Finite Group Databasebeta

← #11781718

Subgroups — #11781718

Order 1152.

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

normal subgroups only

This group has 438 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×#4843C211yesmaximal, characteristic, complemented
2#10590350C211yesmaximal, characteristic, complemented
3#10590349C211yesmaximal, characteristic, complemented
4#10590337C211yesmaximal, characteristic, complemented
5#10589351C211yesmaximal, characteristic, complemented
6C3×#4480C211yesmaximal, characteristic, complemented
7#10589090C211yesmaximal, characteristic, complemented
8#71009—31nomaximal
9#68540—31nomaximal
10#64083C2211yescharacteristic
11C2×C3×D24—21no—
12C3×#874C2211yescharacteristic
13C3×C4×D12C2211yescharacteristic
14C2×#3714—21no—
15C2×#3714—21no—
16C2×#3714—21no—
17C2×#3711—21no—
18C32×C4⋊C8C2211yescharacteristic
19C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
20C3×#821—21no—
21C3×C4⋊(C3⋊C8)C2211yescharacteristic
22C3×C4×C3⋊C8C2211yescharacteristic
23#63564—21no—
24(C2×D3)⋊(C3⋊C8)—21no—
25C3×#459—31no—
26#5073—31no—
27#5015—31no—
28#5012—31no—
29#4843—31no—
30#4843D311yescharacteristic, complemented
31#4695—31no—
32#4688—31no—
33C3×#334—31no—
34#4544—31no—
35#4485—31no—
36#4485—31no—
37#4485—31no—
38#4485—61no—
39#4480D311yescharacteristic, complemented
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×D12D411yescharacteristic
47C2×C3×C4×D3—21no—
48C2×C32×C8—21no—
49C32×C42C2311yescharacteristic
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×D24—42no—
57#3714—42no—
58#3714—42no—
59#3714—42no—
60#3711—42no—
61#1687—91noSylow
62C2×C3×D8—61no—
63C3×#127—31no—
64C3×C4×D4—31no—
65C2×#213—61no—
66C2×#213—61no—
67C2×#213—61no—
68C2×#208—61no—
69C2×D24—21no—
70C2×D24—61no—
71C2×D24—61no—
72C2×D24—61no—
73C2×ΓL(1,𝔽25)—61no—
74#874—31no—
75#874—31no—
76#874—61no—
77#874C2×D311yescharacteristic
78C4×D12C2×D311yescharacteristic
79C3×C4⋊C8—21no—
80C3×C4⋊C8—31no—
81C3×C4⋊C8C2×D311yescharacteristic
82C3×C4⋊C8C2×D311yescharacteristic
83C3×#102—61no—
84C3×C4×C8—31no—
85#830—61no—
86#821—21no—
87#821—61no—
88(C2×D3)⋊C8—61no—
89#809—61no—
90C4⋊(C3⋊C8)—31no—
91C4⋊(C3⋊C8)—31no—
92C4⋊(C3⋊C8)—61no—
93C4⋊(C3⋊C8)C2×D311yescharacteristic
94C4×C3⋊C8C2×D311yescharacteristic
95C22×C3⋊D3—41no—
96C22×C3×D3—21no—
97C22×C3×D3—41no—
98C2×C32×C4C2×D411yescharacteristic
99C2×C32×C4C2×D411yescharacteristic
100C2×C32×C4#4111yescharacteristic
101C4⋊(C3⋊D3)—41no—
102C4⋊(C3⋊D3)—41no—
103C4⋊(C3⋊D3)—41no—
104C4⋊(C3⋊D3)—41no—
105C4⋊(C3⋊D3)—81no—
106C2×C3×Dic3—21no—
107C3×D12—21no—
108C3×D12—21no—
109C3×D12—41no—
110C3×D12—41no—
111C3×D12—41no—
112C3×D12—41no—
113C3×D12—81no—
114C3×C4×D3—41no—
115C3×C4×D3—41no—
116C32×C8—41no—
117C3⋊(C3⋊C8)—41no—
118C3×C3⋊C8—21no—
119C3×C3⋊C8—41no—
120C3×C3⋊C8D812yescomplemented
121#493—91no—
122#459—31no—
123#459—91no—
124#436—91no—
125#334—31no—
126#331—91no—
127#331—91no—
128C2×C3×D4—31no—
129C2×C3×D4—61no—
130C2×C3×D4—61no—
131C2×C3×D4—61no—
132C22×C3×C4—61no—
133C2×D12—21no—
134C2×D12—21no—
135C2×D12—21no—
136C2×D12—61no—
137C2×D12—61no—
138C2×D12—61no—
139C2×D12—61no—
140C2×D12—62no—
141C2×D12—61no—
142C2×D12—61no—
143C2×D12—121no—
144C2×D12—121no—
145C2×D12#6711yescharacteristic
146C2×C4×D3—21no—
147C3×D8—122no—
148C2×C3×C8—21no—
149C2×C3×C8—21no—
150C2×C3×C8—31no—
151C2×C3×C8—31no—
152C2×C3×C8—41no—
153C2×C3×C8—61no—
154C3×C4⋊C4—31no—
155C3×C22⋊C4—61no—
156C3×C42—21no—
157C3×C42C22×D311yescharacteristic
158C3×C42C22×D311yescharacteristic
159#213—122no—
160#213—122no—
161#213—122no—
162(C2×D3)⋊C4—21no—
163C4⋊Dic3#6711yescharacteristic
164#208—122no—
165C2×C3⋊C8—21no—
166C2×C3⋊C8—61no—
167C2×C3⋊C8—61no—
168C2×C3⋊C8—121no—
169C2×C3⋊C8D1211yescharacteristic
170C2×C3⋊C8D1211yescharacteristic
171D24—42no—
172D24—122no—
173D24—122no—
174D24—122no—
175ΓL(1,𝔽25)—122no—
176C22×C32#12111yescharacteristic
177C2×C3⋊D3—81no—
178C2×C3⋊D3—81no—
179C2×C3⋊D3—81no—
180C2×C3×D3—41no—
181C2×C3×D3—41no—
182C2×C3×D3—41no—
183C2×C3×D3—81no—
184C2×C3×D3—81no—
185C2×C3×D3—81no—
186C32×C4—21no—
187C32×C4C2×D811yescharacteristic
188C32×C4AGL(1,ℤ/8)11yescharacteristic
189C32×C4AGL(1,ℤ/8)11yescharacteristic
190C32×C4AGL(1,ℤ/8)11yescharacteristic
191C3×Dic3—41no—
192C2×D8—61no—
193C2×D8—181no—
194C2×D8—181no—
195C2×D8—181no—
196C2×M16—181no—
197#127—31no—
198#127—91no—
199C4×D4—31no—
200C4⋊C8—31no—
201C4⋊C8—91no—
202C4⋊C8D3211yescharacteristic
203#102—61no—
204#102—181no—
205C22⋊C8—181no—
206C4×C8—31no—
207C23×C3—61no—
208C23×C3—121no—
209C22×D3—21no—
210C22×D3—41no—
211C22×D3—122no—
212C22×D3—121no—
213C22×D3—121no—
214C3×D4—61no—
215C3×D4—61no—
216C3×D4—121no—
217C3×D4—121no—
218C3×D4—121no—
219C3×D4—121no—
220C3×D4—241no—
221C2×C3×C4—21no—
222C2×C3×C4—21no—
223C2×C3×C4—21no—
224C2×C3×C4—61no—
225C2×C3×C4—121no—
226C2×C3×C4—121no—
227C2×C3×C4C2×D1211yescharacteristic
228C2×C3×C4D3×D411yescharacteristic
229C2×C3×C4D3×D411yescharacteristic
230C2×C3×C4#23711yescharacteristic
231C2×C3×C4#23911yescharacteristic
232C2×C3×C4C2×#6711yescharacteristic
233C2×Dic3—21no—
234D12—21no—
235D12—21no—
236D12—41no—
237D12—41no—
238D12—41no—
239D12—41no—
240D12—81no—
241D12—121no—
242D12—121no—
243D12—121no—
244D12—121no—
245D12—121no—
246D12—121no—
247D12—121no—
248D12—121no—
249D12—241no—
250D12—241no—
251D12—241no—
252D12—241no—
253D12—241no—
254D12—241no—
255D12—242no—
256C4×D3—41no—
257C4×D3—41no—
258C3×C8—32no—
259C3×C8—41no—
260C3×C8—41no—
261C3×C8—61no—
262C3×C8—81no—
263C3×C8—121no—
264C3⋊C8—21no—
265C3⋊C8—41no—
266C3⋊C8—121no—
267C3⋊C8—121no—
268C3⋊C8—241no—
269C3⋊C8D2412yescomplemented
270C2×C32#45911yescharacteristic
271C2×C32#46911yescharacteristic
272C2×C32#47211yescharacteristic
273C3⋊D3—161no—
274C3×D3—81no—
275C3×D3—161no—
276C2×D4—31no—
277C2×D4—61no—
278C2×D4—61no—
279C2×D4—61no—
280C2×D4—181no—
281C2×D4—181no—
282C2×D4—181no—
283C22×C4—61no—
284D8—122no—
285D8—362no—
286D8—362no—
287D8—362no—
288M16—362no—
289C2×C8—21no—
290C2×C8—31no—
291C2×C8—31no—
292C2×C8—61no—
293C2×C8—181no—
294C4⋊C4—31no—
295C22⋊C4—61no—
296C42C2×D3211yescharacteristic
297C22×C3—21no—
298C22×C3—121no—
299C22×C3—121no—
300C22×C3—121no—
301C22×C3—241no—
302C22×C3—241no—
303C22×C3—241no—
304C22×C3#89511yescharacteristic
305C22×C3#93911yescharacteristic
306C2×D3—41no—
307C2×D3—41no—
308C2×D3—41no—
309C2×D3—81no—
310C2×D3—81no—
311C2×D3—81no—
312C2×D3—242no—
313C2×D3—242no—
314C2×D3—242no—
315C2×D3—241no—
316C2×D3—241no—
317C2×D3—241no—
318C2×D3—241no—
319C2×D3—241no—
320C2×D3—241no—
321C3×C4—21no—
322C3×C4—21no—
323C3×C4—21no—
324C3×C4—21no—
325C3×C4—21no—
326C3×C4—21no—
327C3×C4—41no—
328C3×C4—121no—
329C3×C4C2×D2411yescharacteristic
330C3×C4#90811yescharacteristic
331C3×C4D3×D811yescharacteristic
332C3×C4#91111yescharacteristic
333C3×C4#91411yescharacteristic
334C3×C4#91411yescharacteristic
335C3×C4#93211yescharacteristic
336C3×C4#94911yescharacteristic
337Dic3—41no—
338C32#168711yescharacteristic, complemented, Sylow
339C23—61no—
340C23—121no—
341C23—361no—
342D4—61no—
343D4—61no—
344D4—121no—
345D4—121no—
346D4—121no—
347D4—121no—
348D4—241no—
349D4—361no—
350D4—361no—
351D4—361no—
352D4—361no—
353D4—721no—
354C2×C4—61no—
355C2×C4—121no—
356C2×C4—121no—
357C2×C4#379611yescharacteristic
358C2×C4D3×D1211yescharacteristic
359C2×C4D3×#6711yescharacteristic
360C8—32no—
361C8—41no—
362C8—61no—
363C8—121no—
364C8—361no—
365C2×C3—21no—
366C2×C3—21no—
367C2×C3—21no—
368C2×C3—241no—
369C2×C3—481no—
370C2×C3#484311yescharacteristic
371C2×C3#486511yescharacteristic
372C2×C3#489711yescharacteristic
373C2×C3#503911yescharacteristic
374C2×C3#515011yescharacteristic
375C2×C3#519911yescharacteristic
376D3—81no—
377D3—161no—
378D3—482no—
379D3—481no—
380D3—481no—
381C22—121no—
382C22—121no—
383C22—121no—
384C22—241no—
385C22—241no—
386C22—241no—
387C22—721no—
388C22—721no—
389C22—721no—
390C22#6388611yescharacteristic
391C4—21no—
392C4—121no—
393C4D3×D2411yescharacteristic
394C4#6379511yescharacteristic
395C4#6393411yescharacteristic
396C4#6393911yescharacteristic
397C3—21no—
398C3#6854011yescharacteristic, complemented
399C3#7100911yescharacteristic, complemented
400C2—241no—
401C2—481no—
402C2—1441no—
403C2#1059058611yescharacteristic
404C2#1059075311yescharacteristic
405C2#1059098411yescharacteristic
subgroupG/H
centerC22#63886
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. #10590350C2semidirect
3. #10590349C2semidirect
4. #10590337C2semidirect
5. #10589351C2semidirect
6. C3×#4480C2semidirect
7. #10589090C2semidirect
30. #4843D3semidirect
39. #4480D3semidirect
120. C3×C3⋊C8D8semidirect
269. C3⋊C8D24semidirect
338. C32#1687semidirect
398. C3#68540semidirect
399. C3#71009semidirect

Maximal subgroups

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

subgroupindex
C3×#48432
#105903502
#105903492
#105903372
#105893512
C3×#44802
#105890902
#710093
#685403