Finite Group Databasebeta

← #11781257

Subgroups — #11781257

Order 1152.

406 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 96 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#10592707C211yesmaximal, characteristic, complemented
2C3×#5015C211yesmaximal, characteristic
3C3×D4×C3⋊C8C211yesmaximal, characteristic, complemented
4#10590273C211yesmaximal, characteristic, complemented
5#10589097C211yesmaximal, characteristic, complemented
6#10589096C211yesmaximal, characteristic, complemented
7#10589090C211yesmaximal, characteristic, complemented
8#71006—31nomaximal
9#70848—31nomaximal
10C32×C4×D4C2211yescharacteristic
11#64078C2211yescharacteristic
12C2×C3×#213—21no—
13C22×C3×C3⋊C8—21no—
14C3×#874C2211yescharacteristic
15#63659—21no—
16#63635—21no—
17C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
18C3×#830—21no—
19C3×#809—21no—
20C3×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×C4×C3⋊C8C2211yescharacteristic
23#63563—21no—
24#63563—21no—
25C3×#459—31no—
26C3×C8×D4—31no—
27#5070—31no—
28#5015D311yescharacteristic
29D4×C3⋊C8D311yescharacteristic, complemented
30#5008—31no—
31#5008—31no—
32#5008—61no—
33#4694—31no—
34#4544—31no—
35#4485—31no—
36#4481—31no—
37#4481—31no—
38#4480—31no—
39#4457—31no—
40C2×C32×D4D411yescharacteristic
41C22×C32×C4—21no—
42C2×#634—21no—
43C2×C3×D12—21no—
44C2×C3×D12—21no—
45C2×C3×D12—21no—
46C32×C4⋊C4D411yescharacteristic
47C32×C22⋊C4—21no—
48C32×C42C2311yescharacteristic
49C4⋊(C3⋊Dic3)—21no—
50C4⋊(C3⋊Dic3)—21no—
51C2×C3⋊(C3⋊C8)—21no—
52C3×#213—42no—
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8—42no—
56C2×C3×C3⋊C8D411yescharacteristic
57C2×C3×C3⋊C8D411yescharacteristic
58#1677—91noSylow
59C2×C3×D8—61no—
60C22×C3×C8—61no—
61C3×#127—31no—
62C3×C4×D4—21no—
63C3×C4×D4C2×D311yescharacteristic
64C3×C4×D4C2×D311yescharacteristic
65C2×#213—21no—
66C22×C3⋊C8—21no—
67#874C2×D311yescharacteristic
68#869—31no—
69#869—31no—
70#869—61no—
71C3×C4⋊C8—31no—
72C3×C4⋊C8—31no—
73C3×#102—61no—
74C3×C22⋊C8—61no—
75C3×C4×C8—31no—
76#832—62no—
77#832—61no—
78#832—61no—
79#832—61no—
80#832—61no—
81#830—21no—
82#821—61no—
83#821—61no—
84#809—21no—
85#808—62no—
86#808—61no—
87#808—61no—
88C4⋊(C3⋊C8)—31no—
89C4⋊(C3⋊C8)—31no—
90C4⋊(C3⋊C8)—61no—
91C4⋊(C3⋊C8)C2×D311yescharacteristic
92C4⋊(C3⋊C8)C2×D311yescharacteristic
93C4×C3⋊C8C2×D311yescharacteristic
94C23×C32—21no—
95C22×C3×D3—41no—
96C32×D4—21no—
97C32×D4SD1612yes—
98C2×C32×C4—21no—
99C2×C32×C4—41no—
100C2×C32×C4—41no—
101C2×C32×C4C2×D411yescharacteristic
102C2×C32×C4C2×D411yescharacteristic
103C2×C32×C4#4111yescharacteristic
104C2×C3⋊Dic3—41no—
105#634—81no—
106C3×D12—41no—
107C3×D12—41no—
108C3×D12—41no—
109C3×D12—41no—
110C3×D12—81no—
111C3⋊(C3⋊C8)—41no—
112C3×C3⋊C8—21no—
113C3×C3⋊C8—21no—
114C3×C3⋊C8—41no—
115C3×C3⋊C8—41no—
116#486—91no—
117#476—91no—
118#459—31no—
119C8×D4—31no—
120#334—91no—
121#333—91no—
122#331—91no—
123C2×C3×D4—21no—
124C2×C3×D4—61no—
125C2×C3×D4—61no—
126C2×C3×D4—61no—
127C2×C3×D4D1211yescharacteristic
128C2×C3×D4#6711yescharacteristic
129C22×C3×C4—21no—
130C22×C3×C4—21no—
131C22×C3×C4—41no—
132C2×D12—21no—
133C2×D12—21no—
134C2×D12—21no—
135C2×Dic6—61no—
136C2×Dic6—61no—
137C2×Dic6—121no—
138C3×D8—122no—
139C2×C3×C8—31no—
140C2×C3×C8—31no—
141C2×C3×C8—61no—
142C2×C3×C8—61no—
143C2×C3×C8—122no—
144C3×C4⋊C4—21no—
145C3×C4⋊C4D1211yescharacteristic
146C3×C4⋊C4#6711yescharacteristic
147C3×C22⋊C4—21no—
148C3×C22⋊C4—21no—
149C3×C22⋊C4—41no—
150C3×C42—21no—
151C3×C42C22×D311yescharacteristic
152C3×C42C22×D311yescharacteristic
153#213—42no—
154C4⋊Dic3—62no—
155C4⋊Dic3—61no—
156C4⋊Dic3—61no—
157C4⋊Dic3—61no—
158C4⋊Dic3—61no—
159C4⋊Dic3—121no—
160C2×C3⋊C8—21no—
161C2×C3⋊C8—21no—
162C2×C3⋊C8—42no—
163C2×C3⋊C8—62no—
164C2×C3⋊C8—61no—
165C2×C3⋊C8—61no—
166C2×C3⋊C8#6711yescharacteristic
167C2×C3⋊C8#6711yescharacteristic
168C22×C32—22no—
169C22×C32—41no—
170C22×C32—41no—
171C22×C32#12111yescharacteristic
172C2×C3×D3—81no—
173C2×C3×D3—81no—
174C2×C3×D3—81no—
175C32×C4—21no—
176C32×C4—41no—
177C32×C4C2×SD1611yescharacteristic
178C32×C4#13511yescharacteristic
179C32×C4#13511yescharacteristic
180C32×C4AGL(1,ℤ/8)11yescharacteristic
181C3⋊Dic3—81no—
182C2×D8—61no—
183C22×C8—61no—
184C4⋊Q8—91no—
185#127—31no—
186C4×D4D3211yescharacteristic
187#106—181no—
188C4⋊C8—31no—
189C4⋊C8—31no—
190C4⋊C8—91no—
191#102—61no—
192#102—181no—
193#102—181no—
194#102—181no—
195C22⋊C8—61no—
196C4×C8—31no—
197C23×C3—21no—
198C23×C3—21no—
199C23×C3—41no—
200C23×C3—121no—
201C22×D3—41no—
202C3×D4—21no—
203C3×D4—21no—
204C3×D4—22no—
205C3×D4—41no—
206C3×D4—121no—
207C3×D4—121no—
208C3×D4—121no—
209C3×D4—121no—
210C3×D4—241no—
211C3×D4#20412yes—
212C3×D4#21412yes—
213C2×C3×C4—21no—
214C2×C3×C4—21no—
215C2×C3×C4—21no—
216C2×C3×C4—21no—
217C2×C3×C4—21no—
218C2×C3×C4—41no—
219C2×C3×C4—41no—
220C2×C3×C4—41no—
221C2×C3×C4—41no—
222C2×C3×C4—41no—
223C2×C3×C4—81no—
224C2×C3×C4—81no—
225C2×C3×C4C2×D1211yescharacteristic
226C2×C3×C4#23511yescharacteristic
227C2×C3×C4D3×D411yescharacteristic
228C2×C3×C4#23711yescharacteristic
229C2×C3×C4C2×#6711yescharacteristic
230C2×C3×C4C2×#6711yescharacteristic
231C2×Dic3—122no—
232C2×Dic3—121no—
233C2×Dic3—121no—
234D12—41no—
235D12—41no—
236D12—41no—
237D12—41no—
238D12—81no—
239Dic6—242no—
240Dic6—241no—
241Dic6—241no—
242C3×C8—61no—
243C3×C8—61no—
244C3×C8—121no—
245C3×C8—121no—
246C3⋊C8—21no—
247C3⋊C8—21no—
248C3⋊C8—41no—
249C3⋊C8—41no—
250C3⋊C8—122no—
251C3⋊C8—121no—
252C3⋊C8—121no—
253C2×C32—42no—
254C2×C32#46311yescharacteristic
255C2×C32#46511yescharacteristic
256C2×C32#47211yescharacteristic
257C3×D3—161no—
258C2×Q8—181no—
259C2×D4—61no—
260C2×D4—61no—
261C2×D4—61no—
262C2×D4#62611yescharacteristic
263C22×C4—21no—
264D8—122no—
265C2×C8—31no—
266C2×C8—31no—
267C2×C8—61no—
268C2×C8—61no—
269C2×C8—122no—
270C2×C8—181no—
271C4⋊C4—181no—
272C4⋊C4—181no—
273C4⋊C4#62611yescharacteristic
274C22⋊C4—21no—
275C42C2×D3211yescharacteristic
276C22×C3—22no—
277C22×C3—22no—
278C22×C3—21no—
279C22×C3—42no—
280C22×C3—41no—
281C22×C3—41no—
282C22×C3—41no—
283C22×C3—41no—
284C22×C3—81no—
285C22×C3—81no—
286C22×C3—241no—
287C22×C3—241no—
288C22×C3—241no—
289C22×C3#93011yescharacteristic
290C22×C3#93911yescharacteristic
291C2×D3—81no—
292C2×D3—81no—
293C2×D3—81no—
294C3×C4—21no—
295C3×C4—21no—
296C3×C4—21no—
297C3×C4—21no—
298C3×C4—21no—
299C3×C4—21no—
300C3×C4—41no—
301C3×C4—41no—
302C3×C4—41no—
303C3×C4—81no—
304C3×C4C2×#20411yescharacteristic
305C3×C4#90411yescharacteristic
306C3×C4#91111yescharacteristic
307C3×C4#91211yescharacteristic
308C3×C4#93211yescharacteristic
309C3×C4C2×#21411yescharacteristic
310C3×C4#95011yescharacteristic
311C3×C4#95011yescharacteristic
312Dic3—242no—
313Dic3—241no—
314Dic3—241no—
315C32#167711yescharacteristic, complemented, Sylow
316C23—21no—
317C23—121no—
318Q8—721no—
319D4—21no—
320D4—121no—
321D4—121no—
322D4—121no—
323D4—121no—
324D4—241no—
325D4#371612yes—
326C2×C4—21no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—361no—
330C2×C4#380411yescharacteristic
331C2×C4C2×#62611yescharacteristic
332C2×C4D3×#6711yescharacteristic
333C8—61no—
334C8—61no—
335C8—121no—
336C8—121no—
337C8—361no—
338C2×C3—21no—
339C2×C3—21no—
340C2×C3—21no—
341C2×C3—42no—
342C2×C3—42no—
343C2×C3—82no—
344C2×C3—481no—
345C2×C3#501611yescharacteristic
346C2×C3#504111yescharacteristic
347C2×C3#511411yescharacteristic
348C2×C3#514211yescharacteristic
349C2×C3#515311yescharacteristic
350C2×C3#519911yescharacteristic
351D3—161no—
352C22—22no—
353C22—41no—
354C22—41no—
355C22—241no—
356C22—241no—
357C22—241no—
358C22#6397811yescharacteristic
359C4—21no—
360C4—41no—
361C4—721no—
362C4C2×#371611yescharacteristic
363C4#6382911yescharacteristic
364C4#6393211yescharacteristic
365C4#6393311yescharacteristic
366C3—21no—
367C3#7084811yescharacteristic, complemented
368C3#7100611yescharacteristic, complemented
369C2—42no—
370C2—481no—
371C2#1059117511yescharacteristic
372C2#1059146811yescharacteristic
373C2#1059167711yescharacteristic
subgroupG/H
centerC22#63978
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×D4C22
socleC22×C32#121
prime radicalC3×#5015C2
hypercenterC4×D4D32
hypocenterC32#1677
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #10592707C2semidirect
3. C3×D4×C3⋊C8C2semidirect
4. #10590273C2semidirect
5. #10589097C2semidirect
6. #10589096C2semidirect
7. #10589090C2semidirect
29. D4×C3⋊C8D3semidirect
315. C32#1677semidirect
367. C3#70848semidirect
368. C3#71006semidirect

Maximal subgroups

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

subgroupindex
#105927072
C3×#50152
C3×D4×C3⋊C82
#105902732
#105890972
#105890962
#105890902
#710063
#708483