Finite Group Databasebeta

← #15761001

Subgroups — #15761001

Order 3328.

396 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 99 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#13124962C211yesmaximal, characteristic
2#13113566C211yesmaximal, characteristic
3#13113266C211yesmaximal, characteristic
4#13113179C211yesmaximal, characteristic
5#13112746C211yesmaximal, characteristic
6#13112698C211yesmaximal, characteristic
7C13×#2985C211yesmaximal, characteristic
8C13×#533C2211yescharacteristic
9C2×C4×Dic26C2211yescharacteristic
10C13×#446—22no—
11C13×#446—21no—
12C8×Q8×C13—21no—
13C13×#433—22no—
14C13×#432C2211yescharacteristic
15C13×#431C2211yescharacteristic
16#11718755—21no—
17#11718751—21no—
18#11718711C412yes—
19#11718704C412yes—
20#11718691—22no—
21#11718587C2211yescharacteristic
22#11718587C2211yescharacteristic
23#11718585C2211yescharacteristic
24#11718139—21no—
25#11718138—21no—
26#11718061—22no—
27#11718048—21no—
28#11718048—21no—
29C22×Dic26C2×C411yescharacteristic
30C13×C4⋊Q8D411yescharacteristic
31C13×C4⋊Q8D411yescharacteristic
32C13×#125—21no—
33C13×C22⋊Q8—21no—
34C13×C22⋊Q8C2×C412yes—
35C4×Q8×C13—21no—
36C4×Q8×C13D412yes—
37C13×#117—21no—
38C2×C42×C13C2311yescharacteristic
39C2×#6107—22no—
40C2×C4⋊Dic13C2×C411yescharacteristic
41C2×#6101—21no—
42C2×C4×Dic13—21no—
43C2×#6099—21no—
44C4×Dic26—21no—
45C4×Dic26—21no—
46C4×Dic26—21no—
47C4×Dic26—21no—
48C13×C4⋊C8—22no—
49C13×C4⋊C8—22no—
50C13×C4⋊C8—21no—
51C13×C4⋊C8—21no—
52C13×C22⋊C8—21no—
53C13×C22⋊C8D412yes—
54C13×#97—22no—
55C13×#97—21no—
56C4×C8×C13—22no—
57C4×C8×C13D411yescharacteristic
58C4×C8×C13D411yescharacteristic
59#88075—22no—
60C22⋊#1055—21no—
61C22⋊#1055C2×C412yes—
62#88050—22no—
63#88048—22no—
64C4⋊#1055—21no—
65C4⋊#1055—21no—
66C4⋊#1055—21no—
67C4⋊#1055—21no—
68#88043—21no—
69#88043—21no—
70#9528—131nomaximal, Sylow
71C2×Q8×C13—21no—
72C2×Q8×C13C22⋊C412yes—
73C22×C4×C13C22×C411yescharacteristic
74C22×C4×C13C2×D411yescharacteristic
75C22×C4×C13#4111yescharacteristic
76C22×Dic13—21no—
77C22×Dic13—21no—
78C2×Dic26—21no—
79C2×Dic26—21no—
80C2×Dic26—42no—
81C2×C8×C13—21no—
82C2×C8×C13—22no—
83C2×C8×C13—21no—
84C13×C4⋊C4—22no—
85C13×C4⋊C4—21no—
86C13×C4⋊C4—21no—
87C13×C4⋊C4—21no—
88C13×C4⋊C4—22no—
89C13×C4⋊C4C22⋊C412yes—
90C13×C22⋊C4—22no—
91C42×C13—22no—
92C42×C13C2×D411yescharacteristic
93C42×C13C2×D411yescharacteristic
94C42×C13C2×D411yescharacteristic
95C42×C13#4111yescharacteristic
96#6107—44no—
97C4⋊Dic13—21no—
98C4⋊Dic13—21no—
99#6101—41no—
100#6101—41no—
101C4×Dic13—41no—
102C4×Dic13—41no—
103#6099—81no—
104C2×#1055—22no—
105C2×#1055—41no—
106C2×#1055—41no—
107#3113—131no—
108#2985D1311yescharacteristic
109#1559—131no—
110#1487—131no—
111#1467—131no—
112#1307—131no—
113#1287—131no—
114C23×C13C4×D411yescharacteristic
115Q8×C13—42no—
116Q8×C13—41no—
117Q8×C13—41no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—22no—
121C2×C4×C13—22no—
122C2×C4×C13—41no—
123C2×C4×C13—41no—
124C2×C4×C13C2×C22⋊C411yescharacteristic
125C2×C4×C13C4×D411yescharacteristic
126C2×C4×C13#12011yescharacteristic
127C2×C4×C13#12111yescharacteristic
128C2×C4×C13#12111yescharacteristic
129C2×C4×C13#12311yescharacteristic
130C2×Dic13—22no—
131C2×Dic13—41no—
132C2×Dic13—41no—
133C2×Dic13—41no—
134C2×Dic13—81no—
135Dic26—22no—
136Dic26—22no—
137Dic26—41no—
138Dic26—41no—
139C8×C13—41no—
140C8×C13—42no—
141C8×C13—41no—
142#1055—42no—
143#1055—81no—
144#1055—81no—
145#533C2×D1311yescharacteristic
146C2×C4×Q8—131no—
147#483—132no—
148#475—261no—
149#462—261no—
150#451—132no—
151#446—22no—
152#446—21no—
153C8×Q8—21no—
154#441—262no—
155#433—22no—
156#432—131no—
157#432—131no—
158#432C2×D1311yescharacteristic
159#431C2×D1311yescharacteristic
160#423—131no—
161#333—261no—
162#332—261no—
163Q8⋊C8—261no—
164Q8⋊C8—261no—
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—42no—
177C4×C13#47111yescharacteristic
178C4×C13#47311yescharacteristic
179Dic13—42no—
180Dic13—81no—
181C22×Q8—131no—
182C2×Q16—262no—
183C2×M16—261no—
184C4⋊Q8D5211yescharacteristic
185C4⋊Q8D5211yescharacteristic
186#125—21no—
187C22⋊Q8—21no—
188C22⋊Q8C4×D1312yes—
189C4×Q8—21no—
190C4×Q8—261no—
191C4×Q8—261no—
192C4×Q8—261no—
193C4×Q8—261no—
194C4×Q8C22⋊D1312yes—
195#117—21no—
196C2×C4⋊C4—131no—
197C2×C4⋊C4—261no—
198C2×C42—261no—
199C2×C42C22×D1311yescharacteristic
200#106—262no—
201C4⋊C8—22no—
202C4⋊C8—22no—
203C4⋊C8—21no—
204C4⋊C8—21no—
205C4⋊C8—261no—
206C4⋊C8—261no—
207C4⋊C8—261no—
208C4⋊C8—261no—
209#103—262no—
210#103—262no—
211C22⋊C8—21no—
212C22⋊C8—132no—
213C22⋊C8—261no—
214C22⋊C8C22⋊D1312yes—
215#97—22no—
216#97—21no—
217#97—261no—
218#97—261no—
219C4×C8—22no—
220C4×C8C22⋊D1311yescharacteristic
221C4×C8C22⋊D1311yescharacteristic
222C2×C13—41no—
223C2×C13#189111yescharacteristic
224C2×C13#190511yescharacteristic
225C2×C13#190811yescharacteristic
226C2×Q8—21no—
227C2×Q8—261no—
228C2×Q8—261no—
229C2×Q8—522no—
230C2×Q8#610312yes—
231C22×C4—261no—
232C22×C4—261no—
233C22×C4C2×C4×D1311yescharacteristic
234C22×C4#612711yescharacteristic
235C22×C4C2×C22⋊D1311yescharacteristic
236Q16—524no—
237M16—1041no—
238C2×C8—21no—
239C2×C8—22no—
240C2×C8—21no—
241C2×C8—262no—
242C2×C8—521no—
243C2×C8—521no—
244C4⋊C4—22no—
245C4⋊C4—22no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—261no—
250C4⋊C4—261no—
251C4⋊C4—521no—
252C4⋊C4—521no—
253C4⋊C4#610312yes—
254C22⋊C4—22no—
255C42—22no—
256C42—521no—
257C42—521no—
258C42C2×D5211yescharacteristic
259C42#612711yescharacteristic
260C42C2×C22⋊D1311yescharacteristic
261C42C2×C22⋊D1311yescharacteristic
262C13#952811yescharacteristic, complemented, Sylow
263C23C4×C22⋊D1311yescharacteristic
264Q8—42no—
265Q8—41no—
266Q8—41no—
267Q8—262no—
268Q8—262no—
269Q8—521no—
270Q8—521no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—262no—
278C2×C4—521no—
279C2×C4—521no—
280C2×C4—521no—
281C2×C4—1041no—
282C2×C4C2×#610311yescharacteristic
283C2×C4C4×C22⋊D1311yescharacteristic
284C2×C4#8818311yescharacteristic
285C2×C4#8818411yescharacteristic
286C2×C4#8818411yescharacteristic
287C2×C4#8820711yescharacteristic
288C8—41no—
289C8—42no—
290C8—41no—
291C8—522no—
292C8—1041no—
293C8—1041no—
294C22—21no—
295C22—21no—
296C22—21no—
297C22#1171887411yescharacteristic
298C4—21no—
299C4—21no—
300C4—21no—
301C4—21no—
302C4—21no—
303C4—42no—
304C4—42no—
305C4—522no—
306C4—1041no—
307C4#1171880211yescharacteristic
308C4#1171880411yescharacteristic
309C2—41no—
310C2#1311525411yescharacteristic
311C2#1311533011yescharacteristic
312C2#1311535111yescharacteristic
subgroupG/H
centerC22#11718874
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2985C2
socleC22×C13#386
prime radicalC23×C13C4×D4
cosocleC2×C42×C13C23
hypercenter#2985D13
hypocenterC13#9528
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2985

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
#131249622
#131135662
#131132662
#131131792
#131127462
#131126982
C13×#29852
#952813