Finite Group Databasebeta

← #25013759

Subgroups — #25013759

Order 11008.

484 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147729C211yesmaximal, characteristic
2#19136330C211yesmaximal, characteristic, complemented
3#19136323C211yesmaximal, characteristic, complemented
4#19135483C211yesmaximal, characteristic, complemented
5#19132711C211yesmaximal, characteristic, complemented
6#19132677C211yesmaximal, characteristic, complemented
7C4×#135×C43C211yesmaximal, characteristic, complemented
8C2×#13063347C2211yescharacteristic
9#14583340—21no—
10#14583339C412yescomplemented
11#14583335—21no—
12#14583334C412yescomplemented
13#14583329—22no—
14C2×#13063265C2211yescharacteristic
15C2×#13063265C2211yescharacteristic
16C2×#13063261C2211yescharacteristic
17C2×#13063253—21no—
18#14582865—21no—
19#14582708—22no—
20#14582706—22no—
21C2×#135×C43C2211yescharacteristic
22C4×#41×C43—21no—
23C4×Q16×C43—21no—
24C4×SD16×C43—22no—
25C4×D8×C43—21no—
26C43×#427C2211yescharacteristic
27C43×#416—21no—
28C2×C4×C8×C43C2211yescharacteristic
29C2×#10621898—21no—
30#13063347—21no—
31#13063347—21no—
32#13063347—21no—
33#13063347—21no—
34C2×Dic172C2×C411yescharacteristic, complemented
35C2×#10621873—21no—
36C2×D344C2×C411yescharacteristic, complemented
37C2×#10621877—21no—
38#13063271—22no—
39#13063269—22no—
40#13063268—22no—
41#13063266—22no—
42#13063265—21no—
43#13063265—21no—
44#13063265—21no—
45#13063265C2×C412yescomplemented
46C2×C43⋊C16—21no—
47C2×C43⋊C16—21no—
48#13063261—21no—
49#13063261—21no—
50#13063253—41no—
51#13063253—41no—
52(C2×D43)⋊C8—42no—
53C2×#41×C43—21no—
54#135×C43—21no—
55#135×C43—21no—
56#135×C43C2×C412yes—
57#135×C43D412yes—
58C2×Q16×C43D411yescharacteristic
59C2×SD16×C43—21no—
60C2×D8×C43D411yescharacteristic
61C22×C8×C43D411yescharacteristic
62C22×C8×C43C2311yescharacteristic
63C4×Q8×C43—22no—
64C4×D4×C43—22no—
65C4×D4×C43—42no—
66#117×C43—21no—
67#117×C43—41no—
68C2×C42×C43—41no—
69C2×C42×C43D411yescharacteristic
70#107×C43—21no—
71#106×C43D412yes—
72#103×C43—22no—
73#102×C43—22no—
74C4×C8×C43—21no—
75C4×C8×C43—21no—
76#41×C43—22no—
77#41×C43—22no—
78#41×C43—41no—
79#41×C43—41no—
80C2×Q8×C43—21no—
81C2×D4×C43—21no—
82C2×D4×C43—41no—
83C22×C4×C43—21no—
84C22×C4×C43—42no—
85C22×C4×C43—41no—
86C22×C4×C43C2×D411yescharacteristic
87C2×C22⋊D43—41no—
88#10621898—41no—
89#10621898—41no—
90#10621898—41no—
91#10621898—41no—
92C2×D172—21no—
93C2×C4×D43—41no—
94C2×Dic86—21no—
95Q16×C43—21no—
96Q16×C43C22⋊C412yes—
97SD16×C43—22no—
98SD16×C43—22no—
99D8×C43—21no—
100D8×C43C22⋊C412yes—
101C2×C8×C43—21no—
102C2×C8×C43—21no—
103C2×C8×C43—21no—
104C2×C8×C43C22×C411yescharacteristic
105C2×C8×C43C2×D411yescharacteristic
106C2×C8×C43C2×D411yescharacteristic
107C2×C8×C43C2×D411yescharacteristic
108C2×C8×C43#4111yescharacteristic
109C2×C8×C43#4111yescharacteristic
110C4⋊C4×C43—22no—
111C4⋊C4×C43—42no—
112C22⋊C4×C43—42no—
113C22⋊C4×C43—41no—
114C42×C43—21no—
115C42×C43—42no—
116C42×C43—41no—
117C42×C43D811yescharacteristic
118C42×C43D811yescharacteristic
119#10621877—41no—
120#10621877—41no—
121C2×C43⋊C8—41no—
122Dic172—21no—
123Dic172—21no—
124D344—21no—
125D344—21no—
126#10621873—41no—
127#10621873—41no—
128C43⋊C16—22no—
129C43⋊C16—41no—
130C23×C43—41no—
131C23×C43AGL(1,ℤ/8)11yescharacteristic
132C22×D43—41no—
133Q8×C43—22no—
134Q8×C43—41no—
135D4×C43—22no—
136D4×C43—42no—
137D4×C43—42no—
138D4×C43—41no—
139C2×C4×C43—21no—
140C2×C4×C43—21no—
141C2×C4×C43—42no—
142C2×C4×C43—41no—
143C2×C4×C43—42no—
144C2×C4×C43—42no—
145C2×C4×C43—42no—
146C2×C4×C43—84no—
147C2×C4×C43C4×D411yescharacteristic
148C2×C4×C43#12011yescharacteristic
149C2×C4×C43#12111yescharacteristic
150C2×C4×C43C2×D811yescharacteristic
151C2×C4×C43#13511yescharacteristic
152C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
153C22⋊D43—81no—
154C22⋊D43—81no—
155C2×Dic43—41no—
156D172—41no—
157D172—41no—
158C4×D43—81no—
159C4×D43—81no—
160Dic86—41no—
161Dic86—41no—
162C8×C43—41no—
163C8×C43C2×C22⋊C411yescharacteristic
164C8×C43C4×D411yescharacteristic
165C8×C43#12111yescharacteristic
166C8×C43#12311yescharacteristic
167C43⋊C8—81no—
168#13027—431nomaximal, Sylow
169C22×C43—41no—
170C22×C43—42no—
171C22×C43—82no—
172C22×C43#44211yescharacteristic
173C22×C43#44711yescharacteristic
174C22×C43#46311yescharacteristic
175C2×D43—82no—
176C2×D43—81no—
177C4×C43—22no—
178C4×C43—41no—
179C4×C43—42no—
180C4×C43—82no—
181C4×C43#38611yescharacteristic
182C4×C43C4×D811yescharacteristic
183C4×C43#44911yescharacteristic
184C4×C43#45911yescharacteristic
185Dic43—81no—
186#3414—431no—
187C4×#135D4311yescharacteristic, complemented
188#2145—431no—
189#2143—431no—
190#1974—431no—
191#1389—431no—
192#1376—431no—
193C2×C43—21no—
194C2×C43—21no—
195C2×C43—21no—
196C2×C43—82no—
197C2×C43#187911yescharacteristic
198D43—161no—
199C2×#135—431no—
200C2×#135C2×D4311yescharacteristic
201C4×#41—21no—
202#510—432no—
203#510—861no—
204#509—432no—
205#509—861no—
206#508—862no—
207C2×M32—431no—
208C2×M32—431no—
209C4×Q16—21no—
210C4×SD16—22no—
211C4×D8—21no—
212C2×#108—431no—
213#427C2×D4311yescharacteristic
214C2×#104—861no—
215#416—21no—
216#408—861no—
217C2×C4×C8C2×D4311yescharacteristic
218#360—862no—
219#359—862no—
220C43#1302711yescharacteristic, complemented, Sylow
221C2×#41—21no—
222C2×#41—861no—
223#135—21no—
224#135—21no—
225#135—861no—
226#135—861no—
227#135—861no—
228#135—861no—
229#135C4×D4312yes—
230#135D17212yes—
231C2×Q16—431no—
232C2×Q16C22⋊D4311yescharacteristic
233C2×SD16—21no—
234C2×SD16—861no—
235C2×D8—431no—
236C2×D8C22⋊D4311yescharacteristic
237C2×M16—861no—
238C22×C8C22⋊D4311yescharacteristic
239C22×C8C22×D4311yescharacteristic
240C4×Q8—22no—
241C4×D4—22no—
242C4×D4—42no—
243#117—21no—
244#117—41no—
245C2×C42—41no—
246C2×C42C22⋊D4311yescharacteristic
247Q32—862no—
248SD32—862no—
249SD32—862no—
250D16—862no—
251M32—432no—
252M32—861no—
253M32—861no—
254M32—861no—
255C2×C16—861no—
256C2×C16—861no—
257#108—861no—
258#108—861no—
259#107—21no—
260#106C22⋊D4312yes—
261#104—1721no—
262#104—1721no—
263#103—22no—
264#102—22no—
265C22⋊C8—1722no—
266C4×C8—21no—
267C4×C8—21no—
268#41—22no—
269#41—22no—
270#41—41no—
271#41—41no—
272#41—1721no—
273#41—1721no—
274#41—1721no—
275#41—1721no—
276C2×Q8—21no—
277C2×Q8—861no—
278C2×D4—21no—
279C2×D4—41no—
280C2×D4—861no—
281C2×D4—1721no—
282C22×C4—21no—
283C22×C4—42no—
284C22×C4—41no—
285C22×C4—1721no—
286C22×C4C2×C22⋊D4311yescharacteristic
287Q16—21no—
288Q16—861no—
289Q16—861no—
290Q16(C2×D43)⋊C412yes—
291SD16—22no—
292SD16—22no—
293SD16—1721no—
294SD16—1721no—
295D8—21no—
296D8—861no—
297D8—861no—
298D8(C2×D43)⋊C412yes—
299M16—1721no—
300M16—1721no—
301C2×C8—21no—
302C2×C8—21no—
303C2×C8—21no—
304C2×C8—1721no—
305C2×C8C2×C4×D4311yescharacteristic
306C2×C8C2×D17211yescharacteristic
307C2×C8#1062189811yescharacteristic
308C2×C8#1062189811yescharacteristic
309C2×C8C2×C22⋊D4311yescharacteristic
310C2×C8C2×C22⋊D4311yescharacteristic
311C4⋊C4—22no—
312C4⋊C4—42no—
313C22⋊C4—42no—
314C22⋊C4—41no—
315C42—21no—
316C42—42no—
317C42—41no—
318C42#1062188211yescharacteristic
319C42#1062188211yescharacteristic
320C16—862no—
321C16—1721no—
322C23—41no—
323C23—1721no—
324C23#1306335111yescharacteristic
325Q8—22no—
326Q8—41no—
327Q8—1721no—
328Q8—1721no—
329D4—22no—
330D4—42no—
331D4—42no—
332D4—41no—
333D4—3441no—
334D4—3441no—
335D4—1721no—
336D4—1721no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—42no—
340C2×C4—41no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—84no—
345C2×C4—3441no—
346C2×C4—3441no—
347C2×C4—1721no—
348C2×C4C4×C22⋊D4311yescharacteristic
349C2×C4#1306329411yescharacteristic
350C2×C4#1306329911yescharacteristic
351C2×C4C2×#1062188211yescharacteristic
352C2×C4#1306334511yescharacteristic
353C2×C4#1306335011yescharacteristic
354C8—41no—
355C8—3441no—
356C8C2×(C2×D43)⋊C411yescharacteristic
357C8C4×C22⋊D4311yescharacteristic
358C8#1306329911yescharacteristic
359C8#1306330811yescharacteristic
360C22—41no—
361C22—42no—
362C22—82no—
363C22—3442no—
364C22—3441no—
365C22#1458300911yescharacteristic
366C22#1458303311yescharacteristic
367C22#1458311411yescharacteristic
368C4—22no—
369C4—41no—
370C4—42no—
371C4—82no—
372C4—3441no—
373C4#1458277811yescharacteristic
374C4C4×#1062188211yescharacteristic
375C4#1458304411yescharacteristic
376C4#1458309411yescharacteristic
377C2—21no—
378C2—21no—
379C2—21no—
380C2—82no—
381C2—6881no—
382C2#1913494311yescharacteristic
subgroupG/H
centerC4#14583094
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
FittingC4×#135×C43C2
socleC2×C43#1879
prime radical#19147729C2
cosocleC22×C8×C43C23
hypercenterC4×#135D43
hypocenterC43#13027
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×C4×C8 ◁ C4×#135

Complements

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

NH ≅ G/Ntype
2. #19136330C2semidirect
3. #19136323C2semidirect
4. #19135483C2semidirect
5. #19132711C2semidirect
6. #19132677C2semidirect
7. C4×#135×C43C2semidirect
10. #14583339C4semidirect
12. #14583334C4semidirect
34. C2×Dic172C2×C4semidirect
36. C2×D344C2×C4semidirect
45. #13063265C2×C4semidirect
187. C4×#135D43semidirect
220. C43#13027semidirect

Maximal subgroups

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

subgroupindex
#191477292
#191363302
#191363232
#191354832
#191327112
#191326772
C4×#135×C432
#1302743