Finite Group Databasebeta

← #11779180

Subgroups — #11779180

Order 1152.

452 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 90 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#10593860C211yesmaximal, characteristic, complemented
2C3×#4848C211yesmaximal, characteristic
3#10590364C211yesmaximal, characteristic
4#10590273C211yesmaximal, characteristic
5#10589348C211yesmaximal, characteristic, complemented
6C3×#4484C211yesmaximal, characteristic, complemented
7#10589084C211yesmaximal, characteristic, complemented
8#71034—31nomaximal
9#68252—31nomaximal
10#64078C2211yescharacteristic
11C2×C3×#204—21no—
12C3×#874C2211yescharacteristic
13C3×C4×Dic6C2211yescharacteristic
14C3×C4×Dic6C2211yescharacteristic
15#63869—21no—
16#63866—21no—
17#63845—22no—
18#63844—21no—
19Dic3×Dic6—21no—
20C2×#3715—21no—
21C32×C4⋊C8C2211yescharacteristic
22C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
23C3×#821—21no—
24C3×C4×C3⋊C8C2211yescharacteristic
25#63563—22no—
26#63562—21no—
27#5570—31no—
28#5567—31no—
29C3×#460—31no—
30#5075—31no—
31#5070—31no—
32#5027—31no—
33#4848D311yescharacteristic
34#4694—31no—
35C3×Q8⋊C8—31no—
36#4535—31no—
37#4484D311yescharacteristic, complemented
38#4482—31no—
39#4482—31no—
40#4482—61no—
41#4456—31no—
42C2×#634—21no—
43C2×C3×D12—21no—
44C2×C3×D12—21no—
45C2×C3×D12—21no—
46C2×C3×Dic6D411yescharacteristic
47C2×C3×Dic6D411yescharacteristic
48C2×C32×C8—21no—
49C32×C42C2311yescharacteristic
50C4⋊(C3⋊Dic3)—21no—
51C4⋊(C3⋊Dic3)D412yes—
52C2×C3⋊(C3⋊C8)—21no—
53C3×C4⋊Dic3D411yescharacteristic
54C3×C4⋊Dic3D411yescharacteristic
55C3×Dic3⋊C4—21no—
56C3×Dic3⋊C4—21no—
57C3×C4×Dic3—21no—
58C3×C4×Dic3—21no—
59C2×C3×C3⋊C8—21no—
60C3×#204—42no—
61#3724—22no—
62Dic3⋊Dic3—22no—
63Dic3⋊Dic3—22no—
64Dic32—22no—
65#3715—42no—
66#1626—91noSylow
67C2×C3×SD16—61no—
68C3×#127—31no—
69C3×C4×Q8—31no—
70C3×C4×Q8—31no—
71Q8×Dic3—61no—
72#944—61no—
73C2×#215—61no—
74C2×#214—61no—
75C2×#204—21no—
76#890—61no—
77#890—62no—
78#889—62no—
79#887—61no—
80#874C2×D311yescharacteristic
81#870—61no—
82#869—31no—
83#869—31no—
84#869—61no—
85#869—61no—
86C4×Dic6—61no—
87C4×Dic6—61no—
88C4×Dic6C2×D311yescharacteristic
89C4×Dic6C2×D311yescharacteristic
90C3×C4⋊C8—21no—
91C3×C4⋊C8C2×D311yescharacteristic
92C3×C4⋊C8C2×D311yescharacteristic
93C3×#102—61no—
94C3×C4×C8—31no—
95#832—62no—
96#832—61no—
97#821—21no—
98#821—62no—
99#809—61no—
100C4⋊(C3⋊C8)—31no—
101C4⋊(C3⋊C8)—31no—
102C4⋊(C3⋊C8)—61no—
103C4×C3⋊C8C2×D311yescharacteristic
104C22×C3×D3—41no—
105C2×C32×C4C2×D411yescharacteristic
106C2×C32×C4C2×D411yescharacteristic
107C2×C32×C4C2×D411yescharacteristic
108C2×C3⋊Dic3—22no—
109#634—41no—
110#634—41no—
111C2×C3×Dic3—21no—
112C2×C3×Dic3—21no—
113C2×C3×Dic3—21no—
114C2×C3×Dic3—21no—
115C3×D12—42no—
116C3×D12—41no—
117C3×D12—41no—
118C3×D12—41no—
119C3×D12—41no—
120C3×Dic6—21no—
121C3×Dic6—21no—
122C3×Dic6—21no—
123C3×Dic6SD1612yescomplemented
124C32×C8—41no—
125C3⋊(C3⋊C8)—41no—
126C3×C3⋊C8—41no—
127#557—91no—
128#486—91no—
129#460—31no—
130#460—91no—
131#332—91no—
132Q8⋊C8—31no—
133Q8⋊C8—91no—
134C2×C3×Q8—31no—
135C2×C3×Q8—31no—
136C2×C3×D4—61no—
137C2×C3×D4—61no—
138C2×C3×D4—61no—
139C2×D12—21no—
140C2×D12—21no—
141C2×D12—21no—
142C2×Dic6—61no—
143C2×Dic6—61no—
144C2×Dic6—121no—
145C2×Dic6D1211yescharacteristic
146C2×Dic6#6711yescharacteristic
147C3×SD16—122no—
148C2×C3×C8—21no—
149C2×C3×C8—21no—
150C2×C3×C8—41no—
151C2×C3×C8—61no—
152C3×C4⋊C4—31no—
153C3×C4⋊C4—31no—
154C3×C4⋊C4—61no—
155C3×C4⋊C4—61no—
156C3×C42—21no—
157C3×C42—61no—
158C3×C42—61no—
159C3×C42C22×D311yescharacteristic
160C3×C42C22×D311yescharacteristic
161#215—122no—
162#214—122no—
163C4⋊Dic3—32no—
164C4⋊Dic3—32no—
165C4⋊Dic3—62no—
166C4⋊Dic3—62no—
167C4⋊Dic3—62no—
168C4⋊Dic3—61no—
169C4⋊Dic3—61no—
170C4⋊Dic3—121no—
171C4⋊Dic3D1211yescharacteristic
172C4⋊Dic3#6711yescharacteristic
173Dic3⋊C4—21no—
174Dic3⋊C4—21no—
175Dic3⋊C4—62no—
176Dic3⋊C4—62no—
177Dic3⋊C4—62no—
178Dic3⋊C4—62no—
179C4×Dic3—21no—
180C4×Dic3—21no—
181C4×Dic3—62no—
182C4×Dic3—62no—
183C2×C3⋊C8—21no—
184C2×C3⋊C8—61no—
185C2×C3⋊C8—61no—
186C2×C3⋊C8—121no—
187#204—42no—
188C22×C32#12011yescharacteristic
189C2×C3×D3—81no—
190C2×C3×D3—81no—
191C2×C3×D3—81no—
192C32×C4—21no—
193C32×C4C2×SD1611yescharacteristic
194C32×C4#13511yescharacteristic
195C32×C4AGL(1,ℤ/8)11yescharacteristic
196C32×C4#13711yescharacteristic
197C3⋊Dic3—42no—
198C3×Dic3—22no—
199C3×Dic3—41no—
200C3×Dic3—41no—
201C3×Dic3—41no—
202C2×SD16—61no—
203C2×SD16—181no—
204C4⋊Q8—91no—
205C4⋊Q8—181no—
206#127—31no—
207#125—181no—
208#125—182no—
209C4×Q8—31no—
210C4×Q8—31no—
211C4×Q8—181no—
212C4×Q8—181no—
213C4⋊C8—91no—
214C4⋊C8D3211yescharacteristic
215#102—61no—
216#102—181no—
217#102—182no—
218C4×C8—31no—
219C23×C3—121no—
220C22×D3—41no—
221C3×Q8—32no—
222C3×Q8—61no—
223C3×Q8—61no—
224C3×Q8—61no—
225C3×D4—122no—
226C3×D4—121no—
227C3×D4—121no—
228C3×D4—121no—
229C3×D4—121no—
230C2×C3×C4—21no—
231C2×C3×C4—21no—
232C2×C3×C4—21no—
233C2×C3×C4—61no—
234C2×C3×C4—61no—
235C2×C3×C4—61no—
236C2×C3×C4—61no—
237C2×C3×C4C2×D1211yescharacteristic
238C2×C3×C4D3×D411yescharacteristic
239C2×C3×C4D3×D411yescharacteristic
240C2×C3×C4D3×D411yescharacteristic
241C2×C3×C4D3×D411yescharacteristic
242C2×C3×C4C2×#6711yescharacteristic
243C2×Dic3—21no—
244C2×Dic3—21no—
245C2×Dic3—21no—
246C2×Dic3—21no—
247C2×Dic3—62no—
248C2×Dic3—62no—
249C2×Dic3—122no—
250D12—42no—
251D12—41no—
252D12—41no—
253D12—41no—
254D12—41no—
255Dic6—21no—
256Dic6—21no—
257Dic6—21no—
258Dic6—121no—
259Dic6—121no—
260Dic6—121no—
261Dic6—121no—
262Dic6—241no—
263Dic6—241no—
264Dic6#20412yescomplemented
265C3×C8—41no—
266C3×C8—41no—
267C3×C8—81no—
268C3×C8—121no—
269C3⋊C8—41no—
270C3⋊C8—121no—
271C3⋊C8—121no—
272C3⋊C8—241no—
273C2×C32#44811yescharacteristic
274C2×C32#44911yescharacteristic
275C2×C32#45411yescharacteristic
276C3×D3—161no—
277C2×Q8—31no—
278C2×Q8—31no—
279C2×Q8—181no—
280C2×D4—61no—
281C2×D4—61no—
282C2×D4—61no—
283SD16—122no—
284SD16—362no—
285C2×C8—21no—
286C2×C8—61no—
287C2×C8—181no—
288C4⋊C4—31no—
289C4⋊C4—31no—
290C4⋊C4—61no—
291C4⋊C4—61no—
292C4⋊C4—92no—
293C4⋊C4—182no—
294C4⋊C4—182no—
295C4⋊C4—182no—
296C4⋊C4—181no—
297C42—61no—
298C42—61no—
299C42—182no—
300C42C2×D3211yescharacteristic
301C22×C3—21no—
302C22×C3—241no—
303C22×C3—241no—
304C22×C3—241no—
305C22×C3#88211yescharacteristic
306C22×C3#93711yescharacteristic
307C2×D3—81no—
308C2×D3—81no—
309C2×D3—81no—
310C3×C4—21no—
311C3×C4—21no—
312C3×C4—21no—
313C3×C4—21no—
314C3×C4—21no—
315C3×C4—21no—
316C3×C4—41no—
317C3×C4—62no—
318C3×C4—121no—
319C3×C4—121no—
320C3×C4—121no—
321C3×C4C2×#20411yescharacteristic
322C3×C4#90911yescharacteristic
323C3×C4D3×SD1611yescharacteristic
324C3×C4#91411yescharacteristic
325C3×C4#91511yescharacteristic
326C3×C4#91911yescharacteristic
327C3×C4#93211yescharacteristic
328C3×C4#95011yescharacteristic
329Dic3—22no—
330Dic3—41no—
331Dic3—41no—
332Dic3—41no—
333Dic3—122no—
334Dic3—122no—
335Dic3—242no—
336C32#162611yescharacteristic, complemented, Sylow
337C23—121no—
338Q8—32no—
339Q8—61no—
340Q8—61no—
341Q8—61no—
342Q8—361no—
343Q8—361no—
344D4—122no—
345D4—121no—
346D4—121no—
347D4—121no—
348D4—121no—
349C2×C4—61no—
350C2×C4—61no—
351C2×C4—61no—
352C2×C4—61no—
353C2×C4—182no—
354C2×C4D3×D1211yescharacteristic
355C2×C4#380211yescharacteristic
356C2×C4D3×#6711yescharacteristic
357C8—41no—
358C8—121no—
359C8—361no—
360C2×C3—21no—
361C2×C3—21no—
362C2×C3—21no—
363C2×C3—481no—
364C2×C3#473811yescharacteristic
365C2×C3#481011yescharacteristic
366C2×C3#482711yescharacteristic
367C2×C3#503711yescharacteristic
368C2×C3#517011yescharacteristic
369C2×C3#520111yescharacteristic
370D3—161no—
371C22—241no—
372C22—241no—
373C22—241no—
374C22#6392211yescharacteristic
375C4—21no—
376C4—62no—
377C4—121no—
378C4—121no—
379C4—121no—
380C4—362no—
381C4D3×#20411yescharacteristic
382C4#6380011yescharacteristic
383C4#6393411yescharacteristic
384C4#6394911yescharacteristic
385C3—21no—
386C3#6825211yescharacteristic, complemented
387C3#7103411yescharacteristic, complemented
388C2—481no—
389C2#1059061511yescharacteristic
390C2#1059082211yescharacteristic
391C2#1059101911yescharacteristic
subgroupG/H
centerC22#63922
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#120
prime radicalC3×#874C22
hypercenterC4⋊C8D32
hypocenterC32#1626
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
1. #10593860C2semidirect
5. #10589348C2semidirect
6. C3×#4484C2semidirect
7. #10589084C2semidirect
37. #4484D3semidirect
123. C3×Dic6SD16semidirect
264. Dic6#204semidirect
336. C32#1626semidirect
386. C3#68252semidirect
387. C3#71034semidirect

Maximal subgroups

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

subgroupindex
#105938602
C3×#48482
#105903642
#105902732
#105893482
C3×#44842
#105890842
#710343
#682523