4—171no—
220C22×C4—341no—
221C22×C4—341no—
222C22×C4—342no—
223C22×C4—682no—
224C22×C4C22⋊#59511yescharacteristic
225C22×C4C22×#59511yescharacteristic
226M16—682no—
227M16—682no—
228C2×C8—682no—
229C2×C8—682no—
230C2×C8—1362no—
231C4⋊C4—42no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—681no—
235C4⋊C4—682no—
236C4⋊C4—1362no—
237C22⋊C4—681no—
238C22⋊C4—681no—
239C22⋊C4—682no—
240C22⋊C4—1362no—
241C42—341no—
242C42—341no—
243C23—21no—
244C23—21no—
245C23—41no—
246C23—41no—
247C23—172no—
248C23—341no—
249C23—341no—
250C23—681no—
251C23—681no—
252C23#1058754912yes—
253C23C2×C22⋊#59511yescharacteristic
254D4—682no—
255D4—682no—
256C2×C4—22no—
257C2×C4—21no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—41no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—84no—
265C2×C4—171no—
266C2×C4—171no—
267C2×C4—341no—
268C2×C4—341no—
269C2×C4—341no—
270C2×C4—341no—
271C2×C4—682no—
272C2×C4—681no—
273C2×C4—681no—
274C2×C4—682no—
275C2×C4—682no—
276C2×C4—682no—
277C2×C4—1361no—
278C2×C4#1058755111yescharacteristic
279C2×C4#1058755111yescharacteristic
280C8—1362no—
281C8—1362no—
282C22—21no—
283C22—21no—
284C22—22no—
285C22—42no—
286C22—42no—
287C22—41no—
288C22—41no—
289C22—342no—
290C22—682no—
291C22—681no—
292C22—681no—
293C22—1361no—
294C22C2×#1058755111yescharacteristic
295C22C2×#1058754911yescharacteristic
296C22#1176380811yescharacteristic
297C4—21no—
298C4—41no—
299C4—82no—
300C4—341no—
301C4—341no—
302C4—681no—
303C4—681no—
304C4—1362no—
305C4#1176371112yes—
306C2—21no—
307C2—21no—
308C2—42no—
309C2—682no—
310C2#1454422411yescharacteristic
311C2C2×#1176371111yescharacteristic
312C2#1454508311yescharacteristic
subgroupG/H
centerC22C2×#10587551
commutatorC22×C4×C17C22×C4
FrattiniC22×C4C22×#595
FittingC22×C4⋊C4×C17C4
socleC22×C17C2×#99
prime radicalC22×C22⋊D17D4
cosocleC2×#63225C23
hypercenterC22×C4⋊C4#595
hypocenterC17#11903
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #14543783C2semidirect
204. C17#11903semidirect

Maximal subgroups

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

subgroupindex
#145446482
#145440192
#145437832
#145330952
#1190317