Finite Group Databasebeta

← #25251179

Subgroups — #25251179

Order 11008.

656 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147697C211yesmaximal, characteristic, complemented
2#19144311C211yesmaximal, characteristic, complemented
3C2×#14583166C211yesmaximal, characteristic, complemented
4#19136722C214yesmaximal, complemented
5#19136712C214yesmaximal, complemented
6#19136390C211yesmaximal, characteristic, complemented
7#19136344C211yesmaximal, characteristic, complemented
8C2×#14582712C211yesmaximal, characteristic, complemented
9C2×C43×#509C211yesmaximal, characteristic, complemented
10#14583697—21no—
11C2×#13063351—21no—
12C2×#13063331C2211yescharacteristic
13#14583317—22no—
14#14583315C2214yescomplemented
15C2×#13063265C2211yescharacteristic
16M32×D43—22no—
17#14583171C2212yescomplemented
18#14583166—22no—
19#14583166C2214yes—
20#14583166C2212yescomplemented
21#14583159—22no—
22C2×#13063261C2211yescharacteristic
23C2×#13063261C2211yescharacteristic
24#14582883—21no—
25C2×#13063242—21no—
26#14582729C2214yescomplemented
27#14582715C2212yescomplemented
28#14582712C2214yescomplemented
29#14582712C2212yescomplemented
30C2×#135×C43C2211yescharacteristic
31C22×D8×C43C2211yescharacteristic
32C43×#509—22no—
33C43×#509—22no—
34C2×SD32×C43C2212yescomplemented
35C2×D16×C43C2212yescomplemented
36C2×M32×C43C2211yescharacteristic
37C2×#10621898D411yescharacteristic
38#13063356—22no—
39#13063355—41no—
40#13063351—22no—
41#13063351—24no—
42#13063351—42no—
43#13063350—41no—
44#13063345—42no—
45C2×#10621883—41no—
46C2×#10621882—41no—
47#13063331—21no—
48#13063331—21no—
49#13063331D412yes—
50#13063331C2312yes—
51C2×#10621877—21no—
52C2×#10621877—21no—
53C2×#10621877D411yescharacteristic
54C2×#10621872—21no—
55C2×C8×D43—21no—
56#13063265—21no—
57#13063265C2312yes—
58#13063264—24no—
59C2×C43⋊C16—21no—
60C16×D43—24no—
61#13063261—21no—
62#13063261—21no—
63#13063261C2312yes—
64#13063261C2312yes—
65#13063244—22no—
66#13063242—24no—
67#13063242—22no—
68C2×#41×C43—21no—
69C22×D4×C43—21no—
70#135×C43—21no—
71#135×C43—21no—
72#135×C43—21no—
73#135×C43—21no—
74C2×Q16×C43C2311yescharacteristic
75C2×SD16×C43—21no—
76C2×D8×C43—21no—
77C2×D8×C43—21no—
78C2×D8×C43—21no—
79C2×D8×C43—21no—
80C2×D8×C43—21no—
81C2×D8×C43C2311yescharacteristic
82C2×D8×C43C2312yes—
83C22×C8×C43C2311yescharacteristic
84SD32×C43—24no—
85D16×C43—24no—
86M32×C43D412yes—
87M32×C43D412yes—
88C2×C16×C43C2312yes—
89C24×C43—41no—
90#41×C43—41no—
91#41×C43—41no—
92#41×C43—41no—
93#41×C43—41no—
94C2×Q8×C43—21no—
95C2×D4×C43—22no—
96C2×D4×C43—21no—
97C2×D4×C43—41no—
98C2×D4×C43—41no—
99C2×D4×C43—41no—
100C2×D4×C43—41no—
101C2×D4×C43—41no—
102C2×D4×C43—41no—
103C22×C4×C43—41no—
104C22×C4×C43C2×D411yescharacteristic
105C2×C22⋊D43—21no—
106#10621898—21no—
107#10621898—21no—
108#10621898D812yes—
109#10621898C2×D412yes—
110C2×D172D811yescharacteristic
111C2×C4×D43—21no—
112C2×Dic86D811yescharacteristic
113Q16×C43—21no—
114Q16×C43—21no—
115SD16×C43—41no—
116SD16×C43—41no—
117D8×C43—21no—
118D8×C43—22no—
119D8×C43—22no—
120D8×C43—21no—
121D8×C43—41no—
122D8×C43—41no—
123C2×C8×C43C2×D411yescharacteristic
124C2×C8×C43C2×D411yescharacteristic
125C2×C8×C43C2×D411yescharacteristic
126C2×C8×C43#4111yescharacteristic
127C2×C8×C43#4111yescharacteristic
128C2×C8×C43C2411yescharacteristic
129#10621885—42no—
130#10621884—42no—
131#10621883—44no—
132#10621883—42no—
133#10621882—44no—
134#10621882—42no—
135#10621877—21no—
136#10621877—22no—
137#10621877—22no—
138#10621877—41no—
139#10621877—41no—
140#10621877C2×D412yes—
141C2×C43⋊C8—21no—
142C2×C43⋊C8—41no—
143C2×C43⋊C8—41no—
144#10621872—22no—
145#10621872—22no—
146C8×D43—22no—
147C8×D43—22no—
148C16×C43C2×D414yes—
149C43⋊C16—22no—
150C23×C43—41no—
151C23×C43—42no—
152C23×C43—81no—
153C23×C43—81no—
154C23×C43—162no—
155C23×C43#13511yescharacteristic
156C22×D43—21no—
157Q8×C43—41no—
158Q8×C43—41no—
159D4×C43—42no—
160D4×C43—41no—
161D4×C43—42no—
162D4×C43—41no—
163D4×C43—81no—
164D4×C43—81no—
165D4×C43—81no—
166D4×C43—81no—
167C2×C4×C43—41no—
168C2×C4×C43—81no—
169C2×C4×C43—81no—
170C2×C4×C43#12111yescharacteristic
171C2×C4×C43#12111yescharacteristic
172C2×C4×C43C2×D811yescharacteristic
173C2×C4×C43C2×D811yescharacteristic
174C2×C4×C43#13511yescharacteristic
175C2×C4×C43C22×D411yescharacteristic
176C22⋊D43—22no—
177C22⋊D43—22no—
178C2×Dic43—21no—
179D172—21no—
180D172C2×D812yes—
181C4×D43—22no—
182C4×D43—22no—
183Dic86—21no—
184Dic86C2×D812yes—
185C8×C43#12111yescharacteristic
186C8×C43#12111yescharacteristic
187C8×C43C22×D411yescharacteristic
188C8×C43C2×#4111yescharacteristic
189C43⋊C8—22no—
190C43⋊C8—42no—
191C43⋊C8—42no—
192#33618—431nomaximal, Sylow
193C22×C43—41no—
194C22×C43—82no—
195C22×C43—81no—
196C22×C43—161no—
197C22×C43—162no—
198C22×C43—162no—
199C22×C43—162no—
200C22×C43#46611yescharacteristic
201C22×C43#46611yescharacteristic
202C22×C43C2×#13511yescharacteristic
203C2×D43—22no—
204C2×D43—81no—
205C4×C43—81no—
206C4×C43#46611yescharacteristic
207C4×C43#46611yescharacteristic
208C4×C43C2×#12111yescharacteristic
209C4×C43C22×D811yescharacteristic
210Dic43—22no—
211C2×#509D4311yescharacteristic, complemented
212#3407—431no—
213#3067—431no—
214C2×#472—431no—
215#2223—434no—
216#2221—434no—
217#2161—431no—
218#2148—431no—
219C2×#361—431no—
220C2×C43—21no—
221C2×C43—21no—
222C2×C43—21no—
223C2×C43—161no—
224C2×C43—162no—
225C2×C43C2×#46611yescharacteristic
226D43—42no—
227#575—861no—
228C2×AGL(1,ℤ/8)—861no—
229C2×#135C2×D4311yescharacteristic
230C22×D8C2×D4311yescharacteristic
231C2×#131—431no—
232#509—22no—
233#509—22no—
234C2×SD32C2×D4312yescomplemented
235C2×D16C2×D4312yescomplemented
236#504—434no—
237#504—862no—
238C2×M32—431no—
239C2×M32—862no—
240C2×M32C2×D4311yescharacteristic
241#473—432no—
242#472—434no—
243#472—432no—
244#472—862no—
245#471—862no—
246C2×#108—431no—
247C2×#108—431no—
248#413—861no—
249C2×#100—861no—
250#368—434no—
251#362—432no—
252#361—434no—
253#361—432no—
254C43#3361811yescharacteristic, complemented, Sylow
255C2×#41—21no—
256C2×#41—431no—
257C22×D4—21no—
258#137—862no—
259#137—1721no—
260AGL(1,ℤ/8)—864no—
261AGL(1,ℤ/8)—862no—
262AGL(1,ℤ/8)—1722no—
263AGL(1,ℤ/8)—1721no—
264#135—21no—
265#135—21no—
266#135—21no—
267#135—21no—
268#135—1722no—
269C2×Q16C22×D4311yescharacteristic
270C2×SD16—21no—
271C2×SD16—1721no—
272C2×D8—21no—
273C2×D8—21no—
274C2×D8—21no—
275C2×D8—21no—
276C2×D8—21no—
277C2×D8—1721no—
278C2×D8C22×D4312yes—
279C2×D8C22×D4311yescharacteristic
280#131—432no—
281#131—432no—
282#131—861no—
283#131—861no—
284C2×M16—431no—
285C2×M16—861no—
286C2×M16—861no—
287C2×M16—861no—
288C22×C8—861no—
289C22×C8C22×D4311yescharacteristic
290SD32—24no—
291D16—24no—
292M32—432no—
293M32—861no—
294M32—864no—
295M32C22⋊D4312yes—
296M32C22⋊D4312yes—
297C2×C16—861no—
298C2×C16—864no—
299C2×C16C22×D4312yes—
300#108—432no—
301#108—432no—
302#108—861no—
303#108—861no—
304#101—862no—
305#100—864no—
306#100—862no—
307C24—41no—
308#41—41no—
309#41—41no—
310#41—41no—
311#41—41no—
312#41—432no—
313#41—432no—
314#41—861no—
315#41—861no—
316C2×Q8—21no—
317C2×Q8—431no—
318C2×D4—22no—
319C2×D4—21no—
320C2×D4—41no—
321C2×D4—41no—
322C2×D4—41no—
323C2×D4—41no—
324C2×D4—41no—
325C2×D4—41no—
326C2×D4—431no—
327C2×D4—861no—
328C22×C4—41no—
329C22×C4—861no—
330C22×C4D4×D4311yescharacteristic
331Q16—21no—
332Q16—21no—
333Q16—1722no—
334SD16—41no—
335SD16—41no—
336SD16—1724no—
337SD16—1722no—
338SD16—1722no—
339D8—21no—
340D8—22no—
341D8—22no—
342D8—21no—
343D8—41no—
344D8—41no—
345D8—1724no—
346D8—1722no—
347M16—432no—
348M16—861no—
349M16—862no—
350M16—862no—
351M16—862no—
352M16—862no—
353M16—1721no—
354M16—1721no—
355C2×C8—861no—
356C2×C8—862no—
357C2×C8—862no—
358C2×C8—1721no—
359C2×C8—1721no—
360C2×C8D4×D4311yescharacteristic
361C2×C8#1062190011yescharacteristic
362C2×C8#1062190011yescharacteristic
363C2×C8C2×C22⋊D4311yescharacteristic
364C2×C8C2×C22⋊D4311yescharacteristic
365C2×C8C23×D4311yescharacteristic
366C16—862no—
367C16C2×C22⋊D4314yes—
368C23—41no—
369C23—42no—
370C23—81no—
371C23—81no—
372C23—162no—
373C23—861no—
374C23#1306334411yescharacteristic
375Q8—41no—
376Q8—41no—
377Q8—432no—
378Q8—861no—
379D4—42no—
380D4—41no—
381D4—42no—
382D4—41no—
383D4—81no—
384D4—81no—
385D4—81no—
386D4—81no—
387D4—432no—
388D4—862no—
389D4—862no—
390D4—861no—
391C2×C4—41no—
392C2×C4—81no—
393C2×C4—81no—
394C2×C4—861no—
395C2×C4—862no—
396C2×C4—862no—
397C2×C4#1306329611yescharacteristic
398C2×C4#1306329611yescharacteristic
399C2×C4D8×D4311yescharacteristic
400C2×C4D8×D4311yescharacteristic
401C2×C4#1306334411yescharacteristic
402C2×C4C2×D4×D4311yescharacteristic
403C8—862no—
404C8—1722no—
405C8—1722no—
406C8#1306329611yescharacteristic
407C8#1306329611yescharacteristic
408C8C22×C22⋊D4311yescharacteristic
409C8C2×#1062190011yescharacteristic
410C22—41no—
411C22—81no—
412C22—82no—
413C22—162no—
414C22—161no—
415C22—162no—
416C22—162no—
417C22—862no—
418C22—3441no—
419C22#1458313211yescharacteristic
420C22#1458313211yescharacteristic
421C22C2×#1306334411yescharacteristic
422C4—81no—
423C4—862no—
424C4#1458313211yescharacteristic
425C4#1458313211yescharacteristic
426C4C2×#1306329611yescharacteristic
427C4C2×D8×D4311yescharacteristic
428C2—21no—
429C2—21no—
430C2—21no—
431C2—162no—
432C2—161no—
433C2—1722no—
434C2C2×#1458313211yescharacteristic
subgroupG/H
centerC2C2×#14583132
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC2×C43×#509C2
socleC2×C43C2×#466
hypercenterC2×#509D43
hypocenterC43#33618
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22×C4 ◁ C22×C8 ◁ C2×#509

Complements

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

NH ≅ G/Ntype
1. #19147697C2semidirect
2. #19144311C2semidirect
3. C2×#14583166C2semidirect
4. #19136722C2semidirect
5. #19136712C2semidirect
6. #19136390C2semidirect
7. #19136344C2semidirect
8. C2×#14582712C2semidirect
9. C2×C43×#509C2semidirect
14. #14583315C22semidirect
17. #14583171C22semidirect
20. #14583166C22semidirect
26. #14582729C22semidirect
27. #14582715C22semidirect
28. #14582712C22semidirect
29. #14582712C22semidirect
34. C2×SD32×C43C22semidirect
35. C2×D16×C43C22semidirect
211. C2×#509D43semidirect
234. C2×SD32C2×D43semidirect
235. C2×D16C2×D43semidirect
254. C43#33618semidirect

Maximal subgroups

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

subgroupindex
#191476972
#191443112
C2×#145831662
#191367222
#191367122
#191363902
#191363442
C2×#145827122
C2×C43×#5092
#3361843