Finite Group Databasebeta

← #25014976

Subgroups — #25014976

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×#14582703C211yesmaximal, characteristic, complemented
4C2×#14582699C211yesmaximal, characteristic
5C2×C4×C43⋊C16C211yesmaximal, characteristic, complemented
6#19135461C211yesmaximal, characteristic
7C43×#1969C211yesmaximal, characteristic, complemented
8C22×D344C2211yescharacteristic
9C2×#13063268—22no—
10C2×#13063268—22no—
11C2×#13063268C414yescomplemented
12C22×C43⋊C16C2211yescharacteristic
13C22×C43⋊C16C2211yescharacteristic
14C2×#13063259C2211yescharacteristic
15C2×#13063247—21no—
16#14582801—21no—
17#14582726—22no—
18#14582703—22no—
19#14582699—22no—
20C4×C43⋊C16—22no—
21C22×Q16×C43C2211yescharacteristic
22C2×#107×C43C2211yescharacteristic
23C2×#103×C43—21no—
24C2×C4×C8×C43C2211yescharacteristic
25C43×#391—21no—
26C22×D172—21no—
27C2×D344—21no—
28C2×D344—21no—
29C2×D344—21no—
30C2×D344—21no—
31C2×D344—21no—
32C2×D344C2×C412yes—
33C2×C4⋊Dic43—21no—
34C2×(C2×D43)⋊C4—42no—
35#13063268—28no—
36C2×C43⋊C16—21no—
37C2×C43⋊C16—21no—
38C2×C43⋊C16C2×C412yes—
39C2×C43⋊C16D412yes—
40C2×C43⋊C16D412yes—
41C2×C43⋊C16D412yes—
42#13063259—21no—
43#13063259—21no—
44#13063247—42no—
45C22×Q8×C43—21no—
46C2×Q16×C43—21no—
47C2×Q16×C43—21no—
48C2×Q16×C43—21no—
49C2×Q16×C43—21no—
50C2×Q16×C43—21no—
51C2×Q16×C43C2×C412yes—
52C22×C8×C43D411yescharacteristic
53C22×C8×C43C2311yescharacteristic
54C2×C4⋊C4×C43—21no—
55C2×C42×C43D411yescharacteristic
56#107×C43—21no—
57#107×C43—21no—
58#103×C43—42no—
59C4×C8×C43—21no—
60C4×C8×C43—21no—
61#95×C43—42no—
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×C43D812yes—
72C22×C4×C43C2×D411yescharacteristic
73C22×Dic43—41no—
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×C43—21no—
85C2×C8×C43—21no—
86C2×C8×C43D812yes—
87C2×C8×C43C22×C411yescharacteristic
88C2×C8×C43C2×D411yescharacteristic
89C2×C8×C43C2×D411yescharacteristic
90C2×C8×C43C2×D411yescharacteristic
91C2×C8×C43#4111yescharacteristic
92C2×C8×C43#4111yescharacteristic
93C4⋊C4×C43—41no—
94C4⋊C4×C43—41no—
95C42×C43—21no—
96C42×C43—21no—
97(C2×D43)⋊C4—84no—
98C4⋊Dic43—41no—
99C4⋊Dic43—41no—
100D344—22no—
101D344—22no—
102D344—41no—
103D344—41no—
104C43⋊C16—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—22no—
117C2×C4×C43—22no—
118C2×C4×C43—42no—
119C2×C4×C43—81no—
120C2×C4×C43—81no—
121C2×C4×C43—81no—
122C2×C4×C43—82no—
123C2×C4×C43SD3214yescomplemented
124C2×C4×C43C4×D411yescharacteristic
125C2×C4×C43#12111yescharacteristic
126C2×C4×C43#12711yescharacteristic
127C2×C4×C43C2×D811yescharacteristic
128C2×C4×C43#13511yescharacteristic
129C2×C4×C43#13511yescharacteristic
130C2×Dic43—81no—
131C2×Dic43—82no—
132D172—42no—
133D172—42no—
134D172—81no—
135D172—81no—
136C8×C43—22no—
137C8×C43C2×C22⋊C411yescharacteristic
138C8×C43C4×D411yescharacteristic
139C8×C43#12111yescharacteristic
140C8×C43#12411yescharacteristic
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—24no—
153C4×C43—82no—
154C4×C43—161no—
155C4×C43#39011yescharacteristic
156C4×C43C4×D811yescharacteristic
157C4×C43#46611yescharacteristic
158C4×C43#49511yescharacteristic
159Dic43—161no—
160C22×SD32—431no—
161C2×#367—431no—
162C2×#358—431no—
163C2×#357—431no—
164C2×C4×C16—431no—
165#1970—431no—
166#1969D4311yescharacteristic, complemented
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×C16—431no—
180C2×#107—431no—
181C2×#107C2×D4311yescharacteristic
182C2×#103—21no—
183C2×#102—861no—
184C2×C4×C8C2×D4311yescharacteristic
185#391—21no—
186#390—861no—
187#367—862no—
188#358—862no—
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×C8C22⋊D4311yescharacteristic
207C22×C8C22×D4311yescharacteristic
208C2×C4⋊C4—21no—
209C2×C4⋊C4—861no—
210C2×C22⋊C4—1722no—
211C2×C42C22⋊D4311yescharacteristic
212SD32—868no—
213C2×C16—432no—
214C2×C16—432no—
215C2×C16—432no—
216C2×C16—432no—
217C2×C16—861no—
218C2×C16—861no—
219#107—21no—
220#107—21no—
221#107—861no—
222#107—861no—
223#103—42no—
224#102—1722no—
225C4×C8—21no—
226C4×C8—21no—
227#95—42no—
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—1721no—
244C22×C4#1062188212yes—
245C22×C4C2×C22⋊D4311yescharacteristic
246Q16—22no—
247Q16—22no—
248Q16—41no—
249Q16—41no—
250D8—862no—
251D8—862no—
252D8—1721no—
253D8—1721no—
254C2×C8—21no—
255C2×C8—21no—
256C2×C8#1062188212yes—
257C2×C8C2×C4×D4311yescharacteristic
258C2×C8#1062189811yescharacteristic
259C2×C8D4×D4311yescharacteristic
260C2×C8D4×D4311yescharacteristic
261C2×C8D4×D4311yescharacteristic
262C2×C8#1062190011yescharacteristic
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—1721no—
266C4⋊C4—1721no—
267C22⋊C4—3444no—
268C42—21no—
269C42—21no—
270C16—434no—
271C16—862no—
272C23—3442no—
273C23—3442no—
274C23—3441no—
275C23—3441no—
276C23—1722no—
277C23C2×#1062188211yescharacteristic
278Q8—42no—
279Q8—42no—
280Q8—81no—
281Q8—81no—
282D4—3441no—
283D4—3441no—
284D4—1722no—
285D4—1722no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—42no—
289C2×C4—81no—
290C2×C4—81no—
291C2×C4—82no—
292C2×C4—81no—
293C2×C4—3442no—
294C2×C4—3441no—
295C2×C4#1306326814yescomplemented
296C2×C4C4×C22⋊D4311yescharacteristic
297C2×C4#1306329711yescharacteristic
298C2×C4#1306332111yescharacteristic
299C2×C4C2×#1062188211yescharacteristic
300C2×C4#1306334511yescharacteristic
301C2×C4#1306334511yescharacteristic
302C8—22no—
303C8C22⋊C4×D4311yescharacteristic
304C8(C22⋊D43)⋊C411yescharacteristic
305C8#1306329811yescharacteristic
306C8#1306331111yescharacteristic
307C22—3444no—
308C22—3442no—
309C22—6881no—
310C22—6881no—
311C22—6882no—
312C22C4×#1062188211yescharacteristic
313C22#1458313311yescharacteristic
314C22#1458327511yescharacteristic
315C22C2×#1306326812yes—
316C22#1458332912yes—
317C4—24no—
318C4—82no—
319C4—161no—
320C4—6881no—
321C4#1458279911yescharacteristic
322C4C4×#1062188211yescharacteristic
323C4#1458313311yescharacteristic
324C4#1458328111yescharacteristic
325C2—6882no—
326C2#1913546011yescharacteristic
327C2C4×#1306326812yes—
328C2#1913669312yes—
329C2#1913685211yescharacteristic
330C2#1913685411yescharacteristic
subgroupG/H
centerC23C2×#10621882
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
FittingC43×#1969C2
socleC23×C43C2×D8
prime radicalC22×D344C22
cosocleC22×C8×C43C23
hypercenter#1969D43
hypocenterC43#13237
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ #1969

Complements

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

NH ≅ G/Ntype
2. C2×#14582726C2semidirect
3. C2×#14582703C2semidirect
5. C2×C4×C43⋊C16C2semidirect
7. C43×#1969C2semidirect
11. C2×#13063268C4semidirect
105. C43⋊C16C22⋊C4semidirect
123. C2×C4×C43SD32semidirect
166. #1969D43semidirect
191. C43#13237semidirect
295. C2×C4#13063268semidirect

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×#145827032
C2×#145826992
C2×C4×C43⋊C162
#191354612
C43×#19692
#1323743