Finite Group Databasebeta

← #11781255

Subgroups — #11781255

Order 1152.

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

normal subgroups only

This group has 422 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#10592714C211yesmaximal, characteristic
2C3×D4×C3⋊C8C211yesmaximal, characteristic, complemented
3C3×#5008C211yesmaximal, characteristic, complemented
4#10590281C211yesmaximal, characteristic, complemented
5#10589097C211yesmaximal, characteristic, complemented
6#10589095C211yesmaximal, characteristic, complemented
7#10589091C211yesmaximal, characteristic, complemented
8#71134—31nomaximal
9#70848—31nomaximal
10C32×C4×D4C2211yescharacteristic
11C2×#3753—21no—
12#64083C2211yescharacteristic
13C22×C3×C3⋊C8—21no—
14C3×#869C2211yescharacteristic
15#63636—21no—
16C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
17C3×#832—21no—
18C3×#830—21no—
19C3×#808—21no—
20C3×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×C4×C3⋊C8C2211yescharacteristic
23#63564—21no—
24#63564—21no—
25C3×#476—31no—
26C3×C8×D4—31no—
27#5088—31no—
28#5015—31no—
29#5015—31no—
30#5015—61no—
31D4×C3⋊C8D311yescharacteristic, complemented
32#5008D311yescharacteristic, complemented
33#4694—31no—
34#4546—31no—
35#4485—31no—
36#4485—31no—
37#4481—31no—
38#4480—31no—
39#4457—31no—
40C2×C32×D4D411yescharacteristic
41C22×C32×C4—21no—
42C2×C4⋊(C3⋊D3)—21no—
43C2×C4⋊(C3⋊D3)—21no—
44C2×C4⋊(C3⋊D3)—21no—
45C2×C3×Dic6—21no—
46C32×C4⋊C4D411yescharacteristic
47C32×C22⋊C4—21no—
48C32×C42C2311yescharacteristic
49#3753—42no—
50C2×C3⋊(C3⋊C8)—21no—
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3—21no—
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
59C22×C3×C8—61no—
60C3×C4⋊Q8—31no—
61C3×C4×D4—21no—
62C3×C4×D4C2×D311yescharacteristic
63C3×C4×D4C2×D311yescharacteristic
64C2×#213—62no—
65C2×#213—61no—
66C2×#213—61no—
67C22×C3⋊C8—21no—
68#874—31no—
69#874—31no—
70#874—61no—
71#869C2×D311yescharacteristic
72C3×#106—61no—
73C3×C4⋊C8—31no—
74C3×C4⋊C8—31no—
75C3×#102—61no—
76C3×C22⋊C8—61no—
77C3×C4×C8—31no—
78#832—21no—
79#830—21no—
80#821—61no—
81#821—61no—
82#809—62no—
83#809—61no—
84#809—61no—
85#809—61no—
86#809—61no—
87#808—21no—
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
104C4⋊(C3⋊D3)—41no—
105C4⋊(C3⋊D3)—41no—
106C4⋊(C3⋊D3)—41no—
107C4⋊(C3⋊D3)—41no—
108C4⋊(C3⋊D3)—81no—
109C2×C3×Dic3—41no—
110C3×Dic6—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—31no—
118#459—91no—
119C8×D4—31no—
120#334—91no—
121#333—91no—
122#331—91no—
123C2×C3×Q8—61no—
124C2×C3×D4—21no—
125C2×C3×D4D1211yescharacteristic
126C2×C3×D4#6711yescharacteristic
127C22×C3×C4—21no—
128C22×C3×C4—21no—
129C22×C3×C4—41no—
130C2×D12—62no—
131C2×D12—61no—
132C2×D12—61no—
133C2×D12—61no—
134C2×D12—61no—
135C2×D12—61no—
136C2×D12—61no—
137C2×D12—121no—
138C2×D12—121no—
139C2×Dic6—21no—
140C2×C3×C8—31no—
141C2×C3×C8—31no—
142C2×C3×C8—61no—
143C2×C3×C8—61no—
144C2×C3×C8—122no—
145C3×C4⋊C4—21no—
146C3×C4⋊C4—61no—
147C3×C4⋊C4—61no—
148C3×C4⋊C4D1211yescharacteristic
149C3×C4⋊C4#6711yescharacteristic
150C3×C22⋊C4—21no—
151C3×C22⋊C4—21no—
152C3×C22⋊C4—41no—
153C3×C42—21no—
154C3×C42C22×D311yescharacteristic
155C3×C42C22×D311yescharacteristic
156#213—124no—
157#213—122no—
158#213—122no—
159C4⋊Dic3—21no—
160C4⋊Dic3—21no—
161C2×C3⋊C8—21no—
162C2×C3⋊C8—21no—
163C2×C3⋊C8—42no—
164C2×C3⋊C8—62no—
165C2×C3⋊C8—61no—
166C2×C3⋊C8—61no—
167C2×C3⋊C8#6711yescharacteristic
168C2×C3⋊C8#6711yescharacteristic
169C22×C32—22no—
170C22×C32—41no—
171C22×C32—41no—
172C22×C32#12111yescharacteristic
173C2×C3⋊D3—81no—
174C2×C3⋊D3—81no—
175C2×C3⋊D3—81no—
176C32×C4—21no—
177C32×C4—41no—
178C32×C4C2×SD1611yescharacteristic
179C32×C4#13511yescharacteristic
180C32×C4#13511yescharacteristic
181C32×C4AGL(1,ℤ/8)11yescharacteristic
182C3×Dic3—81no—
183C2×D8—181no—
184C22×C8—61no—
185C4⋊Q8—31no—
186#127—91no—
187C4×D4D3211yescharacteristic
188#106—61no—
189C4⋊C8—31no—
190C4⋊C8—31no—
191C4⋊C8—91no—
192#102—61no—
193#102—181no—
194#102—181no—
195#102—181no—
196C22⋊C8—61no—
197C4×C8—31no—
198C23×C3—21no—
199C23×C3—21no—
200C23×C3—41no—
201C22×D3—122no—
202C22×D3—121no—
203C22×D3—121no—
204C3×Q8—241no—
205C3×D4—21no—
206C3×D4—21no—
207C3×D4—22no—
208C3×D4—41no—
209C3×D4#20412yes—
210C3×D4#21512yes—
211C2×C3×C4—21no—
212C2×C3×C4—21no—
213C2×C3×C4—21no—
214C2×C3×C4—21no—
215C2×C3×C4—21no—
216C2×C3×C4—41no—
217C2×C3×C4—41no—
218C2×C3×C4—41no—
219C2×C3×C4—41no—
220C2×C3×C4—41no—
221C2×C3×C4—81no—
222C2×C3×C4—81no—
223C2×C3×C4—121no—
224C2×C3×C4C2×D1211yescharacteristic
225C2×C3×C4#23511yescharacteristic
226C2×C3×C4D3×D411yescharacteristic
227C2×C3×C4#23711yescharacteristic
228C2×C3×C4C2×#6711yescharacteristic
229C2×C3×C4C2×#6711yescharacteristic
230C2×Dic3—41no—
231D12—122no—
232D12—122no—
233D12—121no—
234D12—121no—
235D12—121no—
236D12—121no—
237D12—121no—
238D12—121no—
239D12—121no—
240D12—121no—
241D12—241no—
242D12—241no—
243D12—241no—
244D12—241no—
245D12—242no—
246Dic6—81no—
247C3×C8—61no—
248C3×C8—61no—
249C3×C8—121no—
250C3×C8—121no—
251C3⋊C8—21no—
252C3⋊C8—21no—
253C3⋊C8—41no—
254C3⋊C8—41no—
255C3⋊C8—122no—
256C3⋊C8—121no—
257C3⋊C8—121no—
258C2×C32—42no—
259C2×C32#46311yescharacteristic
260C2×C32#46511yescharacteristic
261C2×C32#47211yescharacteristic
262C3⋊D3—161no—
263C2×Q8—61no—
264C2×D4—181no—
265C2×D4—181no—
266C2×D4—181no—
267C2×D4#62611yescharacteristic
268C22×C4—21no—
269D8—362no—
270C2×C8—31no—
271C2×C8—31no—
272C2×C8—61no—
273C2×C8—61no—
274C2×C8—122no—
275C2×C8—181no—
276C4⋊C4—61no—
277C4⋊C4—61no—
278C4⋊C4#62611yescharacteristic
279C22⋊C4—21no—
280C42C2×D3211yescharacteristic
281C22×C3—22no—
282C22×C3—22no—
283C22×C3—21no—
284C22×C3—42no—
285C22×C3—41no—
286C22×C3—41no—
287C22×C3—41no—
288C22×C3—41no—
289C22×C3—81no—
290C22×C3—81no—
291C22×C3#93011yescharacteristic
292C22×C3#93911yescharacteristic
293C2×D3—242no—
294C2×D3—242no—
295C2×D3—242no—
296C2×D3—241no—
297C2×D3—241no—
298C2×D3—241no—
299C2×D3—241no—
300C2×D3—241no—
301C2×D3—241no—
302C3×C4—21no—
303C3×C4—21no—
304C3×C4—21no—
305C3×C4—21no—
306C3×C4—21no—
307C3×C4—21no—
308C3×C4—41no—
309C3×C4—41no—
310C3×C4—41no—
311C3×C4—81no—
312C3×C4—241no—
313C3×C4C2×#20411yescharacteristic
314C3×C4#90411yescharacteristic
315C3×C4#91411yescharacteristic
316C3×C4#91611yescharacteristic
317C3×C4#93211yescharacteristic
318C3×C4C2×#21511yescharacteristic
319C3×C4#95011yescharacteristic
320C3×C4#95011yescharacteristic
321Dic3—81no—
322C32#167711yescharacteristic, complemented, Sylow
323C23—21no—
324C23—361no—
325Q8—241no—
326D4—21no—
327D4—361no—
328D4—361no—
329D4—361no—
330D4—361no—
331D4—721no—
332D4#371712yes—
333C2×C4—21no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—121no—
337C2×C4#380411yescharacteristic
338C2×C4C2×#62611yescharacteristic
339C2×C4D3×#6711yescharacteristic
340C8—61no—
341C8—61no—
342C8—121no—
343C8—121no—
344C8—361no—
345C2×C3—21no—
346C2×C3—21no—
347C2×C3—21no—
348C2×C3—42no—
349C2×C3—42no—
350C2×C3—82no—
351C2×C3#501611yescharacteristic
352C2×C3#504811yescharacteristic
353C2×C3#511411yescharacteristic
354C2×C3#514211yescharacteristic
355C2×C3#516511yescharacteristic
356C2×C3#519911yescharacteristic
357D3—482no—
358D3—481no—
359D3—481no—
360C22—22no—
361C22—41no—
362C22—41no—
363C22—721no—
364C22—721no—
365C22—721no—
366C22#6397811yescharacteristic
367C4—21no—
368C4—41no—
369C4—241no—
370C4#6382911yescharacteristic
371C4C2×#371711yescharacteristic
372C4#6393411yescharacteristic
373C4#6393511yescharacteristic
374C3—21no—
375C3#7084811yescharacteristic, complemented
376C3#7113411yescharacteristic, complemented
377C2—42no—
378C2—1441no—
379C2#1059117711yescharacteristic
380C2#1059147111yescharacteristic
381C2#1059167711yescharacteristic
subgroupG/H
centerC22#63978
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×D4C22
socleC22×C32#121
prime radical#10592714C2
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
2. C3×D4×C3⋊C8C2semidirect
3. C3×#5008C2semidirect
4. #10590281C2semidirect
5. #10589097C2semidirect
6. #10589095C2semidirect
7. #10589091C2semidirect
31. D4×C3⋊C8D3semidirect
32. #5008D3semidirect
322. C32#1677semidirect
375. C3#70848semidirect
376. C3#71134semidirect

Maximal subgroups

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

subgroupindex
#105927142
C3×D4×C3⋊C82
C3×#50082
#105902812
#105890972
#105890952
#105890912
#711343
#708483