Finite Group Databasebeta

← #11921902

Subgroups — #11921902

Order 1152.

548 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 71 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
1C4×Dic3×A4C211yesmaximal, characteristic
2C4⋊(C3⋊SL(2,ℤ/4))C211yesmaximal, characteristic
3C3×C4⋊SL(2,ℤ/4)C211yesmaximal, characteristic
4SL(2,ℤ/4)⋊Dic3C212yesmaximal
5#10593238C212yesmaximal
6#85284—31nomaximal
7#73998—31nomaximal
8C2×C3×C4×A4C2211yescharacteristic
9C2×Dic3×A4C2211yescharacteristic
10C2×Dic3×A4C2211yescharacteristic
11C2×C3⋊SL(2,ℤ/4)C2212yes—
12C2×C3×SL(2,ℤ/4)C2212yes—
13#63869—41nomaximal
14C22×C4×Dic3D311yescharacteristic
15C2×#890—31no—
16C42×A4—31no—
17C4⋊SL(2,ℤ/4)—31no—
18C4⋊SL(2,ℤ/4)—61no—
19C4⋊SL(2,ℤ/4)D311yescharacteristic
20SL(2,ℤ/4)⋊C4—32no—
21SL(2,ℤ/4)⋊C4—32no—
22C3×#380—31no—
23#5212—31no—
24#4984—31no—
25#4977—31no—
26#4972—31no—
27#4950—32no—
28#4946—32no—
29#4655—32no—
30#4654—32no—
31C22×C3×A4C2311yescharacteristic
32C3×C4×A4Q812yes—
33Dic3×A4—21no—
34Dic3×A4—21no—
35C3⋊SL(2,ℤ/4)—22no—
36C3×SL(2,ℤ/4)—22no—
37C4⋊(C3⋊Dic3)—41no—
38C3×C4⋊Dic3—41no—
39C3×C4×Dic3—41no—
40#3724—42no—
41Dic3⋊Dic3—42no—
42#2851—91noSylow
43C23×C3×C4C2×D311yescharacteristic
44C23×Dic3C2×D311yescharacteristic
45C23×Dic3C2×D311yescharacteristic
46C2×C4×A4—21no—
47C2×C4×A4—31no—
48C2×C4×A4—31no—
49C2×C4×A4C2×D311yescharacteristic
50C2×SL(2,ℤ/4)—32no—
51C2×SL(2,ℤ/4)—62no—
52C2×SL(2,ℤ/4)C2×D312yes—
53C2×C3×C4⋊C4—31no—
54C2×C3×C4⋊C4—31no—
55C2×C3×C22⋊C4—32no—
56C2×#217—32no—
57C2×C4⋊Dic3—32no—
58C2×C4⋊Dic3—32no—
59C2×C4⋊Dic3—31no—
60C2×C4⋊Dic3—31no—
61C2×Dic3⋊C4—32no—
62C2×Dic3⋊C4—32no—
63C2×C4×Dic3—31no—
64C2×C4×Dic3—31no—
65C2×C4×Dic3—31no—
66C2×C4×Dic3—31no—
67#890—61no—
68#890—61no—
69#890—61no—
70#890—61no—
71#870—121no—
72C3×#95—32no—
73C3⋊#95—32no—
74C3⋊#95—32no—
75C3⋊#95—32no—
76C3⋊#95—32no—
77C3⋊#95—32no—
78C2×C3×A4C2×Q811yescharacteristic
79C2×C3×A4#4111yescharacteristic
80C2×C3×A4#4111yescharacteristic
81C2×C32×C4—41no—
82C2×C3⋊Dic3—42no—
83C2×C3×Dic3—42no—
84C2×C3×Dic3—41no—
85C2×C3×Dic3—41no—
86C2×#125—91no—
87C22×C42—31no—
88#389—91no—
89#389—91no—
90#387—92no—
91#387—92no—
92#385—92no—
93#385—92no—
94#382—91no—
95#380—31no—
96#380—91no—
97C24×C3C22×D311yescharacteristic
98C22×A4—21no—
99C22×A4C22×D311yescharacteristic
100C22×C3×C4—31no—
101C22×C3×C4—31no—
102C22×C3×C4—32no—
103C22×C3×C4—32no—
104C22×C3×C4—32no—
105C22×C3×C4Dic612yes—
106C22×Dic3—21no—
107C22×Dic3—21no—
108C22×Dic3—31no—
109C22×Dic3—31no—
110C22×Dic3—31no—
111C22×Dic3—31no—
112C22×Dic3—32no—
113C22×Dic3—32no—
114C22×Dic3—61no—
115C22×Dic3—61no—
116C4×A4—22no—
117C4×A4—61no—
118C4×A4—61no—
119C4×A4Dic612yes—
120SL(2,ℤ/4)—22no—
121SL(2,ℤ/4)—62no—
122SL(2,ℤ/4)—122no—
123C3×C4⋊C4—61no—
124C3×C4⋊C4—62no—
125C3×C4⋊C4—61no—
126C3×C22⋊C4—62no—
127C3×C22⋊C4—62no—
128C3×C42—121no—
129#217—62no—
130#217—62no—
131C4⋊Dic3—41no—
132C4⋊Dic3—62no—
133C4⋊Dic3—64no—
134C4⋊Dic3—61no—
135C4⋊Dic3—62no—
136C4⋊Dic3—61no—
137C4⋊Dic3—62no—
138C4⋊Dic3—121no—
139C4⋊Dic3—241no—
140Dic3⋊C4—62no—
141Dic3⋊C4—64no—
142Dic3⋊C4—62no—
143Dic3⋊C4—122no—
144Dic3⋊C4—122no—
145C4×Dic3—31no—
146C4×Dic3—31no—
147C4×Dic3—31no—
148C4×Dic3—61no—
149C4×Dic3S411yescharacteristic
150C22×C32—41no—
151C3×A4#12511yescharacteristic, complemented
152C32×C4—42no—
153C3⋊Dic3—82no—
154C3×Dic3—81no—
155C3×Dic3—81no—
156C3×Dic3—82no—
157C23×C4—31no—
158C23×C4—31no—
159C23×C4D3211yescharacteristic
160#125—181no—
161#125—181no—
162#125—181no—
163#125—181no—
164C2×C4⋊C4—31no—
165C2×C4⋊C4—31no—
166C2×C4⋊C4—91no—
167C2×C4⋊C4—92no—
168C2×C4⋊C4—92no—
169C2×C4⋊C4—91no—
170C2×C4⋊C4—92no—
171C2×C4⋊C4—92no—
172C2×C22⋊C4—32no—
173C2×C22⋊C4—92no—
174C2×C42—91no—
175C2×C42—91no—
176C2×C42—91no—
177C2×C42—91no—
178#95—32no—
179#95—92no—
180#95—92no—
181#95—92no—
182#95—92no—
183#95—92no—
184C23×C3—31no—
185C23×C3—31no—
186C23×C3—31no—
187C23×C3—31no—
188C23×C3C2×Dic611yescharacteristic
189C23×C3#23511yescharacteristic
190C23×C3#23511yescharacteristic
191C2×A4—21no—
192C2×A4—21no—
193C2×A4—21no—
194C2×A4C2×Dic611yescharacteristic
195C2×A4#23711yescharacteristic
196C2×A4#23911yescharacteristic
197C2×C3×C4—31no—
198C2×C3×C4—32no—
199C2×C3×C4—32no—
200C2×C3×C4—32no—
201C2×C3×C4—41no—
202C2×C3×C4—61no—
203C2×C3×C4—62no—
204C2×C3×C4—62no—
205C2×C3×C4—62no—
206C2×C3×C4—62no—
207C2×C3×C4—62no—
208C2×C3×C4—62no—
209C2×C3×C4—81no—
210C2×C3×C4—121no—
211C2×C3×C4—121no—
212C2×C3×C4C2×S411yescharacteristic
213C2×Dic3—32no—
214C2×Dic3—32no—
215C2×Dic3—31no—
216C2×Dic3—31no—
217C2×Dic3—42no—
218C2×Dic3—61no—
219C2×Dic3—61no—
220C2×Dic3—61no—
221C2×Dic3—61no—
222C2×Dic3—61no—
223C2×Dic3—61no—
224C2×Dic3—62no—
225C2×Dic3—62no—
226C2×Dic3—62no—
227C2×Dic3—62no—
228C2×Dic3—62no—
229C2×Dic3—62no—
230C2×Dic3—122no—
231C2×Dic3—242no—
232C2×Dic3C2×S411yescharacteristic
233C2×Dic3C2×S411yescharacteristic
234C2×C32—41no—
235C2×C32—41no—
236C2×C32—41no—
237C24C2×D3211yescharacteristic
238C22×C4—31no—
239C22×C4—31no—
240C22×C4—32no—
241C22×C4—32no—
242C22×C4—32no—
243C22×C4—61no—
244C22×C4—61no—
245C22×C4—91no—
246C22×C4—91no—
247C22×C4—91no—
248C22×C4—91no—
249C22×C4—92no—
250C22×C4—92no—
251C22×C4—181no—
252C22×C4—181no—
253C22×C4#62712yes—
254C4⋊C4—61no—
255C4⋊C4—62no—
256C4⋊C4—61no—
257C4⋊C4—182no—
258C4⋊C4—182no—
259C4⋊C4—181no—
260C4⋊C4—182no—
261C4⋊C4—182no—
262C4⋊C4—182no—
263C4⋊C4—184no—
264C4⋊C4—184no—
265C4⋊C4—181no—
266C22⋊C4—62no—
267C22⋊C4—62no—
268C22⋊C4—182no—
269C22⋊C4—182no—
270C42—31no—
271C42—91no—
272C42—91no—
273C42—91no—
274C42—181no—
275C22×C3—31no—
276C22×C3—31no—
277C22×C3—31no—
278C22×C3—31no—
279C22×C3—31no—
280C22×C3—31no—
281C22×C3—31no—
282C22×C3—31no—
283C22×C3—31no—
284C22×C3—41no—
285C22×C3—61no—
286C22×C3—81no—
287C22×C3#87011yescharacteristic, complemented
288C22×C3C22×S411yescharacteristic
289A4—21no—
290A4#89011yescharacteristic, complemented
291C3×C4—32no—
292C3×C4—42no—
293C3×C4—82no—
294C3×C4—122no—
295C3×C4—122no—
296C3×C4—241no—
297C3×C4—241no—
298C3×C4A4⋊Q812yes—
299Dic3—21no—
300Dic3—21no—
301Dic3—61no—
302Dic3—61no—
303Dic3—82no—
304Dic3—122no—
305Dic3—122no—
306Dic3—242no—
307Dic3—482no—
308C32—41noSylow
309C23—31no—
310C23—31no—
311C23—31no—
312C23—31no—
313C23#379511yescharacteristic
314C23#379911yescharacteristic
315C23C2×#62711yescharacteristic
316C2×C4—31no—
317C2×C4—32no—
318C2×C4—32no—
319C2×C4—32no—
320C2×C4—31no—
321C2×C4—31no—
322C2×C4—61no—
323C2×C4—62no—
324C2×C4—62no—
325C2×C4—62no—
326C2×C4—62no—
327C2×C4—62no—
328C2×C4—62no—
329C2×C4—92no—
330C2×C4—92no—
331C2×C4—91no—
332C2×C4—91no—
333C2×C4—181no—
334C2×C4—181no—
335C2×C4—181no—
336C2×C4—181no—
337C2×C4—181no—
338C2×C4—181no—
339C2×C4—182no—
340C2×C4—182no—
341C2×C4—182no—
342C2×C4—182no—
343C2×C4—182no—
344C2×C4—182no—
345C2×C4D3×S411yescharacteristic
346C2×C3—31no—
347C2×C3—31no—
348C2×C3—31no—
349C2×C3—31no—
350C2×C3—41no—
351C2×C3—41no—
352C2×C3—41no—
353C2×C3—81no—
354C2×C3—81no—
355C2×C3—81no—
356C2×C3C2×A4⋊Q811yescharacteristic
357C2×C3#591211yescharacteristic
358C2×C3#591211yescharacteristic
359C22—31no—
360C22—31no—
361C22—31no—
362C22—31no—
363C22—31no—
364C22—31no—
365C22—31no—
366C22—31no—
367C22—31no—
368C22—61no—
369C22#6386911yescharacteristic, complemented
370C22C2×D3×S411yescharacteristic
371C4—32no—
372C4—61no—
373C4—61no—
374C4—122no—
375C4—122no—
376C4—181no—
377C4—181no—
378C4—362no—
379C4—362no—
380C4#6420412yes—
381C3—41no—
382C3—81no—
383C3#8528411yescharacteristic, complemented
384C2—31no—
385C2—31no—
386C2—31no—
387C2—31no—
388C2#1059642711yescharacteristic
389C2#1059642811yescharacteristic
390C2C2×#6420411yescharacteristic
subgroupG/H
center, FrattiniC22C2×D3×S4
commutator, prime radical, cosocleC22×C3×A4C23
FittingC23×C3×C4C2×D3
socleC24×C3C22×D3
hypercenterC2×C4D3×S4
hypocenterC3×A4#125
LCSG ▷ C22×C3×A4 ▷ C3×A4
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
151. C3×A4#125semidirect
287. C22×C3#870semidirect
290. A4#890semidirect
369. C22#63869semidirect
383. C3#85284semidirect

Maximal subgroups

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

subgroupindex
C4×Dic3×A42
C4⋊(C3⋊SL(2,ℤ/4))2
C3×C4⋊SL(2,ℤ/4)2
SL(2,ℤ/4)⋊Dic32
#105932382
#852843
#739983
#638694