Finite Group Databasebeta

← #11781437

Subgroups — #11781437

Order 1152.

423 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 423 conjugacy classes of subgroups — too many to draw. Only its 86 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#10592769C211yesmaximal, characteristic, complemented
2C3×#5072C211yesmaximal, characteristic
3#10590365C211yesmaximal, characteristic, complemented
4#10590329C211yesmaximal, characteristic, complemented
5C3×#4544C211yesmaximal, characteristic, complemented
6#10589100C211yesmaximal, characteristic, complemented
7#10589094C211yesmaximal, characteristic, complemented
8#71007—31nomaximal
9#68397—31nomaximal
10C32×#127C2211yescharacteristic
11#64078C2211yescharacteristic
12C2×C3×#213—21no—
13C3×C4×D12C2211yescharacteristic
14C2×#3716—21no—
15C2×D3×C3⋊C8—21no—
16#63659—21no—
17#63659—21no—
18C4×C3⋊(C3⋊C8)C2211yescharacteristic
19C3×#832—21no—
20C3×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23#63567—21no—
24(C2×D3)⋊(C3⋊C8)—21no—
25C3×#459—31no—
26#5072D311yescharacteristic
27#5070—31no—
28#5070—31no—
29#5070—61no—
30#5019—31no—
31D4×C3⋊C8—31no—
32#4841—31no—
33#4834—31no—
34C3×#331—31no—
35#4544D311yescharacteristic, complemented
36#4486—31no—
37#4482—31no—
38#4479—31no—
39#4479—31no—
40C2×C32×D4—21no—
41C2×C32×D4—21no—
42C2×C32×D4—21no—
43C2×#634—21no—
44C2×C3×D12D411yescharacteristic
45C2×C3×C4×D3—21no—
46C32×C42C2311yescharacteristic
47C4⋊(C3⋊Dic3)—21no—
48C4⋊(C3⋊Dic3)—21no—
49C2×C3⋊(C3⋊C8)D411yescharacteristic
50C2×C3⋊(C3⋊C8)D411yescharacteristic
51C3×#213—42no—
52C3×(C2×D3)⋊C4—21no—
53C3×C4⋊Dic3D411yescharacteristic
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8—21no—
56C2×C3×C3⋊C8—21no—
57#3716—42no—
58D3×C3⋊C8—42no—
59#1681—91noSylow
60C2×C3×D8—61no—
61C3×#127—21no—
62C3×#127C2×D311yescharacteristic
63C3×#127C2×D311yescharacteristic
64C3×C4×D4—31no—
65C2×#214—61no—
66C2×#213—21no—
67C22×C3⋊C8—61no—
68C2×#204—61no—
69C2×D3×C8—61no—
70C4×D12C2×D311yescharacteristic
71#869—31no—
72#869—31no—
73#869—61no—
74C3×C4⋊C8—31no—
75C3×C4⋊C8—31no—
76C3×C4⋊C8—31no—
77C3×#102—61no—
78#832—21no—
79#832—61no—
80#832—61no—
81#832—61no—
82#832—61no—
83#832—62no—
84#832—62no—
85#830—61no—
86(C2×D3)⋊C8—61no—
87#816—61no—
88#810—61no—
89C4⋊(C3⋊C8)C2×D311yescharacteristic
90C4⋊(C3⋊C8)C2×D311yescharacteristic
91C4⋊(C3⋊C8)C2×D311yescharacteristic
92C4×C3⋊C8—31no—
93C4×C3⋊C8—31no—
94C4×C3⋊C8—61no—
95C23×C32—41no—
96C22×C3×D3—21no—
97C32×D4—41no—
98C32×D4—41no—
99C32×D4—41no—
100C32×D4—41no—
101C32×D4—81no—
102C2×C32×C4C2×D411yescharacteristic
103C2×C32×C4C2×D411yescharacteristic
104C2×C32×C4#4111yescharacteristic
105C2×C3⋊Dic3—41no—
106#634—41no—
107#634—41no—
108C2×C3×Dic3—21no—
109C3×D12—21no—
110C3×D12D812yes—
111C3×C4×D3—41no—
112C3×C4×D3—41no—
113C3⋊(C3⋊C8)—21no—
114C3⋊(C3⋊C8)—21no—
115C3×C3⋊C8—41no—
116C3×C3⋊C8—41no—
117C3×C3⋊C8—41no—
118#486—91no—
119#461—91no—
120#459—31no—
121C8×D4—91no—
122#335—91no—
123#332—91no—
124#331—31no—
125C2×C3×D4—22no—
126C2×C3×D4—21no—
127C2×C3×D4—21no—
128C2×C3×D4—21no—
129C2×C3×D4—21no—
130C2×C3×D4—21no—
131C2×C3×D4—21no—
132C2×C3×D4—31no—
133C2×C3×D4—41no—
134C2×C3×D4—41no—
135C22×C3×C4—61no—
136C2×D12#6711yescharacteristic
137C2×C4×D3—21no—
138C2×Dic6—61no—
139C2×Dic6—61no—
140C2×Dic6—121no—
141C3×D8—122no—
142C2×C3×C8—61no—
143C2×C3×C8—61no—
144C2×C3×C8—61no—
145C3×C4⋊C4—31no—
146C3×C22⋊C4—61no—
147C3×C42—21no—
148C3×C42C22×D311yescharacteristic
149C3×C42C22×D311yescharacteristic
150#214—122no—
151#213—42no—
152(C2×D3)⋊C4—21no—
153C4⋊Dic3—62no—
154C4⋊Dic3—61no—
155C4⋊Dic3—61no—
156C4⋊Dic3—61no—
157C4⋊Dic3—61no—
158C4⋊Dic3—121no—
159C4⋊Dic3#6711yescharacteristic
160C2×C3⋊C8—21no—
161C2×C3⋊C8—21no—
162C2×C3⋊C8—21no—
163C2×C3⋊C8—31no—
164C2×C3⋊C8—31no—
165C2×C3⋊C8—31no—
166C2×C3⋊C8—31no—
167C2×C3⋊C8—61no—
168C2×C3⋊C8—61no—
169C2×C3⋊C8—122no—
170#204—122no—
171D3×C8—122no—
172C22×C32—81no—
173C22×C32—81no—
174C22×C32—81no—
175C22×C32#12111yescharacteristic
176C2×C3×D3—22no—
177C2×C3×D3—41no—
178C2×C3×D3—41no—
179C32×C4—21no—
180C32×C4C2×D811yescharacteristic
181C32×C4#13511yescharacteristic
182C32×C4#13511yescharacteristic
183C32×C4AGL(1,ℤ/8)11yescharacteristic
184C3⋊Dic3—81no—
185C3×Dic3—41no—
186C2×SD16—181no—
187C2×D8—61no—
188C22×C8—181no—
189C4⋊Q8—91no—
190#127D3211yescharacteristic
191C4×D4—31no—
192C4⋊C8—31no—
193C4⋊C8—31no—
194C4⋊C8—31no—
195#103—181no—
196#102—61no—
197#102—181no—
198#102—181no—
199C22⋊C8—181no—
200C4×C8—91no—
201C23×C3—42no—
202C23×C3—41no—
203C23×C3—41no—
204C23×C3—61no—
205C22×D3—21no—
206C3×D4—32no—
207C3×D4—42no—
208C3×D4—42no—
209C3×D4—41no—
210C3×D4—41no—
211C3×D4—41no—
212C3×D4—41no—
213C3×D4—41no—
214C3×D4—41no—
215C3×D4—41no—
216C3×D4—41no—
217C3×D4—61no—
218C3×D4—81no—
219C3×D4—81no—
220C3×D4—81no—
221C3×D4—81no—
222C3×D4—82no—
223C2×C3×C4—21no—
224C2×C3×C4—21no—
225C2×C3×C4—21no—
226C2×C3×C4—61no—
227C2×C3×C4—121no—
228C2×C3×C4—121no—
229C2×C3×C4#23511yescharacteristic
230C2×C3×C4D3×D411yescharacteristic
231C2×C3×C4D3×D411yescharacteristic
232C2×C3×C4D3×D411yescharacteristic
233C2×C3×C4#23711yescharacteristic
234C2×C3×C4C2×#6711yescharacteristic
235C2×Dic3—21no—
236C2×Dic3—122no—
237C2×Dic3—121no—
238C2×Dic3—121no—
239D12—21no—
240D12#21312yes—
241C4×D3—41no—
242C4×D3—41no—
243Dic6—121no—
244Dic6—121no—
245Dic6—121no—
246Dic6—121no—
247Dic6—241no—
248Dic6—241no—
249C3×C8—121no—
250C3×C8—121no—
251C3×C8—121no—
252C3⋊C8—41no—
253C3⋊C8—41no—
254C3⋊C8—41no—
255C3⋊C8—61no—
256C3⋊C8—61no—
257C3⋊C8—61no—
258C3⋊C8—61no—
259C3⋊C8—121no—
260C3⋊C8—121no—
261C2×C32—161no—
262C2×C32#46311yescharacteristic
263C2×C32#46611yescharacteristic
264C2×C32#47111yescharacteristic
265C3×D3—42no—
266C2×Q8—181no—
267C2×D4—21no—
268C2×D4—21no—
269C2×D4—21no—
270C2×D4—31no—
271C22×C4—61no—
272SD16—362no—
273D8—122no—
274C2×C8—61no—
275C2×C8—61no—
276C2×C8—61no—
277C2×C8—91no—
278C2×C8—91no—
279C2×C8—362no—
280C4⋊C4—31no—
281C4⋊C4—181no—
282C4⋊C4—181no—
283C22⋊C4—61no—
284C42C2×D3211yescharacteristic
285C22×C3—21no—
286C22×C3—62no—
287C22×C3—82no—
288C22×C3—82no—
289C22×C3—82no—
290C22×C3—81no—
291C22×C3—81no—
292C22×C3—81no—
293C22×C3—81no—
294C22×C3—81no—
295C22×C3—81no—
296C22×C3—121no—
297C22×C3—121no—
298C22×C3#88411yescharacteristic
299C22×C3#93911yescharacteristic
300C2×D3—22no—
301C2×D3—41no—
302C2×D3—41no—
303C3×C4—22no—
304C3×C4—21no—
305C3×C4—21no—
306C3×C4—21no—
307C3×C4—21no—
308C3×C4—21no—
309C3×C4—21no—
310C3×C4—121no—
311C3×C4D3×D811yescharacteristic
312C3×C4#91111yescharacteristic
313C3×C4#91111yescharacteristic
314C3×C4#91211yescharacteristic
315C3×C4#91611yescharacteristic
316C3×C4#91611yescharacteristic
317C3×C4C2×#21311yescharacteristic
318C3×C4#95011yescharacteristic
319Dic3—41no—
320Dic3—242no—
321Dic3—241no—
322Dic3—241no—
323C32#168111yescharacteristic, complemented, Sylow
324C23—41no—
325C23—61no—
326Q8—361no—
327Q8—361no—
328D4—32no—
329D4—41no—
330D4—41no—
331D4—41no—
332D4—41no—
333D4—61no—
334D4—81no—
335C2×C4—61no—
336C2×C4—121no—
337C2×C4—121no—
338C2×C4—361no—
339C2×C4#380411yescharacteristic
340C2×C4D3×#6711yescharacteristic
341C2×C4#381111yescharacteristic
342C8—121no—
343C8—121no—
344C8—121no—
345C8—181no—
346C8—181no—
347C2×C3—21no—
348C2×C3—21no—
349C2×C3—21no—
350C2×C3—122no—
351C2×C3—162no—
352C2×C3—161no—
353C2×C3—161no—
354C2×C3#474811yescharacteristic
355C2×C3#477511yescharacteristic
356C2×C3#478711yescharacteristic
357C2×C3#503811yescharacteristic
358C2×C3#515311yescharacteristic
359C2×C3#520011yescharacteristic
360D3—42no—
361C22—62no—
362C22—81no—
363C22—81no—
364C22—81no—
365C22—121no—
366C22—121no—
367C22#6397111yescharacteristic
368C4—21no—
369C4—121no—
370C4—721no—
371C4D3×#21311yescharacteristic
372C4#6392711yescharacteristic
373C4#6393511yescharacteristic
374C4#6393611yescharacteristic
375C3—21no—
376C3#6839711yescharacteristic, complemented
377C3#7100711yescharacteristic, complemented
378C2—122no—
379C2—161no—
380C2#1059143411yescharacteristic
381C2#1059144911yescharacteristic
382C2#1059150711yescharacteristic
subgroupG/H
centerC22#63971
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×#127C22
socleC22×C32#121
prime radicalC3×#5072C2
hypercenter#127D32
hypocenterC32#1681
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
1. #10592769C2semidirect
3. #10590365C2semidirect
4. #10590329C2semidirect
5. C3×#4544C2semidirect
6. #10589100C2semidirect
7. #10589094C2semidirect
35. #4544D3semidirect
323. C32#1681semidirect
376. C3#68397semidirect
377. C3#71007semidirect

Maximal subgroups

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

subgroupindex
#105927692
C3×#50722
#105903652
#105903292
C3×#45442
#105891002
#105890942
#710073
#683973