Finite Group Databasebeta

← #25094632

Subgroups — #25094632

Order 11008.

1010 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063261C211yesmaximal, characteristic
2#19143014C212yesmaximal
3C2×#14582854C211yesmaximal, characteristic
4#19134481C214yesmaximal, complemented
5#19134476C214yesmaximal, complemented
6#19134304C212yesmaximal
7C2×C43×#427C211yesmaximal, characteristic
8C22×#10621877C2212yes—
9C22×#10621877C2211yescharacteristic
10C2×#13063284C2211yescharacteristic
11C2×#13063261C418yescomplemented
12C2×#13063261C2212yes—
13C2×#13063261C2212yes—
14#14582855—24no—
15#14582855C2218yes—
16#14582854C418yescomplemented
17C4×#10621877—24no—
18C2×#13063235C2212yes—
19C2×C8×Dic43C2212yes—
20#14582658C2218yes—
21C23×C8×C43C2211yescharacteristic
22C2×#117×C43C2212yes—
23C43×#427C412yescomplemented
24C43×#427C412yescomplemented
25C43×#427C2212yes—
26C43×#427C2212yes—
27C2×#107×C43C412yescomplemented
28C2×#106×C43C412yescomplemented
29C2×#10621877—22no—
30C2×#10621877—24no—
31C2×#10621877C2×C418yes—
32C2×#10621877C2×C414yes—
33C2×#10621877D412yes—
34C2×#10621877D412yes—
35C2×#10621877Q814yes—
36C2×#10621877C2314yes—
37C22×C43⋊C8—22no—
38C22×C43⋊C8C2312yes—
39#13063284—22no—
40#13063284C2×C414yes—
41C2×C4⋊Dic43—21no—
42C2×C22⋊Dic43—21no—
43C2×C4×Dic43C2312yes—
44#13063261C2×C418yescomplemented
45#13063261C2×C418yescomplemented
46#13063236—28no—
47#13063235C2×C418yescomplemented
48C4×C43⋊C8—28no—
49C8×Dic43C2×C418yescomplemented
50C23×C4×C43C2311yescharacteristic
51C22×C8×C43C2×C414yes—
52C22×C8×C43C2×C414yes—
53C22×C8×C43C2×C411yescharacteristic
54C22×C8×C43C2×C411yescharacteristic
55C22×C8×C43C2×C411yescharacteristic
56C22×C8×C43C2×C411yescharacteristic
57C22×C8×C43C2311yescharacteristic
58C22×C8×C43C2311yescharacteristic
59#117×C43—22no—
60#117×C43—22no—
61#117×C43C2×C414yes—
62#117×C43C2314yes—
63C2×C4⋊C4×C43C2×C414yes—
64C2×C22⋊C4×C43—22no—
65C2×C42×C43—22no—
66#107×C43C2×C414yes—
67#107×C43C2×C414yes—
68#106×C43C2×C414yes—
69#106×C43C2×C414yes—
70C24×C43#4111yescharacteristic
71C22×C4×C43—24no—
72C22×C4×C43C22×C412yes—
73C22×C4×C43C22×C411yescharacteristic
74C22×C4×C43C22×C411yescharacteristic
75C22×C4×C43C22×C412yes—
76C22×C4×C43C2×D411yescharacteristic
77C22×C4×C43C2×D411yescharacteristic
78C22×C4×C43C2×Q812yes—
79C22×C4×C43#4112yes—
80C22×C4×C43#4111yescharacteristic
81C22×C4×C43C2411yescharacteristic
82C22×Dic43—22no—
83C2×C8×C43C4214yes—
84C2×C8×C43C4214yes—
85C2×C8×C43C4214yes—
86C2×C8×C43C4214yes—
87C2×C8×C43C22×C412yes—
88C2×C8×C43C22×C412yes—
89C2×C8×C43C22×C412yes—
90C2×C8×C43C22×C412yes—
91C2×C8×C43C22×C411yescharacteristic
92C2×C8×C43C22×C411yescharacteristic
93C2×C8×C43C22×C411yescharacteristic
94C2×C8×C43C22×C411yescharacteristic
95C4⋊C4×C43—24no—
96C4⋊C4×C43C22×C418yes—
97C22⋊C4×C43—24no—
98C22⋊C4×C43—24no—
99C42×C43—24no—
100C42×C43—24no—
101C22⋊Dic43—24no—
102C4⋊Dic43—24no—
103C4×Dic43—22no—
104C4×Dic43C22×C414yes—
105#10621877—28no—
106#10621877—24no—
107#10621877C4⋊C418yes—
108#10621877C4⋊C418yes—
109#10621877C22×C418yes—
110C2×C43⋊C8—28no—
111C2×C43⋊C8—24no—
112C2×C43⋊C8C22×C414yes—
113C2×C43⋊C8C2×D414yes—
114C2×C43⋊C8C2×Q814yes—
115C23×C43—42no—
116C23×C43#11712yes—
117C23×C43C4×D411yescharacteristic
118C23×C43C4×D411yescharacteristic
119C23×C43C4×Q812yes—
120C23×C43C2×#4111yescharacteristic
121C2×C4×C43—28no—
122C2×C4×C43—84no—
123C2×C4×C43C2×C4212yes—
124C2×C4×C43C2×C4212yes—
125C2×C4×C43C2×C4⋊C412yes—
126C2×C4×C43C2×C4⋊C412yes—
127C2×C4×C43#11712yes—
128C2×C4×C43C4×D412yes—
129C2×C4×C43C4×D412yes—
130C2×C4×C43C4×D411yescharacteristic
131C2×C4×C43C4×D411yescharacteristic
132C2×C4×C43C4×Q812yes—
133C2×C4×C43C4×Q812yes—
134C2×C4×C43C4×Q812yes—
135C2×C4×C43C23×C411yescharacteristic
136C2×C4×C43C23×C411yescharacteristic
137C2×C4×C43C23×C411yescharacteristic
138C2×C4×C43C22×D411yescharacteristic
139C2×C4×C43C22×Q811yescharacteristic
140C2×C4×C43C2×#4111yescharacteristic
141C2×Dic43—24no—
142C2×Dic43—44no—
143C8×C43C2×C4212yes—
144C8×C43C2×C4212yes—
145C8×C43C2×C4212yes—
146C8×C43C2×C4212yes—
147C43⋊C8—28no—
148C43⋊C8C2×C4⋊C418yes—
149#20446—431nomaximal, Sylow
150C22×C43—22no—
151C22×C43—22no—
152C22×C43—22no—
153C22×C43—42no—
154C22×C43—42no—
155C22×C43C4×C4⋊C412yes—
156C22×C43C4×C4⋊C412yes—
157C22×C43C2×#11711yescharacteristic
158C22×C43C2×C4×D411yescharacteristic
159C22×C43C2×C4×Q811yescharacteristic
160C4×C43—48no—
161C4×C43C4×C4⋊C412yes—
162C4×C43C4×C4⋊C412yes—
163C4×C43C22×C4211yescharacteristic
164C4×C43C22×C4⋊C411yescharacteristic
165C4×C43C2×C4×D411yescharacteristic
166C4×C43C2×C4×Q811yescharacteristic
167Dic43—44no—
168C22×#108—431no—
169C2×#427D4311yescharacteristic
170#2873—432no—
171C2×#405—431no—
172#1773—434no—
173#1772—434no—
174#1733—432no—
175C2×C43—21no—
176C2×C43—21no—
177C2×C43—22no—
178C2×C43—22no—
179C2×C43C2×C4×C4⋊C411yescharacteristic
180C2×C43#295712yes—
181C22×M16—431no—
182C22×M16—432no—
183C23×C8C2×D4311yescharacteristic
184C2×#117—431no—
185C2×#117C2×D4312yes—
186C2×#108—432no—
187C2×#108—432no—
188C2×#108—438no—
189#427Dic4312yescomplemented
190#427Dic4312yescomplemented
191#427C2×D4312yes—
192#427C2×D4312yes—
193C2×#107Dic4312yescomplemented
194C2×#106Dic4312yescomplemented
195#405—438no—
196#405—438no—
197#405—864no—
198C4×M16—864no—
199C2×#97—432no—
200C2×C4×C8—432no—
201#339—438no—
202C43#2044611yescharacteristic, complemented, Sylow
203C23×C4C22×D4311yescharacteristic
204C2×M16—434no—
205C2×M16—432no—
206C2×M16—432no—
207C2×M16—434no—
208C2×M16—438no—
209C2×M16—434no—
210C2×M16—862no—
211C2×M16—864no—
212C22×C8—432no—
213C22×C8—862no—
214C22×C8C4×D4314yes—
215C22×C8C4×D4314yes—
216C22×C8C2×Dic4311yescharacteristic
217C22×C8C2×Dic4311yescharacteristic
218C22×C8C2×Dic4311yescharacteristic
219C22×C8C2×Dic4311yescharacteristic
220C22×C8C22×D4311yescharacteristic
221C22×C8C22×D4311yescharacteristic
222#117—22no—
223#117—22no—
224#117—434no—
225#117—862no—
226#117C2×Dic4314yes—
227#117C22×D4314yes—
228C2×C4⋊C4—861no—
229C2×C4⋊C4C2×Dic4314yes—
230C2×C22⋊C4—22no—
231C2×C22⋊C4—861no—
232C2×C42—22no—
233C2×C42—432no—
234#108—438no—
235#108—438no—
236#107C2×Dic4314yes—
237#107C2×Dic4314yes—
238#106C2×Dic4314yes—
239#106C2×Dic4314yes—
240#97—438no—
241#97—868no—
242C4×C8—438no—
243C4×C8—868no—
244C24#1062190011yescharacteristic
245C22×C4—24no—
246C22×C4—862no—
247C22×C4C2×C4×D4312yes—
248C22×C4C2×C4×D4312yes—
249C22×C4D4×D4311yescharacteristic
250C22×C4D4×D4311yescharacteristic
251C22×C4#1062190011yescharacteristic
252C22×C4Q8×D4312yes—
253C22×C4#1062190212yes—
254C22×C4C22×Dic4311yescharacteristic
255C22×C4C22×Dic4311yescharacteristic
256C22×C4C23×D4311yescharacteristic
257M16—438no—
258M16—438no—
259M16—438no—
260M16—868no—
261M16—864no—
262C2×C8—434no—
263C2×C8—434no—
264C2×C8—434no—
265C2×C8—868no—
266C2×C8—864no—
267C2×C8C4×Dic4314yes—
268C2×C8C4×Dic4314yes—
269C2×C8C4×Dic4314yes—
270C2×C8C4×Dic4314yes—
271C2×C8C2×C4×D4312yes—
272C2×C8C2×C4×D4312yes—
273C2×C8C2×C4×D4312yes—
274C2×C8C2×C4×D4312yes—
275C2×C8C22×Dic4311yescharacteristic
276C2×C8C22×Dic4311yescharacteristic
277C2×C8C22×Dic4311yescharacteristic
278C2×C8C22×Dic4311yescharacteristic
279C4⋊C4—24no—
280C4⋊C4—864no—
281C4⋊C4C22×Dic4318yes—
282C22⋊C4—24no—
283C22⋊C4—24no—
284C22⋊C4—864no—
285C42—24no—
286C42—24no—
287C42—434no—
288C42—862no—
289C23—42no—
290C23#1306328312yes—
291C23D4×Dic4311yescharacteristic
292C23D4×Dic4311yescharacteristic
293C23#1306329012yes—
294C23C2×#1062190011yescharacteristic
295C2×C4—28no—
296C2×C4—84no—
297C2×C4—864no—
298C2×C4—1724no—
299C2×C4C2×C4×Dic4312yes—
300C2×C4C2×C4×Dic4312yes—
301C2×C4C4⋊C4×D4312yes—
302C2×C4C4⋊C4×D4312yes—
303C2×C4#1306328312yes—
304C2×C4#1306328712yes—
305C2×C4#1306328712yes—
306C2×C4D4×Dic4311yescharacteristic
307C2×C4D4×Dic4311yescharacteristic
308C2×C4#1306329012yes—
309C2×C4Q8×Dic4312yes—
310C2×C4Q8×Dic4312yes—
311C2×C4C22×C4×D4311yescharacteristic
312C2×C4C22×C4×D4311yescharacteristic
313C2×C4C23×Dic4311yescharacteristic
314C2×C4C2×D4×D4311yescharacteristic
315C2×C4C2×Q8×D4311yescharacteristic
316C2×C4C2×#1062190211yescharacteristic
317C8—438no—
318C8—868no—
319C8C2×C4×Dic4312yes—
320C8C2×C4×Dic4312yes—
321C8C2×C4×Dic4312yes—
322C8C2×C4×Dic4312yes—
323C22—22no—
324C22—22no—
325C22—22no—
326C22—42no—
327C22—42no—
328C22C4⋊C4×Dic4312yes—
329C22C4⋊C4×Dic4312yes—
330C22C2×#1306328311yescharacteristic
331C22C2×D4×Dic4311yescharacteristic
332C22C2×#1306329011yescharacteristic
333C4—48no—
334C4—1724no—
335C4C4⋊C4×Dic4312yes—
336C4C4⋊C4×Dic4312yes—
337C4C22×C4×Dic4311yescharacteristic
338C4C2×C4⋊C4×D4311yescharacteristic
339C4C2×#1306328711yescharacteristic
340C4C2×Q8×Dic4311yescharacteristic
341C2—21no—
342C2—21no—
343C2—22no—
344C2—22no—
345C2C2×C4⋊C4×Dic4311yescharacteristic
346C2#1914351212yes—
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC4×C43C22×C42
FrattiniC22×C4C23×D43
FittingC2×C43×#427C2
socleC22×C43C2×C4×D4
prime radicalC24×C43#41
cosocleC22×C4×C43C24
hypercenterC2×#427D43
hypocenterC43#20446
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#427

Complements

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

NH ≅ G/Ntype
4. #19134481C2semidirect
5. #19134476C2semidirect
11. C2×#13063261C4semidirect
16. #14582854C4semidirect
23. C43×#427C4semidirect
24. C43×#427C4semidirect
27. C2×#107×C43C4semidirect
28. C2×#106×C43C4semidirect
44. #13063261C2×C4semidirect
45. #13063261C2×C4semidirect
47. #13063235C2×C4semidirect
49. C8×Dic43C2×C4semidirect
189. #427Dic43semidirect
190. #427Dic43semidirect
193. C2×#107Dic43semidirect
194. C2×#106Dic43semidirect
202. C43#20446semidirect

Maximal subgroups

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

subgroupindex
C22×#130632612
#191430142
C2×#145828542
#191344812
#191344762
#191343042
C2×C43×#4272
#2044643