Finite Group Databasebeta

← #16778596

Subgroups — #16778596

Order 3328.

482 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 100 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#13130691C211yesmaximal, 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×C4⋊#1057—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—42no—
45C4⋊#1057—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#7661—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—41no—
71C2×C4×D13—41no—
72C2×C4×D13—41no—
73C2×C4×D13—41no—
74C2×C4×D13SD1612yes—
75C2×C4×D13Q1612yes—
76C2×Dic26—22no—
77C2×Dic26—41no—
78C2×Dic26—41no—
79C2×#1057—24no—
80C2×#1057—42no—
81C2×#1057—42no—
82C2×#1057—42no—
83C2×#1057—42no—
84C2×#1057—42no—
85C13×C4⋊C4—41no—
86C13×C4⋊C4—41no—
87C13×C4⋊C4—42no—
88C42×C13—41no—
89#6103—42no—
90#6103—42no—
91C4⋊Dic13—22no—
92C4⋊Dic13—42no—
93#6101—42no—
94C4×Dic13—22no—
95C4×Dic13—22no—
96C4×Dic13—41no—
97#2855—131no—
98#1797—131no—
99C4×C22⋊C8—131no—
100#1272—132no—
101#1271—132no—
102C23×C13C2×C22⋊C411yescharacteristic
103C22×D13—21no—
104C22×D13—21no—
105C22×D13—21no—
106C22×D13—21no—
107C22×D13—21no—
108C22×D13—21no—
109C22×D13#10312yes—
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#10312yes—
123C2×C4×C13#10412yes—
124C2×C4×C13#13112yes—
125C2×Dic13—21no—
126C2×Dic13—21no—
127C2×Dic13—21no—
128C2×Dic13—21no—
129C2×Dic13—21no—
130C2×Dic13—21no—
131C2×Dic13—41no—
132C2×Dic13—41no—
133C2×Dic13—41no—
134C2×Dic13—41no—
135C2×Dic13—41no—
136C2×Dic13—41no—
137C2×Dic13#9912yes—
138C2×Dic13C2×SD1611yescharacteristic
139C2×Dic13C2×Q1611yescharacteristic
140C2×Dic13#13512yes—
141C4×D13—42no—
142C4×D13—42no—
143C4×D13—44no—
144C4×D13—44no—
145Dic26—82no—
146#1057—44no—
147#1057—82no—
148C2×C22⋊Q8—131no—
149C22×C42—131no—
150C2×C4⋊C8—261no—
151C2×C22⋊C8—261no—
152C2×C22⋊C8—261no—
153C2×C4×C8—261no—
154#391—131no—
155#391—131no—
156#389—131no—
157#389#26111yescharacteristic
158#387—261no—
159#387—261no—
160#385—261no—
161#381—261no—
162#380—131no—
163#336—132no—
164#336—132no—
165C22×C13#40811yescharacteristic
166C22×C13C2×#9911yescharacteristic
167C22×C13#41311yescharacteristic
168C22×C13C2×#10311yescharacteristic
169C22×C13#41611yescharacteristic
170C22×C13C2×#10411yescharacteristic
171C22×C13#42111yescharacteristic
172C2×D13—22no—
173C2×D13—22no—
174C2×D13—22no—
175C2×D13—41no—
176C2×D13—41no—
177C2×D13—41no—
178C2×D13—41no—
179C4×C13—22no—
180C4×C13—22no—
181C4×C13—22no—
182C4×C13—81no—
183C4×C13—81no—
184Dic13—22no—
185Dic13—22no—
186Dic13—21no—
187Dic13—21no—
188Dic13—81no—
189Dic13—81no—
190C22×Q8—131no—
191C23×C4—131no—
192C23×C4—131no—
193C23×C4—131no—
194C22×C8—262no—
195C22×C8—262no—
196C22⋊Q8—522no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—131no—
199C2×C4⋊C4—261no—
200C2×C4⋊C4—261no—
201C2×C4⋊C4C2×#26111yescharacteristic
202C2×C4⋊C4C2×#26111yescharacteristic
203C2×C22⋊C4—261no—
204C2×C22⋊C4—261no—
205C2×C42—131no—
206C2×C42—131no—
207C2×C42—131no—
208C2×C42—522no—
209C2×C42C2×#26111yescharacteristic
210C4⋊C8—522no—
211C22⋊C8—264no—
212C22⋊C8—522no—
213C4×C8—522no—
214#95—21no—
215#95—261no—
216#95—261no—
217#95—261no—
218#95—261no—
219#95—261no—
220#95—261no—
221C2×C13#146811yescharacteristic
222C2×C13#148211yescharacteristic
223C2×C13#149311yescharacteristic
224C2×C13#150111yescharacteristic
225C2×C13#152011yescharacteristic
226C2×C13#152911yescharacteristic
227C2×C13#154211yescharacteristic
228D13—42no—
229C24—131no—
230C2×Q8—262no—
231C2×Q8—521no—
232C2×Q8—521no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—131no—
236C22×C4—131no—
237C22×C4—131no—
238C22×C4—132no—
239C22×C4—132no—
240C22×C4—262no—
241C22×C4—262no—
242C22×C4—262no—
243C22×C4—262no—
244C22×C4—261no—
245C22×C4—261no—
246C22×C4—521no—
247C22×C4—521no—
248C22×C4—521no—
249C22×C4—521no—
250C22×C4C22⋊#26111yescharacteristic
251C22×C4C22⋊#26111yescharacteristic
252C22×C4C22×#26111yescharacteristic
253C2×C8—264no—
254C2×C8—522no—
255C2×C8—522no—
256C2×C8—522no—
257C2×C8—522no—
258C2×C8—522no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—42no—
262C4⋊C4—262no—
263C4⋊C4—522no—
264C4⋊C4—522no—
265C22⋊C4—522no—
266C22⋊C4—522no—
267C42—41no—
268C42—262no—
269C42—262no—
270C42—521no—
271C13#766111yescharacteristic, complemented, Sylow
272C23—132no—
273C23—261no—
274C23—261no—
275C23—261no—
276C23—261no—
277C23—261no—
278C23—261no—
279C23C2×C22⋊#26111yescharacteristic
280Q8—1042no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—132no—
294C2×C4—131no—
295C2×C4—131no—
296C2×C4—132no—
297C2×C4—261no—
298C2×C4—261no—
299C2×C4—261no—
300C2×C4—261no—
301C2×C4—261no—
302C2×C4—261no—
303C2×C4—522no—
304C2×C4—522no—
305C2×C4—524no—
306C2×C4—524no—
307C2×C4—521no—
308C2×C4—521no—
309C2×C4—521no—
310C2×C4—521no—
311C2×C4—521no—
312C2×C4—521no—
313C2×C4#8811612yes—
314C2×C4#8811712yes—
315C2×C4#8824012yes—
316C8—524no—
317C8—1042no—
318C22—262no—
319C22—262no—
320C22—262no—
321C22—521no—
322C22—521no—
323C22—521no—
324C22—521no—
325C22#1171913211yescharacteristic
326C22C2×#8811611yescharacteristic
327C22D13⋊#9911yescharacteristic
328C22C2×#8811711yescharacteristic
329C22#1171915911yescharacteristic
330C22#1171916511yescharacteristic
331C22#1171916611yescharacteristic
332C4—22no—
333C4—22no—
334C4—22no—
335C4—81no—
336C4—81no—
337C4—261no—
338C4—261no—
339C4—262no—
340C4—262no—
341C4—1041no—
342C4—1041no—
343C2—522no—
344C2#1313010411yescharacteristic
345C2#1313015011yescharacteristic
346C2#1313018611yescharacteristic
347C2#1313021211yescharacteristic
348C2#1313027411yescharacteristic
349C2#1313030111yescharacteristic
350C2#1313033711yescharacteristic
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#7661
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
271. C13#7661semidirect

Maximal subgroups

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

subgroupindex
#131306912
C4×#881112
#131296572
#131296552
#131231742
#766113