Finite Group Databasebeta

← #25255197

Subgroups — #25255197

Order 11008.

2390 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063282C211yesmaximal, characteristic
2#19137200C218yesmaximal, complemented
3#19137195C214yesmaximal, complemented
4#19137190C214yesmaximal
5#19137092C214yesmaximal, complemented
6#19137090C214yesmaximal, complemented
7#19136998C212yesmaximal, complemented
8#19136974C212yesmaximal
9C4×#13063284C211yesmaximal, characteristic, complemented
10C4×#117×C43C211yesmaximal, characteristic, complemented
11C23×C4×D43C2211yescharacteristic
12C2×#13063284C2212yes—
13C2×#13063282C4116yescomplemented
14C2×#13063282C2212yes—
15C2×#13063282C2212yes—
16C2×#13063282C2214yes—
17C22×Dic43⋊C4C2212yes—
18C22×(C2×D43)⋊C4C2212yes—
19C22×C4×Dic43C2211yescharacteristic
20#14582790C22116yes—
21#14582788C22116yes—
22#14582783C22116yescomplemented
23#14582781C22116yescomplemented
24#14582768C2214yescomplemented
25#14582764C2214yescomplemented
26#14582760C2214yes—
27#14582757C2218yes—
28#14582756C2218yes—
29#14582754C2214yes—
30C4×Dic43⋊C4C2218yescomplemented
31C4×C4⋊Dic43C2214yescomplemented
32C4×(C2×D43)⋊C4C2218yes—
33C4×C22⋊Dic43C2214yes—
34#14582745C2212yescomplemented
35C42×Dic43C2212yescomplemented
36C2×#117×C43C2212yes—
37C22×C42×C43C2211yescharacteristic
38C4×C4⋊C4×C43C2214yescomplemented
39C4×C22⋊C4×C43C2214yes—
40C43×#376C2212yescomplemented
41C43×C43C2212yescomplemented
42C24×D43C2311yescharacteristic
43C23×Dic43C2311yescharacteristic
44C23×Dic43C2312yes—
45C22×C4×D43—28no—
46C22×C4×D43C2×C418yes—
47C22×C4×D43C2312yes—
48C22×C4×D43C2312yes—
49#13063284—28no—
50#13063282C2×C4116yes—
51#13063282C2×C4116yes—
52#13063282C2×C4132yes—
53C2×C4⋊Dic43C2314yes—
54C2×Dic43⋊C4C2×C4116yes—
55C2×Dic43⋊C4C23116yes—
56C2×Dic43⋊C4C2314yes—
57C2×Dic43⋊C4C2314yes—
58C2×C22⋊Dic43C2314yes—
59C2×(C2×D43)⋊C4C2×C4116yes—
60C2×(C2×D43)⋊C4C23116yes—
61C2×(C2×D43)⋊C4C2314yes—
62C2×(C2×D43)⋊C4C2314yes—
63C2×C4×Dic43C2×C418yes—
64C2×C4×Dic43C2314yes—
65C2×C4×Dic43C2318yes—
66C2×C4×Dic43C2312yes—
67C2×C4×Dic43C2312yes—
68C43⋊#95C23116yes—
69C43⋊#95C2318yes—
70C43⋊#95C23116yes—
71C23×C4×C43C2312yes—
72C23×C4×C43C2311yescharacteristic
73#117×C43—28no—
74C2×C4⋊C4×C43C2314yes—
75C2×C22⋊C4×C43C2314yes—
76C2×C42×C43C2×C418yes—
77C2×C42×C43C2314yes—
78C2×C42×C43C2318yes—
79C2×C42×C43C2311yescharacteristic
80C2×C42×C43C2311yescharacteristic
81C2×C42×C43C2312yes—
82#95×C43C2318yes—
83C24×C43C2411yescharacteristic
84C23×D43—24no—
85C23×D43—44no—
86C23×D43C22×C414yes—
87C23×D43C2412yes—
88C22×C4×C43—44no—
89C22×C4×C43C22×C418yes—
90C22×C4×C43C22×C414yes—
91C22×C4×C43#4118yes—
92C22×C4×C43C2418yes—
93C22×C4×C43C2412yes—
94C22×C4×C43C2412yes—
95C22×C4×C43C2411yescharacteristic
96C22×C4×C43C2411yescharacteristic
97C22×Dic43—24no—
98C22×Dic43—44no—
99C22×Dic43C22×C414yes—
100C22×Dic43C22×C418yes—
101C22×Dic43C2418yes—
102C22×Dic43C2412yes—
103C22×Dic43C2414yes—
104C2×C4×D43—232no—
105C2×C4×D43—28no—
106C2×C4×D43—28no—
107C2×C4×D43C22×C418yes—
108C2×C4×D43C22×C418yes—
109C4⋊C4×C43—28no—
110C22⋊C4×C43—28no—
111C42×C43—28no—
112C42×C43—48no—
113C42×C43C22×C414yes—
114C42×C43C22×C414yes—
115C42×C43C22×C418yes—
116C22⋊Dic43—28no—
117(C2×D43)⋊C4—416no—
118(C2×D43)⋊C4C22×C4116yes—
119(C2×D43)⋊C4C22×C4116yes—
120C4⋊Dic43—28no—
121Dic43⋊C4—416no—
122Dic43⋊C4C22×C4116yes—
123Dic43⋊C4C22×C4116yes—
124C4×Dic43—28no—
125C4×Dic43—48no—
126C4×Dic43C22×C418yes—
127C4×Dic43C22×C418yes—
128C23×C43—24no—
129C23×C43C23×C412yes—
130C23×C43C2×#4114yes—
131C23×C43C2511yescharacteristic
132C22×D43—28no—
133C22×D43—24no—
134C22×D43—28no—
135C22×D43—48no—
136C22×D43—416no—
137C22×D43C23×C414yes—
138C2×C4×C43—24no—
139C2×C4×C43—24no—
140C2×C4×C43—28no—
141C2×C4×C43—216no—
142C2×C4×C43—48no—
143C2×C4×C43#117116yes—
144C2×C4×C43C23×C414yes—
145C2×C4×C43C23×C414yes—
146C2×C4×C43C23×C412yes—
147C2×C4×C43C23×C412yes—
148C2×C4×C43C2×#4114yes—
149C2×C4×C43C2×#4114yes—
150C2×Dic43—28no—
151C2×Dic43—24no—
152C2×Dic43—28no—
153C2×Dic43—28no—
154C2×Dic43—216no—
155C2×Dic43—48no—
156C2×Dic43C23×C418yes—
157C2×Dic43C23×C414yes—
158C4×D43—216no—
159C4×D43—216no—
160#34048—431nomaximal, Sylow
161C22×C43—24no—
162C22×C43—28no—
163C22×C43C2×#11714yes—
164C22×C43C24×C411yescharacteristic
165C22×C43C22×#4112yes—
166C22×C43#58514yes—
167C2×D43—24no—
168C2×D43—28no—
169C2×D43—416no—
170C2×D43—48no—
171C4×C43—24no—
172C4×C43—24no—
173C4×C43—48no—
174C4×C43C2×#11714yes—
175C4×C43C2×#11714yes—
176Dic43—24no—
177Dic43—28no—
178Dic43—48no—
179C22×#117—431no—
180#2314—438no—
181#2313—434no—
182#2312—434no—
183#2298—434no—
184#2298—434no—
185#2285—432no—
186#2280—432no—
187C4×#117—431no—
188C4×#117D4311yescharacteristic, complemented
189C2×C43—24no—
190C2×C43C22×#11711yescharacteristic
191C2×C43#342812yes—
192C2×C43#345514yes—
193D43—44no—
194C24×C4—431no—
195C2×#117—432no—
196C2×#117—434no—
197C2×#117—432no—
198C2×#117—432no—
199C2×#117—4316no—
200C2×#117C2×D4312yes—
201C22×C4⋊C4—432no—
202C22×C22⋊C4—432no—
203C22×C42—431no—
204C22×C42C2×D4311yescharacteristic
205#388—4316no—
206#388—4316no—
207#387—4316no—
208#387—4316no—
209#384—434no—
210#382—434no—
211#381—434no—
212#380—438no—
213#380—438no—
214#379—434no—
215C4×C4⋊C4—434no—
216C4×C4⋊C4—438no—
217C4×C4⋊C4C2×D4314yescomplemented
218C4×C22⋊C4—434no—
219C4×C22⋊C4—438no—
220C4×C22⋊C4C2×D4314yes—
221#376—432no—
222#376C2×D4312yescomplemented
223C43—432no—
224C43C2×D4312yescomplemented
225C43#3404811yescharacteristic, complemented, Sylow
226C25—431no—
227C23×C4—431no—
228C23×C4—432no—
229C23×C4—438no—
230C23×C4—432no—
231C23×C4—432no—
232C23×C4—868no—
233C23×C4C22×D4312yes—
234C23×C4C22×D4311yescharacteristic
235#117—28no—
236#117—4332no—
237#117—4316no—
238#117—4316no—
239#117—868no—
240C2×C4⋊C4—4316no—
241C2×C4⋊C4—434no—
242C2×C4⋊C4—434no—
243C2×C4⋊C4—434no—
244C2×C4⋊C4—4316no—
245C2×C4⋊C4C22×D4314yes—
246C2×C22⋊C4—4316no—
247C2×C22⋊C4—434no—
248C2×C22⋊C4—434no—
249C2×C22⋊C4—434no—
250C2×C22⋊C4—4316no—
251C2×C22⋊C4C22×D4314yes—
252C2×C42—438no—
253C2×C42—432no—
254C2×C42—432no—
255C2×C42—434no—
256C2×C42—438no—
257C2×C42C4×D4318yes—
258C2×C42C22×D4314yes—
259C2×C42C22×D4318yes—
260C2×C42C22×D4312yes—
261C2×C42C22×D4311yescharacteristic
262C2×C42C22×D4311yescharacteristic
263#95—438no—
264#95—4316no—
265#95—4316no—
266#95C22×D4318yes—
267C24—432no—
268C24—434no—
269C24—864no—
270C24—1724no—
271C24C23×D4311yescharacteristic
272C22×C4—44no—
273C22×C4—434no—
274C22×C4—432no—
275C22×C4—434no—
276C22×C4—438no—
277C22×C4—438no—
278C22×C4—438no—
279C22×C4—438no—
280C22×C4—864no—
281C22×C4—8632no—
282C22×C4—868no—
283C22×C4—868no—
284C22×C4—1724no—
285C22×C4C2×C4×D4318yes—
286C22×C4C2×C4×D4314yes—
287C22×C4#1062189818yes—
288C22×C4C23×D4318yes—
289C22×C4C23×D4312yes—
290C22×C4C23×D4312yes—
291C22×C4C23×D4311yescharacteristic
292C22×C4C23×D4311yescharacteristic
293C4⋊C4—28no—
294C4⋊C4—4316no—
295C4⋊C4—4316no—
296C4⋊C4—868no—
297C4⋊C4—17216no—
298C22⋊C4—28no—
299C22⋊C4—4316no—
300C22⋊C4—4316no—
301C22⋊C4—868no—
302C22⋊C4—17216no—
303C42—28no—
304C42—48no—
305C42—438no—
306C42—438no—
307C42—868no—
308C42—1728no—
309C42C2×C4×D4318yes—
310C42C2×C4×D4314yes—
311C42C2×C4×D4314yes—
312C23—24no—
313C23—434no—
314C23—868no—
315C23—864no—
316C23—868no—
317C23—1728no—
318C23—17216no—
319C23C22×C4×D4312yes—
320C23C2×#1062189814yes—
321C23C24×D4311yescharacteristic
322C2×C4—24no—
323C2×C4—24no—
324C2×C4—28no—
325C2×C4—216no—
326C2×C4—48no—
327C2×C4—438no—
328C2×C4—434no—
329C2×C4—868no—
330C2×C4—864no—
331C2×C4—868no—
332C2×C4—8616no—
333C2×C4—8616no—
334C2×C4—868no—
335C2×C4—8616no—
336C2×C4—1728no—
337C2×C4#13063282116yes—
338C2×C4C22×C4×D4314yes—
339C2×C4C22×C4×D4314yes—
340C2×C4C22×C4×D4312yes—
341C2×C4C22×C4×D4312yes—
342C2×C4C2×#1062189814yes—
343C2×C4C2×#1062189814yes—
344C22—24no—
345C22—28no—
346C22—868no—
347C22—864no—
348C22—17216no—
349C22—1728no—
350C22C2×#1306328214yes—
351C22C23×C4×D4311yescharacteristic
352C22C22×#1062189812yes—
353C22#1458373514yes—
354C4—24no—
355C4—24no—
356C4—48no—
357C4—868no—
358C4—864no—
359C4—1728no—
360C4C2×#1306328214yes—
361C4C2×#1306328214yes—
362C2—24no—
363C2—1724no—
364C2C22×#1306328211yescharacteristic
365C2#1914779612yes—
366C2#1914798014yes—
subgroupG/H
centerC22×C4C23×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC4×#117×C43C2
socle, cosocleC23×C43C25
prime radicalC24×D43C23
hypercenterC4×#117D43
hypocenterC43#34048
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C4×#117

Complements

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

NH ≅ G/Ntype
2. #19137200C2semidirect
3. #19137195C2semidirect
5. #19137092C2semidirect
6. #19137090C2semidirect
7. #19136998C2semidirect
9. C4×#13063284C2semidirect
10. C4×#117×C43C2semidirect
13. C2×#13063282C4semidirect
22. #14582783C22semidirect
23. #14582781C22semidirect
24. #14582768C22semidirect
25. #14582764C22semidirect
30. C4×Dic43⋊C4C22semidirect
31. C4×C4⋊Dic43C22semidirect
34. #14582745C22semidirect
35. C42×Dic43C22semidirect
38. C4×C4⋊C4×C43C22semidirect
40. C43×#376C22semidirect
41. C43×C43C22semidirect
188. C4×#117D43semidirect
217. C4×C4⋊C4C2×D43semidirect
222. #376C2×D43semidirect
224. C43C2×D43semidirect
225. C43#34048semidirect

Maximal subgroups

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

subgroupindex
C22×#130632822
#191372002
#191371952
#191371902
#191370922
#191370902
#191369982
#191369742
C4×#130632842
C4×#117×C432
#3404843