Finite Group Databasebeta

← #25960382

Subgroups — #25960382

Order 11008.

2122 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583367C211yesmaximal, characteristic
2#19143259C2116yesmaximal, complemented
3#19143231C214yesmaximal, complemented
4#19143226C214yesmaximal, complemented
5C2×#14582922C212yesmaximal, complemented
6#19143039C212yesmaximal
7#19143014C211yesmaximal, characteristic, complemented
8C43×#2873C211yesmaximal, characteristic, complemented
9C22×#10621898C2211yescharacteristic
10C22×#10621877C2212yes—
11#14583367C414yes—
12#14583367C414yes—
13#14583367C2218yes—
14C2×#13063290C412yes—
15C2×#13063287C412yes—
16C2×(C22⋊D43)⋊C4C414yes—
17C2×#13063282C2212yes—
18C22×C4×Dic43C2211yescharacteristic
19C2×C42×D43C2212yes—
20#14582961C22116yescomplemented
21#14582958C22116yescomplemented
22#14582954C22116yescomplemented
23#14582950C22116yescomplemented
24#14582922C2214yes—
25#14582922C2214yes—
26#14582922C2218yescomplemented
27C2×Dic43⋊C8C2218yescomplemented
28#14582867C2218yes—
29#14582865C2218yes—
30#14582862C2218yes—
31#14582855C2218yescomplemented
32C4×#10621877C2214yes—
33C22×M16×C43C2212yes—
34C2×#117×C43C2211yescharacteristic
35C43×#405C2218yescomplemented
36C4×M16×C43C2214yes—
37C2×#10621898—28no—
38C2×#10621898C2×C414yes—
39C2×#10621898C2314yes—
40C22×Dic86C2×C411yescharacteristic
41C22×D172C2×C411yescharacteristic
42C22×C22⋊D43C2×C412yes—
43C23×Dic43C2×C412yes—
44C22×C4×D43C2×C414yes—
45C22×C4×D43C2312yes—
46C2×#10621877—28no—
47C2×#10621877C2314yes—
48C2×#10621877C2314yes—
49C22×C43⋊C8C2314yes—
50#13063290C2×C418yes—
51#13063290C2×C418yes—
52#13063287C2×C418yes—
53#13063287C2×C418yes—
54(C22⋊D43)⋊C4C2×C4116yes—
55(C22⋊D43)⋊C4C2×C4116yes—
56#13063282C2×C418yes—
57#13063282C2318yes—
58C2×Dic43⋊C4C2×C414yes—
59C2×(C2×D43)⋊C4C2×C414yes—
60C2×C4×Dic43C2×C414yes—
61C2×C4×Dic43C2×C412yes—
62C2×C4×Dic43C2×C412yes—
63C2×C4×Dic43C2×C412yes—
64C2×C4×Dic43C2311yescharacteristic
65C2×C4×Dic43C2311yescharacteristic
66C2×C4×Dic43C2314yes—
67C42×D43C2×C414yes—
68C42×D43C2×C414yes—
69C42×D43C2318yes—
70Dic43⋊C8C23116yes—
71Dic43⋊C8C23116yes—
72(C2×D43)⋊C8C23132yes—
73#13063236C2318yes—
74C4×C43⋊C8C2318yes—
75C23×C4×C43C2311yescharacteristic
76C2×M16×C43—28no—
77C2×M16×C43C2314yes—
78C2×M16×C43C2314yes—
79C22×C8×C43C2314yes—
80#117×C43C2×C414yes—
81#117×C43C2314yes—
82C2×C4⋊C4×C43C2×C412yes—
83C2×C22⋊C4×C43C2×C412yes—
84C2×C42×C43C2312yes—
85#97×C43C2318yes—
86C4×C8×C43C2318yes—
87C24×C43C22×C411yescharacteristic
88C23×D43C22×C412yes—
89C22×C4×C43C22×C414yes—
90C22×C4×C43C22×C411yescharacteristic
91C22×C4×C43C22×C412yes—
92C22×C4×C43#4118yes—
93C22×C4×C43C2411yescharacteristic
94C22×C4×C43C2412yes—
95C2×C22⋊D43—28no—
96C2×C22⋊D43C22×C418yes—
97C22×Dic43—44no—
98C22×Dic43C22×C412yes—
99C22×Dic43C22×C412yes—
100C22×Dic43C22×C414yes—
101C22×Dic43C22×C412yes—
102C22×Dic43C22×C414yes—
103#10621898—216no—
104#10621898—28no—
105#10621898—28no—
106C2×D172—24no—
107C2×D172C22×C414yes—
108C2×C4×D43—28no—
109C2×C4×D43—48no—
110C2×C4×D43C22×C414yes—
111C2×C4×D43C22×C418yes—
112C2×C4×D43C22×C418yes—
113C2×C4×D43C2414yes—
114C2×Dic86—24no—
115C2×Dic86C22×C414yes—
116M16×C43—28no—
117M16×C43—28no—
118C2×C8×C43—28no—
119C2×C8×C43C2418yes—
120C4⋊C4×C43C22×C418yes—
121C22⋊C4×C43C22×C418yes—
122C42×C43C22×C414yes—
123C42×C43C2414yes—
124(C2×D43)⋊C4C22×C4116yes—
125Dic43⋊C4C22×C4116yes—
126C4×Dic43C22×C411yescharacteristic
127C4×Dic43C22×C411yescharacteristic
128C4×Dic43C22×C418yes—
129C4×Dic43C22×C418yes—
130C4×Dic43C22×C412yes—
131C4×Dic43C22×C414yes—
132C4×Dic43C22×C414yes—
133C4×Dic43C2412yes—
134C4×Dic43C2412yes—
135#10621877—28no—
136#10621877—28no—
137C2×C43⋊C8—28no—
138C2×C43⋊C8C2418yes—
139C23×C43—42no—
140C23×C43#11714yes—
141C23×C43C23×C412yes—
142C23×C43C23×C411yescharacteristic
143C22×D43—24no—
144C22×D43—44no—
145C22×D43C23×C414yes—
146C2×C4×C43—44no—
147C2×C4×C43#11714yes—
148C2×C4×C43#11718yes—
149C2×C4×C43C23×C418yes—
150C2×C4×C43C23×C411yescharacteristic
151C2×C4×C43C23×C412yes—
152C2×C4×C43C2×#4114yes—
153C2×C4×C43C2×#4114yes—
154C2×C4×C43C2×#4114yes—
155C2×C4×C43C2511yescharacteristic
156C22⋊D43—216no—
157C2×Dic43—24no—
158C2×Dic43—24no—
159C2×Dic43—28no—
160C2×Dic43—44no—
161C2×Dic43—42no—
162C2×Dic43C23×C412yes—
163C2×Dic43C23×C414yes—
164C2×Dic43C23×C414yes—
165C2×Dic43C23×C412yes—
166D172—28no—
167C4×D43—28no—
168C4×D43—28no—
169C4×D43—216no—
170C4×D43—48no—
171Dic86—28no—
172C8×C43—28no—
173C43⋊C8—28no—
174#60125—431nomaximal, Sylow
175C22×C43—22no—
176C22×C43—24no—
177C22×C43—44no—
178C22×C43C2×#11712yes—
179C22×C43C2×#11714yes—
180C22×C43C24×C411yescharacteristic
181C2×D43—24no—
182C2×D43—28no—
183C2×D43—48no—
184C4×C43—28no—
185C4×C43C2×#11714yes—
186C4×C43C2×#11712yes—
187C4×C43C22×#4112yes—
188Dic43—24no—
189Dic43—22no—
190Dic43—24no—
191Dic43#56814yes—
192C2×C4×#41—431no—
193#2925—4316no—
194#2921—434no—
195#2920—434no—
196C2×#423—432no—
197#2879—432no—
198#2873—431no—
199#2873D4311yescharacteristic, complemented
200C2×C43—22no—
201C2×C43—24no—
202C2×C43C22×#11711yescharacteristic
203C2×C43C2×#56812yes—
204D43—44no—
205C22×#41—431no—
206C22×M16—432no—
207C22×M16C2×D4312yes—
208C4×#41—438no—
209C4×#41—434no—
210C4×#41—434no—
211C2×C4×Q8—432no—
212C2×C4×D4—432no—
213C2×C4×D4—434no—
214C2×#117—432no—
215C2×#117C2×D4311yescharacteristic
216C22×C42—431no—
217C22×C42—432no—
218#433—4316no—
219#433—4316no—
220#432—4316no—
221#431—4316no—
222#423—434no—
223#423—434no—
224#423—438no—
225C2×C4⋊C8—438no—
226#408—438no—
227#408—438no—
228#407—438no—
229#405—438no—
230#405C2×D4318yescomplemented
231C4×M16—434no—
232C4×M16C2×D4314yes—
233C43#6012511yescharacteristic, complemented, Sylow
234C2×#41—434no—
235C2×#41—434no—
236C2×#41—868no—
237C22×Q8—431no—
238C22×D4—432no—
239C22×D4—431no—
240C23×C4—432no—
241C23×C4—432no—
242C23×C4—434no—
243C23×C4C22×D4311yescharacteristic
244C2×M16—28no—
245C2×M16—434no—
246C2×M16—434no—
247C2×M16—868no—
248C2×M16C22×D4314yes—
249C2×M16C22×D4314yes—
250C22×C8—434no—
251C22×C8C22×D4314yes—
252C4×Q8—438no—
253C4×Q8—438no—
254C4×D4—438no—
255C4×D4—438no—
256C4×D4—4316no—
257C4×D4—4316no—
258#117—438no—
259#117—438no—
260#117C4×D4314yes—
261#117C22×D4314yes—
262C2×C4⋊C4—434no—
263C2×C4⋊C4C4×D4312yes—
264C2×C22⋊C4—434no—
265C2×C22⋊C4C4×D4312yes—
266C2×C42—434no—
267C2×C42—432no—
268C2×C42—432no—
269C2×C42—432no—
270C2×C42—431no—
271C2×C42—434no—
272C2×C42—431no—
273C2×C42—434no—
274C2×C42—434no—
275C2×C42—438no—
276C2×C42C22×D4312yes—
277C4⋊C8—4316no—
278C4⋊C8—4316no—
279C22⋊C8—4332no—
280#97—438no—
281#97C22×D4318yes—
282C4×C8—438no—
283C4×C8C22×D4318yes—
284C24—432no—
285C24C2×C4×D4311yescharacteristic
286#41—8616no—
287#41—868no—
288#41—868no—
289C2×Q8—434no—
290C2×Q8—864no—
291C2×D4—438no—
292C2×D4—434no—
293C2×D4—868no—
294C2×D4—864no—
295C22×C4—432no—
296C22×C4—432no—
297C22×C4—434no—
298C22×C4—432no—
299C22×C4—434no—
300C22×C4—434no—
301C22×C4—438no—
302C22×C4—434no—
303C22×C4—438no—
304C22×C4—868no—
305C22×C4—1728no—
306C22×C4—1724no—
307C22×C4C2×C4×D4314yes—
308C22×C4C2×C4×D4311yescharacteristic
309C22×C4C2×C4×D4312yes—
310C22×C4#1062189818yes—
311C22×C4C23×D4311yescharacteristic
312C22×C4C23×D4312yes—
313M16—28no—
314M16—28no—
315M16—868no—
316M16—868no—
317C2×C8—28no—
318C2×C8—438no—
319C2×C8—868no—
320C2×C8C23×D4318yes—
321C4⋊C4—4316no—
322C4⋊C4C2×C4×D4318yes—
323C22⋊C4—4316no—
324C22⋊C4C2×C4×D4318yes—
325C42—431no—
326C42—431no—
327C42—432no—
328C42—434no—
329C42—438no—
330C42—434no—
331C42—438no—
332C42—432no—
333C42—432no—
334C42C2×C4×D4314yes—
335C42C23×D4314yes—
336C23—42no—
337C23—434no—
338C23—864no—
339C23—1724no—
340C23#1306328214yes—
341C23C22×C4×D4312yes—
342C23C22×C4×D4311yescharacteristic
343Q8—868no—
344D4—8616no—
345D4—868no—
346C2×C4—44no—
347C2×C4—432no—
348C2×C4—432no—
349C2×C4—434no—
350C2×C4—434no—
351C2×C4—8616no—
352C2×C4—864no—
353C2×C4—868no—
354C2×C4—864no—
355C2×C4—868no—
356C2×C4—868no—
357C2×C4—1728no—
358C2×C4—1724no—
359C2×C4—1722no—
360C2×C4#1306328214yes—
361C2×C4#1306328218yes—
362C2×C4C22×C4×D4318yes—
363C2×C4C22×C4×D4311yescharacteristic
364C2×C4C22×C4×D4312yes—
365C2×C4C2×#1062189814yes—
366C2×C4C2×#1062189814yes—
367C2×C4C2×#1062189814yes—
368C2×C4C24×D4311yescharacteristic
369C8—28no—
370C8—868no—
371C22—22no—
372C22—24no—
373C22—44no—
374C22—864no—
375C22—868no—
376C22—1728no—
377C22C2×#1306328212yes—
378C22C2×#1306328214yes—
379C22C23×C4×D4311yescharacteristic
380C4—28no—
381C4—434no—
382C4—864no—
383C4—862no—
384C4—864no—
385C4C2×#1306328212yes—
386C4C2×#1306328214yes—
387C4C22×#1062189812yes—
388C2—22no—
389C2—24no—
390C2—1724no—
391C2C22×#1306328211yescharacteristic
392C2#568×D4312yes—
subgroupG/H
center, FrattiniC2×C4C24×D43
commutator, socleC22×C43C24×C4
FittingC43×#2873C2
prime radicalC22×#10621898C22
cosocleC2×C4×C43C25
hypercenter#2873D43
hypocenterC43#60125
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ #2873

Complements

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

NH ≅ G/Ntype
2. #19143259C2semidirect
3. #19143231C2semidirect
4. #19143226C2semidirect
5. C2×#14582922C2semidirect
7. #19143014C2semidirect
8. C43×#2873C2semidirect
20. #14582961C22semidirect
21. #14582958C22semidirect
22. #14582954C22semidirect
23. #14582950C22semidirect
26. #14582922C22semidirect
27. C2×Dic43⋊C8C22semidirect
31. #14582855C22semidirect
35. C43×#405C22semidirect
199. #2873D43semidirect
230. #405C2×D43semidirect
233. C43#60125semidirect

Maximal subgroups

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

subgroupindex
C2×#145833672
#191432592
#191432312
#191432262
C2×#145829222
#191430392
#191430142
C43×#28732
#6012543