Finite Group Databasebeta

← #11780257

Subgroups — #11780257

Order 1152.

448 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 92 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
1C3×#5584C211yesmaximal, characteristic
2#10592719C211yesmaximal, characteristic, complemented
3#10590365C211yesmaximal, characteristic
4#10590311C211yesmaximal, characteristic, complemented
5C3×#4535C211yesmaximal, characteristic, complemented
6#10589093C211yesmaximal, characteristic, complemented
7#10589081C211yesmaximal, characteristic
8#71933—31nomaximal
9#68250—31nomaximal
10C32×C4×Q8C2211yescharacteristic
11#64078C2211yescharacteristic
12C3×#946—21no—
13C3×#898—22no—
14C3×#892—21no—
15C3×#875—21no—
16C3×C4×D12C2211yescharacteristic
17C3×#869C2211yescharacteristic
18C3×C4×Dic6—21no—
19C2×#3716—21no—
20#63662—21no—
21#63635—21no—
22C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4×C3⋊C8C2211yescharacteristic
25#63575—22no—
26#63567—21no—
27C3×#556—31no—
28#5584D311yescharacteristic
29#5078—31no—
30#5020—31no—
31#5020—31no—
32#5020—61no—
33#5019—31no—
34#4841—31no—
35#4682—31no—
36C3×Q8⋊C8—31no—
37#4547—31no—
38#4535D311yescharacteristic, complemented
39D4⋊(C3⋊C8)—31no—
40#4482—31no—
41#4459—31no—
42C2×C32×Q8D411yescharacteristic
43C2×#634—21no—
44C2×C3×D12D411yescharacteristic
45C2×C3×C4×D3—21no—
46C2×C3×Dic6—21no—
47C32×C4⋊C4—21no—
48C32×C4⋊C4D411yescharacteristic
49C32×C42—21no—
50C32×C42C2311yescharacteristic
51C4⋊(C3⋊Dic3)—21no—
52C4⋊(C3⋊Dic3)—21no—
53C2×C3⋊(C3⋊C8)—21no—
54C3×(C2×D3)⋊C4—22no—
55C3×(C2×D3)⋊C4—22no—
56C3×(C2×D3)⋊C4—21no—
57C3×C4⋊Dic3—21no—
58C3×C4⋊Dic3D412yes—
59C3×C4⋊Dic3D411yescharacteristic
60C3×Dic3⋊C4—22no—
61C3×C4×Dic3—22no—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64#3716—42no—
65#1650—91noSylow
66C3×C4⋊Q8—31no—
67C3×#126—62no—
68C3×#124—61no—
69C3×C22⋊Q8—61no—
70C3×C4×Q8—21no—
71C3×C4×Q8—61no—
72C3×C4×Q8C2×D311yescharacteristic
73C3×C4×Q8C2×D311yescharacteristic
74C3×C4×D4—31no—
75C3×#117—61no—
76#946—21no—
77C2×#214—61no—
78C2×#204—61no—
79#898—22no—
80#892—21no—
81#875—21no—
82C4×D12C2×D311yescharacteristic
83#869—31no—
84#869—31no—
85#869—61no—
86#869C2×D311yescharacteristic
87C4×Dic6—21no—
88C3×C4⋊C8—31no—
89C3×C4×C8—31no—
90#835—62no—
91#835—61no—
92#835—61no—
93#818—62no—
94#816—61no—
95#810—61no—
96#808—62no—
97#808—61no—
98#808—61no—
99#807—62no—
100C4⋊(C3⋊C8)—31no—
101C4⋊(C3⋊C8)—31no—
102C4⋊(C3⋊C8)—61no—
103C4⋊(C3⋊C8)C2×D311yescharacteristic
104C4×C3⋊C8C2×D311yescharacteristic
105C22×C3×D3—21no—
106C32×Q8—21no—
107C32×Q8—21no—
108C2×C32×C4—21no—
109C2×C32×C4—21no—
110C2×C32×C4C2×D411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C32×C4C2×D411yescharacteristic
113C2×C3⋊Dic3—41no—
114#634—41no—
115#634—41no—
116C2×C3×Dic3—21no—
117C2×C3×Dic3—22no—
118C3×D12—21no—
119C3×D12—21no—
120C3×C4×D3—41no—
121C3×C4×D3—41no—
122C3×Dic6—41no—
123C3×Dic6—41no—
124C3⋊(C3⋊C8)—41no—
125C3×C3⋊C8—22no—
126C3×C3⋊C8—41no—
127#556—31no—
128#500—91no—
129#475—91no—
130#461—91no—
131#332—91no—
132Q8⋊C8—31no—
133D4⋊C8—91no—
134C2×C3×Q8—21no—
135C2×C3×Q8—61no—
136C2×C3×Q8D1211yescharacteristic
137C2×C3×Q8#6711yescharacteristic
138C2×C3×D4—31no—
139C22×C3×C4—61no—
140C2×D12#6711yescharacteristic
141C2×C4×D3—21no—
142C2×Dic6—21no—
143C2×Dic6—61no—
144C2×Dic6—61no—
145C2×Dic6—121no—
146C2×C3×C8—61no—
147C2×C3×C8—61no—
148C3×C4⋊C4—21no—
149C3×C4⋊C4—21no—
150C3×C4⋊C4—21no—
151C3×C4⋊C4—32no—
152C3×C4⋊C4—31no—
153C3×C4⋊C4—41no—
154C3×C4⋊C4—62no—
155C3×C4⋊C4—61no—
156C3×C4⋊C4D1211yescharacteristic
157C3×C4⋊C4#6711yescharacteristic
158C3×C22⋊C4—62no—
159C3×C22⋊C4—62no—
160C3×C22⋊C4—61no—
161C3×C42—21no—
162C3×C42—21no—
163C3×C42—21no—
164C3×C42—41no—
165C3×C42—62no—
166C3×C42C22×D311yescharacteristic
167C3×C42C22×D311yescharacteristic
168#214—122no—
169(C2×D3)⋊C4—22no—
170(C2×D3)⋊C4—22no—
171(C2×D3)⋊C4—21no—
172C4⋊Dic3—21no—
173C4⋊Dic3—62no—
174C4⋊Dic3—61no—
175C4⋊Dic3—61no—
176C4⋊Dic3—61no—
177C4⋊Dic3—61no—
178C4⋊Dic3—121no—
179C4⋊Dic3#6711yescharacteristic
180C4⋊Dic3#6712yes—
181Dic3⋊C4—22no—
182C4×Dic3—22no—
183C2×C3⋊C8—21no—
184C2×C3⋊C8—21no—
185C2×C3⋊C8—62no—
186C2×C3⋊C8—61no—
187C2×C3⋊C8—61no—
188#204—122no—
189C22×C32#12011yescharacteristic
190C2×C3×D3—41no—
191C2×C3×D3—41no—
192C2×C3×D3—41no—
193C32×C4—21no—
194C32×C4—41no—
195C32×C4—41no—
196C32×C4#13511yescharacteristic
197C32×C4#13511yescharacteristic
198C32×C4AGL(1,ℤ/8)11yescharacteristic
199C32×C4#13711yescharacteristic
200C3⋊Dic3—81no—
201C3×Dic3—42no—
202C3×Dic3—41no—
203C2×SD16—181no—
204C4⋊Q8—31no—
205C4⋊Q8—91no—
206#126—62no—
207#124—61no—
208C22⋊Q8—61no—
209C4×Q8—61no—
210C4×Q8D3211yescharacteristic
211C4×D4—31no—
212#117—61no—
213#107—182no—
214#106—181no—
215C4⋊C8—31no—
216C4⋊C8—91no—
217#103—181no—
218#103—181no—
219C4×C8—31no—
220C23×C3—61no—
221C22×D3—21no—
222C3×Q8—22no—
223C3×Q8—21no—
224C3×Q8—21no—
225C3×Q8—21no—
226C3×Q8—21no—
227C3×Q8—41no—
228C3×Q8—121no—
229C3×Q8—121no—
230C3×D4—61no—
231C3×D4—61no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—21no—
236C2×C3×C4—21no—
237C2×C3×C4—21no—
238C2×C3×C4—21no—
239C2×C3×C4—41no—
240C2×C3×C4—41no—
241C2×C3×C4—61no—
242C2×C3×C4—62no—
243C2×C3×C4—121no—
244C2×C3×C4—121no—
245C2×C3×C4C2×D1211yescharacteristic
246C2×C3×C4D3×D411yescharacteristic
247C2×C3×C4D3×D411yescharacteristic
248C2×C3×C4C2×#6711yescharacteristic
249C2×C3×C4C2×#6711yescharacteristic
250C2×C3×C4C2×#6711yescharacteristic
251C2×Dic3—21no—
252C2×Dic3—22no—
253C2×Dic3—122no—
254C2×Dic3—121no—
255C2×Dic3—121no—
256D12—21no—
257D12—21no—
258C4×D3—41no—
259C4×D3—41no—
260Dic6—41no—
261Dic6—41no—
262Dic6—121no—
263Dic6—121no—
264Dic6—121no—
265Dic6—121no—
266Dic6—241no—
267Dic6—241no—
268C3×C8—62no—
269C3×C8—121no—
270C3⋊C8—22no—
271C3⋊C8—41no—
272C3⋊C8—122no—
273C3⋊C8—121no—
274C3⋊C8—121no—
275C2×C32#44911yescharacteristic
276C2×C32#45211yescharacteristic
277C2×C32#45611yescharacteristic
278C3×D3—81no—
279C2×Q8—61no—
280C2×Q8—181no—
281C2×Q8#62611yescharacteristic
282C2×D4—31no—
283C22×C4—61no—
284SD16—362no—
285C2×C8—61no—
286C2×C8—61no—
287C2×C8—181no—
288C4⋊C4—21no—
289C4⋊C4—31no—
290C4⋊C4—32no—
291C4⋊C4—62no—
292C4⋊C4—61no—
293C4⋊C4—181no—
294C4⋊C4—181no—
295C4⋊C4#62611yescharacteristic
296C22⋊C4—62no—
297C22⋊C4—62no—
298C22⋊C4—61no—
299C42—21no—
300C42—62no—
301C42C2×D3211yescharacteristic
302C22×C3—21no—
303C22×C3—121no—
304C22×C3—121no—
305C22×C3—121no—
306C22×C3#88211yescharacteristic
307C22×C3#95311yescharacteristic
308C2×D3—41no—
309C2×D3—41no—
310C2×D3—41no—
311C3×C4—21no—
312C3×C4—21no—
313C3×C4—21no—
314C3×C4—21no—
315C3×C4—21no—
316C3×C4—21no—
317C3×C4—41no—
318C3×C4—42no—
319C3×C4—41no—
320C3×C4—41no—
321C3×C4—41no—
322C3×C4—41no—
323C3×C4—81no—
324C3×C4—121no—
325C3×C4—122no—
326C3×C4#90411yescharacteristic
327C3×C4#90911yescharacteristic
328C3×C4#91411yescharacteristic
329C3×C4#91911yescharacteristic
330C3×C4#94911yescharacteristic
331C3×C4#95011yescharacteristic
332C3×C4#95011yescharacteristic
333C3×C4#95111yescharacteristic
334Dic3—42no—
335Dic3—41no—
336Dic3—242no—
337Dic3—241no—
338Dic3—241no—
339C32#165011yescharacteristic, complemented, Sylow
340C23—61no—
341Q8—21no—
342Q8—21no—
343Q8—121no—
344Q8—121no—
345Q8—361no—
346Q8—361no—
347D4—61no—
348D4—61no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—61no—
352C2×C4—62no—
353C2×C4—121no—
354C2×C4—121no—
355C2×C4—361no—
356C2×C4C2×#62611yescharacteristic
357C2×C4D3×#6711yescharacteristic
358C2×C4D3×#6711yescharacteristic
359C8—62no—
360C8—121no—
361C8—361no—
362C2×C3—21no—
363C2×C3—21no—
364C2×C3—21no—
365C2×C3—241no—
366C2×C3#473311yescharacteristic
367C2×C3#481011yescharacteristic
368C2×C3#482611yescharacteristic
369C2×C3#523811yescharacteristic
370C2×C3#523911yescharacteristic
371C2×C3#524611yescharacteristic
372D3—81no—
373C22—121no—
374C22—121no—
375C22—121no—
376C22#6397711yescharacteristic
377C4—21no—
378C4—41no—
379C4—41no—
380C4—122no—
381C4—121no—
382C4—721no—
383C4#6382911yescharacteristic
384C4#6383111yescharacteristic
385C4#6393911yescharacteristic
386C4#6394911yescharacteristic
387C3—21no—
388C3#6825011yescharacteristic, complemented
389C3#7193311yescharacteristic, complemented
390C2—241no—
391C2#1059117311yescharacteristic
392C2#1059158811yescharacteristic
393C2#1059168911yescharacteristic
subgroupG/H
centerC22#63977
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×Q8C22
socleC22×C32#120
prime radicalC2×C3×D12D4
hypercenterC4×Q8D32
hypocenterC32#1650
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
2. #10592719C2semidirect
4. #10590311C2semidirect
5. C3×#4535C2semidirect
6. #10589093C2semidirect
38. #4535D3semidirect
339. C32#1650semidirect
388. C3#68250semidirect
389. C3#71933semidirect

Maximal subgroups

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

subgroupindex
C3×#55842
#105927192
#105903652
#105903112
C3×#45352
#105890932
#105890812
#719333
#682503