Finite Group Databasebeta

← #11878839

Subgroups — #11878839

Order 1152.

1087 conjugacy classes of subgroups; only the 172 normal subgroups are shown.

normal subgroups only

This group has 1087 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#10596199C211yesmaximal, characteristic, complemented
2#10594008C211yesmaximal, characteristic
3C3×#5085C212yesmaximal, complemented
4#10591652C214yesmaximal, complemented
5#10591622C214yesmaximal, complemented
6#10590297C211yesmaximal, characteristic, complemented
7#10590273C212yesmaximal, complemented
8#81766—32nomaximal
9C2×#3802—21no—
10C2×#3802—21no—
11C2×#3802C2212yes—
12C32×C4⋊Q8C2211yescharacteristic, complemented
13#64155C2212yes—
14Q8×C3⋊Dic3C2212yescomplemented
15#64106—21no—
16#64101—21no—
17#64099—21no—
18#64096—21no—
19C42×C3⋊D3C2211yescharacteristic
20#64078C2211yescharacteristic, complemented
21C2×C3×#215C2218yescomplemented
22C3×#874C2212yes—
23#63914—21no—
24#63914—21no—
25#63914C2212yes—
26C3×C4×C3⋊C8C2212yescomplemented
27#63572C2212yescomplemented
28#63563C2218yescomplemented
29#63557C2212yes—
30#5728—32no—
31#5728—61no—
32D3×#127—32no—
33C3×#492—32no—
34#5169—38no—
35#5163—38no—
36#5085D312yescomplemented
37#5070—32no—
38#4694—32no—
39#4685—32no—
40C22×D32—22no—
41C2×C32×Q8C2312yes—
42C2×C4×C3⋊D3D411yescharacteristic
43C2×C4×C3⋊D3D411yescharacteristic
44C2×C4×C3⋊D3C2311yescharacteristic
45C2×#634—21no—
46C2×C3×D12—22no—
47C2×C3×D12—22no—
48C2×C3×D12C2314yes—
49C2×#625—22no—
50C2×#625—22no—
51C2×#625—22no—
52#3802—44no—
53#3802—44no—
54#3802—44no—
55C32×C4⋊C4—21no—
56C32×C4⋊C4—21no—
57C32×C42C2311yescharacteristic
58#3752—22no—
59C4⋊(C3⋊Dic3)—21no—
60C4⋊(C3⋊Dic3)—22no—
61C4⋊(C3⋊Dic3)C2312yes—
62#3750—22no—
63C4×C3⋊Dic3—22no—
64C4×C3⋊Dic3D411yescharacteristic
65C4×C3⋊Dic3D411yescharacteristic
66C4×C3⋊Dic3C2311yescharacteristic
67C3×#215—48no—
68C2×C3×C3⋊C8C2314yes—
69#3208—91noSylow
70C2×D3×D4—34no—
71C2×D3×D4—62no—
72C2×D3×D4—62no—
73C2×C3×SD16—38no—
74C3×C4⋊Q8—21no—
75C3×C4⋊Q8C2×D312yescomplemented
76C3×#127—32no—
77#946—34no—
78#946—62no—
79Q8×Dic3—34no—
80Q8×Dic3—62no—
81C2×#215C2×D318yescomplemented
82#940—34no—
83#940—62no—
84#940—62no—
85#897—62no—
86#897—62no—
87#892—62no—
88#892—62no—
89#890—62no—
90#890—62no—
91#887—62no—
92#887—62no—
93#874C2×D312yes—
94C42×D3—32no—
95C42×D3—61no—
96#869—32no—
97#869—61no—
98C3×C4×C8—32no—
99#832—38no—
100#821—38no—
101(C2×D3)⋊C8—34no—
102Dic3⋊C8—34no—
103C4×C3⋊C8C2×D312yescomplemented
104C22×C3⋊D3C2×D411yescharacteristic
105C22×C3×D3—24no—
106C2×D32—44no—
107C2×D32—44no—
108C2×D32—44no—
109C32×Q8—24no—
110C2×C32×C4—22no—
111C2×C32×C4C2×D411yescharacteristic
112C2×C32×C4C2×D411yescharacteristic
113C2×C32×C4C2411yescharacteristic
114C2×C3⋊Dic3—22no—
115C2×C3⋊Dic3C2×D411yescharacteristic
116C2×C3⋊Dic3C2×D411yescharacteristic
117C2×C3⋊Dic3C2×D411yescharacteristic
118C4×C3⋊D3—22no—
119C4×C3⋊D3—22no—
120C4×C3⋊D3SD1614yescomplemented
121#634—42no—
122C3×D12—28no—
123C3×D12—44no—
124C3×D12—44no—
125#625—44no—
126#625—44no—
127#625—44no—
128C3×C3⋊C8—24no—
129#533—91no—
130C2×#127—91no—
131#492—32no—
132#486—92no—
133#460—94no—
134#450—94no—
135#431—91no—
136C23×D3—64no—
137C2×C3×Q8—22no—
138C2×C3×Q8C22×D314yes—
139C2×C3×D4—34no—
140C2×C3×D4—62no—
141C2×C3×D4—62no—
142C2×#67—64no—
143C2×#67—64no—
144C2×#67—64no—
145D3×D4—128no—
146D3×D4—128no—
147D3×D4—128no—
148C2×D12—22no—
149C2×D12—22no—
150C2×D12C22×D314yes—
151C2×C4×D3—32no—
152C2×C4×D3—32no—
153C2×C4×D3—32no—
154C2×C4×D3—61no—
155C2×C4×D3—61no—
156C2×C4×D3—61no—
157C2×Dic6—62no—
158C2×Dic6—62no—
159C3×SD16—128no—
160C2×C3×C8—34no—
161C3×C4⋊C4—22no—
162C3×C4⋊C4—22no—
163C3×C4⋊C4—22no—
164C3×C4⋊C4—22no—
165C3×C42—21no—
166C3×C42C22×D312yes—
167#215—48no—
168(C2×D3)⋊C4—64no—
169(C2×D3)⋊C4—64no—
170C4⋊Dic3—34no—
171C4⋊Dic3—62no—
172C4⋊Dic3—64no—
173C4⋊Dic3—62no—
174C4⋊Dic3—64no—
175C4⋊Dic3—62no—
176Dic3⋊C4—64no—
177Dic3⋊C4—64no—
178C4×Dic3—32no—
179C4×Dic3—32no—
180C4×Dic3—32no—
181C4×Dic3—61no—
182C4×Dic3—61no—
183C4×Dic3—61no—
184C4×Dic3—64no—
185C4×Dic3—64no—
186C2×C3⋊C8C22×D314yes—
187C22×C32C22×D411yescharacteristic
188C2×C3⋊D3—21no—
189C2×C3⋊D3—21no—
190C2×C3⋊D3C2×SD1612yes—
191C2×C3×D3—44no—
192C2×C3×D3—44no—
193C2×C3×D3—44no—
194D32—88no—
195C32×C4—42no—
196C32×C4C2×SD1612yes—
197C32×C4AGL(1,ℤ/8)12yes—
198C32×C4H(5,𝔽2)12yes—
199C3⋊Dic3—21no—
200C3⋊Dic3—21no—
201C3⋊Dic3—42no—
202C3⋊Dic3C2×SD1612yes—
203C22×D4—92no—
204C22×D4—181no—
205C22×D4—181no—
206C2×SD16—38no—
207C4⋊Q8—91no—
208C4⋊Q8D3211yescharacteristic, complemented
209#127—32no—
210#127—92no—
211#127—181no—
212#127—181no—
213#125—181no—
214C22⋊Q8—92no—
215C22⋊Q8—181no—
216C4×Q8—92no—
217C4×Q8—181no—
218#117—181no—
219C2×C42—91no—
220C4⋊C8—92no—
221#102—98no—
222C22⋊C8—92no—
223C4×C8—32no—
224C23×C3—64no—
225C22×D3—24no—
226C22×D3—32no—
227C22×D3—61no—
228C22×D3—128no—
229C22×D3—128no—
230C22×D3—128no—
231C3×Q8—28no—
232C3×Q8—44no—
233C3×D4—68no—
234C3×D4—124no—
235C3×D4—124no—
236C2×C3×C4—24no—
237C2×C3×C4—24no—
238C2×C3×C4—21no—
239C2×C3×C4—21no—
240C2×C3×C4—21no—
241C2×C3×C4D3×D412yes—
242C2×C3×C4D3×D412yes—
243C2×C3×C4C23×D312yes—
244#67—128no—
245#67—128no—
246#67—128no—
247C2×Dic3—32no—
248C2×Dic3—32no—
249C2×Dic3—32no—
250C2×Dic3—61no—
251C2×Dic3—61no—
252C2×Dic3—61no—
253C2×Dic3—64no—
254C2×Dic3—64no—
255D12—28no—
256D12—44no—
257D12—44no—
258C4×D3—38no—
259C4×D3—64no—
260C4×D3—64no—
261C4×D3—64no—
262C4×D3—122no—
263C4×D3—122no—
264Dic6—124no—
265Dic6—124no—
266C3×C8—64no—
267C3⋊C8—24no—
268C2×C32#53511yescharacteristic
269C2×C32C22×SD1611yescharacteristic
270C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
271C3⋊D3—22no—
272C3×D3—84no—
273C24—182no—
274C2×Q8—181no—
275C2×Q8C2×D3212yes—
276C2×D4—34no—
277C2×D4—62no—
278C2×D4—62no—
279C2×D4—182no—
280C2×D4—182no—
281C2×D4—182no—
282C2×D4—364no—
283C2×D4—364no—
284C2×D4—364no—
285C22×C4—91no—
286C22×C4—91no—
287C22×C4—91no—
288SD16—128no—
289C2×C8—34no—
290C4⋊C4—21no—
291C4⋊C4—21no—
292C4⋊C4—92no—
293C4⋊C4—182no—
294C4⋊C4—182no—
295C4⋊C4—181no—
296C22⋊C4—182no—
297C42—91no—
298C42—91no—
299C42—91no—
300C42—182no—
301C42C2×D3211yescharacteristic
302C22×C3—21no—
303C22×C3—124no—
304C22×C3—124no—
305C22×C3—124no—
306C22×C3C2×D3×D412yes—
307C2×D3—34no—
308C2×D3—44no—
309C2×D3—44no—
310C2×D3—44no—
311C2×D3—62no—
312C2×D3—62no—
313C2×D3—62no—
314C2×D3—121no—
315C2×D3—121no—
316C2×D3—2416no—
317C3×C4—22no—
318C3×C4—22no—
319C3×C4—22no—
320C3×C4—44no—
321C3×C4—44no—
322C3×C4D3×SD1614yes—
323C3×C4#91414yes—
324C3×C4#100414yes—
325Dic3—34no—
326Dic3—62no—
327Dic3—62no—
328Dic3—62no—
329Dic3—121no—
330Dic3—121no—
331Dic3—124no—
332Dic3—124no—
333C32#320811yescharacteristic, complemented, Sylow
334C23—64no—
335C23—91no—
336C23—364no—
337C23—364no—
338C23—364no—
339Q8—24no—
340Q8—362no—
341D4—68no—
342D4—124no—
343D4—124no—
344D4—364no—
345D4—364no—
346D4—364no—
347C2×C4—22no—
348C2×C4—91no—
349C2×C4—94no—
350C2×C4—91no—
351C2×C4—91no—
352C2×C4—182no—
353C2×C4—182no—
354C2×C4—182no—
355C2×C4#381111yescharacteristic
356C2×C4#381111yescharacteristic
357C2×C4C22×D3211yescharacteristic
358C8—64no—
359C2×C3—21no—
360C2×C3—21no—
361C2×C3—21no—
362C2×C3—244no—
363C2×C3#571512yes—
364C2×C3C2×D3×SD1612yes—
365C2×C3C2×#91412yes—
366D3—64no—
367D3—84no—
368D3—122no—
369C22—92no—
370C22—124no—
371C22—124no—
372C22—124no—
373C22—181no—
374C22—181no—
375C22—728no—
376C22C2×#381111yescharacteristic
377C4—42no—
378C4—92no—
379C4—181no—
380C4—181no—
381C4—362no—
382C4#6394012yes—
383C4#6394112yes—
384C4#6431312yes—
385C3—21no—
386C3#8176612yescomplemented
387C2—182no—
388C2—244no—
389C2#1059530911yescharacteristic
390C2C2×#6394011yescharacteristic
391C2C2×#6394111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radical#10594008C2
hypercenterC4⋊Q8D32
hypocenterC32#3208
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. #10596199C2semidirect
3. C3×#5085C2semidirect
4. #10591652C2semidirect
5. #10591622C2semidirect
6. #10590297C2semidirect
7. #10590273C2semidirect
12. C32×C4⋊Q8C22semidirect
14. Q8×C3⋊Dic3C22semidirect
20. #64078C22semidirect
21. C2×C3×#215C22semidirect
26. C3×C4×C3⋊C8C22semidirect
27. #63572C22semidirect
28. #63563C22semidirect
36. #5085D3semidirect
75. C3×C4⋊Q8C2×D3semidirect
81. C2×#215C2×D3semidirect
103. C4×C3⋊C8C2×D3semidirect
120. C4×C3⋊D3SD16semidirect
208. C4⋊Q8D32semidirect
333. C32#3208semidirect
386. C3#81766semidirect

Maximal subgroups

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

subgroupindex
#105961992
#105940082
C3×#50852
#105916522
#105916222
#105902972
#105902732
#817663