Finite Group Databasebeta

← #15756499

Subgroups — #15756499

Order 3328.

422 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 107 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#13117756C211yesmaximal, characteristic
2#13114829C211yesmaximal, characteristic
3#13113159C211yesmaximal, characteristic
4#13112739C211yesmaximal, characteristic
5#13112696C211yesmaximal, characteristic
6#13112695C211yesmaximal, characteristic
7C13×#1303C211yesmaximal, characteristic
8C2×C4×Dic26—21no—
9C2×C4×Dic26C2211yescharacteristic
10C13×#431C2211yescharacteristic
11C13×#423C2211yescharacteristic
12C4×C13×C4⋊C4C2211yescharacteristic
13C2×#88064—21no—
14#11718633—22no—
15#11718597C2211yescharacteristic
16#11718589—21no—
17#11718586C2211yescharacteristic
18#11718585C2211yescharacteristic
19#11718311C412yes—
20#11718310C412yes—
21#11718146—21no—
22#11718061—22no—
23C22×Dic26D411yescharacteristic
24C2×C13×M16—21no—
25C2×C13×C4⋊C4—21no—
26C2×C42×C13—21no—
27C2×C42×C13C2311yescharacteristic
28C2×C4⋊Dic13—21no—
29C2×C4⋊Dic13D411yescharacteristic
30C2×#6101—22no—
31C2×#6101—22no—
32C2×#6101D412yes—
33C2×C4×Dic13—22no—
34C2×C4×Dic13C2×C412yes—
35C2×#6099—21no—
36C4×Dic26—21no—
37C4×Dic26—21no—
38C4×Dic26—21no—
39C4×Dic26—21no—
40C4×Dic26—42no—
41C4×Dic26—42no—
42C13×C4⋊C8—21no—
43C13×C4⋊C8—21no—
44C13×C4⋊C8—21no—
45C13×C22⋊C8—21no—
46C4×C8×C13—21no—
47C13×#95C2×C411yescharacteristic
48C13×#95C2×C411yescharacteristic
49#88071—21no—
50#88071—22no—
51#88071C2×C412yes—
52C22⋊#1055—21no—
53#88064—42no—
54C4⋊#1055—21no—
55C4⋊#1055—21no—
56C4⋊#1055—21no—
57C4×#1055—21no—
58#8767—131nomaximal, Sylow
59C22×C4×C13—21no—
60C22×C4×C13—21no—
61C22×C4×C13C22×C411yescharacteristic
62C22×C4×C13C2×D411yescharacteristic
63C22×C4×C13C2×D411yescharacteristic
64C22×Dic13—22no—
65C22×Dic13C22⋊C412yes—
66C22×Dic13C22⋊C412yes—
67C2×Dic26—21no—
68C2×Dic26—21no—
69C2×Dic26—21no—
70C2×Dic26—21no—
71C2×Dic26SD1612yes—
72C2×Dic26Q1612yes—
73C13×M16—41no—
74C13×M16—41no—
75C2×C8×C13—41no—
76C2×C8×C13—41no—
77C13×C4⋊C4—42no—
78C42×C13—41no—
79C42×C13—41no—
80C42×C13#4111yescharacteristic
81C42×C13#4111yescharacteristic
82C42×C13#4111yescharacteristic
83C42×C13#4111yescharacteristic
84C4⋊Dic13—21no—
85C4⋊Dic13—21no—
86C4⋊Dic13—41no—
87C4⋊Dic13—41no—
88#6101—22no—
89#6101—22no—
90#6101—44no—
91#6101—44no—
92C4×Dic13—22no—
93C4×Dic13—22no—
94C4×Dic13—44no—
95#6099—41no—
96#6099—41no—
97C2×#1055—41no—
98C2×#1055—41no—
99#2351—131no—
100#1801—131no—
101#1461—131no—
102#1303—131no—
103#1303D1311yescharacteristic
104#1286—131no—
105#1286—131no—
106C23×C13C2×C22⋊C411yescharacteristic
107C2×C4×C13—22no—
108C2×C4×C13—41no—
109C2×C4×C13—41no—
110C2×C4×C13—41no—
111C2×C4×C13—41no—
112C2×C4×C13—41no—
113C2×C4×C13—41no—
114C2×C4×C13—41no—
115C2×C4×C13#11711yescharacteristic
116C2×C4×C13#11711yescharacteristic
117C2×C4×C13#12311yescharacteristic
118C2×C4×C13#12311yescharacteristic
119C2×C4×C13#12311yescharacteristic
120C2×C4×C13#12311yescharacteristic
121C2×C4×C13C2×SD1611yescharacteristic
122C2×C4×C13C2×Q1611yescharacteristic
123C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
124C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
125C2×Dic13—22no—
126C2×Dic13—22no—
127C2×Dic13—22no—
128C2×Dic13—42no—
129C2×Dic13—42no—
130C2×Dic13—42no—
131C2×Dic13—42no—
132C2×Dic13#10314yes—
133Dic26—22no—
134Dic26—22no—
135Dic26—22no—
136Dic26—22no—
137C8×C13—81no—
138C8×C13—81no—
139#1055—81no—
140#1055—81no—
141C2×C4×Q8—131no—
142C2×C4×Q8—261no—
143#431—131no—
144#431C2×D1311yescharacteristic
145#423—131no—
146#423C2×D1311yescharacteristic
147C2×#101—261no—
148#389—261no—
149#389—262no—
150#382—131no—
151#382—132no—
152C4×C4⋊C4—132no—
153C4×C4⋊C4C2×D1311yescharacteristic
154#343—261no—
155#324—262no—
156C22×C13—21no—
157C22×C13—21no—
158C22×C13#38111yescharacteristic
159C22×C13C2×#10311yescharacteristic
160C22×C13#41811yescharacteristic
161C4×C13—21no—
162C4×C13—21no—
163C4×C13—21no—
164C4×C13—21no—
165C4×C13—42no—
166C4×C13—81no—
167C4×C13#48111yescharacteristic
168C4×C13#48111yescharacteristic
169C4×C13#48411yescharacteristic
170C4×C13#48411yescharacteristic
171Dic13—24no—
172Dic13—42no—
173Dic13—82no—
174C22×Q8—131no—
175C2×M16—21no—
176C2×M16—261no—
177C4×Q8—261no—
178C4×Q8—261no—
179C4×Q8—261no—
180C4×Q8—261no—
181C4×Q8—522no—
182C4×Q8—522no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—132no—
185C2×C4⋊C4—131no—
186C2×C4⋊C4—262no—
187C2×C4⋊C4—262no—
188C2×C4⋊C4—261no—
189C2×C42—21no—
190C2×C42—132no—
191C2×C42—262no—
192C2×C42C22×D1311yescharacteristic
193C4⋊C8—21no—
194C4⋊C8—21no—
195C4⋊C8—21no—
196C4⋊C8—261no—
197C4⋊C8—261no—
198C4⋊C8—261no—
199#101—522no—
200C22⋊C8—21no—
201C22⋊C8—261no—
202C4×C8—21no—
203C4×C8—261no—
204#95—132no—
205#95—262no—
206#95—261no—
207#95C4×D1311yescharacteristic
208#95C4×D1311yescharacteristic
209C2×C13—21no—
210C2×C13—21no—
211C2×C13#182411yescharacteristic
212C2×C13#182711yescharacteristic
213C2×C13#183011yescharacteristic
214C2×Q8—132no—
215C2×Q8—132no—
216C2×Q8—261no—
217C2×Q8—261no—
218C2×Q8—261no—
219C2×Q8—261no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—132no—
223C22×C4—132no—
224C22×C4—262no—
225C22×C4C2×C4×D1311yescharacteristic
226C22×C4D4×D1311yescharacteristic
227C22×C4D4×D1311yescharacteristic
228M16—41no—
229M16—41no—
230M16—521no—
231M16—521no—
232C2×C8—41no—
233C2×C8—41no—
234C2×C8—521no—
235C2×C8—521no—
236C4⋊C4—42no—
237C4⋊C4—262no—
238C4⋊C4—261no—
239C4⋊C4—262no—
240C4⋊C4—261no—
241C4⋊C4—524no—
242C4⋊C4—524no—
243C4⋊C4—521no—
244C4⋊C4—521no—
245C42—41no—
246C42—41no—
247C42—262no—
248C42—262no—
249C42—524no—
250C42#612711yescharacteristic
251C42#612711yescharacteristic
252C42#612911yescharacteristic
253C42#613111yescharacteristic
254C13#876711yescharacteristic, complemented, Sylow
255C23C22⋊C4×D1311yescharacteristic
256Q8—262no—
257Q8—262no—
258Q8—262no—
259Q8—262no—
260C2×C4—22no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—134no—
269C2×C4—262no—
270C2×C4—262no—
271C2×C4—262no—
272C2×C4—522no—
273C2×C4—522no—
274C2×C4—522no—
275C2×C4—522no—
276C2×C4#8812611yescharacteristic
277C2×C4#8813711yescharacteristic
278C2×C4#8813711yescharacteristic
279C2×C4#8814611yescharacteristic
280C2×C4#8814811yescharacteristic
281C2×C4#8814811yescharacteristic
282C2×C4#8816511yescharacteristic
283C2×C4SD16×D1311yescharacteristic
284C2×C4#8816811yescharacteristic
285C2×C4Q16×D1311yescharacteristic
286C8—81no—
287C8—81no—
288C8—1041no—
289C8—1041no—
290C22—21no—
291C22—21no—
292C22#1171832511yescharacteristic
293C22#1171843111yescharacteristic
294C22D13×#10311yescharacteristic
295C4—21no—
296C4—21no—
297C4—21no—
298C4—21no—
299C4—42no—
300C4—81no—
301C4—264no—
302C4—522no—
303C4—1042no—
304C4#1171843811yescharacteristic
305C4#1171847011yescharacteristic
306C4#1171852411yescharacteristic
307C4#1171854511yescharacteristic
308C2—21no—
309C2—21no—
310C2#1311492511yescharacteristic
311C2#1311493911yescharacteristic
312C2#1311494911yescharacteristic
subgroupG/H
centerC22#11718325
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1303C2
socleC22×C13#381
prime radicalC23×C13C2×C22⋊C4
cosocleC2×C42×C13C23
hypercenter#1303D13
hypocenterC13#8767
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1303

Complements

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

NH ≅ G/Ntype
254. C13#8767semidirect

Maximal subgroups

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

subgroupindex
#131177562
#131148292
#131131592
#131127392
#131126962
#131126952
C13×#13032
#876713