Finite Group Databasebeta

← #25079740

Subgroups — #25079740

Order 11008.

714 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145723C211yesmaximal, characteristic, complemented
2#19145515C211yesmaximal, characteristic
3C2×#14583247C211yesmaximal, characteristic, complemented
4#19143306C211yesmaximal, characteristic, complemented
5#19134131C214yesmaximal, complemented
6#19134007C214yesmaximal, complemented
7#19133341C211yesmaximal, characteristic, complemented
8#19133264C211yesmaximal, characteristic, complemented
9C43×#1548C211yesmaximal, characteristic, complemented
10C2×#13063333—21no—
11#14583449C2211yescharacteristic
12C2×#13063322C2211yescharacteristic
13#14583295—21no—
14#14583276—21no—
15#14583247—21no—
16#14583247—21no—
17#14583247—21no—
18#14583247C2212yes—
19#14583247C2212yes—
20#14583246—21no—
21#14583217—22no—
22#14583186C2214yescomplemented
23#14583095C2214yes—
24#14583035—22no—
25#14582976—21no—
26#14582976C2212yescomplemented
27#14582964—21no—
28#14582964C2212yescomplemented
29#14582952C2211yescharacteristic
30C2×#13063245—21no—
31C2×#13063245—21no—
32#14582867—21no—
33C2×C4×C43⋊C8C2211yescharacteristic
34#14582651C2212yescomplemented
35#14582649C2212yescomplemented
36#14582642C2214yes—
37C2×C4⋊Q8×C43C2211yescharacteristic
38C43×#431C2211yescharacteristic
39C43×#423C2211yescharacteristic
40C43×#333C2214yescomplemented
41C2×#10621898—21no—
42C22×D172—21no—
43C22×D172—21no—
44C22×D172—21no—
45C2×D344—24no—
46#13063333—44no—
47C2×#10621872—22no—
48C22×C43⋊C8D411yescharacteristic
49C22×C43⋊C8D411yescharacteristic
50C2×C8×D43—22no—
51#13063325D411yescharacteristic
52#13063322—21no—
53#13063322—21no—
54#13063322—21no—
55#13063322D411yescharacteristic
56#13063322C2312yes—
57#13063313—21no—
58#13063299—21no—
59#13063299D412yes—
60C4×D172—21no—
61C4×D172C2312yes—
62#13063256—24no—
63C4⋊(C43⋊C8)C2312yes—
64#13063247—24no—
65#13063245—24no—
66#13063245—22no—
67#13063245—22no—
68#13063245—22no—
69#13063245—22no—
70C22⋊(C43⋊C8)—21no—
71(C2×D43)⋊C8—22no—
72(C2×D43)⋊C8—22no—
73C4×C43⋊C8—21no—
74C4×C43⋊C8D411yescharacteristic
75C4×C43⋊C8D411yescharacteristic
76C4×C43⋊C8C2311yescharacteristic
77C4×C43⋊C8C2311yescharacteristic
78C22×Q8×C43—21no—
79C2×M16×C43—21no—
80C4⋊Q8×C43—21no—
81C4⋊Q8×C43—21no—
82C4⋊Q8×C43—21no—
83C4⋊Q8×C43C2312yes—
84C2×C4⋊C4×C43—21no—
85C2×C4⋊C4×C43—21no—
86C2×C42×C43C2311yescharacteristic
87C4⋊C8×C43—21no—
88C4⋊C8×C43C2312yes—
89C4⋊C8×C43C2312yes—
90C22⋊C8×C43—21no—
91C4×C8×C43—21no—
92C23×D43—41no—
93C2×Q8×C43—22no—
94C2×Q8×C43—41no—
95C2×Q8×C43—82no—
96C22×C4×C43—41no—
97C22×C4×C43C2×D411yescharacteristic
98C22×C4×C43C2×D411yescharacteristic
99C22×C4×C43#4111yescharacteristic
100C2×C22⋊D43—22no—
101#10621898—42no—
102#10621898—42no—
103C2×D172—21no—
104C2×D172—21no—
105C2×D172—22no—
106C2×D172—22no—
107C2×D172—22no—
108C2×D172—41no—
109C2×D172—41no—
110C2×D172—41no—
111C2×D172—42no—
112C2×D172—42no—
113C2×D172—82no—
114C2×D172—82no—
115C2×D172C2×D412yes—
116C2×C4×D43—22no—
117C2×Dic86—21no—
118M16×C43—42no—
119C2×C8×C43—22no—
120C2×C8×C43—22no—
121C4⋊C4×C43—22no—
122C4⋊C4×C43—22no—
123C4⋊C4×C43—41no—
124C4⋊C4×C43—41no—
125C42×C43C2×D411yescharacteristic
126C42×C43C2×D411yescharacteristic
127C42×C43#4111yescharacteristic
128C42×C43C2411yescharacteristic
129(C2×D43)⋊C4—22no—
130(C2×D43)⋊C4—22no—
131C4⋊Dic43—21no—
132C4⋊Dic43C2×D412yes—
133C2×C43⋊C8—22no—
134C2×C43⋊C8—22no—
135C2×C43⋊C8—22no—
136C2×C43⋊C8C2×D411yescharacteristic
137C2×C43⋊C8C2×D411yescharacteristic
138C2×C43⋊C8C2×D411yescharacteristic
139C2×C43⋊C8C2×D411yescharacteristic
140D344—84no—
141#10621872—44no—
142C8×D43—44no—
143C23×C43#12111yescharacteristic
144C22×D43—22no—
145C22×D43—42no—
146C22×D43—82no—
147C22×D43—82no—
148C22×D43—82no—
149Q8×C43—82no—
150Q8×C43—82no—
151C2×C4×C43—22no—
152C2×C4×C43—22no—
153C2×C4×C43—42no—
154C2×C4×C43—82no—
155C2×C4×C43#12111yescharacteristic
156C2×C4×C43#12111yescharacteristic
157C2×C4×C43#12111yescharacteristic
158C2×C4×C43#13512yes—
159C2×C4×C43AGL(1,ℤ/8)12yes—
160C2×C4×C43C22×D411yescharacteristic
161C2×C4×C43C22×D411yescharacteristic
162C2×C4×C43C2×#4111yescharacteristic
163C22⋊D43—44no—
164C2×Dic43—22no—
165D172—24no—
166D172—42no—
167D172—42no—
168D172—44no—
169D172—42no—
170D172—42no—
171D172—82no—
172D172—82no—
173D172—82no—
174D172—82no—
175C4×D43—42no—
176C4×D43—42no—
177Dic86—42no—
178C8×C43—42no—
179C8×C43—42no—
180C43⋊C8—21no—
181C43⋊C8—21no—
182C43⋊C8—21no—
183C43⋊C8—21no—
184C43⋊C8—42no—
185#19196—431nomaximal, Sylow
186C22×C43—21no—
187C22×C43—21no—
188C22×C43#46312yes—
189C22×C43C2×#12111yescharacteristic
190C2×D43—42no—
191C2×D43—42no—
192C2×D43—42no—
193C2×D43—82no—
194C2×D43—82no—
195C2×D43—82no—
196C2×D43—164no—
197C4×C43—21no—
198C4×C43—21no—
199C4×C43—82no—
200C4×C43#46312yes—
201C4×C43#47212yes—
202C4×C43C2×#13511yescharacteristic
203C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
204C4×C43#57712yes—
205Dic43—42no—
206#3227—431no—
207#3205—431no—
208C2×#486—431no—
209#2931—431no—
210#1697—434no—
211#1677—434no—
212#1564—431no—
213#1548D4311yescharacteristic, complemented
214#1545—431no—
215C2×C43—22no—
216C2×C43C2×#46311yescharacteristic
217C2×C43#305711yescharacteristic
218C2×C43C2×#47211yescharacteristic
219D43—82no—
220D43—162no—
221C2×#131—861no—
222#532—431no—
223C2×C4⋊Q8C2×D4311yescharacteristic
224C2×#127—431no—
225#498—861no—
226#493—861no—
227#486—432no—
228#486—432no—
229#486—861no—
230#486—861no—
231#486—861no—
232#486—861no—
233#481—862no—
234#476—434no—
235#459—434no—
236#447—862no—
237#436—432no—
238#436—861no—
239C8×D4—432no—
240C8×D4—861no—
241#431—431no—
242#431C2×D4311yescharacteristic
243#423C2×D4311yescharacteristic
244C2×#102—861no—
245C2×#102—861no—
246#408—861no—
247C2×C4×C8—431no—
248#335—432no—
249#334—432no—
250#333C2×D4314yescomplemented
251#331—434no—
252C43#1919611yescharacteristic, complemented, Sylow
253C2×#41—861no—
254C22×Q8—21no—
255C22×D4—861no—
256C22×D4—861no—
257C22×D4—861no—
258C2×D8—864no—
259#131—1724no—
260C2×M16—21no—
261C2×M16—862no—
262C22×C8—431no—
263C22×C8—431no—
264C22×C8—862no—
265C4⋊Q8—21no—
266C4⋊Q8—21no—
267C4⋊Q8—21no—
268C4⋊Q8—431no—
269C4⋊Q8C22×D4312yes—
270#127—431no—
271#127—432no—
272#127—861no—
273#127—861no—
274#127—861no—
275#124—861no—
276#121—432no—
277#121—861no—
278C4×D4—432no—
279C4×D4—861no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—21no—
282C2×C42C22×D4311yescharacteristic
283#106—864no—
284C4⋊C8—21no—
285C4⋊C8—432no—
286C4⋊C8C22×D4312yes—
287C4⋊C8C22×D4312yes—
288#102—862no—
289#102—862no—
290#102—862no—
291#102—862no—
292#102—864no—
293#102—864no—
294C22⋊C8—21no—
295C22⋊C8—862no—
296C22⋊C8—862no—
297C22⋊C8—861no—
298C4×C8—21no—
299C4×C8—431no—
300C4×C8—431no—
301C4×C8—431no—
302C4×C8—431no—
303C4×C8—861no—
304C24—1721no—
305#41—1722no—
306#41—1722no—
307C2×Q8—22no—
308C2×Q8—41no—
309C2×Q8—82no—
310C2×Q8—861no—
311C2×D4—432no—
312C2×D4—862no—
313C2×D4—861no—
314C2×D4—861no—
315C2×D4—862no—
316C2×D4—862no—
317C2×D4—862no—
318C2×D4—3442no—
319C2×D4—3442no—
320C2×D4—1721no—
321C2×D4—1721no—
322C2×D4—1721no—
323C2×D4—1722no—
324C2×D4—1722no—
325C22×C4—41no—
326C22×C4—862no—
327C22×C4#1062189811yescharacteristic
328C22×C4D4×D4311yescharacteristic
329C22×C4D4×D4311yescharacteristic
330D8—3444no—
331M16—42no—
332M16—1724no—
333C2×C8—22no—
334C2×C8—22no—
335C2×C8—431no—
336C2×C8—431no—
337C2×C8—431no—
338C2×C8—431no—
339C2×C8—862no—
340C2×C8—862no—
341C2×C8—862no—
342C2×C8—1724no—
343C4⋊C4—22no—
344C4⋊C4—22no—
345C4⋊C4—41no—
346C4⋊C4—41no—
347C4⋊C4—432no—
348C4⋊C4—861no—
349C22⋊C4—862no—
350C22⋊C4—862no—
351C42#1062189811yescharacteristic
352C42D4×D4311yescharacteristic
353C42D4×D4311yescharacteristic
354C42C23×D4311yescharacteristic
355C23—862no—
356C23—3442no—
357C23—3442no—
358C23—3442no—
359C23—1722no—
360C23#1306329811yescharacteristic
361Q8—82no—
362Q8—82no—
363Q8—1722no—
364D4—864no—
365D4—3442no—
366D4—3442no—
367D4—3442no—
368D4—3442no—
369D4—1724no—
370D4—1722no—
371D4—1722no—
372D4—1722no—
373D4—1722no—
374D4—1724no—
375C2×C4—22no—
376C2×C4—22no—
377C2×C4—42no—
378C2×C4—82no—
379C2×C4—862no—
380C2×C4—1722no—
381C2×C4—1722no—
382C2×C4#1306329811yescharacteristic
383C2×C4#1306329811yescharacteristic
384C2×C4#1306329811yescharacteristic
385C2×C4#1306334812yes—
386C2×C4#1306335212yes—
387C2×C4C2×D4×D4311yescharacteristic
388C2×C4C2×D4×D4311yescharacteristic
389C2×C4C2×#1062189811yescharacteristic
390C8—42no—
391C8—42no—
392C8—861no—
393C8—861no—
394C8—861no—
395C8—861no—
396C8—1722no—
397C22—21no—
398C22—21no—
399C22—3442no—
400C22—3442no—
401C22—3442no—
402C22—1722no—
403C22—1722no—
404C22—1722no—
405C22—6884no—
406C22#1458311712yes—
407C22C2×#1306329811yescharacteristic
408C4—21no—
409C4—21no—
410C4—82no—
411C4—1722no—
412C4#1458311712yes—
413C4#1458316812yes—
414C4C2×#1306334811yescharacteristic
415C4C2×#1306335211yescharacteristic
416C4#1458370812yes—
417C2—22no—
418C2—3442no—
419C2—6882no—
420C2C2×#1458311711yescharacteristic
421C2#1914423711yescharacteristic
422C2C2×#1458316811yescharacteristic
subgroupG/H
centerC22C2×#13063298
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC43×#1548C2
socleC22×C43C2×#121
prime radical#19145515C2
hypercenter#1548D43
hypocenterC43#19196
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1548

Complements

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

NH ≅ G/Ntype
1. #19145723C2semidirect
3. C2×#14583247C2semidirect
4. #19143306C2semidirect
5. #19134131C2semidirect
6. #19134007C2semidirect
7. #19133341C2semidirect
8. #19133264C2semidirect
9. C43×#1548C2semidirect
22. #14583186C22semidirect
26. #14582976C22semidirect
28. #14582964C22semidirect
34. #14582651C22semidirect
35. #14582649C22semidirect
40. C43×#333C22semidirect
213. #1548D43semidirect
250. #333C2×D43semidirect
252. C43#19196semidirect

Maximal subgroups

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

subgroupindex
#191457232
#191455152
C2×#145832472
#191433062
#191341312
#191340072
#191333412
#191332642
C43×#15482
#1919643