Finite Group Databasebeta

← #11921910

Subgroups — #11921910

Order 1152.

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

normal subgroups only

This group has 536 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
1A4×C4⋊Dic3C211yesmaximal, characteristic
2C4⋊(C3⋊SL(2,ℤ/4))C211yesmaximal, characteristic
3C3×C4×SL(2,ℤ/4)C211yesmaximal, characteristic
4Dic3⋊SL(2,ℤ/4)C212yesmaximal
5#10593238C212yesmaximal
6#85305—31nomaximal
7#73495—31nomaximal
8C2×C3×C4×A4C2211yescharacteristic
9C2×Dic3×A4C2212yes—
10C2×C3⋊SL(2,ℤ/4)C2212yes—
11C2×C3×SL(2,ℤ/4)C2211yescharacteristic
12C2×C3×SL(2,ℤ/4)C2211yescharacteristic
13#63869—41nomaximal
14C22×C4⋊Dic3D311yescharacteristic
15C2×#870—31no—
16A4×C4⋊C4—31no—
17C4⋊SL(2,ℤ/4)—31no—
18C4⋊SL(2,ℤ/4)—32no—
19C4⋊SL(2,ℤ/4)—61no—
20SL(2,ℤ/4)⋊C4—32no—
21C4×SL(2,ℤ/4)D311yescharacteristic
22C3×C4×C22⋊C4—31no—
23#5212—31no—
24#4946—32no—
25#4942—32no—
26#4936—31no—
27#4928—31no—
28#4928—31no—
29#4660—32no—
30#4657—32no—
31C22×C3×A4C2311yescharacteristic
32C3×C4×A4Q812yes—
33Dic3×A4—22no—
34C3⋊SL(2,ℤ/4)—22no—
35C3×SL(2,ℤ/4)—21no—
36C3×SL(2,ℤ/4)—21no—
37C4⋊(C3⋊Dic3)—41no—
38C3×C4⋊Dic3—41no—
39C3×C4×Dic3—41no—
40#3724—42no—
41Dic3⋊Dic3—42no—
42#2442—91noSylow
43C23×C3×C4C2×D311yescharacteristic
44C23×Dic3C2×D312yes—
45C2×C4×A4—21no—
46C2×C4×A4—32no—
47C2×C4×A4C2×D311yescharacteristic
48C2×SL(2,ℤ/4)—32no—
49C2×SL(2,ℤ/4)—62no—
50C2×SL(2,ℤ/4)C2×D311yescharacteristic
51C2×SL(2,ℤ/4)C2×D311yescharacteristic
52C2×C3×C22⋊C4—31no—
53C2×C3×C22⋊C4—31no—
54C2×C3×C42—31no—
55C2×C3×C42—31no—
56C2×#217—32no—
57C2×C4⋊Dic3—31no—
58C2×C4⋊Dic3—32no—
59C2×C4⋊Dic3—31no—
60C2×C4⋊Dic3—31no—
61C2×C4⋊Dic3—31no—
62C2×Dic3⋊C4—32no—
63C2×Dic3⋊C4—32no—
64C2×Dic3⋊C4—32no—
65C2×Dic3⋊C4—32no—
66#890—121no—
67#870—61no—
68#870—62no—
69#870—61no—
70C3×#95—31no—
71C3×#95—31no—
72C3⋊#95—32no—
73C3⋊#95—32no—
74C3⋊#95—32no—
75C3⋊#95—32no—
76C3⋊#95—32no—
77C2×C3×A4C2×Q811yescharacteristic
78C2×C3×A4#4111yescharacteristic
79C2×C3×A4#4111yescharacteristic
80C2×C32×C4—41no—
81C2×C3⋊Dic3—42no—
82C2×C3×Dic3—41no—
83C2×C3×Dic3—41no—
84C2×C3×Dic3—42no—
85C2×#125—91no—
86C22×C4⋊C4—31no—
87#400—92no—
88#398—92no—
89#389—91no—
90#389—91no—
91#385—92no—
92#382—91no—
93#380—92no—
94#380—91no—
95C4×C22⋊C4—31no—
96C24×C3C22×D311yescharacteristic
97C22×A4—21no—
98C22×A4C22×D311yescharacteristic
99C22×C3×C4—31no—
100C22×C3×C4—31no—
101C22×C3×C4—32no—
102C22×C3×C4—31no—
103C22×C3×C4—31no—
104C22×C3×C4—31no—
105C22×C3×C4—31no—
106C22×C3×C4Dic612yes—
107C22×Dic3—22no—
108C22×Dic3—32no—
109C22×Dic3—32no—
110C22×Dic3—32no—
111C22×Dic3—32no—
112C22×Dic3—62no—
113C4×A4—22no—
114C4×A4—62no—
115C4×A4Dic612yes—
116SL(2,ℤ/4)—21no—
117SL(2,ℤ/4)—21no—
118SL(2,ℤ/4)—62no—
119SL(2,ℤ/4)—122no—
120C3×C4⋊C4—121no—
121C3×C22⋊C4—61no—
122C3×C22⋊C4—61no—
123C3×C22⋊C4—61no—
124C3×C22⋊C4—61no—
125C3×C42—61no—
126C3×C42—62no—
127C3×C42—61no—
128#217—62no—
129#217—62no—
130C4⋊Dic3—31no—
131C4⋊Dic3—32no—
132C4⋊Dic3—61no—
133C4⋊Dic3—61no—
134C4⋊Dic3—62no—
135C4⋊Dic3—61no—
136C4⋊Dic3—122no—
137C4⋊Dic3—121no—
138C4⋊Dic3—241no—
139C4⋊Dic3S411yescharacteristic
140Dic3⋊C4—62no—
141Dic3⋊C4—62no—
142Dic3⋊C4—62no—
143Dic3⋊C4—62no—
144Dic3⋊C4—122no—
145Dic3⋊C4—122no—
146Dic3⋊C4—122no—
147C4×Dic3—41no—
148C22×C32—41no—
149C3×A4#12511yescharacteristic, complemented
150C32×C4—42no—
151C3⋊Dic3—82no—
152C3×Dic3—82no—
153C3×Dic3—81no—
154C3×Dic3—81no—
155C23×C4—32no—
156C23×C4D3211yescharacteristic
157#125—181no—
158#125—182no—
159#125—181no—
160C2×C4⋊C4—91no—
161C2×C4⋊C4—91no—
162C2×C4⋊C4—92no—
163C2×C4⋊C4—91no—
164C2×C4⋊C4—92no—
165C2×C4⋊C4—92no—
166C2×C4⋊C4—91no—
167C2×C4⋊C4—92no—
168C2×C4⋊C4—92no—
169C2×C22⋊C4—31no—
170C2×C22⋊C4—31no—
171C2×C22⋊C4—92no—
172C2×C42—31no—
173C2×C42—31no—
174#95—31no—
175#95—31no—
176#95—92no—
177#95—92no—
178#95—92no—
179#95—92no—
180#95—92no—
181C23×C3—31no—
182C23×C3—31no—
183C23×C3—31no—
184C23×C3—31no—
185C23×C3C2×Dic611yescharacteristic
186C23×C3#23711yescharacteristic
187C23×C3#23911yescharacteristic
188C2×A4—21no—
189C2×A4—21no—
190C2×A4—21no—
191C2×A4C2×Dic611yescharacteristic
192C2×A4#23511yescharacteristic
193C2×A4#23511yescharacteristic
194C2×C3×C4—31no—
195C2×C3×C4—32no—
196C2×C3×C4—32no—
197C2×C3×C4—32no—
198C2×C3×C4—41no—
199C2×C3×C4—61no—
200C2×C3×C4—61no—
201C2×C3×C4—61no—
202C2×C3×C4—61no—
203C2×C3×C4—61no—
204C2×C3×C4—61no—
205C2×C3×C4—61no—
206C2×C3×C4—61no—
207C2×C3×C4—61no—
208C2×C3×C4—61no—
209C2×C3×C4—61no—
210C2×C3×C4—61no—
211C2×C3×C4—61no—
212C2×C3×C4—81no—
213C2×C3×C4—122no—
214C2×C3×C4C2×S411yescharacteristic
215C2×Dic3—32no—
216C2×Dic3—41no—
217C2×Dic3—41no—
218C2×Dic3—62no—
219C2×Dic3—62no—
220C2×Dic3—62no—
221C2×Dic3—62no—
222C2×Dic3—62no—
223C2×Dic3—62no—
224C2×Dic3—62no—
225C2×Dic3—62no—
226C2×Dic3—62no—
227C2×Dic3—62no—
228C2×Dic3—122no—
229C2×Dic3—242no—
230C2×Dic3C2×S412yes—
231C2×C32—41no—
232C2×C32—41no—
233C2×C32—41no—
234C24C2×D3211yescharacteristic
235C22×C4—31no—
236C22×C4—31no—
237C22×C4—32no—
238C22×C4—31no—
239C22×C4—31no—
240C22×C4—31no—
241C22×C4—31no—
242C22×C4—62no—
243C22×C4—92no—
244C22×C4—92no—
245C22×C4—92no—
246C22×C4—92no—
247C22×C4—182no—
248C22×C4#62712yes—
249C4⋊C4—31no—
250C4⋊C4—92no—
251C4⋊C4—91no—
252C4⋊C4—182no—
253C4⋊C4—182no—
254C4⋊C4—181no—
255C4⋊C4—181no—
256C4⋊C4—182no—
257C4⋊C4—182no—
258C4⋊C4—182no—
259C4⋊C4—181no—
260C4⋊C4—362no—
261C4⋊C4—362no—
262C22⋊C4—61no—
263C22⋊C4—61no—
264C22⋊C4—61no—
265C22⋊C4—61no—
266C22⋊C4—182no—
267C22⋊C4—182no—
268C42—61no—
269C42—62no—
270C42—61no—
271C22×C3—31no—
272C22×C3—31no—
273C22×C3—31no—
274C22×C3—31no—
275C22×C3—31no—
276C22×C3—31no—
277C22×C3—31no—
278C22×C3—31no—
279C22×C3—31no—
280C22×C3—41no—
281C22×C3—61no—
282C22×C3—81no—
283C22×C3#89011yescharacteristic, complemented
284C22×C3C22×S411yescharacteristic
285A4—21no—
286A4#87011yescharacteristic, complemented
287C3×C4—32no—
288C3×C4—42no—
289C3×C4—82no—
290C3×C4—121no—
291C3×C4—121no—
292C3×C4—121no—
293C3×C4—121no—
294C3×C4—242no—
295C3×C4A4⋊Q812yes—
296Dic3—22no—
297Dic3—62no—
298Dic3—81no—
299Dic3—81no—
300Dic3—122no—
301Dic3—122no—
302Dic3—242no—
303Dic3—482no—
304C32—41noSylow
305C23—31no—
306C23—31no—
307C23—31no—
308C23—31no—
309C23#379511yescharacteristic
310C23#379911yescharacteristic
311C23C2×#62711yescharacteristic
312C2×C4—31no—
313C2×C4—32no—
314C2×C4—32no—
315C2×C4—32no—
316C2×C4—32no—
317C2×C4—61no—
318C2×C4—61no—
319C2×C4—61no—
320C2×C4—61no—
321C2×C4—61no—
322C2×C4—61no—
323C2×C4—61no—
324C2×C4—61no—
325C2×C4—61no—
326C2×C4—61no—
327C2×C4—61no—
328C2×C4—61no—
329C2×C4—61no—
330C2×C4—92no—
331C2×C4—182no—
332C2×C4—182no—
333C2×C4—182no—
334C2×C4—182no—
335C2×C4—182no—
336C2×C4—182no—
337C2×C4—182no—
338C2×C4—182no—
339C2×C4—182no—
340C2×C4—182no—
341C2×C4D3×S411yescharacteristic
342C2×C3—31no—
343C2×C3—31no—
344C2×C3—31no—
345C2×C3—31no—
346C2×C3—41no—
347C2×C3—41no—
348C2×C3—41no—
349C2×C3—81no—
350C2×C3—81no—
351C2×C3—81no—
352C2×C3C2×A4⋊Q811yescharacteristic
353C2×C3#591411yescharacteristic
354C2×C3#591911yescharacteristic
355C22—31no—
356C22—31no—
357C22—31no—
358C22—31no—
359C22—31no—
360C22—31no—
361C22—31no—
362C22—31no—
363C22—31no—
364C22—61no—
365C22#6386911yescharacteristic, complemented
366C22C2×D3×S411yescharacteristic
367C4—32no—
368C4—62no—
369C4—121no—
370C4—121no—
371C4—121no—
372C4—121no—
373C4—182no—
374C4—362no—
375C4—362no—
376C4#6420412yes—
377C3—41no—
378C3—81no—
379C3#8530511yescharacteristic, complemented
380C2—31no—
381C2—31no—
382C2—31no—
383C2—31no—
384C2#1059642111yescharacteristic
385C2#1059642411yescharacteristic
386C2C2×#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
149. C3×A4#125semidirect
283. C22×C3#890semidirect
286. A4#870semidirect
365. C22#63869semidirect
379. C3#85305semidirect

Maximal subgroups

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

subgroupindex
A4×C4⋊Dic32
C4⋊(C3⋊SL(2,ℤ/4))2
C3×C4×SL(2,ℤ/4)2
Dic3⋊SL(2,ℤ/4)2
#105932382
#853053
#734953
#638694