Finite Group Databasebeta

← #16785069

Subgroups — #16785069

Order 3328.

518 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 126 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#13130751C211yesmaximal, characteristic
2C4×#88110C211yesmaximal, characteristic
3#13129672C212yesmaximal
4#13129672C212yesmaximal
5#13117407C211yesmaximal, characteristic
6C2×#88142C411yescharacteristic
7C2×#88141—21no—
8C2×#88110—21no—
9C2×#88110—21no—
10C2×C4⋊#1057C2212yes—
11C2×C4×#1057C2212yes—
12C13×#389C411yescharacteristic
13#11718637C411yescharacteristic
14C4⋊C4×Dic13C2211yescharacteristic
15C4⋊C4×Dic13C2211yescharacteristic
16#11718633—21no—
17C42×Dic13C2211yescharacteristic
18#11718589C411yescharacteristic
19#11718310—21no—
20#11718307—21no—
21#11718290—21no—
22#11718290—21no—
23C22×Dic26—21no—
24C22×#1057—22no—
25C22×#1057—22no—
26C2×C13×C4⋊C4—21no—
27C2×C13×C4⋊C4C2×C411yescharacteristic
28C2×C13×C4⋊C4C2×C411yescharacteristic
29C2×C42×C13C2×C411yescharacteristic
30C2×C4⋊Dic13C2×C411yescharacteristic
31C2×C4⋊Dic13C2×C411yescharacteristic
32C2×#6101—21no—
33C2×#6101—21no—
34C2×#6101—21no—
35C2×#6101—21no—
36C2×C4×Dic13—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—
46#88141—44no—
47#88110—24no—
48#88110—24no—
49C4⋊#1057—24no—
50C4×#1057—22no—
51C4×#1057Q814yescomplemented
52C13×#95—21no—
53#88071—21no—
54#88071—21no—
55#88071—21no—
56#9877—131nomaximal, Sylow
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13C22⋊C411yescharacteristic
60C22×C4×C13C22⋊C411yescharacteristic
61C22×C4×C13C22×C411yescharacteristic
62C22×Dic13—21no—
63C22×Dic13—21no—
64C22×Dic13C22⋊C411yescharacteristic
65C22×Dic13C22⋊C411yescharacteristic
66C22×Dic13C2×D411yescharacteristic
67C22×Dic13C2×D411yescharacteristic
68C2×Dic26—24no—
69C2×Dic26—42no—
70C2×Dic26—42no—
71C2×#1057—24no—
72C2×#1057—24no—
73C2×#1057—24no—
74C2×#1057—42no—
75C2×#1057—42no—
76C2×#1057—42no—
77C13×C4⋊C4—21no—
78C13×C4⋊C4—22no—
79C13×C4⋊C4—42no—
80C13×C4⋊C4M1612yes—
81C42×C13—22no—
82C4⋊Dic13—21no—
83C4⋊Dic13—22no—
84C4⋊Dic13M1612yes—
85#6101—24no—
86#6101—42no—
87#6101—42no—
88#6101—42no—
89C4×Dic13—21no—
90C4×Dic13—21no—
91C4×Dic13—22no—
92C4×Dic13—22no—
93C4×Dic13—22no—
94C4×Dic13—22no—
95C4×Dic13—42no—
96C4×Dic13—42no—
97C4×Dic13C2×Q812yes—
98C4×Dic13#4112yes—
99C4×C4⋊Q8—131no—
100#1831—131no—
101C4×#97—131no—
102#1279—132no—
103#1279—132no—
104C23×C13C2×C22⋊C411yescharacteristic
105C2×C4×C13—22no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—41no—
113C2×C4×C13—41no—
114C2×C4×C13—41no—
115C2×C4×C13—41no—
116C2×C4×C13—41no—
117C2×C4×C13C4×Q812yes—
118C2×C4×C13C2×M1611yescharacteristic
119C2×C4×C13C2×M1611yescharacteristic
120C2×C4×C13#13112yes—
121C2×Dic13—21no—
122C2×Dic13—21no—
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13—21no—
126C2×Dic13—21no—
127C2×Dic13—22no—
128C2×Dic13—41no—
129C2×Dic13—41no—
130C2×Dic13—41no—
131C2×Dic13—41no—
132C2×Dic13—41no—
133C2×Dic13#10412yes—
134C2×Dic13#10412yes—
135C2×Dic13C22⋊Q812yes—
136C2×Dic13#12411yescharacteristic
137C2×Dic13C4⋊Q811yescharacteristic
138C2×Dic13AGL(1,ℤ/8)12yes—
139C2×Dic13#13712yes—
140Dic26—48no—
141#1057—28no—
142#1057—82no—
143C2×C4⋊Q8—131no—
144C2×C4×Q8—261no—
145C2×C4⋊C8—132no—
146C2×#97—261no—
147C2×#97—261no—
148C2×C4×C8—132no—
149#391—261no—
150#389—131no—
151#389—261no—
152#389#26111yescharacteristic
153#384—131no—
154C4×C4⋊C4—131no—
155C4×C4⋊C4—131no—
156C4×C4⋊C4—261no—
157C43—131no—
158#336—261no—
159#336—261no—
160C22×C13#39111yescharacteristic
161C22×C13#40711yescharacteristic
162C22×C13#40811yescharacteristic
163C22×C13#41811yescharacteristic
164C22×C13#41911yescharacteristic
165C22×C13C2×#10411yescharacteristic
166C22×C13C2×#10411yescharacteristic
167C4×C13—41no—
168C4×C13—41no—
169C4×C13—42no—
170C4×C13—81no—
171C4×C13#44612yes—
172C4×C13#44612yes—
173Dic13—22no—
174Dic13—22no—
175Dic13—22no—
176Dic13—42no—
177Dic13—81no—
178Dic13#48912yes—
179Dic13#50112yes—
180C22×Q8—261no—
181C22×C8—262no—
182C22×C8—262no—
183C4⋊Q8—262no—
184C4⋊Q8—262no—
185C4×Q8—524no—
186C2×C4⋊C4—21no—
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⋊C4C2×#26111yescharacteristic
194C2×C4⋊C4C2×#26111yescharacteristic
195C2×C42—131no—
196C2×C42—131no—
197C2×C42—131no—
198C2×C42—131no—
199C2×C42—131no—
200C2×C42—131no—
201C2×C42—261no—
202C2×C42—261no—
203C2×C42C2×#26111yescharacteristic
204C4⋊C8—264no—
205#97—264no—
206#97—264no—
207C4×C8—134no—
208C4×C8—262no—
209#95—21no—
210#95—261no—
211#95—261no—
212#95—261no—
213C2×C13#148411yescharacteristic
214C2×C13#148511yescharacteristic
215C2×C13#149011yescharacteristic
216C2×C13#149111yescharacteristic
217C2×C13#198511yescharacteristic
218C2×C13#199311yescharacteristic
219C2×C13#199411yescharacteristic
220C2×Q8—264no—
221C2×Q8—522no—
222C2×Q8—522no—
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—131no—
226C22×C4—131no—
227C22×C4—131no—
228C22×C4—131no—
229C22×C4—261no—
230C22×C4—261no—
231C22×C4C22⋊#26111yescharacteristic
232C22×C4C22⋊#26111yescharacteristic
233C22×C4C22×#26111yescharacteristic
234C2×C8—264no—
235C2×C8—264no—
236C2×C8—264no—
237C2×C8—522no—
238C2×C8—522no—
239C2×C8—522no—
240C4⋊C4—21no—
241C4⋊C4—22no—
242C4⋊C4—42no—
243C4⋊C4—132no—
244C4⋊C4—264no—
245C4⋊C4—261no—
246C4⋊C4—262no—
247C4⋊C4—522no—
248C4⋊C4—522no—
249C4⋊C4—522no—
250C4⋊C4#611812yes—
251C42—22no—
252C42—132no—
253C42—132no—
254C42—262no—
255C42—262no—
256C42—262no—
257C42—262no—
258C42—261no—
259C42—261no—
260C42—522no—
261C42—522no—
262C13#987711yescharacteristic, complemented, Sylow
263C23C2×C22⋊#26111yescharacteristic
264Q8—528no—
265C2×C4—22no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—132no—
278C2×C4—132no—
279C2×C4—131no—
280C2×C4—131no—
281C2×C4—132no—
282C2×C4—132no—
283C2×C4—132no—
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×C4C2×#611811yescharacteristic
297C2×C4D13⋊M1611yescharacteristic
298C2×C4#8823812yes—
299C2×C4Q8×#26112yes—
300C8—268no—
301C8—1042no—
302C22#1171912711yescharacteristic
303C22#1171913811yescharacteristic
304C22#1171914611yescharacteristic
305C22#1171915311yescharacteristic
306C22(C2×#261)⋊Q811yescharacteristic
307C22D13⋊#10411yescharacteristic
308C22D13⋊#10411yescharacteristic
309C4—41no—
310C4—41no—
311C4—42no—
312C4—81no—
313C4—132no—
314C4—132no—
315C4—262no—
316C4—262no—
317C4—262no—
318C4—522no—
319C4—1041no—
320C4#1171907812yes—
321C4#1171908012yes—
322C2#1313015511yescharacteristic
323C2#1313015811yescharacteristic
324C2#1313017611yescharacteristic
325C2#1313017911yescharacteristic
326C2#1313100911yescharacteristic
327C2#1313102011yescharacteristic
328C2#1313102211yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC13×#389C4
socle, prime radicalC23×C13C2×C22⋊C4
cosocleC2×C4×Dic13C23
hypercenter#389#261
hypocenterC13#9877
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
51. C4×#1057Q8semidirect
262. C13#9877semidirect

Maximal subgroups

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

subgroupindex
#131307512
C4×#881102
#131296722
#131174072
#987713