Finite Group Databasebeta

← #11808762

Subgroups — #11808762

Order 1152.

1704 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
1C2×Q8×C3⋊Dic3C211yesmaximal, characteristic, complemented
2C2×#64090C211yesmaximal, characteristic
3C32×#393C211yesmaximal, characteristic, complemented
4#10592930C211yesmaximal, characteristic, complemented
5#10592660C212yesmaximal
6#10592652C211yesmaximal, characteristic, complemented
7C22⋊C4×C3⋊Dic3C212yesmaximal, complemented
8#10592373C211yesmaximal, characteristic, complemented
9#10592365C212yesmaximal, complemented
10#10592359C212yesmaximal, complemented
11#10592347C211yesmaximal, characteristic, complemented
12#76779—34nomaximal
13C22×C32×Q8C2211yescharacteristic
14C22×#638C2211yescharacteristic
15C23×C3⋊Dic3C2211yescharacteristic
16C22×C4×C3⋊D3C2211yescharacteristic
17C2×C32×C22⋊C4C2211yescharacteristic
18C2×C32×C22⋊C4C2212yes—
19C2×#3757C2212yes—
20Q8×C3⋊Dic3—24no—
21C2×#3752C2212yes—
22C2×#3752C2212yes—
23C2×#3752C2211yescharacteristic
24C2×C4⋊(C3⋊Dic3)C2212yes—
25C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
26C2×#3750C2211yescharacteristic
27C2×C4×C3⋊Dic3C2212yes—
28C2×C4×C3⋊Dic3C2212yes—
29C2×C4×C3⋊Dic3C2211yescharacteristic
30#64090—24no—
31C32×#95C2211yescharacteristic
32C32×#95C2212yes—
33#63658C2212yes—
34#63658C2211yescharacteristic
35#63658C2212yes—
36#63658C2212yes—
37#63658C2212yes—
38C2×Q8×Dic3—34no—
39C2×#67⋊C4—34no—
40C3×#393D314yescomplemented
41#5231—34no—
42#4961—38no—
43#4953—34no—
44Dic3×C22⋊C4—38no—
45#4674—34no—
46#4666—38no—
47#4660—38no—
48#4648—34no—
49C24×C32C2311yescharacteristic
50C23×C3⋊D3C2311yescharacteristic
51C2×C32×Q8—22no—
52C2×C32×Q8—24no—
53C22×C32×C4C2311yescharacteristic
54C22×C32×C4C2312yes—
55C22×C32×C4C2311yescharacteristic
56C22×C32×C4C2312yes—
57C2×#638—22no—
58C2×#638—22no—
59C2×#638—22no—
60C22×C3⋊Dic3—22no—
61C22×C3⋊Dic3—24no—
62C22×C3⋊Dic3C2311yescharacteristic
63C22×C3⋊Dic3C2312yes—
64C22×C3⋊Dic3C2312yes—
65C22×C3⋊Dic3C2311yescharacteristic
66C22×C3⋊Dic3C2311yescharacteristic
67C2×C4×C3⋊D3—22no—
68C2×C4×C3⋊D3—24no—
69C32×C22⋊C4—22no—
70C32×C22⋊C4—24no—
71#3757—24no—
72#3752—24no—
73#3752—22no—
74#3752—24no—
75C4⋊(C3⋊Dic3)—22no—
76C4⋊(C3⋊Dic3)—24no—
77#3750—22no—
78C4×C3⋊Dic3—24no—
79C4×C3⋊Dic3—24no—
80C4×C3⋊Dic3D414yes—
81#2398—91noSylow
82C22×C3×Q8C2×D314yes—
83C22×#67—34no—
84C23×Dic3—34no—
85C22×C4×D3—34no—
86C2×C3×C22⋊C4C2×D318yes—
87C2×C3×C22⋊C4C2×D314yes—
88C2×#217—38no—
89Q8×Dic3—616no—
90C2×(C2×D3)⋊C4—38no—
91C2×(C2×D3)⋊C4—38no—
92C2×(C2×D3)⋊C4—34no—
93C2×C4⋊Dic3—38no—
94C2×C4⋊Dic3—34no—
95C2×Dic3⋊C4—34no—
96C2×C4×Dic3—34no—
97C2×C4×Dic3—38no—
98C2×C4×Dic3—38no—
99#67⋊C4—616no—
100C3×#95C2×D314yes—
101C3×#95C2×D318yes—
102C3⋊#95—38no—
103C3⋊#95—34no—
104C3⋊#95—38no—
105C3⋊#95—38no—
106C3⋊#95—38no—
107C23×C32—21no—
108C23×C32—22no—
109C23×C32—22no—
110C23×C32—21no—
111C23×C32#4112yes—
112C23×C32C2411yescharacteristic
113C22×C3⋊D3—21no—
114C22×C3⋊D3—22no—
115C22×C3⋊D3—22no—
116C22×C3⋊D3—21no—
117C22×C3⋊D3#4112yes—
118C32×Q8—28no—
119C2×C32×C4—22no—
120C2×C32×C4—22no—
121C2×C32×C4—22no—
122C2×C32×C4—21no—
123C2×C32×C4—22no—
124C2×C32×C4—22no—
125C2×C32×C4—22no—
126C2×C32×C4—22no—
127C2×C32×C4C2×D412yes—
128C2×C32×C4#4114yes—
129#638—28no—
130C2×C3⋊Dic3—21no—
131C2×C3⋊Dic3—21no—
132C2×C3⋊Dic3—22no—
133C2×C3⋊Dic3—21no—
134C2×C3⋊Dic3—22no—
135C2×C3⋊Dic3—22no—
136C2×C3⋊Dic3—22no—
137C2×C3⋊Dic3—22no—
138C2×C3⋊Dic3—22no—
139C2×C3⋊Dic3—22no—
140C2×C3⋊Dic3—44no—
141C2×C3⋊Dic3C2×D412yes—
142C2×C3⋊Dic3C2×D412yes—
143C2×C3⋊Dic3#4114yes—
144C4×C3⋊D3—44no—
145C2×C4×Q8—91no—
146C2×C4×D4—91no—
147#400—92no—
148#397—91no—
149#397—91no—
150#394—92no—
151#393—91no—
152#393C3⋊D311yescharacteristic, complemented
153C4×C22⋊C4—92no—
154C4×C22⋊C4—92no—
155#376—91no—
156C24×C3C22×D314yes—
157C23×D3—34no—
158C2×C3×Q8—28no—
159C2×C3×Q8—216no—
160C22×C3×C4C22×D318yes—
161C22×C3×C4C22×D314yes—
162C22×C3×C4C22×D314yes—
163C22×C3×C4C22×D318yes—
164C2×#67—68no—
165C2×#67—68no—
166C2×#67—68no—
167C22×Dic3—34no—
168C22×Dic3—34no—
169C22×Dic3—38no—
170C22×Dic3—34no—
171C22×Dic3—38no—
172C22×Dic3—68no—
173C22×Dic3—616no—
174C2×C4×D3—68no—
175C2×C4×D3—616no—
176C3×C22⋊C4—28no—
177C3×C22⋊C4—216no—
178#217—616no—
179(C2×D3)⋊C4—616no—
180(C2×D3)⋊C4—68no—
181(C2×D3)⋊C4—616no—
182C4⋊Dic3—616no—
183C4⋊Dic3—68no—
184Dic3⋊C4—68no—
185C4×Dic3—316no—
186C4×Dic3—616no—
187C4×Dic3—616no—
188C22×C32—22no—
189C22×C32—24no—
190C22×C32—41no—
191C22×C32—41no—
192C22×C32—42no—
193C22×C32C22×D411yescharacteristic
194C22×C32C2×#4112yes—
195C22×C32C2×#4111yescharacteristic
196C22×C32C2×#4111yescharacteristic
197C22×C32C2×#4112yes—
198C2×C3⋊D3—22no—
199C2×C3⋊D3—24no—
200C2×C3⋊D3—41no—
201C2×C3⋊D3—41no—
202C2×C3⋊D3—42no—
203C32×C4—22no—
204C32×C4—24no—
205C32×C4—41no—
206C32×C4—42no—
207C3⋊Dic3—22no—
208C3⋊Dic3—42no—
209C3⋊Dic3—41no—
210C3⋊Dic3—42no—
211C3⋊Dic3#12414yes—
212C22×Q8C2×C3⋊D311yescharacteristic
213C22×D4—91no—
214C23×C4—91no—
215C23×C4—91no—
216C4×Q8—184no—
217C4×D4—184no—
218C2×C4⋊C4—91no—
219C2×C4⋊C4—92no—
220C2×C4⋊C4—91no—
221C2×C22⋊C4—92no—
222C2×C22⋊C4—91no—
223C2×C22⋊C4—92no—
224C2×C22⋊C4—92no—
225C2×C22⋊C4C2×C3⋊D311yescharacteristic
226C2×C22⋊C4C2×C3⋊D312yes—
227C2×C42—91no—
228C2×C42—92no—
229C2×C42—92no—
230#95—91no—
231#95—92no—
232#95—92no—
233#95—92no—
234#95—92no—
235#95C2×C3⋊D311yescharacteristic
236#95C2×C3⋊D312yes—
237C23×C3—24no—
238C23×C3—28no—
239C23×C3—28no—
240C23×C3—24no—
241C23×C3#23918yes—
242C23×C3C23×D314yes—
243C22×D3—38no—
244C22×D3—64no—
245C22×D3—68no—
246C22×D3—64no—
247C22×D3—68no—
248C3×Q8—232no—
249C2×C3×C4—28no—
250C2×C3×C4—28no—
251C2×C3×C4—28no—
252C2×C3×C4—24no—
253C2×C3×C4—28no—
254C2×C3×C4—28no—
255C2×C3×C4—28no—
256C2×C3×C4—28no—
257C2×C3×C4D3×D418yes—
258C2×C3×C4#237116yes—
259#67—632no—
260C2×Dic3—38no—
261C2×Dic3—316no—
262C2×Dic3—38no—
263C2×Dic3—64no—
264C2×Dic3—64no—
265C2×Dic3—68no—
266C2×Dic3—64no—
267C2×Dic3—68no—
268C2×Dic3—68no—
269C2×Dic3—68no—
270C2×Dic3—68no—
271C2×Dic3—68no—
272C2×Dic3—68no—
273C2×Dic3—1216no—
274C4×D3—1216no—
275C2×C32—42no—
276C2×C32#52511yescharacteristic
277C2×C32#52511yescharacteristic
278C2×C32C2×#12411yescharacteristic
279C2×C32#52912yes—
280C2×C32#52912yes—
281C3⋊D3—42no—
282C24—91no—
283C24C22×C3⋊D311yescharacteristic
284C2×Q8—22no—
285C2×Q8—24no—
286C2×D4—182no—
287C2×D4—182no—
288C2×D4—182no—
289C22×C4—91no—
290C22×C4—91no—
291C22×C4—92no—
292C22×C4—91no—
293C22×C4—92no—
294C22×C4—182no—
295C22×C4—184no—
296C22×C4—182no—
297C22×C4—184no—
298C22×C4C22×C3⋊D312yes—
299C22×C4C22×C3⋊D311yescharacteristic
300C22×C4C22×C3⋊D311yescharacteristic
301C22×C4C22×C3⋊D312yes—
302C4⋊C4—182no—
303C4⋊C4—184no—
304C4⋊C4—182no—
305C22⋊C4—22no—
306C22⋊C4—24no—
307C22⋊C4—184no—
308C22⋊C4—184no—
309C22⋊C4—182no—
310C22⋊C4—184no—
311C42—94no—
312C42—184no—
313C42—184no—
314C22×C3—216no—
315C22×C3—28no—
316C22×C3—44no—
317C22×C3—48no—
318C22×C3—44no—
319C22×C3C2×D3×D414yes—
320C22×C3C2×#23718yes—
321C22×C3C2×#23914yes—
322C22×C3D3×#4118yes—
323C22×C3D3×#4114yes—
324C2×D3—616no—
325C2×D3—68no—
326C2×D3—124no—
327C2×D3—124no—
328C2×D3—128no—
329C3×C4—28no—
330C3×C4—216no—
331C3×C4—44no—
332C3×C4—48no—
333Dic3—316no—
334Dic3—68no—
335Dic3—124no—
336Dic3—128no—
337Dic3—128no—
338C32#239811yescharacteristic, complemented, Sylow
339C23—21no—
340C23—22no—
341C23—22no—
342C23—21no—
343C23—92no—
344C23—181no—
345C23—182no—
346C23—181no—
347C23—182no—
348C23#383212yes—
349C23C23×C3⋊D311yescharacteristic
350Q8—28no—
351D4—188no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—21no—
356C2×C4—22no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—22no—
360C2×C4—92no—
361C2×C4—94no—
362C2×C4—92no—
363C2×C4—181no—
364C2×C4—181no—
365C2×C4—182no—
366C2×C4—181no—
367C2×C4—182no—
368C2×C4—182no—
369C2×C4—182no—
370C2×C4—182no—
371C2×C4—182no—
372C2×C4—182no—
373C2×C4—364no—
374C2×C4—364no—
375C2×C4D4×C3⋊D312yes—
376C2×C4#383014yes—
377C2×C3—48no—
378C2×C3#558614yes—
379C2×C3#562418yes—
380C2×C3#562714yes—
381C2×C3D3×#12414yes—
382C2×C3#568018yes—
383D3—128no—
384C22—22no—
385C22—24no—
386C22—41no—
387C22—42no—
388C22—41no—
389C22—182no—
390C22—184no—
391C22—361no—
392C22—361no—
393C22—362no—
394C22C2×D4×C3⋊D311yescharacteristic
395C22C2×#383012yes—
396C22C2×#383211yescharacteristic
397C22#41×C3⋊D311yescharacteristic
398C22#41×C3⋊D312yes—
399C4—22no—
400C4—24no—
401C4—41no—
402C4—42no—
403C4—94no—
404C4—182no—
405C4—362no—
406C4—361no—
407C4—362no—
408C3#7677914yescomplemented
409C2—42no—
410C2—362no—
411C2#1059605711yescharacteristic
412C2#1059609512yes—
413C2#1059609811yescharacteristic
414C2C3⋊D3×#12411yescharacteristic
415C2#1059615112yes—
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutator, socle, cosocleC23×C32C24
FittingC32×#393C2
prime radicalC22×#638C22
hypercenter#393C3⋊D3
hypocenterC32#2398
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C2×Q8×C3⋊Dic3C2semidirect
3. C32×#393C2semidirect
4. #10592930C2semidirect
6. #10592652C2semidirect
7. C22⋊C4×C3⋊Dic3C2semidirect
8. #10592373C2semidirect
9. #10592365C2semidirect
10. #10592359C2semidirect
11. #10592347C2semidirect
40. C3×#393D3semidirect
152. #393C3⋊D3semidirect
338. C32#2398semidirect
408. C3#76779semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×C3⋊Dic32
C2×#640902
C32×#3932
#105929302
#105926602
#105926522
C22⋊C4×C3⋊Dic32
#105923732
#105923652
#105923592
#105923472
#767793