Finite Group Databasebeta

← #11781749

Subgroups — #11781749

Order 1152.

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

normal subgroups only

This group has 432 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#10592547C211yesmaximal, characteristic, complemented
2#10590377C211yesmaximal, characteristic, complemented
3#10590350C211yesmaximal, characteristic
4#10590296C211yesmaximal, characteristic, complemented
5C3×#4485C211yesmaximal, characteristic, complemented
6C3×#4480C211yesmaximal, characteristic, complemented
7#10589091C211yesmaximal, characteristic, complemented
8#68550—31nomaximal
9#68413—31nomaximal
10C2×#3744—21no—
11#64083C2211yescharacteristic
12C4×#634C2211yescharacteristic
13C3×#874C2211yescharacteristic
14C2×#3716—21no—
15C2×#3714—21no—
16C2×#3714—21no—
17C32×C4⋊C8C2211yescharacteristic
18#63648—21no—
19C3×C4⋊(C3⋊C8)C2211yescharacteristic
20C3×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×C4×C3⋊C8C2211yescharacteristic
22#63572—21no—
23#63563—21no—
24#63555—21no—
25#5075—31no—
26#5073—31no—
27#4848—31no—
28#4848—31no—
29#4848—31no—
30#4848—61no—
31#4831—31no—
32#4695—31no—
33#4679—31no—
34C3×#334—31no—
35C3×#331—31no—
36#4485—31no—
37#4485—31no—
38#4485D311yescharacteristic, complemented
39#4480D311yescharacteristic, complemented
40C2×C4⋊(C3⋊D3)—21no—
41C2×C4⋊(C3⋊D3)—21no—
42C2×C4⋊(C3⋊D3)—21no—
43C2×#634D411yescharacteristic
44C2×C3×D12—21no—
45C2×C3×D12—21no—
46C2×C3×D12—21no—
47C2×C32×C8—21no—
48C32×C42C2311yescharacteristic
49C4⋊(C3⋊Dic3)D411yescharacteristic
50#3750—21no—
51C4×C3⋊Dic3—21no—
52#3744—42no—
53C2×C3×C3⋊C8—21no—
54C2×C3×C3⋊C8—21no—
55C2×C3×C3⋊C8D411yescharacteristic
56C2×C3×C3⋊C8D411yescharacteristic
57#3716—42no—
58#3714—42no—
59#3714—42no—
60#1688—91noSylow
61C3×#127—31no—
62C2×#214—61no—
63C2×#213—61no—
64C2×#213—61no—
65C2×D24—61no—
66C2×D24—61no—
67C2×#204—61no—
68C2×#204—61no—
69C2×#204—62no—
70C2×#204—61no—
71#874—31no—
72#874—31no—
73#874—61no—
74#874C2×D311yescharacteristic
75C4×Dic6—31no—
76C4×Dic6—31no—
77C4×Dic6—61no—
78C3×C4⋊C8—21no—
79C3×C4⋊C8—31no—
80C3×C4⋊C8—31no—
81C3×C4⋊C8C2×D311yescharacteristic
82C3×C4⋊C8C2×D311yescharacteristic
83C3×C4×C8—31no—
84#832—61no—
85#821—61no—
86#821—61no—
87#821—61no—
88#821—62no—
89#815—61no—
90#815—61no—
91Dic3⋊C8—61no—
92Dic3⋊C8—61no—
93C4⋊(C3⋊C8)C2×D311yescharacteristic
94C4⋊(C3⋊C8)C2×D311yescharacteristic
95C4×C3⋊C8C2×D311yescharacteristic
96C22×C3⋊D3—41no—
97C22×C3×D3—41no—
98C2×C32×C4C2×D411yescharacteristic
99C2×C32×C4C2×D411yescharacteristic
100C2×C32×C4#4111yescharacteristic
101C2×C3⋊Dic3—21no—
102C2×C3⋊Dic3—21no—
103C4⋊(C3⋊D3)—41no—
104C4⋊(C3⋊D3)—41no—
105C4⋊(C3⋊D3)—41no—
106C4⋊(C3⋊D3)—41no—
107C4⋊(C3⋊D3)—81no—
108#634—21no—
109#634—21no—
110C3×D12—41no—
111C3×D12—41no—
112C3×D12—41no—
113C3×D12—41no—
114C3×D12—81no—
115C32×C8—41no—
116C3×C3⋊C8—21no—
117C3×C3⋊C8—41no—
118C3×C3⋊C8—41no—
119C3×C3⋊C8SD1612yescomplemented
120#493—91no—
121#460—91no—
122#460—91no—
123#446—91no—
124#334—31no—
125#331—31no—
126#331—91no—
127C2×C3×D4—61no—
128C2×C3×D4—61no—
129C2×C3×D4—61no—
130C2×D12—21no—
131C2×D12—21no—
132C2×D12—21no—
133C2×D12—62no—
134C2×D12—61no—
135C2×D12—61no—
136C2×D12—61no—
137C2×D12—61no—
138C2×D12—61no—
139C2×D12—61no—
140C2×D12—121no—
141C2×D12—121no—
142C2×Dic6—31no—
143C2×Dic6—31no—
144C2×Dic6—61no—
145C2×C3×C8—22no—
146C2×C3×C8—21no—
147C2×C3×C8—21no—
148C2×C3×C8—31no—
149C2×C3×C8—31no—
150C2×C3×C8—61no—
151C2×C3×C8—61no—
152C3×C42—21no—
153C3×C42C22×D311yescharacteristic
154C3×C42C22×D311yescharacteristic
155#214—122no—
156#213—122no—
157#213—122no—
158C4⋊Dic3—31no—
159C4⋊Dic3—31no—
160C4⋊Dic3—61no—
161Dic3⋊C4—61no—
162Dic3⋊C4—61no—
163Dic3⋊C4—121no—
164C4×Dic3—61no—
165C4×Dic3—61no—
166C4×Dic3—121no—
167C2×C3⋊C8—21no—
168C2×C3⋊C8—21no—
169C2×C3⋊C8D1211yescharacteristic
170C2×C3⋊C8D1211yescharacteristic
171D24—122no—
172D24—122no—
173#204—124no—
174#204—122no—
175#204—122no—
176#204—122no—
177C22×C32#12111yescharacteristic
178C2×C3⋊D3—81no—
179C2×C3⋊D3—81no—
180C2×C3⋊D3—81no—
181C2×C3×D3—81no—
182C2×C3×D3—81no—
183C2×C3×D3—81no—
184C32×C4—21no—
185C32×C4C2×SD1611yescharacteristic
186C32×C4AGL(1,ℤ/8)11yescharacteristic
187C32×C4AGL(1,ℤ/8)11yescharacteristic
188C32×C4AGL(1,ℤ/8)11yescharacteristic
189C3⋊Dic3—41no—
190C3⋊Dic3—41no—
191C2×SD16—181no—
192C2×SD16—181no—
193C2×D8—181no—
194C2×D8—181no—
195#127—31no—
196#127—91no—
197C4×Q8—91no—
198C4⋊C8—31no—
199C4⋊C8—31no—
200C4⋊C8—181no—
201C4⋊C8D3211yescharacteristic
202#102—181no—
203#102—181no—
204#97—181no—
205C4×C8—31no—
206C23×C3—121no—
207C22×D3—41no—
208C22×D3—122no—
209C22×D3—121no—
210C22×D3—121no—
211C3×D4—121no—
212C3×D4—121no—
213C3×D4—121no—
214C3×D4—121no—
215C3×D4—241no—
216C2×C3×C4—21no—
217C2×C3×C4—21no—
218C2×C3×C4—21no—
219C2×C3×C4C2×D1211yescharacteristic
220C2×C3×C4#23511yescharacteristic
221C2×C3×C4D3×D411yescharacteristic
222C2×C3×C4D3×D411yescharacteristic
223C2×C3×C4D3×D411yescharacteristic
224C2×C3×C4#23911yescharacteristic
225C2×Dic3—61no—
226C2×Dic3—61no—
227C2×Dic3—61no—
228C2×Dic3—61no—
229C2×Dic3—121no—
230C2×Dic3—121no—
231D12—41no—
232D12—41no—
233D12—41no—
234D12—41no—
235D12—81no—
236D12—122no—
237D12—122no—
238D12—121no—
239D12—121no—
240D12—121no—
241D12—121no—
242D12—121no—
243D12—121no—
244D12—121no—
245D12—121no—
246D12—241no—
247D12—241no—
248D12—241no—
249D12—241no—
250D12—242no—
251Dic6—62no—
252Dic6—61no—
253Dic6—61no—
254Dic6—61no—
255Dic6—61no—
256Dic6—121no—
257C3×C8—32no—
258C3×C8—42no—
259C3×C8—41no—
260C3×C8—41no—
261C3×C8—61no—
262C3×C8—121no—
263C3×C8—121no—
264C3⋊C8—21no—
265C3⋊C8—41no—
266C3⋊C8—41no—
267C3⋊C8#20412yescomplemented
268C2×C32#46011yescharacteristic
269C2×C32#46911yescharacteristic
270C2×C32#47211yescharacteristic
271C3⋊D3—161no—
272C3×D3—161no—
273C2×Q8—91no—
274C2×D4—61no—
275C2×D4—61no—
276C2×D4—61no—
277C2×D4—181no—
278C2×D4—181no—
279C2×D4—181no—
280SD16—362no—
281SD16—362no—
282D8—362no—
283D8—362no—
284C2×C8—21no—
285C2×C8—31no—
286C2×C8—31no—
287C2×C8—61no—
288C2×C8—61no—
289C4⋊C4—91no—
290C4⋊C4—181no—
291C42—181no—
292C42C2×D3211yescharacteristic
293C22×C3—21no—
294C22×C3—241no—
295C22×C3—241no—
296C22×C3—241no—
297C22×C3#88411yescharacteristic
298C22×C3#89511yescharacteristic
299C2×D3—81no—
300C2×D3—81no—
301C2×D3—81no—
302C2×D3—242no—
303C2×D3—242no—
304C2×D3—242no—
305C2×D3—241no—
306C2×D3—241no—
307C2×D3—241no—
308C2×D3—241no—
309C2×D3—241no—
310C2×D3—241no—
311C3×C4—21no—
312C3×C4—21no—
313C3×C4—21no—
314C3×C4—21no—
315C3×C4—21no—
316C3×C4—21no—
317C3×C4—41no—
318C3×C4C2×#20411yescharacteristic
319C3×C4#90811yescharacteristic
320C3×C4#91111yescharacteristic
321C3×C4#91111yescharacteristic
322C3×C4D3×SD1611yescharacteristic
323C3×C4#91411yescharacteristic
324C3×C4#91411yescharacteristic
325C3×C4#91411yescharacteristic
326Dic3—122no—
327Dic3—121no—
328Dic3—121no—
329Dic3—121no—
330Dic3—121no—
331Dic3—241no—
332C32#168811yescharacteristic, complemented, Sylow
333C23—121no—
334C23—361no—
335Q8—181no—
336Q8—181no—
337D4—121no—
338D4—121no—
339D4—121no—
340D4—121no—
341D4—241no—
342D4—361no—
343D4—361no—
344D4—361no—
345D4—361no—
346D4—721no—
347C2×C4—181no—
348C2×C4—181no—
349C2×C4#379911yescharacteristic
350C2×C4D3×D1211yescharacteristic
351C2×C4#381111yescharacteristic
352C8—32no—
353C8—41no—
354C8—61no—
355C8—121no—
356C8—121no—
357C2×C3—21no—
358C2×C3—21no—
359C2×C3—21no—
360C2×C3—481no—
361C2×C3#474911yescharacteristic
362C2×C3#476211yescharacteristic
363C2×C3#478211yescharacteristic
364C2×C3#484811yescharacteristic
365C2×C3#486511yescharacteristic
366C2×C3#489711yescharacteristic
367D3—161no—
368D3—482no—
369D3—481no—
370D3—481no—
371C22—241no—
372C22—241no—
373C22—241no—
374C22—721no—
375C22—721no—
376C22—721no—
377C22#6391011yescharacteristic
378C4—21no—
379C4—361no—
380C4—361no—
381C4D3×#20411yescharacteristic
382C4#6379511yescharacteristic
383C4#6393711yescharacteristic
384C4#6394111yescharacteristic
385C3—21no—
386C3#6841311yescharacteristic, complemented
387C3#6855011yescharacteristic, complemented
388C2—481no—
389C2—1441no—
390C2#1059050811yescharacteristic
391C2#1059087911yescharacteristic
392C2#1059098711yescharacteristic
subgroupG/H
centerC22#63910
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. #10592547C2semidirect
2. #10590377C2semidirect
4. #10590296C2semidirect
5. C3×#4485C2semidirect
6. C3×#4480C2semidirect
7. #10589091C2semidirect
38. #4485D3semidirect
39. #4480D3semidirect
119. C3×C3⋊C8SD16semidirect
267. C3⋊C8#204semidirect
332. C32#1688semidirect
386. C3#68413semidirect
387. C3#68550semidirect

Maximal subgroups

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

subgroupindex
#105925472
#105903772
#105903502
#105902962
C3×#44852
C3×#44802
#105890912
#685503
#684133