Finite Group Databasebeta

← #15776711

Subgroups — #15776711

Order 3328.

350 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 73 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
1D4×Dic52C211yesmaximal, characteristic
2#13117065C211yesmaximal, characteristic, complemented
3#13116975C211yesmaximal, characteristic, complemented
4#13112884C211yesmaximal, characteristic, complemented
5#13112799C211yesmaximal, characteristic, complemented
6D4⋊#6090C211yesmaximal, characteristic
7C13×#1673C211yesmaximal, characteristic
8C22×Dic52—21no—
9D4×Dic26—21no—
10C13×#500C2211yescharacteristic
11C13×#461—21no—
12C8×D4×C13C2211yescharacteristic
13#11718777—21no—
14#11718510—21no—
15#11718400—22no—
16#11718360C2211yescharacteristic
17C4×Dic52C2211yescharacteristic
18C13×#335C2211yescharacteristic
19C13×#332—21no—
20#11718084—21no—
21#11718084—22no—
22#11718082—21no—
23C4⋊#6090C2211yescharacteristic
24C4×#6090C2211yescharacteristic
25C22×Dic26—22no—
26C2×C13×SD16—41no—
27C22×C8×C13—21no—
28C13×C4⋊Q8—21no—
29C4×D4×C13D411yescharacteristic
30D4×Dic13—41no—
31#88178—22no—
32C2×Dic52—22no—
33C2×Dic52—21no—
34C2×Dic52—42no—
35C2×Dic52—42no—
36C2×Dic52D411yescharacteristic
37C2×Dic52D412yes—
38#88142—41no—
39#88132—42no—
40#88123—21no—
41C4×Dic26—21no—
42C13×#107—21no—
43C13×#107—21no—
44C13×C4⋊C8—21no—
45C13×C4⋊C8D411yescharacteristic
46C13×#103—41no—
47C13×C22⋊C8—21no—
48C4×C8×C13C2311yescharacteristic
49#88058D411yescharacteristic
50#88056—22no—
51#88056—21no—
52C2×#6090—21no—
53C2×#6090—21no—
54#12370—131nomaximal, Sylow
55C2×Q8×C13—41no—
56C2×D4×C13D811yescharacteristic
57C22×C4×C13—21no—
58C22×Dic13—42no—
59C2×Dic26—21no—
60C2×Dic26—22no—
61C2×Dic26—44no—
62C2×Dic26—42no—
63C2×Dic26—82no—
64C13×SD16—82no—
65C2×C8×C13—21no—
66C2×C8×C13—41no—
67C2×C8×C13—41no—
68C2×C8×C13—41no—
69C2×C8×C13C2×D411yescharacteristic
70C2×C8×C13C2×D411yescharacteristic
71C13×C4⋊C4—41no—
72C13×C4⋊C4—41no—
73C13×C4⋊C4D811yescharacteristic
74C13×C22⋊C4—21no—
75C42×C13C2×D411yescharacteristic
76C22⋊Dic13—42no—
77C4⋊Dic13—21no—
78C4⋊Dic13—41no—
79C4⋊Dic13—41no—
80#6101—42no—
81#6101—41no—
82C4×Dic13—41no—
83Dic52—21no—
84Dic52—42no—
85Dic52—44no—
86Dic52—41no—
87Dic52—41no—
88Dic52SD1612yescomplemented
89#6090—41no—
90#6090—41no—
91D4×Q16—131no—
92#2241—131no—
93#2225—131no—
94#1673D1311yescharacteristic
95#1362—131no—
96#1332—131no—
97D4⋊C16—131no—
98C23×C13—21no—
99Q8×C13—81no—
100Q8×C13—81no—
101D4×C13—21no—
102D4×C13SD3212yes—
103C2×C4×C13—21no—
104C2×C4×C13—41no—
105C2×C4×C13—41no—
106C2×C4×C13—81no—
107C2×C4×C13#12011yescharacteristic
108C2×C4×C13C2×D811yescharacteristic
109C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
110C2×Dic13—41no—
111C2×Dic13—41no—
112C2×Dic13—42no—
113C2×Dic13—84no—
114Dic26—22no—
115Dic26—41no—
116Dic26—42no—
117Dic26—42no—
118Dic26—84no—
119C8×C13—21no—
120C8×C13—41no—
121C8×C13—81no—
122C8×C13C2×SD1611yescharacteristic
123C8×C13AGL(1,ℤ/8)11yescharacteristic
124C22×Q16—261no—
125D4×Q8—261no—
126#500C2×D1311yescharacteristic
127#494—131no—
128#467—261no—
129#462—261no—
130#461—21no—
131#451—262no—
132C4×Q16—131no—
133C8×D4C2×D1311yescharacteristic
134#367—261no—
135C4⋊C16—131no—
136#358—261no—
137#358—262no—
138C4×C16—131no—
139#335C2×D1311yescharacteristic
140#332—21no—
141C22×C13—22no—
142C22×C13—41no—
143C22×C13—41no—
144C22×C13#44711yescharacteristic
145C4×C13—21no—
146C4×C13—41no—
147C4×C13—161no—
148C4×C13#45011yescharacteristic
149C4×C13#45511yescharacteristic
150C4×C13C2×SD3211yescharacteristic
151C4×C13#51011yescharacteristic
152Dic13—42no—
153Dic13—82no—
154Dic13—81no—
155C22×Q8—262no—
156C2×Q16—131no—
157C2×Q16—132no—
158C2×Q16—262no—
159C2×Q16—261no—
160C2×Q16—522no—
161C2×Q16—522no—
162C2×SD16—41no—
163C22×C8—21no—
164C4⋊Q8—21no—
165C4⋊Q8—261no—
166C4⋊Q8—521no—
167C22⋊Q8—262no—
168C22⋊Q8—522no—
169C4×Q8—261no—
170C4×D4—521no—
171C4×D4C22⋊D1311yescharacteristic
172C2×C16—261no—
173C2×C16—261no—
174#107—21no—
175#107—21no—
176#107—131no—
177C4⋊C8—21no—
178C4⋊C8C22⋊D1311yescharacteristic
179#103—41no—
180#103—262no—
181#103—261no—
182C22⋊C8—21no—
183C4×C8C22×D1311yescharacteristic
184C2×C13—42no—
185C2×C13#163911yescharacteristic
186C2×C13#218511yescharacteristic
187C2×C13#219511yescharacteristic
188C2×Q8—41no—
189C2×Q8—261no—
190C2×Q8—262no—
191C2×Q8—522no—
192C2×Q8—524no—
193C2×Q8—1042no—
194C2×D4#610411yescharacteristic
195C22×C4—21no—
196C22×C4—522no—
197Q16—132no—
198Q16—261no—
199Q16—522no—
200Q16—524no—
201Q16—521no—
202Q16—521no—
203SD16—82no—
204C2×C8—21no—
205C2×C8—41no—
206C2×C8—41no—
207C2×C8—41no—
208C2×C8D4×D1311yescharacteristic
209C2×C8D4×D1311yescharacteristic
210C4⋊C4—41no—
211C4⋊C4—41no—
212C4⋊C4—261no—
213C4⋊C4—522no—
214C4⋊C4—521no—
215C4⋊C4—521no—
216C4⋊C4—521no—
217C4⋊C4#610411yescharacteristic
218C22⋊C4—21no—
219C22⋊C4—522no—
220C42—521no—
221C42C2×C22⋊D1311yescharacteristic
222C16—521no—
223C16—521no—
224C13#1237011yescharacteristic, complemented, Sylow
225C23—21no—
226Q8—81no—
227Q8—81no—
228Q8—262no—
229Q8—521no—
230Q8—522no—
231Q8—522no—
232Q8—1044no—
233D4—21no—
234D4#8806712yes—
235C2×C4—21no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—81no—
239C2×C4—521no—
240C2×C4—521no—
241C2×C4—522no—
242C2×C4—1044no—
243C2×C4C2×#610411yescharacteristic
244C2×C4#8819111yescharacteristic
245C2×C4#8820311yescharacteristic
246C8—21no—
247C8—41no—
248C8—81no—
249C8SD16×D1311yescharacteristic
250C8#8816811yescharacteristic
251C22—22no—
252C22—41no—
253C22—41no—
254C22#1171869711yescharacteristic
255C4—21no—
256C4—41no—
257C4—161no—
258C4—522no—
259C4—1041no—
260C4—1042no—
261C4C2×#8806711yescharacteristic
262C4#1171883011yescharacteristic
263C4#1171885611yescharacteristic
264C4#1171886311yescharacteristic
265C2—42no—
266C2#1311401311yescharacteristic
267C2#1311675211yescharacteristic
268C2#1311681211yescharacteristic
subgroupG/H
centerC22#11718697
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingC13×#1673C2
socleC22×C13#447
prime radicalC2×D4×C13D8
hypercenter#1673D13
hypocenterC13#12370
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C8×D4 ◁ #1673

Complements

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

NH ≅ G/Ntype
2. #13117065C2semidirect
3. #13116975C2semidirect
4. #13112884C2semidirect
5. #13112799C2semidirect
88. Dic52SD16semidirect
224. C13#12370semidirect

Maximal subgroups

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

subgroupindex
D4×Dic522
#131170652
#131169752
#131128842
#131127992
D4⋊#60902
C13×#16732
#1237013