Finite Group Databasebeta

← #11781262

Subgroups — #11781262

Order 1152.

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

normal subgroups only

This group has 422 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#10592542C211yesmaximal, characteristic
2#10590327C211yesmaximal, characteristic, complemented
3#10590300C211yesmaximal, characteristic, complemented
4#10590281C211yesmaximal, characteristic, complemented
5C3×#4481C211yesmaximal, characteristic, complemented
6C3×#4480C211yesmaximal, characteristic, complemented
7#10589091C211yesmaximal, characteristic, complemented
8#68538—31nomaximal
9#68498—31nomaximal
10C2×#3745—21no—
11#64083C2211yescharacteristic
12C4×C4⋊(C3⋊D3)C2211yescharacteristic
13C3×#869C2211yescharacteristic
14C2×#3710—21no—
15C32×C4⋊C8C2211yescharacteristic
16#63648—21no—
17C3×C4⋊(C3⋊C8)C2211yescharacteristic
18C3×C4⋊(C3⋊C8)C2211yescharacteristic
19C3×C4×C3⋊C8C2211yescharacteristic
20#63573—21no—
21#63564—21no—
22#63564—21no—
23#63564—21no—
24#63557—21no—
25#5088—31no—
26#5084—31no—
27#4843—31no—
28#4843—31no—
29#4843—61no—
30#4842—31no—
31#4834—31no—
32#4694—31no—
33C8×D12—31no—
34C3×#334—31no—
35C3×#333—31no—
36#4485—31no—
37#4485—31no—
38#4481D311yescharacteristic, complemented
39#4480D311yescharacteristic, complemented
40C2×C4⋊(C3⋊D3)—21no—
41C2×C4⋊(C3⋊D3)—21no—
42C2×C4⋊(C3⋊D3)—21no—
43C2×C4⋊(C3⋊D3)D411yescharacteristic
44C2×C4×C3⋊D3—21no—
45C2×C3×Dic6—21no—
46C2×C32×C8—21no—
47C32×C42C2311yescharacteristic
48#3752—21no—
49C4⋊(C3⋊Dic3)D411yescharacteristic
50#3745—42no—
51C3×C4⋊Dic3—21no—
52C3×C4⋊Dic3—21no—
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8D411yescharacteristic
56C2×C3×C3⋊C8D411yescharacteristic
57#3710—42no—
58#1677—91noSylow
59C3×C4⋊Q8—31no—
60C2×D24—61no—
61C2×D24—61no—
62C2×D24—62no—
63C2×D3×C8—61no—
64C2×D3×C8—61no—
65#874—31no—
66#874—31no—
67#874—61no—
68C4×D12—31no—
69C4×D12—31no—
70C4×D12—61no—
71#869C2×D311yescharacteristic
72C3×C4⋊C8—21no—
73C3×C4⋊C8—31no—
74C3×C4⋊C8—31no—
75C3×C4⋊C8C2×D311yescharacteristic
76C3×C4⋊C8C2×D311yescharacteristic
77C3×C4×C8—31no—
78#821—61no—
79#821—61no—
80#821—61no—
81#821—61no—
82#821—61no—
83#821—62no—
84(C2×D3)⋊C8—61no—
85(C2×D3)⋊C8—61no—
86#817—61no—
87#809—61no—
88#809—61no—
89#809—61no—
90#808—61no—
91C4⋊(C3⋊C8)C2×D311yescharacteristic
92C4⋊(C3⋊C8)C2×D311yescharacteristic
93C4×C3⋊C8C2×D311yescharacteristic
94C22×C3⋊D3—21no—
95C22×C3⋊D3—41no—
96C2×C32×C4C2×D411yescharacteristic
97C2×C32×C4C2×D411yescharacteristic
98C2×C32×C4#4111yescharacteristic
99C2×C3⋊Dic3—21no—
100C4⋊(C3⋊D3)—21no—
101C4⋊(C3⋊D3)—41no—
102C4⋊(C3⋊D3)—41no—
103C4⋊(C3⋊D3)—41no—
104C4⋊(C3⋊D3)—41no—
105C4⋊(C3⋊D3)—81no—
106C4⋊(C3⋊D3)SD1612yes—
107C4×C3⋊D3—41no—
108C4×C3⋊D3—41no—
109C2×C3×Dic3—41no—
110C3×Dic6—81no—
111C32×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—91no—
119C8×D4—91no—
120#334—31no—
121#333—31no—
122#331—91no—
123C2×C3×Q8—61no—
124C2×D12—31no—
125C2×D12—31no—
126C2×D12—61no—
127C2×D12—62no—
128C2×D12—61no—
129C2×D12—61no—
130C2×D12—61no—
131C2×D12—61no—
132C2×D12—61no—
133C2×D12—61no—
134C2×D12—121no—
135C2×D12—121no—
136C2×C4×D3—61no—
137C2×C4×D3—61no—
138C2×C4×D3—121no—
139C2×Dic6—21no—
140C2×C3×C8—22no—
141C2×C3×C8—21no—
142C2×C3×C8—21no—
143C2×C3×C8—31no—
144C2×C3×C8—31no—
145C2×C3×C8—61no—
146C2×C3×C8—61no—
147C3×C4⋊C4—61no—
148C3×C4⋊C4—61no—
149C3×C42—21no—
150C3×C42C22×D311yescharacteristic
151C3×C42C22×D311yescharacteristic
152(C2×D3)⋊C4—61no—
153(C2×D3)⋊C4—61no—
154(C2×D3)⋊C4—121no—
155C4⋊Dic3—21no—
156C4⋊Dic3—21no—
157C4⋊Dic3—31no—
158C4⋊Dic3—31no—
159C4⋊Dic3—61no—
160C2×C3⋊C8—21no—
161C2×C3⋊C8—21no—
162C2×C3⋊C8D1211yescharacteristic
163C2×C3⋊C8D1211yescharacteristic
164D24—122no—
165D24—122no—
166D24—124no—
167D3×C8—122no—
168D3×C8—122no—
169C22×C32#12111yescharacteristic
170C2×C3⋊D3—22no—
171C2×C3⋊D3—41no—
172C2×C3⋊D3—41no—
173C2×C3⋊D3—81no—
174C2×C3⋊D3—81no—
175C2×C3⋊D3—81no—
176C32×C4—21no—
177C32×C4C2×SD1611yescharacteristic
178C32×C4#13511yescharacteristic
179C32×C4#13511yescharacteristic
180C32×C4AGL(1,ℤ/8)11yescharacteristic
181C3⋊Dic3—41no—
182C3×Dic3—81no—
183C2×D8—181no—
184C22×C8—181no—
185C4⋊Q8—31no—
186#127—91no—
187C4×D4—91no—
188#106—181no—
189C4⋊C8—31no—
190C4⋊C8—31no—
191C4⋊C8D3211yescharacteristic
192#102—181no—
193#102—181no—
194#102—181no—
195#102—181no—
196C22⋊C8—181no—
197C4×C8—31no—
198C22×D3—61no—
199C22×D3—61no—
200C22×D3—121no—
201C22×D3—122no—
202C22×D3—121no—
203C22×D3—121no—
204C3×Q8—241no—
205C2×C3×C4—21no—
206C2×C3×C4—21no—
207C2×C3×C4—21no—
208C2×C3×C4—121no—
209C2×C3×C4C2×D1211yescharacteristic
210C2×C3×C4#23511yescharacteristic
211C2×C3×C4D3×D411yescharacteristic
212C2×C3×C4D3×D411yescharacteristic
213C2×C3×C4D3×D411yescharacteristic
214C2×C3×C4#23911yescharacteristic
215C2×Dic3—41no—
216C2×Dic3—61no—
217C2×Dic3—61no—
218C2×Dic3—121no—
219D12—32no—
220D12—32no—
221D12—62no—
222D12—61no—
223D12—61no—
224D12—121no—
225D12—122no—
226D12—122no—
227D12—121no—
228D12—121no—
229D12—121no—
230D12—121no—
231D12—121no—
232D12—121no—
233D12—121no—
234D12—121no—
235D12—241no—
236D12—241no—
237D12—241no—
238D12—241no—
239D12—242no—
240C4×D3—121no—
241C4×D3—121no—
242C4×D3—121no—
243C4×D3—121no—
244C4×D3—241no—
245C4×D3—241no—
246Dic6—81no—
247C3×C8—42no—
248C3×C8—41no—
249C3×C8—41no—
250C3×C8—61no—
251C3×C8—61no—
252C3×C8—121no—
253C3×C8—121no—
254C3⋊C8—21no—
255C3⋊C8—21no—
256C3⋊C8—41no—
257C3⋊C8—41no—
258C2×C32#46311yescharacteristic
259C2×C32#46511yescharacteristic
260C2×C32#47211yescharacteristic
261C3⋊D3—42no—
262C3⋊D3—161no—
263C2×Q8—61no—
264C2×D4—91no—
265C2×D4—181no—
266C2×D4—181no—
267C2×D4—181no—
268C22×C4—181no—
269D8—362no—
270C2×C8—21no—
271C2×C8—31no—
272C2×C8—31no—
273C2×C8—61no—
274C2×C8—61no—
275C2×C8—362no—
276C4⋊C4—61no—
277C4⋊C4—61no—
278C4⋊C4—91no—
279C22⋊C4—181no—
280C42C2×D3211yescharacteristic
281C22×C3—21no—
282C22×C3#88411yescharacteristic
283C22×C3#89511yescharacteristic
284C2×D3—62no—
285C2×D3—62no—
286C2×D3—122no—
287C2×D3—121no—
288C2×D3—121no—
289C2×D3—121no—
290C2×D3—121no—
291C2×D3—241no—
292C2×D3—241no—
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—241no—
310C3×C4#90411yescharacteristic
311C3×C4#90811yescharacteristic
312C3×C4D3×SD1611yescharacteristic
313C3×C4D3×SD1611yescharacteristic
314C3×C4#91411yescharacteristic
315C3×C4#91611yescharacteristic
316C3×C4#91911yescharacteristic
317C3×C4#91911yescharacteristic
318Dic3—81no—
319Dic3—121no—
320Dic3—121no—
321Dic3—241no—
322C32#167711yescharacteristic, complemented, Sylow
323C23—181no—
324C23—361no—
325Q8—241no—
326D4—92no—
327D4—181no—
328D4—361no—
329D4—361no—
330D4—361no—
331D4—361no—
332D4—721no—
333C2×C4—121no—
334C2×C4—181no—
335C2×C4—361no—
336C2×C4—361no—
337C2×C4#379911yescharacteristic
338C2×C4D3×D1211yescharacteristic
339C2×C4#381111yescharacteristic
340C8—41no—
341C8—61no—
342C8—61no—
343C8—121no—
344C8—121no—
345C2×C3—21no—
346C2×C3—21no—
347C2×C3—21no—
348C2×C3#474911yescharacteristic
349C2×C3#480711yescharacteristic
350C2×C3#481911yescharacteristic
351C2×C3#484411yescharacteristic
352C2×C3#486411yescharacteristic
353C2×C3#489711yescharacteristic
354D3—122no—
355D3—122no—
356D3—242no—
357D3—482no—
358D3—481no—
359D3—481no—
360C22—182no—
361C22—361no—
362C22—361no—
363C22—721no—
364C22—721no—
365C22—721no—
366C22#6391011yescharacteristic
367C4—21no—
368C4—241no—
369C4—361no—
370C4#6379411yescharacteristic
371C4#6380811yescharacteristic
372C4#6393011yescharacteristic
373C4#6395011yescharacteristic
374C3—21no—
375C3#6849811yescharacteristic, complemented
376C3#6853811yescharacteristic, complemented
377C2—362no—
378C2—1441no—
379C2#1059052311yescharacteristic
380C2#1059077011yescharacteristic
381C2#1059098711yescharacteristic
subgroupG/H
centerC22#63910
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#121
prime radical#10592542C2
hypercenterC4⋊C8D32
hypocenterC32#1677
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #10590327C2semidirect
3. #10590300C2semidirect
4. #10590281C2semidirect
5. C3×#4481C2semidirect
6. C3×#4480C2semidirect
7. #10589091C2semidirect
38. #4481D3semidirect
39. #4480D3semidirect
322. C32#1677semidirect
375. C3#68498semidirect
376. C3#68538semidirect

Maximal subgroups

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

subgroupindex
#105925422
#105903272
#105903002
#105902812
C3×#44812
C3×#44802
#105890912
#685383
#684983