Finite Group Databasebeta

← #11921863

Subgroups — #11921863

Order 1152.

580 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 580 conjugacy classes of subgroups — too many to draw. Only its 67 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
2A4×#208C211yesmaximal, characteristic, complemented
3C2×C3×A4⋊C8C211yesmaximal, characteristic, complemented
4#10593176C212yesmaximal, complemented
5(C3⋊S4)⋊C8C212yesmaximal, complemented
6#85442—31nomaximal
7#78596—31nomaximal
8C2×C3×C4×A4C2211yescharacteristic
9#64269C412yes—
10C4⋊(C3⋊S4)C411yescharacteristic
11C4×C3⋊S4C2212yes—
12#64259C411yescharacteristic
13#63817—41nomaximal
14A4×C3⋊C8C2212yes—
15C3×A4⋊C8C2211yescharacteristic
16C3×A4⋊C8C2211yescharacteristic
17#5912—31no—
18#5912—61no—
19#5791—31no—
20C22×#208D311yescharacteristic, complemented
21C2×#901—31no—
22A4×M16—31no—
23C2×A4⋊C8D311yescharacteristic, complemented
24#5400—32no—
25C8×S4—32no—
26C2×C3×C22⋊C8—31no—
27#5110—31no—
28#5102—31no—
29#5101—31no—
30#4730—32no—
31#4729—32no—
32#4728—32no—
33#67⋊C8—32no—
34C22×C3×A4C2×C411yescharacteristic
35C2×C3⋊S4C2×C412yes—
36#3828—41no—
37C3×C4×A4C2×C411yescharacteristic
38C3×C4×A4C2311yescharacteristic
39C3⋊SL(2,ℤ/4)C2×C412yes—
40C3×#208—41no—
41C2×C3×C3⋊C8—41no—
42#3712—42no—
43#3710—42no—
44#2933—91noSylow
45C23×C3×C4C2×D311yescharacteristic
46C2×#235—31no—
47C2×C4×A4—21no—
48C2×C4×A4C2×D311yescharacteristic
49GL(2,ℤ/4)—32no—
50GL(2,ℤ/4)—62no—
51C4⋊S4—31no—
52C4⋊S4—61no—
53C4×S4—32no—
54C4×S4—62no—
55A4⋊Q8—31no—
56A4⋊Q8—61no—
57C22×C3×C8—31no—
58C22×C3×C8—31no—
59#953—32no—
60#930—31no—
61#930—31no—
62#929—32no—
63C4×#67—32no—
64C4×#67—32no—
65#926—31no—
66#924—31no—
67#924—31no—
68C2×#208—31no—
69C2×#208—32no—
70C2×#208—31no—
71C22×C3⋊C8C2×D312yes—
72#907—121no—
73#901—61no—
74#901—62no—
75#901—61no—
76C2×ΓL(1,𝔽25)—32no—
77C2×D3×C8—32no—
78C8×A4—32no—
79A4⋊C8C2×D311yescharacteristic
80A4⋊C8C2×D311yescharacteristic
81C3×C22⋊C8—31no—
82C3×C22⋊C8—31no—
83C3×C22⋊C8—31no—
84C3×C22⋊C8—31no—
85(C2×D3)⋊C8—32no—
86(C2×D3)⋊C8—32no—
87#815—32no—
88Dic3⋊C8—32no—
89Dic3⋊C8—32no—
90C8×Dic3—32no—
91C2×C3×A4—21no—
92C2×C3×A4C22×C411yescharacteristic
93C3⋊S4—22no—
94C2×C32×C4—41no—
95#638—42no—
96C4⋊(C3⋊D3)—41no—
97C4×C3⋊D3—42no—
98#634—41no—
99C3×C3⋊C8—41no—
100C3×C3⋊C8—41no—
101C3×C3⋊C8—42no—
102C2×#131—91no—
103C22×M16—31no—
104#525—91no—
105#436—92no—
106#435—92no—
107#435—92no—
108C8×D4—92no—
109#424—91no—
110#408—91no—
111C2×C22⋊C8—31no—
112#405—91no—
113C24×C3C4×D311yescharacteristic
114C22×A4—21no—
115C22×A4C4×D311yescharacteristic
116C2×S4—32no—
117C2×S4—62no—
118C22×C3×C4—31no—
119C22×C3×C4—31no—
120C22×C3×C4—31no—
121C22×C3×C4—31no—
122C22×C3×C4C4×D311yescharacteristic
123C22×C3×C4C22×D311yescharacteristic
124C2×#67—32no—
125C2×#67—32no—
126C2×#67—32no—
127#235—61no—
128#235—61no—
129#235—61no—
130#235—61no—
131#235—121no—
132#235—241no—
133C2×D12—31no—
134C2×C4×D3—32no—
135C2×Dic6—31no—
136C4×A4—21no—
137C4×A4—21no—
138C4×A4C4×D311yescharacteristic
139C4×A4C22×D311yescharacteristic
140SL(2,ℤ/4)—32no—
141SL(2,ℤ/4)—62no—
142C3×M16—121no—
143C2×C3×C8—31no—
144C2×C3×C8—31no—
145C2×C3×C8—31no—
146C2×C3×C8—31no—
147C2×C3×C8—61no—
148C2×C3×C8—61no—
149C2×C3×C8—61no—
150C2×C3×C8—61no—
151#217—32no—
152#217—32no—
153#217—32no—
154(C2×D3)⋊C4—32no—
155(C2×D3)⋊C4—32no—
156C4⋊Dic3—31no—
157C4⋊Dic3—31no—
158Dic3⋊C4—32no—
159Dic3⋊C4—32no—
160C4×Dic3—32no—
161#208—31no—
162#208—32no—
163#208—61no—
164#208S411yescharacteristic, complemented
165C2×C3⋊C8—32no—
166C2×C3⋊C8—32no—
167C2×C3⋊C8—41no—
168ΓL(1,𝔽25)—62no—
169ΓL(1,𝔽25)—62no—
170ΓL(1,𝔽25)—122no—
171D3×C8—62no—
172D3×C8—62no—
173D3×C8—122no—
174C22×C32—41no—
175C2×C3⋊D3—42no—
176C3×A4#13111yescharacteristic, complemented
177C32×C4—41no—
178C32×C4—41no—
179C3⋊Dic3—42no—
180C2×#41—91no—
181C23×C4D3211yescharacteristic
182#131—181no—
183#131—182no—
184#131—181no—
185C2×M16—92no—
186C2×M16—91no—
187C2×M16—91no—
188C2×M16—92no—
189C22×C8—31no—
190C22×C8—31no—
191C22×C8—32no—
192C22×C8—92no—
193#123—92no—
194C22⋊Q8—91no—
195C22⋊Q8—91no—
196#121—91no—
197#121—91no—
198#120—92no—
199C4×D4—92no—
200C4×D4—92no—
201#117—91no—
202C4⋊C8—92no—
203C4⋊C8—92no—
204C22⋊C8—31no—
205C22⋊C8—31no—
206C22⋊C8—31no—
207C22⋊C8—31no—
208C22⋊C8—92no—
209C22⋊C8—92no—
210#97—92no—
211C4×C8—92no—
212C23×C3—21no—
213C23×C3—31no—
214C23×C3—31no—
215C23×C3—61no—
216C23×C3C2×C4×D311yescharacteristic
217C22×D3—32no—
218C2×A4—21no—
219C2×A4—21no—
220C2×A4—41no—
221C2×A4C2×C4×D311yescharacteristic
222S4—62no—
223S4—122no—
224C2×C3×C4—31no—
225C2×C3×C4—31no—
226C2×C3×C4—31no—
227C2×C3×C4—31no—
228C2×C3×C4—31no—
229C2×C3×C4—31no—
230C2×C3×C4—31no—
231C2×C3×C4—41no—
232C2×C3×C4—61no—
233C2×C3×C4—81no—
234C2×C3×C4C2×S411yescharacteristic
235#67—62no—
236#67—62no—
237#67—62no—
238#67—62no—
239#67—122no—
240#67—122no—
241#67—242no—
242C2×Dic3—32no—
243C2×Dic3—32no—
244C2×Dic3—32no—
245D12—61no—
246D12—61no—
247D12—121no—
248D12—241no—
249C4×D3—62no—
250C4×D3—62no—
251C4×D3—122no—
252C4×D3—242no—
253Dic6—61no—
254Dic6—61no—
255Dic6—121no—
256Dic6—241no—
257C3×C8—61no—
258C3×C8—61no—
259C3×C8—61no—
260C3×C8—61no—
261C3×C8—122no—
262C3⋊C8—32no—
263C3⋊C8—41no—
264C3⋊C8—41no—
265C3⋊C8C2×S412yes—
266C2×C32—41no—
267C2×C32—81no—
268C3⋊D3—82no—
269C24#62411yescharacteristic
270#41—181no—
271#41—181no—
272#41—181no—
273#41—181no—
274C2×Q8—91no—
275C2×D4—91no—
276C2×D4—92no—
277C2×D4—92no—
278C2×D4—92no—
279C22×C4—31no—
280C22×C4—31no—
281C22×C4—31no—
282C22×C4—31no—
283C22×C4—92no—
284C22×C4#62411yescharacteristic
285C22×C4C2×D3211yescharacteristic
286M16—31no—
287M16—92no—
288M16—91no—
289M16—182no—
290M16—182no—
291M16—181no—
292C2×C8—31no—
293C2×C8—31no—
294C2×C8—31no—
295C2×C8—31no—
296C2×C8—61no—
297C2×C8—61no—
298C2×C8—61no—
299C2×C8—61no—
300C2×C8—92no—
301C2×C8—92no—
302C2×C8—182no—
303C2×C8—182no—
304C4⋊C4—91no—
305C4⋊C4—91no—
306C4⋊C4—92no—
307C4⋊C4—92no—
308C22⋊C4—92no—
309C22⋊C4—92no—
310C22⋊C4—92no—
311C22⋊C4—92no—
312C22⋊C4—92no—
313C42—92no—
314C22×C3—31no—
315C22×C3—31no—
316C22×C3—31no—
317C22×C3—41no—
318C22×C3—61no—
319C22×C3—61no—
320C22×C3—61no—
321C22×C3—61no—
322C22×C3—81no—
323C22×C3#90711yescharacteristic, complemented
324C22×C3C4×S411yescharacteristic
325C2×D3—62no—
326C2×D3—62no—
327C2×D3—62no—
328C2×D3—122no—
329C2×D3—242no—
330A4—21no—
331A4#90111yescharacteristic, complemented
332C3×C4—31no—
333C3×C4—31no—
334C3×C4—41no—
335C3×C4—41no—
336C3×C4—81no—
337C3×C4—81no—
338C3×C4C4×S411yescharacteristic
339C3×C4C22×S411yescharacteristic
340Dic3—62no—
341Dic3—62no—
342Dic3—62no—
343Dic3—122no—
344Dic3—242no—
345C32—41noSylow
346C23—21no—
347C23—31no—
348C23—31no—
349C23—61no—
350C23—92no—
351C23C2×#62411yescharacteristic
352Q8—181no—
353Q8—181no—
354D4—181no—
355D4—182no—
356D4—182no—
357D4—182no—
358D4—182no—
359D4—181no—
360D4—362no—
361C2×C4—31no—
362C2×C4—31no—
363C2×C4—31no—
364C2×C4—31no—
365C2×C4—31no—
366C2×C4—31no—
367C2×C4—31no—
368C2×C4—61no—
369C2×C4—92no—
370C2×C4—92no—
371C2×C4—92no—
372C2×C4—182no—
373C2×C4—182no—
374C2×C4D3×S411yescharacteristic
375C8—32no—
376C8—61no—
377C8—61no—
378C8—61no—
379C8—61no—
380C8—92no—
381C2×C3—21no—
382C2×C3—31no—
383C2×C3—31no—
384C2×C3—41no—
385C2×C3—61no—
386C2×C3—81no—
387C2×C3—81no—
388C2×C3—161no—
389C2×C3C2×C4×S411yescharacteristic
390D3—122no—
391D3—242no—
392D3—482no—
393C22—31no—
394C22—31no—
395C22—31no—
396C22—61no—
397C22—61no—
398C22—61no—
399C22—61no—
400C22—182no—
401C22—182no—
402C22—182no—
403C22#6381711yescharacteristic, complemented
404C22(C3⋊S4)⋊C411yescharacteristic
405C4—31no—
406C4—31no—
407C4—182no—
408C4—182no—
409C4—182no—
410C4(C3⋊S4)⋊C411yescharacteristic
411C4C2×D3×S411yescharacteristic
412C3—41no—
413C3—81no—
414C3#8544211yescharacteristic, complemented
415C2—21no—
416C2—31no—
417C2—31no—
418C2—61no—
419C2—362no—
420C2C2×(C3⋊S4)⋊C411yescharacteristic
subgroupG/H
center, FrattiniC4C2×D3×S4
commutatorC2×C3×A4C22×C4
FittingC23×C3×C4C2×D3
socleC23×C3C2×C4×D3
prime radical#10596575C2
cosocleC3×C4×A4C23
hypercenterC2×C4D3×S4
hypocenterC3×A4#131
LCSG ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C4 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. A4×#208C2semidirect
3. C2×C3×A4⋊C8C2semidirect
4. #10593176C2semidirect
5. (C3⋊S4)⋊C8C2semidirect
20. C22×#208D3semidirect
23. C2×A4⋊C8D3semidirect
164. #208S4semidirect
176. C3×A4#131semidirect
323. C22×C3#907semidirect
331. A4#901semidirect
403. C22#63817semidirect
414. C3#85442semidirect

Maximal subgroups

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

subgroupindex
#105965752
A4×#2082
C2×C3×A4⋊C82
#105931762
(C3⋊S4)⋊C82
#854423
#785963
#638174