Finite Group Databasebeta

← #15773667

Subgroups — #15773667

Order 3328.

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

normal subgroups only

This group has 386 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#13114916C211yesmaximal, characteristic
2#13113166C211yesmaximal, characteristic
3#13112866C212yesmaximal, complemented
4#13112863C212yesmaximal, complemented
5C13×#2627C211yesmaximal, characteristic
6C2×C13×C22⋊Q8C411yescharacteristic
7C22×C13×C4⋊C4C2211yescharacteristic
8C13×#400C411yescharacteristic
9C13×#400C2211yescharacteristic
10C13×#398—21no—
11C13×#398—21no—
12C13×#395C411yescharacteristic
13C13×#395C2211yescharacteristic
14C13×#385—21no—
15C13×#381—21no—
16C13×#380C411yescharacteristic
17#11718868—21no—
18#11718868—21no—
19#11718122—21no—
20#11718122C2212yes—
21#11718120—21no—
22#11718120C2212yes—
23C22×Q8×C13C2×C411yescharacteristic
24C23×C4×C13C2×C411yescharacteristic
25C23×C4×C13D411yescharacteristic
26C23×C4×C13D411yescharacteristic
27C13×C22⋊Q8—41no—
28C13×C22⋊Q8—41no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4—41no—
34C2×C13×C4⋊C4—41no—
35C2×C13×C4⋊C4C2×C411yescharacteristic
36C2×C13×C4⋊C4C2×C411yescharacteristic
37C2×C13×C4⋊C4D411yescharacteristic
38C2×C13×C4⋊C4D411yescharacteristic
39C2×C13×C4⋊C4C2311yescharacteristic
40C2×C13×C22⋊C4—21no—
41C2×C13×C22⋊C4—21no—
42C2×#6099—22no—
43C2×#6099—41no—
44C13×#95—21no—
45C13×#95—21no—
46C13×#95—21no—
47C13×#95—21no—
48C13×#95—21no—
49C13×#95—21no—
50C13×#95C2×C411yescharacteristic
51C13×#95C2×C411yescharacteristic
52C22⋊#1055—22no—
53C22⋊#1055—41no—
54C22⋊#1055—41no—
55C22⋊#1055—41no—
56#11817—131nomaximal, Sylow
57C24×C13C22⋊C411yescharacteristic
58C2×Q8×C13—41no—
59C2×Q8×C13—81no—
60C22×C4×C13—21no—
61C22×C4×C13—21no—
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13—22no—
67C22×C4×C13—21no—
68C22×C4×C13—21no—
69C22×C4×C13—21no—
70C22×C4×C13—21no—
71C22×C4×C13—41no—
72C22×C4×C13—81no—
73C22×C4×C13—81no—
74C22×C4×C13C22⋊C411yescharacteristic
75C22×C4×C13C22⋊C411yescharacteristic
76C22×C4×C13C22⋊C411yescharacteristic
77C22×C4×C13C22×C411yescharacteristic
78C22×C4×C13C2×D411yescharacteristic
79C22×C4×C13C2×D411yescharacteristic
80C13×C4⋊C4—41no—
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×C4⋊C4—81no—
88C13×C4⋊C4—81no—
89C13×C22⋊C4—42no—
90C13×C22⋊C4—41no—
91C13×C22⋊C4—41no—
92#6099—42no—
93#6099—42no—
94#6099—82no—
95C2×#1055—42no—
96C2×#1055—42no—
97#2627D1311yescharacteristic
98#1821—131no—
99#1463—131no—
100#1354—132no—
101#1353—132no—
102C23×C13—21no—
103C23×C13—21no—
104C23×C13—41no—
105C23×C13—41no—
106C23×C13#9911yescharacteristic
107C23×C13#9911yescharacteristic
108C23×C13C2×C22⋊C411yescharacteristic
109Q8×C13—82no—
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—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—42no—
120C2×C4×C13—42no—
121C2×C4×C13—42no—
122C2×C4×C13—41no—
123C2×C4×C13—41no—
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—42no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13—41no—
136C2×C4×C13—41no—
137C2×C4×C13—81no—
138C2×C4×C13—81no—
139C2×C4×C13—81no—
140C2×C4×C13#13712yes—
141#1055—82no—
142#1055—82no—
143C2×C22⋊Q8Dic1311yescharacteristic
144C22×C4⋊C4C2×D1311yescharacteristic
145#407—261no—
146#407—261no—
147#400Dic1311yescharacteristic
148#400C2×D1311yescharacteristic
149#398—21no—
150#398—21no—
151#395Dic1311yescharacteristic
152#395C2×D1311yescharacteristic
153#385—21no—
154#381—21no—
155#380Dic1311yescharacteristic
156#343—132no—
157#343—261no—
158#324—132no—
159#324—261no—
160C22×C13—21no—
161C22×C13—21no—
162C22×C13—21no—
163C22×C13—21no—
164C22×C13—21no—
165C22×C13—21no—
166C22×C13—21no—
167C22×C13—21no—
168C22×C13—42no—
169C22×C13—42no—
170C22×C13C2×#9911yescharacteristic
171C22×C13#41911yescharacteristic
172C22×C13#42111yescharacteristic
173C4×C13—22no—
174C4×C13—41no—
175C4×C13—41no—
176C4×C13—41no—
177C4×C13—41no—
178C4×C13—41no—
179C4×C13—81no—
180C4×C13—81no—
181C4×C13—81no—
182C4×C13—81no—
183C22×Q8C2×Dic1311yescharacteristic
184C23×C4C2×Dic1311yescharacteristic
185C23×C4C22⋊D1311yescharacteristic
186C23×C4C22⋊D1311yescharacteristic
187C2×M16—262no—
188C2×M16—521no—
189C22⋊Q8—41no—
190C22⋊Q8—41no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—41no—
196C2×C4⋊C4—41no—
197C2×C4⋊C4C2×Dic1311yescharacteristic
198C2×C4⋊C4C2×Dic1311yescharacteristic
199C2×C4⋊C4C22⋊D1311yescharacteristic
200C2×C4⋊C4C22⋊D1311yescharacteristic
201C2×C4⋊C4C22×D1311yescharacteristic
202C2×C22⋊C4—21no—
203C2×C22⋊C4—21no—
204C22⋊C8—262no—
205C22⋊C8—521no—
206C22⋊C8—521no—
207C22⋊C8—521no—
208#95—21no—
209#95—21no—
210#95—21no—
211#95—21no—
212#95—21no—
213#95—21no—
214#95C2×Dic1311yescharacteristic
215#95C2×Dic1311yescharacteristic
216C2×C13—21no—
217C2×C13—21no—
218C2×C13—41no—
219C2×C13—41no—
220C2×C13#151111yescharacteristic
221C2×C13#212111yescharacteristic
222C2×C13#213311yescharacteristic
223C24C22⋊Dic1311yescharacteristic
224C2×Q8—41no—
225C2×Q8—81no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—22no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—41no—
238C22×C4—81no—
239C22×C4—81no—
240C22×C4C22⋊Dic1311yescharacteristic
241C22×C4C22⋊Dic1311yescharacteristic
242C22×C4C22⋊Dic1311yescharacteristic
243C22×C4C22×Dic1311yescharacteristic
244C22×C4C2×C22⋊D1311yescharacteristic
245C22×C4C2×C22⋊D1311yescharacteristic
246M16—522no—
247M16—522no—
248M16—1042no—
249C2×C8—522no—
250C2×C8—522no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—42no—
257C4⋊C4—81no—
258C4⋊C4—81no—
259C4⋊C4—81no—
260C22⋊C4—42no—
261C22⋊C4—41no—
262C22⋊C4—41no—
263C13#1181711yescharacteristic, complemented, Sylow
264C23—21no—
265C23—21no—
266C23—41no—
267C23—41no—
268C23#8807411yescharacteristic
269C23#8807411yescharacteristic
270C23C2×C22⋊Dic1311yescharacteristic
271Q8—82no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—42no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4—81no—
302C2×C4#8819612yes—
303C8—1042no—
304C8—1042no—
305C22—21no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22—21no—
312C22—21no—
313C22—42no—
314C22—42no—
315C22C2×#8807411yescharacteristic
316C22#1171888611yescharacteristic
317C22#1171889711yescharacteristic
318C4—22no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—81no—
325C4—81no—
326C4—81no—
327C4—81no—
328C2—21no—
329C2—21no—
330C2—41no—
331C2—41no—
332C2#1311336911yescharacteristic
333C2#1311648211yescharacteristic
334C2#1311652511yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2627C2
socleC22×C13C2×#99
prime radicalC24×C13C22⋊C4
cosocleC2×C13×C4⋊C4C23
hypercenter#2627D13
hypocenterC13#11817
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ #2627

Complements

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

NH ≅ G/Ntype
3. #13112866C2semidirect
4. #13112863C2semidirect
263. C13#11817semidirect

Maximal subgroups

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

subgroupindex
#131149162
#131131662
#131128662
#131128632
C13×#26272
#1181713