Finite Group Databasebeta

← #17948816

Subgroups — #17948816

Order 4352.

372 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 66 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#14544644C211yesmaximal, characteristic
3#14529076C211yesmaximal, characteristic
4#11763812—21no—
5C2×#10587553—21no—
6C2×#10587551—21no—
7#11763751—21no—
8#11763689C412yescomplemented
9#11763687C412yes—
10C2×C4×C22⋊D17C2211yescharacteristic
11C2×C22⋊#3622C411yescharacteristic, complemented
12C2×#10587491—21no—
13#11762563—21no—
14C23×C8×C17C411yescharacteristic, complemented
15C23×C4×C17C2×C411yescharacteristic
16C22×C22⋊D17D411yescharacteristic
17C22×C4×D17D411yescharacteristic
18C2×C22⋊#595—22no—
19C2×#63247—22no—
20C2×C4⋊#595—41no—
21C22×C8×C17—21no—
22C22×C8×C17—42no—
23C22×C8×C17—41no—
24C2×C22⋊Dic17Q811yescharacteristic
25C4×C22⋊D17—41no—
26C4×C22⋊D17—41no—
27C2×#63227C2×C411yescharacteristic
28C2×#63225C2×C411yescharacteristic
29C2×C4×Dic17D411yescharacteristic
30C22×#3622—21no—
31#10587553—41no—
32#10587553—41no—
33#10587551—41no—
34#10587551—41no—
35(C2×#595)⋊C4—41no—
36#10587544—41no—
37C4⋊#3624—41no—
38C22⋊#3622—41no—
39#10587491—42no—
40C24×C17C4⋊C411yescharacteristic
41C23×D17C22⋊C411yescharacteristic
42C22×#595—42no—
43C22×C4×C17—21no—
44C22×C4×C17—21no—
45C22×C4×C17—41no—
46C22×C4×C17—41no—
47C22×C4×C17C4211yescharacteristic
48C22×C4×C17C22⋊C411yescharacteristic
49C2×C22⋊D17—41no—
50C2×C22⋊D17—41no—
51C2×C22⋊D17D811yescharacteristic
52C2×C22⋊D17SD1611yescharacteristic
53C2×C22⋊D17SD1611yescharacteristic
54C2×C22⋊D17Q1611yescharacteristic
55C22×Dic17C22⋊C411yescharacteristic
56C22×Dic17C4⋊C411yescharacteristic
57C22×Dic17C4⋊C411yescharacteristic
58C2×C4×D17—21no—
59C2×C4×D17—21no—
60C2×C4×D17—41no—
61C2×C4×D17—41no—
62C22⋊#595—42no—
63C22⋊#595—42no—
64#63247—42no—
65#63247—42no—
66C2×#3624—42no—
67C4⋊#595—81no—
68C4⋊#595—81no—
69C2×C8×C17—22no—
70C2×C8×C17—41no—
71C2×C8×C17—42no—
72C2×C8×C17—41no—
73C2×C8×C17—42no—
74C22⋊Dic17—41no—
75#63227—41no—
76#63225—41no—
77C4×Dic17—21no—
78C4×Dic17—21no—
79C2×#3622—41no—
80C2×#3622—41no—
81C2×#3622—41no—
82#7236—171nomaximal, Sylow
83C23×C17—21no—
84C23×C17—21no—
85C23×C17—41no—
86C23×C17—41no—
87C23×C17#9511yescharacteristic
88C23×C17#10611yescharacteristic
89C23×C17#10711yescharacteristic
90C22×D17—21no—
91C22×D17—21no—
92C22×D17—41no—
93C22×D17—41no—
94C22×D17#10211yescharacteristic
95C22×D17#10311yescharacteristic
96C2×#595—82no—
97C2×#595—82no—
98C2×#595—82no—
99C2×C4×C17—21no—
100C2×C4×C17—21no—
101C2×C4×C17—21no—
102C2×C4×C17—42no—
103C2×C4×C17—41no—
104C2×C4×C17—41no—
105C2×C4×C17—41no—
106C2×C4×C17#9911yescharacteristic
107C2×C4×C17#9911yescharacteristic
108C22⋊D17—41no—
109C22⋊D17—41no—
110C22⋊D17—41no—
111C22⋊D17—41no—
112C2×Dic17—21no—
113C2×Dic17—21no—
114C2×Dic17—21no—
115C2×Dic17—21no—
116C2×Dic17—41no—
117C2×Dic17—41no—
118C2×Dic17#10211yescharacteristic
119C2×Dic17#10311yescharacteristic
120C4×D17—41no—
121C4×D17—41no—
122C4×D17—81no—
123#3624—82no—
124C8×C17—42no—
125#3622—81no—
126#1869—171no—
127#1800—171no—
128#1799—171no—
129C22×C17—21no—
130C22×C17—21no—
131C22×C17—21no—
132C22×C17—21no—
133C22×C17—41no—
134C22×C17—41no—
135C22×C17—42no—
136C22×C17—41no—
137C22×C17—41no—
138C22×C17H(3,ℤ/4)11yescharacteristic
139C22×C17#34011yescharacteristic
140C22×C17#34211yescharacteristic
141C2×D17—21no—
142C2×D17—21no—
143C2×D17—41no—
144C2×D17—41no—
145C2×D17—41no—
146C2×D17—41no—
147C2×D17—81no—
148#595—162no—
149C4×C17—21no—
150C4×C17—41no—
151C4×C17AΣL(1,𝔽16)11yescharacteristic
152C4×C17#35211yescharacteristic
153Dic17—21no—
154Dic17—21no—
155Dic17—41no—
156Dic17—41no—
157C23×C8#59511yescharacteristic, complemented
158C2×C4×D4—171no—
159#423—341no—
160C2×#100—341no—
161C2×#99—341no—
162C2×C22⋊C8—171no—
163C2×C22⋊C8—341no—
164#380—341no—
165#343—172no—
166#342—172no—
167#336—341no—
168C2×C17—21no—
169C2×C17—21no—
170C2×C17—41no—
171C2×C17—41no—
172C2×C17#128911yescharacteristic
173C2×C17#139011yescharacteristic
174C2×C17#139511yescharacteristic
175D17—41no—
176D17—41no—
177C22×D4—171no—
178C23×C4—171no—
179C23×C4C2×#59511yescharacteristic
180C2×M16—342no—
181C22×C8—21no—
182C22×C8—42no—
183C22×C8—41no—
184C22×C8—341no—
185C4×D4—681no—
186C4×D4—681no—
187C2×C4⋊C4—171no—
188C2×C4⋊C4—681no—
189C2×C22⋊C4—171no—
190C2×C22⋊C4—171no—
191C2×C22⋊C4—342no—
192C2×C42—171no—
193C4⋊C8—681no—
194C4⋊C8—681no—
195#100—681no—
196#100—681no—
197#99—681no—
198#99—681no—
199C22⋊C8—682no—
200C22⋊C8—681no—
201#95—681no—
202C17#723611yescharacteristic, complemented, Sylow
203C24—171no—
204C24C4⋊#59511yescharacteristic
205C2×D4—171no—
206C2×D4—171no—
207C2×D4—171no—
208C2×D4—171no—
209C2×D4—681no—
210C2×D4—681no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—41no—
214C22×C4—41no—
215C22×C4—171no—
216C22×C4—171no—
217C22×C4—171no—
218C22×C4—341no—
219C22×C4—341no—
220C22×C4—681no—
221C22×C4—681no—
222C22×C4—682no—
223C22×C4C4×#59511yescharacteristic
224C22×C4C22⋊#59511yescharacteristic
225M16—682no—
226M16—682no—
227C2×C8—22no—
228C2×C8—41no—
229C2×C8—42no—
230C2×C8—41no—
231C2×C8—42no—
232C2×C8—681no—
233C2×C8—681no—
234C2×C8—682no—
235C2×C8—681no—
236C4⋊C4—681no—
237C4⋊C4—1361no—
238C4⋊C4—1361no—
239C22⋊C4—681no—
240C22⋊C4—681no—
241C22⋊C4—682no—
242C22⋊C4—682no—
243C42—341no—
244C42—341no—
245C23—21no—
246C23—21no—
247C23—41no—
248C23—41no—
249C23—171no—
250C23—171no—
251C23—341no—
252C23—341no—
253C23—681no—
254C23—681no—
255C23#1058753311yescharacteristic
256C23#1058753411yescharacteristic
257C23(C2×#595)⋊C411yescharacteristic
258D4—681no—
259D4—681no—
260D4—681no—
261D4—681no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—42no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—171no—
270C2×C4—171no—
271C2×C4—341no—
272C2×C4—341no—
273C2×C4—341no—
274C2×C4—341no—
275C2×C4—681no—
276C2×C4—681no—
277C2×C4—681no—
278C2×C4—681no—
279C2×C4—1361no—
280C2×C4—1362no—
281C2×C4—1362no—
282C2×C4—1362no—
283C2×C4#1058753911yescharacteristic
284C2×C4#1058755111yescharacteristic
285C8—42no—
286C8—1361no—
287C8—1362no—
288C22—21no—
289C22—21no—
290C22—21no—
291C22—21no—
292C22—41no—
293C22—41no—
294C22—42no—
295C22—41no—
296C22—41no—
297C22—341no—
298C22—341no—
299C22—681no—
300C22—681no—
301C22—681no—
302C22—681no—
303C22—1361no—
304C22#1176367711yescharacteristic
305C22#1176368311yescharacteristic
306C22#1176368711yescharacteristic
307C4—21no—
308C4—41no—
309C4—2722no—
310C4—341no—
311C4—341no—
312C4—681no—
313C4—681no—
314C4#1176370911yescharacteristic
315C4#1176371111yescharacteristic
316C2—21no—
317C2—21no—
318C2—41no—
319C2—41no—
320C2—681no—
321C2—681no—
322C2#1454364711yescharacteristic
323C2#1454386811yescharacteristic
324C2#1454388411yescharacteristic
subgroupG/H
centerC22#11763687
commutatorC22×C4×C17C42
FrattiniC23×C4C2×#595
FittingC23×C8×C17C4
socleC22×C17#342
prime radicalC22×C22⋊D17D4
cosocleC2×C4×C22⋊D17C22
hypercenterC23×C8#595
hypocenterC17#7236
LCSG ▷ C22×C4×C17 ▷ C22×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C23×C8

Complements

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

NH ≅ G/Ntype
8. #11763689C4semidirect
11. C2×C22⋊#3622C4semidirect
14. C23×C8×C17C4semidirect
157. C23×C8#595semidirect
202. C17#7236semidirect

Maximal subgroups

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

subgroupindex
#145446482
#145446442
#145290762
#723617