Finite Group Databasebeta

← #25011813

Subgroups — #25011813

Order 11008.

526 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×#14582700C211yesmaximal, characteristic
3C2×#14582674C211yesmaximal, characteristic, complemented
4#107×Dic43C211yesmaximal, characteristic, complemented
5#19132687C211yesmaximal, characteristic, complemented
6#19132686C211yesmaximal, characteristic, complemented
7C2×C43×#357C211yesmaximal, characteristic
8C2×D4×Dic43—21no—
9C22×C43⋊C16C2211yescharacteristic
10D8×Dic43—22no—
11D8×Dic43C414yescomplemented
12C2×#13063259C2211yescharacteristic
13C2×#13063259C2211yescharacteristic
14C2×#13063246—21no—
15C2×C8×Dic43C2211yescharacteristic
16C4⋊C4×Dic43—21no—
17#14582700C414yescomplemented
18#14582674—22no—
19#14582661—21no—
20C22×D8×C43C2211yescharacteristic
21C22×C16×C43C2211yescharacteristic
22C2×#107×C43C2211yescharacteristic
23C43×#357C414yescomplemented
24C23×Dic43—41no—
25C22×C43⋊C8D411yescharacteristic
26D4×Dic43—24no—
27D4×Dic43—42no—
28C2×C4⋊Dic43—21no—
29C2×C4⋊Dic43—21no—
30C2×C22⋊Dic43—41no—
31C2×C4×Dic43—41no—
32C2×C4×Dic43D411yescharacteristic
33C2×C43⋊C16—21no—
34C2×C43⋊C16—21no—
35C2×C43⋊C16C2×C412yescomplemented
36#13063259—21no—
37#13063259—21no—
38#13063259C2×C412yes—
39#13063259C2×C412yescomplemented
40#13063246—24no—
41C8×Dic43C2×C412yes—
42C8×Dic43D412yes—
43C43⋊#95—41no—
44C22×D4×C43—21no—
45C2×D8×C43—21no—
46C2×D8×C43—21no—
47C2×D8×C43—21no—
48C2×D8×C43C2×C412yes—
49C2×D8×C43C2×C412yes—
50C2×D8×C43C2×C412yes—
51C22×C8×C43C2311yescharacteristic
52C2×C4⋊C4×C43—21no—
53C2×C16×C43—21no—
54C2×C16×C43—21no—
55C2×C16×C43C2×C412yescomplemented
56#107×C43—21no—
57#107×C43C2×C412yescomplemented
58C24×C43—41no—
59C2×D4×C43—22no—
60C2×D4×C43—22no—
61C2×D4×C43—22no—
62C2×D4×C43—41no—
63C2×D4×C43—41no—
64C2×D4×C43—41no—
65C22×C4×C43—41no—
66C22×C4×C43C2×D411yescharacteristic
67C22×Dic43—44no—
68C22×Dic43—41no—
69C22×Dic43—41no—
70C22×Dic43—82no—
71C22×Dic43—82no—
72C22×Dic43D811yescharacteristic
73C22×Dic43D811yescharacteristic
74D8×C43—22no—
75D8×C43—22no—
76D8×C43—22no—
77D8×C43C4214yescomplemented
78C2×C8×C43C22×C411yescharacteristic
79C2×C8×C43C22×C411yescharacteristic
80C2×C8×C43C22×C411yescharacteristic
81C2×C8×C43C2×D411yescharacteristic
82C2×C8×C43#4111yescharacteristic
83C2×C8×C43#4111yescharacteristic
84C4⋊C4×C43—22no—
85C4⋊C4×C43—41no—
86C22⋊Dic43—44no—
87C4⋊Dic43—22no—
88C4⋊Dic43—22no—
89C4⋊Dic43—41no—
90C4⋊Dic43—41no—
91C4×Dic43—82no—
92C4×Dic43C22⋊C412yes—
93C4×Dic43SD1612yes—
94C2×C43⋊C8—21no—
95C2×C43⋊C8—21no—
96C2×C43⋊C8C22⋊C412yes—
97C16×C43—22no—
98C43⋊C16—22no—
99C23×C43—42no—
100C23×C43—42no—
101C23×C43—42no—
102C23×C43—81no—
103C23×C43—81no—
104C23×C43—81no—
105C23×C43—81no—
106C23×C43C2×D811yescharacteristic
107D4×C43—24no—
108D4×C43—42no—
109D4×C43—42no—
110D4×C43—42no—
111C2×C4×C43—42no—
112C2×C4×C43—81no—
113C2×C4×C43—81no—
114C2×C4×C43C2×C22⋊C411yescharacteristic
115C2×C4×C43C4×D411yescharacteristic
116C2×C4×C43C4×D411yescharacteristic
117C2×C4×C43C2×SD1611yescharacteristic
118C2×C4×C43#13511yescharacteristic
119C2×C4×C43#13511yescharacteristic
120C2×Dic43—21no—
121C2×Dic43—21no—
122C2×Dic43—21no—
123C2×Dic43—21no—
124C2×Dic43—42no—
125C2×Dic43—42no—
126C2×Dic43—88no—
127C2×Dic43—81no—
128C2×Dic43—81no—
129C2×Dic43—81no—
130C2×Dic43—81no—
131C2×Dic43#10212yes—
132C2×Dic43#10212yes—
133C8×C43C2×C4211yescharacteristic
134C8×C43#11711yescharacteristic
135C8×C43C4×D411yescharacteristic
136C8×C43C4×D411yescharacteristic
137C43⋊C8—22no—
138#12637—431nomaximal, Sylow
139C22×C43—44no—
140C22×C43—82no—
141C22×C43—82no—
142C22×C43—82no—
143C22×C43—82no—
144C22×C43—82no—
145C22×C43—82no—
146C22×C43C2×#10211yescharacteristic
147C22×C43C4×D811yescharacteristic
148C22×C43C4×D811yescharacteristic
149C22×C43#50911yescharacteristic
150C22×C43#50911yescharacteristic
151C22×C43#50911yescharacteristic
152C22×C43#51011yescharacteristic
153C4×C43—82no—
154C4×C43C4×C22⋊C411yescharacteristic
155C4×C43#41611yescharacteristic
156C4×C43C4×SD1611yescharacteristic
157C4×C43C4×SD1611yescharacteristic
158Dic43—22no—
159Dic43—22no—
160Dic43—82no—
161Dic43—82no—
162C2×C4×D8—431no—
163C2×#357—431no—
164C2×#357D4311yescharacteristic
165C2×#346—431no—
166C4×#107—431no—
167#1380—431no—
168#1380—431no—
169C2×C43—84no—
170C2×C43C4×#10211yescharacteristic
171C2×C43#213911yescharacteristic
172C2×C43#214011yescharacteristic
173C2×C43#217511yescharacteristic
174C2×C43#217511yescharacteristic
175C2×C43#217711yescharacteristic
176C2×C43#217711yescharacteristic
177C22×D8C2×D4311yescharacteristic
178C2×C4×D4—861no—
179C22×C16—431no—
180C22×C16C2×D4311yescharacteristic
181C4×D8—434no—
182C4×D8—862no—
183C2×#107—431no—
184C2×#107—431no—
185C2×#107C2×D4311yescharacteristic
186C2×#102—861no—
187C2×C4×C8—431no—
188C4×C4⋊C4—861no—
189#357—434no—
190#357Dic4314yescomplemented
191#346—862no—
192#340—861no—
193C43#1263711yescharacteristic, complemented, Sylow
194C22×D4—21no—
195C23×C4—1721no—
196C2×D8—21no—
197C2×D8—21no—
198C2×D8—21no—
199C2×D8C4×D4312yes—
200C2×D8C4×D4312yes—
201C2×D8C2×Dic4312yes—
202C22×C8—431no—
203C22×C8C22×D4311yescharacteristic
204C4×D4—864no—
205C4×D4—1722no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—861no—
208C2×C4⋊C4—861no—
209C2×C22⋊C4—1721no—
210C2×C42—431no—
211C2×C42—1721no—
212C2×C16—21no—
213C2×C16—21no—
214C2×C16—432no—
215C2×C16—861no—
216C2×C16—861no—
217C2×C16C2×Dic4312yescomplemented
218#107—21no—
219#107—432no—
220#107—432no—
221#107—861no—
222#107—861no—
223#107C2×Dic4312yescomplemented
224#102—864no—
225C4×C8—432no—
226C4×C8—432no—
227#95—1721no—
228C24—41no—
229C2×D4—22no—
230C2×D4—22no—
231C2×D4—22no—
232C2×D4—41no—
233C2×D4—41no—
234C2×D4—41no—
235C22×C4—41no—
236C22×C4—431no—
237C22×C4—431no—
238C22×C4—3442no—
239C22×C4—3442no—
240C22×C4—1724no—
241C22×C4—1721no—
242C22×C4—1721no—
243C22×C4D4×D4311yescharacteristic
244D8—22no—
245D8—22no—
246D8—22no—
247D8C4×Dic4314yescomplemented
248C2×C8—432no—
249C2×C8—861no—
250C2×C8—861no—
251C2×C8C2×C4×D4311yescharacteristic
252C2×C8C2×C4×D4311yescharacteristic
253C2×C8D4×D4311yescharacteristic
254C2×C8#1062190011yescharacteristic
255C2×C8#1062190011yescharacteristic
256C2×C8C22×Dic4311yescharacteristic
257C4⋊C4—22no—
258C4⋊C4—41no—
259C4⋊C4—862no—
260C4⋊C4—862no—
261C4⋊C4—1721no—
262C4⋊C4—1721no—
263C22⋊C4—1724no—
264C42—432no—
265C42—432no—
266C42—3442no—
267C16—22no—
268C16—862no—
269C23—42no—
270C23—42no—
271C23—42no—
272C23—81no—
273C23—81no—
274C23—81no—
275C23—81no—
276C23D8×D4311yescharacteristic
277D4—24no—
278D4—42no—
279D4—42no—
280D4—42no—
281C2×C4—42no—
282C2×C4—81no—
283C2×C4—81no—
284C2×C4—432no—
285C2×C4—432no—
286C2×C4—861no—
287C2×C4—861no—
288C2×C4—861no—
289C2×C4—861no—
290C2×C4—3448no—
291C2×C4—3441no—
292C2×C4—3441no—
293C2×C4—3441no—
294C2×C4—3441no—
295C2×C4—1722no—
296C2×C4—1722no—
297C2×C4C22⋊C4×D4311yescharacteristic
298C2×C4(C22⋊D43)⋊C411yescharacteristic
299C2×C4D4×Dic4311yescharacteristic
300C2×C4SD16×D4311yescharacteristic
301C2×C4#1306334411yescharacteristic
302C2×C4#1306334611yescharacteristic
303C8—862no—
304C8C2×C4×Dic4311yescharacteristic
305C8#1306328111yescharacteristic
306C8(C22⋊D43)⋊C411yescharacteristic
307C8D4×Dic4311yescharacteristic
308C22—44no—
309C22—82no—
310C22—82no—
311C22—82no—
312C22—82no—
313C22—82no—
314C22—82no—
315C22#102×D4311yescharacteristic
316C22#1458297911yescharacteristic
317C22D8×Dic4311yescharacteristic
318C22#1458333311yescharacteristic
319C22#1458333311yescharacteristic
320C22#1458333611yescharacteristic
321C22#1458333811yescharacteristic
322C4—82no—
323C4—862no—
324C4—862no—
325C4—3442no—
326C4—3442no—
327C4C22⋊C4×Dic4311yescharacteristic
328C4#1458289211yescharacteristic
329C4SD16×Dic4311yescharacteristic
330C4#1458299011yescharacteristic
331C2—84no—
332C2#102×Dic4311yescharacteristic
333C2#1913630411yescharacteristic
334C2#1913630911yescharacteristic
335C2#1913645611yescharacteristic
336C2#1913646011yescharacteristic
337C2#1913646811yescharacteristic
338C2#1913647111yescharacteristic
subgroupG/H
centerC23D8×D43
commutatorC8×C43C2×C42
FrattiniC22×C8C22×D43
FittingC2×C43×#357C2
socleC23×C43C2×D8
prime radicalC22×D8×C43C22
cosocleC22×C8×C43C23
hypercenterC2×#357D43
hypocenterC43#12637
LCSG ▷ C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#357

Complements

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

NH ≅ G/Ntype
3. C2×#14582674C2semidirect
4. #107×Dic43C2semidirect
5. #19132687C2semidirect
6. #19132686C2semidirect
11. D8×Dic43C4semidirect
17. #14582700C4semidirect
23. C43×#357C4semidirect
35. C2×C43⋊C16C2×C4semidirect
39. #13063259C2×C4semidirect
55. C2×C16×C43C2×C4semidirect
57. #107×C43C2×C4semidirect
77. D8×C43C42semidirect
190. #357Dic43semidirect
193. C43#12637semidirect
217. C2×C16C2×Dic43semidirect
223. #107C2×Dic43semidirect
247. D8C4×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×#145827002
C2×#145826742
#107×Dic432
#191326872
#191326862
C2×C43×#3572
#1263743