Finite Group Databasebeta

← #11922851

Subgroups — #11922851

Order 1152.

778 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 778 conjugacy classes of subgroups — too many to draw. Only its 109 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
1C2×#64259C211yesmaximal, characteristic
2C3×A4×C4⋊C4C211yesmaximal, characteristic
3#10593645C212yesmaximal
4C4×C3⋊SL(2,ℤ/4)C211yesmaximal, characteristic
5C4×C3⋊SL(2,ℤ/4)C212yesmaximal
6#85302—33nomaximal
7#82162—31nomaximal
8C2×C3×C4×A4C2212yes—
9C2×C3×C4×A4C2211yescharacteristic
10C2×C3⋊SL(2,ℤ/4)C2211yescharacteristic
11C2×C3⋊SL(2,ℤ/4)C2212yes—
12C2×C3⋊SL(2,ℤ/4)C2211yescharacteristic
13#64259C414yescomplemented
14#64096—41nomaximal
15C2×A4⋊Q8—33no—
16C22×C3×C4⋊C4D311yescharacteristic
17C2×#924—31no—
18C2×#887—31no—
19A4×C4⋊C4D313yes—
20SL(2,ℤ/4)⋊C4—36no—
21C4×SL(2,ℤ/4)—36no—
22C4×SL(2,ℤ/4)—33no—
23#5210—32no—
24C4×#217—32no—
25C4×#217—31no—
26#4978—32no—
27#4976—32no—
28Dic3×C4⋊C4—31no—
29#4973—31no—
30#4972—31no—
31C22×C3×A4C2311yescharacteristic
32C2×#634—41no—
33C3×C4×A4—22no—
34C3×C4×A4C2×C412yes—
35C3⋊SL(2,ℤ/4)—21no—
36C3⋊SL(2,ℤ/4)C2×C414yes—
37C3⋊SL(2,ℤ/4)Q812yescomplemented
38C32×C4⋊C4—41no—
39#3750—42no—
40C4×C3⋊Dic3—42no—
41C4×C3⋊Dic3—41no—
42#2360—91noSylow
43C23×C3×C4C2×D312yes—
44C23×C3×C4C2×D311yescharacteristic
45C22×Dic6—31no—
46C2×C4×A4C2×D316yes—
47C2×C4×A4C2×D313yes—
48C2×SL(2,ℤ/4)—36no—
49C2×SL(2,ℤ/4)—33no—
50C2×SL(2,ℤ/4)—33no—
51A4⋊Q8—312no—
52C2×C3×C4⋊C4—31no—
53C2×C3×C4⋊C4—31no—
54C2×C3×C4⋊C4—32no—
55C2×#217—31no—
56C2×#217—32no—
57C2×#217—31no—
58C2×C4⋊Dic3—31no—
59#924—34no—
60#924—34no—
61C2×Dic3⋊C4—32no—
62C2×Dic3⋊C4—32no—
63C2×Dic3⋊C4—32no—
64C2×C4×Dic3—31no—
65C2×C4×Dic3—31no—
66C2×C4×Dic3—32no—
67C2×C4×Dic3—32no—
68#887—61no—
69#887—62no—
70#887—61no—
71#887—123no—
72C3⋊#95—32no—
73C3⋊#95—32no—
74C3⋊#95—31no—
75C3⋊#95—31no—
76C3⋊#95—32no—
77C3⋊#95—32no—
78C2×C3×A4C22×C411yescharacteristic
79C2×C3×A4C2×Q811yescharacteristic
80C2×C3×A4#4111yescharacteristic
81C2×C32×C4—41no—
82C2×C32×C4—42no—
83C2×C3⋊Dic3—41no—
84C2×C3⋊Dic3—42no—
85C2×C3⋊Dic3—41no—
86#634—44no—
87C2×C22⋊Q8—91no—
88C2×C4×Q8—91no—
89C22×C4⋊C4C3⋊D311yescharacteristic
90#391—91no—
91#389—91no—
92#389—92no—
93#387—92no—
94#385—92no—
95C4×C4⋊C4—91no—
96C4×C22⋊C4—91no—
97C4×C22⋊C4—92no—
98C24×C3C22×D311yescharacteristic
99C22×A4C22×D313yes—
100C22×C3×C4—22no—
101C22×C3×C4—31no—
102C22×C3×C4—31no—
103C22×C3×C4—32no—
104C22×C3×C4—32no—
105C22×C3×C4—32no—
106C22×C3×C4—62no—
107C22×C3×C4C4×D312yes—
108C22×Dic3—31no—
109C22×Dic3—31no—
110C22×Dic3—32no—
111C22×Dic3—32no—
112C22×Dic3—31no—
113C22×Dic3—31no—
114C2×Dic6—34no—
115C2×Dic6—61no—
116C2×Dic6—62no—
117C2×Dic6—61no—
118C2×Dic6—123no—
119C4×A4—26no—
120C4×A4C4×D316yes—
121SL(2,ℤ/4)—312no—
122SL(2,ℤ/4)—36no—
123SL(2,ℤ/4)—63no—
124C3×C4⋊C4—32no—
125C3×C4⋊C4—31no—
126C3×C4⋊C4—43no—
127C3×C4⋊C4—61no—
128C3×C4⋊C4S411yescharacteristic
129#217—34no—
130#217—32no—
131#217—34no—
132#217—32no—
133#217—61no—
134#217—61no—
135C4⋊Dic3—34no—
136Dic3⋊C4—38no—
137Dic3⋊C4—62no—
138Dic3⋊C4—62no—
139Dic3⋊C4—126no—
140Dic3⋊C4—122no—
141C4×Dic3—62no—
142C4×Dic3—61no—
143C4×Dic3—62no—
144C4×Dic3—62no—
145C4×Dic3—61no—
146C4×Dic3—126no—
147C4×Dic3—123no—
148C4×Dic3—122no—
149C22×C32—41no—
150C3×A4C4×Q811yescharacteristic, complemented
151C32×C4—42no—
152C32×C4—82no—
153C3⋊Dic3—44no—
154C3⋊Dic3—42no—
155C3⋊Dic3—81no—
156C22×Q8—91no—
157C23×C4C2×C3⋊D312yes—
158C23×C4C2×C3⋊D311yescharacteristic
159C22⋊Q8—94no—
160C22⋊Q8—94no—
161C4×Q8—181no—
162C4×Q8—182no—
163C4×Q8—181no—
164C2×C4⋊C4—31no—
165C2×C4⋊C4—32no—
166C2×C4⋊C4—31no—
167C2×C4⋊C4—91no—
168C2×C4⋊C4—92no—
169C2×C4⋊C4—92no—
170C2×C4⋊C4—92no—
171C2×C22⋊C4—92no—
172C2×C22⋊C4—91no—
173C2×C22⋊C4—91no—
174C2×C42—92no—
175C2×C42—91no—
176C2×C42—91no—
177C2×C42—92no—
178#95—91no—
179#95—92no—
180#95—91no—
181#95—92no—
182#95—92no—
183#95—92no—
184C23×C3—31no—
185C23×C3—31no—
186C23×C3—31no—
187C23×C3—31no—
188C23×C3C2×C4×D311yescharacteristic
189C23×C3#23711yescharacteristic
190C23×C3D3×Q811yescharacteristic
191C2×A4C2×C4×D313yes—
192C2×A4#23713yes—
193C2×A4D3×Q813yes—
194C2×C3×C4—31no—
195C2×C3×C4—32no—
196C2×C3×C4—32no—
197C2×C3×C4—32no—
198C2×C3×C4—32no—
199C2×C3×C4—43no—
200C2×C3×C4—46no—
201C2×C3×C4—62no—
202C2×C3×C4—62no—
203C2×C3×C4—61no—
204C2×C3×C4—62no—
205C2×C3×C4—62no—
206C2×C3×C4C2×S412yes—
207C2×C3×C4C2×S411yescharacteristic
208C2×Dic3—34no—
209C2×Dic3—34no—
210C2×Dic3—32no—
211C2×Dic3—32no—
212C2×Dic3—61no—
213C2×Dic3—61no—
214C2×Dic3—62no—
215C2×Dic3—62no—
216C2×Dic3—62no—
217C2×Dic3—61no—
218C2×Dic3—61no—
219C2×Dic3—62no—
220C2×Dic3—61no—
221C2×Dic3—61no—
222C2×Dic3—61no—
223C2×Dic3—61no—
224C2×Dic3—61no—
225C2×Dic3—61no—
226C2×Dic3—123no—
227C2×Dic3—126no—
228C2×Dic3—123no—
229Dic6—64no—
230Dic6—64no—
231Dic6—1212no—
232C2×C32—41no—
233C2×C32—41no—
234C2×C32—41no—
235C24C22×C3⋊D311yescharacteristic
236C2×Q8—94no—
237C2×Q8—181no—
238C2×Q8—182no—
239C2×Q8—181no—
240C22×C4—22no—
241C22×C4—31no—
242C22×C4—31no—
243C22×C4—32no—
244C22×C4—32no—
245C22×C4—32no—
246C22×C4—62no—
247C22×C4—91no—
248C22×C4—91no—
249C22×C4—92no—
250C22×C4—92no—
251C22×C4—91no—
252C22×C4—91no—
253C22×C4C4×C3⋊D312yes—
254C4⋊C4—32no—
255C4⋊C4—31no—
256C4⋊C4—61no—
257C4⋊C4—98no—
258C4⋊C4—94no—
259C4⋊C4—182no—
260C4⋊C4—182no—
261C4⋊C4—362no—
262C4⋊C4C3⋊S411yescharacteristic
263C22⋊C4—94no—
264C22⋊C4—92no—
265C22⋊C4—94no—
266C22⋊C4—92no—
267C22⋊C4—181no—
268C22⋊C4—181no—
269C42—181no—
270C42—182no—
271C42—182no—
272C42—182no—
273C42—181no—
274C42—362no—
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—43no—
285C22×C3—61no—
286C22×C3#88711yescharacteristic, complemented
287C22×C3C22×S411yescharacteristic
288A4#88713yescomplemented
289C3×C4—22no—
290C3×C4—32no—
291C3×C4—46no—
292C3×C4—62no—
293C3×C4—86no—
294C3×C4C4×S412yes—
295Dic3—64no—
296Dic3—62no—
297Dic3—64no—
298Dic3—62no—
299Dic3—1212no—
300Dic3—126no—
301Dic3—121no—
302Dic3—121no—
303Dic3—243no—
304C32—41noSylow
305C23—31no—
306C23—31no—
307C23—31no—
308C23—31no—
309C23C2×C4×C3⋊D311yescharacteristic
310C23#383011yescharacteristic
311C23Q8×C3⋊D311yescharacteristic
312Q8—184no—
313Q8—184no—
314C2×C4—31no—
315C2×C4—32no—
316C2×C4—32no—
317C2×C4—32no—
318C2×C4—32no—
319C2×C4—62no—
320C2×C4—62no—
321C2×C4—61no—
322C2×C4—62no—
323C2×C4—62no—
324C2×C4—94no—
325C2×C4—94no—
326C2×C4—92no—
327C2×C4—92no—
328C2×C4—181no—
329C2×C4—181no—
330C2×C4—182no—
331C2×C4—182no—
332C2×C4—182no—
333C2×C4—181no—
334C2×C4—181no—
335C2×C4—182no—
336C2×C4—181no—
337C2×C4—181no—
338C2×C4—181no—
339C2×C4—181no—
340C2×C4—181no—
341C2×C4—181no—
342C2×C4C2×C3⋊S412yes—
343C2×C4C2×C3⋊S411yescharacteristic
344C2×C3—31no—
345C2×C3—31no—
346C2×C3—31no—
347C2×C3—31no—
348C2×C3—43no—
349C2×C3—43no—
350C2×C3—43no—
351C2×C3C2×C4×S411yescharacteristic
352C2×C3#591411yescharacteristic
353C2×C3Q8×S411yescharacteristic
354C22—31no—
355C22—31no—
356C22—31no—
357C22—31no—
358C22—31no—
359C22—31no—
360C22—31no—
361C22—31no—
362C22—31no—
363C22—61no—
364C22#6409611yescharacteristic, complemented
365C22C22×C3⋊S411yescharacteristic
366C4—22no—
367C4—32no—
368C4—62no—
369C4—184no—
370C4—182no—
371C4—184no—
372C4—182no—
373C4—361no—
374C4—361no—
375C4C4×C3⋊S412yes—
376C3—43no—
377C3#8530211yescharacteristic, complemented
378C2—31no—
379C2—31no—
380C2—31no—
381C2—31no—
382C2C2×C4×C3⋊S411yescharacteristic
383C2#1059657711yescharacteristic
384C2Q8×C3⋊S411yescharacteristic
subgroupG/H
center, FrattiniC22C22×C3⋊S4
commutatorC2×C3×A4C22×C4
FittingC22×C3×C4⋊C4D3
socleC24×C3C22×D3
prime radical, cosocleC22×C3×A4C23
hypercenterC4⋊C4C3⋊S4
hypocenterC3×A4C4×Q8
LCSG ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
13. #64259C4semidirect
37. C3⋊SL(2,ℤ/4)Q8semidirect
150. C3×A4C4×Q8semidirect
286. C22×C3#887semidirect
288. A4#887semidirect
364. C22#64096semidirect
377. C3#85302semidirect

Maximal subgroups

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

subgroupindex
C2×#642592
C3×A4×C4⋊C42
#105936452
C4×C3⋊SL(2,ℤ/4)2
#853023
#821623
#640964