Finite Group Databasebeta

← #11808748

Subgroups — #11808748

Order 1152.

1893 conjugacy classes of subgroups; only the 236 normal subgroups are shown.

normal subgroups only

This group has 1893 conjugacy classes of subgroups — too many to draw. Only its 236 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×D4×C3⋊Dic3C211yesmaximal, characteristic, complemented
2C2×#67⋊Dic3C214yesmaximal, complemented
3C2×#63902C211yesmaximal, characteristic, complemented
4C3×#5223C212yesmaximal, complemented
5#10591723C212yesmaximal, complemented
6#10591715C212yesmaximal, complemented
7#10591317C212yesmaximal, complemented
8#10591252C211yesmaximal, characteristic, complemented
9#76667—32nomaximal
10C22×C32×D4C2211yescharacteristic
11C23×C3⋊Dic3C2212yes—
12C22×C3×#67C2214yes—
13C22×#625C2211yescharacteristic
14C22×D3×Dic3C2212yes—
15C2×#3757C2212yes—
16D4×C3⋊Dic3—24no—
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C2×C4×C3⋊Dic3C2211yescharacteristic
19C2×C3×#217C2214yes—
20C2×C3×(C2×D3)⋊C4C2212yes—
21#67⋊Dic3—216no—
22C2×#3724C2211yescharacteristic
23C2×Dic3⋊Dic3C2214yes—
24C2×(C2×D3)⋊Dic3C2214yes—
25C2×Dic32C2212yes—
26#63902—24no—
27C3×C3⋊#95C2212yes—
28#63579C2212yes—
29C2×D4×Dic3—32no—
30C2×D4×Dic3—34no—
31C2×D4×Dic3—61no—
32C2×#67⋊C4—34no—
33C2×#67⋊C4—32no—
34C3×#392—32no—
35#5223—34no—
36#5223D312yescomplemented
37#4949—34no—
38#4949—32no—
39#4677—32no—
40#4648—32no—
41C24×C32C2312yes—
42C23×C3×D3C2312yes—
43C2×C32×D4—24no—
44C2×C32×D4—22no—
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3—24no—
47C22×C3⋊Dic3—28no—
48C22×C3⋊Dic3C2312yes—
49C22×C3⋊Dic3C2311yescharacteristic
50C22×C3⋊Dic3C2311yescharacteristic
51C2×C3×#67—28no—
52C2×C3×#67—28no—
53C2×C3×#67—28no—
54C22×C3×Dic3C2312yes—
55C22×C3×Dic3C2314yes—
56C2×#625—24no—
57C2×#625—22no—
58C2×D3×Dic3—24no—
59C2×D3×Dic3—28no—
60#3757—24no—
61C4⋊(C3⋊Dic3)—22no—
62C4×C3⋊Dic3D414yescomplemented
63C3×#217—28no—
64C3×(C2×D3)⋊C4—24no—
65#3724—22no—
66Dic3⋊Dic3—28no—
67(C2×D3)⋊Dic3—28no—
68Dic32D418yescomplemented
69#2397—91noSylow
70C22×C3×D4—21no—
71C22×C3×D4—34no—
72C22×C3×D4C2×D312yes—
73C22×#67—32no—
74C22×#67C2×D314yes—
75C23×Dic3—34no—
76C23×Dic3—32no—
77C23×Dic3—62no—
78C22×C4×D3—32no—
79C2×C3×C22⋊C4—34no—
80C2×C3×C22⋊C4—32no—
81C2×#217—34no—
82C2×#217—34no—
83C2×#217—62no—
84C2×#217C2×D314yes—
85D4×Dic3—616no—
86D4×Dic3—68no—
87D4×Dic3—68no—
88C2×(C2×D3)⋊C4—34no—
89C2×(C2×D3)⋊C4C2×D312yes—
90C2×C4⋊Dic3—32no—
91C2×C4⋊Dic3—34no—
92C2×C4⋊Dic3—61no—
93C2×Dic3⋊C4—34no—
94C2×Dic3⋊C4—32no—
95C2×C4×Dic3—32no—
96C2×C4×Dic3—34no—
97C2×C4×Dic3—61no—
98#67⋊C4—68no—
99#67⋊C4—616no—
100C3×#95—32no—
101C3⋊#95—34no—
102C3⋊#95C2×D312yes—
103C23×C32—22no—
104C23×C32—22no—
105C23×C32—24no—
106C23×C32—24no—
107C23×C32#4114yes—
108C23×C32C2411yescharacteristic
109C22×C3×D3—24no—
110C22×C3×D3—22no—
111C22×C3×D3—22no—
112C22×C3×D3—24no—
113C22×C3×D3#4114yes—
114C32×D4—28no—
115C2×C32×C4—22no—
116C2×C32×C4C2×D412yes—
117C2×C3⋊Dic3—22no—
118C2×C3⋊Dic3—22no—
119C2×C3⋊Dic3—24no—
120C2×C3⋊Dic3—48no—
121C2×C3⋊Dic3C2×D412yes—
122C2×C3⋊Dic3C2×D414yes—
123C2×C3⋊Dic3C2×D412yes—
124C3×#67—232no—
125C2×C3×Dic3—24no—
126C2×C3×Dic3—24no—
127C2×C3×Dic3—24no—
128C2×C3×Dic3—22no—
129C2×C3×Dic3C2×D418yes—
130#625—28no—
131D3×Dic3—48no—
132C2×C4×D4—91no—
133C2×C4×D4—94no—
134C2×C4×D4—91no—
135#399—92no—
136#399—92no—
137#392—32no—
138#392—92no—
139#376—91no—
140C24×C3—22no—
141C24×C3—32no—
142C24×C3C22×D314yes—
143C23×D3C22×D312yes—
144C2×C3×D4—24no—
145C2×C3×D4—28no—
146C2×C3×D4—28no—
147C2×C3×D4—24no—
148C2×C3×D4—68no—
149C2×C3×D4—68no—
150C2×C3×D4—68no—
151C22×C3×C4—21no—
152C22×C3×C4—34no—
153C22×C3×C4—32no—
154C22×C3×C4C22×D312yes—
155C2×#67—28no—
156C2×#67—28no—
157C2×#67—28no—
158C2×#67—64no—
159C2×#67—64no—
160C2×#67—64no—
161C22×Dic3—32no—
162C22×Dic3—32no—
163C22×Dic3—34no—
164C22×Dic3—61no—
165C22×Dic3—61no—
166C22×Dic3—62no—
167C22×Dic3—64no—
168C22×Dic3—68no—
169C22×Dic3—68no—
170C22×Dic3—68no—
171C22×Dic3—68no—
172C22×Dic3—68no—
173C22×Dic3—128no—
174C22×Dic3C22×D312yes—
175C22×Dic3C22×D314yes—
176C2×C4×D3—64no—
177C2×C4×D3—68no—
178C3×C22⋊C4—68no—
179C3×C22⋊C4—64no—
180#217—28no—
181#217—68no—
182#217—68no—
183#217—68no—
184(C2×D3)⋊C4—24no—
185(C2×D3)⋊C4—68no—
186C4⋊Dic3—68no—
187C4⋊Dic3—64no—
188C4⋊Dic3—64no—
189Dic3⋊C4—64no—
190Dic3⋊C4—68no—
191C4×Dic3—38no—
192C4×Dic3—316no—
193C4×Dic3—64no—
194C22×C32—24no—
195C22×C32—28no—
196C22×C32—44no—
197C22×C32—42no—
198C22×C32—42no—
199C22×C32C22×D412yes—
200C22×C32C22×D411yescharacteristic
201C22×C32C2×#4112yes—
202C22×C32C2×#4112yes—
203C2×C3×D3—24no—
204C2×C3×D3—28no—
205C2×C3×D3—42no—
206C2×C3×D3—44no—
207C2×C3×D3—42no—
208C32×C4—22no—
209C3⋊Dic3—22no—
210C3⋊Dic3—42no—
211C3⋊Dic3#12714yes—
212C3×Dic3—28no—
213C3×Dic3—42no—
214C22×D4—34no—
215C22×D4—91no—
216C22×D4D3211yescharacteristic
217C23×C4—92no—
218C23×C4—92no—
219C4×D4—184no—
220C4×D4—1816no—
221C4×D4—184no—
222C2×C4⋊C4—91no—
223C2×C4⋊C4—94no—
224C2×C4⋊C4—91no—
225C2×C22⋊C4—34no—
226C2×C22⋊C4—32no—
227C2×C22⋊C4—94no—
228C2×C22⋊C4—92no—
229C2×C42—92no—
230C2×C42—91no—
231#95—32no—
232#95—92no—
233C23×C3—24no—
234C23×C3—24no—
235C23×C3—24no—
236C23×C3—24no—
237C23×C3—24no—
238C23×C3—24no—
239C23×C3—24no—
240C23×C3—24no—
241C23×C3—21no—
242C23×C3—24no—
243C23×C3—34no—
244C23×C3—44no—
245C23×C3—44no—
246C23×C3—64no—
247C23×C3—62no—
248C23×C3—62no—
249C23×C3—64no—
250C23×C3#23718yes—
251C23×C3C23×D312yes—
252C22×D3—22no—
253C22×D3—24no—
254C22×D3—24no—
255C22×D3—22no—
256C22×D3#23714yes—
257C3×D4—216no—
258C3×D4—216no—
259C3×D4—632no—
260C2×C3×C4—24no—
261C2×C3×C4—24no—
262C2×C3×C4—22no—
263C2×C3×C4—38no—
264C2×C3×C4—64no—
265C2×C3×C4—64no—
266C2×C3×C4—64no—
267C2×C3×C4—62no—
268C2×C3×C4D3×D414yes—
269#67—232no—
270#67—616no—
271C2×Dic3—24no—
272C2×Dic3—24no—
273C2×Dic3—22no—
274C2×Dic3—24no—
275C2×Dic3—38no—
276C2×Dic3—34no—
277C2×Dic3—34no—
278C2×Dic3—62no—
279C2×Dic3—64no—
280C2×Dic3—62no—
281C2×Dic3—62no—
282C2×Dic3—62no—
283C2×Dic3—64no—
284C2×Dic3—64no—
285C2×Dic3—64no—
286C2×Dic3—64no—
287C2×Dic3—122no—
288C2×Dic3—124no—
289C2×Dic3—128no—
290C2×Dic3—1216no—
291C2×Dic3—1216no—
292C2×Dic3D3×D418yes—
293C4×D3—128no—
294C2×C32—44no—
295C2×C32#52511yescharacteristic
296C2×C32#52514yes—
297C2×C32#52511yescharacteristic
298C2×C32C2×#12711yescharacteristic
299C3×D3—44no—
300C24—32no—
301C24C2×D3212yes—
302C2×D4—24no—
303C2×D4—22no—
304C2×D4—68no—
305C2×D4—68no—
306C2×D4—68no—
307C2×D4—182no—
308C2×D4—184no—
309C22×C4—34no—
310C22×C4—32no—
311C22×C4—91no—
312C22×C4—91no—
313C22×C4—92no—
314C22×C4—188no—
315C22×C4—184no—
316C22×C4—184no—
317C22×C4—188no—
318C22×C4C2×D3211yescharacteristic
319C4⋊C4—188no—
320C4⋊C4—182no—
321C4⋊C4—182no—
322C22⋊C4—68no—
323C22⋊C4—64no—
324C22⋊C4—188no—
325C22⋊C4—184no—
326C42—98no—
327C42—94no—
328C22×C3—28no—
329C22×C3—28no—
330C22×C3—28no—
331C22×C3—28no—
332C22×C3—22no—
333C22×C3—22no—
334C22×C3—22no—
335C22×C3—21no—
336C22×C3—48no—
337C22×C3—44no—
338C22×C3—48no—
339C22×C3—44no—
340C22×C3—44no—
341C22×C3—44no—
342C22×C3—44no—
343C22×C3—44no—
344C22×C3—64no—
345C22×C3—68no—
346C22×C3—122no—
347C22×C3—124no—
348C22×C3—122no—
349C22×C3C2×D3×D414yes—
350C22×C3C2×D3×D412yes—
351C22×C3C2×#23712yes—
352C22×C3C2×#23714yes—
353C22×C3D3×#4112yes—
354C2×D3—28no—
355C2×D3—24no—
356C2×D3—42no—
357C2×D3—42no—
358C2×D3—44no—
359C3×C4—24no—
360C3×C4—24no—
361C3×C4—68no—
362C3×C4—122no—
363Dic3—28no—
364Dic3—38no—
365Dic3—42no—
366Dic3—64no—
367Dic3—64no—
368Dic3—122no—
369Dic3—124no—
370Dic3—124no—
371C32#239711yescharacteristic, complemented, Sylow
372C23—24no—
373C23—24no—
374C23—22no—
375C23—22no—
376C23—34no—
377C23—64no—
378C23—62no—
379C23—64no—
380C23—62no—
381C23#380514yes—
382C23C22×D3211yescharacteristic
383D4—28no—
384D4—632no—
385D4—188no—
386C2×C4—22no—
387C2×C4—38no—
388C2×C4—64no—
389C2×C4—64no—
390C2×C4—64no—
391C2×C4—62no—
392C2×C4—94no—
393C2×C4—92no—
394C2×C4—92no—
395C2×C4—182no—
396C2×C4—184no—
397C2×C4—182no—
398C2×C4—368no—
399C2×C4—368no—
400C2×C4#381112yes—
401C2×C3—24no—
402C2×C3—21no—
403C2×C3—21no—
404C2×C3—21no—
405C2×C3—48no—
406C2×C3—48no—
407C2×C3—124no—
408C2×C3#558614yes—
409C2×C3#558612yes—
410C2×C3#560614yes—
411C2×C3#560612yes—
412C2×C3D3×#12712yes—
413D3—44no—
414C22—28no—
415C22—24no—
416C22—44no—
417C22—42no—
418C22—42no—
419C22—68no—
420C22—64no—
421C22—124no—
422C22—122no—
423C22—122no—
424C22D32×D412yes—
425C22D3×#23712yes—
426C22C2×#380512yes—
427C22C2×#381111yescharacteristic
428C4—22no—
429C4—68no—
430C4—94no—
431C4—122no—
432C4—182no—
433C4—362no—
434C3—21no—
435C3#7666712yescomplemented
436C2—44no—
437C2—124no—
438C2#1059513014yes—
439C2#1059530011yescharacteristic
440C2#1059530611yescharacteristic
441C2#1059550111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC22×C32×D4C22
hypercenterC22×D4D32
hypocenterC32#2397
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×D4×C3⋊Dic3C2semidirect
2. C2×#67⋊Dic3C2semidirect
3. C2×#63902C2semidirect
4. C3×#5223C2semidirect
5. #10591723C2semidirect
6. #10591715C2semidirect
7. #10591317C2semidirect
8. #10591252C2semidirect
36. #5223D3semidirect
62. C4×C3⋊Dic3D4semidirect
68. Dic32D4semidirect
371. C32#2397semidirect
435. C3#76667semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C3⋊Dic32
C2×#67⋊Dic32
C2×#639022
C3×#52232
#105917232
#105917152
#105913172
#105912522
#766673