Finite Group Databasebeta

← #25263997

Subgroups — #25263997

Order 11008.

1570 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19140796C214yesmaximal
2#19140787C214yesmaximal, complemented
3#19140785C214yesmaximal, complemented
4#19140772C214yesmaximal
5#19137900C211yesmaximal, characteristic, complemented
6#19137889C212yesmaximal, complemented
7#19137871C214yesmaximal
8#19137071C214yesmaximal, complemented
9#19136991C212yesmaximal
10#19136934C211yesmaximal, characteristic
11C43×#2402C211yesmaximal, characteristic, complemented
12C2×C4×Dic86C2214yes—
13C2×#13063282C2212yes—
14C2×C42×D43C2211yescharacteristic
15#14582841C2214yes—
16#14582840C2214yes—
17#14582834C2214yes—
18#14582833C2214yes—
19#14582833C2214yes—
20#14582833C2214yes—
21#14582832C2214yes—
22#14582830C2214yes—
23#14582823C2214yes—
24#14582821C2214yes—
25#14582820C2214yes—
26#14582819C2214yes—
27#14582819C2214yes—
28#14582812C2214yes—
29#14582803C2214yes—
30#14582803C2214yes—
31#14582794C2214yes—
32#14582794C2214yes—
33#14582784C2214yes—
34#14582784C2214yes—
35#14582780C2214yes—
36#14582780C2214yes—
37#14582766C2212yes—
38#14582766C2212yes—
39#14582764C2214yes—
40#14582761C2212yes—
41#14582761C2212yes—
42#14582756C2214yes—
43C4×Dic43⋊C4C2214yes—
44C4×Dic43⋊C4C2214yes—
45C4×C4⋊Dic43C2212yes—
46#14582750C2214yes—
47C4×(C2×D43)⋊C4C2214yes—
48#14582746C2214yes—
49#14582745C2214yes—
50#14582745C2211yescharacteristic
51C42×Dic43C2212yes—
52C43×#400C2214yes—
53C43×#398C2214yes—
54C4×C4⋊C4×C43C2214yes—
55C4×C4⋊C4×C43C2212yes—
56C43×#376C2211yescharacteristic
57C22×Dic86C2314yes—
58C22×C4×D43C2311yescharacteristic
59C22×C4×D43C2312yes—
60C4×Dic86—216no—
61#13063282—28no—
62C2×C4⋊Dic43C2314yes—
63C2×C4⋊Dic43C2314yes—
64C2×Dic43⋊C4C2314yes—
65C2×Dic43⋊C4C2314yes—
66C2×Dic43⋊C4C2314yes—
67C2×Dic43⋊C4C2314yes—
68C2×Dic43⋊C4C2314yes—
69C2×Dic43⋊C4C2314yes—
70C2×Dic43⋊C4C2314yes—
71C2×(C2×D43)⋊C4C2314yes—
72C2×(C2×D43)⋊C4C2314yes—
73C2×(C2×D43)⋊C4C2314yes—
74C2×C4×Dic43C2314yes—
75C2×C4×Dic43C2314yes—
76C2×C4×Dic43C2314yes—
77C2×C4×Dic43C2311yescharacteristic
78C2×C4×Dic43C2312yes—
79C2×C4×Dic43C2312yes—
80C42×D43Q818yescomplemented
81C43⋊#95C2314yes—
82C43⋊#95C2314yes—
83C43⋊#95C2314yes—
84C43⋊#95C2314yes—
85C43⋊#95C2314yes—
86C43⋊#95C2314yes—
87C43⋊#95C2314yes—
88C43⋊#95C2314yes—
89C43⋊#95C2312yes—
90C43⋊#95C2314yes—
91C43⋊#95C2314yes—
92C43⋊#95C2314yes—
93C43⋊#95C2312yes—
94C2×C4⋊C4×C43C2314yes—
95C2×C4⋊C4×C43C2314yes—
96C2×C4⋊C4×C43C2314yes—
97C2×C42×C43C2312yes—
98C2×C42×C43C2314yes—
99C2×C42×C43C2311yescharacteristic
100#95×C43C2314yes—
101#95×C43C2314yes—
102#95×C43C2312yes—
103#95×C43C2312yes—
104#95×C43C2314yes—
105C23×D43C2411yescharacteristic
106C22×C4×C43C2414yes—
107C22×C4×C43C2414yes—
108C22×C4×C43C2414yes—
109C22×C4×C43C2412yes—
110C22×C4×C43C2411yescharacteristic
111C22×Dic43C2414yes—
112C22×Dic43C2414yes—
113C22×Dic43C2412yes—
114C22×Dic43C2411yescharacteristic
115C22×Dic43C2414yes—
116C2×C4×D43—24no—
117C2×C4×D43—44no—
118C2×C4×D43C2×Q814yes—
119C2×C4×D43C2×Q818yes—
120C2×Dic86—28no—
121C2×Dic86—44no—
122C2×Dic86—44no—
123C4⋊C4×C43—44no—
124C4⋊C4×C43—44no—
125C4⋊C4×C43—44no—
126C42×C43—24no—
127C42×C43—28no—
128C42×C43C2×Q814yes—
129(C2×D43)⋊C4—28no—
130(C2×D43)⋊C4—44no—
131(C2×D43)⋊C4—44no—
132C4⋊Dic43—28no—
133C4⋊Dic43—44no—
134Dic43⋊C4—28no—
135Dic43⋊C4—28no—
136Dic43⋊C4—28no—
137Dic43⋊C4—44no—
138Dic43⋊C4—44no—
139Dic43⋊C4—44no—
140Dic43⋊C4—44no—
141C4×Dic43—28no—
142C4×Dic43—44no—
143C4×Dic43—44no—
144C4×Dic43C2×Q818yes—
145C4×Dic43C2×Q814yes—
146C4×Dic43#4118yes—
147C23×C43C2511yescharacteristic
148C22×D43—22no—
149C22×D43—24no—
150C22×D43C22×Q812yes—
151C2×C4×C43—24no—
152C2×C4×C43—24no—
153C2×C4×C43—24no—
154C2×C4×C43—24no—
155C2×C4×C43—24no—
156C2×C4×C43—24no—
157C2×C4×C43—24no—
158C2×C4×C43—24no—
159C2×C4×C43—24no—
160C2×C4×C43—24no—
161C2×C4×C43C22×Q814yes—
162C2×C4×C43C22×Q812yes—
163C2×C4×C43C2×#4114yes—
164C2×Dic43—22no—
165C2×Dic43—24no—
166C2×Dic43—24no—
167C2×Dic43—24no—
168C2×Dic43—24no—
169C2×Dic43—24no—
170C2×Dic43—24no—
171C2×Dic43—24no—
172C2×Dic43—24no—
173C2×Dic43—24no—
174C2×Dic43C22×Q812yes—
175C2×Dic43C22×Q814yes—
176C2×Dic43C2×#4118yes—
177C4×D43—28no—
178C4×D43—48no—
179Dic86—416no—
180#34644—431nomaximal, Sylow
181C22×C43C23×Q811yescharacteristic
182C22×C43C22×#4112yes—
183C22×C43#58514yes—
184C2×D43—22no—
185C2×D43—24no—
186C2×D43—44no—
187C4×C43—24no—
188C4×C43—44no—
189C4×C43—44no—
190C4×C43—44no—
191C4×C43#53314yes—
192Dic43—22no—
193Dic43—28no—
194Dic43—24no—
195Dic43—44no—
196Dic43—44no—
197#2667—434no—
198#2666—434no—
199#2666—434no—
200#2665—434no—
201#2402—431no—
202#2402D4311yescharacteristic, complemented
203#2399—432no—
204#2396—434no—
205#2295—434no—
206#2283—432no—
207C4×#117—431no—
208C2×C43C2×#53311yescharacteristic
209C2×C43#345514yes—
210C2×C43#345812yes—
211D43—42no—
212C2×C4×Q8—434no—
213C2×#117—432no—
214C22×C42—431no—
215#400—434no—
216#400—434no—
217#400C2×D4314yes—
218#399—434no—
219#398—434no—
220#398—434no—
221#398—434no—
222#398—434no—
223#398—434no—
224#398C2×D4314yes—
225#396—434no—
226#396—434no—
227#395—434no—
228#395—434no—
229#395—434no—
230#393—434no—
231#391—434no—
232#391—434no—
233#389—434no—
234#389—434no—
235#387—434no—
236#387—434no—
237#387—434no—
238#387—434no—
239#383—432no—
240#383—432no—
241#382—434no—
242#381—432no—
243#381—432no—
244#380—434no—
245C4×C4⋊C4—434no—
246C4×C4⋊C4—434no—
247C4×C4⋊C4—432no—
248C4×C4⋊C4—434no—
249C4×C4⋊C4C2×D4314yes—
250C4×C4⋊C4C2×D4312yes—
251C4×C22⋊C4—434no—
252C4×C22⋊C4—434no—
253#376—431no—
254#376—434no—
255#376C2×D4311yescharacteristic
256C43—432no—
257C43#3464411yescharacteristic, complemented, Sylow
258C22×Q8—434no—
259C23×C4—431no—
260C23×C4—432no—
261C4×Q8—8616no—
262#117—868no—
263C2×C4⋊C4—434no—
264C2×C4⋊C4—434no—
265C2×C4⋊C4—434no—
266C2×C4⋊C4—434no—
267C2×C4⋊C4—434no—
268C2×C4⋊C4—434no—
269C2×C4⋊C4—434no—
270C2×C4⋊C4—434no—
271C2×C4⋊C4—434no—
272C2×C4⋊C4C22×D4314yes—
273C2×C4⋊C4C22×D4314yes—
274C2×C4⋊C4C22×D4314yes—
275C2×C22⋊C4—434no—
276C2×C22⋊C4—434no—
277C2×C22⋊C4—434no—
278C2×C42—432no—
279C2×C42—432no—
280C2×C42—431no—
281C2×C42—438no—
282C2×C42—434no—
283C2×C42—434no—
284C2×C42—434no—
285C2×C42C22×D4312yes—
286C2×C42C22×D4314yes—
287C2×C42C22×D4311yescharacteristic
288#95—434no—
289#95—434no—
290#95—434no—
291#95—434no—
292#95—434no—
293#95—434no—
294#95—434no—
295#95—432no—
296#95—432no—
297#95—434no—
298#95—434no—
299#95—434no—
300#95—434no—
301#95C22×D4314yes—
302#95C22×D4312yes—
303#95C22×D4312yes—
304#95C22×D4314yes—
305#95C22×D4314yes—
306C24—431no—
307C2×Q8—868no—
308C2×Q8—1724no—
309C2×Q8—1724no—
310C22×C4—432no—
311C22×C4—431no—
312C22×C4—434no—
313C22×C4—434no—
314C22×C4—438no—
315C22×C4—434no—
316C22×C4—434no—
317C22×C4—864no—
318C22×C4—1724no—
319C22×C4C23×D4314yes—
320C22×C4C23×D4314yes—
321C22×C4C23×D4314yes—
322C22×C4C23×D4312yes—
323C22×C4C23×D4311yescharacteristic
324C4⋊C4—44no—
325C4⋊C4—44no—
326C4⋊C4—44no—
327C4⋊C4—868no—
328C4⋊C4—868no—
329C4⋊C4—868no—
330C4⋊C4—868no—
331C4⋊C4—1724no—
332C4⋊C4—1724no—
333C4⋊C4—1724no—
334C4⋊C4—1724no—
335C4⋊C4—1724no—
336C22⋊C4—868no—
337C22⋊C4—1724no—
338C22⋊C4—1724no—
339C42—24no—
340C42—28no—
341C42—438no—
342C42—434no—
343C42—438no—
344C42—868no—
345C42—1724no—
346C42—1724no—
347C42Q8×D4314yes—
348C23—432no—
349C23—862no—
350C23—864no—
351C23C24×D4311yescharacteristic
352Q8—17216no—
353C2×C4—24no—
354C2×C4—24no—
355C2×C4—24no—
356C2×C4—24no—
357C2×C4—24no—
358C2×C4—24no—
359C2×C4—24no—
360C2×C4—24no—
361C2×C4—24no—
362C2×C4—24no—
363C2×C4—432no—
364C2×C4—434no—
365C2×C4—438no—
366C2×C4—862no—
367C2×C4—864no—
368C2×C4—864no—
369C2×C4—864no—
370C2×C4—868no—
371C2×C4—864no—
372C2×C4—864no—
373C2×C4—864no—
374C2×C4—864no—
375C2×C4—864no—
376C2×C4—864no—
377C2×C4—1728no—
378C2×C4C2×Q8×D4314yes—
379C2×C4C2×Q8×D4312yes—
380C2×C4#41×D4314yes—
381C22—862no—
382C22—864no—
383C22—1724no—
384C22C22×Q8×D4311yescharacteristic
385C22C2×#41×D4312yes—
386C22#1458373514yes—
387C4—24no—
388C4—44no—
389C4—44no—
390C4—44no—
391C4—862no—
392C4—868no—
393C4—864no—
394C4—1724no—
395C4—1724no—
396C4#1458345514yes—
397C2—1722no—
398C2C2×#1458345511yescharacteristic
399C2#1914797814yes—
400C2#1914799812yes—
subgroupG/H
centerC22×C4C23×D43
commutator, socle, cosocleC23×C43C25
FrattiniC23C24×D43
FittingC43×#2402C2
prime radicalC23×D43C24
hypercenter#2402D43
hypocenterC43#34644
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ #2402

Complements

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

NH ≅ G/Ntype
2. #19140787C2semidirect
3. #19140785C2semidirect
5. #19137900C2semidirect
6. #19137889C2semidirect
8. #19137071C2semidirect
11. C43×#2402C2semidirect
80. C42×D43Q8semidirect
202. #2402D43semidirect
257. C43#34644semidirect

Maximal subgroups

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

subgroupindex
#191407962
#191407872
#191407852
#191407722
#191379002
#191378892
#191378712
#191370712
#191369912
#191369342
C43×#24022
#3464443