Finite Group Databasebeta

← #25965921

Subgroups — #25965921

Order 11008.

2014 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148000C211yesmaximal, characteristic, complemented
2#19144981C214yesmaximal, complemented
3#19144975C214yesmaximal, complemented
4#19144960C2116yesmaximal, complemented
5#19143114C212yesmaximal
6C2×#14582908C212yesmaximal, complemented
7#19143014C211yesmaximal, characteristic, complemented
8C2×C43×#536C211yesmaximal, characteristic
9C22×#10621877C2212yes—
10#14583530—22no—
11#14583527C2218yescomplemented
12#14583525—22no—
13#14583456C2214yes—
14#14583452—24no—
15C2×#13063284C2212yes—
16#14583267C22116yescomplemented
17#14583258C22116yescomplemented
18#14583253C22116yescomplemented
19#14583249C22116yescomplemented
20#14582908C2214yes—
21#14582908C2218yes—
22#14582908C2218yescomplemented
23#14582904C2214yes—
24#14582900C2218yes—
25#14582895C2218yes—
26C2×#13063249C2218yescomplemented
27#14582855C2218yescomplemented
28C4×#10621877C2214yes—
29C22×#41×C43C2211yescharacteristic
30C23×Q8×C43C2211yescharacteristic
31C43×#536—24no—
32C43×#536C2218yes—
33C2×C4⋊Q8×C43C2212yes—
34C2×#124×C43C2212yes—
35C2×#123×C43—22no—
36C2×C22⋊Q8×C43—22no—
37C2×#117×C43C2211yescharacteristic
38C2×#10621877—28no—
39C2×#10621877C2314yes—
40C2×#10621877C2314yes—
41C22×C43⋊C8C2314yes—
42#13063325C2318yes—
43#13063324—28no—
44#13063317C2318yes—
45#13063316—28no—
46#13063304—28no—
47#13063302—216no—
48C4×Dic86—28no—
49#13063284—22no—
50#13063284—22no—
51#13063284C2314yes—
52#13063284C2314yes—
53C2×C4⋊Dic43C2314yes—
54C2×C22⋊Dic43—22no—
55C2×C4×Dic43—22no—
56#13063249C23132yes—
57#13063249C23116yes—
58#13063246C23116yes—
59#13063236C2318yes—
60C4×C43⋊C8C2318yes—
61C2×#41×C43—22no—
62C2×#41×C43—28no—
63C2×#41×C43C2314yes—
64C22×Q8×C43—21no—
65C22×Q8×C43—22no—
66C22×Q8×C43—28no—
67C22×Q8×C43C2312yes—
68C22×Q8×C43C2311yescharacteristic
69C22×Q8×C43C2314yes—
70C22×D4×C43—21no—
71C22×D4×C43C2311yescharacteristic
72C23×C4×C43—21no—
73C23×C4×C43—21no—
74C23×C4×C43C2311yescharacteristic
75C4⋊Q8×C43—24no—
76C4⋊Q8×C43C2318yes—
77#124×C43—24no—
78#124×C43C2318yes—
79#123×C43—216no—
80C22⋊Q8×C43—216no—
81#117×C43D414yes—
82#117×C43C2314yes—
83C2×C4⋊C4×C43—24no—
84C2×C4⋊C4×C43D412yes—
85C2×C22⋊C4×C43—24no—
86C2×C22⋊C4×C43D412yes—
87C2×C42×C43C2312yes—
88C24×C43—21no—
89C24×C43C2×D411yescharacteristic
90#41×C43—28no—
91#41×C43—28no—
92#41×C43—48no—
93C2×Q8×C43—24no—
94C2×Q8×C43—22no—
95C2×Q8×C43—21no—
96C2×Q8×C43—28no—
97C2×Q8×C43—28no—
98C2×Q8×C43—28no—
99C2×Q8×C43—24no—
100C2×Q8×C43—44no—
101C2×Q8×C43—48no—
102C2×Q8×C43C2414yes—
103C2×Q8×C43C2412yes—
104C2×D4×C43—21no—
105C2×D4×C43—24no—
106C2×D4×C43—24no—
107C2×D4×C43—44no—
108C2×D4×C43C2412yes—
109C22×C4×C43—24no—
110C22×C4×C43—22no—
111C22×C4×C43—21no—
112C22×C4×C43—24no—
113C22×C4×C43—44no—
114C22×C4×C43—44no—
115C22×C4×C43C2×D414yes—
116C22×C4×C43C2×D411yescharacteristic
117C22×C4×C43C2×D412yes—
118C22×C4×C43#4118yes—
119C22×C4×C43C2411yescharacteristic
120C22×C4×C43C2412yes—
121C22×Dic43—24no—
122C2×Dic86—28no—
123C4⋊C4×C43—216no—
124C4⋊C4×C43C2×D418yes—
125C22⋊C4×C43—216no—
126C22⋊C4×C43C2×D418yes—
127C42×C43C2×D414yes—
128C42×C43C2414yes—
129C22⋊Dic43—24no—
130C22⋊Dic43—24no—
131C4⋊Dic43—24no—
132C4⋊Dic43—28no—
133C4⋊Dic43C2418yes—
134Dic43⋊C4—216no—
135C4×Dic43—24no—
136C4×Dic43—24no—
137#10621877—28no—
138#10621877—28no—
139C2×C43⋊C8—28no—
140C2×C43⋊C8C2418yes—
141C23×C43—22no—
142C23×C43—42no—
143C23×C43—44no—
144C23×C43—42no—
145C23×C43#12414yes—
146C23×C43C22×D411yescharacteristic
147C23×C43C22×D412yes—
148Q8×C43—28no—
149Q8×C43—24no—
150Q8×C43—48no—
151Q8×C43—44no—
152Q8×C43—42no—
153D4×C43—24no—
154D4×C43—48no—
155D4×C43—42no—
156C2×C4×C43—24no—
157C2×C4×C43—22no—
158C2×C4×C43—44no—
159C2×C4×C43—42no—
160C2×C4×C43—44no—
161C2×C4×C43—48no—
162C2×C4×C43—48no—
163C2×C4×C43#12414yes—
164C2×C4×C43#12418yes—
165C2×C4×C43C22×D418yes—
166C2×C4×C43C22×D411yescharacteristic
167C2×C4×C43C22×D412yes—
168C2×C4×C43C2×#4114yes—
169C2×C4×C43C2×#4114yes—
170C2×C4×C43C2×#4114yes—
171C2×C4×C43C2511yescharacteristic
172C2×Dic43—28no—
173C2×Dic43—84no—
174Dic86—88no—
175C43⋊C8—28no—
176#60620—431nomaximal, Sylow
177C22×C43—22no—
178C22×C43—24no—
179C22×C43—44no—
180C22×C43—44no—
181C22×C43—42no—
182C22×C43—84no—
183C22×C43C2×#12412yes—
184C22×C43C2×#12414yes—
185C22×C43C23×D411yescharacteristic
186C4×C43—28no—
187C4×C43—42no—
188C4×C43—44no—
189C4×C43C2×#12414yes—
190C4×C43C2×#12412yes—
191C4×C43C22×#4112yes—
192Dic43—48no—
193#3458—431no—
194C2×#536D4311yescharacteristic
195#3140—434no—
196#3139—434no—
197#3137—4316no—
198#2896—432no—
199C2×#419—432no—
200#2873—431no—
201C2×C43—22no—
202C2×C43—24no—
203C2×C43—82no—
204C2×C43C22×#12411yescharacteristic
205C2×C43#358612yes—
206C22×#41C2×D4311yescharacteristic
207C23×Q8C2×D4311yescharacteristic
208C22×M16—432no—
209#544—438no—
210#544—862no—
211#543—862no—
212#536—24no—
213#536C2×D4318yes—
214#533—434no—
215#533—864no—
216C2×C4⋊Q8C2×D4312yes—
217C2×#124C2×D4312yes—
218C2×#123—22no—
219C2×C22⋊Q8—22no—
220C2×#117—432no—
221C2×#117C2×D4311yescharacteristic
222#491—4316no—
223#489—4316no—
224#488—4316no—
225#487—4316no—
226#419—438no—
227#419—434no—
228#419—438no—
229#418—434no—
230#417—438no—
231#416—438no—
232C2×#103—438no—
233#405—438no—
234C4×M16—434no—
235C43#6062011yescharacteristic, complemented, Sylow
236C2×#41—22no—
237C2×#41—28no—
238C2×#41C22×D4314yes—
239C22×Q8—21no—
240C22×Q8—22no—
241C22×Q8—28no—
242C22×Q8C22×D4312yes—
243C22×Q8C22×D4311yescharacteristic
244C22×Q8C22×D4314yes—
245C22×D4—21no—
246C22×D4C22×D4311yescharacteristic
247C23×C4—21no—
248C23×C4—21no—
249C23×C4C22×D4311yescharacteristic
250C2×M16—434no—
251C2×M16—434no—
252C2×M16—868no—
253C22×C8—434no—
254C4⋊Q8—24no—
255C4⋊Q8—438no—
256C4⋊Q8—868no—
257C4⋊Q8C22×D4318yes—
258#125—438no—
259#125—868no—
260#124—24no—
261#124C22×D4318yes—
262#123—216no—
263C22⋊Q8—216no—
264C22⋊Q8—868no—
265C22⋊Q8—8616no—
266C4×Q8—868no—
267#117—434no—
268#117—434no—
269#117—862no—
270#117—862no—
271#117C22⋊D4314yes—
272#117C22×D4314yes—
273C2×C4⋊C4—24no—
274C2×C4⋊C4—434no—
275C2×C4⋊C4C22⋊D4312yes—
276C2×C22⋊C4—24no—
277C2×C22⋊C4—862no—
278C2×C22⋊C4C22⋊D4312yes—
279C2×C42—862no—
280C2×C42C22×D4312yes—
281#103—4332no—
282#103—4316no—
283#102—4316no—
284#97—438no—
285C4×C8—438no—
286C24—21no—
287C24C2×C22⋊D4311yescharacteristic
288#41—28no—
289#41—28no—
290#41—48no—
291C2×Q8—24no—
292C2×Q8—22no—
293C2×Q8—21no—
294C2×Q8—28no—
295C2×Q8—28no—
296C2×Q8—28no—
297C2×Q8—24no—
298C2×Q8—44no—
299C2×Q8—48no—
300C2×Q8—868no—
301C2×Q8C23×D4314yes—
302C2×Q8C23×D4312yes—
303C2×D4—24no—
304C2×D4—21no—
305C2×D4—24no—
306C2×D4—44no—
307C2×D4C23×D4312yes—
308C22×C4—22no—
309C22×C4—21no—
310C22×C4—24no—
311C22×C4—24no—
312C22×C4—44no—
313C22×C4—44no—
314C22×C4—864no—
315C22×C4#1062190018yes—
316C22×C4C2×C22⋊D4314yes—
317C22×C4C2×C22⋊D4312yes—
318C22×C4C2×C22⋊D4311yescharacteristic
319C22×C4C23×D4311yescharacteristic
320C22×C4C23×D4312yes—
321M16—868no—
322M16—868no—
323C2×C8—438no—
324C2×C8—868no—
325C4⋊C4—216no—
326C4⋊C4—438no—
327C4⋊C4—864no—
328C4⋊C4—8616no—
329C4⋊C4—868no—
330C4⋊C4C2×C22⋊D4318yes—
331C22⋊C4—216no—
332C22⋊C4—864no—
333C22⋊C4—864no—
334C22⋊C4C2×C22⋊D4318yes—
335C42—864no—
336C42—864no—
337C42C2×C22⋊D4314yes—
338C42C23×D4314yes—
339C23—22no—
340C23—42no—
341C23—44no—
342C23—42no—
343C23#1306331214yes—
344C23C22×C22⋊D4311yescharacteristic
345C23C22×C22⋊D4312yes—
346Q8—28no—
347Q8—24no—
348Q8—48no—
349Q8—44no—
350Q8—42no—
351Q8—3448no—
352D4—24no—
353D4—48no—
354D4—42no—
355C2×C4—24no—
356C2×C4—22no—
357C2×C4—44no—
358C2×C4—42no—
359C2×C4—44no—
360C2×C4—48no—
361C2×C4—48no—
362C2×C4—868no—
363C2×C4—3444no—
364C2×C4#1306331214yes—
365C2×C4#1306331218yes—
366C2×C4C22×C22⋊D4318yes—
367C2×C4C22×C22⋊D4311yescharacteristic
368C2×C4C22×C22⋊D4312yes—
369C2×C4C2×#1062190014yes—
370C2×C4C2×#1062190014yes—
371C2×C4C2×#1062190014yes—
372C2×C4C24×D4311yescharacteristic
373C8—868no—
374C22—22no—
375C22—24no—
376C22—44no—
377C22—42no—
378C22—44no—
379C22—84no—
380C22C2×#1306331212yes—
381C22C2×#1306331214yes—
382C22C23×C22⋊D4311yescharacteristic
383C4—28no—
384C4—42no—
385C4—44no—
386C4—1728no—
387C4C2×#1306331214yes—
388C4C2×#1306331212yes—
389C4C22×#1062190012yes—
390C2—22no—
391C2—24no—
392C2—82no—
393C2C22×#1306331211yescharacteristic
394C2#1914938212yes—
subgroupG/H
centerC22C23×C22⋊D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#536C2
socleC22×C43C23×D4
prime radicalC22×#41×C43C22
hypercenterC2×#536D43
hypocenterC43#60620
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×#117 ◁ C2×#536

Complements

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

NH ≅ G/Ntype
1. #19148000C2semidirect
2. #19144981C2semidirect
3. #19144975C2semidirect
4. #19144960C2semidirect
6. C2×#14582908C2semidirect
7. #19143014C2semidirect
11. #14583527C22semidirect
16. #14583267C22semidirect
17. #14583258C22semidirect
18. #14583253C22semidirect
19. #14583249C22semidirect
22. #14582908C22semidirect
26. C2×#13063249C22semidirect
27. #14582855C22semidirect
235. C43#60620semidirect

Maximal subgroups

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

subgroupindex
#191480002
#191449812
#191449752
#191449602
#191431142
C2×#145829082
#191430142
C2×C43×#5362
#6062043