Finite Group Databasebeta

← #25081795

Subgroups — #25081795

Order 11008.

662 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145553C211yesmaximal, characteristic, complemented
2#19144695C211yesmaximal, characteristic, complemented
3#19144596C211yesmaximal, characteristic
4#19143618C211yesmaximal, characteristic, complemented
5#19134033C212yesmaximal, complemented
6#19134019C212yesmaximal, complemented
7#19133961C212yesmaximal, complemented
8#19133937C212yesmaximal, complemented
9#19133301C211yesmaximal, characteristic, complemented
10#19133259C211yesmaximal, characteristic, complemented
11C43×#1572C211yesmaximal, characteristic, complemented
12#14583456C2211yescharacteristic
13#14583449C2211yescharacteristic
14C2×C4×D172C2211yescharacteristic
15#14583279C2211yescharacteristic, complemented
16#14583272C2211yescharacteristic, complemented
17#14583250C2211yescharacteristic, complemented
18#14583246C2211yescharacteristic, complemented
19#14583235—21no—
20#14583213—21no—
21#14583180C2212yes—
22#14583180C2212yes—
23#14583122—22no—
24#14583105C2212yes—
25#14583095C2212yes—
26#14583063—22no—
27#14583052—21no—
28#14583035—21no—
29#14583001—22no—
30C4×D344—22no—
31C8×D172C2212yes—
32C8×D172C2212yes—
33#14582964—22no—
34#14582952C2211yescharacteristic
35C22⋊C8×D43—22no—
36#14582646C2212yescomplemented
37#14582644C2212yescomplemented
38#14582644C2212yescomplemented
39#14582642C2212yescomplemented
40C43×#432C2211yescharacteristic
41C43×#431C2211yescharacteristic
42C43×#431C2211yescharacteristic
43C43×#335C2212yescomplemented
44C43×#334C2212yescomplemented
45C2×#10621898—21no—
46C22×D172D411yescharacteristic
47C22×C4×D43—21no—
48C2×Dic172—22no—
49C2×#10621873—22no—
50C2×#10621873—22no—
51C2×D344—22no—
52C2×C8×D43—22no—
53C2×C8×D43—22no—
54#13063325C2311yescharacteristic
55#13063325C2311yescharacteristic
56#13063325C2311yescharacteristic
57#13063322C2311yescharacteristic
58#13063317—21no—
59#13063313—21no—
60#13063304—21no—
61#13063304—21no—
62#13063299—21no—
63#13063299—21no—
64C4×Dic86—21no—
65C4×Dic86—21no—
66C4×D172—21no—
67C4×D172—21no—
68C4×D172—21no—
69C4×D172—21no—
70C4×D172D412yes—
71C4×D172C2312yes—
72#13063284—21no—
73C2×C4⋊Dic43D411yescharacteristic
74C2×(C2×D43)⋊C4—21no—
75#13063259—22no—
76#13063259—22no—
77C4⋊(C43⋊C8)C2312yes—
78#13063250—22no—
79#13063250—22no—
80#13063247—22no—
81#13063247—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
103C2×C22⋊D43—41no—
104C22×Dic43—21no—
105#10621898—82no—
106C2×D172—21no—
107C2×D172—24no—
108C2×D172—21no—
109C2×D172—21no—
110C2×D172—21no—
111C2×D172C2×D412yes—
112C2×C4×D43—22no—
113C2×C4×D43—22no—
114C2×C4×D43—41no—
115C2×C4×D43—82no—
116C2×Dic86—21no—
117C2×Dic86—21no—
118C2×Dic86—21no—
119C2×C8×C43—22no—
120C2×C8×C43—22no—
121C2×C8×C43C2×D412yes—
122C2×C8×C43C2×D412yes—
123C42×C43C2×D411yescharacteristic
124C42×C43C2×D411yescharacteristic
125C42×C43#4111yescharacteristic
126C42×C43C2411yescharacteristic
127C22⋊Dic43—41no—
128(C2×D43)⋊C4—22no—
129(C2×D43)⋊C4—22no—
130(C2×D43)⋊C4—41no—
131(C2×D43)⋊C4—41no—
132C4⋊Dic43—21no—
133C4⋊Dic43—21no—
134C4⋊Dic43—21no—
135C4⋊Dic43—21no—
136C4⋊Dic43—21no—
137C4⋊Dic43—21no—
138C4⋊Dic43—21no—
139C4⋊Dic43C2×D412yes—
140Dic43⋊C4—41no—
141Dic43⋊C4—41no—
142C4×Dic43—41no—
143C2×C43⋊C8—22no—
144Dic172—82no—
145D344—44no—
146#10621873—44no—
147#10621873—82no—
148C8×D43—82no—
149C8×D43—82no—
150C23×C43#12111yescharacteristic
151C22×D43—22no—
152C22×D43—24no—
153C22×D43—41no—
154C22×D43—81no—
155C22×D43—81no—
156C2×C4×C43—22no—
157C2×C4×C43—22no—
158C2×C4×C43—41no—
159C2×C4×C43#12111yescharacteristic
160C2×C4×C43#12111yescharacteristic
161C2×C4×C43#12111yescharacteristic
162C2×C4×C43C22×D411yescharacteristic
163C2×C4×C43C22×D411yescharacteristic
164C2×C4×C43C2×#4111yescharacteristic
165C22⋊D43—82no—
166C2×Dic43—22no—
167C2×Dic43—41no—
168C2×Dic43—41no—
169C2×Dic43—41no—
170C2×Dic43—81no—
171D172—24no—
172D172—22no—
173D172—42no—
174D172—42no—
175D172—81no—
176D172#13514yes—
177C4×D43—42no—
178C4×D43—42no—
179C4×D43—82no—
180C4×D43—82no—
181Dic86—42no—
182Dic86—42no—
183Dic86—42no—
184C8×C43—22no—
185C8×C43—22no—
186C8×C43—42no—
187C8×C43—42no—
188C43⋊C8—42no—
189#19388—431nomaximal, Sylow
190C22×C43—21no—
191C22×C43—21no—
192C22×C43—21no—
193C22×C43C2×#12111yescharacteristic
194C2×D43—24no—
195C2×D43—42no—
196C2×D43—42no—
197C2×D43—84no—
198C2×D43—81no—
199C2×D43—81no—
200C2×D43—81no—
201C4×C43—21no—
202C4×C43—21no—
203C4×C43—21no—
204C4×C43—21no—
205C4×C43C2×#13512yes—
206C4×C43#57612yes—
207Dic43—42no—
208Dic43—81no—
209Dic43—81no—
210Dic43—81no—
211#3210—431no—
212#3110—431no—
213#3100—431no—
214#2972—431no—
215#1681—432no—
216#1679—432no—
217#1669—432no—
218#1665—432no—
219#1572D4311yescharacteristic, complemented
220#1553—431no—
221#1544—431no—
222C2×C43—41no—
223C2×C43#304111yescharacteristic
224C2×C43#305011yescharacteristic
225C2×C43#306911yescharacteristic
226D43—44no—
227D43—161no—
228#533—431no—
229#532—431no—
230C2×C4×D4—431no—
231#494—431no—
232#492—431no—
233#487—431no—
234#486—431no—
235#484—861no—
236#480—861no—
237#474—432no—
238#474—432no—
239#464—862no—
240#461—432no—
241#459—432no—
242#452—862no—
243#450—861no—
244#447—861no—
245#440—862no—
246C4×D8—862no—
247C8×D4—432no—
248C8×D4—432no—
249C8×D4—862no—
250#432C2×D4311yescharacteristic
251#431—431no—
252#431C2×D4311yescharacteristic
253#431C2×D4311yescharacteristic
254C2×C22⋊C8—862no—
255#335C2×D4312yescomplemented
256#334C2×D4312yescomplemented
257#332—432no—
258#332—432no—
259#332—432no—
260#331—432no—
261C43#1938811yescharacteristic, complemented, Sylow
262C2×#41—861no—
263C22×D4—431no—
264C23×C4—861no—
265C2×Q16—862no—
266C2×SD16—862no—
267C2×SD16—862no—
268C2×D8—862no—
269C22×C8—862no—
270C22×C8—862no—
271C4⋊Q8—431no—
272C4⋊Q8—431no—
273C4⋊Q8—431no—
274#127—431no—
275#125—861no—
276#124—861no—
277C22⋊Q8—861no—
278C22⋊Q8—861no—
279#121—861no—
280#121—861no—
281C4×Q8—861no—
282C4×Q8—861no—
283C4×D4—432no—
284C4×D4—432no—
285C4×D4—861no—
286C4×D4—861no—
287C4×D4—861no—
288C4×D4—861no—
289#117—861no—
290C2×C4⋊C4—431no—
291C2×C22⋊C4—861no—
292C2×C42C22×D4311yescharacteristic
293#107—862no—
294#107—862no—
295C4⋊C8—432no—
296C4⋊C8D17212yes—
297C4⋊C8C22×D4312yes—
298C4⋊C8C22×D4312yes—
299#103—862no—
300#103—862no—
301#102—862no—
302#102—862no—
303#102—862no—
304#102—862no—
305C22⋊C8—21no—
306C22⋊C8—21no—
307C22⋊C8—861no—
308C22⋊C8—862no—
309C22⋊C8—862no—
310C22⋊C8D17212yes—
311#97—21no—
312C4×C8—21no—
313C4×C8—861no—
314C4×C8C22×D4311yescharacteristic
315C4×C8C22×D4311yescharacteristic
316C24—861no—
317#41—3442no—
318C2×Q8—861no—
319C2×Q8—861no—
320C2×Q8—861no—
321C2×D4—432no—
322C2×D4—864no—
323C2×D4—861no—
324C2×D4—861no—
325C2×D4—861no—
326C2×D4—861no—
327C2×D4—1721no—
328C22×C4—861no—
329C22×C4—862no—
330C22×C4—862no—
331C22×C4—3442no—
332C22×C4—1721no—
333C22×C4C2×D17211yescharacteristic
334C22×C4D4×D4311yescharacteristic
335C22×C4#1062190211yescharacteristic
336Q16—3442no—
337SD16—3442no—
338SD16—1724no—
339D8—1724no—
340C2×C8—22no—
341C2×C8—22no—
342C2×C8—862no—
343C2×C8—3442no—
344C2×C8—3442no—
345C2×C8C2×D17212yes—
346C2×C8C2×D17212yes—
347C4⋊C4—432no—
348C4⋊C4—861no—
349C4⋊C4—861no—
350C4⋊C4—861no—
351C4⋊C4—861no—
352C4⋊C4—861no—
353C4⋊C4—861no—
354C4⋊C4—861no—
355C4⋊C4—1721no—
356C4⋊C4—1721no—
357C22⋊C4—862no—
358C22⋊C4—862no—
359C22⋊C4—1721no—
360C22⋊C4—1721no—
361C22⋊C4—1721no—
362C42—1721no—
363C42C2×D17211yescharacteristic
364C42D4×D4311yescharacteristic
365C42#1062190211yescharacteristic
366C42C23×D4311yescharacteristic
367C23—864no—
368C23—862no—
369C23—3441no—
370C23—3441no—
371C23—1721no—
372C23#1306330011yescharacteristic
373Q8—1722no—
374Q8—1722no—
375Q8—1722no—
376D4—434no—
377D4—864no—
378D4—862no—
379D4—3441no—
380D4—3442no—
381D4—1722no—
382D4—1722no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—41no—
386C2×C4—862no—
387C2×C4—3442no—
388C2×C4—3442no—
389C2×C4—3441no—
390C2×C4—1721no—
391C2×C4—1721no—
392C2×C4—1721no—
393C2×C4—1722no—
394C2×C4—1722no—
395C2×C4#1306330011yescharacteristic
396C2×C4#1306330011yescharacteristic
397C2×C4#1306330011yescharacteristic
398C2×C4C2×D4×D4311yescharacteristic
399C2×C4C22×D17211yescharacteristic
400C2×C4C2×#1062190211yescharacteristic
401C8—22no—
402C8—22no—
403C8—42no—
404C8—42no—
405C8—1722no—
406C22—21no—
407C22—21no—
408C22—21no—
409C22—864no—
410C22—3444no—
411C22—3441no—
412C22—3441no—
413C22—3441no—
414C22—1722no—
415C22—1722no—
416C22C2×#1306330011yescharacteristic
417C4—21no—
418C4—21no—
419C4—21no—
420C4—21no—
421C4—3441no—
422C4—3441no—
423C4—3441no—
424C4—1722no—
425C4#135×D4312yes—
426C4#1458370412yes—
427C2—41no—
428C2—1724no—
429C2—6881no—
430C2#1914409911yescharacteristic
431C2#1914417711yescharacteristic
432C2#1914433311yescharacteristic
subgroupG/H
centerC22C2×#13063300
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1572C2
socleC22×C43C2×#121
prime radical#19144596C2
hypercenter#1572D43
hypocenterC43#19388
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. #19145553C2semidirect
2. #19144695C2semidirect
4. #19143618C2semidirect
5. #19134033C2semidirect
6. #19134019C2semidirect
7. #19133961C2semidirect
8. #19133937C2semidirect
9. #19133301C2semidirect
10. #19133259C2semidirect
11. C43×#1572C2semidirect
15. #14583279C22semidirect
16. #14583272C22semidirect
17. #14583250C22semidirect
18. #14583246C22semidirect
36. #14582646C22semidirect
37. #14582644C22semidirect
38. #14582644C22semidirect
39. #14582642C22semidirect
43. C43×#335C22semidirect
44. C43×#334C22semidirect
219. #1572D43semidirect
255. #335C2×D43semidirect
256. #334C2×D43semidirect
261. C43#19388semidirect

Maximal subgroups

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

subgroupindex
#191455532
#191446952
#191445962
#191436182
#191340332
#191340192
#191339612
#191339372
#191333012
#191332592
C43×#15722
#1938843