Finite Group Databasebeta

← #16778468

Subgroups — #16778468

Order 3328.

462 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 106 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#13130764C211yesmaximal, characteristic
2#13130622C211yesmaximal, characteristic
3#13129655C212yesmaximal
4#13129654C212yesmaximal
5C4×#88142C211yesmaximal, characteristic
6C2×#88142C411yescharacteristic
7C2×C4×Dic26—21no—
8C2×#88110—21no—
9C2×C4⋊#1057—21no—
10C4×C13×C4⋊C4C411yescharacteristic
11#11718646C2211yescharacteristic
12#11718637C411yescharacteristic
13#11718634C2211yescharacteristic
14C4×C4⋊Dic13C411yescharacteristic
15C4×#6101—21no—
16C42×Dic13C2211yescharacteristic
17#11718308—21no—
18#11718307—21no—
19#11718290—21no—
20#11718290—21no—
21#11718290C2212yes—
22#11718290C2212yes—
23C22×Dic26—21no—
24C22×#1057—22no—
25C22×#1057—22no—
26C2×C13×C4⋊C4C2×C411yescharacteristic
27C2×C13×C4⋊C4C2×C411yescharacteristic
28C2×C42×C13—21no—
29C2×C42×C13C2×C411yescharacteristic
30C2×C4⋊Dic13—21no—
31C2×C4⋊Dic13C2×C411yescharacteristic
32C2×C4⋊Dic13C2×C411yescharacteristic
33C2×#6101—21no—
34C2×#6101—21no—
35C2×#6101—21no—
36C2×#6101—21no—
37C2×C4×Dic13—21no—
38C2×C4×Dic13C2×C411yescharacteristic
39C2×C4×Dic13D411yescharacteristic
40C2×C4×Dic13D411yescharacteristic
41C2×C4×Dic13D411yescharacteristic
42C2×C4×Dic13D411yescharacteristic
43C2×C4×Dic13C2311yescharacteristic
44#88142—22no—
45#88142—22no—
46C4×Dic26—42no—
47C4×Dic26—42no—
48#88110—42no—
49C4⋊#1057—24no—
50C13×#95—21no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#7625—131nomaximal, Sylow
55C22×C4×C13—21no—
56C22×C4×C13—21no—
57C22×C4×C13C22⋊C411yescharacteristic
58C22×C4×C13C22⋊C411yescharacteristic
59C22×C4×C13C22×C411yescharacteristic
60C22×Dic13—21no—
61C22×Dic13—21no—
62C22×Dic13C22⋊C411yescharacteristic
63C22×Dic13C22⋊C411yescharacteristic
64C22×Dic13C2×D411yescharacteristic
65C22×Dic13C2×D411yescharacteristic
66C2×Dic26—24no—
67C2×Dic26—42no—
68C2×Dic26—42no—
69C2×#1057—24no—
70C2×#1057—42no—
71C2×#1057—42no—
72C2×#1057—42no—
73C2×#1057—42no—
74C2×#1057—42no—
75C13×C4⋊C4—21no—
76C13×C4⋊C4—41no—
77C13×C4⋊C4M1612yes—
78C42×C13—22no—
79C42×C13—42no—
80C4⋊Dic13—21no—
81C4⋊Dic13—41no—
82C4⋊Dic13—41no—
83C4⋊Dic13—41no—
84C4⋊Dic13M1612yes—
85#6101—24no—
86#6101—42no—
87#6101—42no—
88#6101—41no—
89#6101—41no—
90C4×Dic13—21no—
91C4×Dic13—21no—
92C4×Dic13—22no—
93C4×Dic13—22no—
94C4×Dic13—41no—
95C4×Dic13—41no—
96C4×Dic13—42no—
97C4×Dic13D812yes—
98C4×Dic13SD1612yes—
99C4×C4⋊Q8—131no—
100#1839—131no—
101#1767—131no—
102#1271—132no—
103#1271—132no—
104C23×C13C2×C22⋊C411yescharacteristic
105C2×C4×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—22no—
112C2×C4×C13—41no—
113C2×C4×C13—41no—
114C2×C4×C13—41no—
115C2×C4×C13—41no—
116C2×C4×C13—41no—
117C2×C4×C13#10112yes—
118C2×C4×C13#10212yes—
119C2×C4×C13C2×M1611yescharacteristic
120C2×C4×C13C2×M1611yescharacteristic
121C2×Dic13—21no—
122C2×Dic13—21no—
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13—21no—
126C2×Dic13—21no—
127C2×Dic13—21no—
128C2×Dic13—21no—
129C2×Dic13—22no—
130C2×Dic13—41no—
131C2×Dic13—41no—
132C2×Dic13—41no—
133C2×Dic13—41no—
134C2×Dic13—41no—
135C2×Dic13#10212yes—
136C2×Dic13#10412yes—
137C2×Dic13C2×D811yescharacteristic
138C2×Dic13C2×SD1611yescharacteristic
139C2×Dic13#13712yes—
140Dic26—48no—
141#1057—44no—
142#1057—82no—
143C2×C4⋊Q8—131no—
144C2×C4×Q8—261no—
145C2×C4⋊C8—261no—
146C2×#97—261no—
147#391—261no—
148#389—131no—
149#389—131no—
150#389—261no—
151#384—131no—
152C4×C4⋊C4—131no—
153C4×C4⋊C4—261no—
154C4×C4⋊C4#26111yescharacteristic
155C43—131no—
156#336—132no—
157#336—132no—
158#336—261no—
159#336—261no—
160C22×C13#40711yescharacteristic
161C22×C13#41011yescharacteristic
162C22×C13C2×#10111yescharacteristic
163C22×C13C2×#10211yescharacteristic
164C22×C13#41911yescharacteristic
165C22×C13C2×#10411yescharacteristic
166C22×C13#42111yescharacteristic
167C4×C13—22no—
168C4×C13—21no—
169C4×C13—21no—
170C4×C13—22no—
171C4×C13—42no—
172C4×C13—81no—
173Dic13—22no—
174Dic13—22no—
175Dic13—21no—
176Dic13—21no—
177Dic13—22no—
178Dic13—42no—
179Dic13—81no—
180C22×Q8—261no—
181C22×C8—262no—
182C22×C8—262no—
183C4⋊Q8—262no—
184C4⋊Q8—262no—
185C4×Q8—522no—
186C4×Q8—522no—
187C2×C4⋊C4—131no—
188C2×C4⋊C4—131no—
189C2×C4⋊C4—261no—
190C2×C4⋊C4—261no—
191C2×C4⋊C4—261no—
192C2×C4⋊C4—261no—
193C2×C4⋊C4—261no—
194C2×C4⋊C4C2×#26111yescharacteristic
195C2×C4⋊C4C2×#26111yescharacteristic
196C2×C42—21no—
197C2×C42—131no—
198C2×C42—131no—
199C2×C42—131no—
200C2×C42—131no—
201C2×C42—131no—
202C2×C42—131no—
203C2×C42—261no—
204C2×C42C2×#26111yescharacteristic
205C4⋊C8—264no—
206#97—522no—
207#95—21no—
208#95—261no—
209#95—261no—
210#95—261no—
211C2×C13#146711yescharacteristic
212C2×C13#148611yescharacteristic
213C2×C13#149111yescharacteristic
214C2×C13#150211yescharacteristic
215C2×C13#151511yescharacteristic
216C2×C13#153111yescharacteristic
217C2×C13#154611yescharacteristic
218C2×Q8—264no—
219C2×Q8—522no—
220C2×Q8—522no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4—131no—
224C22×C4—131no—
225C22×C4—131no—
226C22×C4—131no—
227C22×C4—261no—
228C22×C4—261no—
229C22×C4C22⋊#26111yescharacteristic
230C22×C4C22⋊#26111yescharacteristic
231C22×C4C22×#26111yescharacteristic
232C2×C8—264no—
233C2×C8—522no—
234C2×C8—522no—
235C2×C8—522no—
236C2×C8—522no—
237C2×C8—522no—
238C4⋊C4—21no—
239C4⋊C4—41no—
240C4⋊C4—132no—
241C4⋊C4—264no—
242C4⋊C4—261no—
243C4⋊C4—521no—
244C4⋊C4—521no—
245C4⋊C4—521no—
246C4⋊C4—522no—
247C4⋊C4—521no—
248C4⋊C4—521no—
249C4⋊C4—522no—
250C4⋊C4#611812yes—
251C42—22no—
252C42—42no—
253C42—132no—
254C42—132no—
255C42—262no—
256C42—262no—
257C42—261no—
258C42—261no—
259C42—521no—
260C42—521no—
261C42—522no—
262C13#762511yescharacteristic, complemented, Sylow
263C23C2×C22⋊#26111yescharacteristic
264Q8—528no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—22no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—131no—
278C2×C4—131no—
279C2×C4—132no—
280C2×C4—132no—
281C2×C4—132no—
282C2×C4—261no—
283C2×C4—261no—
284C2×C4—261no—
285C2×C4—261no—
286C2×C4—261no—
287C2×C4—261no—
288C2×C4—261no—
289C2×C4—261no—
290C2×C4—262no—
291C2×C4—521no—
292C2×C4—521no—
293C2×C4—521no—
294C2×C4—521no—
295C2×C4—521no—
296C2×C4#8811312yes—
297C2×C4#8811512yes—
298C2×C4C2×#611811yescharacteristic
299C2×C4D13⋊M1611yescharacteristic
300C8—524no—
301C8—1042no—
302C22#1171911611yescharacteristic
303C22#1171912711yescharacteristic
304C22C2×#8811311yescharacteristic
305C22C2×#8811511yescharacteristic
306C22#1171915311yescharacteristic
307C22D13⋊#10411yescharacteristic
308C22#1171916611yescharacteristic
309C4—22no—
310C4—22no—
311C4—21no—
312C4—21no—
313C4—42no—
314C4—81no—
315C4—262no—
316C4—262no—
317C4—262no—
318C4—261no—
319C4—261no—
320C4—522no—
321C4—1041no—
322C2#1313009811yescharacteristic
323C2#1313016211yescharacteristic
324C2#1313017911yescharacteristic
325C2#1313021511yescharacteristic
326C2#1313025811yescharacteristic
327C2#1313030811yescharacteristic
328C2#1313034511yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC4×C13×C4⋊C4C4
socle, prime radicalC23×C13C2×C22⋊C4
cosocleC2×C4×Dic13C23
hypercenterC4×C4⋊C4#261
hypocenterC13#7625
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
262. C13#7625semidirect

Maximal subgroups

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

subgroupindex
#131307642
#131306222
#131296552
#131296542
C4×#881422
#762513