Finite Group Databasebeta

← #361×Dic43 #25011852

Subgroups — #361×Dic43 #25011852

Order 11008.

498 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D8×Dic43C211yesmaximal, characteristic
2C2×#14582712C211yesmaximal, characteristic
3M32×Dic43C211yesmaximal, characteristic, complemented
4#108×Dic43C211yesmaximal, characteristic, complemented
5#19132705C211yesmaximal, characteristic, complemented
6#19132704C211yesmaximal, characteristic, complemented
7C2×C43×#361C211yesmaximal, characteristic
8C2×D4×Dic43—21no—
9C2×#13063265C2211yescharacteristic
10D8×Dic43—21no—
11D8×Dic43—21no—
12D8×Dic43C412yes—
13D8×Dic43C412yes—
14C2×#13063261C2211yescharacteristic
15C2×#13063259C2211yescharacteristic
16C2×#13063246—21no—
17M16×Dic43—21no—
18C2×C8×Dic43C2211yescharacteristic
19#14582712C414yescomplemented
20#14582674—21no—
21C16×Dic43—21no—
22#14582663—21no—
23C22×D8×C43C2211yescharacteristic
24C2×M32×C43C2211yescharacteristic
25C2×#108×C43C2211yescharacteristic
26C43×#361C414yescomplemented
27C23×Dic43—41no—
28C2×#10621877—21no—
29C22×C43⋊C8D411yescharacteristic
30D4×Dic43—22no—
31D4×Dic43—22no—
32D4×Dic43—41no—
33D4×Dic43—41no—
34C2×C4⋊Dic43—21no—
35C2×C22⋊Dic43—41no—
36C2×C4×Dic43D411yescharacteristic
37#13063265—21no—
38#13063265C2×C412yescomplemented
39C2×C43⋊C16—21no—
40#13063261—21no—
41#13063261C2×C412yescomplemented
42#13063259—21no—
43#13063259C2×C412yes—
44#13063246—22no—
45#13063246—22no—
46#13063235—41no—
47C8×Dic43—41no—
48C8×Dic43C2×C411yescharacteristic
49C8×Dic43C2×C411yescharacteristic
50C8×Dic43D411yescharacteristic
51C8×Dic43D411yescharacteristic
52C22×D4×C43—21no—
53C2×D8×C43—21no—
54C2×D8×C43—21no—
55C2×D8×C43—21no—
56C2×D8×C43C2×C412yes—
57C2×D8×C43C2×C412yes—
58C2×D8×C43C2×C412yes—
59C2×M16×C43—21no—
60C22×C8×C43C2311yescharacteristic
61M32×C43—21no—
62M32×C43C2×C412yescomplemented
63C2×C16×C43—21no—
64#108×C43—21no—
65#108×C43C2×C412yescomplemented
66C24×C43—41no—
67C2×D4×C43—22no—
68C2×D4×C43—22no—
69C2×D4×C43—22no—
70C2×D4×C43—41no—
71C2×D4×C43—41no—
72C2×D4×C43—41no—
73C22×C4×C43C2×D411yescharacteristic
74C22×Dic43—42no—
75C22×Dic43—42no—
76C22×Dic43—41no—
77C22×Dic43—84no—
78C22×Dic43SD1611yescharacteristic
79C22×Dic43SD1611yescharacteristic
80D8×C43—22no—
81D8×C43—22no—
82D8×C43—22no—
83D8×C43C4214yes—
84M16×C43—22no—
85M16×C43—41no—
86C2×C8×C43—41no—
87C2×C8×C43C22×C411yescharacteristic
88C2×C8×C43C22×C411yescharacteristic
89C2×C8×C43C22×C411yescharacteristic
90C2×C8×C43C2×D411yescharacteristic
91C2×C8×C43#4111yescharacteristic
92C2×C8×C43#4111yescharacteristic
93C22⋊Dic43—42no—
94C22⋊Dic43—42no—
95C4⋊Dic43—22no—
96C4⋊Dic43—41no—
97C4×Dic43C22⋊C411yescharacteristic
98C4×Dic43C22⋊C411yescharacteristic
99C4×Dic43D811yescharacteristic
100C4×Dic43D811yescharacteristic
101#10621877—22no—
102#10621877—41no—
103C2×C43⋊C8—21no—
104C2×C43⋊C8—21no—
105C2×C43⋊C8—41no—
106C2×C43⋊C8C22⋊C411yescharacteristic
107C2×C43⋊C8C22⋊C411yescharacteristic
108C16×C43—22no—
109C43⋊C16—22no—
110C23×C43—42no—
111C23×C43—42no—
112C23×C43—42no—
113C23×C43—82no—
114C23×C43—82no—
115C23×C43C2×SD1611yescharacteristic
116D4×C43—24no—
117D4×C43—42no—
118D4×C43—42no—
119D4×C43—42no—
120C2×C4×C43C2×C22⋊C411yescharacteristic
121C2×C4×C43C4×D411yescharacteristic
122C2×C4×C43C4×D411yescharacteristic
123C2×C4×C43C2×D811yescharacteristic
124C2×C4×C43#13511yescharacteristic
125C2×C4×C43#13511yescharacteristic
126C2×Dic43—22no—
127C2×Dic43—41no—
128C2×Dic43—42no—
129C2×Dic43—84no—
130C2×Dic43—82no—
131C2×Dic43—84no—
132C2×Dic43#10211yescharacteristic
133C2×Dic43#10211yescharacteristic
134C2×Dic43#10211yescharacteristic
135C2×Dic43#10211yescharacteristic
136C8×C43—42no—
137C8×C43C2×C4211yescharacteristic
138C8×C43#11711yescharacteristic
139C8×C43C4×D411yescharacteristic
140C8×C43C4×D411yescharacteristic
141C43⋊C8—21no—
142C43⋊C8—21no—
143C43⋊C8—42no—
144C4×#361—431nomaximal, Sylow
145C22×C43—21no—
146C22×C43—21no—
147C22×C43—44no—
148C22×C43—84no—
149C22×C43—84no—
150C22×C43—82no—
151C22×C43—82no—
152C22×C43C2×#10211yescharacteristic
153C22×C43C4×SD1611yescharacteristic
154C22×C43C4×SD1611yescharacteristic
155C4×C43C4×C22⋊C411yescharacteristic
156C4×C43#41611yescharacteristic
157C4×C43C4×D811yescharacteristic
158C4×C43C4×D811yescharacteristic
159Dic43—21no—
160Dic43—21no—
161Dic43—21no—
162Dic43—82no—
163Dic43#36112yesdirect product factor
164C2×C4×D8—431no—
165C2×#361—431no—
166C2×#361D4311yescharacteristic
167C4×M32—431no—
168C4×#108—431no—
169#1387—431no—
170#1387—431no—
171C2×C43—21no—
172C2×C43—21no—
173C2×C43—84no—
174C2×C43C4×#10211yescharacteristic
175C2×C43C2×#36111yescharacteristic
176C2×C43#214811yescharacteristic
177C22×D8C2×D4311yescharacteristic
178C2×C4×D4—861no—
179C2×M32—431no—
180C2×M32C2×D4311yescharacteristic
181C4×D8—432no—
182C4×D8—432no—
183C4×D8—861no—
184C4×D8—861no—
185C2×#108—431no—
186C2×#108C2×D4311yescharacteristic
187C2×#107—431no—
188C2×#102—861no—
189C4×M16—861no—
190C2×C4×C8—431no—
191#361—434no—
192#361Dic4314yesdirect product factor
193#346—861no—
194C4×C16—861no—
195#341—861no—
196C43C4×#36111yescharacteristic, complemented, Sylow
197C22×D4—21no—
198C23×C4—1721no—
199C2×D8—21no—
200C2×D8—21no—
201C2×D8—21no—
202C2×D8C4×D4312yes—
203C2×D8C4×D4312yes—
204C2×D8C2×Dic4312yes—
205C2×M16—21no—
206C2×M16—861no—
207C22×C8—431no—
208C22×C8C22×D4311yescharacteristic
209C4×D4—862no—
210C4×D4—862no—
211C4×D4—1721no—
212C4×D4—1721no—
213C2×C4⋊C4—861no—
214C2×C22⋊C4—1721no—
215C2×C42—431no—
216M32—21no—
217M32—432no—
218M32—861no—
219M32C2×Dic4312yescomplemented
220C2×C16—21no—
221C2×C16—861no—
222#108—21no—
223#108—432no—
224#108—861no—
225#108C2×Dic4312yescomplemented
226#107—432no—
227#107—861no—
228#102—862no—
229#102—862no—
230#97—1721no—
231C4×C8—431no—
232C4×C8—431no—
233C4×C8—431no—
234C4×C8—431no—
235C4×C8—1721no—
236C24—41no—
237C2×D4—22no—
238C2×D4—22no—
239C2×D4—22no—
240C2×D4—41no—
241C2×D4—41no—
242C2×D4—41no—
243C22×C4—431no—
244C22×C4—431no—
245C22×C4—3444no—
246C22×C4—1722no—
247C22×C4—1722no—
248C22×C4—1721no—
249C22×C4D4×D4311yescharacteristic
250D8—22no—
251D8—22no—
252D8—22no—
253D8C4×Dic4314yes—
254M16—22no—
255M16—41no—
256M16—862no—
257M16—1721no—
258C2×C8—41no—
259C2×C8—431no—
260C2×C8—431no—
261C2×C8—861no—
262C2×C8—861no—
263C2×C8—1721no—
264C2×C8C2×C4×D4311yescharacteristic
265C2×C8C2×C4×D4311yescharacteristic
266C2×C8D4×D4311yescharacteristic
267C2×C8#1062190011yescharacteristic
268C2×C8#1062190011yescharacteristic
269C2×C8C22×Dic4311yescharacteristic
270C4⋊C4—862no—
271C4⋊C4—1721no—
272C22⋊C4—1722no—
273C22⋊C4—1722no—
274C42—431no—
275C42—431no—
276C42—431no—
277C42—431no—
278C16—22no—
279C16—862no—
280C23—42no—
281C23—42no—
282C23—42no—
283C23—82no—
284C23—82no—
285C23SD16×D4311yescharacteristic
286D4—24no—
287D4—42no—
288D4—42no—
289D4—42no—
290C2×C4—431no—
291C2×C4—431no—
292C2×C4—431no—
293C2×C4—431no—
294C2×C4—862no—
295C2×C4—3444no—
296C2×C4—3444no—
297C2×C4—3442no—
298C2×C4—1721no—
299C2×C4—1722no—
300C2×C4C22⋊C4×D4311yescharacteristic
301C2×C4(C22⋊D43)⋊C411yescharacteristic
302C2×C4D4×Dic4311yescharacteristic
303C2×C4D8×D4311yescharacteristic
304C2×C4#1306334411yescharacteristic
305C2×C4#1306334611yescharacteristic
306C8—42no—
307C8—861no—
308C8—861no—
309C8—1722no—
310C8C2×C4×Dic4311yescharacteristic
311C8#1306328111yescharacteristic
312C8(C22⋊D43)⋊C411yescharacteristic
313C8D4×Dic4311yescharacteristic
314C22—21no—
315C22—21no—
316C22—44no—
317C22—84no—
318C22—84no—
319C22—82no—
320C22—82no—
321C22#102×D4311yescharacteristic
322C22SD16×Dic4311yescharacteristic
323C22#1458299011yescharacteristic
324C4—432no—
325C4—861no—
326C4—861no—
327C4—861no—
328C4—3442no—
329C4C22⋊C4×Dic4311yescharacteristic
330C4#1458289211yescharacteristic
331C4#1458297911yescharacteristic
332C4D8×Dic4311yescharacteristic
333C2—21no—
334C2—21no—
335C2—84no—
336C2#102×Dic4311yescharacteristic
337C2#361×D4311yescharacteristic
338C2#1913634111yescharacteristic
subgroupG/H
centerC22#102×D43
commutatorC8×C43C2×C42
FrattiniC22×C8C22×D43
FittingC2×C43×#361C2
socleC22×C43C2×#102
prime radicalC22×D8×C43C22
cosocleC22×C8×C43C23
hypercenterC2×#361D43
hypocenterC43C4×#361
LCSG ▷ C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#361

Complements

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

NH ≅ G/Ntype
3. M32×Dic43C2semidirect
4. #108×Dic43C2semidirect
5. #19132705C2semidirect
6. #19132704C2semidirect
19. #14582712C4semidirect
26. C43×#361C4semidirect
38. #13063265C2×C4semidirect
41. #13063261C2×C4semidirect
62. M32×C43C2×C4semidirect
65. #108×C43C2×C4semidirect
163. Dic43#361direct (N × H)
192. #361Dic43direct (N × H)
196. C43C4×#361semidirect
219. M32C2×Dic43semidirect
225. #108C2×Dic43semidirect

Maximal subgroups

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

subgroupindex
C2×D8×Dic432
C2×#145827122
M32×Dic432
#108×Dic432
#191327052
#191327042
C2×C43×#3612
C4×#36143