Finite Group Databasebeta

← #11878655

Subgroups — #11878655

Order 1152.

1219 conjugacy classes of subgroups; only the 172 normal subgroups are shown.

normal subgroups only

This group has 1219 conjugacy classes of subgroups — too many to draw. Only its 172 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596196C211yesmaximal, characteristic, complemented
2#10594008C211yesmaximal, characteristic, complemented
3C3×#5088C212yesmaximal, complemented
4#10590598C214yesmaximal, complemented
5#10590551C214yesmaximal, complemented
6#10590350C212yesmaximal, complemented
7#10590297C211yesmaximal, characteristic, complemented
8#81566—32nomaximal
9C2×#3832—21no—
10C2×#3802—21no—
11C2×#3802—21no—
12C2×#3802C2212yes—
13C32×C4⋊Q8C2211yescharacteristic, complemented
14#64156—21no—
15#64104—21no—
16#64104C2212yes—
17#64102—21no—
18#64102C2212yescomplemented
19#64083C2211yescharacteristic, complemented
20C42×C3⋊D3C2211yescharacteristic
21C3×#874C2212yes—
22#63914—21no—
23#63914—21no—
24#63914C2212yes—
25C2×#3714C2218yescomplemented
26C3×#809C2218yescomplemented
27C3×C4×C3⋊C8C2212yescomplemented
28#63572C2212yescomplemented
29#63557C2212yes—
30#5725—32no—
31#5725—61no—
32D3×#127—32no—
33C3×#486—32no—
34#5088D312yescomplemented
35#5073—32no—
36#4786—38no—
37#4773—38no—
38#4695—32no—
39#4685—32no—
40C22×D32—22no—
41C2×C32×Q8—21no—
42#3832—44no—
43C2×C4⋊(C3⋊D3)—22no—
44C2×C4⋊(C3⋊D3)—21no—
45C2×C4⋊(C3⋊D3)—21no—
46C2×C4⋊(C3⋊D3)C2312yes—
47C2×C4×C3⋊D3—22no—
48C2×C4×C3⋊D3D411yescharacteristic
49C2×C4×C3⋊D3D411yescharacteristic
50C2×C4×C3⋊D3C2311yescharacteristic
51C2×C3×D12—22no—
52C2×C3×D12—22no—
53C2×C3×D12C2314yes—
54C2×#625—22no—
55C2×#625—22no—
56C2×#625—22no—
57#3802—44no—
58#3802—44no—
59#3802—44no—
60C32×C4⋊C4—21no—
61C32×C4⋊C4C2312yes—
62C32×C42C2311yescharacteristic
63#3752—22no—
64#3752—22no—
65C4×C3⋊Dic3D411yescharacteristic
66C4×C3⋊Dic3D411yescharacteristic
67C4×C3⋊Dic3C2311yescharacteristic
68C2×C3×C3⋊C8C2314yes—
69#3714—48no—
70#3205—91noSylow
71C2×#239—62no—
72C2×#239—62no—
73C2×D3×D4—34no—
74C2×D3×D4—62no—
75C2×D3×D4—62no—
76C3×C4⋊Q8—21no—
77C3×C4⋊Q8C2×D312yescomplemented
78C3×#127—32no—
79#947—62no—
80#947—62no—
81#940—34no—
82#940—62no—
83#940—62no—
84C2×#213—38no—
85C2×D24—38no—
86#895—34no—
87#895—62no—
88#895—62no—
89#895—62no—
90#893—34no—
91#893—62no—
92#893—62no—
93#893—62no—
94#874—32no—
95#874—61no—
96#874C2×D312yes—
97C42×D3—32no—
98C42×D3—61no—
99C3×#102—38no—
100C3×C4×C8—32no—
101(C2×D3)⋊C8—34no—
102Dic3⋊C8—34no—
103#809C2×D318yescomplemented
104C4×C3⋊C8C2×D312yescomplemented
105C22×C3⋊D3—22no—
106C22×C3⋊D3C2×D411yescharacteristic
107C22×C3×D3—24no—
108C2×D32—44no—
109C2×D32—44no—
110C2×D32—44no—
111C32×Q8—42no—
112C2×C32×C4—22no—
113C2×C32×C4C2×D411yescharacteristic
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4C2411yescharacteristic
116C2×C3⋊Dic3C2×D411yescharacteristic
117C2×C3⋊Dic3C2×D411yescharacteristic
118C2×C3⋊Dic3C2×D411yescharacteristic
119C4⋊(C3⋊D3)—24no—
120C4⋊(C3⋊D3)—44no—
121C4⋊(C3⋊D3)—42no—
122C4⋊(C3⋊D3)—42no—
123C4×C3⋊D3—22no—
124C4×C3⋊D3—22no—
125C4×C3⋊D3—44no—
126C4×C3⋊D3D814yescomplemented
127C3×D12—28no—
128C3×D12—44no—
129C3×D12—44no—
130#625—44no—
131#625—44no—
132#625—44no—
133C3×C3⋊C8—24no—
134#532—91no—
135C2×#127—91no—
136#493—92no—
137#486—32no—
138#459—94no—
139#447—94no—
140#431—91no—
141C23×D3—64no—
142C2×C3×Q8—22no—
143C2×C3×Q8—22no—
144C2×C3×D4—34no—
145C2×C3×D4—62no—
146C2×C3×D4—62no—
147C2×#67—64no—
148C2×#67—64no—
149C2×#67—64no—
150#239—128no—
151#239—128no—
152D3×D4—128no—
153D3×D4—128no—
154D3×D4—128no—
155C2×D12—22no—
156C2×D12—22no—
157C2×D12—34no—
158C2×D12—62no—
159C2×D12—64no—
160C2×D12—62no—
161C2×D12—62no—
162C2×D12—64no—
163C2×D12—62no—
164C2×D12—62no—
165C2×D12C22×D314yes—
166C2×C4×D3—32no—
167C2×C4×D3—32no—
168C2×C4×D3—32no—
169C2×C4×D3—61no—
170C2×C4×D3—61no—
171C2×C4×D3—61no—
172C2×C4×D3—64no—
173C2×C4×D3—64no—
174C2×C3×C8—34no—
175C3×C4⋊C4—22no—
176C3×C4⋊C4—22no—
177C3×C4⋊C4—22no—
178C3×C4⋊C4C22×D314yes—
179C3×C42—21no—
180C3×C42C22×D312yes—
181#213—128no—
182(C2×D3)⋊C4—64no—
183(C2×D3)⋊C4—64no—
184(C2×D3)⋊C4—64no—
185(C2×D3)⋊C4—64no—
186C4×Dic3—32no—
187C4×Dic3—32no—
188C4×Dic3—32no—
189C4×Dic3—61no—
190C4×Dic3—61no—
191C4×Dic3—61no—
192C2×C3⋊C8C22×D314yes—
193D24—128no—
194C22×C32C22×D411yescharacteristic
195C2×C3⋊D3—21no—
196C2×C3⋊D3—21no—
197C2×C3⋊D3—42no—
198C2×C3⋊D3—42no—
199C2×C3⋊D3—42no—
200C2×C3⋊D3C2×D812yes—
201C2×C3×D3—44no—
202C2×C3×D3—44no—
203C2×C3×D3—44no—
204D32—88no—
205C32×C4—42no—
206C32×C4C2×D812yes—
207C32×C4AGL(1,ℤ/8)12yes—
208C32×C4H(5,𝔽2)12yes—
209C3⋊Dic3—21no—
210C3⋊Dic3—21no—
211C3⋊Dic3C2×D812yes—
212C2×#41—181no—
213C22×D4—92no—
214C22×D4—181no—
215C22×D4—181no—
216C2×D8—98no—
217C4⋊Q8D3211yescharacteristic, complemented
218#127—32no—
219#127—92no—
220#127—91no—
221#127—181no—
222#127—181no—
223#124—181no—
224#121—92no—
225#121—181no—
226C4×D4—92no—
227C4×D4—181no—
228C2×C42—91no—
229C4⋊C8—92no—
230#102—38no—
231C22⋊C8—92no—
232C4×C8—32no—
233C23×C3—64no—
234C22×D3—24no—
235C22×D3—32no—
236C22×D3—61no—
237C22×D3—64no—
238C22×D3—64no—
239C22×D3—128no—
240C22×D3—128no—
241C22×D3—128no—
242C3×Q8—44no—
243C3×Q8—44no—
244C3×D4—68no—
245C3×D4—124no—
246C3×D4—124no—
247C2×C3×C4—24no—
248C2×C3×C4—24no—
249C2×C3×C4—21no—
250C2×C3×C4—21no—
251C2×C3×C4—21no—
252C2×C3×C4D3×D412yes—
253C2×C3×C4D3×D412yes—
254C2×C3×C4C23×D312yes—
255#67—128no—
256#67—128no—
257#67—128no—
258C2×Dic3—32no—
259C2×Dic3—32no—
260C2×Dic3—32no—
261C2×Dic3—61no—
262C2×Dic3—61no—
263C2×Dic3—61no—
264D12—28no—
265D12—44no—
266D12—44no—
267D12—68no—
268D12—124no—
269D12—124no—
270D12—124no—
271D12—128no—
272D12—128no—
273D12—124no—
274D12—124no—
275C4×D3—38no—
276C4×D3—64no—
277C4×D3—64no—
278C4×D3—64no—
279C4×D3—122no—
280C4×D3—122no—
281C4×D3—128no—
282C4×D3—128no—
283C3×C8—64no—
284C3⋊C8—24no—
285C2×C32#53511yescharacteristic
286C2×C32C22×D811yescharacteristic
287C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
288C3⋊D3—22no—
289C3⋊D3—82no—
290C3×D3—84no—
291C24—182no—
292#41—364no—
293C2×Q8—21no—
294C2×D4—34no—
295C2×D4—62no—
296C2×D4—62no—
297C2×D4—92no—
298C2×D4—182no—
299C2×D4—182no—
300C2×D4—182no—
301C2×D4—182no—
302C2×D4—181no—
303C2×D4—181no—
304C2×D4—364no—
305C2×D4—364no—
306C2×D4—364no—
307C22×C4—91no—
308C22×C4—91no—
309C22×C4—91no—
310C22×C4—182no—
311D8—368no—
312C2×C8—34no—
313C4⋊C4—21no—
314C4⋊C4C2×D3212yes—
315C22⋊C4—182no—
316C22⋊C4—182no—
317C42—91no—
318C42—91no—
319C42—91no—
320C42C2×D3211yescharacteristic
321C22×C3—21no—
322C22×C3—124no—
323C22×C3—124no—
324C22×C3—124no—
325C22×C3C2×D3×D412yes—
326C2×D3—34no—
327C2×D3—44no—
328C2×D3—44no—
329C2×D3—44no—
330C2×D3—62no—
331C2×D3—62no—
332C2×D3—62no—
333C2×D3—121no—
334C2×D3—121no—
335C2×D3—124no—
336C2×D3—124no—
337C2×D3—124no—
338C2×D3—124no—
339C2×D3—124no—
340C2×D3—124no—
341C2×D3—2416no—
342C3×C4—22no—
343C3×C4—22no—
344C3×C4—22no—
345C3×C4—44no—
346C3×C4—44no—
347C3×C4D3×D814yes—
348C3×C4#91414yes—
349C3×C4#100914yes—
350Dic3—34no—
351Dic3—62no—
352Dic3—62no—
353Dic3—62no—
354Dic3—121no—
355Dic3—121no—
356C32#320511yescharacteristic, complemented, Sylow
357C23—64no—
358C23—91no—
359C23—182no—
360C23—364no—
361C23—364no—
362C23—364no—
363Q8—42no—
364D4—68no—
365D4—124no—
366D4—124no—
367D4—184no—
368D4—364no—
369D4—364no—
370D4—364no—
371D4—364no—
372D4—362no—
373D4—362no—
374C2×C4—22no—
375C2×C4—91no—
376C2×C4—94no—
377C2×C4—91no—
378C2×C4—91no—
379C2×C4—182no—
380C2×C4—182no—
381C2×C4—364no—
382C2×C4#381111yescharacteristic
383C2×C4#381111yescharacteristic
384C2×C4C22×D3211yescharacteristic
385C8—64no—
386C2×C3—21no—
387C2×C3—21no—
388C2×C3—21no—
389C2×C3—244no—
390C2×C3#567412yes—
391C2×C3C2×D3×D812yes—
392C2×C3C2×#91412yes—
393D3—64no—
394D3—84no—
395D3—122no—
396D3—244no—
397D3—244no—
398C22—92no—
399C22—124no—
400C22—124no—
401C22—124no—
402C22—181no—
403C22—181no—
404C22—362no—
405C22—362no—
406C22—362no—
407C22—728no—
408C22C2×#381111yescharacteristic
409C4—42no—
410C4—92no—
411C4—181no—
412C4—181no—
413C4#6392612yes—
414C4#6394112yes—
415C4#6432012yes—
416C3—21no—
417C3#8156612yescomplemented
418C2—182no—
419C2—244no—
420C2—722no—
421C2C2×#6392611yescharacteristic
422C2C2×#6394111yescharacteristic
423C2#1059543311yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
hypercenterC4⋊Q8D32
hypocenterC32#3205
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #10596196C2semidirect
2. #10594008C2semidirect
3. C3×#5088C2semidirect
4. #10590598C2semidirect
5. #10590551C2semidirect
6. #10590350C2semidirect
7. #10590297C2semidirect
13. C32×C4⋊Q8C22semidirect
18. #64102C22semidirect
19. #64083C22semidirect
25. C2×#3714C22semidirect
26. C3×#809C22semidirect
27. C3×C4×C3⋊C8C22semidirect
28. #63572C22semidirect
34. #5088D3semidirect
77. C3×C4⋊Q8C2×D3semidirect
103. #809C2×D3semidirect
104. C4×C3⋊C8C2×D3semidirect
126. C4×C3⋊D3D8semidirect
217. C4⋊Q8D32semidirect
356. C32#3205semidirect
417. C3#81566semidirect

Maximal subgroups

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

subgroupindex
#105961962
#105940082
C3×#50882
#105905982
#105905512
#105903502
#105902972
#815663