Finite Group Databasebeta

← #11781638

Subgroups — #11781638

Order 1152.

396 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 88 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×#4838C211yesmaximal, characteristic, complemented
2#10590369C211yesmaximal, characteristic, complemented
3#10590347C211yesmaximal, characteristic
4#10590272C211yesmaximal, characteristic, complemented
5#10589348C211yesmaximal, characteristic, complemented
6C3×#4485C211yesmaximal, characteristic, complemented
7#10589099C211yesmaximal, characteristic, complemented
8#70867—31nomaximal
9#68398—31nomaximal
10#64078C2211yescharacteristic
11C2×C3×ΓL(1,𝔽25)—21no—
12C3×#874C2211yescharacteristic
13C3×C4×D12C2211yescharacteristic
14C2×#3716—21no—
15C2×#3716—21no—
16C2×#3713—21no—
17C32×C4⋊C8C2211yescharacteristic
18C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
19C3×(C2×D3)⋊C8—21no—
20C3×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×C4×C3⋊C8C2211yescharacteristic
22#63575—21no—
23#63563—21no—
24#63562—21no—
25C3×#436—31no—
26#5076—31no—
27#5072—31no—
28#5015—31no—
29#5007—31no—
30#4846—31no—
31#4838D311yescharacteristic, complemented
32#4693—31no—
33C3×#331—31no—
34#4485D311yescharacteristic, complemented
35#4482—31no—
36#4482—31no—
37#4482—61no—
38#4479—31no—
39#4458—31no—
40C2×#634—21no—
41C2×C3×D12—21no—
42C2×C3×D12—21no—
43C2×C3×D12—21no—
44C2×C3×D12D411yescharacteristic
45C2×C3×C4×D3—21no—
46C2×C32×C8—21no—
47C32×C42C2311yescharacteristic
48C4⋊(C3⋊Dic3)—21no—
49C4⋊(C3⋊Dic3)—21no—
50C2×C3⋊(C3⋊C8)—21no—
51C3×(C2×D3)⋊C4—21no—
52C3×C4⋊Dic3D411yescharacteristic
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8D411yescharacteristic
55C2×C3×C3⋊C8D411yescharacteristic
56C3×ΓL(1,𝔽25)—42no—
57#3716—42no—
58#3716—42no—
59#3713—42no—
60#1685—91noSylow
61C2×C3×M16—61no—
62C3×#127—31no—
63C3×C4×D4—31no—
64C2×#214—61no—
65C2×#214—61no—
66C2×#213—61no—
67C2×#213—61no—
68C2×#204—61no—
69C2×#204—61no—
70C2×ΓL(1,𝔽25)—21no—
71#874C2×D311yescharacteristic
72C4×D12C2×D311yescharacteristic
73#869—31no—
74#869—31no—
75#869—61no—
76C3×C4⋊C8—21no—
77C3×C4⋊C8—31no—
78C3×C4⋊C8C2×D311yescharacteristic
79C3×C4⋊C8C2×D311yescharacteristic
80C3×C22⋊C8—61no—
81C3×C4×C8—31no—
82#832—61no—
83#832—61no—
84#821—61no—
85(C2×D3)⋊C8—21no—
86#818—61no—
87#809—61no—
88#807—61no—
89C4⋊(C3⋊C8)—31no—
90C4⋊(C3⋊C8)—31no—
91C4⋊(C3⋊C8)—61no—
92C4⋊(C3⋊C8)C2×D311yescharacteristic
93C4×C3⋊C8C2×D311yescharacteristic
94C22×C3×D3—21no—
95C22×C3×D3—41no—
96C2×C32×C4C2×D411yescharacteristic
97C2×C32×C4C2×D411yescharacteristic
98C2×C32×C4#4111yescharacteristic
99C2×C3⋊Dic3—41no—
100#634—41no—
101#634—41no—
102C2×C3×Dic3—21no—
103C3×D12—21no—
104C3×D12—21no—
105C3×D12—41no—
106C3×D12—41no—
107C3×D12—41no—
108C3×D12—41no—
109C3×D12—81no—
110C3×C4×D3—41no—
111C3×C4×D3—41no—
112C32×C8—41no—
113C3⋊(C3⋊C8)—41no—
114C3×C3⋊C8—21no—
115C3×C3⋊C8—41no—
116C3×C3⋊C8D812yescomplemented
117#492—91no—
118#474—91no—
119#459—91no—
120#436—31no—
121#335—91no—
122#332—91no—
123#331—31no—
124C2×C3×D4—31no—
125C2×C3×D4—61no—
126C2×C3×D4—61no—
127C2×C3×D4—61no—
128C22×C3×C4—61no—
129C2×D12—21no—
130C2×D12—21no—
131C2×D12—21no—
132C2×D12D1211yescharacteristic
133C2×C4×D3—21no—
134C2×Dic6—61no—
135C2×Dic6—61no—
136C2×Dic6—121no—
137C3×M16—122no—
138C2×C3×C8—21no—
139C2×C3×C8—21no—
140C2×C3×C8—31no—
141C2×C3×C8—31no—
142C2×C3×C8—41no—
143C2×C3×C8—61no—
144C3×C4⋊C4—31no—
145C3×C22⋊C4—61no—
146C3×C42—21no—
147C3×C42C22×D311yescharacteristic
148C3×C42C22×D311yescharacteristic
149#214—122no—
150#214—122no—
151#213—122no—
152#213—122no—
153(C2×D3)⋊C4—21no—
154C4⋊Dic3—62no—
155C4⋊Dic3—61no—
156C4⋊Dic3—61no—
157C4⋊Dic3—61no—
158C4⋊Dic3—61no—
159C4⋊Dic3—121no—
160C4⋊Dic3D1211yescharacteristic
161C2×C3⋊C8—21no—
162C2×C3⋊C8—61no—
163C2×C3⋊C8—61no—
164C2×C3⋊C8—121no—
165C2×C3⋊C8#6711yescharacteristic
166C2×C3⋊C8#6711yescharacteristic
167#204—122no—
168#204—122no—
169ΓL(1,𝔽25)—42no—
170C22×C32#12111yescharacteristic
171C2×C3×D3—41no—
172C2×C3×D3—41no—
173C2×C3×D3—41no—
174C2×C3×D3—81no—
175C2×C3×D3—81no—
176C2×C3×D3—81no—
177C32×C4—21no—
178C32×C4C2×D811yescharacteristic
179C32×C4AGL(1,ℤ/8)11yescharacteristic
180C32×C4AGL(1,ℤ/8)11yescharacteristic
181C32×C4#13711yescharacteristic
182C3⋊Dic3—81no—
183C3×Dic3—41no—
184C2×SD16—181no—
185C2×SD16—181no—
186C2×D8—181no—
187C2×M16—61no—
188C4⋊Q8—91no—
189#127—31no—
190C4×D4—31no—
191#107—181no—
192C4⋊C8—31no—
193C4⋊C8—91no—
194C4⋊C8D3211yescharacteristic
195#102—181no—
196#102—181no—
197C22⋊C8—61no—
198C4×C8—31no—
199C23×C3—61no—
200C23×C3—121no—
201C22×D3—21no—
202C22×D3—41no—
203C3×D4—61no—
204C3×D4—61no—
205C3×D4—121no—
206C3×D4—121no—
207C3×D4—121no—
208C3×D4—121no—
209C3×D4—241no—
210C2×C3×C4—21no—
211C2×C3×C4—21no—
212C2×C3×C4—21no—
213C2×C3×C4—61no—
214C2×C3×C4—121no—
215C2×C3×C4—121no—
216C2×C3×C4C2×D1211yescharacteristic
217C2×C3×C4#23511yescharacteristic
218C2×C3×C4#23511yescharacteristic
219C2×C3×C4D3×D411yescharacteristic
220C2×C3×C4D3×D411yescharacteristic
221C2×C3×C4C2×#6711yescharacteristic
222C2×Dic3—21no—
223C2×Dic3—122no—
224C2×Dic3—121no—
225C2×Dic3—121no—
226D12—21no—
227D12—21no—
228D12—41no—
229D12—41no—
230D12—41no—
231D12—41no—
232D12—81no—
233C4×D3—41no—
234C4×D3—41no—
235Dic6—121no—
236Dic6—121no—
237Dic6—121no—
238Dic6—121no—
239Dic6—241no—
240Dic6—241no—
241C3×C8—32no—
242C3×C8—41no—
243C3×C8—41no—
244C3×C8—61no—
245C3×C8—81no—
246C3×C8—121no—
247C3⋊C8—21no—
248C3⋊C8—41no—
249C3⋊C8—121no—
250C3⋊C8—121no—
251C3⋊C8—241no—
252C3⋊C8#21312yescomplemented
253C2×C32#45911yescharacteristic
254C2×C32#46811yescharacteristic
255C2×C32#47111yescharacteristic
256C3×D3—81no—
257C3×D3—161no—
258C2×Q8—181no—
259C2×D4—31no—
260C2×D4—61no—
261C2×D4—61no—
262C2×D4—61no—
263C22×C4—61no—
264SD16—362no—
265SD16—362no—
266D8—362no—
267M16—122no—
268C2×C8—21no—
269C2×C8—31no—
270C2×C8—31no—
271C2×C8—61no—
272C2×C8—181no—
273C4⋊C4—31no—
274C4⋊C4—181no—
275C4⋊C4—181no—
276C22⋊C4—61no—
277C42C2×D3211yescharacteristic
278C22×C3—21no—
279C22×C3—121no—
280C22×C3—121no—
281C22×C3—121no—
282C22×C3—241no—
283C22×C3—241no—
284C22×C3—241no—
285C22×C3#88411yescharacteristic
286C22×C3#93011yescharacteristic
287C2×D3—41no—
288C2×D3—41no—
289C2×D3—41no—
290C2×D3—81no—
291C2×D3—81no—
292C2×D3—81no—
293C3×C4—21no—
294C3×C4—21no—
295C3×C4—21no—
296C3×C4—21no—
297C3×C4—21no—
298C3×C4—21no—
299C3×C4—41no—
300C3×C4—121no—
301C3×C4#90811yescharacteristic
302C3×C4#90911yescharacteristic
303C3×C4D3×D811yescharacteristic
304C3×C4#91111yescharacteristic
305C3×C4#91411yescharacteristic
306C3×C4#91511yescharacteristic
307C3×C4C2×#21311yescharacteristic
308C3×C4#94911yescharacteristic
309Dic3—41no—
310Dic3—242no—
311Dic3—241no—
312Dic3—241no—
313C32#168511yescharacteristic, complemented, Sylow
314C23—61no—
315C23—121no—
316Q8—361no—
317Q8—361no—
318D4—61no—
319D4—61no—
320D4—121no—
321D4—121no—
322D4—121no—
323D4—121no—
324D4—241no—
325C2×C4—61no—
326C2×C4—121no—
327C2×C4—121no—
328C2×C4—361no—
329C2×C4#379811yescharacteristic
330C2×C4D3×D1211yescharacteristic
331C2×C4D3×#6711yescharacteristic
332C8—32no—
333C8—41no—
334C8—61no—
335C8—121no—
336C8—361no—
337C2×C3—21no—
338C2×C3—21no—
339C2×C3—21no—
340C2×C3—241no—
341C2×C3—481no—
342C2×C3#474811yescharacteristic
343C2×C3#478011yescharacteristic
344C2×C3#478611yescharacteristic
345C2×C3#501511yescharacteristic
346C2×C3#513411yescharacteristic
347C2×C3#514111yescharacteristic
348D3—81no—
349D3—161no—
350C22—121no—
351C22—121no—
352C22—121no—
353C22—241no—
354C22—241no—
355C22—241no—
356C22#6390611yescharacteristic
357C4—21no—
358C4—121no—
359C4—721no—
360C4#6379511yescharacteristic
361C4#6380011yescharacteristic
362C4D3×#21311yescharacteristic
363C4#6393911yescharacteristic
364C3—21no—
365C3#6839811yescharacteristic, complemented
366C3#7086711yescharacteristic, complemented
367C2—241no—
368C2—481no—
369C2#1059054711yescharacteristic
370C2#1059082811yescharacteristic
371C2#1059099611yescharacteristic
subgroupG/H
centerC22#63906
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#121
prime radical#10590347C2
hypercenterC4⋊C8D32
hypocenterC32#1685
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
1. C3×#4838C2semidirect
2. #10590369C2semidirect
4. #10590272C2semidirect
5. #10589348C2semidirect
6. C3×#4485C2semidirect
7. #10589099C2semidirect
31. #4838D3semidirect
34. #4485D3semidirect
116. C3×C3⋊C8D8semidirect
252. C3⋊C8#213semidirect
313. C32#1685semidirect
365. C3#68398semidirect
366. C3#70867semidirect

Maximal subgroups

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

subgroupindex
C3×#48382
#105903692
#105903472
#105902722
#105893482
C3×#44852
#105890992
#708673
#683983