Finite Group Databasebeta

← #11780807

Subgroups — #11780807

Order 1152.

430 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 100 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#10592706C211yesmaximal, characteristic, complemented
2C3×#5015C211yesmaximal, characteristic
3C3×D4×C3⋊C8C211yesmaximal, characteristic, complemented
4#10590369C211yesmaximal, characteristic, complemented
5#10589097C211yesmaximal, characteristic, complemented
6#10589094C211yesmaximal, characteristic, complemented
7#10589090C211yesmaximal, characteristic, complemented
8#71004—31nomaximal
9#70846—31nomaximal
10C32×C4×D4C2211yescharacteristic
11#64078C2211yescharacteristic
12C2×C3×#213—21no—
13C22×C3×C3⋊C8—21no—
14C3×#874C2211yescharacteristic
15C2×#3716—21no—
16C2×#3716—21no—
17#63659—21no—
18#63634—21no—
19C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
20C3×#830—21no—
21C3×#809—21no—
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4×C3⋊C8C2211yescharacteristic
25C3×#459—31no—
26C3×C8×D4—31no—
27#5076—31no—
28#5015D311yescharacteristic
29D4×C3⋊C8D311yescharacteristic, complemented
30#5007—31no—
31#5007—31no—
32#5007—61no—
33#4693—31no—
34#4544—31no—
35#4486—31no—
36#4485—31no—
37#4482—31no—
38#4480—31no—
39#4457—31no—
40C2×C32×D4D411yescharacteristic
41C22×C32×C4—21no—
42C2×#634—21no—
43C2×C3×D12—21no—
44C2×C3×D12—21no—
45C2×C3×D12—21no—
46C32×C4⋊C4D411yescharacteristic
47C32×C22⋊C4—21no—
48C32×C42C2311yescharacteristic
49C4⋊(C3⋊Dic3)—21no—
50C4⋊(C3⋊Dic3)—21no—
51C2×C3⋊(C3⋊C8)—21no—
52C3×#213—42no—
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8—42no—
56C2×C3×C3⋊C8D411yescharacteristic
57C2×C3×C3⋊C8D411yescharacteristic
58#3716—42no—
59#3716—42no—
60#1665—91noSylow
61C2×C3×D8—61no—
62C22×C3×C8—61no—
63C3×#127—31no—
64C3×C4×D4—21no—
65C3×C4×D4C2×D311yescharacteristic
66C3×C4×D4C2×D311yescharacteristic
67C2×#214—61no—
68C2×#214—61no—
69C2×#213—21no—
70C22×C3⋊C8—21no—
71C2×#204—61no—
72C2×#204—61no—
73#874C2×D311yescharacteristic
74#869—31no—
75#869—31no—
76#869—61no—
77C3×C4⋊C8—31no—
78C3×C4⋊C8—31no—
79C3×#102—61no—
80C3×C22⋊C8—61no—
81C3×C4×C8—31no—
82#832—62no—
83#832—61no—
84#832—61no—
85#830—21no—
86#809—21no—
87#807—62no—
88#807—61no—
89#807—61no—
90C4⋊(C3⋊C8)—31no—
91C4⋊(C3⋊C8)—31no—
92C4⋊(C3⋊C8)—61no—
93C4⋊(C3⋊C8)C2×D311yescharacteristic
94C4⋊(C3⋊C8)C2×D311yescharacteristic
95C4×C3⋊C8C2×D311yescharacteristic
96C23×C32—21no—
97C22×C3×D3—41no—
98C32×D4—21no—
99C32×D4SD1612yescomplemented
100C2×C32×C4—21no—
101C2×C32×C4—41no—
102C2×C32×C4—41no—
103C2×C32×C4C2×D411yescharacteristic
104C2×C32×C4C2×D411yescharacteristic
105C2×C32×C4#4111yescharacteristic
106C2×C3⋊Dic3—41no—
107#634—41no—
108#634—41no—
109C3×D12—41no—
110C3×D12—41no—
111C3×D12—41no—
112C3×D12—41no—
113C3×D12—81no—
114C3⋊(C3⋊C8)—41no—
115C3×C3⋊C8—21no—
116C3×C3⋊C8—41no—
117C3×C3⋊C8—41no—
118C3×C3⋊C8D812yescomplemented
119#492—91no—
120#474—91no—
121#459—31no—
122C8×D4—31no—
123#334—91no—
124#332—91no—
125#331—91no—
126C2×C3×D4—21no—
127C2×C3×D4—61no—
128C2×C3×D4—61no—
129C2×C3×D4—61no—
130C2×C3×D4D1211yescharacteristic
131C2×C3×D4#6711yescharacteristic
132C22×C3×C4—21no—
133C22×C3×C4—21no—
134C22×C3×C4—41no—
135C2×D12—21no—
136C2×D12—21no—
137C2×D12—21no—
138C2×Dic6—61no—
139C2×Dic6—61no—
140C2×Dic6—121no—
141C3×D8—122no—
142C2×C3×C8—31no—
143C2×C3×C8—31no—
144C2×C3×C8—61no—
145C2×C3×C8—61no—
146C2×C3×C8—122no—
147C3×C4⋊C4—21no—
148C3×C4⋊C4D1211yescharacteristic
149C3×C4⋊C4#6711yescharacteristic
150C3×C22⋊C4—21no—
151C3×C22⋊C4—21no—
152C3×C22⋊C4—41no—
153C3×C42—21no—
154C3×C42C22×D311yescharacteristic
155C3×C42C22×D311yescharacteristic
156#214—122no—
157#214—122no—
158#213—42no—
159C4⋊Dic3—62no—
160C4⋊Dic3—61no—
161C4⋊Dic3—61no—
162C4⋊Dic3—61no—
163C4⋊Dic3—61no—
164C4⋊Dic3—121no—
165C2×C3⋊C8—21no—
166C2×C3⋊C8—21no—
167C2×C3⋊C8—42no—
168C2×C3⋊C8—62no—
169C2×C3⋊C8—61no—
170C2×C3⋊C8—61no—
171C2×C3⋊C8#6711yescharacteristic
172C2×C3⋊C8#6711yescharacteristic
173#204—122no—
174#204—122no—
175C22×C32—22no—
176C22×C32—41no—
177C22×C32—41no—
178C22×C32#12111yescharacteristic
179C2×C3×D3—81no—
180C2×C3×D3—81no—
181C2×C3×D3—81no—
182C32×C4—21no—
183C32×C4—41no—
184C32×C4C2×D811yescharacteristic
185C32×C4C2×SD1611yescharacteristic
186C32×C4#13511yescharacteristic
187C32×C4AGL(1,ℤ/8)11yescharacteristic
188C3⋊Dic3—81no—
189C2×SD16—181no—
190C2×SD16—181no—
191C2×D8—61no—
192C22×C8—61no—
193C4⋊Q8—91no—
194#127—31no—
195C4×D4D3211yescharacteristic
196#107—181no—
197C4⋊C8—31no—
198C4⋊C8—31no—
199C4⋊C8—91no—
200#102—61no—
201#102—181no—
202C22⋊C8—61no—
203C4×C8—31no—
204C23×C3—21no—
205C23×C3—21no—
206C23×C3—41no—
207C23×C3—121no—
208C22×D3—41no—
209C3×D4—21no—
210C3×D4—21no—
211C3×D4—22no—
212C3×D4—41no—
213C3×D4—121no—
214C3×D4—121no—
215C3×D4—121no—
216C3×D4—121no—
217C3×D4—241no—
218C3×D4#20412yescomplemented
219C3×D4#21412yescomplemented
220C2×C3×C4—21no—
221C2×C3×C4—21no—
222C2×C3×C4—21no—
223C2×C3×C4—21no—
224C2×C3×C4—21no—
225C2×C3×C4—41no—
226C2×C3×C4—41no—
227C2×C3×C4—41no—
228C2×C3×C4—41no—
229C2×C3×C4—41no—
230C2×C3×C4—81no—
231C2×C3×C4—81no—
232C2×C3×C4C2×D1211yescharacteristic
233C2×C3×C4#23511yescharacteristic
234C2×C3×C4D3×D411yescharacteristic
235C2×C3×C4#23711yescharacteristic
236C2×C3×C4C2×#6711yescharacteristic
237C2×C3×C4C2×#6711yescharacteristic
238C2×Dic3—122no—
239C2×Dic3—121no—
240C2×Dic3—121no—
241D12—41no—
242D12—41no—
243D12—41no—
244D12—41no—
245D12—81no—
246Dic6—121no—
247Dic6—121no—
248Dic6—121no—
249Dic6—121no—
250Dic6—241no—
251Dic6—241no—
252C3×C8—32no—
253C3×C8—61no—
254C3×C8—121no—
255C3×C8—121no—
256C3⋊C8—21no—
257C3⋊C8—41no—
258C3⋊C8—41no—
259C3⋊C8—122no—
260C3⋊C8—121no—
261C3⋊C8—121no—
262C3⋊C8#21312yescomplemented
263C2×C32—42no—
264C2×C32#45911yescharacteristic
265C2×C32#46511yescharacteristic
266C2×C32#47111yescharacteristic
267C3×D3—161no—
268C2×Q8—181no—
269C2×D4—61no—
270C2×D4—61no—
271C2×D4—61no—
272C2×D4#62611yescharacteristic
273C22×C4—21no—
274SD16—362no—
275SD16—362no—
276D8—122no—
277C2×C8—31no—
278C2×C8—31no—
279C2×C8—61no—
280C2×C8—61no—
281C2×C8—122no—
282C2×C8—181no—
283C4⋊C4—181no—
284C4⋊C4—181no—
285C4⋊C4#62611yescharacteristic
286C22⋊C4—21no—
287C42C2×D3211yescharacteristic
288C22×C3—22no—
289C22×C3—22no—
290C22×C3—21no—
291C22×C3—42no—
292C22×C3—41no—
293C22×C3—41no—
294C22×C3—41no—
295C22×C3—41no—
296C22×C3—81no—
297C22×C3—81no—
298C22×C3—241no—
299C22×C3—241no—
300C22×C3—241no—
301C22×C3#93011yescharacteristic
302C22×C3#93911yescharacteristic
303C2×D3—81no—
304C2×D3—81no—
305C2×D3—81no—
306C3×C4—21no—
307C3×C4—21no—
308C3×C4—21no—
309C3×C4—21no—
310C3×C4—21no—
311C3×C4—21no—
312C3×C4—41no—
313C3×C4—41no—
314C3×C4—41no—
315C3×C4—81no—
316C3×C4C2×#20411yescharacteristic
317C3×C4#90411yescharacteristic
318C3×C4D3×D811yescharacteristic
319C3×C4#91111yescharacteristic
320C3×C4C2×#21311yescharacteristic
321C3×C4C2×#21411yescharacteristic
322C3×C4#94911yescharacteristic
323C3×C4#95011yescharacteristic
324Dic3—242no—
325Dic3—241no—
326Dic3—241no—
327C32#166511yescharacteristic, complemented, Sylow
328C23—21no—
329C23—121no—
330Q8—361no—
331Q8—361no—
332D4—21no—
333D4—121no—
334D4—121no—
335D4—121no—
336D4—121no—
337D4—241no—
338D4#371612yescomplemented
339C2×C4—21no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—361no—
343C2×C4#380411yescharacteristic
344C2×C4C2×#62611yescharacteristic
345C2×C4D3×#6711yescharacteristic
346C8—32no—
347C8—61no—
348C8—121no—
349C8—121no—
350C8—361no—
351C2×C3—21no—
352C2×C3—21no—
353C2×C3—21no—
354C2×C3—42no—
355C2×C3—42no—
356C2×C3—82no—
357C2×C3—481no—
358C2×C3#501511yescharacteristic
359C2×C3#504111yescharacteristic
360C2×C3#511411yescharacteristic
361C2×C3#514111yescharacteristic
362C2×C3#515011yescharacteristic
363C2×C3#520011yescharacteristic
364D3—161no—
365C22—22no—
366C22—41no—
367C22—41no—
368C22—241no—
369C22—241no—
370C22—241no—
371C22#6397811yescharacteristic
372C4—21no—
373C4—41no—
374C4—721no—
375C4C2×#371611yescharacteristic
376C4#6382911yescharacteristic
377C4D3×#21311yescharacteristic
378C4#6392511yescharacteristic
379C3—21no—
380C3#7084611yescharacteristic, complemented
381C3#7100411yescharacteristic, complemented
382C2—42no—
383C2—481no—
384C2#1059117511yescharacteristic
385C2#1059148111yescharacteristic
386C2#1059167911yescharacteristic
subgroupG/H
centerC22#63978
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×D4C22
socleC22×C32#121
prime radicalC3×#5015C2
hypercenterC4×D4D32
hypocenterC32#1665
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #10592706C2semidirect
3. C3×D4×C3⋊C8C2semidirect
4. #10590369C2semidirect
5. #10589097C2semidirect
6. #10589094C2semidirect
7. #10589090C2semidirect
29. D4×C3⋊C8D3semidirect
99. C32×D4SD16semidirect
118. C3×C3⋊C8D8semidirect
218. C3×D4#204semidirect
219. C3×D4#214semidirect
262. C3⋊C8#213semidirect
327. C32#1665semidirect
338. D4#3716semidirect
380. C3#70846semidirect
381. C3#71004semidirect

Maximal subgroups

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

subgroupindex
#105927062
C3×#50152
C3×D4×C3⋊C82
#105903692
#105890972
#105890942
#105890902
#710043
#708463