Finite Group Databasebeta

← #15756051

Subgroups — #15756051

Order 3328.

466 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×#1055C211yesmaximal, characteristic
2#13114973C211yesmaximal, characteristic, complemented
3#13113582C211yesmaximal, characteristic, complemented
4#13113261C211yesmaximal, characteristic
5#13112732C211yesmaximal, characteristic, complemented
6#13112731C211yesmaximal, characteristic, complemented
7C13×#1486C211yesmaximal, characteristic
8C2×C4×D4×C13C2211yescharacteristic
9C23×#1055—21no—
10C13×#431C2211yescharacteristic
11C13×#423C2211yescharacteristic
12C2×C22⋊#1055—21no—
13D4×#1055—21no—
14D4×#1055—21no—
15D4×#1055C412yes—
16D4×#1055C412yes—
17#11718586C2211yescharacteristic
18#11718585C2211yescharacteristic
19C2×C4⋊#1055C2211yescharacteristic
20C2×C4×#1055C2211yescharacteristic
21C13×D4⋊C8—22no—
22#11718150—21no—
23#11718150—21no—
24D4⋊#1055—22no—
25#11718072—21no—
26#11718071—21no—
27C22×D4×C13Q811yescharacteristic
28C23×C4×C13—21no—
29C2×C13×M16—21no—
30C4×D4×C13—21no—
31C4×D4×C13—21no—
32C4×D4×C13C2×C412yes—
33C4×D4×C13D412yes—
34C2×C13×C4⋊C4Q811yescharacteristic
35C2×C13×C22⋊C4—21no—
36C2×C42×C13C2311yescharacteristic
37C2×#6099—21no—
38C22×#1055—21no—
39C22×#1055—22no—
40C22×#1055—22no—
41C22×#1055—42no—
42C22×#1055—42no—
43C22×#1055D411yescharacteristic
44C22×#1055D411yescharacteristic
45C13×C4⋊C8—21no—
46C13×C4⋊C8—21no—
47C13×C4⋊C8—21no—
48C13×C22⋊C8—21no—
49C4×C8×C13—21no—
50C22⋊#1055—22no—
51C22⋊#1055—22no—
52C22⋊#1055—21no—
53C4⋊#1055—21no—
54C4⋊#1055—21no—
55C4⋊#1055—21no—
56C4⋊#1055—21no—
57C4⋊#1055C2×C412yes—
58C4×#1055—21no—
59C4×#1055C2×C411yescharacteristic
60C4×#1055C2×C411yescharacteristic
61C4×#1055D411yescharacteristic
62C4×#1055D411yescharacteristic
63#8660—131nomaximal, Sylow
64C24×C13—21no—
65C2×D4×C13—24no—
66C2×D4×C13—21no—
67C2×D4×C13C4⋊C412yes—
68C22×C4×C13—21no—
69C22×C4×C13—22no—
70C22×C4×C13—22no—
71C22×C4×C13—41no—
72C22×C4×C13—41no—
73C22×C4×C13—41no—
74C22×C4×C13—41no—
75C22×C4×C13C2×D411yescharacteristic
76C22×C4×C13C2×Q811yescharacteristic
77C22×C4×C13#4111yescharacteristic
78C13×M16—41no—
79C13×M16—41no—
80C2×C8×C13—41no—
81C2×C8×C13—41no—
82C13×C4⋊C4—21no—
83C13×C4⋊C4C4⋊C412yes—
84C13×C22⋊C4—22no—
85C13×C22⋊C4—22no—
86C42×C13C22×C411yescharacteristic
87C42×C13C2×D411yescharacteristic
88C42×C13C2×D411yescharacteristic
89C42×C13#4111yescharacteristic
90#6099—41no—
91#6099—41no—
92C2×#1055—21no—
93C2×#1055—21no—
94C2×#1055—21no—
95C2×#1055—21no—
96C2×#1055—22no—
97C2×#1055—44no—
98C2×#1055—44no—
99C2×#1055—41no—
100C2×#1055—41no—
101C2×#1055—41no—
102C2×#1055—41no—
103C2×#1055C22⋊C411yescharacteristic
104C2×#1055C22⋊C411yescharacteristic
105C2×#1055C22⋊C411yescharacteristic
106C2×#1055C22⋊C411yescharacteristic
107C2×C8×D4—131no—
108#1837—131no—
109#1564—131no—
110#1486—131no—
111#1486D1311yescharacteristic
112#1301—131no—
113#1301—131no—
114C23×C13—24no—
115C23×C13—22no—
116C23×C13—42no—
117C23×C13—41no—
118C23×C13—41no—
119C23×C13C22⋊Q811yescharacteristic
120D4×C13—24no—
121D4×C13—22no—
122D4×C13#10814yes—
123C2×C4×C13—22no—
124C2×C4×C13—22no—
125C2×C4×C13—41no—
126C2×C4×C13—41no—
127C2×C4×C13—41no—
128C2×C4×C13—42no—
129C2×C4×C13—42no—
130C2×C4×C13—42no—
131C2×C4×C13—42no—
132C2×C4×C13C2×C22⋊C411yescharacteristic
133C2×C4×C13C2×C4⋊C411yescharacteristic
134C2×C4×C13#11711yescharacteristic
135C2×C4×C13#12111yescharacteristic
136C2×C4×C13#12111yescharacteristic
137C2×C4×C13C22⋊Q811yescharacteristic
138C2×C4×C13#13511yescharacteristic
139C2×C4×C13#13511yescharacteristic
140C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
142C8×C13—81no—
143C8×C13—81no—
144#1055—21no—
145#1055—21no—
146#1055—21no—
147#1055—21no—
148#1055—42no—
149#1055—81no—
150#1055—81no—
151C23×C8—261no—
152C2×C4×D4C2×D1311yescharacteristic
153C8×D4—132no—
154C8×D4—132no—
155C8×D4—261no—
156C8×D4—261no—
157#431—131no—
158#431C2×D1311yescharacteristic
159#423—131no—
160#423C2×D1311yescharacteristic
161C2×C4⋊C8—131no—
162C2×C22⋊C8—261no—
163C2×C4×C8—131no—
164#341—261no—
165#341—261no—
166#335—261no—
167#334—261no—
168D4⋊C8—22no—
169D4⋊C8—262no—
170C22×C13—21no—
171C22×C13—21no—
172C22×C13—24no—
173C22×C13—44no—
174C22×C13—44no—
175C22×C13—42no—
176C22×C13—42no—
177C22×C13#38011yescharacteristic
178C22×C13#47811yescharacteristic
179C22×C13#47811yescharacteristic
180C4×C13—21no—
181C4×C13—21no—
182C4×C13—21no—
183C4×C13—42no—
184C4×C13#41611yescharacteristic
185C4×C13#41811yescharacteristic
186C4×C13C2×#10812yes—
187C4×C13#46311yescharacteristic
188C4×C13#46311yescharacteristic
189C22×D4Dic2611yescharacteristic
190C23×C4—21no—
191C2×M16—21no—
192C2×M16—261no—
193C22×C8—131no—
194C22×C8—131no—
195C22×C8—262no—
196C22×C8—262no—
197C22×C8—261no—
198C22×C8—522no—
199C22×C8—522no—
200C4×D4—21no—
201C4×D4—21no—
202C4×D4C4×D1312yes—
203C4×D4C22⋊D1312yes—
204C2×C4⋊C4Dic2611yescharacteristic
205C2×C22⋊C4—21no—
206C2×C42C22×D1311yescharacteristic
207C4⋊C8—21no—
208C4⋊C8—21no—
209C4⋊C8—21no—
210C4⋊C8—132no—
211C4⋊C8—261no—
212C4⋊C8—261no—
213C4⋊C8—261no—
214C4⋊C8—261no—
215C22⋊C8—21no—
216C22⋊C8—262no—
217C22⋊C8—262no—
218C22⋊C8—261no—
219C4×C8—21no—
220C4×C8—131no—
221C4×C8—131no—
222C4×C8—131no—
223C4×C8—131no—
224C4×C8—261no—
225C2×C13—21no—
226C2×C13—21no—
227C2×C13—44no—
228C2×C13#180411yescharacteristic
229C2×C13#181011yescharacteristic
230C2×C13#181411yescharacteristic
231C24—21no—
232C2×D4—24no—
233C2×D4—21no—
234C2×D4#610112yes—
235C22×C4—21no—
236C22×C4—22no—
237C22×C4—22no—
238C22×C4—41no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4C2×Dic2611yescharacteristic
243C22×C4D4×D1311yescharacteristic
244C22×C4#612911yescharacteristic
245M16—41no—
246M16—41no—
247M16—521no—
248M16—521no—
249C2×C8—41no—
250C2×C8—41no—
251C2×C8—131no—
252C2×C8—131no—
253C2×C8—131no—
254C2×C8—131no—
255C2×C8—261no—
256C2×C8—261no—
257C2×C8—261no—
258C2×C8—261no—
259C2×C8—262no—
260C2×C8—524no—
261C2×C8—524no—
262C2×C8—521no—
263C2×C8—521no—
264C2×C8—521no—
265C2×C8—521no—
266C4⋊C4—21no—
267C4⋊C4#610112yes—
268C22⋊C4—22no—
269C22⋊C4—22no—
270C42C2×C4×D1311yescharacteristic
271C42D4×D1311yescharacteristic
272C42#612911yescharacteristic
273C42C2×C22⋊D1311yescharacteristic
274C13#866011yescharacteristic, complemented, Sylow
275C23—24no—
276C23—22no—
277C23—42no—
278C23—41no—
279C23—41no—
280C23#8813211yescharacteristic
281D4—24no—
282D4—22no—
283D4#8806214yes—
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—42no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4#8813111yescharacteristic
294C2×C4#8813211yescharacteristic
295C2×C4C22⋊C4×D1311yescharacteristic
296C2×C4#8816511yescharacteristic
297C2×C4#8816611yescharacteristic
298C2×C4#8816811yescharacteristic
299C2×C4#8817011yescharacteristic
300C2×C4C2×#610111yescharacteristic
301C2×C4#8819311yescharacteristic
302C2×C4#8819311yescharacteristic
303C8—81no—
304C8—81no—
305C8—261no—
306C8—261no—
307C8—261no—
308C8—261no—
309C8—522no—
310C8—1041no—
311C8—1041no—
312C22—21no—
313C22—21no—
314C22—24no—
315C22—44no—
316C22—44no—
317C22—42no—
318C22—42no—
319C22#1171842411yescharacteristic
320C22#1171842711yescharacteristic
321C22#1171860311yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—42no—
326C4#1171843111yescharacteristic
327C4#1171843311yescharacteristic
328C4C2×#8806212yes—
329C4#1171881411yescharacteristic
330C4#1171882611yescharacteristic
331C2—21no—
332C2—21no—
333C2—44no—
334C2#1311484411yescharacteristic
335C2#1311487211yescharacteristic
336C2#1311488811yescharacteristic
subgroupG/H
centerC2×C4#88193
commutatorC42×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1486C2
socleC22×C13#380
prime radicalC22×D4×C13Q8
cosocleC2×C42×C13C23
hypercenter#1486D13
hypocenterC13#8660
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1486

Complements

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

NH ≅ G/Ntype
2. #13114973C2semidirect
3. #13113582C2semidirect
5. #13112732C2semidirect
6. #13112731C2semidirect
274. C13#8660semidirect

Maximal subgroups

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

subgroupindex
C2×D4×#10552
#131149732
#131135822
#131132612
#131127322
#131127312
C13×#14862
#866013