Finite Group Databasebeta

← #11808342

Subgroups — #11808342

Order 1152.

1593 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C4×C3⋊D3C211yesmaximal, characteristic
2C2×#63900C211yesmaximal, characteristic
3C2×#63883C212yesmaximal
4C3×#4981C212yesmaximal, complemented
5#10591370C212yesmaximal
6#10591370C211yesmaximal, characteristic
7#10591358C212yesmaximal, complemented
8#10591356C212yesmaximal, complemented
9#10591215C212yesmaximal, complemented
10D3×#398—32nomaximal
11C22×C4×C3⋊D3C2211yescharacteristic
12C22×C4×C3⋊D3C2211yescharacteristic
13C22×C4×C3⋊D3C2211yescharacteristic
14C22×#624C2212yes—
15C22×#624C2212yes—
16C2×C32×C4⋊C4C2211yescharacteristic
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18C2×#3750C2211yescharacteristic
19C2×#3750C2211yescharacteristic
20C4⋊C4×C3⋊D3—24no—
21C2×C3×C4⋊Dic3C2212yes—
22C2×C3×Dic3⋊C4C2214yes—
23C2×#3724C2212yes—
24C2×Dic3⋊Dic3C2214yes—
25#63900—24no—
26#63883—28no—
27C3×C3⋊#95C2214yes—
28C3×C3⋊#95C2212yes—
29#63579C2212yes—
30#63579C2214yes—
31C2×D3×C4⋊C4—32no—
32C2×D3×C4⋊C4—32no—
33C2×D3×C4⋊C4—34no—
34C2×D3×C4⋊C4—61no—
35C3×#398—32no—
36#4983—32no—
37#4982—34no—
38#4981D312yescomplemented
39D3×#95—32no—
40D3×#95—34no—
41#4661—32no—
42#4657—34no—
43C23×C3⋊D3C2311yescharacteristic
44C22×C32×C4C2311yescharacteristic
45C22×C32×C4C2311yescharacteristic
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3C2311yescharacteristic
48C22×C3⋊Dic3C2311yescharacteristic
49C22×C3⋊Dic3C2311yescharacteristic
50C2×C4×C3⋊D3—22no—
51C2×C4×C3⋊D3—22no—
52C2×C4×C3⋊D3—24no—
53C2×C4×C3⋊D3—22no—
54C2×C4×C3⋊D3—24no—
55C2×C4×C3⋊D3D414yes—
56C2×C4×C3⋊D3D414yes—
57C22×C3×Dic3C2314yes—
58C22×C3×Dic3C2314yes—
59C2×#624—24no—
60C2×#624—24no—
61C2×#624—24no—
62C2×#624—24no—
63C2×#624—24no—
64C2×#624Q818yes—
65C32×C4⋊C4—22no—
66C4⋊(C3⋊Dic3)—22no—
67#3750—22no—
68#3750—22no—
69C3×C4⋊Dic3—24no—
70C3×Dic3⋊C4—28no—
71#3724—24no—
72Dic3⋊Dic3—28no—
73C2×#398—91noSylow
74C22×C4×D3—32no—
75C22×C4×D3—32no—
76C22×C4×D3—34no—
77C22×C4×D3—32no—
78C22×C4×D3—34no—
79C22×C4×D3—61no—
80C22×C4×D3—61no—
81C22×C4×D3—61no—
82C2×C3×C4⋊C4—21no—
83C2×C3×C4⋊C4—34no—
84C2×C3×C4⋊C4—32no—
85C2×C3×C4⋊C4C2×D312yes—
86C2×C4⋊Dic3—32no—
87C2×C4⋊Dic3—34no—
88C2×C4⋊Dic3—61no—
89C2×C4⋊Dic3C2×D312yes—
90C2×Dic3⋊C4—32no—
91C2×Dic3⋊C4—32no—
92C2×Dic3⋊C4—34no—
93C2×Dic3⋊C4—34no—
94C2×Dic3⋊C4—61no—
95C2×Dic3⋊C4—61no—
96C2×Dic3⋊C4C2×D314yes—
97D3×C4⋊C4—616no—
98D3×C4⋊C4—68no—
99D3×C4⋊C4—68no—
100D3×C4⋊C4—68no—
101C3×#95—34no—
102C3×#95—32no—
103C3⋊#95—34no—
104C3⋊#95—34no—
105C3⋊#95—34no—
106C3⋊#95C2×D314yes—
107C3⋊#95C2×D312yes—
108C23×C32C2411yescharacteristic
109C22×C3⋊D3C2×D412yes—
110C22×C3⋊D3C2×D412yes—
111C22×C3⋊D3C2×Q814yes—
112C22×C3⋊D3#4112yes—
113C22×C3⋊D3#4114yes—
114C2×C32×C4—21no—
115C2×C32×C4—21no—
116C2×C32×C4—21no—
117C2×C32×C4—22no—
118C2×C32×C4—22no—
119C2×C32×C4C2×D412yes—
120C2×C32×C4C2×D412yes—
121C2×C3⋊Dic3—21no—
122C2×C3⋊Dic3—21no—
123C2×C3⋊Dic3—21no—
124C2×C3⋊Dic3—22no—
125C2×C3⋊Dic3—22no—
126C2×C3⋊Dic3C2×D412yes—
127C2×C3⋊Dic3C2×D412yes—
128C4×C3⋊D3—28no—
129C4×C3⋊D3—28no—
130C4×C3⋊D3—44no—
131C2×C3×Dic3—24no—
132C2×C3×Dic3—24no—
133C2×C3×Dic3—24no—
134C2×C3×Dic3—24no—
135C2×C3×Dic3—24no—
136C2×C3×Dic3C2×Q818yes—
137#624—216no—
138#624—48no—
139C22×C4⋊C4—92no—
140C22×C4⋊C4—91no—
141C22×C4⋊C4—91no—
142#398—32no—
143#398—92no—
144#398—92no—
145#398—92no—
146C2×#95—91no—
147C2×#95—92no—
148C23×D3—32no—
149C23×D3—61no—
150C22×C3×C4—21no—
151C22×C3×C4—21no—
152C22×C3×C4—21no—
153C22×C3×C4—34no—
154C22×C3×C4—34no—
155C22×C3×C4C22×D312yes—
156C22×C3×C4C22×D312yes—
157C22×C3×C4C22×D312yes—
158C22×Dic3—32no—
159C22×Dic3—32no—
160C22×Dic3—32no—
161C22×Dic3—61no—
162C22×Dic3—61no—
163C22×Dic3—61no—
164C22×Dic3C22×D314yes—
165C22×Dic3C22×D314yes—
166C2×C4×D3—38no—
167C2×C4×D3—38no—
168C2×C4×D3—316no—
169C2×C4×D3—64no—
170C2×C4×D3—64no—
171C2×C4×D3—68no—
172C2×C4×D3—68no—
173C2×C4×D3—64no—
174C2×C4×D3—64no—
175C2×C4×D3—68no—
176C2×C4×D3—64no—
177C2×C4×D3—64no—
178C2×C4×D3—68no—
179C2×C4×D3—68no—
180C2×C4×D3—68no—
181C2×C4×D3—64no—
182C2×C4×D3—68no—
183C2×C4×D3—64no—
184C2×C4×D3—124no—
185C2×C4×D3—124no—
186C3×C4⋊C4—24no—
187C3×C4⋊C4—24no—
188C3×C4⋊C4—68no—
189C3×C4⋊C4—64no—
190C4⋊Dic3—24no—
191C4⋊Dic3—68no—
192C4⋊Dic3—64no—
193C4⋊Dic3—64no—
194Dic3⋊C4—28no—
195Dic3⋊C4—68no—
196Dic3⋊C4—68no—
197Dic3⋊C4—64no—
198Dic3⋊C4—64no—
199Dic3⋊C4—64no—
200Dic3⋊C4—64no—
201C22×C32C22×D411yescharacteristic
202C22×C32C22×D411yescharacteristic
203C22×C32C22×Q812yes—
204C22×C32C2×#4111yescharacteristic
205C22×C32C2×#4112yes—
206C2×C3⋊D3#12114yes—
207C2×C3⋊D3C22⋊Q818yes—
208C2×C3⋊D3#12314yes—
209C2×C3⋊D3#12518yes—
210C2×C3⋊D3C4⋊Q814yes—
211C32×C4—22no—
212C32×C4—22no—
213C32×C4—41no—
214C3⋊Dic3—22no—
215C3⋊Dic3—22no—
216C3⋊Dic3—41no—
217C3×Dic3—28no—
218C3×Dic3—44no—
219C23×C4—92no—
220C23×C4—92no—
221C23×C4—91no—
222C23×C4—91no—
223C23×C4—91no—
224C2×C4⋊C4—34no—
225C2×C4⋊C4—32no—
226C2×C4⋊C4—92no—
227C2×C4⋊C4—94no—
228C2×C4⋊C4—91no—
229C2×C4⋊C4—91no—
230C2×C4⋊C4—91no—
231C2×C4⋊C4—184no—
232C2×C4⋊C4—188no—
233C2×C4⋊C4—184no—
234C2×C4⋊C4D3211yescharacteristic
235#95—32no—
236#95—34no—
237#95—92no—
238#95—94no—
239C23×C3—21no—
240C23×C3C23×D312yes—
241C22×D3—34no—
242C22×D3—34no—
243C22×D3—38no—
244C22×D3—34no—
245C22×D3—38no—
246C22×D3—62no—
247C22×D3—62no—
248C22×D3—64no—
249C22×D3—62no—
250C22×D3—64no—
251C2×C3×C4—22no—
252C2×C3×C4—22no—
253C2×C3×C4—22no—
254C2×C3×C4—22no—
255C2×C3×C4—24no—
256C2×C3×C4—22no—
257C2×C3×C4—22no—
258C2×C3×C4—24no—
259C2×C3×C4—22no—
260C2×C3×C4—22no—
261C2×C3×C4—38no—
262C2×C3×C4—42no—
263C2×C3×C4—42no—
264C2×C3×C4—64no—
265C2×C3×C4—64no—
266C2×C3×C4—64no—
267C2×C3×C4—64no—
268C2×C3×C4—64no—
269C2×C3×C4D3×D414yes—
270C2×C3×C4D3×D414yes—
271C2×Dic3—24no—
272C2×Dic3—24no—
273C2×Dic3—24no—
274C2×Dic3—24no—
275C2×Dic3—24no—
276C2×Dic3—34no—
277C2×Dic3—34no—
278C2×Dic3—62no—
279C2×Dic3—62no—
280C2×Dic3—62no—
281C2×Dic3—62no—
282C2×Dic3—62no—
283C2×Dic3—62no—
284C2×Dic3—64no—
285C2×Dic3—62no—
286C2×Dic3—62no—
287C2×Dic3—64no—
288C2×Dic3—122no—
289C2×Dic3—122no—
290C2×Dic3D3×Q818yes—
291C4×D3—632no—
292C4×D3—616no—
293C4×D3—616no—
294C4×D3—616no—
295C4×D3—128no—
296C4×D3—1216no—
297C4×D3—128no—
298C4×D3—128no—
299C2×C32C2×#12111yescharacteristic
300C2×C32C2×C22⋊Q812yes—
301C2×C32C2×#12311yescharacteristic
302C2×C32C2×#12512yes—
303C2×C32C2×C4⋊Q811yescharacteristic
304C3⋊D3#39818yescomplemented
305C24—91no—
306C22×C4—34no—
307C22×C4—34no—
308C22×C4—98no—
309C22×C4—91no—
310C22×C4—91no—
311C22×C4—94no—
312C22×C4—94no—
313C22×C4—91no—
314C22×C4—182no—
315C22×C4—182no—
316C22×C4—184no—
317C22×C4—182no—
318C22×C4—184no—
319C22×C4—184no—
320C22×C4—184no—
321C22×C4—184no—
322C22×C4—184no—
323C22×C4—184no—
324C22×C4C2×D3211yescharacteristic
325C22×C4C2×D3211yescharacteristic
326C22×C4C2×D3211yescharacteristic
327C4⋊C4—22no—
328C4⋊C4—68no—
329C4⋊C4—64no—
330C4⋊C4—182no—
331C4⋊C4—182no—
332C4⋊C4—184no—
333C4⋊C4—188no—
334C4⋊C4—182no—
335C22×C3—21no—
336C22×C3—21no—
337C22×C3—22no—
338C22×C3—22no—
339C22×C3—21no—
340C22×C3C2×D3×D412yes—
341C22×C3C2×D3×D412yes—
342C22×C3C2×D3×Q814yes—
343C22×C3D3×#4112yes—
344C22×C3D3×#4114yes—
345C2×D3—38no—
346C2×D3—316no—
347C2×D3—38no—
348C2×D3—38no—
349C2×D3—316no—
350C2×D3—64no—
351C2×D3—64no—
352C2×D3—68no—
353C2×D3—68no—
354C2×D3—64no—
355C3×C4—24no—
356C3×C4—24no—
357C3×C4—24no—
358C3×C4—42no—
359C3×C4—42no—
360C3×C4—42no—
361C3×C4—68no—
362C3×C4—124no—
363Dic3—28no—
364Dic3—44no—
365Dic3—64no—
366Dic3—64no—
367Dic3—64no—
368Dic3—122no—
369Dic3—122no—
370Dic3—122no—
371C32C2×#39811yescharacteristic, complemented, Sylow
372C23—92no—
373C23—92no—
374C23—94no—
375C23—94no—
376C23—92no—
377C23C22×D3211yescharacteristic
378C2×C4—21no—
379C2×C4—22no—
380C2×C4—21no—
381C2×C4—22no—
382C2×C4—21no—
383C2×C4—38no—
384C2×C4—64no—
385C2×C4—64no—
386C2×C4—64no—
387C2×C4—64no—
388C2×C4—64no—
389C2×C4—92no—
390C2×C4—92no—
391C2×C4—188no—
392C2×C4—188no—
393C2×C4—1816no—
394C2×C4—181no—
395C2×C4—182no—
396C2×C4—181no—
397C2×C4—182no—
398C2×C4—181no—
399C2×C4—364no—
400C2×C4—368no—
401C2×C4#380212yes—
402C2×C4#381112yes—
403C2×C3—21no—
404C2×C3—21no—
405C2×C3—22no—
406C2×C3—22no—
407C2×C3—21no—
408C2×C3D3×#12112yes—
409C2×C3D3×C22⋊Q814yes—
410C2×C3D3×#12312yes—
411C2×C3D3×#12514yes—
412C2×C3D3×C4⋊Q812yes—
413D3—316no—
414D3—68no—
415C22—94no—
416C22—94no—
417C22—98no—
418C22—98no—
419C22—94no—
420C22C2×#380211yescharacteristic
421C22#6430611yescharacteristic
422C22#6431212yes—
423C22D32×Q812yes—
424C22C2×#381111yescharacteristic
425C4—22no—
426C4—22no—
427C4—41no—
428C4—68no—
429C4—124no—
430C4—182no—
431C4—182no—
432C4—361no—
433C3—21no—
434C3D3×#39812yescomplemented
435C2—98no—
436C2#1059439912yes—
437C2#1059463112yes—
438C2#1059508111yescharacteristic
439C2#1059516911yescharacteristic
440C2#1059536511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
prime radicalC23×C3⋊D3C23
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#398
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. C3×#4981C2semidirect
7. #10591358C2semidirect
8. #10591356C2semidirect
9. #10591215C2semidirect
38. #4981D3semidirect
304. C3⋊D3#398semidirect
371. C32C2×#398semidirect
434. C3D3×#398semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×C3⋊D32
C2×#639002
C2×#638832
C3×#49812
#105913702
#105913582
#105913562
#105912152
D3×#3983