Finite Group Databasebeta

← #16948033

Subgroups — #16948033

Order 4352.

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

normal subgroups only

This group has 282 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#14541676C211yesmaximal, characteristic
2#14531011C211yesmaximal, characteristic
3#14530831C211yesmaximal, characteristic
4#14526840C211yesmaximal, characteristic
5Q8⋊#63214C211yesmaximal, characteristic
6#14526747C211yesmaximal, characteristic
7C17×#1670C211yesmaximal, characteristic
8#11763537—21no—
9C2×#10587500—21no—
10#11763214C2211yescharacteristic
11#11763211—21no—
12#11763117—22no—
13#11763095—21no—
14C4×Dic68—21no—
15C4×Dic68C2211yescharacteristic
16C4⋊#63214C2211yescharacteristic
17#11762613—21no—
18#11762613—22no—
19C4×#63214C2211yescharacteristic
20C17×#494C2211yescharacteristic
21C17×#475—21no—
22C8×Q8×C17C2211yescharacteristic
23C17×#335C2211yescharacteristic
24C17×#332—21no—
25C2×Q16×C17—21no—
26C2×Q16×C17—21no—
27C17×C4⋊Q8—21no—
28C4×Q8×C17D411yescharacteristic
29#10587630—41no—
30C2×Dic68D411yescharacteristic
31#10587575—42no—
32#10587573—41no—
33#10587556—22no—
34#10587555—21no—
35C4×Dic34—22no—
36C4×Dic34—21no—
37C17×#106—41no—
38C17×C4⋊C8—21no—
39C17×C4⋊C8—21no—
40C17×C4⋊C8D411yescharacteristic
41C17×#103—41no—
42C4×C8×C17—21no—
43C4×C8×C17C2311yescharacteristic
44#10587500—42no—
45#10587489—21no—
46#10587489D411yescharacteristic
47#10587489D412yes—
48#10587488—22no—
49#10587487—22no—
50#10587487—21no—
51C2×#63214—21no—
52C2×#63214—21no—
53C2×Q8×C17—41no—
54C2×Q8×C17D811yescharacteristic
55C2×Dic34—21no—
56C2×Dic34—41no—
57Q16×C17—42no—
58Q16×C17—41no—
59Q16×C17—41no—
60C2×C8×C17—21no—
61C2×C8×C17—41no—
62C2×C8×C17C2×D411yescharacteristic
63C2×C8×C17C2×D411yescharacteristic
64C4⋊C4×C17—21no—
65C4⋊C4×C17—41no—
66C4⋊C4×C17—41no—
67C4⋊C4×C17D811yescharacteristic
68C42×C17—21no—
69C42×C17C2×D411yescharacteristic
70C4⋊Dic17—21no—
71C4⋊Dic17—22no—
72C4⋊Dic17—41no—
73#63225—42no—
74#63225—42no—
75#63225—42no—
76#63225—41no—
77C4×Dic17—42no—
78C4×Dic17—41no—
79Dic68—21no—
80Dic68SD1612yes—
81#63214—41no—
82#63214—41no—
83#12357—171nomaximal, Sylow
84Q8×C17—21no—
85Q8×C17—21no—
86Q8×C17—81no—
87Q8×C17—81no—
88C2×C4×C17—21no—
89C2×C4×C17—21no—
90C2×C4×C17—81no—
91C2×C4×C17#12011yescharacteristic
92C2×C4×C17C2×D811yescharacteristic
93C2×C4×C17AGL(1,ℤ/8)11yescharacteristic
94C2×Dic17—41no—
95C2×Dic17—42no—
96C2×Dic17—41no—
97Dic34—22no—
98Dic34—41no—
99Dic34—81no—
100Dic34—81no—
101C8×C17—21no—
102C8×C17—41no—
103C8×C17—81no—
104C8×C17C2×SD1611yescharacteristic
105C8×C17#13711yescharacteristic
106#3383—171no—
107#2241—171no—
108#2209—171no—
109#1670D1711yescharacteristic
110#1364—171no—
111Q8⋊C16—171no—
112#1332—171no—
113C22×C17#44711yescharacteristic
114C4×C17—21no—
115C4×C17—41no—
116C4×C17—41no—
117C4×C17—161no—
118C4×C17#44811yescharacteristic
119C4×C17#45411yescharacteristic
120C4×C17#50811yescharacteristic
121C4×C17#51011yescharacteristic
122Dic17—42no—
123Dic17—82no—
124Dic17—81no—
125#557—341no—
126C2×Q32—341no—
127#500—171no—
128#499—341no—
129#494C2×D1711yescharacteristic
130#479—342no—
131#475—21no—
132#475—341no—
133C8×Q8C2×D1711yescharacteristic
134C4×Q16—171no—
135C4×Q16—341no—
136C4⋊C16—171no—
137#358—341no—
138#358—342no—
139C4×C16—171no—
140#335C2×D1711yescharacteristic
141#332—21no—
142C2×C17#162711yescharacteristic
143C2×C17#218911yescharacteristic
144C2×C17#219511yescharacteristic
145C2×Q16—21no—
146C2×Q16—21no—
147C2×Q16—171no—
148C4⋊Q8—21no—
149C4⋊Q8—341no—
150C4⋊Q8—681no—
151#125—342no—
152#125—682no—
153C4×Q8—342no—
154C4×Q8—341no—
155C4×Q8—681no—
156C4×Q8C22⋊D1711yescharacteristic
157Q32—682no—
158C2×C16—341no—
159C2×C16—341no—
160#107—171no—
161#107—172no—
162#107—341no—
163#106—41no—
164#106—342no—
165C4⋊C8—21no—
166C4⋊C8—21no—
167C4⋊C8C22⋊D1711yescharacteristic
168#103—41no—
169#103—342no—
170#103—341no—
171C4×C8—21no—
172C4×C8C22×D1711yescharacteristic
173C17#1235711yescharacteristic, complemented, Sylow
174C2×Q8—41no—
175C2×Q8—341no—
176C2×Q8—681no—
177C2×Q8#6322811yescharacteristic
178Q16—42no—
179Q16—41no—
180Q16—41no—
181Q16—172no—
182Q16—341no—
183C2×C8—21no—
184C2×C8—41no—
185C2×C8D4×D1711yescharacteristic
186C2×C8D4×D1711yescharacteristic
187C4⋊C4—21no—
188C4⋊C4—41no—
189C4⋊C4—41no—
190C4⋊C4—341no—
191C4⋊C4—342no—
192C4⋊C4—682no—
193C4⋊C4—682no—
194C4⋊C4—682no—
195C4⋊C4—681no—
196C4⋊C4—681no—
197C4⋊C4#6322811yescharacteristic
198C42—21no—
199C42—682no—
200C42—681no—
201C42C2×C22⋊D1711yescharacteristic
202C16—681no—
203C16—681no—
204Q8—21no—
205Q8—21no—
206Q8—81no—
207Q8—81no—
208Q8—342no—
209Q8—681no—
210Q8—1361no—
211Q8—1361no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—81no—
215C2×C4—681no—
216C2×C4—681no—
217C2×C4—682no—
218C2×C4C2×#6322811yescharacteristic
219C2×C4#1058762311yescharacteristic
220C2×C4#1058763511yescharacteristic
221C8—21no—
222C8—41no—
223C8—81no—
224C8SD16×D1711yescharacteristic
225C8#1058760111yescharacteristic
226C22#1176294211yescharacteristic
227C4—21no—
228C4—41no—
229C4—41no—
230C4—161no—
231C4—682no—
232C4—1362no—
233C4—1361no—
234C4#1176294611yescharacteristic
235C4#1176298011yescharacteristic
236C4#1176323911yescharacteristic
237C4#1176325011yescharacteristic
238C2#1452788511yescharacteristic
239C2#1453072211yescharacteristic
240C2#1453076011yescharacteristic
subgroupG/H
centerC22#11762942
commutator, cosocleC4×C8×C17C23
FrattiniC4×C8C22×D17
FittingC17×#1670C2
socle, prime radicalC22×C17#447
hypercenter#1670D17
hypocenterC17#12357
LCSG ▷ C4×C8×C17 ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C42 ◁ C8×Q8 ◁ #1670

Complements

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

NH ≅ G/Ntype
173. C17#12357semidirect

Maximal subgroups

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

subgroupindex
#145416762
#145310112
#145308312
#145268402
Q8⋊#632142
#145267472
C17×#16702
#1235717