Finite Group Databasebeta

← #15776199

Subgroups — #15776199

Order 3328.

354 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 71 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#13117019C212yesmaximal, complemented
2#13116329C211yesmaximal, characteristic, complemented
3#13112845C212yesmaximal, complemented
4#13112776C211yesmaximal, characteristic, complemented
5C13×#3245C211yesmaximal, characteristic
6C13×#532—21no—
7C13×#474—22no—
8C13×#466—21no—
9C13×#466C2212yes—
10C13×#459—22no—
11C2×C13×C4⋊C8C2211yescharacteristic
12C2×#88058C2211yescharacteristic
13#11718589—21no—
14#11718154—22no—
15#11718143—21no—
16#11718143C2211yescharacteristic
17C22⋊#6090C2212yes—
18#11718082—22no—
19C2×C13×#41—41no—
20C2×C13×D8—21no—
21C2×C13×D8D412yes—
22C22×C8×C13D411yescharacteristic
23C22×C8×C13C2311yescharacteristic
24C13×C4⋊Q8—21no—
25C13×#127—21no—
26C13×#124—41no—
27C13×#121—22no—
28C13×#121—41no—
29C4×D4×C13—22no—
30C4×D4×C13—41no—
31C2×C42×C13D411yescharacteristic
32C2×C4⋊Dic13—21no—
33C2×C4⋊Dic13—21no—
34C2×#6101—41no—
35C13×#107—21no—
36C13×#107D412yes—
37C13×C4⋊C8—22no—
38C13×#102—22no—
39C13×#102—22no—
40#88071—41no—
41#88058—22no—
42C2×#6090—22no—
43#12291—131nomaximal, Sylow
44C13×#41—82no—
45C13×#41—82no—
46C2×Q8×C13—41no—
47C2×D4×C13—22no—
48C2×D4×C13—41no—
49C2×D4×C13—41no—
50C2×D4×C13—42no—
51C22×C4×C13—42no—
52C22×C4×C13D811yescharacteristic
53C22×C4×C13D811yescharacteristic
54C22×C4×C13C2×D411yescharacteristic
55C22×Dic13—41no—
56C22×Dic13—41no—
57C13×D8—42no—
58C13×D8—81no—
59C2×C8×C13—21no—
60C2×C8×C13—41no—
61C2×C8×C13—41no—
62C2×C8×C13C2×D412yes—
63C13×C4⋊C4—22no—
64C13×C4⋊C4—41no—
65C13×C22⋊C4—42no—
66C13×C22⋊C4—42no—
67C42×C13—21no—
68C42×C13—21no—
69C4⋊Dic13—22no—
70C4⋊Dic13—41no—
71C4⋊Dic13—41no—
72C4⋊Dic13—41no—
73#6101—82no—
74#6090—42no—
75#3245D1311yescharacteristic
76#2233—132no—
77#2087—131no—
78#1347—132no—
79#1322—131no—
80C23×C13—42no—
81C23×C13C2×D811yescharacteristic
82Q8×C13—82no—
83D4×C13—42no—
84D4×C13—42no—
85D4×C13—82no—
86D4×C13—82no—
87D4×C13—82no—
88D4×C13—82no—
89C2×C4×C13—21no—
90C2×C4×C13—21no—
91C2×C4×C13—21no—
92C2×C4×C13—21no—
93C2×C4×C13—21no—
94C2×C4×C13—41no—
95C2×C4×C13—42no—
96C2×C4×C13—84no—
97C2×C4×C13SD3212yes—
98C2×C4×C13#12011yescharacteristic
99C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
100C2×Dic13—42no—
101C2×Dic13—81no—
102C2×Dic13—81no—
103C2×Dic13—81no—
104C2×Dic13—81no—
105C2×Dic13—81no—
106C8×C13—22no—
107C8×C13—41no—
108#532—21no—
109#474—22no—
110#466—21no—
111#466C2×D1312yes—
112#459—22no—
113C2×#107—131no—
114C2×C4⋊C8C2×D1311yescharacteristic
115#389—261no—
116#367—262no—
117#357—262no—
118C22⋊C16—132no—
119#340—131no—
120#340—261no—
121C22×C13—21no—
122C22×C13—21no—
123C22×C13—82no—
124C22×C13—82no—
125C22×C13—82no—
126C22×C13#44711yescharacteristic
127C22×C13C2×SD3211yescharacteristic
128C22×C13#50911yescharacteristic
129C4×C13—21no—
130C4×C13—22no—
131C4×C13—41no—
132C4×C13—82no—
133C4×C13#45611yescharacteristic
134C4×C13#45811yescharacteristic
135Dic13—82no—
136Dic13—161no—
137C2×#41—41no—
138C2×D8—21no—
139C2×D8C22⋊D1312yes—
140C22×C8C22⋊D1311yescharacteristic
141C22×C8C22×D1311yescharacteristic
142C4⋊Q8—21no—
143#127—21no—
144#124—41no—
145#121—22no—
146#121—41no—
147C4×D4—22no—
148C4×D4—41no—
149C2×C4⋊C4—261no—
150C2×C4⋊C4—261no—
151C2×C4⋊C4—521no—
152C2×C42C22⋊D1311yescharacteristic
153C2×C16—262no—
154#107—21no—
155#107—262no—
156#107C22⋊D1312yes—
157C4⋊C8—22no—
158#102—22no—
159#102—22no—
160#95—521no—
161C2×C13—21no—
162C2×C13—21no—
163C2×C13—162no—
164C2×C13#161011yescharacteristic
165C2×C13#218711yescharacteristic
166C2×C13#219011yescharacteristic
167#41—82no—
168#41—82no—
169C2×Q8—41no—
170C2×D4—22no—
171C2×D4—41no—
172C2×D4—41no—
173C2×D4—42no—
174C22×C4—42no—
175C22×C4—521no—
176C22×C4—521no—
177C22×C4#610411yescharacteristic
178C22×C4#610411yescharacteristic
179C22×C4C2×C22⋊D1311yescharacteristic
180D8—42no—
181D8—81no—
182C2×C8—21no—
183C2×C8—41no—
184C2×C8—41no—
185C2×C8C2×C22⋊D1312yes—
186C4⋊C4—22no—
187C4⋊C4—41no—
188C4⋊C4—262no—
189C4⋊C4—521no—
190C4⋊C4—521no—
191C4⋊C4—521no—
192C4⋊C4—1042no—
193C22⋊C4—42no—
194C22⋊C4—42no—
195C42—21no—
196C42—21no—
197C16—522no—
198C13#1229111yescharacteristic, complemented, Sylow
199C23—42no—
200C23C2×#610411yescharacteristic
201Q8—82no—
202D4—42no—
203D4—42no—
204D4—82no—
205D4—82no—
206D4—82no—
207D4—82no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—41no—
214C2×C4—42no—
215C2×C4—84no—
216C2×C4—522no—
217C2×C4—1041no—
218C2×C4—1041no—
219C2×C4—1041no—
220C2×C4—1041no—
221C2×C4—1041no—
222C2×C4#8806712yes—
223C2×C4#8818611yescharacteristic
224C2×C4#8820711yescharacteristic
225C8—22no—
226C8—41no—
227C22—21no—
228C22—21no—
229C22—82no—
230C22—82no—
231C22—82no—
232C22#1171880811yescharacteristic
233C22C2×#8806711yescharacteristic
234C22#1171887811yescharacteristic
235C4—22no—
236C4—21no—
237C4—41no—
238C4—82no—
239C4—1042no—
240C4—2081no—
241C4#1171890411yescharacteristic
242C4#1171890711yescharacteristic
243C2—21no—
244C2—21no—
245C2—162no—
246C2#1311383911yescharacteristic
247C2#1311676511yescharacteristic
248C2#1311678211yescharacteristic
subgroupG/H
centerC22#11718878
commutator, cosocleC22×C8×C13C23
FrattiniC22×C8C22×D13
Fitting, prime radicalC13×#3245C2
socleC22×C13#447
hypercenter#3245D13
hypocenterC13#12291
LCSG ▷ C22×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C8 ◁ #3245

Complements

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

NH ≅ G/Ntype
1. #13117019C2semidirect
2. #13116329C2semidirect
3. #13112845C2semidirect
4. #13112776C2semidirect
198. C13#12291semidirect

Maximal subgroups

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

subgroupindex
#131170192
#131163292
#131128452
#131127762
C13×#32452
#1229113