Finite Group Databasebeta

← #11922986

Subgroups — #11922986

Order 1152.

670 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 670 conjugacy classes of subgroups — too many to draw. Only its 91 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#10596575C211yesmaximal, characteristic
2C2×C3×C8×A4C211yesmaximal, characteristic, complemented
3#10593643C211yesmaximal, characteristic, complemented
4#10593634C212yesmaximal, complemented
5C8×C3⋊S4C212yesmaximal, complemented
6#85437—33nomaximal
7#83734—31nomaximal
8C2×C3×C4×A4C2211yescharacteristic
9#64269C412yes—
10C4⋊(C3⋊S4)C411yescharacteristic
11C4×C3⋊S4C2212yes—
12#64259C411yescharacteristic
13#64110—41nomaximal
14C3×C8×A4C2211yescharacteristic
15C3×C8×A4C2211yescharacteristic
16C3⋊(A4⋊C8)C2212yes—
17#5912—33no—
18C23×C3×C8D311yescharacteristic, complemented
19#5791—31no—
20C2×#901—31no—
21C2×C8×A4D313yescomplemented
22#5409—33no—
23#5400—36no—
24C8×S4—36no—
25#5207—31no—
26#5111—32no—
27#5111—32no—
28#5110—31no—
29C8×#67—32no—
30C8×#67—32no—
31#5102—31no—
32#5101—31no—
33C22×C3×A4C2×C411yescharacteristic
34C2×C3⋊S4C2×C412yes—
35#3828—41no—
36C3×C4×A4C2×C411yescharacteristic
37C3×C4×A4C2311yescharacteristic
38C3⋊SL(2,ℤ/4)C2×C412yes—
39C2×C32×C8—41no—
40#3748—41no—
41#3743—42no—
42C8×C3⋊D3—42no—
43#2929—91noSylow
44C23×C3×C4C2×D311yescharacteristic
45C2×#235—31no—
46C2×C4×A4C2×D313yes—
47GL(2,ℤ/4)—36no—
48C4⋊S4—33no—
49C4×S4—36no—
50A4⋊Q8—33no—
51C22×C3×C8—31no—
52C22×C3×C8—31no—
53C22×C3×C8—31no—
54C22×C3×C8—31no—
55C22×C3×C8C2×D311yescharacteristic
56C22×C3×C8C2×D311yescharacteristic
57#953—32no—
58#930—31no—
59#930—31no—
60#929—32no—
61C4×#67—32no—
62C4×#67—32no—
63#926—31no—
64#924—31no—
65#924—31no—
66C2×#208—31no—
67C2×#208—31no—
68#901—61no—
69#901—61no—
70#901—61no—
71#901—61no—
72#901—123no—
73C2×ΓL(1,𝔽25)—32no—
74C2×D3×C8—32no—
75C8×A4C2×D313yes—
76C8×A4C2×D313yes—
77A4⋊C8—36no—
78#830—32no—
79#830—32no—
80(C2×D3)⋊C8—32no—
81(C2×D3)⋊C8—32no—
82#815—32no—
83Dic3⋊C8—32no—
84Dic3⋊C8—32no—
85C8×Dic3—32no—
86C2×C3×A4—21no—
87C2×C3×A4C22×C411yescharacteristic
88C3⋊S4—22no—
89C2×C32×C4—41no—
90#638—42no—
91C4⋊(C3⋊D3)—41no—
92C4×C3⋊D3—42no—
93#634—41no—
94C32×C8—41no—
95C32×C8—41no—
96C3⋊(C3⋊C8)—42no—
97C2×#131—91no—
98C23×C8C3⋊D311yescharacteristic, complemented
99#525—91no—
100#435—92no—
101#435—92no—
102C8×D4—92no—
103C8×D4—92no—
104#424—91no—
105#408—91no—
106#407—91no—
107#405—91no—
108C24×C3C4×D311yescharacteristic
109C22×A4C4×D313yes—
110C2×S4—36no—
111C22×C3×C4—31no—
112C22×C3×C4—31no—
113C22×C3×C4—31no—
114C22×C3×C4—31no—
115C22×C3×C4C4×D311yescharacteristic
116C22×C3×C4C22×D311yescharacteristic
117C2×#67—32no—
118C2×#67—32no—
119C2×#67—32no—
120#235—61no—
121#235—61no—
122#235—61no—
123#235—61no—
124#235—123no—
125C2×D12—31no—
126C2×C4×D3—32no—
127C2×Dic6—31no—
128C4×A4C4×D313yes—
129C4×A4C22×D313yes—
130SL(2,ℤ/4)—36no—
131C2×C3×C8—31no—
132C2×C3×C8—31no—
133C2×C3×C8—31no—
134C2×C3×C8—31no—
135C2×C3×C8—31no—
136C2×C3×C8—31no—
137C2×C3×C8—31no—
138C2×C3×C8—43no—
139C2×C3×C8—61no—
140C2×C3×C8S411yescharacteristic, complemented
141#217—32no—
142#217—32no—
143#217—32no—
144(C2×D3)⋊C4—32no—
145(C2×D3)⋊C4—32no—
146C4⋊Dic3—31no—
147C4⋊Dic3—31no—
148Dic3⋊C4—32no—
149Dic3⋊C4—32no—
150C4×Dic3—32no—
151#208—61no—
152#208—61no—
153#208—61no—
154#208—61no—
155#208—123no—
156C2×C3⋊C8—32no—
157C2×C3⋊C8—32no—
158ΓL(1,𝔽25)—62no—
159ΓL(1,𝔽25)—62no—
160ΓL(1,𝔽25)—126no—
161D3×C8—62no—
162D3×C8—62no—
163D3×C8—126no—
164C22×C32—41no—
165C2×C3⋊D3—42no—
166C3×A4#13111yescharacteristic, complemented
167C32×C4—41no—
168C32×C4—41no—
169C3⋊Dic3—42no—
170C2×#41—91no—
171C23×C4C2×C3⋊D311yescharacteristic
172#131—181no—
173#131—181no—
174#131—181no—
175#131—181no—
176C2×M16—92no—
177C2×M16—91no—
178C2×M16—91no—
179C22×C8—31no—
180C22×C8—31no—
181C22×C8—31no—
182C22×C8—31no—
183C22×C8—92no—
184C22×C8C2×C3⋊D311yescharacteristic
185C22×C8C2×C3⋊D311yescharacteristic
186#123—92no—
187C22⋊Q8—91no—
188C22⋊Q8—91no—
189#121—91no—
190#121—91no—
191#120—92no—
192C4×D4—92no—
193C4×D4—92no—
194#117—91no—
195C4⋊C8—92no—
196C4⋊C8—92no—
197C22⋊C8—92no—
198C22⋊C8—92no—
199C22⋊C8—92no—
200C22⋊C8—92no—
201#97—92no—
202C4×C8—92no—
203C23×C3—21no—
204C23×C3—31no—
205C23×C3—31no—
206C23×C3—61no—
207C23×C3C2×C4×D311yescharacteristic
208C22×D3—32no—
209C2×A4—23no—
210C2×A4C2×C4×D313yes—
211S4—66no—
212C2×C3×C4—31no—
213C2×C3×C4—31no—
214C2×C3×C4—31no—
215C2×C3×C4—31no—
216C2×C3×C4—31no—
217C2×C3×C4—31no—
218C2×C3×C4—31no—
219C2×C3×C4—43no—
220C2×C3×C4—61no—
221C2×C3×C4C2×S411yescharacteristic
222#67—62no—
223#67—62no—
224#67—64no—
225#67—62no—
226#67—62no—
227#67—126no—
228C2×Dic3—32no—
229C2×Dic3—32no—
230C2×Dic3—32no—
231D12—61no—
232D12—61no—
233D12—123no—
234C4×D3—62no—
235C4×D3—62no—
236C4×D3—126no—
237Dic6—61no—
238Dic6—61no—
239Dic6—123no—
240C3×C8—31no—
241C3×C8—31no—
242C3×C8—43no—
243C3×C8—43no—
244C3×C8C2×S411yescharacteristic
245C3×C8C2×S411yescharacteristic
246C3⋊C8—62no—
247C3⋊C8—62no—
248C3⋊C8—126no—
249C2×C32—41no—
250C2×C32—81no—
251C3⋊D3—82no—
252C24C4×C3⋊D311yescharacteristic
253#41—181no—
254#41—181no—
255#41—181no—
256#41—181no—
257C2×Q8—91no—
258C2×D4—91no—
259C2×D4—92no—
260C2×D4—92no—
261C2×D4—92no—
262C22×C4—31no—
263C22×C4—31no—
264C22×C4—31no—
265C22×C4—31no—
266C22×C4—92no—
267C22×C4C4×C3⋊D311yescharacteristic
268C22×C4C22×C3⋊D311yescharacteristic
269M16—182no—
270M16—181no—
271M16—181no—
272M16—181no—
273M16—181no—
274M16—182no—
275C2×C8—31no—
276C2×C8—31no—
277C2×C8—31no—
278C2×C8—31no—
279C2×C8—31no—
280C2×C8—31no—
281C2×C8—31no—
282C2×C8—61no—
283C2×C8—92no—
284C2×C8—92no—
285C2×C8—182no—
286C2×C8—182no—
287C2×C8C3⋊S411yescharacteristic, complemented
288C4⋊C4—91no—
289C4⋊C4—91no—
290C4⋊C4—92no—
291C4⋊C4—92no—
292C22⋊C4—92no—
293C22⋊C4—92no—
294C22⋊C4—92no—
295C22⋊C4—92no—
296C22⋊C4—92no—
297C42—92no—
298C22×C3—31no—
299C22×C3—31no—
300C22×C3—32no—
301C22×C3—31no—
302C22×C3—43no—
303C22×C3—61no—
304C22×C3—61no—
305C22×C3—61no—
306C22×C3#90111yescharacteristic, complemented
307C22×C3C4×S411yescharacteristic
308C2×D3—62no—
309C2×D3—62no—
310C2×D3—62no—
311C2×D3—126no—
312A4#90113yescomplemented
313C3×C4—31no—
314C3×C4—31no—
315C3×C4—43no—
316C3×C4—43no—
317C3×C4C4×S411yescharacteristic
318C3×C4C22×S411yescharacteristic
319Dic3—62no—
320Dic3—62no—
321Dic3—62no—
322Dic3—126no—
323C32—41noSylow
324C23—21no—
325C23—31no—
326C23—31no—
327C23—61no—
328C23—92no—
329C23C2×C4×C3⋊D311yescharacteristic
330Q8—181no—
331Q8—181no—
332D4—181no—
333D4—182no—
334D4—182no—
335D4—184no—
336D4—182no—
337D4—182no—
338D4—181no—
339C2×C4—31no—
340C2×C4—31no—
341C2×C4—31no—
342C2×C4—31no—
343C2×C4—31no—
344C2×C4—31no—
345C2×C4—31no—
346C2×C4—61no—
347C2×C4—92no—
348C2×C4—92no—
349C2×C4—92no—
350C2×C4—182no—
351C2×C4—182no—
352C2×C4C2×C3⋊S411yescharacteristic
353C8—31no—
354C8—31no—
355C8—182no—
356C8—182no—
357C8C2×C3⋊S411yescharacteristic
358C8C2×C3⋊S411yescharacteristic
359C2×C3—21no—
360C2×C3—31no—
361C2×C3—31no—
362C2×C3—43no—
363C2×C3—61no—
364C2×C3—83no—
365C2×C3C2×C4×S411yescharacteristic
366D3—122no—
367D3—246no—
368C22—31no—
369C22—31no—
370C22—32no—
371C22—31no—
372C22—61no—
373C22—61no—
374C22—61no—
375C22—182no—
376C22—182no—
377C22—182no—
378C22#6411011yescharacteristic, complemented
379C22C4×C3⋊S411yescharacteristic
380C4—31no—
381C4—31no—
382C4—182no—
383C4—182no—
384C4—182no—
385C4C4×C3⋊S411yescharacteristic
386C4C22×C3⋊S411yescharacteristic
387C3—43no—
388C3#8543711yescharacteristic, complemented
389C2—21no—
390C2—31no—
391C2—31no—
392C2—61no—
393C2—362no—
394C2C2×C4×C3⋊S411yescharacteristic
subgroupG/H
centerC8C2×C3⋊S4
commutatorC2×C3×A4C22×C4
FrattiniC4C22×C3⋊S4
FittingC23×C3×C8D3
socleC23×C3C2×C4×D3
prime radical#10596575C2
cosocleC3×C4×A4C23
hypercenterC2×C8C3⋊S4
hypocenterC3×A4#131
LCSG ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C8 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
2. C2×C3×C8×A4C2semidirect
3. #10593643C2semidirect
4. #10593634C2semidirect
5. C8×C3⋊S4C2semidirect
18. C23×C3×C8D3semidirect
21. C2×C8×A4D3semidirect
98. C23×C8C3⋊D3semidirect
140. C2×C3×C8S4semidirect
166. C3×A4#131semidirect
287. C2×C8C3⋊S4semidirect
306. C22×C3#901semidirect
312. A4#901semidirect
378. C22#64110semidirect
388. C3#85437semidirect

Maximal subgroups

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

subgroupindex
#105965752
C2×C3×C8×A42
#105936432
#105936342
C8×C3⋊S42
#854373
#837343
#641104