Finite Group Databasebeta

← #15760618

Subgroups — #15760618

Order 3328.

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

normal subgroups only

This group has 554 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#13119789C211yesmaximal, characteristic
2#13113554C212yesmaximal, complemented
3#13113177C211yesmaximal, characteristic
4#13112693C212yesmaximal, complemented
5C13×#2973C211yesmaximal, characteristic
6C2×C4×D4×C13C2211yescharacteristic
7C2×#88178—21no—
8C2×#88178—21no—
9C2×#88123C2211yescharacteristic
10C13×#435—24no—
11C13×#432C2212yes—
12C13×#407—21no—
13C2×C13×C22⋊C8—21no—
14#11718882C412yes—
15#11718637C412yes—
16#11718610—21no—
17#11718610—21no—
18C4×C4⋊Dic13C2211yescharacteristic
19#11718587C2212yes—
20#11718117—21no—
21#11718117—21no—
22#11718074—24no—
23C22×D4×C13C2×C411yescharacteristic
24C23×C4×C13D411yescharacteristic
25C23×C4×C13D411yescharacteristic
26C22×Dic26—21no—
27C2×C13×M16—22no—
28C22×C8×C13—22no—
29C4×D4×C13—22no—
30C4×D4×C13—22no—
31C2×C13×C4⋊C4C2×C411yescharacteristic
32C2×C13×C22⋊C4D411yescharacteristic
33C2×C13×C22⋊C4D411yescharacteristic
34C2×C42×C13C2311yescharacteristic
35C2×C22⋊Dic13—22no—
36C2×C22⋊Dic13—22no—
37C2×C4⋊Dic13—21no—
38C2×C4⋊Dic13—21no—
39C2×C4⋊Dic13C2×C412yes—
40#88178—44no—
41#88178—44no—
42C2×#6101—22no—
43C2×#6101—22no—
44C2×C4×Dic13C2×C412yes—
45#88123—22no—
46#88123—22no—
47C13×C4⋊C8D414yes—
48C13×C22⋊C8—22no—
49C13×C22⋊C8—22no—
50C13×C22⋊C8—22no—
51C13×#97—22no—
52#88071—21no—
53C22⋊#1055—22no—
54C4⋊#1055—22no—
55#88043—22no—
56#9455—131nomaximal, Sylow
57C24×C13C22⋊C411yescharacteristic
58C24×C13C22⋊C411yescharacteristic
59C2×D4×C13—22no—
60C2×D4×C13—22no—
61C2×D4×C13—41no—
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13—42no—
67C22×C4×C13—42no—
68C22×C4×C13C22⋊C411yescharacteristic
69C22×C4×C13C22⋊C411yescharacteristic
70C22×C4×C13C22×C411yescharacteristic
71C22×C4×C13C2×D411yescharacteristic
72C22×C4×C13C2×D411yescharacteristic
73C22×Dic13—22no—
74C22×Dic13—22no—
75C2×Dic26—42no—
76C2×Dic26—42no—
77C2×Dic26—41no—
78C2×Dic26—41no—
79C13×M16—82no—
80C2×C8×C13—24no—
81C2×C8×C13—82no—
82C13×C4⋊C4—22no—
83C13×C22⋊C4—22no—
84C13×C22⋊C4—22no—
85C42×C13C2×D412yes—
86C42×C13#4112yes—
87C22⋊Dic13—44no—
88C22⋊Dic13—44no—
89C4⋊Dic13—24no—
90C4⋊Dic13—24no—
91C4⋊Dic13—42no—
92#6101—44no—
93#6101—44no—
94C4×Dic13—42no—
95C2×#1055—42no—
96#2973D1311yescharacteristic
97#2542—131no—
98#1556—132no—
99#1466—131no—
100#1285—132no—
101C23×C13—21no—
102C23×C13—21no—
103C23×C13—21no—
104C23×C13—21no—
105C23×C13—21no—
106C23×C13—41no—
107C23×C13—41no—
108C23×C13—41no—
109C23×C13—41no—
110C23×C13#10112yes—
111C23×C13C2×C22⋊C411yescharacteristic
112D4×C13—44no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—22no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—41no—
119C2×C4×C13—42no—
120C2×C4×C13—42no—
121C2×C4×C13—41no—
122C2×C4×C13—41no—
123C2×C4×C13—81no—
124C2×C4×C13—81no—
125C2×C4×C13C4×D412yes—
126C2×C4×C13#12011yescharacteristic
127C2×C4×C13#12112yes—
128C2×C4×C13#12311yescharacteristic
129C2×Dic13—24no—
130C2×Dic13—42no—
131C2×Dic13—42no—
132C2×Dic13—42no—
133C2×Dic13—42no—
134C2×Dic13—42no—
135Dic26—82no—
136Dic26—82no—
137C8×C13—44no—
138#1055—82no—
139C2×C4⋊Q8—131no—
140C2×C22⋊Q8—261no—
141C2×C22⋊Q8—261no—
142C2×C4×D4C2×D1311yescharacteristic
143#435—24no—
144#432—132no—
145#432C2×D1312yes—
146#407—21no—
147C2×C22⋊C8—21no—
148#399—261no—
149#399—261no—
150#390—132no—
151#384—132no—
152C4×C4⋊C4—131no—
153#332—264no—
154#323—261no—
155#323—261no—
156C22×C13—21no—
157C22×C13—21no—
158C22×C13—22no—
159C22×C13—42no—
160C22×C13—42no—
161C22×C13—41no—
162C22×C13—41no—
163C22×C13—41no—
164C22×C13—41no—
165C22×C13—41no—
166C22×C13—81no—
167C22×C13—81no—
168C22×C13#38611yescharacteristic
169C22×C13C2×#10111yescharacteristic
170C22×C13#41311yescharacteristic
171C4×C13—21no—
172C4×C13—22no—
173C4×C13—22no—
174C4×C13—41no—
175C4×C13—41no—
176C4×C13#45312yes—
177Dic13—44no—
178Dic13—82no—
179C22×Q8—261no—
180C22×D4C4×D1311yescharacteristic
181C23×C4C22⋊D1311yescharacteristic
182C23×C4C22⋊D1311yescharacteristic
183C2×M16—22no—
184C22×C8—22no—
185C4⋊Q8—262no—
186C4⋊Q8—262no—
187C22⋊Q8—524no—
188C22⋊Q8—524no—
189C4×D4—22no—
190C4×D4—22no—
191C2×C4⋊C4—132no—
192C2×C4⋊C4—261no—
193C2×C4⋊C4—262no—
194C2×C4⋊C4—262no—
195C2×C4⋊C4—261no—
196C2×C4⋊C4C4×D1311yescharacteristic
197C2×C22⋊C4—262no—
198C2×C22⋊C4—262no—
199C2×C22⋊C4D5211yescharacteristic
200C2×C22⋊C4D5211yescharacteristic
201C2×C42—132no—
202C2×C42C22×D1311yescharacteristic
203C4⋊C8—262no—
204C4⋊C8C22⋊D1314yes—
205C22⋊C8—22no—
206C22⋊C8—22no—
207C22⋊C8—22no—
208C22⋊C8—262no—
209#97—22no—
210#97—262no—
211#95—261no—
212C2×C13—21no—
213C2×C13—21no—
214C2×C13—42no—
215C2×C13—81no—
216C2×C13#188711yescharacteristic
217C2×C13#190111yescharacteristic
218C2×C13#190911yescharacteristic
219C24#610311yescharacteristic
220C24#610311yescharacteristic
221C2×Q8—522no—
222C2×Q8—522no—
223C2×Q8—521no—
224C2×Q8—521no—
225C2×D4—22no—
226C2×D4—22no—
227C2×D4—41no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—42no—
233C22×C4—42no—
234C22×C4—262no—
235C22×C4—262no—
236C22×C4#610311yescharacteristic
237C22×C4#610311yescharacteristic
238C22×C4C2×C4×D1311yescharacteristic
239C22×C4C2×D5211yescharacteristic
240C22×C4C2×C22⋊D1311yescharacteristic
241M16—82no—
242C2×C8—24no—
243C2×C8—82no—
244C2×C8—522no—
245C4⋊C4—22no—
246C4⋊C4—264no—
247C4⋊C4—264no—
248C4⋊C4—524no—
249C4⋊C4—524no—
250C4⋊C4—522no—
251C22⋊C4—22no—
252C22⋊C4—22no—
253C22⋊C4—524no—
254C22⋊C4—524no—
255C42—522no—
256C42#612712yes—
257C42C2×C22⋊D1312yes—
258C13#945511yescharacteristic, complemented, Sylow
259C23—21no—
260C23—21no—
261C23—21no—
262C23—21no—
263C23—21no—
264C23—41no—
265C23—41no—
266C23—41no—
267C23—41no—
268C23#8806412yes—
269C23C2×#610311yescharacteristic
270Q8—1042no—
271Q8—1042no—
272D4—44no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—22no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—41no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—81no—
284C2×C4—81no—
285C2×C4—264no—
286C2×C4—522no—
287C2×C4—522no—
288C2×C4—522no—
289C2×C4—522no—
290C2×C4—522no—
291C2×C4C4×C22⋊D1312yes—
292C2×C4#8818311yescharacteristic
293C2×C4#8818412yes—
294C2×C4#8820711yescharacteristic
295C8—44no—
296C8—1042no—
297C22—21no—
298C22—21no—
299C22—22no—
300C22—42no—
301C22—42no—
302C22—41no—
303C22—41no—
304C22—41no—
305C22—41no—
306C22—41no—
307C22—81no—
308C22—81no—
309C22#1171879311yescharacteristic
310C22C2×#8806411yescharacteristic
311C22#1171887411yescharacteristic
312C4—21no—
313C4—22no—
314C4—22no—
315C4—41no—
316C4—41no—
317C4—524no—
318C4—1042no—
319C4#1171890212yes—
320C2—21no—
321C2—21no—
322C2—42no—
323C2—81no—
324C2#1311523411yescharacteristic
325C2#1311530411yescharacteristic
326C2#1311535811yescharacteristic
subgroupG/H
centerC22#11718874
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#2973C2
socleC22×C13#386
prime radicalC22×D4×C13C2×C4
cosocleC2×C42×C13C23
hypercenter#2973D13
hypocenterC13#9455
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2973

Complements

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

NH ≅ G/Ntype
2. #13113554C2semidirect
4. #13112693C2semidirect
258. C13#9455semidirect

Maximal subgroups

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

subgroupindex
#131197892
#131135542
#131131772
#131126932
C13×#29732
#945513