Finite Group Databasebeta

← #25081864

Subgroups — #25081864

Order 11008.

628 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145756C211yesmaximal, characteristic, complemented
2#19144695C211yesmaximal, characteristic
3#19144604C211yesmaximal, characteristic
4#19143618C211yesmaximal, characteristic
5#19134047C212yesmaximal, complemented
6#19134019C212yesmaximal, complemented
7#19133985C212yesmaximal, complemented
8#19133971C212yesmaximal, complemented
9#19133306C211yesmaximal, characteristic, complemented
10#19133259C211yesmaximal, characteristic, complemented
11C43×#1572C211yesmaximal, characteristic, complemented
12#14583456C2211yescharacteristic
13#14583456C2211yescharacteristic
14C2×C4×D172C2211yescharacteristic
15#14583304C2211yescharacteristic, complemented
16#14583297C2211yescharacteristic, complemented
17#14583250C2211yescharacteristic, complemented
18#14583250C2211yescharacteristic, complemented
19#14583241—22no—
20#14583235—21no—
21#14583230—21no—
22#14583207—22no—
23#14583190C2212yes—
24#14583180C2212yes—
25#14583105C2212yes—
26#14583105C2212yes—
27#14583052—21no—
28#14583052—21no—
29#14583001—22no—
30C4×#10621873—22no—
31C8×D172C2212yes—
32C8×D172C2212yes—
33#14582964—22no—
34#14582952C2211yescharacteristic
35C22⋊C8×D43—22no—
36#14582647C2212yescomplemented
37#14582646C2212yescomplemented
38#14582646C2212yescomplemented
39#14582644C2212yescomplemented
40C43×#432C2211yescharacteristic
41C43×#431C2211yescharacteristic
42C43×#431C2211yescharacteristic
43C43×#335C2212yescomplemented
44C43×#334C2212yescomplemented
45C22×D172D411yescharacteristic
46C22×C4×D43—21no—
47C2×#10621873—22no—
48C2×#10621873—22no—
49C2×C8×D43—22no—
50C2×C8×D43—22no—
51#13063325C2311yescharacteristic
52#13063325C2311yescharacteristic
53#13063325C2311yescharacteristic
54#13063325C2311yescharacteristic
55#13063317—21no—
56#13063317—21no—
57#13063304—21no—
58#13063304—21no—
59#13063304—21no—
60#13063304—21no—
61C4×Dic86—21no—
62C4×Dic86—21no—
63C4×Dic86—21no—
64C4×Dic86—21no—
65C4×D172—21no—
66C4×D172—21no—
67C4×D172D412yes—
68C4×D172C2312yes—
69#13063284—21no—
70#13063284—21no—
71C2×C4⋊Dic43D411yescharacteristic
72C2×(C2×D43)⋊C4—21no—
73#13063259—22no—
74#13063259—22no—
75#13063257—22no—
76#13063257—22no—
77C4⋊(C43⋊C8)C2312yes—
78#13063250—22no—
79#13063250—22no—
80#13063250—22no—
81#13063250—22no—
82#13063247—22no—
83#13063247—22no—
84C22⋊(C43⋊C8)—21no—
85(C2×D43)⋊C8—22no—
86(C2×D43)⋊C8—22no—
87C4×C43⋊C8—21no—
88C2×C42×C43C2311yescharacteristic
89C4⋊C8×C43D412yes—
90C4⋊C8×C43C2312yes—
91C4⋊C8×C43C2312yes—
92C22⋊C8×C43—21no—
93C22⋊C8×C43—21no—
94C22⋊C8×C43D412yes—
95#97×C43—21no—
96C4×C8×C43—21no—
97C4×C8×C43C2311yescharacteristic
98C4×C8×C43C2311yescharacteristic
99C23×D43—21no—
100C22×C4×C43C2×D411yescharacteristic
101C22×C4×C43C2×D411yescharacteristic
102C22×C4×C43#4111yescharacteristic
103C22×Dic43—21no—
104C2×D172—21no—
105C2×D172—24no—
106C2×D172C2×D412yes—
107C2×C4×D43—22no—
108C2×C4×D43—22no—
109C2×C4×D43—82no—
110C2×Dic86—21no—
111C2×Dic86—21no—
112C2×Dic86—21no—
113C2×Dic86—21no—
114C2×C8×C43—22no—
115C2×C8×C43—22no—
116C2×C8×C43C2×D412yes—
117C2×C8×C43C2×D412yes—
118C42×C43C2×D411yescharacteristic
119C42×C43C2×D411yescharacteristic
120C42×C43#4111yescharacteristic
121C42×C43C2411yescharacteristic
122C22⋊Dic43—41no—
123C22⋊Dic43—41no—
124(C2×D43)⋊C4—22no—
125(C2×D43)⋊C4—22no—
126C4⋊Dic43—21no—
127C4⋊Dic43—21no—
128C4⋊Dic43—21no—
129C4⋊Dic43—21no—
130C4⋊Dic43—21no—
131C4⋊Dic43—21no—
132C4⋊Dic43—21no—
133C4⋊Dic43—21no—
134C4⋊Dic43—21no—
135C4⋊Dic43C2×D412yes—
136Dic43⋊C4—41no—
137Dic43⋊C4—41no—
138Dic43⋊C4—41no—
139Dic43⋊C4—41no—
140C4×Dic43—41no—
141C4×Dic43—41no—
142C2×C43⋊C8—22no—
143#10621873—44no—
144#10621873—44no—
145C8×D43—82no—
146C8×D43—82no—
147C23×C43#12111yescharacteristic
148C22×D43—22no—
149C22×D43—24no—
150C22×D43—81no—
151C22×D43—81no—
152C2×C4×C43—22no—
153C2×C4×C43—22no—
154C2×C4×C43—41no—
155C2×C4×C43#12111yescharacteristic
156C2×C4×C43#12111yescharacteristic
157C2×C4×C43#12111yescharacteristic
158C2×C4×C43C22×D411yescharacteristic
159C2×C4×C43C22×D411yescharacteristic
160C2×C4×C43C2×#4111yescharacteristic
161C2×Dic43—22no—
162C2×Dic43—41no—
163C2×Dic43—41no—
164C2×Dic43—41no—
165C2×Dic43—41no—
166C2×Dic43—81no—
167D172—24no—
168D172—22no—
169D172#13514yes—
170C4×D43—42no—
171C4×D43—42no—
172C4×D43—82no—
173Dic86—42no—
174Dic86—42no—
175Dic86—42no—
176Dic86—81no—
177C8×C43—22no—
178C8×C43—22no—
179C8×C43—42no—
180C8×C43—42no—
181C43⋊C8—42no—
182#19395—431nomaximal, Sylow
183C22×C43—21no—
184C22×C43—21no—
185C22×C43—21no—
186C22×C43C2×#12111yescharacteristic
187C2×D43—24no—
188C2×D43—42no—
189C2×D43—42no—
190C2×D43—84no—
191C4×C43—21no—
192C4×C43—21no—
193C4×C43—21no—
194C4×C43—21no—
195C4×C43C2×#13512yes—
196C4×C43#57712yes—
197Dic43—42no—
198Dic43—81no—
199Dic43—81no—
200Dic43—81no—
201Dic43—81no—
202#3231—431no—
203#3110—431no—
204#3101—431no—
205#2972—431no—
206#1683—432no—
207#1679—432no—
208#1673—432no—
209#1671—432no—
210#1572D4311yescharacteristic, complemented
211#1554—431no—
212#1544—431no—
213C2×C43—41no—
214C2×C43#304211yescharacteristic
215C2×C43#305011yescharacteristic
216C2×C43#306911yescharacteristic
217D43—44no—
218#533—431no—
219#533—431no—
220C2×C4×D4—431no—
221#500—431no—
222#498—431no—
223#487—431no—
224#487—431no—
225#485—862no—
226#484—861no—
227#483—861no—
228#479—862no—
229#476—432no—
230#474—432no—
231#461—432no—
232#461—432no—
233#450—861no—
234#450—861no—
235#440—862no—
236C4×SD16—862no—
237C8×D4—432no—
238C8×D4—432no—
239C8×D4—862no—
240#432C2×D4311yescharacteristic
241#431—431no—
242#431C2×D4311yescharacteristic
243#431C2×D4311yescharacteristic
244C2×C22⋊C8—862no—
245#335C2×D4312yescomplemented
246#334C2×D4312yescomplemented
247#333—432no—
248#332—432no—
249#332—432no—
250#332—432no—
251C43#1939511yescharacteristic, complemented, Sylow
252C22×D4—431no—
253C23×C4—861no—
254C2×SD16—862no—
255C2×SD16—862no—
256C22×C8—862no—
257C22×C8—862no—
258C4⋊Q8—431no—
259C4⋊Q8—431no—
260C4⋊Q8—431no—
261C4⋊Q8—431no—
262#125—861no—
263#125—861no—
264C22⋊Q8—861no—
265C22⋊Q8—861no—
266C22⋊Q8—861no—
267C22⋊Q8—861no—
268C4×Q8—861no—
269C4×Q8—861no—
270C4×Q8—861no—
271C4×Q8—861no—
272C4×D4—432no—
273C4×D4—432no—
274C4×D4—861no—
275C4×D4—861no—
276#117—861no—
277#117—861no—
278C2×C4⋊C4—431no—
279C2×C22⋊C4—861no—
280C2×C42C22×D4311yescharacteristic
281#107—862no—
282#107—862no—
283#106—862no—
284#106—862no—
285C4⋊C8—432no—
286C4⋊C8D17212yes—
287C4⋊C8C22×D4312yes—
288C4⋊C8C22×D4312yes—
289#103—862no—
290#103—862no—
291#103—862no—
292#103—862no—
293#102—862no—
294#102—862no—
295C22⋊C8—21no—
296C22⋊C8—21no—
297C22⋊C8—861no—
298C22⋊C8—862no—
299C22⋊C8—862no—
300C22⋊C8D17212yes—
301#97—21no—
302C4×C8—21no—
303C4×C8—861no—
304C4×C8C22×D4311yescharacteristic
305C4×C8C22×D4311yescharacteristic
306C24—861no—
307C2×Q8—861no—
308C2×Q8—861no—
309C2×Q8—861no—
310C2×Q8—861no—
311C2×D4—432no—
312C2×D4—864no—
313C2×D4—861no—
314C22×C4—861no—
315C22×C4—862no—
316C22×C4—862no—
317C22×C4—3442no—
318C22×C4C2×D17211yescharacteristic
319C22×C4D4×D4311yescharacteristic
320C22×C4#1062190211yescharacteristic
321SD16—1724no—
322SD16—1724no—
323C2×C8—22no—
324C2×C8—22no—
325C2×C8—862no—
326C2×C8—3442no—
327C2×C8—3442no—
328C2×C8C2×D17212yes—
329C2×C8C2×D17212yes—
330C4⋊C4—432no—
331C4⋊C4—861no—
332C4⋊C4—861no—
333C4⋊C4—861no—
334C4⋊C4—861no—
335C4⋊C4—861no—
336C4⋊C4—861no—
337C4⋊C4—861no—
338C4⋊C4—861no—
339C4⋊C4—861no—
340C4⋊C4—1721no—
341C4⋊C4—1721no—
342C4⋊C4—1721no—
343C4⋊C4—1721no—
344C22⋊C4—862no—
345C22⋊C4—862no—
346C22⋊C4—1721no—
347C22⋊C4—1721no—
348C42—1721no—
349C42—1721no—
350C42C2×D17211yescharacteristic
351C42D4×D4311yescharacteristic
352C42#1062190211yescharacteristic
353C42C23×D4311yescharacteristic
354C23—864no—
355C23—862no—
356C23—3441no—
357C23—3441no—
358C23#1306330011yescharacteristic
359Q8—3441no—
360Q8—1722no—
361Q8—1722no—
362Q8—1722no—
363D4—434no—
364D4—864no—
365D4—862no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—41no—
369C2×C4—862no—
370C2×C4—3442no—
371C2×C4—3441no—
372C2×C4—1721no—
373C2×C4—1721no—
374C2×C4—1721no—
375C2×C4—1721no—
376C2×C4—1722no—
377C2×C4—1722no—
378C2×C4#1306330011yescharacteristic
379C2×C4#1306330011yescharacteristic
380C2×C4#1306330011yescharacteristic
381C2×C4C2×D4×D4311yescharacteristic
382C2×C4C22×D17211yescharacteristic
383C2×C4C2×#1062190211yescharacteristic
384C8—22no—
385C8—22no—
386C8—42no—
387C8—42no—
388C8—1722no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—864no—
393C22—3444no—
394C22—1722no—
395C22—1722no—
396C22C2×#1306330011yescharacteristic
397C4—21no—
398C4—21no—
399C4—21no—
400C4—21no—
401C4—3441no—
402C4—3441no—
403C4—3441no—
404C4—3441no—
405C4—1722no—
406C4#135×D4312yes—
407C4#1458371112yes—
408C2—41no—
409C2—1724no—
410C2#1914410811yescharacteristic
411C2#1914417711yescharacteristic
412C2#1914433311yescharacteristic
subgroupG/H
centerC22C2×#13063300
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1572C2
socleC22×C43C2×#121
prime radicalC22×D172D4
hypercenter#1572D43
hypocenterC43#19395
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1572

Complements

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

NH ≅ G/Ntype
1. #19145756C2semidirect
5. #19134047C2semidirect
6. #19134019C2semidirect
7. #19133985C2semidirect
8. #19133971C2semidirect
9. #19133306C2semidirect
10. #19133259C2semidirect
11. C43×#1572C2semidirect
15. #14583304C22semidirect
16. #14583297C22semidirect
17. #14583250C22semidirect
18. #14583250C22semidirect
36. #14582647C22semidirect
37. #14582646C22semidirect
38. #14582646C22semidirect
39. #14582644C22semidirect
43. C43×#335C22semidirect
44. C43×#334C22semidirect
210. #1572D43semidirect
245. #335C2×D43semidirect
246. #334C2×D43semidirect
251. C43#19395semidirect

Maximal subgroups

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

subgroupindex
#191457562
#191446952
#191446042
#191436182
#191340472
#191340192
#191339852
#191339712
#191333062
#191332592
C43×#15722
#1939543