Finite Group Databasebeta

← #11779178

Subgroups — #11779178

Order 1152.

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

normal subgroups only

This group has 455 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#10593861C211yesmaximal, characteristic, complemented
2C3×#4694C211yesmaximal, characteristic
3#10590377C211yesmaximal, characteristic
4#10590364C211yesmaximal, characteristic
5#10589322C211yesmaximal, characteristic, complemented
6C3×#4456C211yesmaximal, characteristic, complemented
7#10589093C211yesmaximal, characteristic, complemented
8#71204—31nomaximal
9#68252—31nomaximal
10C4×#634C2211yescharacteristic
11C3×#874C2211yescharacteristic
12C3×#869C2211yescharacteristic
13C3×C4×Dic6C2211yescharacteristic
14#63872—21no—
15#63866—21no—
16#63846—22no—
17#63843—21no—
18Dic3×Dic6—21no—
19C2×#3716—21no—
20C2×#3715—21no—
21C32×C4×C8C2211yescharacteristic
22C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
23C3×#821—22no—
24C3×C4⋊(C3⋊C8)C2211yescharacteristic
25#63563—21no—
26#63562—21no—
27#5721—31no—
28#5570—31no—
29C3×#486—31no—
30#5075—31no—
31#5075—31no—
32#5027—31no—
33#4848—31no—
34#4694D311yescharacteristic
35C3×Q8⋊C8—31no—
36#4547—31no—
37#4482—31no—
38#4456—31no—
39#4456—31no—
40#4456—61no—
41#4456D311yescharacteristic, complemented
42C2×#634D411yescharacteristic
43C2×C3×D12—21no—
44C2×C3×D12—21no—
45C2×C3×D12—21no—
46C2×C3×Dic6—21no—
47C2×C3×Dic6D411yescharacteristic
48C2×C32×C8—21no—
49C32×C42C2311yescharacteristic
50C4⋊(C3⋊Dic3)D411yescharacteristic
51#3750—21no—
52C4×C3⋊Dic3—21no—
53C2×C3⋊(C3⋊C8)—21no—
54C3×C4⋊Dic3—21no—
55C3×C4⋊Dic3D411yescharacteristic
56C3×C4⋊Dic3D412yes—
57C3×Dic3⋊C4—21no—
58C3×C4×Dic3—21no—
59C2×C3×C3⋊C8—21no—
60Dic3⋊Dic3—22no—
61Dic3⋊Dic3—22no—
62Dic3⋊Dic3—22no—
63Dic32—22no—
64#3716—42no—
65#3715—42no—
66#1626—91noSylow
67C3×C4⋊Q8—31no—
68C3×#127—31no—
69C3×C4×Q8—31no—
70Q8×Dic3—61no—
71Q8×Dic3—61no—
72#944—61no—
73C2×#215—61no—
74C2×#214—61no—
75C2×#214—61no—
76C2×#204—61no—
77#890—61no—
78#890—61no—
79#890—62no—
80#889—62no—
81#887—61no—
82#874C2×D311yescharacteristic
83#869—61no—
84#869C2×D311yescharacteristic
85C4×Dic6—31no—
86C4×Dic6—31no—
87C4×Dic6—61no—
88C4×Dic6—61no—
89C4×Dic6C2×D311yescharacteristic
90C3×C4⋊C8—31no—
91C3×#102—62no—
92C3×C4×C8—21no—
93C3×C4×C8C2×D311yescharacteristic
94C3×C4×C8C2×D311yescharacteristic
95#832—61no—
96#832—61no—
97#821—22no—
98#821—61no—
99#809—61no—
100C4⋊(C3⋊C8)—31no—
101C4⋊(C3⋊C8)—31no—
102C4⋊(C3⋊C8)—61no—
103C4⋊(C3⋊C8)C2×D311yescharacteristic
104C22×C3×D3—41no—
105C2×C32×C4C2×D411yescharacteristic
106C2×C32×C4C2×D411yescharacteristic
107C2×C32×C4C2×D411yescharacteristic
108C2×C3⋊Dic3—21no—
109C2×C3⋊Dic3—21no—
110#634—21no—
111#634—21no—
112C2×C3×Dic3—21no—
113C2×C3×Dic3—22no—
114C2×C3×Dic3—21no—
115C3×D12—42no—
116C3×D12—41no—
117C3×D12—41no—
118C3×D12—41no—
119C3×D12—41no—
120C3×Dic6—21no—
121C3×Dic6—41no—
122C3×Dic6—41no—
123C3×Dic6SD1612yescomplemented
124C32×C8—41no—
125C3⋊(C3⋊C8)—41no—
126C3×C3⋊C8—41no—
127#557—91no—
128#486—31no—
129#460—91no—
130#460—91no—
131#332—91no—
132Q8⋊C8—31no—
133Q8⋊C8—91no—
134C2×C3×Q8—31no—
135C2×C3×Q8—61no—
136C2×C3×D4—61no—
137C2×C3×D4—61no—
138C2×C3×D4—61no—
139C2×D12—21no—
140C2×D12—21no—
141C2×D12—21no—
142C2×Dic6—21no—
143C2×Dic6—31no—
144C2×Dic6—31no—
145C2×Dic6—61no—
146C2×Dic6D1211yescharacteristic
147C2×C3×C8—21no—
148C2×C3×C8—21no—
149C2×C3×C8—41no—
150C2×C3×C8—61no—
151C3×C4⋊C4—31no—
152C3×C4⋊C4—32no—
153C3×C4⋊C4—61no—
154C3×C4⋊C4—61no—
155C3×C42—21no—
156C3×C42—61no—
157C3×C42C22×D311yescharacteristic
158C3×C42C22×D311yescharacteristic
159#215—122no—
160#214—122no—
161#214—122no—
162C4⋊Dic3—21no—
163C4⋊Dic3—31no—
164C4⋊Dic3—31no—
165C4⋊Dic3—61no—
166C4⋊Dic3—62no—
167C4⋊Dic3—62no—
168C4⋊Dic3—62no—
169C4⋊Dic3D1211yescharacteristic
170C4⋊Dic3#6712yes—
171Dic3⋊C4—21no—
172Dic3⋊C4—62no—
173Dic3⋊C4—62no—
174Dic3⋊C4—62no—
175Dic3⋊C4—61no—
176Dic3⋊C4—61no—
177Dic3⋊C4—121no—
178C4×Dic3—21no—
179C4×Dic3—62no—
180C4×Dic3—62no—
181C4×Dic3—61no—
182C4×Dic3—61no—
183C4×Dic3—121no—
184C2×C3⋊C8—21no—
185C2×C3⋊C8—61no—
186C2×C3⋊C8—61no—
187C2×C3⋊C8—121no—
188#204—122no—
189C22×C32#12011yescharacteristic
190C2×C3×D3—81no—
191C2×C3×D3—81no—
192C2×C3×D3—81no—
193C32×C4—21no—
194C32×C4C2×SD1611yescharacteristic
195C32×C4#13511yescharacteristic
196C32×C4AGL(1,ℤ/8)11yescharacteristic
197C32×C4#13711yescharacteristic
198C3⋊Dic3—41no—
199C3⋊Dic3—41no—
200C3×Dic3—22no—
201C3×Dic3—42no—
202C3×Dic3—41no—
203C2×SD16—181no—
204C2×SD16—181no—
205C4⋊Q8—31no—
206C4⋊Q8—181no—
207#127—31no—
208#125—182no—
209#125—181no—
210C4×Q8—31no—
211C4×Q8—91no—
212C4×Q8—181no—
213C4×Q8—181no—
214C4⋊C8—31no—
215C4⋊C8—91no—
216#102—62no—
217#102—181no—
218#102—181no—
219C4×C8D3211yescharacteristic
220C23×C3—121no—
221C22×D3—41no—
222C3×Q8—32no—
223C3×Q8—61no—
224C3×Q8—121no—
225C3×Q8—121no—
226C3×D4—122no—
227C3×D4—121no—
228C3×D4—121no—
229C3×D4—121no—
230C3×D4—121no—
231C2×C3×C4—21no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—61no—
235C2×C3×C4—62no—
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—22no—
246C2×Dic3—61no—
247C2×Dic3—61no—
248C2×Dic3—61no—
249C2×Dic3—61no—
250C2×Dic3—121no—
251C2×Dic3—121no—
252D12—42no—
253D12—41no—
254D12—41no—
255D12—41no—
256D12—41no—
257Dic6—21no—
258Dic6—41no—
259Dic6—41no—
260Dic6—62no—
261Dic6—61no—
262Dic6—61no—
263Dic6—61no—
264Dic6—61no—
265Dic6—121no—
266Dic6#20412yescomplemented
267C3×C8—41no—
268C3×C8—41no—
269C3×C8—42no—
270C3×C8—121no—
271C3⋊C8—41no—
272C3⋊C8—121no—
273C3⋊C8—121no—
274C3⋊C8—241no—
275C2×C32#44811yescharacteristic
276C2×C32#44911yescharacteristic
277C2×C32#45411yescharacteristic
278C3×D3—161no—
279C2×Q8—31no—
280C2×Q8—61no—
281C2×Q8—91no—
282C2×D4—61no—
283C2×D4—61no—
284C2×D4—61no—
285SD16—362no—
286SD16—362no—
287C2×C8—21no—
288C2×C8—61no—
289C2×C8—181no—
290C4⋊C4—31no—
291C4⋊C4—32no—
292C4⋊C4—61no—
293C4⋊C4—61no—
294C4⋊C4—91no—
295C4⋊C4—182no—
296C4⋊C4—182no—
297C4⋊C4—182no—
298C4⋊C4—181no—
299C42—61no—
300C42—182no—
301C42—181no—
302C42C2×D3211yescharacteristic
303C22×C3—21no—
304C22×C3—241no—
305C22×C3—241no—
306C22×C3—241no—
307C22×C3#88211yescharacteristic
308C22×C3#93711yescharacteristic
309C2×D3—81no—
310C2×D3—81no—
311C2×D3—81no—
312C3×C4—21no—
313C3×C4—21no—
314C3×C4—21no—
315C3×C4—21no—
316C3×C4—21no—
317C3×C4—21no—
318C3×C4—41no—
319C3×C4—62no—
320C3×C4—121no—
321C3×C4—122no—
322C3×C4C2×#20411yescharacteristic
323C3×C4#90911yescharacteristic
324C3×C4#91111yescharacteristic
325C3×C4#91211yescharacteristic
326C3×C4D3×SD1611yescharacteristic
327C3×C4#91411yescharacteristic
328C3×C4#91511yescharacteristic
329C3×C4#91911yescharacteristic
330Dic3—22no—
331Dic3—42no—
332Dic3—41no—
333Dic3—122no—
334Dic3—121no—
335Dic3—121no—
336Dic3—121no—
337Dic3—121no—
338Dic3—241no—
339C32#162611yescharacteristic, complemented, Sylow
340C23—121no—
341Q8—32no—
342Q8—61no—
343Q8—121no—
344Q8—121no—
345Q8—181no—
346Q8—181no—
347D4—122no—
348D4—121no—
349D4—121no—
350D4—121no—
351D4—121no—
352C2×C4—61no—
353C2×C4—61no—
354C2×C4—62no—
355C2×C4—181no—
356C2×C4—181no—
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—481no—
367C2×C3#473811yescharacteristic
368C2×C3#481011yescharacteristic
369C2×C3#482711yescharacteristic
370C2×C3#506211yescharacteristic
371C2×C3#515811yescharacteristic
372C2×C3#517011yescharacteristic
373D3—161no—
374C22—241no—
375C22—241no—
376C22—241no—
377C22#6392211yescharacteristic
378C4—21no—
379C4—62no—
380C4—121no—
381C4—122no—
382C4—361no—
383C4—361no—
384C4D3×#20411yescharacteristic
385C4#6379811yescharacteristic
386C4#6380011yescharacteristic
387C4#6381011yescharacteristic
388C3—21no—
389C3#6825211yescharacteristic, complemented
390C3#7120411yescharacteristic, complemented
391C2—481no—
392C2#1059040011yescharacteristic
393C2#1059082211yescharacteristic
394C2#1059096311yescharacteristic
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. #10593861C2semidirect
5. #10589322C2semidirect
6. C3×#4456C2semidirect
7. #10589093C2semidirect
41. #4456D3semidirect
123. C3×Dic6SD16semidirect
266. Dic6#204semidirect
339. C32#1626semidirect
389. C3#68252semidirect
390. C3#71204semidirect

Maximal subgroups

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

subgroupindex
#105938612
C3×#46942
#105903772
#105903642
#105893222
C3×#44562
#105890932
#712043
#682523