Finite Group Databasebeta

← #11781259

Subgroups — #11781259

Order 1152.

406 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 84 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#10592783C211yesmaximal, characteristic, complemented
2C3×#5088C211yesmaximal, characteristic, complemented
3#10590355C211yesmaximal, characteristic
4#10590327C211yesmaximal, characteristic, complemented
5C3×#4546C211yesmaximal, characteristic, complemented
6#10589097C211yesmaximal, characteristic, complemented
7#10589090C211yesmaximal, characteristic, complemented
8#71200—31nomaximal
9#68498—31nomaximal
10C32×C4⋊Q8C2211yescharacteristic
11C4×C4⋊(C3⋊D3)C2211yescharacteristic
12C3×#874C2211yescharacteristic
13C2×#3714—21no—
14C2×#3710—21no—
15#63636—21no—
16#63635—21no—
17C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
18C3×#809—21no—
19C3×#809—21no—
20C3×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×C4×C3⋊C8C2211yescharacteristic
23#63563—21no—
24#63557—21no—
25C3×#486—31no—
26#5088D311yescharacteristic, complemented
27#5084—31no—
28#5084—31no—
29#5084—61no—
30#5072—31no—
31#4843—31no—
32#4834—31no—
33C8×D12—31no—
34C3×#333—31no—
35#4546D311yescharacteristic, complemented
36#4544—31no—
37#4485—31no—
38#4480—31no—
39#4457—31no—
40C2×C32×Q8—21no—
41C2×C4⋊(C3⋊D3)D411yescharacteristic
42C2×C4×C3⋊D3—21no—
43C2×C3×D12—21no—
44C2×C3×D12—21no—
45C2×C3×D12—21no—
46C32×C4⋊C4—21no—
47C32×C4⋊C4—21no—
48C32×C42C2311yescharacteristic
49#3752—21no—
50C4⋊(C3⋊Dic3)D411yescharacteristic
51C2×C3⋊(C3⋊C8)—21no—
52C2×C3×C3⋊C8—21no—
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8D411yescharacteristic
55C2×C3×C3⋊C8D411yescharacteristic
56#3714—42no—
57#3710—42no—
58#1677—91noSylow
59C3×C4⋊Q8—21no—
60C3×C4⋊Q8C2×D311yescharacteristic
61C3×C4⋊Q8C2×D311yescharacteristic
62C3×#127—31no—
63C2×#213—61no—
64C2×D24—61no—
65C2×D3×C8—61no—
66C2×D3×C8—61no—
67#874C2×D311yescharacteristic
68C4×D12—31no—
69C4×D12—31no—
70C4×D12—61no—
71C3×C4⋊C8—31no—
72C3×C4⋊C8—31no—
73C3×#102—61no—
74C3×#102—61no—
75C3×C4×C8—31no—
76#832—61no—
77#821—61no—
78(C2×D3)⋊C8—61no—
79(C2×D3)⋊C8—61no—
80#809—21no—
81#809—21no—
82#809—61no—
83#809—61no—
84#809—62no—
85#808—61no—
86#808—61no—
87#808—62no—
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
94C22×C3⋊D3—21no—
95C22×C3×D3—41no—
96C32×Q8—81no—
97C2×C32×C4—41no—
98C2×C32×C4C2×D411yescharacteristic
99C2×C32×C4C2×D411yescharacteristic
100C2×C32×C4#4111yescharacteristic
101C2×C3⋊Dic3—21no—
102C4⋊(C3⋊D3)—21no—
103C4⋊(C3⋊D3)SD1612yes—
104C4×C3⋊D3—41no—
105C4×C3⋊D3—41no—
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—31no—
117#476—91no—
118#459—91no—
119C8×D4—91no—
120#334—91no—
121#333—31no—
122#331—91no—
123C2×C3×Q8—21no—
124C2×C3×Q8—21no—
125C2×C3×Q8—41no—
126C2×C3×D4—61no—
127C2×C3×D4—61no—
128C2×C3×D4—61no—
129C2×D12—21no—
130C2×D12—21no—
131C2×D12—21no—
132C2×D12—31no—
133C2×D12—31no—
134C2×D12—61no—
135C2×C4×D3—61no—
136C2×C4×D3—61no—
137C2×C4×D3—121no—
138C2×C3×C8—31no—
139C2×C3×C8—31no—
140C2×C3×C8—61no—
141C2×C3×C8—61no—
142C3×C4⋊C4—22no—
143C3×C4⋊C4—21no—
144C3×C4⋊C4—21no—
145C3×C4⋊C4—21no—
146C3×C4⋊C4—21no—
147C3×C4⋊C4—41no—
148C3×C42—21no—
149C3×C42C22×D311yescharacteristic
150C3×C42C22×D311yescharacteristic
151#213—122no—
152(C2×D3)⋊C4—61no—
153(C2×D3)⋊C4—61no—
154(C2×D3)⋊C4—121no—
155C4⋊Dic3—31no—
156C4⋊Dic3—31no—
157C4⋊Dic3—61no—
158C2×C3⋊C8—21no—
159C2×C3⋊C8—21no—
160C2×C3⋊C8—62no—
161C2×C3⋊C8—61no—
162C2×C3⋊C8—61no—
163C2×C3⋊C8#6711yescharacteristic
164C2×C3⋊C8#6711yescharacteristic
165D24—122no—
166D3×C8—122no—
167D3×C8—122no—
168C22×C32#12111yescharacteristic
169C2×C3⋊D3—22no—
170C2×C3⋊D3—41no—
171C2×C3⋊D3—41no—
172C2×C3×D3—81no—
173C2×C3×D3—81no—
174C2×C3×D3—81no—
175C32×C4—21no—
176C32×C4—81no—
177C32×C4C2×SD1611yescharacteristic
178C32×C4#13511yescharacteristic
179C32×C4#13511yescharacteristic
180C32×C4AGL(1,ℤ/8)11yescharacteristic
181C3⋊Dic3—41no—
182C2×D8—181no—
183C22×C8—181no—
184C4⋊Q8D3211yescharacteristic
185#127—31no—
186C4×D4—91no—
187#106—181no—
188C4⋊C8—31no—
189C4⋊C8—31no—
190C4⋊C8—91no—
191#102—61no—
192#102—61no—
193#102—181no—
194#102—181no—
195C22⋊C8—181no—
196C4×C8—31no—
197C23×C3—121no—
198C22×D3—41no—
199C22×D3—61no—
200C22×D3—61no—
201C22×D3—121no—
202C3×Q8—81no—
203C3×Q8—81no—
204C3×Q8—82no—
205C3×D4—121no—
206C3×D4—121no—
207C3×D4—121no—
208C3×D4—121no—
209C3×D4—241no—
210C2×C3×C4—21no—
211C2×C3×C4—21no—
212C2×C3×C4—21no—
213C2×C3×C4—42no—
214C2×C3×C4—41no—
215C2×C3×C4—41no—
216C2×C3×C4#23511yescharacteristic
217C2×C3×C4D3×D411yescharacteristic
218C2×C3×C4D3×D411yescharacteristic
219C2×C3×C4D3×D411yescharacteristic
220C2×C3×C4#23711yescharacteristic
221C2×C3×C4C2×#6711yescharacteristic
222C2×Dic3—61no—
223C2×Dic3—61no—
224C2×Dic3—121no—
225D12—32no—
226D12—32no—
227D12—41no—
228D12—41no—
229D12—41no—
230D12—41no—
231D12—62no—
232D12—61no—
233D12—61no—
234D12—81no—
235D12—121no—
236C4×D3—121no—
237C4×D3—121no—
238C4×D3—121no—
239C4×D3—121no—
240C4×D3—241no—
241C4×D3—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#46311yescharacteristic
254C2×C32#46511yescharacteristic
255C2×C32#47211yescharacteristic
256C3⋊D3—42no—
257C3×D3—161no—
258C2×Q8—21no—
259C2×D4—61no—
260C2×D4—61no—
261C2×D4—61no—
262C2×D4—91no—
263C22×C4—181no—
264D8—362no—
265C2×C8—31no—
266C2×C8—31no—
267C2×C8—61no—
268C2×C8—61no—
269C2×C8—181no—
270C2×C8—362no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—91no—
274C22⋊C4—181no—
275C42C2×D3211yescharacteristic
276C22×C3—21no—
277C22×C3—241no—
278C22×C3—241no—
279C22×C3—241no—
280C22×C3#88411yescharacteristic
281C22×C3#93811yescharacteristic
282C2×D3—62no—
283C2×D3—62no—
284C2×D3—81no—
285C2×D3—81no—
286C2×D3—81no—
287C2×D3—122no—
288C2×D3—121no—
289C2×D3—121no—
290C2×D3—121no—
291C2×D3—121no—
292C2×D3—241no—
293C2×D3—241no—
294C3×C4—21no—
295C3×C4—21no—
296C3×C4—21no—
297C3×C4—21no—
298C3×C4—21no—
299C3×C4—21no—
300C3×C4—41no—
301C3×C4—82no—
302C3×C4—81no—
303C3×C4—81no—
304C3×C4D3×SD1611yescharacteristic
305C3×C4D3×SD1611yescharacteristic
306C3×C4#91411yescharacteristic
307C3×C4#91611yescharacteristic
308C3×C4#91911yescharacteristic
309C3×C4#91911yescharacteristic
310C3×C4#94911yescharacteristic
311C3×C4#95011yescharacteristic
312Dic3—121no—
313Dic3—121no—
314Dic3—241no—
315C32#167711yescharacteristic, complemented, Sylow
316C23—121no—
317C23—181no—
318Q8—81no—
319D4—92no—
320D4—121no—
321D4—121no—
322D4—121no—
323D4—121no—
324D4—181no—
325D4—241no—
326C2×C4—41no—
327C2×C4—181no—
328C2×C4—361no—
329C2×C4—361no—
330C2×C4#380411yescharacteristic
331C2×C4D3×#6711yescharacteristic
332C2×C4#381111yescharacteristic
333C8—61no—
334C8—61no—
335C8—121no—
336C8—121no—
337C8—361no—
338C2×C3—21no—
339C2×C3—21no—
340C2×C3—21no—
341C2×C3—481no—
342C2×C3#474911yescharacteristic
343C2×C3#480711yescharacteristic
344C2×C3#481911yescharacteristic
345C2×C3#505711yescharacteristic
346C2×C3#516011yescharacteristic
347C2×C3#517111yescharacteristic
348D3—122no—
349D3—122no—
350D3—161no—
351D3—242no—
352C22—182no—
353C22—241no—
354C22—241no—
355C22—241no—
356C22—361no—
357C22—361no—
358C22#6395811yescharacteristic
359C4—21no—
360C4—81no—
361C4—361no—
362C4#6393911yescharacteristic
363C4#6394011yescharacteristic
364C4#6394911yescharacteristic
365C4#6395011yescharacteristic
366C3—21no—
367C3#6849811yescharacteristic, complemented
368C3#7120011yescharacteristic, complemented
369C2—362no—
370C2—481no—
371C2#1059140611yescharacteristic
372C2#1059156811yescharacteristic
373C2#1059159111yescharacteristic
subgroupG/H
centerC22#63958
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socleC22×C32#121
prime radical#10590355C2
hypercenterC4⋊Q8D32
hypocenterC32#1677
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #10592783C2semidirect
2. C3×#5088C2semidirect
4. #10590327C2semidirect
5. C3×#4546C2semidirect
6. #10589097C2semidirect
7. #10589090C2semidirect
26. #5088D3semidirect
35. #4546D3semidirect
315. C32#1677semidirect
367. C3#68498semidirect
368. C3#71200semidirect

Maximal subgroups

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

subgroupindex
#105927832
C3×#50882
#105903552
#105903272
C3×#45462
#105890972
#105890902
#712003
#684983