Finite Group Databasebeta

← #15760998

Subgroups — #15760998

Order 3328.

396 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 89 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#13124966C211yesmaximal, characteristic
2#13123930C211yesmaximal, characteristic
3#13113564C211yesmaximal, characteristic
4#13113180C211yesmaximal, characteristic
5#13112747C211yesmaximal, characteristic
6#13112698C211yesmaximal, characteristic
7C13×#1487C211yesmaximal, characteristic
8C2×C4×Q8×C13C2211yescharacteristic
9#11719175C2211yescharacteristic
10C13×#431C2211yescharacteristic
11C13×#423C2211yescharacteristic
12#11718889C412yes—
13#11718692—21no—
14#11718691—22no—
15#11718681—21no—
16#11718632C412yes—
17#11718587C2211yescharacteristic
18#11718587C2211yescharacteristic
19#11718587C2211yescharacteristic
20#11718489—22no—
21#11718381—22no—
22#11718340—21no—
23C8×Dic26—21no—
24C13×Q8⋊C8—21no—
25C13×Q8⋊C8—21no—
26#11718120—22no—
27#11718074—21no—
28#11718073—21no—
29C22×Q8×C13C2×C411yescharacteristic
30C2×C13×M16—21no—
31C4×Q8×C13—21no—
32C4×Q8×C13—21no—
33C4×Q8×C13—21no—
34C4×Q8×C13—21no—
35C2×C13×C4⋊C4—21no—
36C2×C13×C4⋊C4C2×C411yescharacteristic
37C2×C42×C13—21no—
38C2×C42×C13C2311yescharacteristic
39C2×#6107—22no—
40#88180—21no—
41#88178—21no—
42#88178C2×C412yes—
43#88124—21no—
44#88123D411yescharacteristic
45#88123D411yescharacteristic
46C4×Dic26—21no—
47C4×Dic26D412yes—
48C13×C4⋊C8—21no—
49C13×C4⋊C8—21no—
50C13×C4⋊C8—21no—
51C13×C22⋊C8—21no—
52C4×C8×C13D411yescharacteristic
53C4×C8×C13D411yescharacteristic
54#88075—22no—
55C22⋊#1055—21no—
56C22⋊#1055C2×C412yes—
57C22⋊#1055D412yes—
58#88055—22no—
59#88054—22no—
60#88054—22no—
61C8×Dic13—22no—
62#88050—22no—
63#88048—22no—
64C4⋊#1055—21no—
65C4⋊#1055—21no—
66C4⋊#1055—21no—
67#88043—21no—
68#88043—21no—
69#88043—21no—
70#9528—131nomaximal, Sylow
71C2×Q8×C13—21no—
72C2×Q8×C13—21no—
73C2×Q8×C13—42no—
74C22×C4×C13—21no—
75C22×C4×C13—21no—
76C22×C4×C13C22×C411yescharacteristic
77C22×C4×C13C2×D411yescharacteristic
78C22×C4×C13#4111yescharacteristic
79C2×Dic26—21no—
80C2×Dic26C22⋊C412yes—
81C13×M16—81no—
82C2×C8×C13—21no—
83C2×C8×C13—21no—
84C2×C8×C13—41no—
85C13×C4⋊C4—21no—
86C13×C4⋊C4—21no—
87C13×C4⋊C4—41no—
88C13×C4⋊C4—41no—
89C42×C13—41no—
90C42×C13—41no—
91C42×C13C2×D411yescharacteristic
92C42×C13C2×D411yescharacteristic
93C42×C13C2×D411yescharacteristic
94C42×C13#4111yescharacteristic
95C22⋊Dic13—22no—
96#6107—44no—
97C4⋊Dic13—21no—
98C4⋊Dic13—21no—
99C4⋊Dic13—21no—
100C4⋊Dic13C22⋊C412yes—
101#6101—22no—
102#6101—22no—
103C4×Dic13—22no—
104C2×#1055—22no—
105C2×#1055—22no—
106C2×#1055—41no—
107#3113—131no—
108#2985—131no—
109#1559—131no—
110#1487D1311yescharacteristic
111#1467—131no—
112#1307—131no—
113#1287—131no—
114C23×C13C4×D411yescharacteristic
115Q8×C13—22no—
116Q8×C13—22no—
117Q8×C13—41no—
118Q8×C13—41no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—22no—
122C2×C4×C13—41no—
123C2×C4×C13—41no—
124C2×C4×C13—41no—
125C2×C4×C13—41no—
126C2×C4×C13—41no—
127C2×C4×C13—81no—
128C2×C4×C13C2×C22⋊C411yescharacteristic
129C2×C4×C13C4×D411yescharacteristic
130C2×C4×C13#12011yescharacteristic
131C2×C4×C13#12111yescharacteristic
132C2×C4×C13#12111yescharacteristic
133C2×C4×C13#12311yescharacteristic
134C2×Dic13—22no—
135C2×Dic13—22no—
136Dic26—41no—
137Dic26—41no—
138Dic26—42no—
139C8×C13—41no—
140C8×C13—41no—
141C8×C13—81no—
142#1055—42no—
143#1055—42no—
144#1055—81no—
145#533—131no—
146C2×C4×Q8C2×D1311yescharacteristic
147#483—132no—
148#475—261no—
149#462—261no—
150#451—132no—
151#446—262no—
152#446—261no—
153C8×Q8—261no—
154#441—262no—
155#433—262no—
156#432—131no—
157#432—131no—
158#432—131no—
159#431C2×D1311yescharacteristic
160#423C2×D1311yescharacteristic
161#333—261no—
162#332—261no—
163Q8⋊C8—21no—
164Q8⋊C8—21no—
165#324—262no—
166C22×C13—21no—
167C22×C13—21no—
168C22×C13—21no—
169C22×C13#38611yescharacteristic
170C4×C13—21no—
171C4×C13—21no—
172C4×C13—21no—
173C4×C13—21no—
174C4×C13—21no—
175C4×C13—42no—
176C4×C13—81no—
177C4×C13#47111yescharacteristic
178C4×C13#47311yescharacteristic
179Dic13—42no—
180Dic13—42no—
181C22×Q8C4×D1311yescharacteristic
182C2×Q16—262no—
183C2×M16—21no—
184C4⋊Q8—131no—
185C4⋊Q8—131no—
186#125—261no—
187C22⋊Q8—132no—
188C22⋊Q8—261no—
189C4×Q8—21no—
190C4×Q8—21no—
191C4×Q8—21no—
192C4×Q8—21no—
193C4×Q8—132no—
194C4×Q8—261no—
195#117—261no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4C4×D1311yescharacteristic
198C2×C42—21no—
199C2×C42C22×D1311yescharacteristic
200#106—262no—
201C4⋊C8—21no—
202C4⋊C8—21no—
203C4⋊C8—21no—
204C4⋊C8—262no—
205C4⋊C8—262no—
206C4⋊C8—261no—
207C4⋊C8—261no—
208C4⋊C8—261no—
209#103—262no—
210#103—262no—
211C22⋊C8—21no—
212C22⋊C8—132no—
213C22⋊C8—132no—
214C22⋊C8—261no—
215#97—262no—
216#97—261no—
217#97—261no—
218#97—261no—
219C4×C8—262no—
220C4×C8C22⋊D1311yescharacteristic
221C4×C8C22⋊D1311yescharacteristic
222C2×C13—41no—
223C2×C13#189111yescharacteristic
224C2×C13#190511yescharacteristic
225C2×C13#190811yescharacteristic
226C2×Q8—21no—
227C2×Q8—21no—
228C2×Q8—42no—
229C2×Q8—132no—
230C2×Q8—261no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4C2×C4×D1311yescharacteristic
234C22×C4D4×D1311yescharacteristic
235C22×C4#612911yescharacteristic
236Q16—524no—
237M16—81no—
238C2×C8—21no—
239C2×C8—21no—
240C2×C8—41no—
241C2×C8—262no—
242C2×C8—262no—
243C2×C8—521no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—132no—
249C4⋊C4—262no—
250C4⋊C4—261no—
251C4⋊C4—261no—
252C4⋊C4—262no—
253C4⋊C4—261no—
254C22⋊C4—262no—
255C42—41no—
256C42—41no—
257C42—262no—
258C42#612711yescharacteristic
259C42D4×D1311yescharacteristic
260C42D4×D1311yescharacteristic
261C42C2×C22⋊D1311yescharacteristic
262C13#952811yescharacteristic, complemented, Sylow
263C23#8813511yescharacteristic
264Q8—22no—
265Q8—22no—
266Q8—41no—
267Q8—41no—
268Q8—522no—
269Q8—521no—
270Q8—521no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—22no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—81no—
280C2×C4—262no—
281C2×C4—262no—
282C2×C4C22⋊C4×D1311yescharacteristic
283C2×C4#8813711yescharacteristic
284C2×C4#8813811yescharacteristic
285C2×C4C4×C22⋊D1311yescharacteristic
286C2×C4#8819111yescharacteristic
287C2×C4#8819211yescharacteristic
288C8—41no—
289C8—41no—
290C8—81no—
291C8—522no—
292C8—522no—
293C8—1041no—
294C22—21no—
295C22—21no—
296C22—21no—
297C22#1171861711yescharacteristic
298C4—21no—
299C4—21no—
300C4—21no—
301C4—21no—
302C4—21no—
303C4—42no—
304C4—81no—
305C4—522no—
306C4—522no—
307C4#1171883811yescharacteristic
308C4#1171885311yescharacteristic
309C2—41no—
310C2#1311525111yescharacteristic
311C2#1311532711yescharacteristic
312C2#1311535411yescharacteristic
subgroupG/H
centerC22#11718617
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1487C2
socleC22×C13#386
prime radicalC23×C13C4×D4
cosocleC2×C42×C13C23
hypercenter#1487D13
hypocenterC13#9528
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1487

Complements

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

NH ≅ G/Ntype
262. C13#9528semidirect

Maximal subgroups

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

subgroupindex
#131249662
#131239302
#131135642
#131131802
#131127472
#131126982
C13×#14872
#952813