Finite Group Databasebeta

← #15776790

Subgroups — #15776790

Order 3328.

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

normal subgroups only

This group has 306 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#13117059C211yesmaximal, characteristic
2#13116978C211yesmaximal, characteristic, complemented
3#13114230C211yesmaximal, characteristic, complemented
4#13112882C211yesmaximal, characteristic
5Q8⋊#6090C211yesmaximal, characteristic, complemented
6#13112800C211yesmaximal, characteristic, complemented
7C13×#3396C211yesmaximal, characteristic
8C13×#559—21no—
9C13×#495—21no—
10C13×#493C2211yescharacteristic
11C13×#463—22no—
12C13×#460—21no—
13C8×Q8×C13C2211yescharacteristic
14C4×C13×Q16C2211yescharacteristic
15C4×C13×D8—21no—
16#11718692—21no—
17#11718343C2211yescharacteristic
18#11718156—21no—
19#11718154—22no—
20#11718082—21no—
21#11718078—21no—
22C4⋊#6090C2211yescharacteristic
23C4×#6090C2211yescharacteristic
24#11718050C2211yescharacteristic
25C2×C13×Q16D411yescharacteristic
26C2×C13×SD16—22no—
27C2×C13×D8—21no—
28C2×C13×D8D412yes—
29C13×#127—21no—
30C13×#124—22no—
31C13×#124—41no—
32C13×#123—42no—
33C4×Q8×C13—21no—
34C4×Q8×C13D411yescharacteristic
35C4×D4×C13—22no—
36C4×D4×C13—41no—
37C2×#6107—41no—
38#88123—21no—
39C13×#107D411yescharacteristic
40C13×C4⋊C8—21no—
41C13×C4⋊C8D411yescharacteristic
42C13×#103—21no—
43C13×#102—22no—
44C4×C8×C13—21no—
45C4×C8×C13C2311yescharacteristic
46#88058—21no—
47#88058—21no—
48C2×#6090—21no—
49C2×#6090—21no—
50#88050—41no—
51C4⋊#1055—21no—
52#12381—131nomaximal, Sylow
53C2×Q8×C13—21no—
54C2×Q8×C13D811yescharacteristic
55C2×D4×C13—22no—
56C2×D4×C13—41no—
57C2×D4×C13—41no—
58C22×C4×C13—42no—
59C2×Dic26—41no—
60C13×Q16—21no—
61C13×Q16—21no—
62C13×SD16—82no—
63C13×D8—42no—
64C13×D8—41no—
65C13×D8—41no—
66C2×C8×C13—21no—
67C2×C8×C13C2×D411yescharacteristic
68C2×C8×C13C2×D411yescharacteristic
69C13×C4⋊C4—21no—
70C13×C4⋊C4—21no—
71C13×C4⋊C4—41no—
72C13×C4⋊C4D811yescharacteristic
73C13×C22⋊C4—42no—
74C13×C22⋊C4—42no—
75C13×C22⋊C4—42no—
76C42×C13—21no—
77C42×C13—41no—
78C42×C13C2×D411yescharacteristic
79#6107—82no—
80C4⋊Dic13—41no—
81C4⋊Dic13—41no—
82C2×#1055—41no—
83#6090—41no—
84#6090—41no—
85#3396D1311yescharacteristic
86#2240—131no—
87#2225—131no—
88#1674—131no—
89#1361—131no—
90Q8⋊C16—131no—
91#1332—131no—
92C23×C13—42no—
93Q8×C13—21no—
94Q8×C13—21no—
95Q8×C13—41no—
96Q8×C13—41no—
97D4×C13—42no—
98D4×C13—42no—
99D4×C13—81no—
100D4×C13—81no—
101D4×C13—161no—
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—41no—
105C2×C4×C13—41no—
106C2×C4×C13—162no—
107C2×C4×C13#12011yescharacteristic
108C2×C4×C13C2×D811yescharacteristic
109C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
110C2×Dic13—81no—
111Dic26—81no—
112Dic26—81no—
113C8×C13—21no—
114C8×C13—41no—
115C8×C13#13511yescharacteristic
116C8×C13#13711yescharacteristic
117#1055—81no—
118#559—21no—
119#500—131no—
120#495—21no—
121#493C2×D1311yescharacteristic
122#463—22no—
123#462—261no—
124#460—21no—
125C8×Q8C2×D1311yescharacteristic
126C4×Q16C2×D1311yescharacteristic
127C4×D8—21no—
128#367—261no—
129C4⋊C16—131no—
130#358—261no—
131#357—262no—
132C4×C16—131no—
133#335—131no—
134#332—261no—
135C22×C13—82no—
136C22×C13—82no—
137C22×C13—82no—
138C22×C13#44711yescharacteristic
139C4×C13—21no—
140C4×C13—41no—
141C4×C13—41no—
142C4×C13—81no—
143C4×C13—81no—
144C4×C13#45211yescharacteristic
145C4×C13#45511yescharacteristic
146C4×C13#50811yescharacteristic
147C4×C13#50911yescharacteristic
148Dic13—161no—
149C2×Q16—521no—
150C2×Q16C22⋊D1311yescharacteristic
151C2×SD16—22no—
152C2×D8—21no—
153C2×D8C22⋊D1312yes—
154C4⋊Q8—261no—
155#127—21no—
156#124—22no—
157#124—41no—
158#123—42no—
159C4×Q8—21no—
160C4×Q8C22⋊D1311yescharacteristic
161C4×D4—22no—
162C4×D4—41no—
163C2×C16—261no—
164C2×C16—261no—
165#107—261no—
166#107—261no—
167#107C22⋊D1311yescharacteristic
168C4⋊C8—21no—
169C4⋊C8—261no—
170C4⋊C8C22⋊D1311yescharacteristic
171#103—21no—
172#103—521no—
173#102—22no—
174C4×C8—21no—
175C4×C8C22×D1311yescharacteristic
176C2×C13—162no—
177C2×C13#164111yescharacteristic
178C2×C13#218611yescharacteristic
179C2×C13#219411yescharacteristic
180C2×Q8—21no—
181C2×Q8—521no—
182C2×Q8#610411yescharacteristic
183C2×D4—22no—
184C2×D4—41no—
185C2×D4—41no—
186C22×C4—42no—
187Q16—21no—
188Q16—21no—
189Q16—1042no—
190SD16—82no—
191D8—42no—
192D8—41no—
193D8—41no—
194C2×C8—21no—
195C2×C8—521no—
196C2×C8C2×C22⋊D1311yescharacteristic
197C2×C8C2×C22⋊D1311yescharacteristic
198C4⋊C4—21no—
199C4⋊C4—21no—
200C4⋊C4—41no—
201C4⋊C4—521no—
202C4⋊C4—521no—
203C4⋊C4#610411yescharacteristic
204C22⋊C4—42no—
205C22⋊C4—42no—
206C22⋊C4—42no—
207C42—21no—
208C42—41no—
209C42C2×C22⋊D1311yescharacteristic
210C16—521no—
211C16—521no—
212C13#1238111yescharacteristic, complemented, Sylow
213C23—42no—
214Q8—21no—
215Q8—21no—
216Q8—41no—
217Q8—41no—
218Q8—1041no—
219Q8—1041no—
220D4—42no—
221D4—42no—
222D4—81no—
223D4—81no—
224D4—161no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—162no—
230C2×C4—1041no—
231C2×C4C2×#610411yescharacteristic
232C2×C4#8818611yescharacteristic
233C2×C4#8820711yescharacteristic
234C8—21no—
235C8—41no—
236C8—1041no—
237C8#8820411yescharacteristic
238C8#8820511yescharacteristic
239C22—82no—
240C22—82no—
241C22—82no—
242C22#1171887811yescharacteristic
243C4—21no—
244C4—41no—
245C4—41no—
246C4—81no—
247C4—81no—
248C4—2081no—
249C4#1171885411yescharacteristic
250C4#1171885511yescharacteristic
251C4#1171890011yescharacteristic
252C4#1171890311yescharacteristic
253C2—162no—
254C2#1311402911yescharacteristic
255C2#1311675911yescharacteristic
256C2#1311680711yescharacteristic
subgroupG/H
centerC22#11718878
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingC13×#3396C2
socleC22×C13#447
prime radicalC13×#493C22
hypercenter#3396D13
hypocenterC13#12381
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C8×Q8 ◁ #3396

Complements

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

NH ≅ G/Ntype
2. #13116978C2semidirect
3. #13114230C2semidirect
5. Q8⋊#6090C2semidirect
6. #13112800C2semidirect
212. C13#12381semidirect

Maximal subgroups

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

subgroupindex
#131170592
#131169782
#131142302
#131128822
Q8⋊#60902
#131128002
C13×#33962
#1238113