Finite Group Databasebeta

← #11781716

Subgroups — #11781716

Order 1152.

423 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 423 conjugacy classes of subgroups — too many to draw. Only its 84 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×#4843C211yesmaximal, characteristic, complemented
2#10590352C211yesmaximal, characteristic, complemented
3#10590347C211yesmaximal, characteristic, complemented
4#10590339C211yesmaximal, characteristic, complemented
5#10589346C211yesmaximal, characteristic, complemented
6C3×#4485C211yesmaximal, characteristic, complemented
7#10589090C211yesmaximal, characteristic, complemented
8#71009—31nomaximal
9#68399—31nomaximal
10C2×C3×D24—21no—
11C3×#874C2211yescharacteristic
12C3×#874C2211yescharacteristic
13C3×C4×D12C2211yescharacteristic
14C2×#3713—21no—
15C2×#3713—21no—
16C2×#3713—21no—
17C2×#3711—21no—
18C32×C4⋊C8C2211yescharacteristic
19C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
20C4×C3⋊(C3⋊C8)C2211yescharacteristic
21C3×#821—21no—
22C3×C4⋊(C3⋊C8)C2211yescharacteristic
23#63562—21no—
24(C2×D3)⋊(C3⋊C8)—21no—
25C3×#459—31no—
26#5073—31no—
27#5073—31no—
28#5072—31no—
29#5015—31no—
30#5012—31no—
31#4843D311yescharacteristic, complemented
32#4838—31no—
33C3×#331—31no—
34#4544—31no—
35#4485—31no—
36#4485D311yescharacteristic, complemented
37#4480—31no—
38#4480—31no—
39#4480—61no—
40C2×C3×D12—21no—
41C2×C3×D12—21no—
42C2×C3×D12—21no—
43C2×C3×D12—21no—
44C2×C3×D12—21no—
45C2×C3×D12—21no—
46C2×C3×D12D411yescharacteristic
47C2×C3×C4×D3—21no—
48C2×C32×C8—21no—
49C32×C42C2311yescharacteristic
50C2×C3⋊(C3⋊C8)—21no—
51C2×C3⋊(C3⋊C8)D411yescharacteristic
52C2×C3⋊(C3⋊C8)D411yescharacteristic
53C3×(C2×D3)⋊C4—21no—
54C3×C4⋊Dic3D411yescharacteristic
55C2×C3×C3⋊C8—21no—
56C3×D24—42no—
57#3713—42no—
58#3713—42no—
59#3713—42no—
60#3711—42no—
61#1687—91noSylow
62C2×C3×D8—61no—
63C3×#127—31no—
64C3×#127—31no—
65C3×C4×D4—31no—
66C2×#213—61no—
67C2×#213—61no—
68C2×#213—61no—
69C2×#213—61no—
70C2×#213—61no—
71C2×#213—61no—
72C2×#208—61no—
73C2×D24—21no—
74C2×ΓL(1,𝔽25)—61no—
75#874C2×D311yescharacteristic
76#874C2×D311yescharacteristic
77C4×D12C2×D311yescharacteristic
78C3×C4⋊C8—21no—
79C3×C4⋊C8—31no—
80C3×C4⋊C8C2×D311yescharacteristic
81C3×C4⋊C8C2×D311yescharacteristic
82C3×#102—61no—
83#832—61no—
84#830—61no—
85#821—21no—
86(C2×D3)⋊C8—61no—
87#809—61no—
88C4⋊(C3⋊C8)—31no—
89C4⋊(C3⋊C8)—31no—
90C4⋊(C3⋊C8)—61no—
91C4⋊(C3⋊C8)C2×D311yescharacteristic
92C4×C3⋊C8—31no—
93C4×C3⋊C8—31no—
94C4×C3⋊C8—61no—
95C22×C3×D3—21no—
96C22×C3×D3—41no—
97C22×C3×D3—41no—
98C2×C32×C4C2×D411yescharacteristic
99C2×C32×C4C2×D411yescharacteristic
100C2×C32×C4#4111yescharacteristic
101C2×C3×Dic3—21no—
102C3×D12—21no—
103C3×D12—21no—
104C3×D12—41no—
105C3×D12—41no—
106C3×D12—41no—
107C3×D12—41no—
108C3×D12—41no—
109C3×D12—41no—
110C3×D12—41no—
111C3×D12—41no—
112C3×D12—81no—
113C3×D12—81no—
114C3×C4×D3—41no—
115C3×C4×D3—41no—
116C32×C8—41no—
117C3⋊(C3⋊C8)—21no—
118C3⋊(C3⋊C8)—41no—
119C3⋊(C3⋊C8)D812yescomplemented
120C3×C3⋊C8—41no—
121#493—91no—
122#459—31no—
123#459—91no—
124#436—91no—
125#334—91no—
126#331—31no—
127#331—91no—
128C2×C3×D4—31no—
129C2×C3×D4—61no—
130C2×C3×D4—61no—
131C2×C3×D4—61no—
132C2×C3×D4—61no—
133C2×C3×D4—61no—
134C2×C3×D4—61no—
135C22×C3×C4—61no—
136C2×D12—21no—
137C2×D12—21no—
138C2×D12—21no—
139C2×D12—21no—
140C2×D12—21no—
141C2×D12—21no—
142C2×D12#6711yescharacteristic
143C2×C4×D3—21no—
144C3×D8—122no—
145C2×C3×C8—21no—
146C2×C3×C8—21no—
147C2×C3×C8—41no—
148C2×C3×C8—61no—
149C3×C4⋊C4—31no—
150C3×C22⋊C4—61no—
151C3×C42—21no—
152C3×C42C22×D311yescharacteristic
153C3×C42C22×D311yescharacteristic
154#213—122no—
155#213—122no—
156#213—122no—
157#213—122no—
158#213—122no—
159#213—122no—
160(C2×D3)⋊C4—21no—
161C4⋊Dic3#6711yescharacteristic
162#208—122no—
163C2×C3⋊C8—21no—
164C2×C3⋊C8—31no—
165C2×C3⋊C8—31no—
166C2×C3⋊C8—31no—
167C2×C3⋊C8—31no—
168C2×C3⋊C8—61no—
169C2×C3⋊C8—61no—
170C2×C3⋊C8—61no—
171C2×C3⋊C8—61no—
172C2×C3⋊C8—121no—
173D24—42no—
174ΓL(1,𝔽25)—122no—
175C22×C32#12111yescharacteristic
176C2×C3×D3—41no—
177C2×C3×D3—41no—
178C2×C3×D3—41no—
179C2×C3×D3—81no—
180C2×C3×D3—81no—
181C2×C3×D3—81no—
182C2×C3×D3—81no—
183C2×C3×D3—81no—
184C2×C3×D3—81no—
185C32×C4—21no—
186C32×C4C2×D811yescharacteristic
187C32×C4AGL(1,ℤ/8)11yescharacteristic
188C32×C4AGL(1,ℤ/8)11yescharacteristic
189C32×C4AGL(1,ℤ/8)11yescharacteristic
190C3×Dic3—41no—
191C2×D8—61no—
192C2×D8—181no—
193C2×D8—181no—
194C2×D8—181no—
195C2×M16—181no—
196#127—31no—
197#127—31no—
198C4×D4—31no—
199C4⋊C8—31no—
200C4⋊C8—91no—
201C4⋊C8D3211yescharacteristic
202#102—61no—
203#102—181no—
204C22⋊C8—181no—
205C4×C8—91no—
206C23×C3—61no—
207C23×C3—121no—
208C23×C3—121no—
209C22×D3—21no—
210C22×D3—41no—
211C22×D3—41no—
212C3×D4—61no—
213C3×D4—61no—
214C3×D4—121no—
215C3×D4—121no—
216C3×D4—121no—
217C3×D4—121no—
218C3×D4—121no—
219C3×D4—121no—
220C3×D4—121no—
221C3×D4—121no—
222C3×D4—241no—
223C3×D4—241no—
224C2×C3×C4—21no—
225C2×C3×C4—21no—
226C2×C3×C4—21no—
227C2×C3×C4—61no—
228C2×C3×C4—121no—
229C2×C3×C4—121no—
230C2×C3×C4#23511yescharacteristic
231C2×C3×C4D3×D411yescharacteristic
232C2×C3×C4D3×D411yescharacteristic
233C2×C3×C4D3×D411yescharacteristic
234C2×C3×C4#23711yescharacteristic
235C2×C3×C4C2×#6711yescharacteristic
236C2×Dic3—21no—
237D12—21no—
238D12—21no—
239D12—41no—
240D12—41no—
241D12—41no—
242D12—41no—
243D12—41no—
244D12—41no—
245D12—41no—
246D12—41no—
247D12—81no—
248D12—81no—
249C4×D3—41no—
250C4×D3—41no—
251C3×C8—41no—
252C3×C8—41no—
253C3×C8—81no—
254C3×C8—121no—
255C3⋊C8—32no—
256C3⋊C8—32no—
257C3⋊C8—41no—
258C3⋊C8—62no—
259C3⋊C8—61no—
260C3⋊C8—61no—
261C3⋊C8—121no—
262C3⋊C8—121no—
263C3⋊C8—121no—
264C3⋊C8—241no—
265C2×C32#45911yescharacteristic
266C2×C32#46911yescharacteristic
267C2×C32#47211yescharacteristic
268C3×D3—81no—
269C3×D3—161no—
270C3×D3—161no—
271C2×D4—31no—
272C2×D4—61no—
273C2×D4—61no—
274C2×D4—61no—
275C2×D4—61no—
276C2×D4—61no—
277C2×D4—61no—
278C22×C4—61no—
279D8—122no—
280D8—362no—
281D8—362no—
282D8—362no—
283M16—362no—
284C2×C8—21no—
285C2×C8—61no—
286C2×C8—91no—
287C2×C8—91no—
288C2×C8—181no—
289C4⋊C4—31no—
290C22⋊C4—61no—
291C42C2×D3211yescharacteristic
292C22×C3—21no—
293C22×C3—121no—
294C22×C3—121no—
295C22×C3—121no—
296C22×C3—241no—
297C22×C3—241no—
298C22×C3—241no—
299C22×C3—241no—
300C22×C3—241no—
301C22×C3—241no—
302C22×C3#88411yescharacteristic
303C22×C3#93911yescharacteristic
304C2×D3—41no—
305C2×D3—41no—
306C2×D3—41no—
307C2×D3—81no—
308C2×D3—81no—
309C2×D3—81no—
310C2×D3—81no—
311C2×D3—81no—
312C2×D3—81no—
313C3×C4—21no—
314C3×C4—21no—
315C3×C4—21no—
316C3×C4—21no—
317C3×C4—21no—
318C3×C4—21no—
319C3×C4—41no—
320C3×C4—121no—
321C3×C4D3×D811yescharacteristic
322C3×C4D3×D811yescharacteristic
323C3×C4#91111yescharacteristic
324C3×C4#91111yescharacteristic
325C3×C4#91411yescharacteristic
326C3×C4#91411yescharacteristic
327C3×C4#93211yescharacteristic
328C3×C4#94911yescharacteristic
329Dic3—41no—
330C32#168711yescharacteristic, complemented, Sylow
331C23—61no—
332C23—121no—
333C23—121no—
334D4—61no—
335D4—61no—
336D4—121no—
337D4—121no—
338D4—121no—
339D4—121no—
340D4—121no—
341D4—121no—
342D4—121no—
343D4—121no—
344D4—241no—
345D4—241no—
346C2×C4—61no—
347C2×C4—121no—
348C2×C4—121no—
349C2×C4#379511yescharacteristic
350C2×C4#380211yescharacteristic
351C2×C4D3×#6711yescharacteristic
352C8—41no—
353C8—92no—
354C8—121no—
355C8—181no—
356C8—361no—
357C2×C3—21no—
358C2×C3—21no—
359C2×C3—21no—
360C2×C3—241no—
361C2×C3—481no—
362C2×C3—481no—
363C2×C3#474911yescharacteristic
364C2×C3#478211yescharacteristic
365C2×C3#478611yescharacteristic
366C2×C3#503911yescharacteristic
367C2×C3#515011yescharacteristic
368C2×C3#519911yescharacteristic
369D3—81no—
370D3—161no—
371D3—161no—
372C22—121no—
373C22—121no—
374C22—121no—
375C22—241no—
376C22—241no—
377C22—241no—
378C22—241no—
379C22—241no—
380C22—241no—
381C22#6388511yescharacteristic
382C4—21no—
383C4—121no—
384C4#6379711yescharacteristic
385C4#6379811yescharacteristic
386C4#6393211yescharacteristic
387C4#6393911yescharacteristic
388C3—21no—
389C3#6839911yescharacteristic, complemented
390C3#7100911yescharacteristic, complemented
391C2—241no—
392C2—481no—
393C2—481no—
394C2#1059050411yescharacteristic
395C2#1059074911yescharacteristic
396C2#1059098211yescharacteristic
subgroupG/H
centerC22#63885
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socleC22×C32#121
hypercenterC4⋊C8D32
hypocenterC32#1687
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×#4843C2semidirect
2. #10590352C2semidirect
3. #10590347C2semidirect
4. #10590339C2semidirect
5. #10589346C2semidirect
6. C3×#4485C2semidirect
7. #10589090C2semidirect
31. #4843D3semidirect
36. #4485D3semidirect
119. C3⋊(C3⋊C8)D8semidirect
330. C32#1687semidirect
389. C3#68399semidirect
390. C3#71009semidirect

Maximal subgroups

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

subgroupindex
C3×#48432
#105903522
#105903472
#105903392
#105893462
C3×#44852
#105890902
#710093
#683993