Finite Group Databasebeta

← #11779964

Subgroups — #11779964

Order 1152.

448 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 96 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×#5730C211yesmaximal, characteristic
2C3×#5079C211yesmaximal, characteristic, complemented
3#10590384C211yesmaximal, characteristic, complemented
4#10590269C211yesmaximal, characteristic
5#10589412C211yesmaximal, characteristic, complemented
6#10589084C211yesmaximal, characteristic, complemented
7#10589081C211yesmaximal, characteristic
8#71926—31nomaximal
9#71238—31nomaximal
10C32×C4⋊Q8C2211yescharacteristic
11C3×#946—22no—
12C3×#897—21no—
13C3×#893—21no—
14C3×D3×C4⋊C4—21no—
15C3×#890—21no—
16C3×C4×D12C2211yescharacteristic
17C3×#869C2211yescharacteristic
18C3×C4×Dic6C2211yescharacteristic
19C2×#3718—21no—
20C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
21C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
22C3×#835—22no—
23C3×C4×C3⋊C8C2211yescharacteristic
24#63576—21no—
25#63565—21no—
26#63562—21no—
27C3×#554—31no—
28#5730D311yescharacteristic
29C3×#487—31no—
30#5090—31no—
31#5087—31no—
32#5079D311yescharacteristic, complemented
33#5031—31no—
34#5007—31no—
35#4546—31no—
36#4546—31no—
37#4546—61no—
38#4535—31no—
39D4⋊(C3⋊C8)—31no—
40#4459—31no—
41#4456—31no—
42C2×C32×Q8D412yes—
43C2×C3×D12D411yescharacteristic
44C2×C3×C4×D3—21no—
45C2×C3×C4×D3—22no—
46C2×C3×Dic6—21no—
47C2×C3×Dic6D411yescharacteristic
48C32×C4⋊C4—21no—
49C32×C4⋊C4—21no—
50C32×C42C2311yescharacteristic
51C2×C3⋊(C3⋊C8)—21no—
52C2×C3⋊(C3⋊C8)—21no—
53C3×(C2×D3)⋊C4—22no—
54C3×(C2×D3)⋊C4—21no—
55C3×C4⋊Dic3—22no—
56C3×C4⋊Dic3—21no—
57C3×C4⋊Dic3—21no—
58C3×C4⋊Dic3D411yescharacteristic
59C3×C4⋊Dic3D411yescharacteristic
60C3×Dic3⋊C4—22no—
61C3×Dic3⋊C4—21no—
62C3×C4×Dic3—21no—
63C2×C3×C3⋊C8—21no—
64#3718—42no—
65#1644—91noSylow
66C3×C4⋊Q8—21no—
67C3×C4⋊Q8—31no—
68C3×C4⋊Q8C2×D311yescharacteristic
69C3×C4⋊Q8C2×D311yescharacteristic
70C3×#125—61no—
71C3×C22⋊Q8—61no—
72C3×C22⋊Q8—62no—
73C3×C4×Q8—31no—
74C3×C4×D4—31no—
75C3×C4×D4—61no—
76C2×C3×C4⋊C4—61no—
77#946—22no—
78C2×#216—61no—
79C2×#216—61no—
80#897—21no—
81#893—21no—
82D3×C4⋊C4—21no—
83#890—21no—
84C4×D12C2×D311yescharacteristic
85#869C2×D311yescharacteristic
86C4×Dic6C2×D311yescharacteristic
87C3×#103—62no—
88C3×C4×C8—31no—
89#835—22no—
90#835—61no—
91#832—61no—
92#810—61no—
93#809—61no—
94#807—61no—
95#807—61no—
96C4⋊(C3⋊C8)—31no—
97C4⋊(C3⋊C8)—31no—
98C4⋊(C3⋊C8)—31no—
99C4⋊(C3⋊C8)—31no—
100C4⋊(C3⋊C8)—61no—
101C4⋊(C3⋊C8)—61no—
102C4×C3⋊C8C2×D311yescharacteristic
103C22×C3×D3—21no—
104C32×Q8—42no—
105C2×C32×C4—22no—
106C2×C32×C4C2×D411yescharacteristic
107C2×C32×C4C2×D411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
109C2×C3×Dic3—21no—
110C2×C3×Dic3—21no—
111C2×C3×Dic3—21no—
112C2×C3×Dic3—41no—
113C3×D12—21no—
114C3×D12Q1612yescomplemented
115C3×C4×D3—41no—
116C3×C4×D3—41no—
117C3×C4×D3—82no—
118C3×Dic6—21no—
119C3×Dic6—21no—
120C3×Dic6—41no—
121C3×Dic6—41no—
122C3⋊(C3⋊C8)—41no—
123C3⋊(C3⋊C8)—41no—
124C3×C3⋊C8—41no—
125#554—31no—
126#487—31no—
127#474—91no—
128#462—91no—
129#333—91no—
130Q8⋊C8—91no—
131D4⋊C8—91no—
132C2×C3×Q8—22no—
133C2×C3×Q8—31no—
134C2×C3×Q8—61no—
135C2×C3×Q8#6712yes—
136C2×C3×Q8#6712yes—
137C2×C3×D4—31no—
138C22×C3×C4—62no—
139C22×C3×C4—61no—
140C2×D12#6711yescharacteristic
141C2×C4×D3—21no—
142C2×C4×D3—22no—
143C2×Dic6—21no—
144C2×Dic6#6711yescharacteristic
145C2×C3×C8—61no—
146C3×C4⋊C4—21no—
147C3×C4⋊C4—21no—
148C3×C4⋊C4—21no—
149C3×C4⋊C4—21no—
150C3×C4⋊C4—31no—
151C3×C4⋊C4—31no—
152C3×C4⋊C4—41no—
153C3×C4⋊C4—41no—
154C3×C4⋊C4—62no—
155C3×C4⋊C4—62no—
156C3×C4⋊C4—61no—
157C3×C4⋊C4—61no—
158C3×C4⋊C4—61no—
159C3×C22⋊C4—62no—
160C3×C22⋊C4—61no—
161C3×C42—21no—
162C3×C42—61no—
163C3×C42C22×D311yescharacteristic
164C3×C42C22×D311yescharacteristic
165#216—122no—
166#216—122no—
167(C2×D3)⋊C4—22no—
168(C2×D3)⋊C4—21no—
169C4⋊Dic3—22no—
170C4⋊Dic3—21no—
171C4⋊Dic3—21no—
172C4⋊Dic3#6711yescharacteristic
173C4⋊Dic3#6711yescharacteristic
174Dic3⋊C4—22no—
175Dic3⋊C4—21no—
176C4×Dic3—21no—
177C2×C3⋊C8—21no—
178C2×C3⋊C8—61no—
179C2×C3⋊C8—61no—
180C2×C3⋊C8—61no—
181C2×C3⋊C8—61no—
182C2×C3⋊C8—121no—
183C2×C3⋊C8—121no—
184C22×C32#12011yescharacteristic
185C2×C3×D3—22no—
186C2×C3×D3—41no—
187C2×C3×D3—41no—
188C32×C4—21no—
189C32×C4—42no—
190C32×C4C2×Q1611yescharacteristic
191C32×C4#13511yescharacteristic
192C32×C4AGL(1,ℤ/8)11yescharacteristic
193C32×C4#13711yescharacteristic
194C3×Dic3—41no—
195C3×Dic3—41no—
196C3×Dic3—41no—
197C3×Dic3—81no—
198C2×Q16—181no—
199C4⋊Q8—31no—
200C4⋊Q8D3211yescharacteristic
201#125—61no—
202C22⋊Q8—61no—
203C22⋊Q8—62no—
204C4×Q8—31no—
205C4×D4—31no—
206C4×D4—61no—
207C2×C4⋊C4—61no—
208#107—181no—
209C4⋊C8—91no—
210C4⋊C8—91no—
211#103—62no—
212#103—181no—
213#102—181no—
214C4×C8—31no—
215C23×C3—61no—
216C22×D3—21no—
217C3×Q8—42no—
218C3×Q8—42no—
219C3×Q8—61no—
220C3×Q8—61no—
221C3×Q8—82no—
222C3×Q8—121no—
223C3×Q8—121no—
224C3×D4—32no—
225C3×D4—61no—
226C2×C3×C4—22no—
227C2×C3×C4—22no—
228C2×C3×C4—21no—
229C2×C3×C4—21no—
230C2×C3×C4—21no—
231C2×C3×C4—42no—
232C2×C3×C4—61no—
233C2×C3×C4—61no—
234C2×C3×C4—61no—
235C2×C3×C4—121no—
236C2×C3×C4—121no—
237C2×C3×C4—121no—
238C2×C3×C4—242no—
239C2×C3×C4D3×D411yescharacteristic
240C2×C3×C4D3×D411yescharacteristic
241C2×C3×C4C2×#6711yescharacteristic
242C2×C3×C4C2×#6711yescharacteristic
243C2×C3×C4C2×#6711yescharacteristic
244C2×C3×C4C2×#6711yescharacteristic
245C2×Dic3—21no—
246C2×Dic3—21no—
247C2×Dic3—21no—
248C2×Dic3—41no—
249D12—21no—
250D12#21612yescomplemented
251C4×D3—41no—
252C4×D3—41no—
253C4×D3—82no—
254Dic6—21no—
255Dic6—21no—
256Dic6—41no—
257Dic6—41no—
258C3×C8—121no—
259C3⋊C8—41no—
260C3⋊C8—121no—
261C3⋊C8—121no—
262C3⋊C8—121no—
263C3⋊C8—121no—
264C3⋊C8—241no—
265C3⋊C8—241no—
266C2×C32#44911yescharacteristic
267C2×C32#45111yescharacteristic
268C2×C32#45511yescharacteristic
269C3×D3—42no—
270C2×Q8—31no—
271C2×Q8—61no—
272C2×Q8#62512yes—
273C2×D4—31no—
274C22×C4—62no—
275C22×C4—61no—
276Q16—362no—
277C2×C8—61no—
278C2×C8—181no—
279C2×C8—181no—
280C4⋊C4—21no—
281C4⋊C4—21no—
282C4⋊C4—31no—
283C4⋊C4—31no—
284C4⋊C4—62no—
285C4⋊C4—62no—
286C4⋊C4—61no—
287C4⋊C4—61no—
288C4⋊C4—61no—
289C22⋊C4—62no—
290C22⋊C4—61no—
291C42—61no—
292C42C2×D3211yescharacteristic
293C22×C3—21no—
294C22×C3—62no—
295C22×C3—121no—
296C22×C3—121no—
297C22×C3#93711yescharacteristic
298C22×C3#95311yescharacteristic
299C2×D3—22no—
300C2×D3—41no—
301C2×D3—41no—
302C3×C4—21no—
303C3×C4—21no—
304C3×C4—21no—
305C3×C4—21no—
306C3×C4—21no—
307C3×C4—21no—
308C3×C4—41no—
309C3×C4—42no—
310C3×C4—42no—
311C3×C4—82no—
312C3×C4—121no—
313C3×C4—121no—
314C3×C4—121no—
315C3×C4—241no—
316C3×C4#91411yescharacteristic
317C3×C4#91611yescharacteristic
318C3×C4D3×Q1611yescharacteristic
319C3×C4#91811yescharacteristic
320C3×C4#94211yescharacteristic
321C3×C4C2×#21611yescharacteristic
322C3×C4#94911yescharacteristic
323C3×C4#95011yescharacteristic
324Dic3—41no—
325Dic3—41no—
326Dic3—41no—
327Dic3—81no—
328C32#164411yescharacteristic, complemented, Sylow
329C23—61no—
330Q8—42no—
331Q8—61no—
332Q8—61no—
333Q8—121no—
334Q8—121no—
335D4—32no—
336D4—61no—
337C2×C4—22no—
338C2×C4—61no—
339C2×C4—61no—
340C2×C4—61no—
341C2×C4—121no—
342C2×C4—121no—
343C2×C4—121no—
344C2×C4—242no—
345C2×C4C2×#62511yescharacteristic
346C2×C4D3×#6711yescharacteristic
347C2×C4D3×#6711yescharacteristic
348C8—121no—
349C8—361no—
350C8—361no—
351C2×C3—21no—
352C2×C3—21no—
353C2×C3—21no—
354C2×C3—122no—
355C2×C3#506111yescharacteristic
356C2×C3#517211yescharacteristic
357C2×C3#518611yescharacteristic
358C2×C3#522811yescharacteristic
359C2×C3#523811yescharacteristic
360C2×C3#524211yescharacteristic
361D3—42no—
362C22—62no—
363C22—121no—
364C22—121no—
365C22#6397611yescharacteristic
366C4—21no—
367C4—42no—
368C4—121no—
369C4—121no—
370C4—121no—
371C4—241no—
372C4#6393911yescharacteristic
373C4D3×#21611yescharacteristic
374C4#6394711yescharacteristic
375C4#6394811yescharacteristic
376C3—21no—
377C3#7123811yescharacteristic, complemented
378C3#7192611yescharacteristic, complemented
379C2—122no—
380C2#1059151211yescharacteristic
381C2#1059158611yescharacteristic
382C2#1059159411yescharacteristic
subgroupG/H
centerC22#63976
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socleC22×C32#120
prime radicalC2×C3×D12D4
hypercenterC4⋊Q8D32
hypocenterC32#1644
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. C3×#5079C2semidirect
3. #10590384C2semidirect
5. #10589412C2semidirect
6. #10589084C2semidirect
32. #5079D3semidirect
114. C3×D12Q16semidirect
250. D12#216semidirect
328. C32#1644semidirect
377. C3#71238semidirect
378. C3#71926semidirect

Maximal subgroups

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

subgroupindex
C3×#57302
C3×#50792
#105903842
#105902692
#105894122
#105890842
#105890812
#719263
#712383