Finite Group Databasebeta

← #11779967

Subgroups — #11779967

Order 1152.

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

normal subgroups only

This group has 451 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×#5579C211yesmaximal, characteristic
2C3×#5031C211yesmaximal, characteristic, complemented
3#10590290C211yesmaximal, characteristic, complemented
4#10590269C211yesmaximal, characteristic
5#10589401C211yesmaximal, characteristic, complemented
6#10589095C211yesmaximal, characteristic, complemented
7#10589080C211yesmaximal, characteristic
8#71926—31nomaximal
9#71062—31nomaximal
10C32×C4×Q8C2211yescharacteristic
11C3×#946—21no—
12C2×C3×#216—21no—
13C3×#896—22no—
14C3×D3×C4⋊C4—21no—
15C3×C4×D12—21no—
16C3×C4×D12C2211yescharacteristic
17C3×#870—21no—
18C3×#869C2211yescharacteristic
19C3×#869C2211yescharacteristic
20C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
21C4×C3⋊(C3⋊C8)C2211yescharacteristic
22C3×#810—21no—
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24#63576—21no—
25#63565—22no—
26#63562—21no—
27C3×#554—31no—
28#5579D311yescharacteristic
29C3×#462—31no—
30#5093—31no—
31#5087—31no—
32#5079—31no—
33#5031D311yescharacteristic, complemented
34#5007—31no—
35#4546—31no—
36#4535—31no—
37#4535—31no—
38#4535—61no—
39D4⋊(C3⋊C8)—31no—
40#4483—31no—
41#4481—31no—
42C2×C32×Q8D411yescharacteristic
43C2×C3×D12D411yescharacteristic
44C2×C3×C4×D3—21no—
45C2×C3×C4×D3—22no—
46C2×C3×Dic6—21no—
47C2×C3×Dic6D412yes—
48C32×C4⋊C4—21no—
49C32×C4⋊C4D411yescharacteristic
50C32×C42—21no—
51C32×C42C2311yescharacteristic
52C2×C3⋊(C3⋊C8)—21no—
53C2×C3⋊(C3⋊C8)—21no—
54C3×#216—42no—
55C3×(C2×D3)⋊C4—22no—
56C3×(C2×D3)⋊C4—21no—
57C3×C4⋊Dic3—21no—
58C3×C4⋊Dic3—21no—
59C3×C4⋊Dic3—21no—
60C3×C4⋊Dic3—21no—
61C3×C4⋊Dic3D411yescharacteristic
62C3×Dic3⋊C4—22no—
63C3×Dic3⋊C4—22no—
64C2×C3×C3⋊C8—21no—
65#1644—91noSylow
66C2×C3×Q16—61no—
67C3×C4⋊Q8—31no—
68C3×C4⋊Q8—31no—
69C3×#125—61no—
70C3×C22⋊Q8—62no—
71C3×C22⋊Q8—61no—
72C3×C4×Q8—21no—
73C3×C4×Q8C2×D311yescharacteristic
74C3×C4×Q8C2×D311yescharacteristic
75C3×C4×D4—31no—
76C3×C4×D4—61no—
77C2×C3×C4⋊C4—61no—
78#946—21no—
79C2×#216—21no—
80#896—22no—
81D3×C4⋊C4—21no—
82C4×D12—21no—
83C4×D12C2×D311yescharacteristic
84#870—21no—
85#869C2×D311yescharacteristic
86#869C2×D311yescharacteristic
87C3×C4⋊C8—31no—
88C3×#103—61no—
89#835—62no—
90#832—61no—
91#810—21no—
92#810—62no—
93#809—61no—
94#807—61no—
95#807—61no—
96C4⋊(C3⋊C8)—31no—
97C4⋊(C3⋊C8)—31no—
98C4⋊(C3⋊C8)—61no—
99C4⋊(C3⋊C8)C2×D311yescharacteristic
100C4×C3⋊C8—31no—
101C4×C3⋊C8—31no—
102C4×C3⋊C8—61no—
103C22×C3×D3—21no—
104C32×Q8—21no—
105C32×Q8—21no—
106C2×C32×C4—21no—
107C2×C32×C4—21no—
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D411yescharacteristic
111C2×C3×Dic3—21no—
112C2×C3×Dic3—22no—
113C2×C3×Dic3—41no—
114C3×D12—21no—
115C3×D12Q1612yescomplemented
116C3×C4×D3—41no—
117C3×C4×D3—41no—
118C3×C4×D3—82no—
119C3×Dic6—42no—
120C3×Dic6—41no—
121C3×Dic6—41no—
122C3⋊(C3⋊C8)—41no—
123C3⋊(C3⋊C8)—41no—
124C3×C3⋊C8—41no—
125#554—31no—
126#487—91no—
127#474—91no—
128#462—31no—
129#333—91no—
130Q8⋊C8—91no—
131D4⋊C8—91no—
132C2×C3×Q8—21no—
133C2×C3×Q8—32no—
134C2×C3×Q8—61no—
135C2×C3×Q8#6711yescharacteristic
136C2×C3×Q8#6711yescharacteristic
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#6712yes—
145C3×Q16—122no—
146C2×C3×C8—61no—
147C3×C4⋊C4—21no—
148C3×C4⋊C4—21no—
149C3×C4⋊C4—21no—
150C3×C4⋊C4—31no—
151C3×C4⋊C4—41no—
152C3×C4⋊C4—62no—
153C3×C4⋊C4—62no—
154C3×C4⋊C4—61no—
155C3×C4⋊C4—61no—
156C3×C4⋊C4—61no—
157C3×C4⋊C4—61no—
158C3×C4⋊C4#6711yescharacteristic
159C3×C4⋊C4#6711yescharacteristic
160C3×C22⋊C4—62no—
161C3×C22⋊C4—61no—
162C3×C42—21no—
163C3×C42—21no—
164C3×C42—21no—
165C3×C42—41no—
166C3×C42C22×D311yescharacteristic
167C3×C42C22×D311yescharacteristic
168#216—42no—
169(C2×D3)⋊C4—22no—
170(C2×D3)⋊C4—21no—
171C4⋊Dic3—21no—
172C4⋊Dic3—21no—
173C4⋊Dic3—21no—
174C4⋊Dic3—21no—
175C4⋊Dic3#6711yescharacteristic
176Dic3⋊C4—22no—
177Dic3⋊C4—22no—
178C2×C3⋊C8—21no—
179C2×C3⋊C8—61no—
180C2×C3⋊C8—61no—
181C2×C3⋊C8—61no—
182C2×C3⋊C8—61no—
183C2×C3⋊C8—121no—
184C2×C3⋊C8—121no—
185C22×C32#12011yescharacteristic
186C2×C3×D3—22no—
187C2×C3×D3—41no—
188C2×C3×D3—41no—
189C32×C4—21no—
190C32×C4—41no—
191C32×C4—41no—
192C32×C4C2×Q1611yescharacteristic
193C32×C4#13511yescharacteristic
194C32×C4AGL(1,ℤ/8)11yescharacteristic
195C32×C4#13711yescharacteristic
196C3×Dic3—41no—
197C3×Dic3—42no—
198C3×Dic3—81no—
199C2×Q16—61no—
200C4⋊Q8—31no—
201C4⋊Q8—31no—
202#125—61no—
203C22⋊Q8—62no—
204C22⋊Q8—61no—
205C4×Q8D3211yescharacteristic
206C4×D4—31no—
207C4×D4—61no—
208C2×C4⋊C4—61no—
209#107—181no—
210C4⋊C8—31no—
211C4⋊C8—91no—
212#103—61no—
213#103—182no—
214#102—181no—
215C4×C8—91no—
216C23×C3—61no—
217C22×D3—21no—
218C3×Q8—22no—
219C3×Q8—21no—
220C3×Q8—21no—
221C3×Q8—21no—
222C3×Q8—21no—
223C3×Q8—41no—
224C3×Q8—122no—
225C3×Q8—121no—
226C3×Q8—121no—
227C3×D4—32no—
228C3×D4—61no—
229C2×C3×C4—21no—
230C2×C3×C4—21no—
231C2×C3×C4—21no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—21no—
236C2×C3×C4—41no—
237C2×C3×C4—41no—
238C2×C3×C4—61no—
239C2×C3×C4—62no—
240C2×C3×C4—121no—
241C2×C3×C4—121no—
242C2×C3×C4—121no—
243C2×C3×C4—242no—
244C2×C3×C4D3×D411yescharacteristic
245C2×C3×C4D3×D411yescharacteristic
246C2×C3×C4C2×#6711yescharacteristic
247C2×C3×C4C2×#6711yescharacteristic
248C2×C3×C4C2×#6711yescharacteristic
249C2×C3×C4C2×#6711yescharacteristic
250C2×Dic3—21no—
251C2×Dic3—22no—
252C2×Dic3—41no—
253D12—21no—
254D12#21612yescomplemented
255C4×D3—41no—
256C4×D3—41no—
257C4×D3—82no—
258Dic6—42no—
259Dic6—41no—
260Dic6—41no—
261C3×C8—121no—
262C3⋊C8—41no—
263C3⋊C8—121no—
264C3⋊C8—121no—
265C3⋊C8—122no—
266C3⋊C8—121no—
267C3⋊C8—121no—
268C3⋊C8—241no—
269C2×C32#44911yescharacteristic
270C2×C32#45111yescharacteristic
271C2×C32#45511yescharacteristic
272C3×D3—42no—
273C2×Q8—32no—
274C2×Q8—61no—
275C2×Q8#62511yescharacteristic
276C2×D4—31no—
277C22×C4—62no—
278C22×C4—61no—
279Q16—122no—
280C2×C8—61no—
281C2×C8—181no—
282C2×C8—181no—
283C4⋊C4—21no—
284C4⋊C4—31no—
285C4⋊C4—62no—
286C4⋊C4—62no—
287C4⋊C4—61no—
288C4⋊C4—61no—
289C4⋊C4—61no—
290C4⋊C4—61no—
291C4⋊C4#62511yescharacteristic
292C22⋊C4—62no—
293C22⋊C4—61no—
294C42—21no—
295C42C2×D3211yescharacteristic
296C22×C3—21no—
297C22×C3—62no—
298C22×C3—121no—
299C22×C3—121no—
300C22×C3#93711yescharacteristic
301C22×C3#95311yescharacteristic
302C2×D3—22no—
303C2×D3—41no—
304C2×D3—41no—
305C3×C4—21no—
306C3×C4—21no—
307C3×C4—21no—
308C3×C4—21no—
309C3×C4—21no—
310C3×C4—21no—
311C3×C4—41no—
312C3×C4—42no—
313C3×C4—41no—
314C3×C4—41no—
315C3×C4—41no—
316C3×C4—41no—
317C3×C4—81no—
318C3×C4—122no—
319C3×C4—121no—
320C3×C4—241no—
321C3×C4D3×Q1611yescharacteristic
322C3×C4#91811yescharacteristic
323C3×C4#93211yescharacteristic
324C3×C4#94211yescharacteristic
325C3×C4C2×#21611yescharacteristic
326C3×C4#94911yescharacteristic
327C3×C4#95011yescharacteristic
328C3×C4#95011yescharacteristic
329Dic3—41no—
330Dic3—42no—
331Dic3—81no—
332C32#164411yescharacteristic, complemented, Sylow
333C23—61no—
334Q8—21no—
335Q8—21no—
336Q8—122no—
337Q8—121no—
338Q8—121no—
339D4—32no—
340D4—61no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—61no—
344C2×C4—62no—
345C2×C4—121no—
346C2×C4—121no—
347C2×C4—121no—
348C2×C4—242no—
349C2×C4C2×#62511yescharacteristic
350C2×C4D3×#6711yescharacteristic
351C2×C4D3×#6711yescharacteristic
352C8—121no—
353C8—361no—
354C8—361no—
355C2×C3—21no—
356C2×C3—21no—
357C2×C3—21no—
358C2×C3—122no—
359C2×C3#503711yescharacteristic
360C2×C3#518611yescharacteristic
361C2×C3#520211yescharacteristic
362C2×C3#522811yescharacteristic
363C2×C3#523811yescharacteristic
364C2×C3#524211yescharacteristic
365D3—42no—
366C22—62no—
367C22—121no—
368C22—121no—
369C22#6397611yescharacteristic
370C4—21no—
371C4—41no—
372C4—41no—
373C4—122no—
374C4—121no—
375C4—241no—
376C4#6382211yescharacteristic
377C4#6382311yescharacteristic
378C4D3×#21611yescharacteristic
379C4#6394811yescharacteristic
380C3—21no—
381C3#7106211yescharacteristic, complemented
382C3#7192611yescharacteristic, complemented
383C2—122no—
384C2#1059116111yescharacteristic
385C2#1059159411yescharacteristic
386C2#1059166411yescharacteristic
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×#5031C2semidirect
3. #10590290C2semidirect
5. #10589401C2semidirect
6. #10589095C2semidirect
33. #5031D3semidirect
115. C3×D12Q16semidirect
254. D12#216semidirect
332. C32#1644semidirect
381. C3#71062semidirect
382. C3#71926semidirect

Maximal subgroups

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

subgroupindex
C3×#55792
C3×#50312
#105902902
#105902692
#105894012
#105890952
#105890802
#719263
#710623