Finite Group Databasebeta

← #25251185

Subgroups — #25251185

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
1C2×#14583334C211yesmaximal, characteristic, complemented
2#19147698C211yesmaximal, characteristic, complemented
3C2×#14583169C211yesmaximal, characteristic, complemented
4#19136727C214yesmaximal, complemented
5#19136713C214yesmaximal, complemented
6#19136389C211yesmaximal, characteristic, complemented
7#19136344C211yesmaximal, characteristic, complemented
8C2×#14582711C211yesmaximal, characteristic, complemented
9C43×#3067C211yesmaximal, characteristic, complemented
10C2×#13063350—21no—
11C22×D344C2211yescharacteristic
12#14583334—22no—
13#14583334—22no—
14C2×#13063268C2212yescomplemented
15C2×#13063266C2212yescomplemented
16#14583316—22no—
17#14583316C2214yescomplemented
18C2×#13063265—22no—
19C2×#13063265C2211yescharacteristic
20C2×#13063265C2211yescharacteristic
21#14583169—22no—
22#14583169C2214yes—
23C2×#13063261C2211yescharacteristic
24C2×#13063241—21no—
25#14582728C2214yescomplemented
26#14582715C2212yescomplemented
27#14582712C2212yescomplemented
28#14582711C2214yescomplemented
29C43×#575—21no—
30C2×#135×C43C2211yescharacteristic
31C2×#131×C43C2211yescharacteristic
32C43×#473C2212yescomplemented
33C43×#472C2212yescomplemented
34C43×#471—22no—
35C2×#108×C43C2211yescharacteristic
36C43×#413—21no—
37C22×D172—21no—
38#13063350—24no—
39#13063350—42no—
40C2×#10621884—41no—
41C2×D344—21no—
42C2×D344—21no—
43C2×D344—21no—
44C2×D344—21no—
45C2×D344—21no—
46C2×D344C2312yes—
47C2×#10621882—41no—
48C2×#10621877—21no—
49#13063268—24no—
50#13063266—24no—
51#13063265—21no—
52#13063265—24no—
53#13063265D412yes—
54#13063265D412yes—
55#13063265C2312yes—
56C2×C43⋊C16—21no—
57C2×C43⋊C16—24no—
58C2×C43⋊C16C2312yes—
59#13063261—21no—
60#13063261C2312yes—
61#13063241—24no—
62C2×#41×C43—21no—
63C2×#41×C43D411yescharacteristic
64#137×C43—22no—
65#137×C43—41no—
66AGL(1,ℤ/8)×C43—22no—
67AGL(1,ℤ/8)×C43—41no—
68#135×C43—21no—
69#135×C43—21no—
70#135×C43—21no—
71#135×C43—21no—
72#135×C43—42no—
73C2×Q16×C43C2311yescharacteristic
74C2×SD16×C43—21no—
75C2×D8×C43C2311yescharacteristic
76#131×C43—21no—
77#131×C43—21no—
78#131×C43D412yes—
79#131×C43C2312yes—
80C2×M16×C43—21no—
81C2×M16×C43—21no—
82C2×M16×C43D411yescharacteristic
83C22×C8×C43—21no—
84C22×C8×C43C2311yescharacteristic
85#108×C43—21no—
86#108×C43C2312yes—
87#101×C43—22no—
88#100×C43—22no—
89C23×D43—41no—
90#41×C43—21no—
91#41×C43—21no—
92#41×C43—41no—
93#41×C43—41no—
94#41×C43—41no—
95#41×C43—41no—
96#41×C43D812yes—
97#41×C43C2×D412yes—
98C2×Q8×C43—21no—
99C2×Q8×C43D811yescharacteristic
100C2×D4×C43—21no—
101C2×D4×C43—21no—
102C2×D4×C43—41no—
103C2×D4×C43D811yescharacteristic
104C22×C4×C43—21no—
105C22×C4×C43—41no—
106C22×C4×C43C2×D411yescharacteristic
107C2×D172—22no—
108C2×D172—41no—
109C2×D172—41no—
110C2×D172—41no—
111C2×D172—41no—
112C2×D172—41no—
113Q16×C43—21no—
114Q16×C43—21no—
115Q16×C43—42no—
116SD16×C43—42no—
117SD16×C43—42no—
118SD16×C43—41no—
119SD16×C43—41no—
120D8×C43—21no—
121D8×C43—21no—
122D8×C43—42no—
123M16×C43—21no—
124M16×C43—22no—
125M16×C43—22no—
126M16×C43—22no—
127M16×C43—41no—
128M16×C43C2×D412yes—
129C2×C8×C43—21no—
130C2×C8×C43—22no—
131C2×C8×C43—22no—
132C2×C8×C43—41no—
133C2×C8×C43C2×D411yescharacteristic
134C2×C8×C43C2×D411yescharacteristic
135C2×C8×C43C2×D411yescharacteristic
136C2×C8×C43#4111yescharacteristic
137C2×C8×C43#4111yescharacteristic
138C2×C8×C43C2411yescharacteristic
139#10621884—44no—
140#10621882—44no—
141#10621877—22no—
142#10621877—41no—
143C2×C43⋊C8—41no—
144D344—22no—
145D344—22no—
146D344—41no—
147D344—41no—
148C43⋊C16—22no—
149C43⋊C16C2×D414yes—
150C23×C43—21no—
151C23×C43—41no—
152C23×C43#13511yescharacteristic
153C22×D43—42no—
154C22×D43—81no—
155C22×D43—81no—
156C22×D43—162no—
157Q8×C43—21no—
158Q8×C43—41no—
159Q8×C43—41no—
160Q8×C43C2×D812yes—
161D4×C43—22no—
162D4×C43—22no—
163D4×C43—21no—
164D4×C43—41no—
165D4×C43—41no—
166D4×C43—81no—
167D4×C43—81no—
168D4×C43C2×D812yes—
169C2×C4×C43—21no—
170C2×C4×C43—22no—
171C2×C4×C43—22no—
172C2×C4×C43—41no—
173C2×C4×C43—81no—
174C2×C4×C43—81no—
175C2×C4×C43#12111yescharacteristic
176C2×C4×C43#12111yescharacteristic
177C2×C4×C43C2×D811yescharacteristic
178C2×C4×C43C2×D811yescharacteristic
179C2×C4×C43#13511yescharacteristic
180C2×C4×C43C22×D411yescharacteristic
181D172—42no—
182D172—42no—
183D172—81no—
184D172—81no—
185C8×C43—22no—
186C8×C43—42no—
187C8×C43#12111yescharacteristic
188C8×C43#12111yescharacteristic
189C8×C43C22×D411yescharacteristic
190C8×C43C2×#4111yescharacteristic
191C43⋊C8—42no—
192#33618—431nomaximal, Sylow
193C22×C43—22no—
194C22×C43—41no—
195C22×C43—81no—
196C22×C43—81no—
197C22×C43—161no—
198C22×C43#46611yescharacteristic
199C22×C43#46611yescharacteristic
200C22×C43C2×#13511yescharacteristic
201C2×D43—82no—
202C2×D43—162no—
203C2×D43—162no—
204C2×D43—162no—
205C4×C43—22no—
206C4×C43—81no—
207C4×C43#46611yescharacteristic
208C4×C43#46611yescharacteristic
209C4×C43C2×#12111yescharacteristic
210C4×C43C22×D811yescharacteristic
211C2×#509—431no—
212#3407—431no—
213#3067D4311yescharacteristic, complemented
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—42no—
224C2×C43—161no—
225C2×C43C2×#46611yescharacteristic
226D43—162no—
227#575—21no—
228C2×AGL(1,ℤ/8)—861no—
229C2×#135C2×D4311yescharacteristic
230C22×D8—431no—
231C2×#131C2×D4311yescharacteristic
232#509—862no—
233#509—862no—
234C2×SD32—432no—
235C2×D16—432no—
236#504—434no—
237#504—862no—
238C2×M32—431no—
239C2×M32—431no—
240C2×M32—862no—
241#473C2×D4312yescomplemented
242#472—434no—
243#472—862no—
244#472C2×D4312yescomplemented
245#471—22no—
246C2×#108—431no—
247C2×#108C2×D4311yescharacteristic
248#413—21no—
249C2×#100—861no—
250#368—434no—
251#362—432no—
252#361—432no—
253#361—434no—
254C43#3361811yescharacteristic, complemented, Sylow
255C2×#41—21no—
256C2×#41C22⋊D4311yescharacteristic
257C22×D4—861no—
258#137—22no—
259#137—41no—
260AGL(1,ℤ/8)—22no—
261AGL(1,ℤ/8)—41no—
262AGL(1,ℤ/8)—864no—
263AGL(1,ℤ/8)—1722no—
264#135—21no—
265#135—21no—
266#135—21no—
267#135—21no—
268#135—42no—
269C2×Q16C22×D4311yescharacteristic
270C2×SD16—21no—
271C2×SD16—1721no—
272C2×D8—432no—
273C2×D8—861no—
274C2×D8—861no—
275C2×D8—861no—
276C2×D8—861no—
277C2×D8—861no—
278C2×D8—1721no—
279C2×D8C22×D4311yescharacteristic
280#131—21no—
281#131—21no—
282#131C22⋊D4312yes—
283#131C22×D4312yes—
284C2×M16—21no—
285C2×M16—21no—
286C2×M16—861no—
287C2×M16C22⋊D4311yescharacteristic
288C22×C8—21no—
289C22×C8C22×D4311yescharacteristic
290SD32—864no—
291D16—864no—
292M32—432no—
293M32—432no—
294M32—432no—
295M32—864no—
296M32—861no—
297C2×C16—432no—
298C2×C16—864no—
299C2×C16—861no—
300#108—21no—
301#108—432no—
302#108—861no—
303#108C22×D4312yes—
304#101—22no—
305#100—22no—
306#100—864no—
307C24—1721no—
308#41—21no—
309#41—21no—
310#41—41no—
311#41—41no—
312#41—41no—
313#41—41no—
314#41#1062188212yes—
315#41C2×C22⋊D4312yes—
316C2×Q8—21no—
317C2×Q8#1062188211yescharacteristic
318C2×D4—21no—
319C2×D4—21no—
320C2×D4—41no—
321C2×D4—862no—
322C2×D4—1721no—
323C2×D4—1721no—
324C2×D4—1721no—
325C2×D4—1721no—
326C2×D4—1721no—
327C2×D4#1062188211yescharacteristic
328C22×C4—21no—
329C22×C4—41no—
330C22×C4C2×C22⋊D4311yescharacteristic
331Q16—21no—
332Q16—21no—
333Q16—42no—
334SD16—42no—
335SD16—42no—
336SD16—41no—
337SD16—41no—
338SD16—1724no—
339D8—21no—
340D8—21no—
341D8—42no—
342D8—862no—
343D8—862no—
344D8—1724no—
345D8—1721no—
346D8—1721no—
347M16—21no—
348M16—22no—
349M16—22no—
350M16—22no—
351M16—41no—
352M16—862no—
353M16—1721no—
354M16C2×C22⋊D4312yes—
355C2×C8—21no—
356C2×C8—22no—
357C2×C8—22no—
358C2×C8—41no—
359C2×C8—1721no—
360C2×C8D4×D4311yescharacteristic
361C2×C8D4×D4311yescharacteristic
362C2×C8#1062190011yescharacteristic
363C2×C8#1062190011yescharacteristic
364C2×C8C2×C22⋊D4311yescharacteristic
365C2×C8C23×D4311yescharacteristic
366C16—434no—
367C16—862no—
368C23—21no—
369C23—41no—
370C23—3441no—
371C23—3441no—
372C23—1722no—
373C23—6882no—
374C23#1306334511yescharacteristic
375Q8—21no—
376Q8—41no—
377Q8—41no—
378Q8C2×#1062188212yes—
379D4—22no—
380D4—22no—
381D4—21no—
382D4—41no—
383D4—41no—
384D4—81no—
385D4—81no—
386D4—3441no—
387D4—3441no—
388D4—1722no—
389D4—1722no—
390D4C2×#1062188212yes—
391C2×C4—21no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—41no—
395C2×C4—81no—
396C2×C4—81no—
397C2×C4#1306329711yescharacteristic
398C2×C4#1306329711yescharacteristic
399C2×C4C2×#1062188211yescharacteristic
400C2×C4C2×#1062188211yescharacteristic
401C2×C4#1306334511yescharacteristic
402C2×C4C22×C22⋊D4311yescharacteristic
403C8—22no—
404C8—42no—
405C8—1722no—
406C8#1306329711yescharacteristic
407C8#1306329711yescharacteristic
408C8C2×D4×D4311yescharacteristic
409C8C2×#1062190011yescharacteristic
410C22—22no—
411C22—41no—
412C22—81no—
413C22—81no—
414C22—161no—
415C22—3442no—
416C22—6882no—
417C22—6882no—
418C22—6882no—
419C22#1458313311yescharacteristic
420C22#1458313311yescharacteristic
421C22C2×#1306334511yescharacteristic
422C4—22no—
423C4—81no—
424C4#1458313311yescharacteristic
425C4#1458313311yescharacteristic
426C4C2×#1306329711yescharacteristic
427C4C22×#1062188211yescharacteristic
428C2—21no—
429C2—21no—
430C2—21no—
431C2—42no—
432C2—161no—
433C2—6882no—
434C2C2×#1458313311yescharacteristic
subgroupG/H
centerC2C2×#14583133
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC43×#3067C2
socleC2×C43C2×#466
hypercenter#3067D43
hypocenterC43#33618
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#131 ◁ #3067

Complements

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

NH ≅ G/Ntype
1. C2×#14583334C2semidirect
2. #19147698C2semidirect
3. C2×#14583169C2semidirect
4. #19136727C2semidirect
5. #19136713C2semidirect
6. #19136389C2semidirect
7. #19136344C2semidirect
8. C2×#14582711C2semidirect
9. C43×#3067C2semidirect
14. C2×#13063268C22semidirect
15. C2×#13063266C22semidirect
17. #14583316C22semidirect
25. #14582728C22semidirect
26. #14582715C22semidirect
27. #14582712C22semidirect
28. #14582711C22semidirect
32. C43×#473C22semidirect
33. C43×#472C22semidirect
213. #3067D43semidirect
241. #473C2×D43semidirect
244. #472C2×D43semidirect
254. C43#33618semidirect

Maximal subgroups

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

subgroupindex
C2×#145833342
#191476982
C2×#145831692
#191367272
#191367132
#191363892
#191363442
C2×#145827112
C43×#30672
#3361843