Finite Group Databasebeta

← #25015094

Subgroups — #25015094

Order 11008.

472 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#19145019C211yesmaximal, characteristic
2C2×#14582719C211yesmaximal, characteristic, complemented
3#19136330C211yesmaximal, characteristic, complemented
4#19136324C211yesmaximal, characteristic, complemented
5#19136323C211yesmaximal, characteristic, complemented
6#19134476C211yesmaximal, characteristic, complemented
7C43×#2145C211yesmaximal, characteristic, complemented
8C2×#13063347C2211yescharacteristic
9C2×#13063345—21no—
10#14583445—21no—
11C2×#13063265C2211yescharacteristic
12#14583284C411yescharacteristic, complemented
13#14583282C411yescharacteristic, complemented
14#14583280—21no—
15#14583277C411yescharacteristic, complemented
16#14583274C411yescharacteristic, complemented
17#14583270—21no—
18C2×#13063261C2211yescharacteristic
19#14582855—21no—
20C2×C8×Dic43C2211yescharacteristic
21#14582719—21no—
22#14582719—21no—
23#14582708—22no—
24#14582707—22no—
25#14582706—22no—
26#14582658—21no—
27C2×#135×C43C2211yescharacteristic
28C2×M32×C43C2211yescharacteristic
29C43×#427C2211yescharacteristic
30C43×#360—22no—
31C2×#10621898—21no—
32#13063347—21no—
33#13063347—21no—
34#13063347—21no—
35#13063347—21no—
36#13063345—41no—
37#13063345—41no—
38#13063345—41no—
39#13063345—41no—
40C2×Dic172C2×C411yescharacteristic
41C2×#10621885—21no—
42C2×#10621873—21no—
43C2×#10621883—21no—
44C2×#10621884—21no—
45C2×D344C2×C411yescharacteristic
46C2×#10621882—21no—
47C2×#10621877—21no—
48C22×C43⋊C8D411yescharacteristic
49#13063323—21no—
50#13063321—21no—
51#13063314—21no—
52#13063312—21no—
53#13063297—42no—
54C4×C22⋊D43—42no—
55C2×C4×Dic43D411yescharacteristic
56#13063265—21no—
57#13063265—21no—
58C2×C43⋊C16—21no—
59#13063261—21no—
60#13063261D412yescomplemented
61#13063236—41no—
62C4×C43⋊C8—41no—
63C8×Dic43C2×C411yescharacteristic
64C8×Dic43C2×C411yescharacteristic
65C8×Dic43D411yescharacteristic
66C8×Dic43D411yescharacteristic
67C2×#41×C43—21no—
68#135×C43—21no—
69#135×C43—21no—
70#135×C43—21no—
71#135×C43—21no—
72C2×Q16×C43C2×C411yescharacteristic
73C2×SD16×C43—21no—
74C2×D8×C43C2×C411yescharacteristic
75C22×C8×C43C2311yescharacteristic
76#117×C43—21no—
77M32×C43—21no—
78M32×C43—21no—
79C2×C16×C43—21no—
80#107×C43—21no—
81#106×C43D412yescomplemented
82#41×C43—41no—
83#41×C43—41no—
84#41×C43—41no—
85#41×C43—41no—
86C2×Q8×C43—21no—
87C2×D4×C43—21no—
88C2×D4×C43—41no—
89C22×C4×C43—41no—
90C22×C4×C43C2×D411yescharacteristic
91C2×C22⋊D43—42no—
92C2×C22⋊D43—41no—
93C22×Dic43—21no—
94#10621898—41no—
95#10621898—41no—
96#10621898—41no—
97#10621898—41no—
98C2×D172—21no—
99C2×C4×D43—41no—
100C2×Dic86—21no—
101Q16×C43—21no—
102Q16×C43—21no—
103SD16×C43—41no—
104SD16×C43—41no—
105D8×C43—21no—
106D8×C43—21no—
107C2×C8×C43C22×C411yescharacteristic
108C2×C8×C43C2×D411yescharacteristic
109C2×C8×C43C2×D411yescharacteristic
110C2×C8×C43C2×D411yescharacteristic
111C2×C8×C43#4111yescharacteristic
112C2×C8×C43#4111yescharacteristic
113C4⋊C4×C43—22no—
114C22⋊C4×C43—41no—
115C42×C43—41no—
116C22⋊Dic43—42no—
117#10621885—41no—
118#10621885—41no—
119#10621884—41no—
120#10621884—41no—
121#10621883—41no—
122#10621883—41no—
123#10621882—41no—
124#10621882—41no—
125(C2×D43)⋊C4—42no—
126Dic43⋊C4—42no—
127C4×Dic43—21no—
128C4×Dic43C22⋊C411yescharacteristic
129C4×Dic43C22⋊C411yescharacteristic
130#10621877—22no—
131#10621877—41no—
132C2×C43⋊C8—41no—
133C2×C43⋊C8C22⋊C411yescharacteristic
134C2×C43⋊C8C22⋊C411yescharacteristic
135C2×C43⋊C8D811yescharacteristic
136C2×C43⋊C8D811yescharacteristic
137C2×C43⋊C8SD1611yescharacteristic
138C2×C43⋊C8SD1611yescharacteristic
139Dic172—21no—
140Dic172—21no—
141D344—21no—
142D344—21no—
143#10621873—41no—
144#10621873—41no—
145C16×C43—41no—
146C43⋊C16—41no—
147C23×C43—41no—
148C23×C43AGL(1,ℤ/8)11yescharacteristic
149C22×D43—41no—
150Q8×C43—41no—
151Q8×C43—41no—
152D4×C43—41no—
153D4×C43—41no—
154D4×C43—81no—
155D4×C43—81no—
156C2×C4×C43—41no—
157C2×C4×C43—42no—
158C2×C4×C43—81no—
159C2×C4×C43—81no—
160C2×C4×C43C2×C22⋊C411yescharacteristic
161C2×C4×C43#12111yescharacteristic
162C2×C4×C43#12111yescharacteristic
163C2×C4×C43C2×D811yescharacteristic
164C2×C4×C43C2×SD1611yescharacteristic
165C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
166C22⋊D43—84no—
167C22⋊D43—81no—
168C22⋊D43—81no—
169C2×Dic43—21no—
170C2×Dic43—21no—
171C2×Dic43—42no—
172C2×Dic43—41no—
173D172—41no—
174D172—41no—
175C4×D43—81no—
176C4×D43—81no—
177Dic86—41no—
178Dic86—41no—
179C8×C43C4×D411yescharacteristic
180C8×C43C4×D411yescharacteristic
181C8×C43#12411yescharacteristic
182C8×C43#12711yescharacteristic
183C43⋊C8—42no—
184C43⋊C8#10211yescharacteristic
185C43⋊C8#10211yescharacteristic
186C43⋊C8#10211yescharacteristic
187C43⋊C8#10211yescharacteristic
188#13259—431nomaximal, Sylow
189C22×C43—41no—
190C22×C43—82no—
191C22×C43—81no—
192C22×C43#41811yescharacteristic
193C22×C43#45911yescharacteristic
194C22×C43#46011yescharacteristic
195C2×D43—82no—
196C2×D43—81no—
197C4×C43—82no—
198C4×C43—81no—
199C4×C43#39011yescharacteristic
200C4×C43C2×#10211yescharacteristic
201C4×C43#45911yescharacteristic
202C4×C43#46011yescharacteristic
203Dic43—22no—
204Dic43—41no—
205Dic43—81no—
206#3147—431no—
207C2×#364—431no—
208#2145—431no—
209#2145D4311yescharacteristic, complemented
210#2143—431no—
211#2143—431no—
212#1772—431no—
213C2×C43—21no—
214C2×C43—21no—
215C2×C43—21no—
216C2×C43—161no—
217C2×C43#198211yescharacteristic
218D43—161no—
219C2×#135—431no—
220C2×#135—861no—
221C2×#135C2×D4311yescharacteristic
222#532—861no—
223C2×M32—431no—
224C2×M32C2×D4311yescharacteristic
225#495—431no—
226#495—431no—
227#495—861no—
228#494—431no—
229#493—431no—
230#492—861no—
231C2×#108—431no—
232#427C2×D4311yescharacteristic
233#405—861no—
234C2×C4×C8—431no—
235#364—861no—
236#364—861no—
237#360—22no—
238#360—862no—
239#359—862no—
240#359—862no—
241#339—861no—
242C43#1325911yescharacteristic, complemented, Sylow
243C2×#41—21no—
244C2×#41—861no—
245#135—21no—
246#135—21no—
247#135—21no—
248#135—21no—
249#135—861no—
250#135—861no—
251#135—861no—
252#135—861no—
253#135—1721no—
254#135—1721no—
255#135—1721no—
256#135—1721no—
257C2×Q16—431no—
258C2×Q16—861no—
259C2×Q16C4×D4311yescharacteristic
260C2×SD16—21no—
261C2×SD16—861no—
262C2×SD16—861no—
263C2×SD16—861no—
264C2×D8—431no—
265C2×D8—861no—
266C2×D8C4×D4311yescharacteristic
267C2×M16—861no—
268C22×C8—431no—
269C22×C8C22×D4311yescharacteristic
270C4⋊Q8—861no—
271#127—861no—
272#124—861no—
273#124—861no—
274#121—1722no—
275C4×D4—1722no—
276#117—21no—
277C2×C42—431no—
278M32—21no—
279M32—21no—
280M32—861no—
281M32—861no—
282C2×C16—21no—
283C2×C16—861no—
284#108—432no—
285#108—861no—
286#107—21no—
287#106C22⋊D4312yescomplemented
288#97—1721no—
289C4×C8—431no—
290C4×C8—431no—
291C4×C8—431no—
292C4×C8—431no—
293C4×C8—1721no—
294#41—41no—
295#41—41no—
296#41—41no—
297#41—41no—
298#41—1721no—
299#41—1721no—
300#41—1721no—
301#41—1721no—
302C2×Q8—21no—
303C2×Q8—861no—
304C2×D4—21no—
305C2×D4—41no—
306C2×D4—861no—
307C2×D4—1722no—
308C2×D4—1721no—
309C22×C4—41no—
310C22×C4—861no—
311C22×C4—1721no—
312C22×C4D4×D4311yescharacteristic
313Q16—21no—
314Q16—21no—
315Q16—861no—
316Q16—861no—
317Q16—1721no—
318Q16—1721no—
319SD16—41no—
320SD16—41no—
321SD16—1721no—
322SD16—1721no—
323SD16—1721no—
324SD16—1721no—
325SD16—1721no—
326SD16—1721no—
327D8—21no—
328D8—21no—
329D8—861no—
330D8—861no—
331D8—1721no—
332D8—1721no—
333M16—862no—
334M16—1721no—
335C2×C8—431no—
336C2×C8—431no—
337C2×C8—431no—
338C2×C8—431no—
339C2×C8—431no—
340C2×C8—431no—
341C2×C8—1721no—
342C2×C8C2×C4×D4311yescharacteristic
343C2×C8#1062189811yescharacteristic
344C2×C8D4×D4311yescharacteristic
345C2×C8D4×D4311yescharacteristic
346C2×C8#1062190011yescharacteristic
347C2×C8C2×C22⋊D4311yescharacteristic
348C4⋊C4—22no—
349C4⋊C4—1722no—
350C22⋊C4—41no—
351C22⋊C4—1722no—
352C22⋊C4—1722no—
353C42—41no—
354C42—431no—
355C42—431no—
356C42—861no—
357C16—41no—
358C16—1721no—
359C23—41no—
360C23—1721no—
361C23#1306334911yescharacteristic
362Q8—41no—
363Q8—41no—
364Q8—1721no—
365Q8—1721no—
366D4—41no—
367D4—41no—
368D4—81no—
369D4—81no—
370D4—3444no—
371D4—3441no—
372D4—3441no—
373D4—1721no—
374D4—1721no—
375C2×C4—42no—
376C2×C4—41no—
377C2×C4—81no—
378C2×C4—81no—
379C2×C4—861no—
380C2×C4—861no—
381C2×C4—3441no—
382C2×C4—3441no—
383C2×C4—1722no—
384C2×C4—1721no—
385C2×C4C22⋊C4×D4311yescharacteristic
386C2×C4#1306329711yescharacteristic
387C2×C4#1306329811yescharacteristic
388C2×C4D8×D4311yescharacteristic
389C2×C4SD16×D4311yescharacteristic
390C2×C4#1306335211yescharacteristic
391C8—431no—
392C8—431no—
393C8—431no—
394C8—431no—
395C8—1722no—
396C8(C22⋊D43)⋊C411yescharacteristic
397C8C4×C22⋊D4311yescharacteristic
398C8#1306331111yescharacteristic
399C8#1306332111yescharacteristic
400C22—41no—
401C22—82no—
402C22—81no—
403C22—3442no—
404C22—3441no—
405C22#1458290211yescharacteristic
406C22#1458309211yescharacteristic
407C22#1458309811yescharacteristic
408C4—82no—
409C4—81no—
410C4—862no—
411C4—3441no—
412C4—1721no—
413C4#1458279911yescharacteristic
414C4#102×D4311yescharacteristic
415C4#1458309311yescharacteristic
416C4#1458309711yescharacteristic
417C2—21no—
418C2—21no—
419C2—21no—
420C2—161no—
421C2—6881no—
422C2#1913552011yescharacteristic
subgroupG/H
centerC4#14583093
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
FittingC43×#2145C2
socleC2×C43#1982
prime radical#19145019C2
cosocleC22×C8×C43C23
hypercenter#2145D43
hypocenterC43#13259
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×C8 ◁ #2145

Complements

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

NH ≅ G/Ntype
2. C2×#14582719C2semidirect
3. #19136330C2semidirect
4. #19136324C2semidirect
5. #19136323C2semidirect
6. #19134476C2semidirect
7. C43×#2145C2semidirect
12. #14583284C4semidirect
13. #14583282C4semidirect
15. #14583277C4semidirect
16. #14583274C4semidirect
60. #13063261D4semidirect
81. #106×C43D4semidirect
209. #2145D43semidirect
242. C43#13259semidirect
287. #106C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
#191450192
C2×#145827192
#191363302
#191363242
#191363232
#191344762
C43×#21452
#1325943