Finite Group Databasebeta

← #16782449

Subgroups — #16782449

Order 3328.

556 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊#1057C211yesmaximal, characteristic
2#13130690C211yesmaximal, characteristic
3C2×#11718254C212yesmaximal, complemented
4#13129666C212yesmaximal, complemented
5C22⋊C8×Dic13C211yesmaximal, characteristic
6C23×#1057—21no—
7C22×C4×Dic13C2211yescharacteristic
8C2×C22⋊#1057—21no—
9C2×C4⋊#1057—21no—
10C2×C4⋊#1057—24no—
11C2×C4⋊#1057C2211yescharacteristic
12C2×C4⋊#1057C2211yescharacteristic
13C2×C4⋊#1057C2212yes—
14C2×C13×C22⋊C8C411yescharacteristic
15C2×C22⋊#1055C411yescharacteristic
16C2×C8×Dic13C2212yes—
17#11718290—21no—
18#11718254—24no—
19#11718142C412yes—
20C23×C4×C13C2×C411yescharacteristic
21C23×Dic13D411yescharacteristic
22C23×Dic13Q811yescharacteristic
23C22×#1057—24no—
24C22×#1057—22no—
25C22×#1057—21no—
26C22×#1057—21no—
27C22×#1057—42no—
28C22×#1057—42no—
29C22×C8×C13C2×C412yes—
30C2×C4×Dic13—22no—
31C2×C4×Dic13—22no—
32C2×C4×Dic13C2×C411yescharacteristic
33C2×C4×Dic13D411yescharacteristic
34C2×C4×Dic13Q811yescharacteristic
35C2×C4×Dic13C2311yescharacteristic
36C22×#1055C2×C412yes—
37C22⋊#1057—42no—
38C4⋊#1057—24no—
39C4⋊#1057—22no—
40C4⋊#1057—22no—
41C4⋊#1057—22no—
42C4⋊#1057D414yes—
43C13×C22⋊C8C814yescomplemented
44C22⋊#1055—22no—
45C8×Dic13—22no—
46C8×Dic13—22no—
47#8829—131nomaximal, Sylow
48C24×C13C4⋊C411yescharacteristic
49C22×C4×C13—22no—
50C22×C4×C13—22no—
51C22×C4×C13C4⋊C411yescharacteristic
52C22×C4×C13C2×C812yes—
53C22×C4×C13M1612yes—
54C22×C4×C13C22×C411yescharacteristic
55C22×Dic13—21no—
56C22×Dic13—21no—
57C22×Dic13—21no—
58C22×Dic13—21no—
59C22×Dic13—22no—
60C22×Dic13—22no—
61C22×Dic13—41no—
62C22×Dic13C4⋊C411yescharacteristic
63C22×Dic13C4⋊C411yescharacteristic
64C22×Dic13D812yes—
65C22×Dic13Q1612yes—
66C22×Dic13C2×D411yescharacteristic
67C22×Dic13C2×Q811yescharacteristic
68C2×#1057—24no—
69C2×#1057—48no—
70C2×#1057—42no—
71C2×#1057—42no—
72C2×#1057—41no—
73C2×#1057—41no—
74C2×#1057—41no—
75C2×#1057—41no—
76C2×#1057—41no—
77C2×#1057—41no—
78C2×C8×C13—22no—
79C2×C8×C13—22no—
80C2×C8×C13C2×C814yescomplemented
81C4×Dic13—22no—
82C4×Dic13—21no—
83C4×Dic13—22no—
84C4×Dic13—21no—
85C4×Dic13C2×D412yes—
86C4×Dic13#4112yes—
87C2×#1055—22no—
88C2×#1055—22no—
89C2×#1055—22no—
90C22×C4⋊C8—131no—
91#1797—131no—
92C4×C22⋊C8—131no—
93C2×#335—132no—
94#1277—132no—
95C23×C13—21no—
96C23×C13—21no—
97C23×C13—21no—
98C23×C13—21no—
99C23×C13C4⋊C812yes—
100C23×C13#10712yes—
101C23×C13#10812yes—
102C23×C13C2×C4⋊C411yescharacteristic
103C2×C4×C13—21no—
104C2×C4×C13—21no—
105C2×C4×C13—24no—
106C2×C4×C13—24no—
107C2×C4×C13C4⋊C812yes—
108C2×C4×C13C4×D412yes—
109C2×C4×C13C22×C811yescharacteristic
110C2×C4×C13C2×M1611yescharacteristic
111C2×C4×C13#13112yes—
112C2×Dic13—21no—
113C2×Dic13—21no—
114C2×Dic13—21no—
115C2×Dic13—21no—
116C2×Dic13—22no—
117C2×Dic13—22no—
118C2×Dic13—22no—
119C2×Dic13—22no—
120C2×Dic13—21no—
121C2×Dic13—21no—
122C2×Dic13—21no—
123C2×Dic13—44no—
124C2×Dic13#10712yes—
125C2×Dic13#12011yescharacteristic
126C2×Dic13C22⋊Q812yes—
127C2×Dic13#12311yescharacteristic
128C2×Dic13C2×D811yescharacteristic
129C2×Dic13C2×Q1611yescharacteristic
130C2×Dic13AGL(1,ℤ/8)11yescharacteristic
131C2×Dic13#13711yescharacteristic
132#1057—44no—
133#1057—81no—
134#1057—81no—
135C8×C13—24no—
136#1055—42no—
137C23×C8—261no—
138C22×C42—131no—
139C2×C4⋊C8—132no—
140C2×C4⋊C8—131no—
141C2×C4⋊C8—131no—
142C2×C4⋊C8—264no—
143C2×C4⋊C8—261no—
144C2×C22⋊C8—131no—
145C2×C22⋊C8—261no—
146C2×C22⋊C8#26111yescharacteristic
147C2×C4×C8—132no—
148#336—132no—
149#336—261no—
150#335—264no—
151C22×C13—22no—
152C22×C13—22no—
153C22×C13—22no—
154C22×C13—22no—
155C22×C13—22no—
156C22×C13—22no—
157C22×C13#33514yescomplemented
158C22×C13#38511yescharacteristic
159C22×C13C2×C4⋊C811yescharacteristic
160C22×C13#42411yescharacteristic
161C22×C13C2×#10711yescharacteristic
162C22×C13#42811yescharacteristic
163C22×C13C2×#10811yescharacteristic
164C22×C13#43011yescharacteristic
165C4×C13—22no—
166C4×C13C8×D412yes—
167C4×C13#43512yes—
168Dic13—22no—
169Dic13—22no—
170Dic13—41no—
171Dic13#44711yescharacteristic
172Dic13#45111yescharacteristic
173Dic13#48011yescharacteristic
174Dic13#48411yescharacteristic
175C23×C4—131no—
176C23×C4—131no—
177C23×C4C2×#26111yescharacteristic
178C22×C8—132no—
179C22×C8—262no—
180C22×C8—264no—
181C22×C8—261no—
182C22×C8—261no—
183C22×C8—522no—
184C22×C8—522no—
185C22×C8C2×#26112yes—
186C2×C42—131no—
187C2×C42—131no—
188C2×C42—131no—
189C2×C42—131no—
190C2×C42—262no—
191C2×C42—262no—
192C4⋊C8—134no—
193C4⋊C8—262no—
194C4⋊C8—262no—
195C4⋊C8—262no—
196C4⋊C8—264no—
197C22⋊C8—262no—
198C22⋊C8—522no—
199C22⋊C8#105714yescomplemented
200C4×C8—262no—
201C4×C8—262no—
202C2×C13—24no—
203C2×C13C2×#33511yescharacteristic
204C2×C13#156511yescharacteristic
205C2×C13#157111yescharacteristic
206C2×C13#157311yescharacteristic
207C2×C13#185011yescharacteristic
208C2×C13#185211yescharacteristic
209C2×C13#185511yescharacteristic
210C24C4⋊#26111yescharacteristic
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—131no—
214C22×C4—132no—
215C22×C4—132no—
216C22×C4—131no—
217C22×C4—131no—
218C22×C4—131no—
219C22×C4—261no—
220C22×C4—261no—
221C22×C4—261no—
222C22×C4—261no—
223C22×C4—262no—
224C22×C4—262no—
225C22×C4—521no—
226C22×C4#611812yes—
227C22×C4C4⋊#26111yescharacteristic
228C22×C4C2×#105712yes—
229C22×C4C22×#26111yescharacteristic
230C2×C8—22no—
231C2×C8—22no—
232C2×C8—264no—
233C2×C8—262no—
234C2×C8—262no—
235C2×C8—262no—
236C2×C8—522no—
237C2×C8—522no—
238C2×C8—528no—
239C2×C8—521no—
240C2×C8—521no—
241C2×C8—521no—
242C2×C8—521no—
243C2×C8—521no—
244C2×C8—521no—
245C2×C8C2×#105714yescomplemented
246C42—132no—
247C42—132no—
248C42—261no—
249C42—261no—
250C42—262no—
251C42—262no—
252C13#882911yescharacteristic, complemented, Sylow
253C23—21no—
254C23—21no—
255C23—21no—
256C23—21no—
257C23#8810212yes—
258C23#8810412yes—
259C23C4⋊#105712yes—
260C23C2×C4⋊#26111yescharacteristic
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—24no—
264C2×C4—24no—
265C2×C4—131no—
266C2×C4—131no—
267C2×C4—131no—
268C2×C4—131no—
269C2×C4—131no—
270C2×C4—131no—
271C2×C4—132no—
272C2×C4—132no—
273C2×C4—262no—
274C2×C4—262no—
275C2×C4—262no—
276C2×C4—262no—
277C2×C4—261no—
278C2×C4—261no—
279C2×C4—261no—
280C2×C4—261no—
281C2×C4—261no—
282C2×C4—261no—
283C2×C4—261no—
284C2×C4—524no—
285C2×C4C4⋊#105712yes—
286C2×C4C2×#611811yescharacteristic
287C2×C4#8823812yes—
288C2×C4D4×#26112yes—
289C2×C4C22×#105711yescharacteristic
290C8—24no—
291C8—524no—
292C8—522no—
293C8—1041no—
294C8—1041no—
295C22—22no—
296C22—22no—
297C22—22no—
298C22—22no—
299C22—22no—
300C22—22no—
301C22#1171825414yescomplemented
302C22#1171906711yescharacteristic
303C22#1171907011yescharacteristic
304C22C2×#8810211yescharacteristic
305C22C2×#8810411yescharacteristic
306C22#1171909811yescharacteristic
307C22#1171910011yescharacteristic
308C22C2×C4⋊#105711yescharacteristic
309C4—22no—
310C4—131no—
311C4—131no—
312C4—131no—
313C4—131no—
314C4—262no—
315C4—262no—
316C4—521no—
317C4#1171906412yes—
318C4D4×#105712yes—
319C2—24no—
320C2C2×#1171825411yescharacteristic
321C2#1313038711yescharacteristic
322C2#1313040511yescharacteristic
323C2#1313041111yescharacteristic
324C2#1313077911yescharacteristic
325C2#1313078511yescharacteristic
326C2#1313078811yescharacteristic
subgroupG/H
centerC23C2×C4⋊#261
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
FittingC2×C13×C22⋊C8C4
socleC23×C13C2×C4⋊C4
prime radicalC24×C13C4⋊C4
cosocleC2×C4×Dic13C23
hypercenterC2×C22⋊C8#261
hypocenterC13#8829
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
3. C2×#11718254C2semidirect
4. #13129666C2semidirect
43. C13×C22⋊C8C8semidirect
80. C2×C8×C13C2×C8semidirect
157. C22×C13#335semidirect
199. C22⋊C8#1057semidirect
245. C2×C8C2×#1057semidirect
252. C13#8829semidirect
301. C22#11718254semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊#10572
#131306902
C2×#117182542
#131296662
C22⋊C8×Dic132
#882913