Finite Group Databasebeta

← #11788211

Subgroups — #11788211

Order 1152.

811 conjugacy classes of subgroups.

The subgroup lattice has 443 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5791C211yesmaximal, characteristic
2C2×C3×#926C211yesmaximal, characteristic, complemented
3#10592906C211yesmaximal, characteristic, complemented
4C2×#63569C212yesmaximal, complemented
5#10589161C212yesmaximal, complemented
6#71712—31nomaximal
7#71591—31nomaximal
8C23×C32×C4C2211yescharacteristic
9C2×C3×#235C2211yescharacteristic
10C2×#3748C2212yes—
11C3×#953—21no—
12C2×C3×#217—21no—
13C3×#930C412yescomplemented
14C3×#929—21no—
15C3×C4×#67—22no—
16C3×#926—24no—
17C3×#926C2211yescharacteristic
18C2×C3×C4⋊Dic3—21no—
19C3×#924C412yescomplemented
20C2×C3×C4×Dic3C2212yes—
21#63657—22no—
22#63569—24no—
23C3×#525—31no—
24C2×C3×#117—31no—
25#5791D311yescharacteristic
26C2×#926D311yescharacteristic, complemented
27C2×#837—32no—
28#5207—31no—
29#5207—31no—
30#5207—61no—
31C2×#805—32no—
32#4532—32no—
33#4523—32no—
34C24×C32D411yescharacteristic
35C22×C32×C4—22no—
36C22×C32×C4—22no—
37C22×C32×C4C2×C412yes—
38C22×C32×C4D411yescharacteristic
39C22×C32×C4D412yes—
40C22×C32×C4C2311yescharacteristic
41C2×C3×#67—22no—
42C2×C3×#67—21no—
43C22×C3×Dic3—22no—
44C3×#235—22no—
45C3×#235—22no—
46C2×C3×D12C2×C411yescharacteristic
47C2×C3×C4×D3—21no—
48C2×C3×Dic6C2×C411yescharacteristic
49#3748—22no—
50#3748—22no—
51C2×C3⋊(C3⋊C8)—22no—
52C3×#217—24no—
53C3×#217—22no—
54C3×#217—21no—
55C3×(C2×D3)⋊C4—22no—
56C3×C4⋊Dic3—24no—
57C3×C4⋊Dic3C2×C412yes—
58C3×Dic3⋊C4—22no—
59C3×C4×Dic3—22no—
60C3×C4×Dic3—21no—
61C3×C4×Dic3D414yescomplemented
62#1897—91noSylow
63C2×C3×#41—31no—
64C23×C3×C4—21no—
65C23×C3×C4C2×D311yescharacteristic
66C23×C3×C4C2×D311yescharacteristic
67C2×#235C2×D311yescharacteristic
68C3×#123—61no—
69C3×C22⋊Q8—32no—
70C3×#121—32no—
71C3×#120—61no—
72C3×C4×D4—62no—
73C3×#117—31no—
74C3×#117—64no—
75C2×C3×C4⋊C4—61no—
76C2×C3×C22⋊C4—61no—
77C2×C3×C42—32no—
78#953—21no—
79C2×#217—21no—
80#930Dic312yescomplemented
81#929—21no—
82C4×#67—22no—
83#926—24no—
84#926C2×D311yescharacteristic
85C2×C4⋊Dic3—21no—
86#924Dic312yescomplemented
87C2×C4×Dic3C2×D312yes—
88C2×#208—32no—
89C2×#208—32no—
90C2×#208—62no—
91#837—64no—
92#830—64no—
93#830—62no—
94#830—62no—
95#805—64no—
96C23×C32—21no—
97C23×C32—21no—
98C23×C32—42no—
99C23×C32C22⋊C412yes—
100C23×C32C2×D411yescharacteristic
101C22×C3×D3—21no—
102C2×C32×C4—21no—
103C2×C32×C4—21no—
104C2×C32×C4—24no—
105C2×C32×C4—24no—
106C2×C32×C4C22⋊C412yes—
107C2×C32×C4C22×C411yescharacteristic
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×D412yes—
110C2×C32×C4#4112yes—
111C3×#67—44no—
112C3×#67—41no—
113C3×#67—41no—
114C2×C3×Dic3—22no—
115C2×C3×Dic3—21no—
116C2×C3×Dic3—24no—
117C2×C3×Dic3—44no—
118C3×D12—22no—
119C3×C4×D3—42no—
120C3×Dic6—22no—
121C3⋊(C3⋊C8)—42no—
122#525—31no—
123C2×#117—31no—
124C2×#104—92no—
125#407—91no—
126#339—92no—
127C24×C3—21no—
128C24×C3#6711yescharacteristic
129C24×C3#6711yescharacteristic
130C3×#41—62no—
131C3×#41—62no—
132C2×C3×Q8—31no—
133C2×C3×D4—31no—
134C2×C3×D4—62no—
135C2×C3×D4—61no—
136C22×C3×C4—22no—
137C22×C3×C4—22no—
138C22×C3×C4—22no—
139C22×C3×C4—22no—
140C22×C3×C4—22no—
141C22×C3×C4—21no—
142C22×C3×C4—22no—
143C22×C3×C4—21no—
144C22×C3×C4—42no—
145C22×C3×C4—42no—
146C22×C3×C4—62no—
147C22×C3×C4—61no—
148C22×C3×C4C4×D312yes—
149C22×C3×C4D1212yes—
150C22×C3×C4C2×Dic312yes—
151C22×C3×C4#6711yescharacteristic
152C22×C3×C4#6711yescharacteristic
153C22×C3×C4#6712yes—
154C22×C3×C4C22×D311yescharacteristic
155C22×C3×C4C22×D311yescharacteristic
156C2×#67—22no—
157C2×#67—21no—
158C22×Dic3—22no—
159#235—22no—
160#235—22no—
161C2×D12C2×Dic311yescharacteristic
162C2×C4×D3—21no—
163C2×Dic6C2×Dic311yescharacteristic
164C3×C4⋊C4—32no—
165C3×C4⋊C4—64no—
166C3×C4⋊C4—62no—
167C3×C22⋊C4—64no—
168C3×C22⋊C4—62no—
169C3×C22⋊C4—61no—
170C3×C22⋊C4—62no—
171C3×C42—34no—
172C3×C42—61no—
173C3×C42—62no—
174#217—24no—
175#217—22no—
176#217—21no—
177(C2×D3)⋊C4—22no—
178C4⋊Dic3—24no—
179C4⋊Dic3C2×Dic312yes—
180Dic3⋊C4—22no—
181C4×Dic3—22no—
182C4×Dic3—21no—
183C4×Dic3#6714yescomplemented
184#208—62no—
185#208—62no—
186#208—62no—
187#208—62no—
188#208—122no—
189#208—122no—
190C2×C3⋊C8—64no—
191C2×C3⋊C8—62no—
192C2×C3⋊C8—62no—
193C22×C32—22no—
194C22×C32—22no—
195C22×C32—22no—
196C22×C32—22no—
197C22×C32—42no—
198C22×C32—42no—
199C22×C32C2×C22⋊C411yescharacteristic
200C22×C32#12011yescharacteristic
201C22×C32#12311yescharacteristic
202C2×C3×D3—41no—
203C2×C3×D3—42no—
204C32×C4—22no—
205C32×C4C4×D412yes—
206C32×C4#12112yes—
207C3×Dic3—44no—
208C3×Dic3—41no—
209C3×Dic3—42no—
210C2×#41—31no—
211C23×C4D3211yescharacteristic
212C2×M16—92no—
213#123—61no—
214C22⋊Q8—32no—
215#121—32no—
216#120—61no—
217C4×D4—62no—
218#117—31no—
219#117—64no—
220C2×C4⋊C4—61no—
221C2×C22⋊C4—61no—
222C2×C42—32no—
223#104—184no—
224C22⋊C8—182no—
225C23×C3—21no—
226C23×C3—21no—
227C23×C3—21no—
228C23×C3—21no—
229C23×C3—22no—
230C23×C3—21no—
231C23×C3—41no—
232C23×C3—41no—
233C23×C3—42no—
234C23×C3—42no—
235C23×C3—44no—
236C23×C3—61no—
237C23×C3(C2×D3)⋊C412yes—
238C23×C3#21712yes—
239C23×C3C2×#6711yescharacteristic
240C23×C3C2×#6711yescharacteristic
241C22×D3—21no—
242C3×Q8—62no—
243C3×D4—62no—
244C3×D4—124no—
245C3×D4—121no—
246C3×D4—121no—
247C2×C3×C4—21no—
248C2×C3×C4—21no—
249C2×C3×C4—21no—
250C2×C3×C4—21no—
251C2×C3×C4—24no—
252C2×C3×C4—24no—
253C2×C3×C4—24no—
254C2×C3×C4—24no—
255C2×C3×C4—22no—
256C2×C3×C4—21no—
257C2×C3×C4—22no—
258C2×C3×C4—21no—
259C2×C3×C4—22no—
260C2×C3×C4—44no—
261C2×C3×C4—44no—
262C2×C3×C4—41no—
263C2×C3×C4—41no—
264C2×C3×C4—62no—
265C2×C3×C4—61no—
266C2×C3×C4—64no—
267C2×C3×C4—124no—
268C2×C3×C4—122no—
269C2×C3×C4(C2×D3)⋊C412yes—
270C2×C3×C4#21712yes—
271C2×C3×C4C2×C4×D311yescharacteristic
272C2×C3×C4C2×D1211yescharacteristic
273C2×C3×C4#23512yes—
274C2×C3×C4D3×D412yes—
275C2×C3×C4#23712yes—
276C2×C3×C4C22×Dic311yescharacteristic
277C2×C3×C4C2×#6711yescharacteristic
278C2×C3×C4C2×#6712yes—
279#67—44no—
280#67—41no—
281#67—41no—
282C2×Dic3—22no—
283C2×Dic3—21no—
284C2×Dic3—24no—
285C2×Dic3—44no—
286D12—22no—
287C4×D3—42no—
288Dic6—22no—
289C3⋊C8—124no—
290C3⋊C8—122no—
291C3⋊C8—122no—
292C2×C32—21no—
293C2×C32—21no—
294C2×C32—42no—
295C2×C32#38611yescharacteristic
296C2×C32#42112yes—
297C3×D3—81no—
298C24#62511yescharacteristic
299#41—62no—
300#41—62no—
301C2×Q8—31no—
302C2×D4—31no—
303C2×D4—62no—
304C2×D4—61no—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—62no—
308C22×C4—61no—
309C22×C4D3×Dic312yes—
310C22×C4#62511yescharacteristic
311C22×C4#62612yes—
312C22×C4C2×D3211yescharacteristic
313M16—182no—
314M16—182no—
315C2×C8—182no—
316C4⋊C4—32no—
317C4⋊C4—64no—
318C4⋊C4—62no—
319C22⋊C4—64no—
320C22⋊C4—62no—
321C22⋊C4—61no—
322C22⋊C4—62no—
323C42—34no—
324C42—61no—
325C42—62no—
326C22×C3—22no—
327C22×C3—22no—
328C22×C3—24no—
329C22×C3—22no—
330C22×C3—22no—
331C22×C3—22no—
332C22×C3—22no—
333C22×C3—22no—
334C22×C3—22no—
335C22×C3—21no—
336C22×C3—21no—
337C22×C3—21no—
338C22×C3—42no—
339C22×C3—42no—
340C22×C3—42no—
341C22×C3—42no—
342C22×C3—42no—
343C22×C3—42no—
344C22×C3—42no—
345C22×C3—44no—
346C22×C3—44no—
347C22×C3—121no—
348C22×C3—122no—
349C22×C3C2×(C2×D3)⋊C411yescharacteristic
350C22×C3#92911yescharacteristic
351C22×C3#93511yescharacteristic
352C22×C3#93711yescharacteristic
353C22×C3C2×#21711yescharacteristic
354C22×C3#95311yescharacteristic
355C2×D3—41no—
356C2×D3—42no—
357C3×C4—22no—
358C3×C4—22no—
359C3×C4—22no—
360C3×C4—22no—
361C3×C4—42no—
362C3×C4—124no—
363C3×C4—121no—
364C3×C4—122no—
365C3×C4C4×#6712yes—
366C3×C4#93012yes—
367C3×C4D4×Dic312yes—
368C3×C4#93912yes—
369Dic3—44no—
370Dic3—41no—
371Dic3—42no—
372C32#189711yescharacteristic, complemented, Sylow
373C23—21no—
374C23—21no—
375C23—42no—
376C23—61no—
377C23(C2×D3)⋊Dic312yes—
378C23C2×#62511yescharacteristic
379Q8—62no—
380D4—62no—
381D4—124no—
382D4—121no—
383D4—121no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—24no—
387C2×C4—24no—
388C2×C4—62no—
389C2×C4—61no—
390C2×C4—64no—
391C2×C4—124no—
392C2×C4—122no—
393C2×C4(C2×D3)⋊Dic312yes—
394C2×C4C2×D3×Dic311yescharacteristic
395C2×C4#380412yes—
396C2×C4C2×#62611yescharacteristic
397C2×C4D3×#6712yes—
398C8—362no—
399C2×C3—21no—
400C2×C3—21no—
401C2×C3—21no—
402C2×C3—21no—
403C2×C3—22no—
404C2×C3—21no—
405C2×C3—41no—
406C2×C3—41no—
407C2×C3—44no—
408C2×C3—42no—
409C2×C3—42no—
410C2×C3—241no—
411C2×C3#500512yes—
412C2×C3#521311yescharacteristic
413C2×C3#522011yescharacteristic
414C2×C3#523612yes—
415D3—81no—
416C22—22no—
417C22—22no—
418C22—22no—
419C22—22no—
420C22—42no—
421C22—42no—
422C22—122no—
423C22—121no—
424C22C2×(C2×D3)⋊Dic311yescharacteristic
425C22#6396111yescharacteristic
426C22#6397611yescharacteristic
427C4—22no—
428C4—124no—
429C4—122no—
430C4—121no—
431C4Dic3×#6712yes—
432C4#6397812yes—
433C3—21no—
434C3#7159111yescharacteristic, complemented
435C3#7171211yescharacteristic, complemented
436C2—21no—
437C2—21no—
438C2—42no—
439C2—241no—
440C2#1059111112yes—
441C2#1059171011yescharacteristic
subgroupG/H
centerC2×C4C2×#626
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC23×C32×C4C22
socleC22×C32C2×C22⋊C4
prime radicalC3×#5791C2
cosocleC22×C32×C4C23
hypercenterC23×C4D32
hypocenterC32#1897
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#926C2semidirect
3. #10592906C2semidirect
4. C2×#63569C2semidirect
5. #10589161C2semidirect
13. C3×#930C4semidirect
19. C3×#924C4semidirect
26. C2×#926D3semidirect
61. C3×C4×Dic3D4semidirect
80. #930Dic3semidirect
86. #924Dic3semidirect
183. C4×Dic3#67semidirect
372. C32#1897semidirect
434. C3#71591semidirect
435. C3#71712semidirect

Maximal subgroups

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

subgroupindex
C3×#57912
C2×C3×#9262
#105929062
C2×#635692
#105891612
#717123
#715913