Finite Group Databasebeta

← #15778526

Subgroups — #15778526

Order 3328.

694 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 694 conjugacy classes of subgroups — too many to draw. Only its 127 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#13116528C211yesmaximal, characteristic
2#13116508C211yesmaximal, characteristic
3#13116490C212yesmaximal, complemented
4#13114940C212yesmaximal, complemented
5C13×#3510C211yesmaximal, characteristic
6C13×#559—22no—
7C13×#556—22no—
8C13×#551—24no—
9C13×#542—22no—
10C13×#536C2211yescharacteristic
11C13×#535C2211yescharacteristic
12C13×#533C411yescharacteristic, complemented
13C13×#529—22no—
14C2×C13×#124C411yescharacteristic, complemented
15C13×#519C411yescharacteristic, complemented
16C13×#518C411yescharacteristic, complemented
17C4×C13×#41C2211yescharacteristic
18#11718901C2212yes—
19#11718898C2212yes—
20#11718137—22no—
21#11718134—22no—
22#11718131—24no—
23#11718123—22no—
24#11718115—22no—
25C2×C13×#41C2311yescharacteristic
26C22×Q8×C13C2×C411yescharacteristic
27C22×D4×C13C2×C411yescharacteristic
28C13×C4⋊Q8—21no—
29C13×C4⋊Q8—21no—
30C13×#127D412yes—
31C13×#126—24no—
32C13×#126—24no—
33C13×#125—21no—
34C13×#124—24no—
35C13×#124—22no—
36C13×#124—21no—
37C13×#124—21no—
38C13×#124—21no—
39C13×#124D412yes—
40C13×#123—24no—
41C13×#123—24no—
42C13×#123D414yes—
43C13×C22⋊Q8—24no—
44C13×C22⋊Q8—22no—
45C13×C22⋊Q8—22no—
46C13×#121—22no—
47C13×#120—22no—
48C4×Q8×C13—21no—
49C4×Q8×C13—22no—
50C4×Q8×C13—22no—
51C4×Q8×C13—22no—
52C4×D4×C13—24no—
53C4×D4×C13—22no—
54C4×D4×C13—22no—
55C4×D4×C13—21no—
56C4×D4×C13—22no—
57C13×#117—24no—
58C13×#117—22no—
59C13×#117C2×C411yescharacteristic
60C13×#117C2×C411yescharacteristic
61C13×#117C2×C411yescharacteristic
62C13×#117D412yes—
63C2×C13×C22⋊C4—22no—
64C2×C13×C22⋊C4—22no—
65C2×C42×C13C2×C411yescharacteristic
66C2×C42×C13D412yes—
67#88180—22no—
68C2×#6099—22no—
69#88076—22no—
70#88074—22no—
71#88074—22no—
72#88073—22no—
73#12723—131nomaximal, Sylow
74C24×C13—21no—
75C13×#41—42no—
76C2×Q8×C13—22no—
77C2×Q8×C13—21no—
78C2×Q8×C13—21no—
79C2×Q8×C13—42no—
80C2×Q8×C13C2×D411yescharacteristic
81C2×D4×C13—24no—
82C2×D4×C13—21no—
83C2×D4×C13—42no—
84C2×D4×C13C22⋊C412yes—
85C2×D4×C13C2×D411yescharacteristic
86C2×D4×C13C2×D412yes—
87C22×C4×C13—24no—
88C22×C4×C13—21no—
89C22×C4×C13—22no—
90C22×C4×C13C22⋊C412yes—
91C22×C4×C13C22×C411yescharacteristic
92C22×C4×C13C2×D412yes—
93C13×C4⋊C4—22no—
94C13×C4⋊C4—24no—
95C13×C4⋊C4—22no—
96C13×C4⋊C4—22no—
97C13×C4⋊C4—21no—
98C13×C4⋊C4—21no—
99C13×C4⋊C4—21no—
100C13×C4⋊C4—24no—
101C13×C4⋊C4—22no—
102C13×C22⋊C4—24no—
103C13×C22⋊C4—24no—
104C13×C22⋊C4—24no—
105C13×C22⋊C4—21no—
106C13×C22⋊C4—21no—
107C13×C22⋊C4—22no—
108C13×C22⋊C4—24no—
109C13×C22⋊C4—24no—
110C13×C22⋊C4C22⋊C412yes—
111C42×C13—24no—
112C42×C13—21no—
113C42×C13—21no—
114C42×C13—22no—
115C42×C13C22⋊C411yescharacteristic
116C42×C13C22⋊C411yescharacteristic
117C42×C13C22⋊C412yes—
118C42×C13C22⋊C412yes—
119C22⋊Dic13—42no—
120C4⋊Dic13—42no—
121C4×Dic13—42no—
122#6099—42no—
123#6099—42no—
124C2×#1055—42no—
125#3510D1311yescharacteristic
126#2134—131no—
127#2128—131no—
128#2123—132no—
129#1827—132no—
130C23×C13—22no—
131C23×C13—42no—
132C23×C13—82no—
133C23×C13C2×C22⋊C411yescharacteristic
134C23×C13#12012yes—
135Q8×C13—41no—
136Q8×C13—42no—
137Q8×C13—42no—
138Q8×C13—82no—
139D4×C13—42no—
140D4×C13—41no—
141D4×C13—42no—
142D4×C13—42no—
143D4×C13—84no—
144C2×C4×C13—22no—
145C2×C4×C13—22no—
146C2×C4×C13—22no—
147C2×C4×C13—22no—
148C2×C4×C13—21no—
149C2×C4×C13—22no—
150C2×C4×C13—22no—
151C2×C4×C13—21no—
152C2×C4×C13—22no—
153C2×C4×C13—42no—
154C2×C4×C13—82no—
155C2×C4×C13—84no—
156C2×C4×C13—81no—
157C2×C4×C13C2×C22⋊C411yescharacteristic
158C2×C4×C13C2×C22⋊C411yescharacteristic
159C2×C4×C13#12012yes—
160C2×Dic13—82no—
161#1055—82no—
162#559—22no—
163#556—22no—
164#551—24no—
165#542—22no—
166#536C2×D1311yescharacteristic
167#535C2×D1311yescharacteristic
168#533Dic1311yescharacteristic, complemented
169#529—22no—
170C2×#124Dic1311yescharacteristic, complemented
171#519Dic1311yescharacteristic, complemented
172#518Dic1311yescharacteristic, complemented
173C4×#41C2×D1311yescharacteristic
174#413—132no—
175#410—132no—
176#355—262no—
177#353—262no—
178#352—264no—
179#339—262no—
180H(3,ℤ/4)—262no—
181C22×C13—22no—
182C22×C13—21no—
183C22×C13—42no—
184C22×C13—41no—
185C22×C13—44no—
186C22×C13—42no—
187C22×C13—162no—
188C22×C13#37911yescharacteristic
189C4×C13—22no—
190C4×C13—21no—
191C4×C13—42no—
192C4×C13—41no—
193C4×C13—42no—
194C4×C13—41no—
195C4×C13—42no—
196C4×C13—42no—
197C4×C13#41012yes—
198Dic13—162no—
199C2×#41C22×D1311yescharacteristic
200C22×Q8C2×Dic1311yescharacteristic
201C22×D4C2×Dic1311yescharacteristic
202C2×M16—262no—
203C4⋊Q8—21no—
204C4⋊Q8—21no—
205#127C22⋊D1312yes—
206#126—24no—
207#126—24no—
208#125—21no—
209#124—24no—
210#124—22no—
211#124—21no—
212#124—21no—
213#124—21no—
214#124C22⋊D1312yes—
215#123—24no—
216#123—24no—
217#123C22⋊D1314yes—
218C22⋊Q8—24no—
219C22⋊Q8—22no—
220C22⋊Q8—22no—
221#121—22no—
222#120—22no—
223C4×Q8—21no—
224C4×Q8—22no—
225C4×Q8—22no—
226C4×Q8—22no—
227C4×D4—24no—
228C4×D4—22no—
229C4×D4—22no—
230C4×D4—21no—
231C4×D4—22no—
232#117—24no—
233#117—22no—
234#117—262no—
235#117C2×Dic1311yescharacteristic
236#117C2×Dic1311yescharacteristic
237#117C2×Dic1311yescharacteristic
238#117C22⋊D1312yes—
239C2×C22⋊C4—22no—
240C2×C22⋊C4—22no—
241C2×C42C2×Dic1311yescharacteristic
242C2×C42C22⋊D1312yes—
243#101—262no—
244#100—262no—
245#99—262no—
246#99—262no—
247C2×C13—21no—
248C2×C13—42no—
249C2×C13—41no—
250C2×C13—82no—
251C2×C13#178211yescharacteristic
252C24—21no—
253#41—42no—
254C2×Q8—22no—
255C2×Q8—21no—
256C2×Q8—21no—
257C2×Q8—42no—
258C2×Q8C2×C22⋊D1311yescharacteristic
259C2×D4—24no—
260C2×D4—21no—
261C2×D4—42no—
262C2×D4C22⋊Dic1312yes—
263C2×D4C2×C22⋊D1311yescharacteristic
264C2×D4C2×C22⋊D1312yes—
265C22×C4—24no—
266C22×C4—21no—
267C22×C4—22no—
268C22×C4C22⋊Dic1312yes—
269C22×C4C22×Dic1311yescharacteristic
270C22×C4C2×C22⋊D1312yes—
271M16—522no—
272M16—522no—
273C2×C8—522no—
274C4⋊C4—22no—
275C4⋊C4—24no—
276C4⋊C4—22no—
277C4⋊C4—22no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—24no—
282C4⋊C4—22no—
283C4⋊C4—522no—
284C22⋊C4—24no—
285C22⋊C4—24no—
286C22⋊C4—24no—
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—22no—
290C22⋊C4—24no—
291C22⋊C4—24no—
292C22⋊C4—522no—
293C22⋊C4C22⋊Dic1312yes—
294C42—24no—
295C42—21no—
296C42—21no—
297C42—22no—
298C42—522no—
299C42C22⋊Dic1312yes—
300C42C22⋊Dic1311yescharacteristic
301C42C22⋊Dic1311yescharacteristic
302C42C22⋊Dic1312yes—
303C13#1272311yescharacteristic, complemented, Sylow
304C23—22no—
305C23—42no—
306C23—82no—
307C23C2×C22⋊Dic1311yescharacteristic
308C23#8820712yes—
309Q8—41no—
310Q8—42no—
311Q8—42no—
312Q8—82no—
313D4—42no—
314D4—41no—
315D4—42no—
316D4—42no—
317D4—84no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—21no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—21no—
326C2×C4—22no—
327C2×C4—42no—
328C2×C4—82no—
329C2×C4—84no—
330C2×C4—81no—
331C2×C4—1042no—
332C2×C4C2×C22⋊Dic1311yescharacteristic
333C2×C4C2×C22⋊Dic1311yescharacteristic
334C2×C4#8820712yes—
335C8—1042no—
336C22—21no—
337C22—22no—
338C22—42no—
339C22—41no—
340C22—44no—
341C22—42no—
342C22—162no—
343C22#1171890811yescharacteristic
344C4—22no—
345C4—21no—
346C4—42no—
347C4—41no—
348C4—42no—
349C4—41no—
350C4—42no—
351C4—42no—
352C4—2082no—
353C4#1171890112yes—
354C2—21no—
355C2—42no—
356C2—41no—
357C2—82no—
358C2#1311475411yescharacteristic
subgroupG/H
centerC2#13114754
commutatorC22×C4×C13C22×C4
FrattiniC2×#41C22×D13
FittingC13×#3510C2
socleC2×C13#1782
prime radicalC13×#535C22
cosocleC2×C13×#41C23
hypercenter#3510D13
hypocenterC13#12723
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×#41 ◁ #3510

Complements

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

NH ≅ G/Ntype
3. #13116490C2semidirect
4. #13114940C2semidirect
12. C13×#533C4semidirect
14. C2×C13×#124C4semidirect
15. C13×#519C4semidirect
16. C13×#518C4semidirect
168. #533Dic13semidirect
170. C2×#124Dic13semidirect
171. #519Dic13semidirect
172. #518Dic13semidirect
303. C13#12723semidirect

Maximal subgroups

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

subgroupindex
#131165282
#131165082
#131164902
#131149402
C13×#35102
#1272313