Finite Group Databasebeta

← #11781751

Subgroups — #11781751

Order 1152.

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

normal subgroups only

This group has 410 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×#4831C211yesmaximal, characteristic, complemented
2#10590367C211yesmaximal, characteristic, complemented
3#10590364C211yesmaximal, characteristic, complemented
4#10590350C211yesmaximal, characteristic
5#10589351C211yesmaximal, characteristic, complemented
6C3×#4485C211yesmaximal, characteristic, complemented
7#10589097C211yesmaximal, characteristic, complemented
8#70959—31nomaximal
9#68413—31nomaximal
10#64083C2211yescharacteristic
11C3×#874C2211yescharacteristic
12C3×C4×Dic6C2211yescharacteristic
13C2×#3717—21no—
14C2×#3715—21no—
15C2×#3714—21no—
16C2×#3714—21no—
17C32×C4⋊C8C2211yescharacteristic
18C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
19C3×#815—21no—
20C3×Dic3⋊C8—21no—
21C3×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×C4×C3⋊C8C2211yescharacteristic
23#63564—21no—
24#63562—21no—
25C3×#446—31no—
26#5075—31no—
27#5073—31no—
28#5027—31no—
29#5027—31no—
30#4848—31no—
31#4831D311yescharacteristic, complemented
32#4695—31no—
33C3×#331—31no—
34#4485—31no—
35#4485—31no—
36#4485—61no—
37#4485D311yescharacteristic, complemented
38#4480—31no—
39#4457—31no—
40C2×C4⋊(C3⋊D3)—21no—
41C2×C4⋊(C3⋊D3)—21no—
42C2×C4⋊(C3⋊D3)—21no—
43C2×C3×D12—21no—
44C2×C3×D12—21no—
45C2×C3×D12—21no—
46C2×C3×Dic6D411yescharacteristic
47C2×C32×C8—21no—
48C32×C42C2311yescharacteristic
49C2×C3⋊(C3⋊C8)—21no—
50C3×C4⋊Dic3D411yescharacteristic
51C3×Dic3⋊C4—21no—
52C3×C4×Dic3—21no—
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8D411yescharacteristic
55C2×C3×C3⋊C8D411yescharacteristic
56#3717—42no—
57#3715—42no—
58#3714—42no—
59#3714—42no—
60#1688—91noSylow
61C3×#127—31no—
62C3×C4×Q8—31no—
63C2×#215—61no—
64C2×#215—61no—
65C2×#214—61no—
66C2×#213—61no—
67C2×#213—61no—
68C2×D24—61no—
69C2×D24—61no—
70C2×#204—61no—
71#874—31no—
72#874—31no—
73#874—61no—
74#874C2×D311yescharacteristic
75C4×Dic6C2×D311yescharacteristic
76C3×C4⋊C8—21no—
77C3×C4⋊C8—31no—
78C3×C4⋊C8—61no—
79C3×C4⋊C8C2×D311yescharacteristic
80C3×C4⋊C8C2×D311yescharacteristic
81C3×#97—61no—
82C3×C4×C8—31no—
83#832—61no—
84#821—61no—
85#815—21no—
86Dic3⋊C8—21no—
87#809—61no—
88#809—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—41no—
95C22×C3×D3—41no—
96C2×C32×C4C2×D411yescharacteristic
97C2×C32×C4C2×D411yescharacteristic
98C2×C32×C4#4111yescharacteristic
99C4⋊(C3⋊D3)—41no—
100C4⋊(C3⋊D3)—41no—
101C4⋊(C3⋊D3)—41no—
102C4⋊(C3⋊D3)—41no—
103C4⋊(C3⋊D3)—81no—
104C2×C3×Dic3—21no—
105C2×C3×Dic3—21no—
106C3×D12—41no—
107C3×D12—41no—
108C3×D12—41no—
109C3×D12—41no—
110C3×D12—81no—
111C3×Dic6—21no—
112C3×Dic6—21no—
113C32×C8—41no—
114C3⋊(C3⋊C8)—41no—
115C3×C3⋊C8—21no—
116C3×C3⋊C8—41no—
117C3×C3⋊C8SD1612yescomplemented
118#493—91no—
119#460—91no—
120#460—91no—
121#446—31no—
122#334—91no—
123#331—31no—
124#331—91no—
125C2×C3×Q8—31no—
126C2×C3×D4—61no—
127C2×C3×D4—61no—
128C2×C3×D4—61no—
129C2×D12—21no—
130C2×D12—21no—
131C2×D12—21no—
132C2×D12—61no—
133C2×D12—61no—
134C2×D12—61no—
135C2×D12—61no—
136C2×D12—62no—
137C2×D12—61no—
138C2×D12—61no—
139C2×D12—121no—
140C2×D12—121no—
141C2×Dic6D1211yescharacteristic
142C2×C3×C8—21no—
143C2×C3×C8—21no—
144C2×C3×C8—31no—
145C2×C3×C8—31no—
146C2×C3×C8—41no—
147C2×C3×C8—61no—
148C3×C4⋊C4—31no—
149C3×C4⋊C4—61no—
150C3×C42—21no—
151C3×C42—61no—
152C3×C42C22×D311yescharacteristic
153C3×C42C22×D311yescharacteristic
154#215—122no—
155#215—122no—
156#214—122no—
157#213—122no—
158#213—122no—
159C4⋊Dic3D1211yescharacteristic
160Dic3⋊C4—21no—
161C4×Dic3—21no—
162C2×C3⋊C8—21no—
163C2×C3⋊C8—61no—
164C2×C3⋊C8—61no—
165C2×C3⋊C8—121no—
166C2×C3⋊C8#6711yescharacteristic
167C2×C3⋊C8#6711yescharacteristic
168D24—122no—
169D24—122no—
170#204—122no—
171C22×C32#12111yescharacteristic
172C2×C3⋊D3—81no—
173C2×C3⋊D3—81no—
174C2×C3⋊D3—81no—
175C2×C3×D3—81no—
176C2×C3×D3—81no—
177C2×C3×D3—81no—
178C32×C4—21no—
179C32×C4C2×SD1611yescharacteristic
180C32×C4AGL(1,ℤ/8)11yescharacteristic
181C32×C4AGL(1,ℤ/8)11yescharacteristic
182C32×C4AGL(1,ℤ/8)11yescharacteristic
183C3×Dic3—41no—
184C3×Dic3—41no—
185C2×SD16—181no—
186C2×SD16—181no—
187C2×D8—181no—
188C2×D8—181no—
189#127—31no—
190#127—91no—
191C4×Q8—31no—
192C4⋊C8—31no—
193C4⋊C8—61no—
194C4⋊C8—91no—
195C4⋊C8D3211yescharacteristic
196#102—181no—
197#102—181no—
198#97—61no—
199C4×C8—31no—
200C23×C3—121no—
201C22×D3—41no—
202C22×D3—122no—
203C22×D3—121no—
204C22×D3—121no—
205C3×Q8—61no—
206C3×Q8—61no—
207C3×D4—121no—
208C3×D4—121no—
209C3×D4—121no—
210C3×D4—121no—
211C3×D4—241no—
212C2×C3×C4—21no—
213C2×C3×C4—21no—
214C2×C3×C4—21no—
215C2×C3×C4—61no—
216C2×C3×C4—61no—
217C2×C3×C4C2×D1211yescharacteristic
218C2×C3×C4#23511yescharacteristic
219C2×C3×C4#23511yescharacteristic
220C2×C3×C4D3×D411yescharacteristic
221C2×C3×C4D3×D411yescharacteristic
222C2×C3×C4C2×#6711yescharacteristic
223C2×Dic3—21no—
224C2×Dic3—21no—
225D12—41no—
226D12—41no—
227D12—41no—
228D12—41no—
229D12—81no—
230D12—121no—
231D12—121no—
232D12—121no—
233D12—121no—
234D12—121no—
235D12—121no—
236D12—121no—
237D12—121no—
238D12—241no—
239D12—241no—
240D12—241no—
241D12—241no—
242D12—241no—
243D12—241no—
244D12—242no—
245Dic6—21no—
246Dic6—21no—
247C3×C8—32no—
248C3×C8—41no—
249C3×C8—41no—
250C3×C8—61no—
251C3×C8—81no—
252C3×C8—121no—
253C3⋊C8—21no—
254C3⋊C8—41no—
255C3⋊C8—121no—
256C3⋊C8—121no—
257C3⋊C8—241no—
258C3⋊C8#21512yescomplemented
259C2×C32#46011yescharacteristic
260C2×C32#46911yescharacteristic
261C2×C32#47211yescharacteristic
262C3⋊D3—161no—
263C3×D3—161no—
264C2×Q8—31no—
265C2×D4—61no—
266C2×D4—61no—
267C2×D4—61no—
268C2×D4—181no—
269C2×D4—181no—
270C2×D4—181no—
271SD16—362no—
272SD16—362no—
273D8—362no—
274D8—362no—
275C2×C8—21no—
276C2×C8—31no—
277C2×C8—31no—
278C2×C8—61no—
279C2×C8—181no—
280C4⋊C4—31no—
281C4⋊C4—61no—
282C42—61no—
283C42C2×D3211yescharacteristic
284C22×C3—21no—
285C22×C3—241no—
286C22×C3—241no—
287C22×C3—241no—
288C22×C3#88411yescharacteristic
289C22×C3#93011yescharacteristic
290C2×D3—81no—
291C2×D3—81no—
292C2×D3—81no—
293C2×D3—242no—
294C2×D3—242no—
295C2×D3—242no—
296C2×D3—241no—
297C2×D3—241no—
298C2×D3—241no—
299C2×D3—241no—
300C2×D3—241no—
301C2×D3—241no—
302C3×C4—21no—
303C3×C4—21no—
304C3×C4—21no—
305C3×C4—21no—
306C3×C4—21no—
307C3×C4—21no—
308C3×C4—41no—
309C3×C4—121no—
310C3×C4—121no—
311C3×C4#90811yescharacteristic
312C3×C4#90811yescharacteristic
313C3×C4#91111yescharacteristic
314C3×C4#91111yescharacteristic
315C3×C4D3×SD1611yescharacteristic
316C3×C4#91411yescharacteristic
317C3×C4C2×#21511yescharacteristic
318C3×C4#94911yescharacteristic
319Dic3—41no—
320Dic3—41no—
321C32#168811yescharacteristic, complemented, Sylow
322C23—121no—
323C23—361no—
324Q8—61no—
325Q8—61no—
326D4—121no—
327D4—121no—
328D4—121no—
329D4—121no—
330D4—241no—
331D4—361no—
332D4—361no—
333D4—361no—
334D4—361no—
335D4—721no—
336C2×C4—61no—
337C2×C4—61no—
338C2×C4#379811yescharacteristic
339C2×C4D3×D1211yescharacteristic
340C2×C4D3×#6711yescharacteristic
341C8—32no—
342C8—41no—
343C8—61no—
344C8—121no—
345C8—361no—
346C2×C3—21no—
347C2×C3—21no—
348C2×C3—21no—
349C2×C3—481no—
350C2×C3#474911yescharacteristic
351C2×C3#476211yescharacteristic
352C2×C3#478211yescharacteristic
353C2×C3#502711yescharacteristic
354C2×C3#513511yescharacteristic
355C2×C3#514211yescharacteristic
356D3—161no—
357D3—482no—
358D3—481no—
359D3—481no—
360C22—241no—
361C22—241no—
362C22—241no—
363C22—721no—
364C22—721no—
365C22—721no—
366C22#6390611yescharacteristic
367C4—21no—
368C4—121no—
369C4—121no—
370C4#6379411yescharacteristic
371C4#6379511yescharacteristic
372C4#6392511yescharacteristic
373C4D3×#21511yescharacteristic
374C3—21no—
375C3#6841311yescharacteristic, complemented
376C3#7095911yescharacteristic, complemented
377C2—481no—
378C2—1441no—
379C2#1059054911yescharacteristic
380C2#1059082711yescharacteristic
381C2#1059099711yescharacteristic
subgroupG/H
centerC22#63906
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#121
prime radical#10590350C2
hypercenterC4⋊C8D32
hypocenterC32#1688
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×#4831C2semidirect
2. #10590367C2semidirect
3. #10590364C2semidirect
5. #10589351C2semidirect
6. C3×#4485C2semidirect
7. #10589097C2semidirect
31. #4831D3semidirect
37. #4485D3semidirect
117. C3×C3⋊C8SD16semidirect
258. C3⋊C8#215semidirect
321. C32#1688semidirect
375. C3#68413semidirect
376. C3#70959semidirect

Maximal subgroups

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

subgroupindex
C3×#48312
#105903672
#105903642
#105903502
#105893512
C3×#44852
#105890972
#709593
#684133