Finite Group Databasebeta

← #15773750

Subgroups — #15773750

Order 3328.

400 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 87 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#13114828C211yesmaximal, characteristic
2#13113174C211yesmaximal, characteristic
3#13112866C212yesmaximal, complemented
4#13112842C212yesmaximal, complemented
5C13×#2638C211yesmaximal, characteristic
6C2×C13×C22⋊Q8C411yescharacteristic
7C2×C4×D4×C13C2211yescharacteristic
8C13×#398C2211yescharacteristic
9C13×#397—21no—
10C13×#397C411yescharacteristic
11C13×#395C2211yescharacteristic
12C13×#394—21no—
13C13×#393C411yescharacteristic
14C13×#387—21no—
15C13×#385—21no—
16C13×#381C411yescharacteristic
17C2×#88073—21no—
18#11718868—21no—
19#11718585—21no—
20#11718122C2212yes—
21#11718120C2212yes—
22#11718117—21no—
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⋊C4C2311yescharacteristic
36C2×C13×C22⋊C4—21no—
37C2×C13×C22⋊C4—21no—
38C2×C13×C22⋊C4—21no—
39C2×C13×C22⋊C4—21no—
40C2×C13×C22⋊C4C2×C411yescharacteristic
41C2×C13×C22⋊C4D411yescharacteristic
42C2×C42×C13D411yescharacteristic
43C2×#6099—22no—
44C2×#6099—41no—
45C13×#95—21no—
46C13×#95—21no—
47C13×#95—21no—
48C13×#95—21no—
49C13×#95—21no—
50C13×#95C2×C411yescharacteristic
51C13×#95C2×C411yescharacteristic
52#88073—42no—
53C22⋊#1055—22no—
54C22⋊#1055—41no—
55C4⋊#1055—41no—
56C4⋊#1055—41no—
57#11834—131nomaximal, Sylow
58C24×C13C22⋊C411yescharacteristic
59C24×C13C22⋊C411yescharacteristic
60C2×Q8×C13—41no—
61C2×Q8×C13—81no—
62C2×D4×C13—21no—
63C2×D4×C13—21no—
64C2×D4×C13—41no—
65C2×D4×C13—41no—
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—21no—
74C22×C4×C13—81no—
75C22×C4×C13—81no—
76C22×C4×C13C22⋊C411yescharacteristic
77C22×C4×C13C22⋊C411yescharacteristic
78C22×C4×C13C22×C411yescharacteristic
79C22×C4×C13C2×D411yescharacteristic
80C22×C4×C13C2×D411yescharacteristic
81C13×C4⋊C4—41no—
82C13×C4⋊C4—41no—
83C13×C4⋊C4—41no—
84C13×C4⋊C4—41no—
85C13×C4⋊C4—41no—
86C13×C4⋊C4—41no—
87C13×C4⋊C4—81no—
88C13×C22⋊C4—41no—
89C13×C22⋊C4—41no—
90C13×C22⋊C4—42no—
91C13×C22⋊C4—42no—
92C13×C22⋊C4—81no—
93C13×C22⋊C4—81no—
94C42×C13—21no—
95C42×C13—21no—
96#6099—42no—
97#6099—42no—
98#6099—82no—
99C2×#1055—42no—
100C2×#1055—42no—
101#2638D1311yescharacteristic
102#1800—131no—
103#1465—131no—
104#1354—132no—
105#1346—132no—
106C23×C13—21no—
107C23×C13—21no—
108C23×C13—21no—
109C23×C13—21no—
110C23×C13—21no—
111C23×C13—21no—
112C23×C13—41no—
113C23×C13—41no—
114C23×C13—41no—
115C23×C13—41no—
116C23×C13C2×C22⋊C411yescharacteristic
117Q8×C13—82no—
118D4×C13—42no—
119D4×C13—42no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—41no—
126C2×C4×C13—42no—
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—41no—
140C2×C4×C13—41no—
141C2×C4×C13—41no—
142C2×C4×C13—81no—
143C2×C4×C13—81no—
144C2×C4×C13—81no—
145C2×C4×C13#9911yescharacteristic
146C2×C4×C13#9911yescharacteristic
147C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
148C2×C4×C13#13711yescharacteristic
149#1055—82no—
150#1055—82no—
151C2×C22⋊Q8Dic1311yescharacteristic
152C2×C4×D4C2×D1311yescharacteristic
153#423—261no—
154C2×#100—261no—
155#407—261no—
156#398C2×D1311yescharacteristic
157#397—21no—
158#397Dic1311yescharacteristic
159#395C2×D1311yescharacteristic
160#394—21no—
161#393Dic1311yescharacteristic
162#387—21no—
163#385—21no—
164#381Dic1311yescharacteristic
165#343—132no—
166#324—132no—
167#323—261no—
168C22×C13—21no—
169C22×C13—21no—
170C22×C13—42no—
171C22×C13—41no—
172C22×C13—41no—
173C22×C13—41no—
174C22×C13—41no—
175C22×C13—41no—
176C22×C13—41no—
177C22×C13—81no—
178C22×C13—81no—
179C22×C13—81no—
180C22×C13C2×#9911yescharacteristic
181C22×C13#41711yescharacteristic
182C22×C13#42111yescharacteristic
183C4×C13—21no—
184C4×C13—21no—
185C4×C13—21no—
186C4×C13—21no—
187C4×C13—41no—
188C4×C13—41no—
189C4×C13—41no—
190C4×C13—81no—
191C4×C13—81no—
192C4×C13—81no—
193C4×C13—81no—
194C22×Q8C2×Dic1311yescharacteristic
195C22×D4C22⋊D1311yescharacteristic
196C23×C4C2×Dic1311yescharacteristic
197C23×C4C22⋊D1311yescharacteristic
198C2×M16—262no—
199C2×M16—521no—
200C22⋊Q8—41no—
201C22⋊Q8—41no—
202C4×D4—41no—
203C4×D4—41no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4C2×Dic1311yescharacteristic
208C2×C4⋊C4C22×D1311yescharacteristic
209C2×C22⋊C4—21no—
210C2×C22⋊C4—21no—
211C2×C22⋊C4—21no—
212C2×C22⋊C4—21no—
213C2×C22⋊C4C2×Dic1311yescharacteristic
214C2×C22⋊C4C22⋊D1311yescharacteristic
215C2×C42C22⋊D1311yescharacteristic
216C4⋊C8—521no—
217C4⋊C8—521no—
218#100—522no—
219C22⋊C8—262no—
220C22⋊C8—521no—
221#95—21no—
222#95—21no—
223#95—21no—
224#95—21no—
225#95—21no—
226#95C2×Dic1311yescharacteristic
227#95C2×Dic1311yescharacteristic
228C2×C13—21no—
229C2×C13—21no—
230C2×C13—81no—
231C2×C13—81no—
232C2×C13#151311yescharacteristic
233C2×C13#212111yescharacteristic
234C2×C13#213511yescharacteristic
235C24C22⋊Dic1311yescharacteristic
236C24C22⋊Dic1311yescharacteristic
237C2×Q8—41no—
238C2×Q8—81no—
239C2×D4—21no—
240C2×D4—21no—
241C2×D4—41no—
242C2×D4—41no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—81no—
252C22×C4—81no—
253C22×C4C22⋊Dic1311yescharacteristic
254C22×C4C22⋊Dic1311yescharacteristic
255C22×C4C22×Dic1311yescharacteristic
256C22×C4C2×C22⋊D1311yescharacteristic
257C22×C4C2×C22⋊D1311yescharacteristic
258M16—522no—
259M16—522no—
260M16—1042no—
261C2×C8—522no—
262C2×C8—522no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—81no—
270C22⋊C4—41no—
271C22⋊C4—41no—
272C22⋊C4—42no—
273C22⋊C4—42no—
274C22⋊C4—81no—
275C22⋊C4—81no—
276C42—21no—
277C42—21no—
278C13#1183411yescharacteristic, complemented, Sylow
279C23—21no—
280C23—21no—
281C23—21no—
282C23—21no—
283C23—21no—
284C23—21no—
285C23—41no—
286C23—41no—
287C23—41no—
288C23—41no—
289C23C2×C22⋊Dic1311yescharacteristic
290Q8—82no—
291D4—42no—
292D4—42no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—41no—
299C2×C4—42no—
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—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4#8807411yescharacteristic
319C2×C4#8807411yescharacteristic
320C2×C4#8820311yescharacteristic
321C2×C4#8820511yescharacteristic
322C8—1042no—
323C8—1042no—
324C22—21no—
325C22—21no—
326C22—42no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—81no—
334C22—81no—
335C22—81no—
336C22C2×#8807411yescharacteristic
337C22#1171889311yescharacteristic
338C22#1171889711yescharacteristic
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—81no—
347C4—81no—
348C4—81no—
349C4—81no—
350C2—21no—
351C2—21no—
352C2—81no—
353C2—81no—
354C2#1311337911yescharacteristic
355C2#1311648211yescharacteristic
356C2#1311653111yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2638C2
socleC22×C13C2×#99
prime radicalC22×D4×C13D4
cosocleC2×C13×C4⋊C4C23
hypercenter#2638D13
hypocenterC13#11834
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. #13112866C2semidirect
4. #13112842C2semidirect
278. C13#11834semidirect

Maximal subgroups

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

subgroupindex
#131148282
#131131742
#131128662
#131128422
C13×#26382
#1183413