Finite Group Databasebeta

← #11788161

Subgroups — #11788161

Order 1152.

1326 conjugacy classes of subgroups; only the 195 normal subgroups are shown.

normal subgroups only

This group has 1326 conjugacy classes of subgroups — too many to draw. Only its 195 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#10595995C211yesmaximal, characteristic
2C2×C42×C3⋊D3C211yesmaximal, characteristic, complemented
3C2×#63652C211yesmaximal, characteristic, complemented
4#10592825C211yesmaximal, characteristic, complemented
5C2×#63632C211yesmaximal, characteristic, complemented
6C32×#339C211yesmaximal, characteristic, complemented
7#10589398C211yesmaximal, characteristic, complemented
8#68756—34nomaximal
9C2×#3828C2211yescharacteristic
10C22×C4×C3⋊D3—21no—
11C22×C4×C3⋊D3C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C32×#117C2211yescharacteristic
14C2×C32×C42C2211yescharacteristic
15C2×C4×C3⋊Dic3—21no—
16C2×C4×C3⋊Dic3C2211yescharacteristic
17C2×#3748C2211yescharacteristic
18#64106C412yescomplemented
19#64104C412yescomplemented
20#64095—21no—
21#64091—21no—
22C4×C4⋊(C3⋊D3)—22no—
23C42×C3⋊D3—22no—
24C42×C3⋊D3—22no—
25#63652—22no—
26#63647—22no—
27#63632—22no—
28#5524—34no—
29C2×C42×D3—34no—
30C2×#825—34no—
31#5126—34no—
32C2×#805—34no—
33C3×#339D314yescomplemented
34#4532—34no—
35C23×C3⋊D3D411yescharacteristic
36C22×C32×C4—21no—
37C22×C32×C4C2311yescharacteristic
38C2×#638—21no—
39C22×C3⋊Dic3—21no—
40C22×C3⋊Dic3D411yescharacteristic
41#3828—21no—
42#3828—21no—
43#3828—21no—
44#3828—21no—
45C2×C4⋊(C3⋊D3)—22no—
46C2×C4⋊(C3⋊D3)C2×C411yescharacteristic, complemented
47C2×C4×C3⋊D3—24no—
48C2×C4×C3⋊D3—28no—
49C2×C4×C3⋊D3—21no—
50C2×C4×C3⋊D3—21no—
51C2×C4×C3⋊D3—21no—
52C2×C4×C3⋊D3—21no—
53C2×C4×C3⋊D3—21no—
54C2×C4×C3⋊D3C2×C412yes—
55C2×C4×C3⋊D3D412yes—
56C2×#634C2×C411yescharacteristic, complemented
57C32×M16—21no—
58C32×M16—21no—
59C2×C32×C8—21no—
60C32×C4⋊C4C2×C412yescomplemented
61C32×C22⋊C4—21no—
62C32×C42—21no—
63C32×C42—21no—
64C32×C42D412yescomplemented
65#3752—22no—
66#3752—22no—
67C4⋊(C3⋊Dic3)—22no—
68C4×C3⋊Dic3—24no—
69C4×C3⋊Dic3—21no—
70C4×C3⋊Dic3D412yescomplemented
71#3748—21no—
72#3748—21no—
73C2×C3⋊(C3⋊C8)—21no—
74#1896—91noSylow
75C2×#235—34no—
76C22×C4×D3—34no—
77C22×C4×D3—64no—
78C2×C3×M16C2×D314yes—
79C3×#117C2×D314yes—
80C2×C3×C42C2×D314yes—
81C2×C4×Dic3—34no—
82C2×C4×Dic3—64no—
83C2×#208—34no—
84#897—38no—
85#895—38no—
86#886—64no—
87#882—64no—
88C4×D12—68no—
89C42×D3—68no—
90C42×D3—68no—
91#825—68no—
92(C2×D3)⋊C8—68no—
93#805—68no—
94C23×C32C2×D411yescharacteristic
95C22×C3⋊D3—21no—
96C22×C3⋊D3—21no—
97C22×C3⋊D3—24no—
98C22×C3⋊D3—21no—
99C22×C3⋊D3C22⋊C412yes—
100C2×C32×C4—24no—
101C2×C32×C4—22no—
102C2×C32×C4—22no—
103C2×C32×C4C22×C411yescharacteristic
104C2×C32×C4C2×D411yescharacteristic
105C2×C32×C4C2×D411yescharacteristic
106C2×C32×C4C2×D411yescharacteristic
107C2×C32×C4#4111yescharacteristic
108C2×C32×C4#4111yescharacteristic
109#638—41no—
110#638—41no—
111C2×C3⋊Dic3—24no—
112C2×C3⋊Dic3—21no—
113C2×C3⋊Dic3—22no—
114C2×C3⋊Dic3—21no—
115C2×C3⋊Dic3—21no—
116C2×C3⋊Dic3C22⋊C412yes—
117C4⋊(C3⋊D3)—21no—
118C4⋊(C3⋊D3)—21no—
119C4⋊(C3⋊D3)—44no—
120C4×C3⋊D3—216no—
121C4×C3⋊D3—22no—
122C4×C3⋊D3—22no—
123C4×C3⋊D3—22no—
124C4×C3⋊D3—22no—
125C4×C3⋊D3—41no—
126C4×C3⋊D3—41no—
127#634—21no—
128#634—21no—
129C32×C8—41no—
130C3⋊(C3⋊C8)—41no—
131#525—91no—
132C22×C42—91no—
133C2×#104—91no—
134C2×#104—91no—
135#407—91no—
136#339—91no—
137#339C3⋊D311yescharacteristic, complemented
138C23×D3—34no—
139C22×C3×C4—24no—
140C22×C3×C4C22×D314yes—
141C2×#67—64no—
142C22×Dic3—34no—
143C22×Dic3—64no—
144#235—64no—
145#235—64no—
146#235—64no—
147#235—64no—
148C2×D12—34no—
149C2×D12—68no—
150C2×C4×D3—38no—
151C2×C4×D3—38no—
152C2×C4×D3—616no—
153C2×C4×D3—632no—
154C2×C4×D3—64no—
155C2×C4×D3—64no—
156C2×C4×D3—64no—
157C2×C4×D3—64no—
158C2×C4×D3—64no—
159C2×Dic6—34no—
160C3×M16—24no—
161C3×M16—24no—
162C2×C3×C8—24no—
163C3×C4⋊C4C4×D318yescomplemented
164C3×C22⋊C4—24no—
165C3×C42—24no—
166C3×C42—24no—
167C3×C42D1218yescomplemented
168(C2×D3)⋊C4—68no—
169(C2×D3)⋊C4—68no—
170C4⋊Dic3—68no—
171C4×Dic3—38no—
172C4×Dic3—616no—
173C4×Dic3—64no—
174#208—64no—
175#208—64no—
176C2×C3⋊C8—64no—
177C22×C32—22no—
178C22×C32C2×C22⋊C411yescharacteristic
179C22×C32#12011yescharacteristic
180C22×C32#12311yescharacteristic
181C2×C3⋊D3—24no—
182C2×C3⋊D3—24no—
183C2×C3⋊D3—22no—
184C2×C3⋊D3—22no—
185C2×C3⋊D3—41no—
186C2×C3⋊D3—42no—
187C2×C3⋊D3#10414yescomplemented
188C32×C4—24no—
189C32×C4—42no—
190C32×C4C4×D411yescharacteristic
191C32×C4C4×D411yescharacteristic
192C32×C4#12111yescharacteristic
193C32×C4#12111yescharacteristic
194C3⋊Dic3—24no—
195C3⋊Dic3—22no—
196C3⋊Dic3—41no—
197C2×#41—91no—
198C23×C4—91no—
199C23×C4—181no—
200C2×M16—91no—
201C2×M16C2×C3⋊D311yescharacteristic
202#123—181no—
203C22⋊Q8—92no—
204#121—92no—
205#120—181no—
206C4×D4—182no—
207#117C2×C3⋊D311yescharacteristic
208C2×C42—91no—
209C2×C42—182no—
210C2×C42—181no—
211C2×C42—182no—
212C2×C42C2×C3⋊D311yescharacteristic
213#104—182no—
214#104—182no—
215C22⋊C8—182no—
216C23×C3D3×D414yes—
217C22×D3—38no—
218C22×D3—616no—
219C22×D3—64no—
220C22×D3—64no—
221C22×D3—64no—
222C2×C3×C4—216no—
223C2×C3×C4—28no—
224C2×C3×C4—28no—
225C2×C3×C4C2×C4×D314yes—
226C2×C3×C4C2×D1214yes—
227C2×C3×C4#23514yes—
228C2×C3×C4D3×D414yes—
229C2×C3×C4D3×D414yes—
230C2×C3×C4#23914yes—
231#67—124no—
232#67—124no—
233C2×Dic3—38no—
234C2×Dic3—616no—
235C2×Dic3—68no—
236C2×Dic3—64no—
237C2×Dic3—64no—
238C2×Dic3—64no—
239D12—64no—
240D12—64no—
241D12—1216no—
242C4×D3—664no—
243C4×D3—68no—
244C4×D3—68no—
245C4×D3—68no—
246C4×D3—68no—
247C4×D3—124no—
248C4×D3—124no—
249Dic6—64no—
250Dic6—64no—
251C3×C8—44no—
252C3⋊C8—124no—
253C2×C32—21no—
254C2×C32—21no—
255C2×C32#38611yescharacteristic
256C2×C32C2×#10412yes—
257C3⋊D3—24no—
258C3⋊D3—81no—
259C24—91no—
260#41—181no—
261#41—181no—
262#41—181no—
263#41—181no—
264C2×Q8—91no—
265C2×D4—91no—
266C2×D4—182no—
267C2×D4—181no—
268C22×C4—21no—
269C22×C4—91no—
270C22×C4—92no—
271C22×C4—92no—
272C22×C4—184no—
273C22×C4—188no—
274C22×C4—181no—
275C22×C4—181no—
276C22×C4—181no—
277C22×C4—181no—
278C22×C4—181no—
279C22×C4—181no—
280C22×C4C22×C3⋊D311yescharacteristic
281M16—21no—
282M16—21no—
283M16—181no—
284M16—181no—
285C2×C8—21no—
286C2×C8—181no—
287C4⋊C4—182no—
288C4⋊C4C4×C3⋊D312yescomplemented
289C22⋊C4—21no—
290C22⋊C4—182no—
291C22⋊C4—182no—
292C42—21no—
293C42—21no—
294C42—92no—
295C42—184no—
296C42—181no—
297C42C4⋊(C3⋊D3)12yescomplemented
298C22×C3—28no—
299C22×C3D3×C22⋊C414yes—
300C22×C3#88214yes—
301C22×C3#89414yes—
302C2×D3—316no—
303C2×D3—616no—
304C2×D3—616no—
305C2×D3—68no—
306C2×D3—68no—
307C2×D3—124no—
308C2×D3—128no—
309C3×C4—216no—
310C3×C4—48no—
311C3×C4C4×D1214yes—
312C3×C4#88414yes—
313C3×C4#89314yes—
314C3×C4#89514yes—
315Dic3—616no—
316Dic3—68no—
317Dic3—124no—
318C32#189611yescharacteristic, complemented, Sylow
319C23—92no—
320C23—184no—
321C23—181no—
322C23—181no—
323C23—181no—
324C23D4×C3⋊D311yescharacteristic
325Q8—181no—
326Q8—181no—
327D4—181no—
328D4—181no—
329D4—364no—
330D4—361no—
331D4—361no—
332C2×C4—24no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—92no—
336C2×C4—1816no—
337C2×C4—184no—
338C2×C4—182no—
339C2×C4—181no—
340C2×C4—181no—
341C2×C4—182no—
342C2×C4—182no—
343C2×C4—182no—
344C2×C4—182no—
345C2×C4—181no—
346C2×C4—361no—
347C2×C4—361no—
348C2×C4C2×C4×C3⋊D311yescharacteristic
349C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
350C2×C4#382811yescharacteristic
351C2×C4D4×C3⋊D311yescharacteristic
352C2×C4D4×C3⋊D311yescharacteristic
353C2×C4#383211yescharacteristic
354C8—41no—
355C8—361no—
356C2×C3—24no—
357C2×C3—24no—
358C2×C3#466514yes—
359C2×C3D3×#10418yes—
360D3—616no—
361D3—244no—
362C22—22no—
363C22—94no—
364C22—184no—
365C22—184no—
366C22—182no—
367C22—182no—
368C22—362no—
369C22—361no—
370C22C22⋊C4×C3⋊D311yescharacteristic
371C22#6409111yescharacteristic
372C22#6410311yescharacteristic
373C4—24no—
374C4—42no—
375C4—184no—
376C4—182no—
377C4—361no—
378C4C4×C4⋊(C3⋊D3)11yescharacteristic
379C4#6409311yescharacteristic
380C4#6410211yescharacteristic
381C4#6410411yescharacteristic
382C3#6875614yescomplemented
383C2—21no—
384C2—21no—
385C2—184no—
386C2—721no—
387C2#1059236411yescharacteristic
388C2C3⋊D3×#10412yes—
subgroupG/H
centerC2×C4D4×C3⋊D3
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#339C2
socleC22×C32C2×C22⋊C4
prime radical#10595995C2
cosocleC22×C32×C4C23
hypercenter#339C3⋊D3
hypocenterC32#1896
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
2. C2×C42×C3⋊D3C2semidirect
3. C2×#63652C2semidirect
4. #10592825C2semidirect
5. C2×#63632C2semidirect
6. C32×#339C2semidirect
7. #10589398C2semidirect
18. #64106C4semidirect
19. #64104C4semidirect
33. C3×#339D3semidirect
46. C2×C4⋊(C3⋊D3)C2×C4semidirect
56. C2×#634C2×C4semidirect
60. C32×C4⋊C4C2×C4semidirect
64. C32×C42D4semidirect
70. C4×C3⋊Dic3D4semidirect
137. #339C3⋊D3semidirect
163. C3×C4⋊C4C4×D3semidirect
167. C3×C42D12semidirect
187. C2×C3⋊D3#104semidirect
288. C4⋊C4C4×C3⋊D3semidirect
297. C42C4⋊(C3⋊D3)semidirect
318. C32#1896semidirect
382. C3#68756semidirect

Maximal subgroups

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

subgroupindex
#105959952
C2×C42×C3⋊D32
C2×#636522
#105928252
C2×#636322
C32×#3392
#105893982
#687563