Finite Group Databasebeta

← #15773498

Subgroups — #15773498

Order 3328.

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

normal subgroups only

This group has 446 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×#88076C211yesmaximal, characteristic, complemented
2#13113180C211yesmaximal, characteristic, complemented
3#13112842C212yesmaximal, complemented
4#13112839C212yesmaximal
5C13×#2536C211yesmaximal, characteristic
6C2×C13×C22⋊Q8—21no—
7C2×C4×Q8×C13C2211yescharacteristic
8C2×C4×D4×C13C411yescharacteristic
9C13×#398C411yescharacteristic
10C13×#398C2211yescharacteristic
11C13×#394C411yescharacteristic
12C13×#394C2211yescharacteristic
13C13×#388—21no—
14C13×#388—21no—
15C13×#382C411yescharacteristic
16C13×#380—21no—
17C2×#88076—21no—
18#11718587—21no—
19C4×#6099—21no—
20#11718122C2212yes—
21#11718120—21no—
22#11718120C2212yes—
23C22×Q8×C13D411yescharacteristic
24C22×D4×C13C2×C411yescharacteristic
25C23×C4×C13—21no—
26C13×C22⋊Q8—44no—
27C4×Q8×C13—41no—
28C4×Q8×C13—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×C4⋊C4D411yescharacteristic
37C2×C13×C4⋊C4C2311yescharacteristic
38C2×C13×C22⋊C4—21no—
39C2×C13×C22⋊C4—21no—
40C2×C13×C22⋊C4—21no—
41C2×C13×C22⋊C4—21no—
42C2×C13×C22⋊C4—21no—
43C2×C42×C13C2×C411yescharacteristic
44C2×C42×C13D411yescharacteristic
45C2×C42×C13D411yescharacteristic
46C2×#6099—22no—
47C13×#95—21no—
48C13×#95—21no—
49C13×#95—21no—
50C13×#95C2×C411yescharacteristic
51C13×#95C2×C411yescharacteristic
52#88076—24no—
53C22⋊#1055—22no—
54C4⋊#1055—41no—
55#88043—41no—
56#88043—41no—
57C4×#1055—41no—
58#11778—131nomaximal, Sylow
59C24×C13—21no—
60C2×Q8×C13—22no—
61C2×Q8×C13—22no—
62C2×Q8×C13—41no—
63C2×D4×C13—41no—
64C2×D4×C13—42no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13—42no—
69C22×C4×C13—42no—
70C22×C4×C13—42no—
71C22×C4×C13C22⋊C411yescharacteristic
72C22×C4×C13C22⋊C411yescharacteristic
73C22×C4×C13C22⋊C411yescharacteristic
74C22×C4×C13C22⋊C411yescharacteristic
75C22×C4×C13C22×C411yescharacteristic
76C22×C4×C13C2×D411yescharacteristic
77C22×C4×C13C2×D411yescharacteristic
78C13×C4⋊C4—41no—
79C13×C4⋊C4—41no—
80C13×C4⋊C4—41no—
81C13×C4⋊C4—41no—
82C13×C4⋊C4—42no—
83C13×C4⋊C4—42no—
84C13×C4⋊C4—42no—
85C13×C22⋊C4—42no—
86C13×C22⋊C4—42no—
87C13×C22⋊C4—42no—
88C13×C22⋊C4—41no—
89C13×C22⋊C4—41no—
90C13×C22⋊C4—42no—
91C42×C13—21no—
92C42×C13—21no—
93C42×C13—21no—
94C42×C13—21no—
95C42×C13—21no—
96C42×C13—21no—
97#6099—24no—
98#6099—42no—
99C2×#1055—42no—
100C2×#1055—42no—
101#2536D1311yescharacteristic
102C4×#101—131no—
103#1467—131no—
104#1346—132no—
105#1345—132no—
106C23×C13—22no—
107C23×C13—41no—
108C23×C13—41no—
109C23×C13—41no—
110C23×C13—41no—
111C23×C13—41no—
112C23×C13—41no—
113C23×C13C2×C22⋊C411yescharacteristic
114Q8×C13—44no—
115D4×C13—42no—
116D4×C13—42no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
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—84no—
141C2×C4×C13#9911yescharacteristic
142C2×C4×C13#9911yescharacteristic
143C2×C4×C13#10412yes—
144C2×C4×C13AGL(1,ℤ/8)12yes—
145#1055—44no—
146#1055—82no—
147C2×C22⋊Q8—21no—
148C2×C4×Q8C2×D1311yescharacteristic
149C2×C4×D4Dic1311yescharacteristic
150#432—261no—
151C2×#101—261no—
152C4×M16—261no—
153#398Dic1311yescharacteristic
154#398C2×D1311yescharacteristic
155#394Dic1311yescharacteristic
156#394C2×D1311yescharacteristic
157#388—21no—
158#388—21no—
159#382Dic1311yescharacteristic
160#380—21no—
161#343—132no—
162#324—132no—
163#324—261no—
164C22×C13—21no—
165C22×C13—21no—
166C22×C13—42no—
167C22×C13—42no—
168C22×C13—42no—
169C22×C13—81no—
170C22×C13—81no—
171C22×C13—81no—
172C22×C13—81no—
173C22×C13C2×#9911yescharacteristic
174C22×C13#41811yescharacteristic
175C22×C13C2×#10411yescharacteristic
176C4×C13—21no—
177C4×C13—21no—
178C4×C13—22no—
179C4×C13—22no—
180C4×C13—41no—
181C4×C13—41no—
182C4×C13—41no—
183C4×C13—41no—
184C4×C13—81no—
185C4×C13—81no—
186C4×C13—81no—
187C22×Q8C22⋊D1311yescharacteristic
188C22×D4C2×Dic1311yescharacteristic
189C23×C4—21no—
190C2×M16—262no—
191C22⋊Q8—44no—
192C4×Q8—41no—
193C4×Q8—41no—
194C4×D4—41no—
195C4×D4—41no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4C2×Dic1311yescharacteristic
200C2×C4⋊C4C2×Dic1311yescharacteristic
201C2×C4⋊C4C22⋊D1311yescharacteristic
202C2×C4⋊C4C22×D1311yescharacteristic
203C2×C22⋊C4—21no—
204C2×C22⋊C4—21no—
205C2×C22⋊C4—21no—
206C2×C22⋊C4—21no—
207C2×C22⋊C4—21no—
208C2×C42C2×Dic1311yescharacteristic
209C2×C42C22⋊D1311yescharacteristic
210C2×C42C22⋊D1311yescharacteristic
211C4⋊C8—521no—
212#101—264no—
213C22⋊C8—262no—
214#97—521no—
215#97—521no—
216C4×C8—521no—
217#95—21no—
218#95—21no—
219#95—21no—
220#95C2×Dic1311yescharacteristic
221#95C2×Dic1311yescharacteristic
222C2×C13—21no—
223C2×C13—21no—
224C2×C13—82no—
225C2×C13#150711yescharacteristic
226C2×C13#212011yescharacteristic
227C2×C13#213311yescharacteristic
228C24—21no—
229C2×Q8—22no—
230C2×Q8—22no—
231C2×Q8—41no—
232C2×D4—41no—
233C2×D4—42no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—42no—
238C22×C4—42no—
239C22×C4—42no—
240C22×C4C22⋊Dic1311yescharacteristic
241C22×C4C22⋊Dic1311yescharacteristic
242C22×C4C22⋊Dic1311yescharacteristic
243C22×C4C22⋊Dic1311yescharacteristic
244C22×C4C22×Dic1311yescharacteristic
245C22×C4C2×C22⋊D1311yescharacteristic
246C22×C4C2×C22⋊D1311yescharacteristic
247M16—264no—
248M16—522no—
249C2×C8—522no—
250C2×C8—522no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—42no—
256C4⋊C4—42no—
257C4⋊C4—42no—
258C22⋊C4—42no—
259C22⋊C4—42no—
260C22⋊C4—42no—
261C22⋊C4—41no—
262C22⋊C4—41no—
263C22⋊C4—42no—
264C42—21no—
265C42—21no—
266C42—21no—
267C42—21no—
268C42—21no—
269C42—21no—
270C13#1177811yescharacteristic, complemented, Sylow
271C23—22no—
272C23—41no—
273C23—41no—
274C23—41no—
275C23—41no—
276C23—41no—
277C23—41no—
278C23C2×C22⋊Dic1311yescharacteristic
279Q8—44no—
280D4—42no—
281D4—42no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
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—84no—
306C2×C4#8807411yescharacteristic
307C2×C4#8807411yescharacteristic
308C2×C4#8807712yes—
309C2×C4#8818612yes—
310C8—524no—
311C8—1042no—
312C22—21no—
313C22—21no—
314C22—42no—
315C22—42no—
316C22—42no—
317C22—81no—
318C22—81no—
319C22—81no—
320C22—81no—
321C22#1171887611yescharacteristic
322C22C2×#8807411yescharacteristic
323C22C2×#8807711yescharacteristic
324C4—22no—
325C4—22no—
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—81no—
333C4—81no—
334C4—81no—
335C2—21no—
336C2—21no—
337C2—82no—
338C2#1311335211yescharacteristic
339C2#1311647711yescharacteristic
340C2#1311652511yescharacteristic
subgroupG/H
centerC22C2×#88074
commutatorC22×C4×C13C22×C4
FrattiniC2×C4⋊C4C22×D13
FittingC13×#2536C2
socleC22×C13C2×#99
prime radicalC22×D4×C13C2×C4
cosocleC2×C13×C4⋊C4C23
hypercenter#2536D13
hypocenterC13#11778
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2536

Complements

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

NH ≅ G/Ntype
1. C4×#88076C2semidirect
2. #13113180C2semidirect
3. #13112842C2semidirect
270. C13#11778semidirect

Maximal subgroups

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

subgroupindex
C4×#880762
#131131802
#131128422
#131128392
C13×#25362
#1177813