Finite Group Databasebeta

← #11808759

Subgroups — #11808759

Order 1152.

1893 conjugacy classes of subgroups; only the 224 normal subgroups are shown.

normal subgroups only

This group has 1893 conjugacy classes of subgroups — too many to draw. Only its 224 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×#64102C211yesmaximal, characteristic, complemented
2C2×#63902C211yesmaximal, characteristic, complemented
3C2×#63881C214yesmaximal, complemented
4C3×#4993C212yesmaximal, complemented
5#10591395C212yesmaximal, complemented
6#10591393C212yesmaximal, complemented
7#10591252C211yesmaximal, characteristic, complemented
8#10591203C212yesmaximal, complemented
9#78019—32nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C22×C4×C3⋊D3C2212yes—
12C22×#626C2214yes—
13C22×#625C2211yescharacteristic
14C22×D3×Dic3C2212yes—
15C2×C32×C4⋊C4C2211yescharacteristic
16C2×#3752C2212yes—
17C2×C4×C3⋊Dic3C2211yescharacteristic
18#64102—24no—
19C2×C3×(C2×D3)⋊C4C2214yes—
20C2×C3×(C2×D3)⋊C4C2212yes—
21C2×C3×Dic3⋊C4C2214yes—
22C2×#3724C2211yescharacteristic
23C2×#3722C2214yes—
24C2×Dic32C2212yes—
25#63902—24no—
26#63881—216no—
27C3×C3⋊#95C2212yes—
28#63579C2212yes—
29C2×#893—32no—
30C2×#893—34no—
31C2×#893—61no—
32C2×#67⋊C4—32no—
33C2×#67⋊C4—34no—
34C3×#399—32no—
35#4993—34no—
36#4993D312yescomplemented
37#4960—34no—
38#4960—32no—
39#4671—32no—
40#4648—32no—
41C23×C3⋊D3C2312yes—
42C23×C3×D3C2312yes—
43C22×C32×C4C2312yes—
44C22×C32×C4C2311yescharacteristic
45C22×C3⋊Dic3C2311yescharacteristic
46C22×C3⋊Dic3C2311yescharacteristic
47C2×C4⋊(C3⋊D3)—24no—
48C2×C4⋊(C3⋊D3)—22no—
49C2×C4×C3⋊D3—24no—
50C2×C4×C3⋊D3—28no—
51C22×C3×Dic3C2312yes—
52C22×C3×Dic3C2314yes—
53C2×#626—28no—
54C2×#626—28no—
55C2×#626—28no—
56C2×#625—24no—
57C2×#625—22no—
58C2×D3×Dic3—28no—
59C2×D3×Dic3—24no—
60C32×C4⋊C4—22no—
61#3752—24no—
62C4×C3⋊Dic3D414yescomplemented
63C3×(C2×D3)⋊C4—24no—
64C3×(C2×D3)⋊C4—28no—
65C3×Dic3⋊C4—28no—
66#3724—22no—
67#3722—28no—
68Dic32D418yescomplemented
69#2397—91noSylow
70C22×#67—32no—
71C22×#67—34no—
72C23×Dic3—32no—
73C22×D12—34no—
74C22×D12—32no—
75C22×D12—61no—
76C22×C4×D3—32no—
77C22×C4×D3—34no—
78C22×C4×D3—62no—
79C2×C3×C4⋊C4—21no—
80C2×C3×C4⋊C4—34no—
81C2×C3×C4⋊C4C2×D312yes—
82C2×C3×C22⋊C4—34no—
83C2×C3×C22⋊C4—32no—
84C2×(C2×D3)⋊C4—34no—
85C2×(C2×D3)⋊C4—34no—
86C2×(C2×D3)⋊C4—34no—
87C2×(C2×D3)⋊C4—62no—
88C2×(C2×D3)⋊C4C2×D312yes—
89C2×(C2×D3)⋊C4C2×D314yes—
90C2×Dic3⋊C4—32no—
91C2×Dic3⋊C4C2×D314yes—
92C2×C4×Dic3—32no—
93C2×C4×Dic3—34no—
94C2×C4×Dic3—61no—
95#893—616no—
96#893—68no—
97#893—68no—
98#67⋊C4—616no—
99#67⋊C4—68no—
100C3×#95—32no—
101C3⋊#95—34no—
102C3⋊#95C2×D312yes—
103C23×C32C2411yescharacteristic
104C22×C3⋊D3—22no—
105C22×C3⋊D3—22no—
106C22×C3⋊D3—24no—
107C22×C3⋊D3—24no—
108C22×C3⋊D3#4114yes—
109C22×C3×D3—22no—
110C22×C3×D3—24no—
111C22×C3×D3—22no—
112C22×C3×D3—24no—
113C22×C3×D3#4114yes—
114C2×C32×C4—22no—
115C2×C32×C4—22no—
116C2×C32×C4—24no—
117C2×C32×C4C2×D412yes—
118C2×C3⋊Dic3—22no—
119C2×C3⋊Dic3C2×D412yes—
120C2×C3⋊Dic3C2×D414yes—
121C2×C3⋊Dic3C2×D412yes—
122C4⋊(C3⋊D3)—28no—
123C4×C3⋊D3—48no—
124C2×C3×Dic3—24no—
125C2×C3×Dic3—24no—
126C2×C3×Dic3—24no—
127C2×C3×Dic3—22no—
128C2×C3×Dic3C2×D418yes—
129#626—232no—
130#625—28no—
131D3×Dic3—48no—
132C2×C4×D4—91no—
133C2×C4×D4—94no—
134C2×C4×D4—91no—
135#399—32no—
136#399—92no—
137#392—92no—
138#392—92no—
139#376—91no—
140C24×C3—32no—
141C23×D3—34no—
142C23×D3—62no—
143C23×D3C22×D312yes—
144C22×C3×C4—21no—
145C22×C3×C4—22no—
146C22×C3×C4—34no—
147C22×C3×C4—32no—
148C22×C3×C4C22×D314yes—
149C22×C3×C4C22×D312yes—
150C2×#67—68no—
151C2×#67—68no—
152C2×#67—64no—
153C2×#67—64no—
154C2×#67—64no—
155C2×#67—68no—
156C22×Dic3—32no—
157C22×Dic3—32no—
158C22×Dic3—61no—
159C22×Dic3—61no—
160C22×Dic3—68no—
161C22×Dic3—64no—
162C22×Dic3C22×D312yes—
163C22×Dic3C22×D314yes—
164C2×D12—68no—
165C2×D12—64no—
166C2×D12—68no—
167C2×D12—68no—
168C2×D12—68no—
169C2×D12—68no—
170C2×D12—64no—
171C2×C4×D3—68no—
172C2×C4×D3—68no—
173C2×C4×D3—68no—
174C2×C4×D3—64no—
175C2×C4×D3—68no—
176C2×C4×D3—68no—
177C2×C4×D3—128no—
178C3×C4⋊C4—24no—
179C3×C4⋊C4—24no—
180C3×C4⋊C4—68no—
181C3×C22⋊C4—68no—
182C3×C22⋊C4—64no—
183(C2×D3)⋊C4—24no—
184(C2×D3)⋊C4—28no—
185(C2×D3)⋊C4—68no—
186(C2×D3)⋊C4—68no—
187(C2×D3)⋊C4—68no—
188(C2×D3)⋊C4—68no—
189Dic3⋊C4—28no—
190Dic3⋊C4—64no—
191C4×Dic3—38no—
192C4×Dic3—316no—
193C4×Dic3—64no—
194C22×C32C22×D412yes—
195C22×C32C22×D411yescharacteristic
196C22×C32C2×#4112yes—
197C22×C32C2×#4112yes—
198C2×C3⋊D3—24no—
199C2×C3⋊D3—28no—
200C2×C3⋊D3—44no—
201C2×C3⋊D3—42no—
202C2×C3⋊D3—42no—
203C2×C3×D3—24no—
204C2×C3×D3—28no—
205C2×C3×D3—42no—
206C2×C3×D3—44no—
207C2×C3×D3—42no—
208C32×C4—22no—
209C32×C4—42no—
210C3⋊Dic3—22no—
211C3⋊Dic3#12714yes—
212C3×Dic3—28no—
213C3×Dic3—42no—
214C22×D4—94no—
215C22×D4—91no—
216C22×D4—91no—
217C23×C4—92no—
218C23×C4—92no—
219C4×D4—184no—
220C4×D4—1816no—
221C4×D4—184no—
222C2×C4⋊C4—34no—
223C2×C4⋊C4—91no—
224C2×C4⋊C4D3211yescharacteristic
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—21no—
234C23×C3—34no—
235C23×C3—64no—
236C23×C3—62no—
237C23×C3—62no—
238C23×C3—64no—
239C23×C3C23×D312yes—
240C22×D3—24no—
241C22×D3—22no—
242C22×D3—24no—
243C22×D3—22no—
244C22×D3—38no—
245C22×D3—64no—
246C22×D3—64no—
247C22×D3—64no—
248C22×D3—64no—
249C22×D3—64no—
250C22×D3—64no—
251C22×D3—64no—
252C22×D3—64no—
253C22×D3—64no—
254C22×D3—124no—
255C22×D3—124no—
256C22×D3#23914yes—
257C2×C3×C4—24no—
258C2×C3×C4—24no—
259C2×C3×C4—24no—
260C2×C3×C4—24no—
261C2×C3×C4—24no—
262C2×C3×C4—24no—
263C2×C3×C4—22no—
264C2×C3×C4—38no—
265C2×C3×C4—44no—
266C2×C3×C4—64no—
267C2×C3×C4—64no—
268C2×C3×C4—62no—
269C2×C3×C4—64no—
270C2×C3×C4D3×D414yes—
271#67—632no—
272#67—616no—
273C2×Dic3—24no—
274C2×Dic3—24no—
275C2×Dic3—24no—
276C2×Dic3—22no—
277C2×Dic3—38no—
278C2×Dic3—34no—
279C2×Dic3—34no—
280C2×Dic3—62no—
281C2×Dic3—64no—
282C2×Dic3—62no—
283C2×Dic3—62no—
284C2×Dic3—62no—
285C2×Dic3—122no—
286C2×Dic3—128no—
287C2×Dic3D3×D418yes—
288D12—616no—
289D12—616no—
290D12—632no—
291C4×D3—1216no—
292C4×D3—128no—
293C4×D3—1216no—
294C2×C32#52511yescharacteristic
295C2×C32#52514yes—
296C2×C32#52511yescharacteristic
297C2×C32C2×#12711yescharacteristic
298C3⋊D3—44no—
299C3×D3—44no—
300C24—32no—
301C24—92no—
302C2×D4—184no—
303C2×D4—188no—
304C2×D4—188no—
305C2×D4—188no—
306C2×D4—182no—
307C2×D4—184no—
308C2×D4—182no—
309C22×C4—34no—
310C22×C4—32no—
311C22×C4—91no—
312C22×C4—91no—
313C22×C4—184no—
314C22×C4—188no—
315C22×C4—188no—
316C22×C4—184no—
317C22×C4C2×D3212yes—
318C22×C4C2×D3211yescharacteristic
319C4⋊C4—22no—
320C4⋊C4—68no—
321C4⋊C4—182no—
322C22⋊C4—68no—
323C22⋊C4—64no—
324C22⋊C4—184no—
325C22⋊C4—188no—
326C42—98no—
327C42—94no—
328C22×C3—22no—
329C22×C3—22no—
330C22×C3—22no—
331C22×C3—21no—
332C22×C3—68no—
333C22×C3—64no—
334C22×C3—122no—
335C22×C3—122no—
336C22×C3—124no—
337C22×C3C2×D3×D414yes—
338C22×C3C2×D3×D412yes—
339C22×C3C2×#23912yes—
340C22×C3D3×#4114yes—
341C22×C3D3×#4112yes—
342C2×D3—28no—
343C2×D3—24no—
344C2×D3—44no—
345C2×D3—42no—
346C2×D3—42no—
347C2×D3—68no—
348C2×D3—68no—
349C2×D3—68no—
350C2×D3—68no—
351C2×D3—128no—
352C2×D3—124no—
353C2×D3—128no—
354C2×D3—124no—
355C2×D3—124no—
356C2×D3—124no—
357C2×D3—124no—
358C2×D3—124no—
359C3×C4—24no—
360C3×C4—24no—
361C3×C4—44no—
362C3×C4—44no—
363C3×C4—68no—
364C3×C4—122no—
365Dic3—28no—
366Dic3—38no—
367Dic3—42no—
368Dic3—64no—
369Dic3—64no—
370Dic3—122no—
371C32#239711yescharacteristic, complemented, Sylow
372C23—34no—
373C23—64no—
374C23—64no—
375C23—62no—
376C23—62no—
377C23—94no—
378C23—182no—
379C23—184no—
380C23—184no—
381C23—182no—
382C23C22×D3211yescharacteristic
383D4—188no—
384D4—1832no—
385D4—188no—
386C2×C4—22no—
387C2×C4—24no—
388C2×C4—22no—
389C2×C4—38no—
390C2×C4—64no—
391C2×C4—64no—
392C2×C4—64no—
393C2×C4—62no—
394C2×C4—94no—
395C2×C4—92no—
396C2×C4—92no—
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—124no—
406C2×C3#562714yes—
407C2×C3#562712yes—
408C2×C3#565614yes—
409C2×C3#565612yes—
410C2×C3D3×#12712yes—
411D3—44no—
412D3—128no—
413D3—128no—
414C22—68no—
415C22—64no—
416C22—124no—
417C22—122no—
418C22—122no—
419C22—188no—
420C22—184no—
421C22—364no—
422C22—362no—
423C22—362no—
424C22#6430612yes—
425C22D32×D412yes—
426C22D3×#23912yes—
427C22C2×#381111yescharacteristic
428C4—22no—
429C4—42no—
430C4—68no—
431C4—94no—
432C4—122no—
433C4—182no—
434C3—21no—
435C3#7801912yescomplemented
436C2—124no—
437C2—364no—
438C2#1059461514yes—
439C2#1059492011yescharacteristic
440C2#1059530011yescharacteristic
441C2#1059543011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
hypercenterC2×C4⋊C4D32
hypocenterC32#2397
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#64102C2semidirect
2. C2×#63902C2semidirect
3. C2×#63881C2semidirect
4. C3×#4993C2semidirect
5. #10591395C2semidirect
6. #10591393C2semidirect
7. #10591252C2semidirect
8. #10591203C2semidirect
36. #4993D3semidirect
62. C4×C3⋊Dic3D4semidirect
68. Dic32D4semidirect
371. C32#2397semidirect
435. C3#78019semidirect

Maximal subgroups

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

subgroupindex
C2×#641022
C2×#639022
C2×#638812
C3×#49932
#105913952
#105913932
#105912522
#105912032
#780193