Finite Group Databasebeta

← #16785035

Subgroups — #16785035

Order 3328.

476 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C4⋊#1057C211yesmaximal, characteristic
2C4×C4⋊#1057C211yesmaximal, characteristic
3#13129672C212yesmaximal
4#13129672C212yesmaximal
5#13117391C211yesmaximal, characteristic
6C2×#88124C411yescharacteristic
7C2×C4⋊#1057—21no—
8C2×C4⋊#1057C2212yes—
9C2×C4×#1057—21no—
10C2×C4×#1057C2212yes—
11C13×#382C411yescharacteristic
12C4⋊C4×Dic13C2211yescharacteristic
13C4⋊C4×Dic13C2211yescharacteristic
14#11718634C411yescharacteristic
15#11718634C411yescharacteristic
16C42×Dic13C2211yescharacteristic
17#11718313—21no—
18#11718313—21no—
19#11718310—21no—
20#11718310—21no—
21#11718290—21no—
22#11718290—21no—
23C22×#1057—22no—
24C22×#1057—22no—
25C2×C13×C4⋊C4C2×C411yescharacteristic
26C2×C13×C4⋊C4C2×C411yescharacteristic
27C2×C42×C13C2×C411yescharacteristic
28C2×C4⋊Dic13C2×C411yescharacteristic
29C2×C4⋊Dic13C2×C411yescharacteristic
30C2×#6101—21no—
31C2×#6101—21no—
32C2×#6101—21no—
33C2×#6101—21no—
34C2×C4×Dic13—21no—
35C2×C4×Dic13—21no—
36C2×C4×Dic13C2×C411yescharacteristic
37C2×C4×Dic13D411yescharacteristic
38C2×C4×Dic13D411yescharacteristic
39C2×C4×Dic13D411yescharacteristic
40C2×C4×Dic13D411yescharacteristic
41C2×C4×Dic13C2311yescharacteristic
42#88124—22no—
43#88124C814yescomplemented
44C4⋊#1057—24no—
45C4⋊#1057—22no—
46C4⋊#1057Q814yes—
47C4×#1057—24no—
48C4×#1057—42no—
49C13×#95—21no—
50C13×#95—21no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#88071—21no—
55#9866—131nomaximal, Sylow
56C22×C4×C13—21no—
57C22×C4×C13—21no—
58C22×C4×C13C22⋊C411yescharacteristic
59C22×C4×C13C22⋊C411yescharacteristic
60C22×C4×C13C22×C411yescharacteristic
61C22×Dic13—21no—
62C22×Dic13—21no—
63C22×Dic13C22⋊C411yescharacteristic
64C22×Dic13C22⋊C411yescharacteristic
65C22×Dic13C2×D411yescharacteristic
66C22×Dic13C2×D411yescharacteristic
67C2×#1057—24no—
68C2×#1057—24no—
69C2×#1057—42no—
70C2×#1057—42no—
71C2×#1057—42no—
72C2×#1057—42no—
73C13×C4⋊C4—22no—
74C13×C4⋊C4—22no—
75C42×C13C2×C812yes—
76C42×C13M1612yes—
77C4⋊Dic13—21no—
78C4⋊Dic13—21no—
79C4⋊Dic13C2×C812yes—
80C4⋊Dic13C2×C812yes—
81#6101—24no—
82#6101—24no—
83#6101—42no—
84#6101—42no—
85C4×Dic13—22no—
86C4×Dic13—22no—
87C4×Dic13—22no—
88C4×Dic13—21no—
89C4×Dic13—21no—
90C4×Dic13—41no—
91C4×Dic13—42no—
92C4×Dic13—41no—
93C4×Dic13—41no—
94C4×Dic13C2×Q812yes—
95C4×Dic13#4112yes—
96C4×#125—131no—
97C4×C4⋊C8—131no—
98C4×C4⋊C8—131no—
99#1279—132no—
100#1279—132no—
101C23×C13C2×C22⋊C411yescharacteristic
102C2×C4×C13—21no—
103C2×C4×C13—21no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—41no—
107C2×C4×C13—41no—
108C2×C4×C13—41no—
109C2×C4×C13—41no—
110C2×C4×C13—41no—
111C2×C4×C13—41no—
112C2×C4×C13C22⋊C812yes—
113C2×C4×C13C22⋊C812yes—
114C2×C4×C13C4×Q812yes—
115C2×C4×C13C22×C811yescharacteristic
116C2×C4×C13C2×M1611yescharacteristic
117C2×C4×C13#13112yes—
118C2×Dic13—21no—
119C2×Dic13—21no—
120C2×Dic13—21no—
121C2×Dic13—21no—
122C2×Dic13—22no—
123C2×Dic13—22no—
124C2×Dic13—21no—
125C2×Dic13—21no—
126C2×Dic13—21no—
127C2×Dic13—41no—
128C2×Dic13—41no—
129C2×Dic13—41no—
130C2×Dic13—41no—
131C2×Dic13#10412yes—
132C2×Dic13C22⋊Q812yes—
133C2×Dic13#12411yescharacteristic
134C2×Dic13C4⋊Q811yescharacteristic
135C2×Dic13#13512yes—
136C2×Dic13AGL(1,ℤ/8)11yescharacteristic
137C2×Dic13#13711yescharacteristic
138#1057—44no—
139#1057—44no—
140C2×#125—131no—
141C2×C4⋊C8—132no—
142C2×C4⋊C8—261no—
143C2×C4×C8—132no—
144C2×C4×C8—261no—
145#389—131no—
146#389—131no—
147#387—261no—
148#387—261no—
149#382#26111yescharacteristic
150C4×C4⋊C4—131no—
151C4×C4⋊C4—131no—
152C4×C4⋊C4—261no—
153C4×C4⋊C4—261no—
154C43—131no—
155#336—261no—
156#336—261no—
157C22×C13#39111yescharacteristic
158C22×C13C2×C22⋊C811yescharacteristic
159C22×C13#40811yescharacteristic
160C22×C13#41611yescharacteristic
161C22×C13#41711yescharacteristic
162C22×C13C2×#10411yescharacteristic
163C22×C13#42111yescharacteristic
164C4×C13—22no—
165C4×C13—22no—
166C4×C13—81no—
167C4×C13—81no—
168C4×C13C8×Q812yes—
169C4×C13#44612yes—
170Dic13—21no—
171Dic13—21no—
172Dic13—22no—
173Dic13—42no—
174Dic13—42no—
175Dic13—41no—
176Dic13#47812yes—
177Dic13#47912yes—
178C22×C8—262no—
179C22×C8—262no—
180#125—134no—
181#125—262no—
182C2×C4⋊C4—131no—
183C2×C4⋊C4—131no—
184C2×C4⋊C4—261no—
185C2×C4⋊C4—261no—
186C2×C4⋊C4—261no—
187C2×C4⋊C4—261no—
188C2×C4⋊C4C2×#26111yescharacteristic
189C2×C4⋊C4C2×#26111yescharacteristic
190C2×C42—131no—
191C2×C42—131no—
192C2×C42—131no—
193C2×C42—131no—
194C2×C42—131no—
195C2×C42—131no—
196C2×C42—261no—
197C2×C42—261no—
198C2×C42C2×#26111yescharacteristic
199C4⋊C8—134no—
200C4⋊C8—262no—
201C4⋊C8—264no—
202C4×C8—264no—
203C4×C8—522no—
204#95—21no—
205#95—21no—
206#95—261no—
207#95—261no—
208#95—261no—
209#95—261no—
210C2×C13#147611yescharacteristic
211C2×C13#147711yescharacteristic
212C2×C13#148211yescharacteristic
213C2×C13#148311yescharacteristic
214C2×C13#198411yescharacteristic
215C2×C13#198611yescharacteristic
216C2×C13#198911yescharacteristic
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—131no—
220C22×C4—131no—
221C22×C4—131no—
222C22×C4—131no—
223C22×C4—261no—
224C22×C4—261no—
225C22×C4C22⋊#26111yescharacteristic
226C22×C4C22⋊#26111yescharacteristic
227C22×C4C22×#26111yescharacteristic
228C2×C8—264no—
229C2×C8—264no—
230C2×C8—522no—
231C2×C8—522no—
232C2×C8—522no—
233C2×C8—522no—
234C4⋊C4—22no—
235C4⋊C4—22no—
236C4⋊C4—132no—
237C4⋊C4—132no—
238C4⋊C4—264no—
239C4⋊C4—264no—
240C4⋊C4—261no—
241C4⋊C4—261no—
242C4⋊C4—522no—
243C4⋊C4—522no—
244C42—132no—
245C42—132no—
246C42—261no—
247C42—262no—
248C42—261no—
249C42—262no—
250C42—262no—
251C42—521no—
252C42—521no—
253C42—521no—
254C42—522no—
255C42D13⋊C812yes—
256C42#611812yes—
257C13#986611yescharacteristic, complemented, Sylow
258C23C2×C22⋊#26111yescharacteristic
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—132no—
270C2×C4—131no—
271C2×C4—131no—
272C2×C4—132no—
273C2×C4—131no—
274C2×C4—131no—
275C2×C4—132no—
276C2×C4—261no—
277C2×C4—261no—
278C2×C4—261no—
279C2×C4—261no—
280C2×C4—262no—
281C2×C4—262no—
282C2×C4—261no—
283C2×C4—261no—
284C2×C4—261no—
285C2×C4—521no—
286C2×C4—521no—
287C2×C4—521no—
288C2×C4—521no—
289C2×C4#8811112yes—
290C2×C4#8811112yes—
291C2×C4C2×D13⋊C811yescharacteristic
292C2×C4C2×#611811yescharacteristic
293C2×C4#8823812yes—
294C2×C4Q8×#26112yes—
295C8—524no—
296C8—524no—
297C22C2×#8811111yescharacteristic
298C22#1171914711yescharacteristic
299C22(C2×#261)⋊Q811yescharacteristic
300C22D13⋊#10411yescharacteristic
301C22#1171916411yescharacteristic
302C22#1171916511yescharacteristic
303C22#1171916611yescharacteristic
304C4—22no—
305C4—22no—
306C4—81no—
307C4—81no—
308C4—132no—
309C4—132no—
310C4—261no—
311C4—261no—
312C4—262no—
313C4—522no—
314C4—522no—
315C4—521no—
316C4#1171907412yes—
317C4#1171908012yes—
318C2#1313012911yescharacteristic
319C2#1313013311yescharacteristic
320C2#1313014811yescharacteristic
321C2#1313015211yescharacteristic
322C2#1313100611yescharacteristic
323C2#1313101311yescharacteristic
324C2#1313101611yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
FittingC13×#382C4
socle, prime radicalC23×C13C2×C22⋊C4
cosocleC2×C4×Dic13C23
hypercenter#382#261
hypocenterC13#9866
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #382

Complements

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

NH ≅ G/Ntype
43. #88124C8semidirect
257. C13#9866semidirect

Maximal subgroups

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

subgroupindex
C4×C4⋊#10572
#131296722
#131173912
#986613