Finite Group Databasebeta

← #16948212

Subgroups — #16948212

Order 4352.

294 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 65 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#14541770C211yesmaximal, characteristic
2#14531012C211yesmaximal, characteristic, complemented
3#14530921C211yesmaximal, characteristic
4#14528179C211yesmaximal, characteristic, complemented
5#14526832C211yesmaximal, characteristic, complemented
6#14526764C211yesmaximal, characteristic, complemented
7C17×#1331C211yesmaximal, characteristic
8#11763529—21no—
9#11763214C2211yescharacteristic
10#11763192—21no—
11#11763189C2211yescharacteristic
12#11763030—22no—
13#11763020—21no—
14#11763014—21no—
15C8×Dic34C2211yescharacteristic
16#11762903—21no—
17#11762634—21no—
18C4⋊#63214C2211yescharacteristic
19#11762614—22no—
20#11762610—21no—
21#11762556—21no—
22C4×D8×C17C2211yescharacteristic
23C4×C16×C17C2211yescharacteristic
24C17×#335C2211yescharacteristic
25C2×D8×C17D411yescharacteristic
26C4×D4×C17—21no—
27#10587622—22no—
28C2×#63229—22no—
29#10587612—41no—
30#10587610—41no—
31C2×Dic68—21no—
32C2×Dic68—41no—
33C2×Dic68D412yes—
34#10587573—22no—
35#10587565—42no—
36#10587555—21no—
37#10587555—21no—
38C4×Dic34D411yescharacteristic
39C2×C16×C17—21no—
40C17×#107D411yescharacteristic
41C17×C4⋊C8—21no—
42C17×#102—21no—
43C4×C8×C17C2311yescharacteristic
44#10587489—21no—
45#10587489—21no—
46#10587487—41no—
47#10587485—21no—
48C8×Dic17—21no—
49C2×#63214—21no—
50#10587481—22no—
51C4⋊#3622D411yescharacteristic
52C2×D4×C17—21no—
53C22×C4×C17—41no—
54C2×Dic34—22no—
55C2×Dic34—41no—
56C2×Dic34D811yescharacteristic
57D8×C17—21no—
58D8×C17—21no—
59C2×C8×C17—41no—
60C2×C8×C17C2×D411yescharacteristic
61C2×C8×C17C2×D411yescharacteristic
62C4⋊C4×C17—21no—
63C22⋊C4×C17—41no—
64C42×C17C2×D411yescharacteristic
65C22⋊Dic17—42no—
66C22⋊Dic17—42no—
67#63229—82no—
68C4⋊Dic17—41no—
69C4⋊Dic17—41no—
70C4⋊Dic17—41no—
71C4⋊Dic17—41no—
72C4⋊Dic17D811yescharacteristic
73#63225—21no—
74#63225—42no—
75C4×Dic17—21no—
76C4×Dic17—42no—
77C2×#3622—21no—
78Dic68—42no—
79Dic68—41no—
80Dic68—41no—
81Dic68—82no—
82C16×C17—41no—
83#63214—41no—
84#12383—171nomaximal, Sylow
85C23×C17—41no—
86D4×C17—41no—
87D4×C17—41no—
88C2×C4×C17—41no—
89C2×C4×C17—81no—
90C2×C4×C17—81no—
91C2×C4×C17#12011yescharacteristic
92C2×C4×C17C2×D811yescharacteristic
93C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
94C2×Dic17—21no—
95C2×Dic17—21no—
96C2×Dic17—42no—
97C2×Dic17—81no—
98Dic34—21no—
99Dic34—21no—
100Dic34—42no—
101Dic34—42no—
102Dic34—81no—
103Dic34—81no—
104C8×C17—21no—
105C8×C17—81no—
106C8×C17#13511yescharacteristic
107C8×C17#13711yescharacteristic
108#3622—41no—
109#3393—171no—
110#2241—171no—
111#2224—171no—
112#1674—171no—
113#1362—171no—
114Q8⋊C16—171no—
115#1331D1711yescharacteristic
116C22×C17—81no—
117C22×C17—81no—
118C22×C17—81no—
119C22×C17#44711yescharacteristic
120C4×C17—21no—
121C4×C17—81no—
122C4×C17#45211yescharacteristic
123C4×C17#45511yescharacteristic
124C4×C17#50811yescharacteristic
125C4×C17#50911yescharacteristic
126Dic17—41no—
127Dic17—41no—
128Dic17—82no—
129Dic17—161no—
130#556—341no—
131#500—171no—
132#495—341no—
133#494—171no—
134#464—342no—
135#462—341no—
136#461—341no—
137C8×Q8—171no—
138C4×Q16—341no—
139C4×D8C2×D1711yescharacteristic
140#366—341no—
141C4⋊C16—171no—
142#358—342no—
143#357—341no—
144C4×C16C2×D1711yescharacteristic
145#335C2×D1711yescharacteristic
146#332—341no—
147C2×C17—161no—
148C2×C17#164111yescharacteristic
149C2×C17#218611yescharacteristic
150C2×C17#219511yescharacteristic
151C2×Q16—172no—
152C2×Q16—341no—
153C2×Q16—681no—
154C2×SD16—342no—
155C2×D8D6811yescharacteristic
156C4⋊Q8—341no—
157C4⋊Q8—341no—
158#126—682no—
159#124—342no—
160C22⋊Q8—681no—
161C4×Q8—171no—
162C4×Q8—342no—
163C4×D4—21no—
164#117—681no—
165C2×C16—21no—
166C2×C16—341no—
167#107—341no—
168#107—341no—
169#107D6811yescharacteristic
170C4⋊C8—21no—
171C4⋊C8—171no—
172C4⋊C8—341no—
173#103—342no—
174#103—681no—
175#102—21no—
176C4×C8—341no—
177C4×C8C22×D1711yescharacteristic
178C17#1238311yescharacteristic, complemented, Sylow
179C2×Q8—171no—
180C2×Q8—342no—
181C2×Q8—681no—
182C2×D4—21no—
183C22×C4—41no—
184Q16—682no—
185Q16—681no—
186Q16—681no—
187Q16—1362no—
188SD16—1362no—
189D8—21no—
190D8—21no—
191C2×C8—41no—
192C2×C8—341no—
193C2×C8C2×D6811yescharacteristic
194C2×C8D4×D1711yescharacteristic
195C4⋊C4—21no—
196C4⋊C4—171no—
197C4⋊C4—341no—
198C4⋊C4—682no—
199C4⋊C4—681no—
200C4⋊C4—681no—
201C4⋊C4—681no—
202C4⋊C4—681no—
203C22⋊C4—41no—
204C22⋊C4—682no—
205C22⋊C4—682no—
206C42—341no—
207C42—682no—
208C42D4×D1711yescharacteristic
209C16—41no—
210C16—681no—
211C23—41no—
212Q8—341no—
213Q8—341no—
214Q8—682no—
215Q8—682no—
216Q8—1361no—
217Q8—1361no—
218D4—41no—
219D4—41no—
220C2×C4—41no—
221C2×C4—81no—
222C2×C4—81no—
223C2×C4—341no—
224C2×C4—341no—
225C2×C4—682no—
226C2×C4—1361no—
227C2×C4#1058756811yescharacteristic
228C2×C4D8×D1711yescharacteristic
229C2×C4#1058760011yescharacteristic
230C8—21no—
231C8—81no—
232C8—681no—
233C8#1058759011yescharacteristic
234C8#1058759511yescharacteristic
235C22—81no—
236C22—81no—
237C22—81no—
238C22#1176294411yescharacteristic
239C4—21no—
240C4—81no—
241C4—2721no—
242C4—681no—
243C4—681no—
244C4—1362no—
245C4#1176297311yescharacteristic
246C4#1176298811yescharacteristic
247C4#1176324011yescharacteristic
248C4#1176324311yescharacteristic
249C2—161no—
250C2#1452798011yescharacteristic
251C2#1453070811yescharacteristic
252C2#1453076311yescharacteristic
subgroupG/H
centerC22#11762944
commutator, cosocleC4×C8×C17C23
FrattiniC4×C8C22×D17
FittingC17×#1331C2
socleC22×C17#447
prime radicalC2×D8×C17D4
hypercenter#1331D17
hypocenterC17#12383
LCSG ▷ C4×C8×C17 ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1331

Complements

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

NH ≅ G/Ntype
2. #14531012C2semidirect
4. #14528179C2semidirect
5. #14526832C2semidirect
6. #14526764C2semidirect
178. C17#12383semidirect

Maximal subgroups

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

subgroupindex
#145417702
#145310122
#145309212
#145281792
#145268322
#145267642
C17×#13312
#1238317