Finite Group Databasebeta

← #16948020

Subgroups — #16948020

Order 4352.

312 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 69 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#14541649C211yesmaximal, characteristic, complemented
2#14531007C211yesmaximal, characteristic, complemented
3#14528141C211yesmaximal, characteristic, complemented
4#14526841C211yesmaximal, characteristic, complemented
5#14526762C211yesmaximal, characteristic, complemented
6#14526745C211yesmaximal, characteristic, complemented
7C17×#2206C211yesmaximal, characteristic
8#11763516—21no—
9#11763214C2211yescharacteristic
10#11763210—21no—
11#11763107—22no—
12#11763099—21no—
13#11763006—21no—
14C8×Dic34C2211yescharacteristic
15D8×Dic17—21no—
16#11762610—22no—
17C4×#63214C2211yescharacteristic
18#11762562C2211yescharacteristic
19#11762553—21no—
20C2×C17×D16—21no—
21C17×#493C2211yescharacteristic
22C4×D8×C17C2211yescharacteristic
23C17×C4⋊C16C2211yescharacteristic
24C17×#357—21no—
25C2×D8×C17—21no—
26C2×D8×C17—21no—
27C2×D8×C17D411yescharacteristic
28C17×#127—21no—
29C4×D4×C17—21no—
30D4×Dic17—22no—
31C2×#63229—41no—
32C2×C4⋊Dic17—41no—
33#10587610—41no—
34#10587576—22no—
35#10587564—42no—
36#10587555—21no—
37C4×Dic34D411yescharacteristic
38C17×D16—42no—
39C2×C16×C17—21no—
40C17×#107D411yescharacteristic
41C17×#102—21no—
42C4×C8×C17C2311yescharacteristic
43#10587503—22no—
44#10587503—41no—
45#10587489—21no—
46#10587489D412yes—
47#10587485—21no—
48C8×Dic17—21no—
49C2×#63214—21no—
50#10587479—22no—
51C4⋊#3622—21no—
52C4⋊#3622D411yescharacteristic
53C2×D4×C17—21no—
54C2×D4×C17—41no—
55C2×D4×C17—41no—
56C2×D4×C17—41no—
57C22×C4×C17—41no—
58C22×Dic17—42no—
59C2×Dic34—41no—
60C2×Dic34D811yescharacteristic
61D8×C17—21no—
62D8×C17—42no—
63D8×C17—41no—
64D8×C17—41no—
65D8×C17SD1612yescomplemented
66C2×C8×C17C2×D411yescharacteristic
67C2×C8×C17C2×D411yescharacteristic
68C4⋊C4×C17—21no—
69C22⋊C4×C17—41no—
70C42×C17C2×D411yescharacteristic
71C22⋊Dic17—42no—
72#63229—82no—
73C4⋊Dic17—22no—
74C4⋊Dic17—42no—
75C4⋊Dic17—41no—
76C4⋊Dic17D811yescharacteristic
77#63225—21no—
78#63225—42no—
79C4×Dic17—21no—
80C2×#3622—21no—
81C2×#3622—41no—
82C16×C17—41no—
83#63214—41no—
84#12355—171nomaximal, Sylow
85C23×C17—41no—
86C23×C17—81no—
87D4×C17—22no—
88D4×C17—41no—
89D4×C17—81no—
90D4×C17—81no—
91D4×C17—81no—
92D4×C17—81no—
93D4×C17—161no—
94C2×C4×C17—41no—
95C2×C4×C17—81no—
96C2×C4×C17—81no—
97C2×C4×C17#12011yescharacteristic
98C2×C4×C17C2×D811yescharacteristic
99C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
100C2×Dic17—21no—
101C2×Dic17—21no—
102C2×Dic17—42no—
103C2×Dic17—162no—
104Dic34—21no—
105Dic34—21no—
106Dic34—161no—
107C8×C17—21no—
108C8×C17C2×SD1611yescharacteristic
109C8×C17#13711yescharacteristic
110#3622—41no—
111#3622—81no—
112#3380—171no—
113#2240—171no—
114#2206D1711yescharacteristic
115#1668—171no—
116#1365—171no—
117Q8⋊C16—171no—
118#1331—171no—
119C22×C17—42no—
120C22×C17—81no—
121C22×C17—81no—
122C22×C17—161no—
123C22×C17—161no—
124C22×C17—161no—
125C22×C17#44711yescharacteristic
126C4×C17—21no—
127C4×C17—81no—
128C4×C17#44811yescharacteristic
129C4×C17#45411yescharacteristic
130C4×C17#50811yescharacteristic
131C4×C17#50911yescharacteristic
132Dic17—41no—
133Dic17—41no—
134Dic17—82no—
135#554—341no—
136C2×D16—21no—
137#500—171no—
138#499—341no—
139#493C2×D1711yescharacteristic
140#478—342no—
141#476—341no—
142#460—341no—
143C8×Q8—171no—
144C4×D8—341no—
145C4×D8C2×D1711yescharacteristic
146C4⋊C16C2×D1711yescharacteristic
147#357—21no—
148#357—342no—
149C4×C16—171no—
150#335—171no—
151#331—341no—
152C2×C17—82no—
153C2×C17—321no—
154C2×C17#162711yescharacteristic
155C2×C17#218611yescharacteristic
156C2×C17#219211yescharacteristic
157C2×SD16—681no—
158C2×D8—21no—
159C2×D8—21no—
160C2×D8C22⋊D1711yescharacteristic
161C4⋊Q8—341no—
162#127—21no—
163#125—342no—
164C22⋊Q8—682no—
165C22⋊Q8—681no—
166C4×Q8—171no—
167C4×D4—21no—
168C4×D4—342no—
169C2×C4⋊C4—681no—
170D16—42no—
171C2×C16—21no—
172C2×C16—341no—
173#107—172no—
174#107—341no—
175#107C22⋊D1711yescharacteristic
176#106—342no—
177C4⋊C8—171no—
178C4⋊C8—341no—
179C4⋊C8—341no—
180#102—21no—
181#102—342no—
182#102—681no—
183C4×C8—341no—
184C4×C8C22×D1711yescharacteristic
185C17#1235511yescharacteristic, complemented, Sylow
186C2×Q8—171no—
187C2×Q8—681no—
188C2×D4—21no—
189C2×D4—41no—
190C2×D4—41no—
191C2×D4—41no—
192C22×C4—41no—
193C22×C4—682no—
194SD16—1362no—
195D8—21no—
196D8—42no—
197D8—41no—
198D8—41no—
199D8#6322912yescomplemented
200C2×C8—341no—
201C2×C8—681no—
202C2×C8D4×D1711yescharacteristic
203C2×C8C2×C22⋊D1711yescharacteristic
204C4⋊C4—21no—
205C4⋊C4—171no—
206C4⋊C4—341no—
207C4⋊C4—342no—
208C4⋊C4—682no—
209C4⋊C4—682no—
210C4⋊C4—681no—
211C22⋊C4—41no—
212C22⋊C4—682no—
213C42—341no—
214C42D4×D1711yescharacteristic
215C16—41no—
216C16—681no—
217C23—41no—
218C23—81no—
219Q8—2721no—
220Q8—341no—
221Q8—341no—
222D4—22no—
223D4—41no—
224D4—81no—
225D4—81no—
226D4—81no—
227D4—81no—
228D4—161no—
229C2×C4—41no—
230C2×C4—81no—
231C2×C4—81no—
232C2×C4—2722no—
233C2×C4—341no—
234C2×C4—341no—
235C2×C4—682no—
236C2×C4D8×D1711yescharacteristic
237C2×C4#1058759711yescharacteristic
238C2×C4#1058762311yescharacteristic
239C8—21no—
240C8—681no—
241C8—1361no—
242C8C2×#6322911yescharacteristic
243C8#1058763711yescharacteristic
244C22—42no—
245C22—81no—
246C22—81no—
247C22—161no—
248C22—161no—
249C22—161no—
250C22#1176294111yescharacteristic
251C4—21no—
252C4—81no—
253C4—681no—
254C4—681no—
255C4—1362no—
256C4#1176294711yescharacteristic
257C4#1176298011yescharacteristic
258C4#1176323811yescharacteristic
259C4#1176324311yescharacteristic
260C2—82no—
261C2—321no—
262C2#1452788611yescharacteristic
263C2#1453070411yescharacteristic
264C2#1453073811yescharacteristic
subgroupG/H
centerC22#11762941
commutator, cosocleC4×C8×C17C23
FrattiniC4×C8C22×D17
Fitting, prime radicalC17×#2206C2
socleC22×C17#447
hypercenter#2206D17
hypocenterC17#12355
LCSG ▷ C4×C8×C17 ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2206

Complements

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

NH ≅ G/Ntype
1. #14541649C2semidirect
2. #14531007C2semidirect
3. #14528141C2semidirect
4. #14526841C2semidirect
5. #14526762C2semidirect
6. #14526745C2semidirect
65. D8×C17SD16semidirect
185. C17#12355semidirect
199. D8#63229semidirect

Maximal subgroups

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

subgroupindex
#145416492
#145310072
#145281412
#145268412
#145267622
#145267452
C17×#22062
#1235517