Finite Group Databasebeta

← #15778531

Subgroups — #15778531

Order 3328.

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

normal subgroups only

This group has 670 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#13116531C211yesmaximal, characteristic
2#13116511C211yesmaximal, characteristic
3#13116490C212yesmaximal
4#13114940C212yesmaximal
5C13×#3509C211yesmaximal, characteristic
6C13×#557—22no—
7C13×#556—22no—
8C13×#552—24no—
9C13×#541—22no—
10C13×#536C2211yescharacteristic
11C13×#536C2211yescharacteristic
12C13×#533—22no—
13C13×#533C411yescharacteristic, complemented
14C2×C13×C4⋊Q8C411yescharacteristic, complemented
15C13×#519C411yescharacteristic, complemented
16C13×#519C411yescharacteristic, complemented
17C4×C13×#41C2211yescharacteristic
18#11718901C2212yes—
19#11718898C2212yes—
20#11718140—22no—
21#11718133—22no—
22#11718131—24no—
23#11718123—22no—
24#11718115—22no—
25C2×C13×#41C2311yescharacteristic
26C22×Q8×C13C2×C411yescharacteristic
27C22×Q8×C13C2×C411yescharacteristic
28C13×C4⋊Q8—22no—
29C13×C4⋊Q8—21no—
30C13×C4⋊Q8—21no—
31C13×C4⋊Q8—21no—
32C13×C4⋊Q8—21no—
33C13×C4⋊Q8D412yes—
34C13×#126—24no—
35C13×#126—24no—
36C13×#125—24no—
37C13×#125—24no—
38C13×#125—24no—
39C13×#125—21no—
40C13×#124—21no—
41C13×#124D412yes—
42C13×#123—22no—
43C13×#123D414yes—
44C13×C22⋊Q8—24no—
45C13×C22⋊Q8—22no—
46C13×C22⋊Q8—22no—
47C13×C22⋊Q8—22no—
48C4×Q8×C13—24no—
49C4×Q8×C13—22no—
50C4×Q8×C13—21no—
51C4×Q8×C13—22no—
52C4×Q8×C13—22no—
53C4×Q8×C13—22no—
54C4×Q8×C13—22no—
55C4×D4×C13—22no—
56C4×D4×C13—21no—
57C13×#117—24no—
58C13×#117—22no—
59C13×#117—22no—
60C13×#117C2×C411yescharacteristic
61C13×#117C2×C411yescharacteristic
62C13×#117C2×C411yescharacteristic
63C13×#117D412yes—
64C2×C13×C4⋊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#12724—131nomaximal, Sylow
74C13×#41—42no—
75C2×Q8×C13—22no—
76C2×Q8×C13—21no—
77C2×Q8×C13—21no—
78C2×Q8×C13—21no—
79C2×Q8×C13—42no—
80C2×Q8×C13—42no—
81C2×Q8×C13C22⋊C412yes—
82C2×Q8×C13C2×D411yescharacteristic
83C2×D4×C13C2×D411yescharacteristic
84C2×D4×C13C2×D412yes—
85C22×C4×C13—21no—
86C22×C4×C13—21no—
87C22×C4×C13—22no—
88C22×C4×C13C22⋊C412yes—
89C22×C4×C13C22×C411yescharacteristic
90C22×C4×C13C2×D412yes—
91C13×C4⋊C4—24no—
92C13×C4⋊C4—24no—
93C13×C4⋊C4—22no—
94C13×C4⋊C4—24no—
95C13×C4⋊C4—24no—
96C13×C4⋊C4—22no—
97C13×C4⋊C4—22no—
98C13×C4⋊C4—21no—
99C13×C4⋊C4—21no—
100C13×C4⋊C4—21no—
101C13×C4⋊C4—22no—
102C13×C4⋊C4—24no—
103C13×C4⋊C4—24no—
104C13×C22⋊C4—21no—
105C13×C22⋊C4—21no—
106C13×C22⋊C4—24no—
107C13×C22⋊C4—24no—
108C13×C22⋊C4—22no—
109C13×C22⋊C4C22⋊C412yes—
110C42×C13—24no—
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#3509D1311yescharacteristic
126#2135—131no—
127#2129—131no—
128#2123—132no—
129#1827—132no—
130C23×C13C2×C22⋊C411yescharacteristic
131C23×C13#12012yes—
132Q8×C13—41no—
133Q8×C13—44no—
134Q8×C13—42no—
135Q8×C13—42no—
136Q8×C13—42no—
137Q8×C13—42no—
138D4×C13—42no—
139D4×C13—41no—
140C2×C4×C13—21no—
141C2×C4×C13—22no—
142C2×C4×C13—22no—
143C2×C4×C13—22no—
144C2×C4×C13—22no—
145C2×C4×C13—22no—
146C2×C4×C13—22no—
147C2×C4×C13—22no—
148C2×C4×C13—22no—
149C2×C4×C13—21no—
150C2×C4×C13—42no—
151C2×C4×C13—44no—
152C2×C4×C13—42no—
153C2×C4×C13—42no—
154C2×C4×C13C2×C22⋊C411yescharacteristic
155C2×C4×C13C2×C22⋊C411yescharacteristic
156C2×C4×C13#12012yes—
157C2×Dic13—82no—
158#1055—82no—
159#557—22no—
160#556—22no—
161#552—24no—
162#541—22no—
163#536C2×D1311yescharacteristic
164#536C2×D1311yescharacteristic
165#533—22no—
166#533Dic1311yescharacteristic, complemented
167C2×C4⋊Q8Dic1311yescharacteristic, complemented
168#519Dic1311yescharacteristic, complemented
169#519Dic1311yescharacteristic, complemented
170C4×#41C2×D1311yescharacteristic
171#413—132no—
172#410—132no—
173#356—262no—
174#354—262no—
175#352—264no—
176#339—262no—
177H(3,ℤ/4)—262no—
178C22×C13—22no—
179C22×C13—21no—
180C22×C13—41no—
181C22×C13—42no—
182C22×C13#37911yescharacteristic
183C4×C13—22no—
184C4×C13—22no—
185C4×C13—21no—
186C4×C13—42no—
187C4×C13—41no—
188C4×C13—42no—
189C4×C13—42no—
190C4×C13—42no—
191C4×C13—42no—
192C4×C13#41012yes—
193Dic13—162no—
194C2×#41C22×D1311yescharacteristic
195C22×Q8C2×Dic1311yescharacteristic
196C22×Q8C2×Dic1311yescharacteristic
197C2×M16—262no—
198C4⋊Q8—22no—
199C4⋊Q8—21no—
200C4⋊Q8—21no—
201C4⋊Q8—21no—
202C4⋊Q8—21no—
203C4⋊Q8C22⋊D1312yes—
204#126—24no—
205#126—24no—
206#125—24no—
207#125—24no—
208#125—24no—
209#125—21no—
210#124—21no—
211#124C22⋊D1312yes—
212#123—22no—
213#123C22⋊D1314yes—
214C22⋊Q8—24no—
215C22⋊Q8—22no—
216C22⋊Q8—22no—
217C22⋊Q8—22no—
218C4×Q8—24no—
219C4×Q8—22no—
220C4×Q8—21no—
221C4×Q8—22no—
222C4×Q8—22no—
223C4×Q8—22no—
224C4×Q8—22no—
225C4×D4—22no—
226C4×D4—21no—
227#117—24no—
228#117—22no—
229#117—22no—
230#117—262no—
231#117C2×Dic1311yescharacteristic
232#117C2×Dic1311yescharacteristic
233#117C2×Dic1311yescharacteristic
234#117C22⋊D1312yes—
235C2×C4⋊C4—22no—
236C2×C42C2×Dic1311yescharacteristic
237C2×C42C22⋊D1312yes—
238#101—262no—
239#100—262no—
240#99—262no—
241#99—262no—
242C2×C13—21no—
243C2×C13—42no—
244C2×C13—41no—
245C2×C13#178211yescharacteristic
246#41—42no—
247C2×Q8—22no—
248C2×Q8—21no—
249C2×Q8—21no—
250C2×Q8—21no—
251C2×Q8—42no—
252C2×Q8—42no—
253C2×Q8C22⋊Dic1312yes—
254C2×Q8C2×C22⋊D1311yescharacteristic
255C2×D4C2×C22⋊D1311yescharacteristic
256C2×D4C2×C22⋊D1312yes—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—22no—
260C22×C4C22⋊Dic1312yes—
261C22×C4C22×Dic1311yescharacteristic
262C22×C4C2×C22⋊D1312yes—
263M16—522no—
264M16—522no—
265C2×C8—522no—
266C4⋊C4—24no—
267C4⋊C4—24no—
268C4⋊C4—22no—
269C4⋊C4—24no—
270C4⋊C4—24no—
271C4⋊C4—22no—
272C4⋊C4—22no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—22no—
277C4⋊C4—24no—
278C4⋊C4—24no—
279C4⋊C4—522no—
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—24no—
283C22⋊C4—24no—
284C22⋊C4—22no—
285C22⋊C4—522no—
286C22⋊C4C22⋊Dic1312yes—
287C42—24no—
288C42—24no—
289C42—21no—
290C42—21no—
291C42—22no—
292C42—522no—
293C42C22⋊Dic1312yes—
294C42C22⋊Dic1311yescharacteristic
295C42C22⋊Dic1311yescharacteristic
296C42C22⋊Dic1312yes—
297C13#1272411yescharacteristic, complemented, Sylow
298C23C2×C22⋊Dic1311yescharacteristic
299C23#8820712yes—
300Q8—41no—
301Q8—42no—
302Q8—42no—
303Q8—44no—
304Q8—42no—
305Q8—42no—
306D4—42no—
307D4—41no—
308C2×C4—21no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—21no—
318C2×C4—42no—
319C2×C4—44no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—1042no—
323C2×C4C2×C22⋊Dic1311yescharacteristic
324C2×C4C2×C22⋊Dic1311yescharacteristic
325C2×C4#8820712yes—
326C8—1042no—
327C22—21no—
328C22—22no—
329C22—41no—
330C22—42no—
331C22#1171890811yescharacteristic
332C4—22no—
333C4—22no—
334C4—21no—
335C4—42no—
336C4—41no—
337C4—42no—
338C4—42no—
339C4—42no—
340C4—42no—
341C4—2082no—
342C4#1171890112yes—
343C2—21no—
344C2—42no—
345C2—41no—
346C2#1311475411yescharacteristic
subgroupG/H
centerC2#13114754
commutatorC22×C4×C13C22×C4
FrattiniC2×#41C22×D13
FittingC13×#3509C2
socleC2×C13#1782
prime radical, cosocleC2×C13×#41C23
hypercenter#3509D13
hypocenterC13#12724
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×#41 ◁ #3509

Complements

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

NH ≅ G/Ntype
13. C13×#533C4semidirect
14. C2×C13×C4⋊Q8C4semidirect
15. C13×#519C4semidirect
16. C13×#519C4semidirect
166. #533Dic13semidirect
167. C2×C4⋊Q8Dic13semidirect
168. #519Dic13semidirect
169. #519Dic13semidirect
297. C13#12724semidirect

Maximal subgroups

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

subgroupindex
#131165312
#131165112
#131164902
#131149402
C13×#35092
#1272413