Finite Group Databasebeta

← #15760789

Subgroups — #15760789

Order 3328.

602 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 602 conjugacy classes of subgroups — too many to draw. Only its 119 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#13123877C211yesmaximal, characteristic, complemented
2#13114828C211yesmaximal, characteristic, complemented
3#13113261C212yesmaximal, complemented
4#13112694C212yesmaximal, complemented
5C13×#2535C211yesmaximal, characteristic
6C2×C13×#121—21no—
7C2×C4×D4×C13C2211yescharacteristic
8C2×C4×D4×C13C2211yescharacteristic
9C13×#397C412yes—
10C13×#392C412yes—
11C13×#386—22no—
12C13×#382C2211yescharacteristic
13C13×#380—21no—
14C2×#88073—21no—
15#11718868—22no—
16#11718673—24no—
17#11718586C2212yes—
18#11718585C2212yes—
19D4⋊#1055—24no—
20#11718122—21no—
21C22×D4×C13—22no—
22C22×D4×C13C2×C411yescharacteristic
23C22×D4×C13D411yescharacteristic
24C23×C4×C13—21no—
25C23×C4×C13D412yes—
26C13×#121—44no—
27C4×D4×C13—22no—
28C4×D4×C13—22no—
29C4×D4×C13—22no—
30C4×D4×C13—22no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4C2×C411yescharacteristic
33C2×C13×C4⋊C4D411yescharacteristic
34C2×C13×C22⋊C4—22no—
35C2×C13×C22⋊C4—21no—
36C2×C13×C22⋊C4—22no—
37C2×C13×C22⋊C4C2×C412yes—
38C2×C42×C13C2311yescharacteristic
39C2×#6099—24no—
40C2×#6099—22no—
41C13×#95—22no—
42C13×#95—21no—
43C13×#95C2×C412yes—
44#88073—42no—
45C22⋊#1055—24no—
46C22⋊#1055—22no—
47C4⋊#1055—22no—
48C4⋊#1055—22no—
49C4⋊#1055—22no—
50C4×#1055D414yescomplemented
51#9489—131nomaximal, Sylow
52C24×C13—21no—
53C24×C13C22⋊C412yes—
54C2×D4×C13—22no—
55C2×D4×C13—22no—
56C2×D4×C13—21no—
57C2×D4×C13—22no—
58C2×D4×C13—21no—
59C2×D4×C13—42no—
60C2×D4×C13—44no—
61C2×D4×C13—44no—
62C2×D4×C13—82no—
63C22×C4×C13—22no—
64C22×C4×C13—22no—
65C22×C4×C13—22no—
66C22×C4×C13—21no—
67C22×C4×C13—42no—
68C22×C4×C13—42no—
69C22×C4×C13—41no—
70C22×C4×C13—41no—
71C22×C4×C13—82no—
72C22×C4×C13C22⋊C412yes—
73C22×C4×C13C22×C411yescharacteristic
74C22×C4×C13C2×D411yescharacteristic
75C22×C4×C13C2×D411yescharacteristic
76C13×C4⋊C4—22no—
77C13×C4⋊C4—22no—
78C13×C4⋊C4—42no—
79C13×C22⋊C4—24no—
80C13×C22⋊C4—44no—
81C13×C22⋊C4—41no—
82C13×C22⋊C4—41no—
83C13×C22⋊C4—82no—
84C42×C13C2×D412yes—
85C42×C13#4112yes—
86#6099—42no—
87#6099—42no—
88#6099—84no—
89C2×#1055—24no—
90C2×#1055—42no—
91#2975—131no—
92#2535D1311yescharacteristic
93#1800—131no—
94#1486—132no—
95#1286—132no—
96C23×C13—22no—
97C23×C13—22no—
98C23×C13—22no—
99C23×C13—22no—
100C23×C13—42no—
101C23×C13—42no—
102C23×C13—41no—
103C23×C13—41no—
104C23×C13—41no—
105C23×C13—41no—
106C23×C13—41no—
107C23×C13—41no—
108C23×C13C2×C22⋊C411yescharacteristic
109D4×C13—24no—
110D4×C13—42no—
111D4×C13—42no—
112D4×C13—42no—
113D4×C13—88no—
114C2×C4×C13—22no—
115C2×C4×C13—41no—
116C2×C4×C13—41no—
117C2×C4×C13—44no—
118C2×C4×C13—42no—
119C2×C4×C13—42no—
120C2×C4×C13—42no—
121C2×C4×C13—41no—
122C2×C4×C13—41no—
123C2×C4×C13—41no—
124C2×C4×C13—42no—
125C2×C4×C13—82no—
126C2×C4×C13—82no—
127C2×C4×C13—82no—
128C2×C4×C13C4×D412yes—
129C2×C4×C13#12011yescharacteristic
130C2×C4×C13#12112yes—
131C2×C4×C13#12311yescharacteristic
132C2×C4×C13AGL(1,ℤ/8)12yes—
133C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
134C2×C4×C13#13711yescharacteristic
135#1055—44no—
136#1055—82no—
137C2×#121—21no—
138C2×C4×D4C2×D1311yescharacteristic
139C2×C4×D4C2×D1311yescharacteristic
140#436—264no—
141#431—132no—
142#423—132no—
143C2×#100—261no—
144#407—262no—
145#397Dic1312yes—
146#392Dic1312yes—
147#386—22no—
148#382C2×D1311yescharacteristic
149#380—21no—
150#343—261no—
151D4⋊C8—264no—
152C22×C13—21no—
153C22×C13—21no—
154C22×C13—42no—
155C22×C13—44no—
156C22×C13—42no—
157C22×C13—42no—
158C22×C13—42no—
159C22×C13—42no—
160C22×C13—42no—
161C22×C13—82no—
162C22×C13—81no—
163C22×C13—81no—
164C22×C13—81no—
165C22×C13—81no—
166C22×C13#38611yescharacteristic
167C22×C13#41711yescharacteristic
168C22×C13#41811yescharacteristic
169C4×C13—22no—
170C4×C13—21no—
171C4×C13—21no—
172C4×C13—42no—
173C4×C13—82no—
174C4×C13—81no—
175C4×C13#46812yes—
176C4×C13#46912yes—
177C22×D4—22no—
178C22×D4C2×Dic1311yescharacteristic
179C22×D4C22⋊D1311yescharacteristic
180C23×C4—21no—
181C23×C4C22⋊D1312yes—
182C2×M16—264no—
183C2×M16—262no—
184#121—44no—
185C4×D4—22no—
186C4×D4—22no—
187C4×D4—22no—
188C4×D4—22no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4C2×Dic1311yescharacteristic
191C2×C4⋊C4C22⋊D1311yescharacteristic
192C2×C22⋊C4—22no—
193C2×C22⋊C4—21no—
194C2×C22⋊C4—22no—
195C2×C22⋊C4C2×Dic1312yes—
196C2×C42C22×D1311yescharacteristic
197C4⋊C8—262no—
198C4⋊C8—262no—
199C4⋊C8—262no—
200#100—522no—
201C22⋊C8—264no—
202C22⋊C8—262no—
203C4×C8—134no—
204#95—22no—
205#95—21no—
206#95C2×Dic1312yes—
207C2×C13—21no—
208C2×C13—21no—
209C2×C13—82no—
210C2×C13—82no—
211C2×C13#189111yescharacteristic
212C2×C13#189511yescharacteristic
213C2×C13#191111yescharacteristic
214C24—21no—
215C24C22⋊Dic1312yes—
216C2×D4—22no—
217C2×D4—22no—
218C2×D4—22no—
219C2×D4—21no—
220C2×D4—21no—
221C2×D4—42no—
222C2×D4—44no—
223C2×D4—44no—
224C2×D4—82no—
225C22×C4—22no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—21no—
229C22×C4—42no—
230C22×C4—42no—
231C22×C4—41no—
232C22×C4—41no—
233C22×C4—82no—
234C22×C4C22⋊Dic1312yes—
235C22×C4C22×Dic1311yescharacteristic
236C22×C4C2×C22⋊D1311yescharacteristic
237C22×C4C2×C22⋊D1311yescharacteristic
238M16—522no—
239M16—522no—
240M16—1044no—
241C2×C8—264no—
242C2×C8—522no—
243C4⋊C4—22no—
244C4⋊C4—22no—
245C4⋊C4—42no—
246C22⋊C4—24no—
247C22⋊C4—44no—
248C22⋊C4—41no—
249C22⋊C4—41no—
250C22⋊C4—82no—
251C42D4×D1312yes—
252C42#612912yes—
253C13#948911yescharacteristic, complemented, Sylow
254C23—22no—
255C23—22no—
256C23—22no—
257C23—22no—
258C23—42no—
259C23—42no—
260C23—41no—
261C23—41no—
262C23—41no—
263C23—41no—
264C23—41no—
265C23—41no—
266C23C2×C22⋊Dic1311yescharacteristic
267D4—24no—
268D4—42no—
269D4—42no—
270D4—42no—
271D4—88no—
272C2×C4—22no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—44no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—41no—
280C2×C4—42no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—82no—
284C2×C4—82no—
285C2×C4—82no—
286C2×C4#8818612yes—
287C2×C4D4×Dic1312yes—
288C2×C4#8818911yescharacteristic
289C2×C4#8819111yescharacteristic
290C2×C4#8819312yes—
291C2×C4#8820311yescharacteristic
292C2×C4#8820511yescharacteristic
293C8—524no—
294C8—1042no—
295C22—21no—
296C22—21no—
297C22—42no—
298C22—44no—
299C22—42no—
300C22—42no—
301C22—42no—
302C22—42no—
303C22—42no—
304C22—82no—
305C22—81no—
306C22—81no—
307C22—81no—
308C22—81no—
309C22#1171887611yescharacteristic
310C22#1171888111yescharacteristic
311C22#1171889311yescharacteristic
312C4—22no—
313C4—21no—
314C4—21no—
315C4—42no—
316C4—82no—
317C4—81no—
318C4#1171870012yes—
319C4#1171870312yes—
320C2—21no—
321C2—21no—
322C2—82no—
323C2—82no—
324C2#1311525511yescharacteristic
325C2#1311527511yescharacteristic
326C2#1311536911yescharacteristic
subgroupG/H
centerC22#11718881
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
Fitting, prime radicalC13×#2535C2
socleC22×C13#386
cosocleC2×C42×C13C23
hypercenter#2535D13
hypocenterC13#9489
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2535

Complements

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

NH ≅ G/Ntype
1. #13123877C2semidirect
2. #13114828C2semidirect
3. #13113261C2semidirect
4. #13112694C2semidirect
50. C4×#1055D4semidirect
253. C13#9489semidirect

Maximal subgroups

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

subgroupindex
#131238772
#131148282
#131132612
#131126942
C13×#25352
#948913