Finite Group Databasebeta

← #11788177

Subgroups — #11788177

Order 1152.

979 conjugacy classes of subgroups.

The subgroup lattice has 451 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5791C211yesmaximal, characteristic
2C22×C3×C4×Dic3C211yesmaximal, characteristic, complemented
3#10592906C211yesmaximal, characteristic, complemented
4C2×#63569C212yesmaximal, complemented
5#10589161C212yesmaximal, complemented
6#71711—31nomaximal
7#71532—31nomaximal
8C23×C32×C4C2211yescharacteristic
9C23×C3×Dic3—21no—
10C2×C3×#235C2211yescharacteristic
11C2×#3748C2212yes—
12C3×#953—21no—
13C3×#930C412yescomplemented
14C3×#929—21no—
15C3×C4×#67—22no—
16C3×#926C2211yescharacteristic
17C3×#924C412yescomplemented
18C2×C3×C4×Dic3—21no—
19C2×C3×C4×Dic3—24no—
20C2×C3×C4×Dic3C2212yes—
21#63657—22no—
22#63569—24no—
23C3×#525—31no—
24C22×C3×C42—31no—
25#5791D311yescharacteristic
26C22×C4×Dic3D311yescharacteristic, 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—24no—
44C22×C3×Dic3—28no—
45C22×C3×Dic3—22no—
46C3×#235—22no—
47C3×#235—22no—
48C2×C3×D12C2×C411yescharacteristic, complemented
49C2×C3×C4×D3—21no—
50C2×C3×Dic6C2×C411yescharacteristic, complemented
51#3748—22no—
52#3748—22no—
53C2×C3⋊(C3⋊C8)—22no—
54C3×#217—22no—
55C3×#217—21no—
56C3×(C2×D3)⋊C4—22no—
57C3×C4⋊Dic3C2×C412yescomplemented
58C3×Dic3⋊C4—22no—
59C3×C4×Dic3—24no—
60C3×C4×Dic3—22no—
61C3×C4×Dic3—21no—
62C3×C4×Dic3D414yescomplemented
63#1896—91noSylow
64C2×C3×#41—31no—
65C23×C3×C4—21no—
66C23×C3×C4—61no—
67C23×C3×C4C2×D311yescharacteristic
68C23×C3×C4C2×D311yescharacteristic
69C23×Dic3—21no—
70C2×#235C2×D311yescharacteristic
71C3×#123—61no—
72C3×C22⋊Q8—32no—
73C3×#121—32no—
74C3×#120—61no—
75C3×C4×D4—62no—
76C3×#117—31no—
77C2×C3×C42—32no—
78C2×C3×C42—64no—
79C2×C3×C42—61no—
80#953—21no—
81#930Dic312yescomplemented
82#929—21no—
83C4×#67—22no—
84#926C2×D311yescharacteristic
85#924Dic312yescomplemented
86C2×C4×Dic3—21no—
87C2×C4×Dic3—24no—
88C2×C4×Dic3C2×D312yes—
89C2×#208—32no—
90C2×#208—32no—
91C2×#208—62no—
92#837—64no—
93#830—64no—
94#830—62no—
95#830—62no—
96#805—64no—
97C23×C32—24no—
98C23×C32—21no—
99C23×C32—21no—
100C23×C32C22⋊C412yes—
101C23×C32C2×D411yescharacteristic
102C22×C3×D3—21no—
103C2×C32×C4—21no—
104C2×C32×C4—21no—
105C2×C32×C4—24no—
106C2×C32×C4—24no—
107C2×C32×C4C22⋊C412yes—
108C2×C32×C4C22×C411yescharacteristic
109C2×C32×C4C2×D411yescharacteristic
110C2×C32×C4C2×D412yes—
111C2×C32×C4#4112yes—
112C3×#67—44no—
113C3×#67—41no—
114C3×#67—41no—
115C2×C3×Dic3—216no—
116C2×C3×Dic3—28no—
117C2×C3×Dic3—24no—
118C2×C3×Dic3—22no—
119C2×C3×Dic3—21no—
120C3×D12—22no—
121C3×C4×D3—42no—
122C3×Dic6—22no—
123C3⋊(C3⋊C8)—42no—
124#525—31no—
125C22×C42—31no—
126C2×#104—92no—
127#407—91no—
128#339—92no—
129C24×C3—21no—
130C24×C3#6711yescharacteristic
131C24×C3#6711yescharacteristic
132C3×#41—62no—
133C3×#41—62no—
134C2×C3×Q8—31no—
135C2×C3×D4—31no—
136C2×C3×D4—62no—
137C2×C3×D4—61no—
138C22×C3×C4—22no—
139C22×C3×C4—22no—
140C22×C3×C4—22no—
141C22×C3×C4—22no—
142C22×C3×C4—22no—
143C22×C3×C4—21no—
144C22×C3×C4—22no—
145C22×C3×C4—21no—
146C22×C3×C4—42no—
147C22×C3×C4—42no—
148C22×C3×C4—64no—
149C22×C3×C4—68no—
150C22×C3×C4—62no—
151C22×C3×C4—61no—
152C22×C3×C4C4×D312yes—
153C22×C3×C4D1212yes—
154C22×C3×C4C2×Dic312yes—
155C22×C3×C4#6711yescharacteristic
156C22×C3×C4#6711yescharacteristic
157C22×C3×C4#6712yes—
158C22×C3×C4C22×D311yescharacteristic
159C22×C3×C4C22×D311yescharacteristic
160C2×#67—22no—
161C2×#67—21no—
162C22×Dic3—24no—
163C22×Dic3—28no—
164C22×Dic3—22no—
165#235—22no—
166#235—22no—
167C2×D12C2×Dic311yescharacteristic, complemented
168C2×C4×D3—21no—
169C2×Dic6C2×Dic311yescharacteristic, complemented
170C3×C4⋊C4—32no—
171C3×C4⋊C4—62no—
172C3×C22⋊C4—62no—
173C3×C22⋊C4—61no—
174C3×C22⋊C4—62no—
175C3×C42—34no—
176C3×C42—64no—
177C3×C42—61no—
178C3×C42—62no—
179#217—22no—
180#217—21no—
181(C2×D3)⋊C4—22no—
182C4⋊Dic3C2×Dic312yescomplemented
183Dic3⋊C4—22no—
184C4×Dic3—24no—
185C4×Dic3—22no—
186C4×Dic3—21no—
187C4×Dic3#6714yescomplemented
188#208—62no—
189#208—62no—
190#208—62no—
191#208—62no—
192#208—122no—
193#208—122no—
194C2×C3⋊C8—64no—
195C2×C3⋊C8—62no—
196C2×C3⋊C8—62no—
197C22×C32—24no—
198C22×C32—24no—
199C22×C32—22no—
200C22×C32—22no—
201C22×C32—22no—
202C22×C32#10414yescomplemented
203C22×C32C2×C22⋊C411yescharacteristic
204C22×C32#12011yescharacteristic
205C22×C32#12311yescharacteristic
206C2×C3×D3—41no—
207C2×C3×D3—42no—
208C32×C4—22no—
209C32×C4C4×D412yes—
210C32×C4#12112yes—
211C3×Dic3—28no—
212C3×Dic3—41no—
213C3×Dic3—42no—
214C2×#41—31no—
215C23×C4—61no—
216C23×C4D3211yescharacteristic
217C2×M16—92no—
218#123—61no—
219C22⋊Q8—32no—
220#121—32no—
221#120—61no—
222C4×D4—62no—
223#117—31no—
224C2×C42—32no—
225C2×C42—64no—
226C2×C42—61no—
227#104—184no—
228C22⋊C8—182no—
229C23×C3—24no—
230C23×C3—24no—
231C23×C3—21no—
232C23×C3—21no—
233C23×C3—21no—
234C23×C3—21no—
235C23×C3—22no—
236C23×C3—21no—
237C23×C3—41no—
238C23×C3—41no—
239C23×C3—44no—
240C23×C3—61no—
241C23×C3(C2×D3)⋊C412yes—
242C23×C3#21712yes—
243C23×C3C2×#6711yescharacteristic
244C23×C3C2×#6711yescharacteristic
245C22×D3—21no—
246C3×Q8—62no—
247C3×D4—62no—
248C3×D4—124no—
249C3×D4—121no—
250C3×D4—121no—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—24no—
256C2×C3×C4—24no—
257C2×C3×C4—24no—
258C2×C3×C4—24no—
259C2×C3×C4—22no—
260C2×C3×C4—21no—
261C2×C3×C4—22no—
262C2×C3×C4—21no—
263C2×C3×C4—22no—
264C2×C3×C4—44no—
265C2×C3×C4—44no—
266C2×C3×C4—41no—
267C2×C3×C4—41no—
268C2×C3×C4—616no—
269C2×C3×C4—68no—
270C2×C3×C4—64no—
271C2×C3×C4—62no—
272C2×C3×C4—61no—
273C2×C3×C4—122no—
274C2×C3×C4(C2×D3)⋊C412yes—
275C2×C3×C4#21712yes—
276C2×C3×C4C2×C4×D311yescharacteristic
277C2×C3×C4C2×D1211yescharacteristic
278C2×C3×C4#23512yes—
279C2×C3×C4D3×D412yes—
280C2×C3×C4#23712yes—
281C2×C3×C4C22×Dic311yescharacteristic
282C2×C3×C4C2×#6711yescharacteristic
283C2×C3×C4C2×#6712yes—
284#67—44no—
285#67—41no—
286#67—41no—
287C2×Dic3—216no—
288C2×Dic3—28no—
289C2×Dic3—24no—
290C2×Dic3—22no—
291C2×Dic3—21no—
292D12—22no—
293C4×D3—42no—
294Dic6—22no—
295C3⋊C8—124no—
296C3⋊C8—122no—
297C3⋊C8—122no—
298C2×C32—21no—
299C2×C32—24no—
300C2×C32—21no—
301C2×C32#38611yescharacteristic
302C2×C32C2×#10412yes—
303C3×D3—81no—
304C24#62511yescharacteristic
305#41—62no—
306#41—62no—
307C2×Q8—31no—
308C2×D4—31no—
309C2×D4—62no—
310C2×D4—61no—
311C22×C4—22no—
312C22×C4—22no—
313C22×C4—64no—
314C22×C4—68no—
315C22×C4—62no—
316C22×C4—61no—
317C22×C4D3×Dic312yes—
318C22×C4#62511yescharacteristic
319C22×C4#62612yes—
320C22×C4C2×D3211yescharacteristic
321M16—182no—
322M16—182no—
323C2×C8—182no—
324C4⋊C4—32no—
325C4⋊C4—62no—
326C22⋊C4—62no—
327C22⋊C4—61no—
328C22⋊C4—62no—
329C42—34no—
330C42—64no—
331C42—61no—
332C42—62no—
333C22×C3—24no—
334C22×C3—24no—
335C22×C3—24no—
336C22×C3—24no—
337C22×C3—22no—
338C22×C3—22no—
339C22×C3—22no—
340C22×C3—22no—
341C22×C3—22no—
342C22×C3—22no—
343C22×C3—24no—
344C22×C3—21no—
345C22×C3—21no—
346C22×C3—21no—
347C22×C3—42no—
348C22×C3—42no—
349C22×C3—42no—
350C22×C3—44no—
351C22×C3—44no—
352C22×C3—122no—
353C22×C3—121no—
354C22×C3#80514yescomplemented
355C22×C3#83714yescomplemented
356C22×C3C2×(C2×D3)⋊C411yescharacteristic
357C22×C3#92911yescharacteristic
358C22×C3#93511yescharacteristic
359C22×C3#93711yescharacteristic
360C22×C3C2×#21711yescharacteristic
361C22×C3#95311yescharacteristic
362C2×D3—41no—
363C2×D3—42no—
364C3×C4—22no—
365C3×C4—22no—
366C3×C4—22no—
367C3×C4—22no—
368C3×C4—42no—
369C3×C4—68no—
370C3×C4—122no—
371C3×C4—121no—
372C3×C4C4×#6712yes—
373C3×C4#93012yes—
374C3×C4D4×Dic312yes—
375C3×C4#93912yes—
376Dic3—28no—
377Dic3—41no—
378Dic3—42no—
379C32#189611yescharacteristic, complemented, Sylow
380C23—24no—
381C23—21no—
382C23—21no—
383C23—61no—
384C23(C2×D3)⋊Dic312yes—
385C23C2×#62511yescharacteristic
386Q8—62no—
387D4—62no—
388D4—124no—
389D4—121no—
390D4—121no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—24no—
394C2×C4—24no—
395C2×C4—616no—
396C2×C4—68no—
397C2×C4—64no—
398C2×C4—62no—
399C2×C4—61no—
400C2×C4—122no—
401C2×C4(C2×D3)⋊Dic312yes—
402C2×C4C2×D3×Dic311yescharacteristic
403C2×C4#380412yes—
404C2×C4C2×#62611yescharacteristic
405C2×C4D3×#6712yes—
406C8—362no—
407C2×C3—21no—
408C2×C3—24no—
409C2×C3—21no—
410C2×C3—21no—
411C2×C3—24no—
412C2×C3—21no—
413C2×C3—22no—
414C2×C3—21no—
415C2×C3—41no—
416C2×C3—44no—
417C2×C3—41no—
418C2×C3—241no—
419C2×C3C2×#80512yes—
420C2×C3#521311yescharacteristic
421C2×C3#522011yescharacteristic
422C2×C3C2×#83712yes—
423D3—81no—
424C22—24no—
425C22—24no—
426C22—22no—
427C22—22no—
428C22—22no—
429C22—122no—
430C22—121no—
431C22#6356914yescomplemented
432C22C2×(C2×D3)⋊Dic311yescharacteristic
433C22#6396111yescharacteristic
434C22#6397611yescharacteristic
435C4—22no—
436C4—68no—
437C4—122no—
438C4—121no—
439C4Dic3×#6712yes—
440C4#6397812yes—
441C3—21no—
442C3#7153211yescharacteristic, complemented
443C3#7171111yescharacteristic, complemented
444C2—21no—
445C2—24no—
446C2—21no—
447C2—241no—
448C2C2×#6356912yes—
449C2#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#1896
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. C22×C3×C4×Dic3C2semidirect
3. #10592906C2semidirect
4. C2×#63569C2semidirect
5. #10589161C2semidirect
13. C3×#930C4semidirect
17. C3×#924C4semidirect
26. C22×C4×Dic3D3semidirect
48. C2×C3×D12C2×C4semidirect
50. C2×C3×Dic6C2×C4semidirect
57. C3×C4⋊Dic3C2×C4semidirect
62. C3×C4×Dic3D4semidirect
81. #930Dic3semidirect
85. #924Dic3semidirect
167. C2×D12C2×Dic3semidirect
169. C2×Dic6C2×Dic3semidirect
182. C4⋊Dic3C2×Dic3semidirect
187. C4×Dic3#67semidirect
202. C22×C32#104semidirect
354. C22×C3#805semidirect
355. C22×C3#837semidirect
379. C32#1896semidirect
431. C22#63569semidirect
442. C3#71532semidirect
443. C3#71711semidirect

Maximal subgroups

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

subgroupindex
C3×#57912
C22×C3×C4×Dic32
#105929062
C2×#635692
#105891612
#717113
#715323