Finite Group Databasebeta

← #15773273

Subgroups — #15773273

Order 3328.

436 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 91 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
1C4×#88074C211yesmaximal, characteristic
2#13113157C211yesmaximal, characteristic
3#13112857C212yesmaximal, complemented
4#13112836C212yesmaximal, complemented
5C13×#2638C211yesmaximal, characteristic
6C2×C13×C22⋊Q8C411yescharacteristic, complemented
7C2×C4×D4×C13C2211yescharacteristic
8C13×#398C411yescharacteristic, complemented
9C13×#397—21no—
10C13×#397C2211yescharacteristic
11C13×#395C411yescharacteristic, complemented
12C13×#394—21no—
13C13×#393C2211yescharacteristic
14C13×#387—21no—
15C13×#385—21no—
16C13×#381C411yescharacteristic, complemented
17C2×#88074—21no—
18C4×C22⋊Dic13—21no—
19#11718586—21no—
20#11718118C2212yes—
21#11718117—21no—
22#11718117C2212yes—
23C22×Q8×C13C2×C411yescharacteristic
24C22×D4×C13D411yescharacteristic
25C23×C4×C13C2×C411yescharacteristic
26C23×C4×C13D411yescharacteristic
27C13×C22⋊Q8—41no—
28C13×C22⋊Q8—41no—
29C4×D4×C13—41no—
30C4×D4×C13—41no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4C2×C411yescharacteristic
35C2×C13×C4⋊C4C2×C411yescharacteristic
36C2×C13×C22⋊C4—21no—
37C2×C13×C22⋊C4—21no—
38C2×C13×C22⋊C4—21no—
39C2×C13×C22⋊C4—21no—
40C2×C13×C22⋊C4D411yescharacteristic
41C2×C13×C22⋊C4C2311yescharacteristic
42C2×C42×C13D411yescharacteristic
43C2×C22⋊Dic13—22no—
44C2×C4×Dic13—41no—
45C13×#95—21no—
46C13×#95—21no—
47C13×#95—21no—
48C13×#95—21no—
49C13×#95—21no—
50C13×#95C2×C411yescharacteristic
51C13×#95C2×C411yescharacteristic
52#88074—24no—
53#88071—41no—
54C22⋊#1055—22no—
55C4⋊#1055—41no—
56C4×#1055—41no—
57#11731—131nomaximal, Sylow
58C24×C13C22⋊C411yescharacteristic
59C24×C13C2×D411yescharacteristic
60C2×Q8×C13—41no—
61C2×Q8×C13—81no—
62C2×D4×C13—22no—
63C2×D4×C13—22no—
64C2×D4×C13—41no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13—21no—
72C22×C4×C13—21no—
73C22×C4×C13—81no—
74C22×C4×C13—81no—
75C22×C4×C13C22⋊C411yescharacteristic
76C22×C4×C13C22⋊C411yescharacteristic
77C22×C4×C13C22⋊C411yescharacteristic
78C22×C4×C13C22×C411yescharacteristic
79C22×C4×C13C2×D411yescharacteristic
80C22×Dic13—42no—
81C13×C4⋊C4—41no—
82C13×C4⋊C4—41no—
83C13×C4⋊C4—41no—
84C13×C4⋊C4—41no—
85C13×C4⋊C4—42no—
86C13×C4⋊C4—81no—
87C13×C22⋊C4—41no—
88C13×C22⋊C4—41no—
89C13×C22⋊C4—42no—
90C13×C22⋊C4—42no—
91C13×C22⋊C4—81no—
92C13×C22⋊C4—81no—
93C42×C13—21no—
94C42×C13—21no—
95C22⋊Dic13—24no—
96C22⋊Dic13—42no—
97C4×Dic13—82no—
98C2×#1055—42no—
99#2638D1311yescharacteristic
100C4×#99—131no—
101#1460—131no—
102#1351—132no—
103#1344—132no—
104C23×C13—21no—
105C23×C13—21no—
106C23×C13—21no—
107C23×C13—21no—
108C23×C13—21no—
109C23×C13—41no—
110C23×C13—41no—
111C23×C13—41no—
112C23×C13—41no—
113C23×C13C2×C22⋊C411yescharacteristic
114C23×C13#13512yes—
115Q8×C13—82no—
116D4×C13—44no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—41no—
123C2×C4×C13—42no—
124C2×C4×C13—41no—
125C2×C4×C13—41no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13—41no—
129C2×C4×C13—41no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13—41no—
136C2×C4×C13—41no—
137C2×C4×C13—41no—
138C2×C4×C13—41no—
139C2×C4×C13—81no—
140C2×C4×C13—81no—
141C2×C4×C13—81no—
142C2×C4×C13#9911yescharacteristic
143C2×C4×C13#9911yescharacteristic
144C2×C4×C13#10412yes—
145C2×Dic13—44no—
146C2×Dic13—82no—
147C2×Dic13—82no—
148#1055—82no—
149C2×C22⋊Q8Dic1311yescharacteristic, complemented
150C2×C4×D4C2×D1311yescharacteristic
151#431—261no—
152C2×#99—261no—
153#398Dic1311yescharacteristic, complemented
154#397—21no—
155#397C2×D1311yescharacteristic
156#395Dic1311yescharacteristic, complemented
157#394—21no—
158#393C2×D1311yescharacteristic
159#387—21no—
160#385—21no—
161#381Dic1311yescharacteristic, complemented
162C4×C22⋊C4—261no—
163#342—132no—
164#323—132no—
165#323—261no—
166C22×C13—21no—
167C22×C13—21no—
168C22×C13—22no—
169C22×C13—42no—
170C22×C13—41no—
171C22×C13—41no—
172C22×C13—41no—
173C22×C13—41no—
174C22×C13—41no—
175C22×C13—81no—
176C22×C13—81no—
177C22×C13—81no—
178C22×C13C2×#9911yescharacteristic
179C22×C13#41611yescharacteristic
180C22×C13C2×#10411yescharacteristic
181C4×C13—21no—
182C4×C13—21no—
183C4×C13—22no—
184C4×C13—41no—
185C4×C13—41no—
186C4×C13—41no—
187C4×C13—81no—
188C4×C13—81no—
189C4×C13—81no—
190C4×C13—81no—
191Dic13—84no—
192C22×Q8C2×Dic1311yescharacteristic
193C22×D4C22⋊D1311yescharacteristic
194C23×C4C2×Dic1311yescharacteristic
195C23×C4C22⋊D1311yescharacteristic
196C22⋊Q8—41no—
197C22⋊Q8—41no—
198C4×D4—41no—
199C4×D4—41no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4C2×Dic1311yescharacteristic
204C2×C4⋊C4C2×Dic1311yescharacteristic
205C2×C22⋊C4—21no—
206C2×C22⋊C4—21no—
207C2×C22⋊C4—21no—
208C2×C22⋊C4—21no—
209C2×C22⋊C4—262no—
210C2×C22⋊C4C22⋊D1311yescharacteristic
211C2×C22⋊C4C22×D1311yescharacteristic
212C2×C42—521no—
213C2×C42C22⋊D1311yescharacteristic
214C4⋊C8—521no—
215#99—264no—
216C22⋊C8—262no—
217C4×C8—521no—
218#95—21no—
219#95—21no—
220#95—21no—
221#95—21no—
222#95—21no—
223#95—521no—
224#95C2×Dic1311yescharacteristic
225#95C2×Dic1311yescharacteristic
226C2×C13—21no—
227C2×C13—21no—
228C2×C13—42no—
229C2×C13—81no—
230C2×C13#150111yescharacteristic
231C2×C13#212111yescharacteristic
232C2×C13#212911yescharacteristic
233C24C22⋊Dic1311yescharacteristic
234C24C2×C22⋊D1311yescharacteristic
235C2×Q8—41no—
236C2×Q8—81no—
237C2×D4—22no—
238C2×D4—22no—
239C2×D4—41no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—81no—
249C22×C4—81no—
250C22×C4—522no—
251C22×C4C22⋊Dic1311yescharacteristic
252C22×C4C22⋊Dic1311yescharacteristic
253C22×C4C22⋊Dic1311yescharacteristic
254C22×C4C22×Dic1311yescharacteristic
255C22×C4C2×C22⋊D1311yescharacteristic
256C2×C8—522no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—42no—
262C4⋊C4—81no—
263C22⋊C4—41no—
264C22⋊C4—41no—
265C22⋊C4—42no—
266C22⋊C4—42no—
267C22⋊C4—81no—
268C22⋊C4—81no—
269C22⋊C4—264no—
270C22⋊C4—522no—
271C42—21no—
272C42—21no—
273C42—1042no—
274C13#1173111yescharacteristic, complemented, Sylow
275C23—21no—
276C23—21no—
277C23—21no—
278C23—21no—
279C23—21no—
280C23—41no—
281C23—41no—
282C23—41no—
283C23—41no—
284C23#8820412yes—
285C23C2×C22⋊Dic1311yescharacteristic
286Q8—82no—
287D4—44no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—41no—
294C2×C4—42no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4—524no—
314C2×C4—1042no—
315C2×C4—1042no—
316C2×C4#8807411yescharacteristic
317C2×C4#8807411yescharacteristic
318C2×C4#8807712yes—
319C8—1042no—
320C22—21no—
321C22—21no—
322C22—22no—
323C22—42no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—81no—
330C22—81no—
331C22—81no—
332C22C2×#8807411yescharacteristic
333C22#1171889411yescharacteristic
334C22C2×#8807711yescharacteristic
335C4—21no—
336C4—21no—
337C4—22no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—81no—
342C4—81no—
343C4—81no—
344C4—81no—
345C4—1044no—
346C2—21no—
347C2—21no—
348C2—42no—
349C2—81no—
350C2#1311332711yescharacteristic
351C2#1311648211yescharacteristic
352C2#1311651111yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C22⋊C4C22×D13
FittingC13×#2638C2
socleC22×C13C2×#99
prime radicalC22×D4×C13D4
cosocleC2×C13×C22⋊C4C23
hypercenter#2638D13
hypocenterC13#11731
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2638

Complements

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

NH ≅ G/Ntype
3. #13112857C2semidirect
4. #13112836C2semidirect
6. C2×C13×C22⋊Q8C4semidirect
8. C13×#398C4semidirect
11. C13×#395C4semidirect
16. C13×#381C4semidirect
149. C2×C22⋊Q8Dic13semidirect
153. #398Dic13semidirect
156. #395Dic13semidirect
161. #381Dic13semidirect
274. C13#11731semidirect

Maximal subgroups

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

subgroupindex
C4×#880742
#131131572
#131128572
#131128362
C13×#26382
#1173113