Finite Group Databasebeta

← #16778646

Subgroups — #16778646

Order 3328.

488 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 92 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#13130563C211yesmaximal, characteristic
2C4×#88111C211yesmaximal, characteristic
3#13129657C212yesmaximal, complemented
4#13129655C212yesmaximal, complemented
5#13123174C211yesmaximal, characteristic
6C2×#88151C411yescharacteristic
7C2×C42×D13C2211yescharacteristic
8C2×#88111—21no—
9C2×#88111—21no—
10C2×#88110—21no—
11C2×C4×#1057—21no—
12C13×#389C411yescharacteristic
13#11718650—21no—
14#11718648C411yescharacteristic
15#11718642—21no—
16#11718635C2211yescharacteristic
17#11718634C2211yescharacteristic
18#11718590C411yescharacteristic
19#11718325—21no—
20#11718316—21no—
21#11718290C2212yes—
22#11718290C2212yes—
23C22×C4×D13C2×C411yescharacteristic
24C22×C4×D13D411yescharacteristic
25C22×C4×D13D411yescharacteristic
26C22×Dic26C2×C411yescharacteristic
27C22×#1057—22no—
28C22×#1057—22no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4C2×C411yescharacteristic
31C2×C13×C4⋊C4C2×C411yescharacteristic
32C2×C42×C13C2×C411yescharacteristic
33C2×#6103—21no—
34C2×#6103—21no—
35C2×C4⋊Dic13—21no—
36C2×C4⋊Dic13C2×C411yescharacteristic
37C2×#6101—21no—
38C2×C4×Dic13D411yescharacteristic
39C2×C4×Dic13D411yescharacteristic
40C2×C4×Dic13C2311yescharacteristic
41#88151—42no—
42C42×D13—42no—
43#88111—24no—
44#88111—24no—
45#88110—42no—
46C4×#1057—42no—
47C13×#95—21no—
48#88071—21no—
49#88071—21no—
50#88071—21no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#7675—131nomaximal, Sylow
55C23×D13C22⋊C411yescharacteristic
56C22×C4×C13—21no—
57C22×C4×C13—21no—
58C22×C4×C13C22⋊C411yescharacteristic
59C22×C4×C13C22⋊C411yescharacteristic
60C22×C4×C13C22×C411yescharacteristic
61C22×Dic13—21no—
62C22×Dic13—21no—
63C22×Dic13C22⋊C411yescharacteristic
64C22×Dic13C2×D411yescharacteristic
65C22×Dic13C2×D411yescharacteristic
66C2×C4×D13—22no—
67C2×C4×D13—22no—
68C2×C4×D13—22no—
69C2×C4×D13—22no—
70C2×C4×D13—22no—
71C2×C4×D13—22no—
72C2×C4×D13—41no—
73C2×C4×D13—41no—
74C2×C4×D13—41no—
75C2×Dic26—22no—
76C2×Dic26—41no—
77C2×Dic26—41no—
78C2×#1057—24no—
79C2×#1057—24no—
80C2×#1057—42no—
81C2×#1057—42no—
82C2×#1057—42no—
83C2×#1057—42no—
84C13×C4⋊C4—41no—
85C13×C4⋊C4—41no—
86C13×C4⋊C4—42no—
87C42×C13—41no—
88#6103—42no—
89#6103—42no—
90C4⋊Dic13—22no—
91C4⋊Dic13—42no—
92#6101—42no—
93C4×Dic13—22no—
94C4×Dic13—22no—
95C4×Dic13—41no—
96#2855—131no—
97#1749—131no—
98C4×C22⋊C8—131no—
99#1272—132no—
100#1271—132no—
101C23×C13C2×C22⋊C411yescharacteristic
102C22×D13—21no—
103C22×D13—21no—
104C22×D13—21no—
105C22×D13—21no—
106C22×D13—21no—
107C22×D13—21no—
108C22×D13#10412yes—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—41no—
117C2×C4×C13—41no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13—41no—
122C2×C4×C13#10412yes—
123C2×C4×C13#13112yes—
124C2×Dic13—21no—
125C2×Dic13—21no—
126C2×Dic13—21no—
127C2×Dic13—21no—
128C2×Dic13—21no—
129C2×Dic13—21no—
130C2×Dic13—41no—
131C2×Dic13—41no—
132C2×Dic13—41no—
133C2×Dic13—41no—
134C2×Dic13—41no—
135C2×Dic13—41no—
136C2×Dic13#9912yes—
137C2×Dic13#13512yes—
138C2×Dic13#13712yes—
139C4×D13—44no—
140C4×D13—44no—
141C4×D13—44no—
142Dic26—82no—
143#1057—44no—
144#1057—44no—
145C2×C22⋊Q8—131no—
146C22×C42—131no—
147C2×C22⋊C8—261no—
148C2×C22⋊C8—261no—
149C2×#97—261no—
150C2×C4×C8—261no—
151#391—131no—
152#391—131no—
153#389—131no—
154#389#26111yescharacteristic
155#387—261no—
156#387—261no—
157#385—261no—
158#381—261no—
159#380—131no—
160#336—132no—
161#336—132no—
162C22×C13#40811yescharacteristic
163C22×C13C2×#9911yescharacteristic
164C22×C13#41311yescharacteristic
165C22×C13#41611yescharacteristic
166C22×C13#41911yescharacteristic
167C22×C13C2×#10411yescharacteristic
168C22×C13C2×#10411yescharacteristic
169C2×D13—22no—
170C2×D13—22no—
171C2×D13—22no—
172C2×D13—41no—
173C2×D13—41no—
174C2×D13—41no—
175C2×D13—41no—
176C4×C13—22no—
177C4×C13—22no—
178C4×C13—41no—
179C4×C13—81no—
180C4×C13—81no—
181Dic13—22no—
182Dic13—22no—
183Dic13—22no—
184Dic13—81no—
185Dic13—81no—
186C22×Q8—131no—
187C23×C4—131no—
188C23×C4—131no—
189C23×C4—131no—
190C22×C8—262no—
191C22×C8—262no—
192C22⋊Q8—522no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—131no—
195C2×C4⋊C4—261no—
196C2×C4⋊C4—261no—
197C2×C4⋊C4C2×#26111yescharacteristic
198C2×C4⋊C4C2×#26111yescharacteristic
199C2×C22⋊C4—261no—
200C2×C22⋊C4—261no—
201C2×C42—131no—
202C2×C42—131no—
203C2×C42—131no—
204C2×C42—522no—
205C2×C42C2×#26111yescharacteristic
206C22⋊C8—264no—
207C22⋊C8—264no—
208#97—522no—
209C4×C8—522no—
210#95—21no—
211#95—261no—
212#95—261no—
213#95—261no—
214#95—261no—
215#95—261no—
216#95—261no—
217C2×C13#146811yescharacteristic
218C2×C13#148511yescharacteristic
219C2×C13#149411yescharacteristic
220C2×C13#150111yescharacteristic
221C2×C13#150811yescharacteristic
222C2×C13#152411yescharacteristic
223C2×C13#155411yescharacteristic
224D13—42no—
225C24—131no—
226C2×Q8—262no—
227C2×Q8—521no—
228C2×Q8—521no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—131no—
232C22×C4—131no—
233C22×C4—131no—
234C22×C4—262no—
235C22×C4—262no—
236C22×C4—262no—
237C22×C4—262no—
238C22×C4—262no—
239C22×C4—262no—
240C22×C4—261no—
241C22×C4—261no—
242C22×C4—521no—
243C22×C4—521no—
244C22×C4—521no—
245C22×C4C22⋊#26111yescharacteristic
246C22×C4C22⋊#26111yescharacteristic
247C22×C4C22×#26111yescharacteristic
248C2×C8—264no—
249C2×C8—264no—
250C2×C8—522no—
251C2×C8—522no—
252C2×C8—522no—
253C2×C8—522no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—42no—
257C4⋊C4—262no—
258C4⋊C4—522no—
259C4⋊C4—522no—
260C22⋊C4—522no—
261C22⋊C4—522no—
262C42—41no—
263C42—262no—
264C42—262no—
265C42—521no—
266C13#767511yescharacteristic, complemented, Sylow
267C23—132no—
268C23—261no—
269C23—261no—
270C23—261no—
271C23—261no—
272C23—261no—
273C23—261no—
274C23C2×C22⋊#26111yescharacteristic
275Q8—1042no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—132no—
290C2×C4—132no—
291C2×C4—132no—
292C2×C4—261no—
293C2×C4—261no—
294C2×C4—261no—
295C2×C4—261no—
296C2×C4—261no—
297C2×C4—261no—
298C2×C4—524no—
299C2×C4—524no—
300C2×C4—524no—
301C2×C4—521no—
302C2×C4—521no—
303C2×C4—521no—
304C2×C4—521no—
305C2×C4—521no—
306C2×C4—521no—
307C2×C4#8811612yes—
308C2×C4#8824012yes—
309C8—524no—
310C8—524no—
311C22—262no—
312C22—262no—
313C22—262no—
314C22—521no—
315C22—521no—
316C22—521no—
317C22—521no—
318C22#1171913211yescharacteristic
319C22C2×#8811611yescharacteristic
320C22D13⋊#9911yescharacteristic
321C22#1171915311yescharacteristic
322C22#1171915911yescharacteristic
323C22D13⋊#10411yescharacteristic
324C22#1171916511yescharacteristic
325C4—22no—
326C4—22no—
327C4—41no—
328C4—81no—
329C4—81no—
330C4—262no—
331C4—262no—
332C4—262no—
333C4—1041no—
334C4—1041no—
335C2—522no—
336C2#1313010411yescharacteristic
337C2#1313016011yescharacteristic
338C2#1313019011yescharacteristic
339C2#1313021211yescharacteristic
340C2#1313023411yescharacteristic
341C2#1313028611yescharacteristic
342C2#1313036111yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC13×#389C4
socleC23×C13C2×C22⋊C4
prime radicalC23×D13C22⋊C4
cosocleC2×C4×Dic13C23
hypercenter#389#261
hypocenterC13#7675
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
3. #13129657C2semidirect
4. #13129655C2semidirect
266. C13#7675semidirect

Maximal subgroups

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

subgroupindex
#131305632
C4×#881112
#131296572
#131296552
#131231742
#767513