Finite Group Databasebeta

← #11785838

Subgroups — #11785838

Order 1152.

918 conjugacy classes of subgroups.

The subgroup lattice has 417 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊D3×#117C211yesmaximal, characteristic
2#10592825C211yesmaximal, characteristic
3C4×#3752C211yesmaximal, characteristic
4C32×#339C211yesmaximal, characteristic, complemented
5#10589421C211yesmaximal, characteristic, complemented
6#10589398C211yesmaximal, characteristic, complemented
7#10589389C211yesmaximal, characteristic, complemented
8#68754—34nomaximal
9C22×C4×C3⋊D3C2211yescharacteristic
10C2×C32×M16C2211yescharacteristic
11C32×#117C2211yescharacteristic
12C2×C32×C42C2211yescharacteristic
13C2×#3752—21no—
14#64135C2211yescharacteristic
15C2×C4×C3⋊Dic3C2211yescharacteristic
16C2×#3748C2211yescharacteristic
17#64101C411yescharacteristic, complemented
18#64101C411yescharacteristic, complemented
19C4⋊C4×C3⋊D3C411yescharacteristic, complemented
20C4⋊C4×C3⋊D3C411yescharacteristic, complemented
21C22⋊C4×C3⋊D3—21no—
22#64086—21no—
23#64081—21no—
24C42×C3⋊D3—21no—
25#63658—21no—
26#63647—21no—
27#63647—21no—
28D3×#117—34no—
29#5126—34no—
30C4×(C2×D3)⋊C4—34no—
31C3×#339D314yescomplemented
32#4555—34no—
33#4532—34no—
34#4523—34no—
35C23×C3⋊D3D411yescharacteristic
36C22×C32×C4—21no—
37C22×C32×C4C2311yescharacteristic
38C22×C3⋊Dic3—21no—
39C22×C3⋊Dic3D411yescharacteristic
40C2×C4×C3⋊D3—21no—
41C2×C4×C3⋊D3—21no—
42C2×C4×C3⋊D3—21no—
43C2×C4×C3⋊D3—21no—
44C2×C4×C3⋊D3—21no—
45C2×C4×C3⋊D3—21no—
46C2×C4×C3⋊D3C2×C411yescharacteristic
47C2×C4×C3⋊D3C2×C411yescharacteristic
48C2×C4×C3⋊D3D411yescharacteristic
49C2×C4×C3⋊D3D411yescharacteristic
50C32×M16—21no—
51C32×M16—21no—
52C2×C32×C8—21no—
53C32×C4⋊C4C2×C411yescharacteristic
54C32×C4⋊C4C2×C411yescharacteristic
55C32×C22⋊C4—21no—
56C32×C42—21no—
57C32×C42—21no—
58C32×C42—21no—
59#3757—21no—
60#3752—24no—
61#3752—21no—
62#3752—21no—
63C4⋊(C3⋊Dic3)C2×C411yescharacteristic
64C4⋊(C3⋊Dic3)C2×C411yescharacteristic
65#3750—21no—
66#3750—21no—
67C4×C3⋊Dic3—21no—
68C4×C3⋊Dic3—21no—
69C4×C3⋊Dic3—21no—
70C4×C3⋊Dic3—21no—
71C4×C3⋊Dic3—21no—
72#3748—21no—
73#3748—21no—
74C2×C3⋊(C3⋊C8)—21no—
75#1826—91noSylow
76C22×C4×D3—34no—
77C2×C3×M16C2×D314yes—
78C3×#117C2×D314yes—
79C2×C3×C42C2×D314yes—
80C2×(C2×D3)⋊C4—64no—
81#926—34no—
82C2×C4×Dic3—34no—
83C2×#208—34no—
84#892—34no—
85#892—34no—
86D3×C4⋊C4—34no—
87D3×C4⋊C4—34no—
88D3×C22⋊C4—64no—
89#877—64no—
90#872—64no—
91C42×D3—64no—
92C3⋊#95—64no—
93(C2×D3)⋊C8—64no—
94(C2×D3)⋊C8—64no—
95C23×C32C2×D411yescharacteristic
96C22×C3⋊D3—21no—
97C22×C3⋊D3—21no—
98C22×C3⋊D3—22no—
99C22×C3⋊D3—41no—
100C22×C3⋊D3C22⋊C411yescharacteristic
101C22×C3⋊D3C22⋊C411yescharacteristic
102C2×C32×C4—22no—
103C2×C32×C4—21no—
104C2×C32×C4—21no—
105C2×C32×C4—41no—
106C2×C32×C4—41no—
107C2×C32×C4C22×C411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4#4111yescharacteristic
110C2×C32×C4#4111yescharacteristic
111C2×C32×C4#4111yescharacteristic
112C2×C32×C4#4111yescharacteristic
113C2×C3⋊Dic3—21no—
114C2×C3⋊Dic3—21no—
115C2×C3⋊Dic3—22no—
116C2×C3⋊Dic3—21no—
117C2×C3⋊Dic3—21no—
118C2×C3⋊Dic3—41no—
119C2×C3⋊Dic3—41no—
120C2×C3⋊Dic3C22⋊C411yescharacteristic
121C2×C3⋊Dic3C22⋊C411yescharacteristic
122C4×C3⋊D3—21no—
123C4×C3⋊D3—21no—
124C4×C3⋊D3—21no—
125C4×C3⋊D3—21no—
126C4×C3⋊D3—21no—
127C4×C3⋊D3—21no—
128C4×C3⋊D3—21no—
129C4×C3⋊D3—21no—
130C4×C3⋊D3—42no—
131C4×C3⋊D3—42no—
132C32×C8—41no—
133C3⋊(C3⋊C8)—41no—
134C2×#117—91no—
135#407—91no—
136C4×C22⋊C4—91no—
137#339—91no—
138#339—91no—
139#339—91no—
140#339C3⋊D311yescharacteristic, complemented
141C23×D3—34no—
142C22×C3×C4—24no—
143C22×C3×C4C22×D314yes—
144C22×Dic3—34no—
145C22×Dic3—64no—
146C2×C4×D3—34no—
147C2×C4×D3—34no—
148C2×C4×D3—34no—
149C2×C4×D3—34no—
150C2×C4×D3—64no—
151C2×C4×D3—64no—
152C2×C4×D3—64no—
153C2×C4×D3—64no—
154C2×C4×D3—64no—
155C2×C4×D3—64no—
156C3×M16—24no—
157C3×M16—24no—
158C2×C3×C8—24no—
159C3×C4⋊C4C4×D314yes—
160C3×C4⋊C4C4×D314yes—
161C3×C22⋊C4—24no—
162C3×C42—24no—
163C3×C42—24no—
164C3×C42—24no—
165#217—64no—
166(C2×D3)⋊C4—64no—
167(C2×D3)⋊C4—64no—
168(C2×D3)⋊C4—616no—
169C4⋊Dic3—34no—
170C4⋊Dic3—34no—
171Dic3⋊C4—64no—
172Dic3⋊C4—64no—
173C4×Dic3—64no—
174C4×Dic3—64no—
175C4×Dic3—64no—
176C4×Dic3—64no—
177C4×Dic3—64no—
178#208—64no—
179#208—64no—
180C2×C3⋊C8—64no—
181C22×C32—21no—
182C22×C32—21no—
183C22×C32C2×C22⋊C411yescharacteristic
184C22×C32#12311yescharacteristic
185C22×C32#12311yescharacteristic
186C2×C3⋊D3—21no—
187C2×C3⋊D3—21no—
188C2×C3⋊D3—21no—
189C2×C3⋊D3—21no—
190C2×C3⋊D3—21no—
191C2×C3⋊D3—42no—
192C2×C3⋊D3—42no—
193C2×C3⋊D3#10412yes—
194C32×C4—42no—
195C32×C4—41no—
196C32×C4—41no—
197C32×C4#11711yescharacteristic
198C32×C4#11711yescharacteristic
199C32×C4#12311yescharacteristic
200C32×C4#12311yescharacteristic
201C3⋊Dic3—21no—
202C3⋊Dic3—21no—
203C3⋊Dic3—42no—
204C3⋊Dic3—41no—
205C3⋊Dic3—41no—
206C23×C4—91no—
207C2×M16—91no—
208C2×M16C2×C3⋊D311yescharacteristic
209#117—91no—
210#117—91no—
211#117—91no—
212#117—181no—
213#117—181no—
214#117C2×C3⋊D311yescharacteristic
215C2×C4⋊C4—91no—
216C2×C4⋊C4—91no—
217C2×C22⋊C4—181no—
218C2×C22⋊C4—181no—
219C2×C42—91no—
220C2×C42—181no—
221C2×C42C2×C3⋊D311yescharacteristic
222C22⋊C8—181no—
223C22⋊C8—181no—
224#95—181no—
225C23×C3D3×D414yes—
226C22×D3—34no—
227C22×D3—34no—
228C22×D3—68no—
229C22×D3—64no—
230C22×D3—64no—
231C22×D3—124no—
232C2×C3×C4—28no—
233C2×C3×C4—24no—
234C2×C3×C4—24no—
235C2×C3×C4—44no—
236C2×C3×C4—44no—
237C2×C3×C4C2×C4×D314yes—
238C2×C3×C4#23514yes—
239C2×C3×C4#23514yes—
240C2×C3×C4D3×D414yes—
241C2×C3×C4#23714yes—
242C2×C3×C4#23914yes—
243C2×Dic3—34no—
244C2×Dic3—34no—
245C2×Dic3—64no—
246C2×Dic3—64no—
247C2×Dic3—68no—
248C2×Dic3—64no—
249C2×Dic3—64no—
250C2×Dic3—124no—
251C2×Dic3—124no—
252C4×D3—64no—
253C4×D3—64no—
254C4×D3—64no—
255C4×D3—64no—
256C4×D3—64no—
257C4×D3—64no—
258C4×D3—64no—
259C4×D3—64no—
260C4×D3—128no—
261C4×D3—128no—
262C3×C8—44no—
263C3⋊C8—124no—
264C2×C32—21no—
265C2×C32—21no—
266C2×C32#38111yescharacteristic
267C2×C32C2×#10411yescharacteristic
268C2×C32#42111yescharacteristic
269C3⋊D3—22no—
270C3⋊D3—41no—
271C24—91no—
272C22×C4—21no—
273C22×C4—91no—
274C22×C4—91no—
275C22×C4—91no—
276C22×C4—91no—
277C22×C4—91no—
278C22×C4—181no—
279C22×C4—181no—
280C22×C4—181no—
281C22×C4—181no—
282C22×C4—181no—
283C22×C4—181no—
284C22×C4—181no—
285C22×C4C22×C3⋊D311yescharacteristic
286M16—21no—
287M16—21no—
288M16—181no—
289M16—181no—
290C2×C8—21no—
291C2×C8—181no—
292C4⋊C4—91no—
293C4⋊C4—91no—
294C4⋊C4—181no—
295C4⋊C4—181no—
296C4⋊C4C4×C3⋊D311yescharacteristic
297C4⋊C4C4×C3⋊D311yescharacteristic
298C22⋊C4—21no—
299C22⋊C4—181no—
300C22⋊C4—181no—
301C22⋊C4—184no—
302C22⋊C4—181no—
303C42—21no—
304C42—21no—
305C42—21no—
306C42—181no—
307C42—181no—
308C42—181no—
309C42—181no—
310C42—181no—
311C22×C3—24no—
312C22×C3—24no—
313C22×C3D3×C22⋊C414yes—
314C22×C3#88314yes—
315C22×C3#89414yes—
316C2×D3—38no—
317C2×D3—64no—
318C2×D3—64no—
319C2×D3—64no—
320C2×D3—64no—
321C2×D3—64no—
322C2×D3—128no—
323C2×D3—128no—
324C3×C4—48no—
325C3×C4—44no—
326C3×C4—44no—
327C3×C4#87214yes—
328C3×C4#88314yes—
329C3×C4#89214yes—
330C3×C4#89414yes—
331Dic3—64no—
332Dic3—64no—
333Dic3—128no—
334Dic3—124no—
335Dic3—124no—
336C32#182611yescharacteristic, complemented, Sylow
337C23—91no—
338C23—91no—
339C23—182no—
340C23—181no—
341C23—181no—
342C23—361no—
343C23D4×C3⋊D311yescharacteristic
344C2×C4—22no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—91no—
350C2×C4—91no—
351C2×C4—181no—
352C2×C4—181no—
353C2×C4—181no—
354C2×C4—181no—
355C2×C4—181no—
356C2×C4—181no—
357C2×C4—181no—
358C2×C4—181no—
359C2×C4—181no—
360C2×C4—181no—
361C2×C4—182no—
362C2×C4—181no—
363C2×C4—181no—
364C2×C4—362no—
365C2×C4—362no—
366C2×C4—361no—
367C2×C4—361no—
368C2×C4C2×C4×C3⋊D311yescharacteristic
369C2×C4#382811yescharacteristic
370C2×C4#382811yescharacteristic
371C2×C4D4×C3⋊D311yescharacteristic
372C2×C4#383011yescharacteristic
373C2×C4#383211yescharacteristic
374C8—41no—
375C8—361no—
376C2×C3—24no—
377C2×C3—24no—
378C2×C3#466414yes—
379C2×C3D3×#10414yes—
380C2×C3#482114yes—
381D3—68no—
382D3—124no—
383C22—21no—
384C22—21no—
385C22—92no—
386C22—181no—
387C22—181no—
388C22—181no—
389C22—181no—
390C22—181no—
391C22—362no—
392C22—362no—
393C22C22⋊C4×C3⋊D311yescharacteristic
394C22#6409211yescharacteristic
395C22#6410311yescharacteristic
396C4—42no—
397C4—41no—
398C4—41no—
399C4—181no—
400C4—181no—
401C4—362no—
402C4—361no—
403C4—361no—
404C4#6408111yescharacteristic
405C4#6409211yescharacteristic
406C4#6410111yescharacteristic
407C4#6410311yescharacteristic
408C3#6875414yescomplemented
409C2—21no—
410C2—21no—
411C2—182no—
412C2—361no—
413C2#1059236311yescharacteristic
414C2C3⋊D3×#10411yescharacteristic
415C2#1059252011yescharacteristic
subgroupG/H
centerC2×C4D4×C3⋊D3
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C22×C3⋊D3
FittingC32×#339C2
socleC22×C32C2×C22⋊C4
prime radicalC23×C3⋊D3D4
cosocleC22×C32×C4C23
hypercenter#339C3⋊D3
hypocenterC32#1826
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
4. C32×#339C2semidirect
5. #10589421C2semidirect
6. #10589398C2semidirect
7. #10589389C2semidirect
17. #64101C4semidirect
18. #64101C4semidirect
19. C4⋊C4×C3⋊D3C4semidirect
20. C4⋊C4×C3⋊D3C4semidirect
31. C3×#339D3semidirect
140. #339C3⋊D3semidirect
336. C32#1826semidirect
408. C3#68754semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×#1172
#105928252
C4×#37522
C32×#3392
#105894212
#105893982
#105893892
#687543