Finite Group Databasebeta

← #11779788

Subgroups — #11779788

Order 1152.

459 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 459 conjugacy classes of subgroups — too many to draw. Only its 86 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#10593951C211yesmaximal, characteristic
2C3×#4851C211yesmaximal, characteristic, complemented
3#10590388C211yesmaximal, characteristic, complemented
4#10590277C211yesmaximal, characteristic
5#10589350C211yesmaximal, characteristic, complemented
6C3×#4485C211yesmaximal, characteristic
7#10589083C211yesmaximal, characteristic, complemented
8#71128—31nomaximal
9#68406—31nomaximal
10C4×#634C2211yescharacteristic
11C3×#874C2211yescharacteristic
12C3×#869C2211yescharacteristic
13C3×C4×Dic6C2211yescharacteristic
14#63898—21no—
15Dic3×D12—21no—
16#63884—22no—
17#63863—21no—
18#63860—21no—
19C2×#3719—21no—
20C32×C4⋊C8C2211yescharacteristic
21C4×C3⋊(C3⋊C8)C2211yescharacteristic
22C3×#817—21no—
23C3×#816—21no—
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25#63566—21no—
26#63562—22no—
27#5713—31no—
28#5585—31no—
29C3×#475—31no—
30#5090—31no—
31#5088—31no—
32#5070—31no—
33#4851D311yescharacteristic, complemented
34#4849—31no—
35C3×#331—31no—
36#4535—31no—
37#4485D311yescharacteristic
38#4484—31no—
39#4484—31no—
40#4484—31no—
41#4484—61no—
42C2×#634D411yescharacteristic
43C2×C3×D12—21no—
44C2×C3×D12—21no—
45C2×C3×D12D412yes—
46C2×C3×Dic6—21no—
47C2×C3×Dic6D411yescharacteristic
48C2×D3×Dic3—22no—
49C2×C32×C8—21no—
50C32×C42C2311yescharacteristic
51C4⋊(C3⋊Dic3)D411yescharacteristic
52#3750—21no—
53C4×C3⋊Dic3—21no—
54C2×C3⋊(C3⋊C8)—21no—
55C3×C4⋊Dic3—21no—
56C3×C4⋊Dic3—21no—
57C3×C4⋊Dic3D411yescharacteristic
58C3×Dic3⋊C4—21no—
59C3×C4×Dic3—21no—
60C2×C3×C3⋊C8—21no—
61(C2×D3)⋊Dic3—22no—
62(C2×D3)⋊Dic3—22no—
63(C2×D3)⋊Dic3—22no—
64#3719—42no—
65#1640—91noSylow
66C3×C4⋊Q8—31no—
67C3×#127—31no—
68C3×C4×Q8—31no—
69#947—61no—
70C2×#216—61no—
71#936—61no—
72#936—61no—
73#935—62no—
74D4×Dic3—61no—
75D4×Dic3—61no—
76C2×Dic12—61no—
77#894—62no—
78#893—61no—
79#875—61no—
80#874C2×D311yescharacteristic
81C4×D12—61no—
82#869C2×D311yescharacteristic
83C4×Dic6—31no—
84C4×Dic6—31no—
85C4×Dic6—61no—
86C4×Dic6C2×D311yescharacteristic
87C3×#106—61no—
88C3×C4⋊C8—21no—
89C3×C4⋊C8—31no—
90C3×C4⋊C8C2×D311yescharacteristic
91C3×C4⋊C8C2×D311yescharacteristic
92C3×#103—61no—
93#835—61no—
94#832—62no—
95#817—21no—
96#816—21no—
97#816—61no—
98#809—62no—
99C4⋊(C3⋊C8)C2×D311yescharacteristic
100C4×C3⋊C8—31no—
101C4×C3⋊C8—31no—
102C4×C3⋊C8—61no—
103C22×C3×D3—22no—
104C2×C32×C4C2×D411yescharacteristic
105C2×C32×C4C2×D411yescharacteristic
106C2×C32×C4C2×D411yescharacteristic
107C2×C3⋊Dic3—21no—
108C2×C3⋊Dic3—21no—
109#634—21no—
110#634—21no—
111C2×C3×Dic3—21no—
112C2×C3×Dic3—21no—
113C2×C3×Dic3—41no—
114C3×D12—42no—
115C3×D12—41no—
116C3×D12—41no—
117C3×D12—41no—
118C3×D12—41no—
119C3×Dic6—21no—
120C3×Dic6—21no—
121C3×Dic6—41no—
122C3×Dic6—41no—
123D3×Dic3—82no—
124C32×C8—41no—
125C3⋊(C3⋊C8)—41no—
126C3×C3⋊C8—41no—
127#559—91no—
128#486—91no—
129#475—31no—
130#462—91no—
131#331—31no—
132Q8⋊C8—91no—
133Q8⋊C8—91no—
134C2×C3×Q8—31no—
135C2×C3×Q8—61no—
136C2×C3×D4—32no—
137C2×C3×D4—61no—
138C2×C3×D4—61no—
139C22×Dic3—62no—
140C2×D12—21no—
141C2×D12—21no—
142C2×D12D1212yes—
143C2×C4×D3—62no—
144C2×Dic6—21no—
145C2×Dic6—31no—
146C2×Dic6—31no—
147C2×Dic6—61no—
148C2×Dic6#6711yescharacteristic
149C2×C3×C8—21no—
150C2×C3×C8—21no—
151C2×C3×C8—41no—
152C2×C3×C8—61no—
153C3×C4⋊C4—31no—
154C3×C4⋊C4—61no—
155C3×C4⋊C4—61no—
156C3×C4⋊C4—61no—
157C3×C42—21no—
158C3×C42—61no—
159C3×C42C22×D311yescharacteristic
160C3×C42C22×D311yescharacteristic
161#217—62no—
162#217—62no—
163#217—62no—
164#216—122no—
165(C2×D3)⋊C4—62no—
166(C2×D3)⋊C4—62no—
167(C2×D3)⋊C4—62no—
168C4⋊Dic3—21no—
169C4⋊Dic3—21no—
170C4⋊Dic3—31no—
171C4⋊Dic3—31no—
172C4⋊Dic3—61no—
173C4⋊Dic3#6711yescharacteristic
174Dic3⋊C4—21no—
175Dic3⋊C4—61no—
176Dic3⋊C4—61no—
177Dic3⋊C4—121no—
178C4×Dic3—21no—
179C4×Dic3—61no—
180C4×Dic3—61no—
181C4×Dic3—121no—
182C2×C3⋊C8—21no—
183C2×C3⋊C8—61no—
184C2×C3⋊C8—61no—
185C2×C3⋊C8—121no—
186Dic12—122no—
187C22×C32#12011yescharacteristic
188C2×C3×D3—42no—
189C2×C3×D3—42no—
190C2×C3×D3—42no—
191C32×C4—21no—
192C32×C4#13511yescharacteristic
193C32×C4#13511yescharacteristic
194C32×C4AGL(1,ℤ/8)11yescharacteristic
195C32×C4#13711yescharacteristic
196C3⋊Dic3—41no—
197C3⋊Dic3—41no—
198C3×Dic3—41no—
199C3×Dic3—41no—
200C3×Dic3—81no—
201C2×Q16—181no—
202C4⋊Q8—31no—
203#127—31no—
204#124—181no—
205#124—181no—
206#123—182no—
207C4×Q8—31no—
208C4×Q8—91no—
209C4×D4—181no—
210C4×D4—181no—
211#106—61no—
212C4⋊C8—31no—
213C4⋊C8D3211yescharacteristic
214#103—61no—
215#103—181no—
216#102—182no—
217C4×C8—91no—
218C23×C3—62no—
219C22×D3—22no—
220C3×Q8—61no—
221C3×Q8—61no—
222C3×Q8—121no—
223C3×Q8—121no—
224C3×D4—122no—
225C3×D4—121no—
226C3×D4—121no—
227C3×D4—121no—
228C3×D4—121no—
229C2×C3×C4—21no—
230C2×C3×C4—21no—
231C2×C3×C4—21no—
232C2×C3×C4—61no—
233C2×C3×C4—61no—
234C2×C3×C4—121no—
235C2×C3×C4C2×D1211yescharacteristic
236C2×C3×C4D3×D411yescharacteristic
237C2×C3×C4D3×D411yescharacteristic
238C2×C3×C4D3×D411yescharacteristic
239C2×C3×C4D3×D411yescharacteristic
240C2×C3×C4C2×#6711yescharacteristic
241C2×Dic3—21no—
242C2×Dic3—21no—
243C2×Dic3—41no—
244C2×Dic3—61no—
245C2×Dic3—61no—
246C2×Dic3—61no—
247C2×Dic3—61no—
248C2×Dic3—121no—
249C2×Dic3—121no—
250C2×Dic3—242no—
251D12—42no—
252D12—41no—
253D12—41no—
254D12—41no—
255D12—41no—
256C4×D3—242no—
257Dic6—21no—
258Dic6—21no—
259Dic6—41no—
260Dic6—41no—
261Dic6—62no—
262Dic6—61no—
263Dic6—61no—
264Dic6—61no—
265Dic6—61no—
266Dic6—121no—
267C3×C8—41no—
268C3×C8—41no—
269C3×C8—81no—
270C3×C8—121no—
271C3⋊C8—41no—
272C3⋊C8—121no—
273C3⋊C8—121no—
274C3⋊C8—122no—
275C2×C32#44911yescharacteristic
276C2×C32#45211yescharacteristic
277C2×C32#45511yescharacteristic
278C3×D3—82no—
279C2×Q8—31no—
280C2×Q8—61no—
281C2×Q8—91no—
282C2×D4—32no—
283C2×D4—61no—
284C2×D4—61no—
285C22×C4—182no—
286Q16—362no—
287C2×C8—21no—
288C2×C8—61no—
289C2×C8—181no—
290C4⋊C4—31no—
291C4⋊C4—61no—
292C4⋊C4—61no—
293C4⋊C4—61no—
294C4⋊C4—91no—
295C4⋊C4—181no—
296C22⋊C4—182no—
297C22⋊C4—182no—
298C22⋊C4—182no—
299C42—61no—
300C42—181no—
301C42C2×D3211yescharacteristic
302C22×C3—21no—
303C22×C3—122no—
304C22×C3—122no—
305C22×C3—122no—
306C22×C3#88211yescharacteristic
307C22×C3#93711yescharacteristic
308C2×D3—42no—
309C2×D3—42no—
310C2×D3—42no—
311C3×C4—21no—
312C3×C4—21no—
313C3×C4—21no—
314C3×C4—21no—
315C3×C4—21no—
316C3×C4—21no—
317C3×C4—41no—
318C3×C4—121no—
319C3×C4—121no—
320C3×C4—241no—
321C3×C4#91111yescharacteristic
322C3×C4#91211yescharacteristic
323C3×C4#91411yescharacteristic
324C3×C4#91511yescharacteristic
325C3×C4#91611yescharacteristic
326C3×C4#91611yescharacteristic
327C3×C4#94211yescharacteristic
328C3×C4#95011yescharacteristic
329Dic3—41no—
330Dic3—41no—
331Dic3—81no—
332Dic3—122no—
333Dic3—121no—
334Dic3—121no—
335Dic3—121no—
336Dic3—121no—
337Dic3—241no—
338C32#164011yescharacteristic, complemented, Sylow
339C23—62no—
340Q8—61no—
341Q8—61no—
342Q8—121no—
343Q8—121no—
344Q8—181no—
345Q8—181no—
346D4—122no—
347D4—121no—
348D4—121no—
349D4—121no—
350D4—121no—
351C2×C4—61no—
352C2×C4—61no—
353C2×C4—121no—
354C2×C4—181no—
355C2×C4—181no—
356C2×C4—722no—
357C2×C4D3×D1211yescharacteristic
358C2×C4#380211yescharacteristic
359C2×C4D3×#6711yescharacteristic
360C8—41no—
361C8—121no—
362C8—361no—
363C2×C3—21no—
364C2×C3—21no—
365C2×C3—21no—
366C2×C3—242no—
367C2×C3#474611yescharacteristic
368C2×C3#478111yescharacteristic
369C2×C3#478311yescharacteristic
370C2×C3#504711yescharacteristic
371C2×C3#517211yescharacteristic
372C2×C3#520211yescharacteristic
373D3—82no—
374C22—122no—
375C22—122no—
376C22—122no—
377C22#6392211yescharacteristic
378C4—21no—
379C4—121no—
380C4—121no—
381C4—241no—
382C4—361no—
383C4—361no—
384C4#6379811yescharacteristic
385C4#6380911yescharacteristic
386C4#6393311yescharacteristic
387C4#6394611yescharacteristic
388C3—21no—
389C3#6840611yescharacteristic, complemented
390C3#7112811yescharacteristic, complemented
391C2—242no—
392C2#1059061411yescharacteristic
393C2#1059096411yescharacteristic
394C2#1059101211yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#120
prime radicalC3×#874C22
hypercenterC4⋊C8D32
hypocenterC32#1640
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. C3×#4851C2semidirect
3. #10590388C2semidirect
5. #10589350C2semidirect
7. #10589083C2semidirect
33. #4851D3semidirect
338. C32#1640semidirect
389. C3#68406semidirect
390. C3#71128semidirect

Maximal subgroups

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

subgroupindex
#105939512
C3×#48512
#105903882
#105902772
#105893502
C3×#44852
#105890832
#711283
#684063