Finite Group Databasebeta

← #15783338

Subgroups — #15783338

Order 3328.

304 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 67 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#13125919C211yesmaximal, characteristic
2#13116531C211yesmaximal, characteristic
3#13113008C212yesmaximal, complemented
4#13113004C212yesmaximal, complemented
5C13×#2133C211yesmaximal, characteristic
6C13×#536C2211yescharacteristic
7#11719223C411yescharacteristic
8C2×C13×#101—21no—
9#11718900—21no—
10#11718898—21no—
11#11718889—21no—
12#11718753C2211yescharacteristic
13#11718751—21no—
14#11718743C2211yescharacteristic
15#11718721C411yescharacteristic
16#11718717C411yescharacteristic
17#11718715—21no—
18#11718661C411yescharacteristic
19C13×#356C2212yes—
20C13×#355—21no—
21#11718140—21no—
22#11718140C2212yes—
23C2×C13×#41D411yescharacteristic
24C22×Q8×C13D411yescharacteristic
25C2×C13×M16—41no—
26C13×C4⋊Q8D411yescharacteristic
27C13×C4⋊Q8C2311yescharacteristic
28C13×#124C2×C411yescharacteristic
29C13×#124D411yescharacteristic
30C13×#123—41no—
31C13×C22⋊Q8—41no—
32C13×#117C2×C411yescharacteristic
33C2×#6107—21no—
34C2×#6107—21no—
35C2×#6107—21no—
36C2×#6105—21no—
37#88178—21no—
38C2×#6099—41no—
39#88143—41no—
40#88133—41no—
41#88124C2×C411yescharacteristic
42#88123C2×C411yescharacteristic
43C4×Dic26—21no—
44C13×#101—22no—
45C13×#101—41no—
46#88076—22no—
47#88075—21no—
48#88075—21no—
49#88075—21no—
50#88073—41no—
51#88072—21no—
52C22⋊#1055—21no—
53C4⋊#1055—21no—
54#88043C2×C411yescharacteristic
55C4×#1055C2×C411yescharacteristic
56#13612—131nomaximal, Sylow
57C13×#41—81no—
58C2×Q8×C13—21no—
59C2×Q8×C13—81no—
60C2×Q8×C13C22⋊C411yescharacteristic
61C2×Q8×C13C2×D411yescharacteristic
62C2×Q8×C13C2×D411yescharacteristic
63C2×D4×C13—21no—
64C2×D4×C13C22⋊C411yescharacteristic
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13C22⋊C411yescharacteristic
68C2×Dic26—21no—
69C13×M16—42no—
70C13×M16—81no—
71C2×C8×C13—81no—
72C13×C4⋊C4—21no—
73C13×C4⋊C4—41no—
74C13×C4⋊C4—41no—
75C13×C22⋊C4—21no—
76C13×C22⋊C4—41no—
77C13×C22⋊C4—41no—
78C42×C13C22⋊C411yescharacteristic
79C42×C13C22×C411yescharacteristic
80C22⋊Dic13—41no—
81#6107—81no—
82#6107—81no—
83#6107—81no—
84#6105—81no—
85C4⋊Dic13—21no—
86C4⋊Dic13—41no—
87#6101—41no—
88#6101—41no—
89#6101—41no—
90C4×Dic13—41no—
91#6099—42no—
92#6099—81no—
93C2×#1055—21no—
94C2×#1055—21no—
95C2×#1055—81no—
96#3223—131no—
97#2135—131no—
98#2133D1311yescharacteristic
99#1413—132no—
100#1411—132no—
101C23×C13—21no—
102C23×C13#9911yescharacteristic
103Q8×C13—41no—
104Q8×C13—41no—
105Q8×C13—41no—
106Q8×C13—81no—
107D4×C13—41no—
108D4×C13—81no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—41no—
115C2×C4×C13—41no—
116C2×C4×C13—41no—
117C2×C4×C13—41no—
118C2×C4×C13—41no—
119C2×C4×C13#9911yescharacteristic
120C2×C4×C13C2×C22⋊C411yescharacteristic
121C2×Dic13—41no—
122C2×Dic13—41no—
123Dic26—41no—
124Dic26—41no—
125C8×C13—82no—
126#1055—41no—
127#1055—41no—
128#1055—82no—
129#541—131no—
130#536C2×D1311yescharacteristic
131#497—131no—
132#494—131no—
133#491—131no—
134#488—131no—
135#464—261no—
136#462—261no—
137#452—261no—
138#451—261no—
139#433—131no—
140#413—261no—
141C2×#101—21no—
142#356—132no—
143#356—261no—
144#356C2×D1312yes—
145#355—21no—
146C22×C13—21no—
147C22×C13—41no—
148C22×C13—41no—
149C22×C13—81no—
150C22×C13C2×#9911yescharacteristic
151C4×C13—21no—
152C4×C13—21no—
153C4×C13—41no—
154C4×C13—41no—
155C4×C13—41no—
156C4×C13—41no—
157C4×C13—41no—
158Dic13—81no—
159Dic13—81no—
160C2×#41D5211yescharacteristic
161C22×Q8C22⋊D1311yescharacteristic
162C2×Q16—261no—
163C2×Q16—261no—
164C2×Q16—261no—
165C2×SD16—261no—
166C2×M16—41no—
167C2×M16—521no—
168C4⋊Q8—131no—
169C4⋊Q8D5211yescharacteristic
170C4⋊Q8C22×D1311yescharacteristic
171#126—521no—
172#125—131no—
173#125—521no—
174#124C4×D1311yescharacteristic
175#124C22⋊D1311yescharacteristic
176#123—41no—
177C22⋊Q8—41no—
178C22⋊Q8—261no—
179C4×Q8—261no—
180#117C4×D1311yescharacteristic
181C4⋊C8—261no—
182#103—261no—
183#103—261no—
184#103—261no—
185#102—261no—
186#101—22no—
187#101—41no—
188#101—262no—
189#100—521no—
190C22⋊C8—261no—
191#97—131no—
192C4×C8—131no—
193C2×C13—21no—
194C2×C13—41no—
195C2×C13—81no—
196C2×C13#212711yescharacteristic
197#41—81no—
198C2×Q8—21no—
199C2×Q8—81no—
200C2×Q8—261no—
201C2×Q8#610311yescharacteristic
202C2×Q8C2×D5211yescharacteristic
203C2×Q8C2×C22⋊D1311yescharacteristic
204C2×D4—21no—
205C2×D4#610311yescharacteristic
206C22×C4—21no—
207C22×C4—21no—
208C22×C4#610311yescharacteristic
209Q16—1041no—
210Q16—1041no—
211Q16—1041no—
212SD16—1041no—
213M16—42no—
214M16—81no—
215M16—522no—
216M16—1041no—
217C2×C8—81no—
218C2×C8—261no—
219C2×C8—261no—
220C2×C8—1041no—
221C4⋊C4—21no—
222C4⋊C4—41no—
223C4⋊C4—41no—
224C4⋊C4—261no—
225C4⋊C4—521no—
226C4⋊C4—521no—
227C4⋊C4—521no—
228C4⋊C4—521no—
229C22⋊C4—21no—
230C22⋊C4—41no—
231C22⋊C4—41no—
232C22⋊C4—521no—
233C42—521no—
234C42#610311yescharacteristic
235C42C2×C4×D1311yescharacteristic
236C13#1361211yescharacteristic, complemented, Sylow
237C23—21no—
238C23#8804611yescharacteristic
239Q8—41no—
240Q8—41no—
241Q8—41no—
242Q8—81no—
243Q8—521no—
244Q8—521no—
245D4—41no—
246D4—81no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—521no—
258C2×C4—521no—
259C2×C4#8804611yescharacteristic
260C2×C4C2×#610311yescharacteristic
261C8—82no—
262C8—521no—
263C8—521no—
264C8—1042no—
265C22—21no—
266C22—41no—
267C22—41no—
268C22—81no—
269C22C2×#8804611yescharacteristic
270C4—21no—
271C4—21no—
272C4—41no—
273C4—41no—
274C4—41no—
275C4—41no—
276C4—41no—
277C4—1041no—
278C4—1041no—
279C2—21no—
280C2—41no—
281C2—81no—
282C2#1311650311yescharacteristic
subgroupG/H
centerC2#13116503
commutatorC42×C13C22×C4
FrattiniC4⋊Q8C22×D13
FittingC13×#2133C2
socleC2×C13#2127
prime radicalC2×C13×#41D4
cosocleC13×C4⋊Q8C23
hypercenter#2133D13
hypocenterC13#13612
LCSG ▷ C42×C13 ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C22 ◁ C22×C4 ◁ #536 ◁ #2133

Complements

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

NH ≅ G/Ntype
3. #13113008C2semidirect
4. #13113004C2semidirect
236. C13#13612semidirect

Maximal subgroups

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

subgroupindex
#131259192
#131165312
#131130082
#131130042
C13×#21332
#1361213