Finite Group Databasebeta

← #15773637

Subgroups — #15773637

Order 3328.

402 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 79 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#13118104C211yesmaximal, characteristic
2#13114913C211yesmaximal, characteristic
3#13112861C212yesmaximal
4#13112858C212yesmaximal
5C13×#1464C211yesmaximal, characteristic
6C2×C13×#117C2211yescharacteristic
7C2×C4×Dic26C411yescharacteristic, complemented
8C13×#432—21no—
9#11718872—21no—
10C4×C22⋊Dic13—21no—
11#11718647C411yescharacteristic, complemented
12#11718645—21no—
13#11718640C411yescharacteristic, complemented
14#11718610C2211yescharacteristic
15#11718609—21no—
16#11718608C2211yescharacteristic
17C4×C4⋊Dic13C411yescharacteristic, complemented
18C4×#6101—21no—
19C13×#324—21no—
20C13×#323C2212yes—
21#11718118—21no—
22#11718118C2212yes—
23C23×C4×C13D411yescharacteristic
24C22×Dic26C2×C411yescharacteristic
25C13×#117—41no—
26C13×#117—41no—
27C2×C13×C4⋊C4C2×C411yescharacteristic
28C2×C13×C4⋊C4D411yescharacteristic
29C2×C13×C22⋊C4D411yescharacteristic
30C2×C13×C22⋊C4C2311yescharacteristic
31C2×C42×C13C2×C411yescharacteristic
32C2×C42×C13D411yescharacteristic
33C2×C22⋊Dic13—21no—
34C2×C22⋊Dic13—21no—
35C2×C22⋊Dic13—22no—
36C2×C4⋊Dic13—21no—
37C2×C4⋊Dic13C2×C411yescharacteristic
38C2×#6101—21no—
39C2×#6101—21no—
40C2×#6101—21no—
41C2×C4×Dic13—21no—
42C2×C4×Dic13—21no—
43C4×Dic26—41no—
44C4×Dic26—41no—
45C13×C4⋊C8—41no—
46C13×C22⋊C8—22no—
47C13×#97—41no—
48#88071—21no—
49#88071—21no—
50#88071—21no—
51#88071—21no—
52#88071—41no—
53#88071—41no—
54#88071C2×C411yescharacteristic
55#88071C2×C411yescharacteristic
56#11810—131nomaximal, Sylow
57C24×C13C2×D411yescharacteristic
58C22×C4×C13—22no—
59C22×C4×C13—21no—
60C22×C4×C13—21no—
61C22×C4×C13—41no—
62C22×C4×C13C22⋊C411yescharacteristic
63C22×C4×C13C22⋊C411yescharacteristic
64C22×C4×C13C22⋊C411yescharacteristic
65C22×C4×C13C22⋊C411yescharacteristic
66C22×C4×C13C22×C411yescharacteristic
67C22×C4×C13C2×D411yescharacteristic
68C22×Dic13—21no—
69C22×Dic13—21no—
70C22×Dic13—21no—
71C22×Dic13—21no—
72C22×Dic13—42no—
73C2×Dic26—41no—
74C2×Dic26—42no—
75C2×C8×C13—42no—
76C13×C4⋊C4—41no—
77C13×C4⋊C4—41no—
78C13×C22⋊C4—41no—
79C13×C22⋊C4—41no—
80C42×C13—21no—
81C42×C13—21no—
82C42×C13—21no—
83C42×C13—21no—
84C22⋊Dic13—42no—
85C22⋊Dic13—42no—
86C22⋊Dic13—42no—
87C22⋊Dic13—42no—
88C4⋊Dic13—42no—
89C4⋊Dic13—41no—
90#6101—42no—
91#6101—42no—
92#6101—42no—
93C4×Dic13—42no—
94C4×Dic13—41no—
95C4×Dic13—41no—
96#2396—131no—
97#1820—131no—
98#1464D1311yescharacteristic
99#1352—132no—
100#1351—132no—
101C23×C13—21no—
102C23×C13—21no—
103C23×C13—41no—
104C23×C13—41no—
105C23×C13C2×C22⋊C411yescharacteristic
106C23×C13#13712yes—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
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—42no—
117C2×C4×C13—42no—
118C2×C4×C13—41no—
119C2×C4×C13—41no—
120C2×C4×C13—41no—
121C2×C4×C13—41no—
122C2×C4×C13#9911yescharacteristic
123C2×C4×C13#9911yescharacteristic
124C2×Dic13—22no—
125C2×Dic13—22no—
126C2×Dic13—41no—
127C2×Dic13—41no—
128C2×Dic13—41no—
129C2×Dic13—41no—
130C2×Dic13—41no—
131C2×Dic13—41no—
132C2×Dic13—41no—
133C2×Dic13—41no—
134C2×Dic13—41no—
135C2×Dic13—41no—
136C2×Dic13—82no—
137C2×Dic13—82no—
138C2×Dic13—82no—
139Dic26—42no—
140Dic26—42no—
141C8×C13—82no—
142C2×C4×Q8—131no—
143C2×#117C2×D1311yescharacteristic
144#432—21no—
145#400—131no—
146#399—131no—
147#398—261no—
148#396—261no—
149#395—131no—
150#393—131no—
151#381—261no—
152C4×C4⋊C4—131no—
153C4×C4⋊C4—261no—
154C4×C22⋊C4—261no—
155#342—132no—
156#342—261no—
157#324—21no—
158#323C2×D1312yes—
159C22×C13—21no—
160C22×C13—21no—
161C22×C13—22no—
162C22×C13—42no—
163C22×C13—41no—
164C22×C13—41no—
165C22×C13—81no—
166C22×C13C2×#9911yescharacteristic
167C22×C13#41911yescharacteristic
168C22×C13#42111yescharacteristic
169C4×C13—21no—
170C4×C13—21no—
171C4×C13—41no—
172C4×C13—41no—
173C4×C13—41no—
174C4×C13—41no—
175C4×C13—41no—
176Dic13—42no—
177Dic13—42no—
178Dic13—81no—
179Dic13—81no—
180Dic13—162no—
181C22×Q8—131no—
182C23×C4D5211yescharacteristic
183C4×Q8—521no—
184C4×Q8—521no—
185#117—41no—
186#117—41no—
187C2×C4⋊C4—131no—
188C2×C4⋊C4—261no—
189C2×C4⋊C4—261no—
190C2×C4⋊C4—261no—
191C2×C4⋊C4—261no—
192C2×C4⋊C4C4×D1311yescharacteristic
193C2×C4⋊C4C22⋊D1311yescharacteristic
194C2×C22⋊C4—261no—
195C2×C22⋊C4—261no—
196C2×C22⋊C4—262no—
197C2×C22⋊C4D5211yescharacteristic
198C2×C22⋊C4C22×D1311yescharacteristic
199C2×C42—261no—
200C2×C42—261no—
201C2×C42C4×D1311yescharacteristic
202C2×C42C22⋊D1311yescharacteristic
203C4⋊C8—41no—
204C22⋊C8—22no—
205#97—41no—
206#95—131no—
207#95—131no—
208#95—261no—
209#95—261no—
210#95—261no—
211#95—261no—
212#95—521no—
213#95—521no—
214C2×C13—21no—
215C2×C13—21no—
216C2×C13—42no—
217C2×C13#151111yescharacteristic
218C2×C13#212011yescharacteristic
219C2×C13#212611yescharacteristic
220C24C2×D5211yescharacteristic
221C2×Q8—521no—
222C2×Q8—522no—
223C22×C4—22no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—41no—
227C22×C4—261no—
228C22×C4—261no—
229C22×C4—261no—
230C22×C4—261no—
231C22×C4—522no—
232C22×C4#610311yescharacteristic
233C22×C4#610311yescharacteristic
234C22×C4#610311yescharacteristic
235C22×C4#610311yescharacteristic
236C22×C4C2×C4×D1311yescharacteristic
237C22×C4C2×C22⋊D1311yescharacteristic
238C2×C8—42no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—521no—
242C4⋊C4—522no—
243C4⋊C4—522no—
244C4⋊C4—522no—
245C4⋊C4—522no—
246C22⋊C4—41no—
247C22⋊C4—41no—
248C22⋊C4—522no—
249C22⋊C4—522no—
250C22⋊C4—522no—
251C22⋊C4—522no—
252C42—21no—
253C42—21no—
254C42—21no—
255C42—21no—
256C42—522no—
257C42—521no—
258C42—521no—
259C13#1181011yescharacteristic, complemented, Sylow
260C23—21no—
261C23—21no—
262C23—41no—
263C23—41no—
264C23#8816312yes—
265C23C2×#610311yescharacteristic
266Q8—522no—
267Q8—522no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—262no—
284C2×C4—262no—
285C2×C4—521no—
286C2×C4—521no—
287C2×C4—521no—
288C2×C4—521no—
289C2×C4—521no—
290C2×C4—521no—
291C2×C4—521no—
292C2×C4—521no—
293C2×C4—521no—
294C2×C4—521no—
295C2×C4—1042no—
296C2×C4—1042no—
297C2×C4—1042no—
298C2×C4#8804611yescharacteristic
299C2×C4#8804611yescharacteristic
300C8—82no—
301C22—21no—
302C22—21no—
303C22—22no—
304C22—42no—
305C22—41no—
306C22—41no—
307C22—81no—
308C22C2×#8804611yescharacteristic
309C22#1171878111yescharacteristic
310C22#1171880011yescharacteristic
311C4—21no—
312C4—21no—
313C4—41no—
314C4—41no—
315C4—41no—
316C4—41no—
317C4—41no—
318C4—522no—
319C4—522no—
320C4—1041no—
321C4—1041no—
322C4—2082no—
323C2—21no—
324C2—21no—
325C2—42no—
326C2#1311337011yescharacteristic
327C2#1311647811yescharacteristic
328C2#1311649911yescharacteristic
subgroupG/H
centerC22C2×#88046
commutatorC22×C4×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
FittingC13×#1464C2
socleC22×C13C2×#99
prime radicalC24×C13C2×D4
cosocleC2×C13×C22⋊C4C23
hypercenter#1464D13
hypocenterC13#11810
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1464

Complements

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

NH ≅ G/Ntype
7. C2×C4×Dic26C4semidirect
11. #11718647C4semidirect
13. #11718640C4semidirect
17. C4×C4⋊Dic13C4semidirect
259. C13#11810semidirect

Maximal subgroups

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

subgroupindex
#131181042
#131149132
#131128612
#131128582
C13×#14642
#1181013