Finite Group Databasebeta

← #25014978

Subgroups — #25014978

Order 11008.

474 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063268C211yesmaximal, characteristic
2C2×#14582726C211yesmaximal, characteristic, complemented
3C2×#14582701C211yesmaximal, characteristic
4C2×C16×Dic43C211yesmaximal, characteristic, complemented
5#19135459C211yesmaximal, characteristic
6#19135457C211yesmaximal, characteristic, complemented
7C2×C43×#358C211yesmaximal, characteristic, complemented
8C22×D344C2211yescharacteristic
9C2×#13063268—22no—
10C2×#13063268—22no—
11C2×#13063268C414yescomplemented
12C22×C43⋊C16C2211yescharacteristic
13C2×#13063259C2211yescharacteristic
14C2×#13063249—21no—
15C2×#13063245—21no—
16C2×C8×Dic43C2211yescharacteristic
17#14582806—21no—
18#14582800—21no—
19#14582726—22no—
20#14582701—22no—
21C16×Dic43—22no—
22C22×Q16×C43C2211yescharacteristic
23C22×C16×C43C2211yescharacteristic
24C2×#107×C43C2211yescharacteristic
25C43×#358—22no—
26C22×D172—21no—
27C2×D344—21no—
28C2×D344—21no—
29C2×D344—21no—
30C2×D344—21no—
31C2×D344—21no—
32C2×D344C2×C412yes—
33C22×C43⋊C8D411yescharacteristic
34C2×C4⋊Dic43—21no—
35C2×(C2×D43)⋊C4—42no—
36C2×C4×Dic43D411yescharacteristic
37#13063268—28no—
38C2×C43⋊C16C2×C412yes—
39C2×C43⋊C16D412yes—
40C2×C43⋊C16D412yes—
41#13063259—21no—
42#13063259—21no—
43#13063249—42no—
44#13063245—42no—
45C8×Dic43—21no—
46C8×Dic43—21no—
47C43⋊#95—42no—
48C22×Q8×C43—21no—
49C2×Q16×C43—21no—
50C2×Q16×C43—21no—
51C2×Q16×C43—21no—
52C2×Q16×C43—21no—
53C2×Q16×C43—21no—
54C2×Q16×C43C2×C412yes—
55C22×C8×C43C2311yescharacteristic
56C2×C4⋊C4×C43—21no—
57C2×C16×C43—21no—
58C2×C16×C43—21no—
59C2×C16×C43D412yes—
60#107×C43—21no—
61#107×C43—21no—
62C23×D43—41no—
63C2×Q8×C43—22no—
64C2×Q8×C43—41no—
65C2×Q8×C43—41no—
66C2×Q8×C43—41no—
67C2×Q8×C43—41no—
68C2×Q8×C43—41no—
69C22×C4×C43—41no—
70C22×C4×C43—41no—
71C22×C4×C43C2×D411yescharacteristic
72C22×Dic43—41no—
73C22×Dic43D812yes—
74C2×D172—22no—
75C2×D172—41no—
76C2×D172—41no—
77C2×D172—41no—
78C2×D172—41no—
79C2×D172—41no—
80Q16×C43—22no—
81Q16×C43—22no—
82Q16×C43—41no—
83Q16×C43—41no—
84C2×C8×C43C22×C411yescharacteristic
85C2×C8×C43C2×D411yescharacteristic
86C2×C8×C43C2×D411yescharacteristic
87C2×C8×C43C2×D411yescharacteristic
88C2×C8×C43#4111yescharacteristic
89C2×C8×C43#4111yescharacteristic
90C4⋊C4×C43—41no—
91C4⋊C4×C43—41no—
92(C2×D43)⋊C4—84no—
93C4⋊Dic43—41no—
94C4⋊Dic43—41no—
95C4×Dic43—21no—
96C4×Dic43—21no—
97C2×C43⋊C8—21no—
98C2×C43⋊C8—21no—
99C2×C43⋊C8D812yes—
100D344—22no—
101D344—22no—
102D344—41no—
103D344—41no—
104C16×C43—22no—
105C43⋊C16C22⋊C414yescomplemented
106C23×C43C2×D811yescharacteristic
107C22×D43—42no—
108C22×D43—81no—
109C22×D43—81no—
110C22×D43—82no—
111C22×D43—82no—
112Q8×C43—42no—
113Q8×C43—42no—
114Q8×C43—81no—
115Q8×C43—81no—
116C2×C4×C43—42no—
117C2×C4×C43—81no—
118C2×C4×C43—81no—
119C2×C4×C43—81no—
120C2×C4×C43—82no—
121C2×C4×C43C4×D411yescharacteristic
122C2×C4×C43#12111yescharacteristic
123C2×C4×C43#12711yescharacteristic
124C2×C4×C43C2×D811yescharacteristic
125C2×C4×C43#13511yescharacteristic
126C2×C4×C43#13511yescharacteristic
127C2×Dic43—22no—
128C2×Dic43—22no—
129C2×Dic43—81no—
130C2×Dic43—82no—
131C2×Dic43SD3214yescomplemented
132D172—42no—
133D172—42no—
134D172—81no—
135D172—81no—
136C8×C43C2×C22⋊C411yescharacteristic
137C8×C43C4×D411yescharacteristic
138C8×C43#12111yescharacteristic
139C8×C43#12411yescharacteristic
140C43⋊C8—22no—
141#13237—431nomaximal, Sylow
142C22×C43C4×D811yescharacteristic
143C22×C43#46611yescharacteristic
144C22×C43#49311yescharacteristic
145C22×C43C2×SD3212yes—
146C22×C43#50812yes—
147C2×D43—84no—
148C2×D43—82no—
149C2×D43—162no—
150C2×D43—161no—
151C2×D43—161no—
152C4×C43—82no—
153C4×C43—161no—
154C4×C43#39011yescharacteristic
155C4×C43C4×D811yescharacteristic
156C4×C43#46611yescharacteristic
157C4×C43#49511yescharacteristic
158Dic43—24no—
159Dic43—161no—
160C22×SD32—431no—
161C2×#367—431no—
162C2×#358D4311yescharacteristic, complemented
163C2×#357—431no—
164C2×C4×C16—431no—
165#1970—431no—
166#1969—431no—
167C2×C43#197011yescharacteristic
168C2×C43C4×SD3212yes—
169C2×C43#221712yes—
170C2×C43#224811yescharacteristic
171C2×C43#224911yescharacteristic
172D43—162no—
173C22×Q16C2×D4311yescharacteristic
174C22×D8—431no—
175C2×SD32—434no—
176C2×SD32—862no—
177C2×SD32—862no—
178C22×C16—431no—
179C22×C16C2×D4311yescharacteristic
180C2×#107—431no—
181C2×#107C2×D4311yescharacteristic
182C2×#103—861no—
183C2×#102—861no—
184C2×C4×C8—431no—
185#391—861no—
186#390—861no—
187#367—862no—
188#358—22no—
189#357—862no—
190C4×C16—862no—
191C43#1323711yescharacteristic, complemented, Sylow
192C22×Q8—21no—
193C22×D4—861no—
194C2×Q16—21no—
195C2×Q16—21no—
196C2×Q16—21no—
197C2×Q16—21no—
198C2×Q16—21no—
199C2×Q16C4×D4312yes—
200C2×D8—432no—
201C2×D8—861no—
202C2×D8—861no—
203C2×D8—861no—
204C2×D8—861no—
205C2×D8—861no—
206C22×C8—431no—
207C22×C8C22×D4311yescharacteristic
208C2×C4⋊C4—21no—
209C2×C4⋊C4—861no—
210C2×C22⋊C4—1722no—
211C2×C42—431no—
212SD32—868no—
213C2×C16—21no—
214C2×C16—21no—
215C2×C16—432no—
216C2×C16—432no—
217C2×C16—432no—
218C2×C16C22⋊D4312yes—
219#107—21no—
220#107—21no—
221#107—861no—
222#107—861no—
223#103—1722no—
224#102—1722no—
225C4×C8—861no—
226C4×C8—861no—
227#95—1722no—
228C24—1721no—
229C2×Q8—22no—
230C2×Q8—41no—
231C2×Q8—41no—
232C2×Q8—41no—
233C2×Q8—41no—
234C2×Q8—41no—
235C2×D4—862no—
236C2×D4—1721no—
237C2×D4—1721no—
238C2×D4—1721no—
239C2×D4—1721no—
240C2×D4—1721no—
241C22×C4—41no—
242C22×C4—41no—
243C22×C4—432no—
244C22×C4—1721no—
245C22×C4D4×D4311yescharacteristic
246Q16—22no—
247Q16—22no—
248Q16—41no—
249Q16—41no—
250D8—862no—
251D8—862no—
252D8—1721no—
253D8—1721no—
254C2×C8—432no—
255C2×C8—861no—
256C2×C8—861no—
257C2×C8C2×C4×D4311yescharacteristic
258C2×C8#1062189811yescharacteristic
259C2×C8D4×D4311yescharacteristic
260C2×C8D4×D4311yescharacteristic
261C2×C8#1062190011yescharacteristic
262C2×C8C2×C22⋊D4311yescharacteristic
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—1721no—
266C4⋊C4—1721no—
267C22⋊C4—3444no—
268C42—861no—
269C42—861no—
270C16—22no—
271C16—434no—
272C23—3442no—
273C23—3442no—
274C23—3441no—
275C23—3441no—
276C23—1722no—
277C23D8×D4311yescharacteristic
278Q8—42no—
279Q8—42no—
280Q8—81no—
281Q8—81no—
282D4—3441no—
283D4—3441no—
284D4—1722no—
285D4—1722no—
286C2×C4—42no—
287C2×C4—81no—
288C2×C4—81no—
289C2×C4—82no—
290C2×C4—81no—
291C2×C4—434no—
292C2×C4—862no—
293C2×C4—862no—
294C2×C4—3442no—
295C2×C4—3441no—
296C2×C4(C22⋊D43)⋊C411yescharacteristic
297C2×C4#1306329811yescharacteristic
298C2×C4#1306332111yescharacteristic
299C2×C4D8×D4311yescharacteristic
300C2×C4#1306334611yescharacteristic
301C2×C4#1306334611yescharacteristic
302C8—862no—
303C8C22⋊C4×D4311yescharacteristic
304C8C4×C22⋊D4311yescharacteristic
305C8#1306329711yescharacteristic
306C8#1306331111yescharacteristic
307C22—3444no—
308C22—3442no—
309C22—6881no—
310C22—6881no—
311C22—6882no—
312C22#1458297911yescharacteristic
313C22#1458313411yescharacteristic
314C22#1458327411yescharacteristic
315C22SD32×D4312yes—
316C22#1458333212yes—
317C4—82no—
318C4—161no—
319C4—864no—
320C4—6881no—
321C4#1458279911yescharacteristic
322C4#1458297911yescharacteristic
323C4#1458313411yescharacteristic
324C4#1458328011yescharacteristic
325C2—6882no—
326C2#1913545811yescharacteristic
327C2#1913644412yes—
328C2#1913669412yes—
329C2#1913684911yescharacteristic
330C2#1913685711yescharacteristic
subgroupG/H
centerC23D8×D43
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
FittingC2×C43×#358C2
socleC23×C43C2×D8
prime radicalC22×D344C22
cosocleC22×C8×C43C23
hypercenterC2×#358D43
hypocenterC43#13237
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#358

Complements

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

NH ≅ G/Ntype
2. C2×#14582726C2semidirect
4. C2×C16×Dic43C2semidirect
6. #19135457C2semidirect
7. C2×C43×#358C2semidirect
11. C2×#13063268C4semidirect
105. C43⋊C16C22⋊C4semidirect
131. C2×Dic43SD32semidirect
162. C2×#358D43semidirect
191. C43#13237semidirect

Maximal subgroups

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

subgroupindex
C22×#130632682
C2×#145827262
C2×#145827012
C2×C16×Dic432
#191354592
#191354572
C2×C43×#3582
#1323743