Finite Group Databasebeta

← #11865642

Subgroups — #11865642

Order 1152.

1109 conjugacy classes of subgroups.

The subgroup lattice has 467 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×Q8×C3⋊D3C211yesmaximal, characteristic
2C2×#63944C212yesmaximal
3#10593909C211yesmaximal, characteristic
4C3×#5031C212yesmaximal, complemented
5#10591633C212yesmaximal, complemented
6#10590601C212yesmaximal
7#10590566C212yesmaximal, complemented
8#10590388C212yesmaximal, complemented
9#10590331C211yesmaximal, characteristic
10D3×#462—32nomaximal
11C2×Q8×C3⋊D3C2211yescharacteristic
12C2×#3797C2212yes—
13C32×C4×Q8C2211yescharacteristic
14Q8×C3⋊Dic3C2211yescharacteristic
15C4⋊C4×C3⋊D3—21no—
16C4⋊C4×C3⋊D3C2211yescharacteristic
17#64096—21no—
18#64096C2211yescharacteristic
19C42×C3⋊D3—21no—
20C42×C3⋊D3C2211yescharacteristic
21C4×#634—21no—
22C4×#634C2211yescharacteristic
23C2×C3×#216C2214yes—
24C3×#869C2212yes—
25#63944—28no—
26#63919—21no—
27#63919—21no—
28#63900—21no—
29#63900—21no—
30#63873C2212yes—
31C2×#3719C2214yes—
32C2×#3710C2212yes—
33C3×#810C2214yes—
34C3×C4⋊(C3⋊C8)C2212yes—
35#63572C2212yes—
36#63566C2214yes—
37C2×D3×Q16—34no—
38D3×C4⋊Q8—32no—
39C4×D3×Q8—32no—
40C4×D3×Q8—61no—
41C3×#462—32no—
42#5182—34no—
43#5090—32no—
44#5031D312yescomplemented
45#4849—32no—
46D3×C4⋊C8—32no—
47D3×#103—34no—
48#4795—34no—
49C2×C32×Q8C2311yescharacteristic
50Q8×C3⋊D3—22no—
51Q8×C3⋊D3D414yes—
52C2×C4×C3⋊D3—21no—
53C2×C4×C3⋊D3—21no—
54C2×C4×C3⋊D3D411yescharacteristic
55C2×C4×C3⋊D3D411yescharacteristic
56C2×C4×C3⋊D3C2311yescharacteristic
57C2×#634—21no—
58C2×#634C2311yescharacteristic
59C2×C3×Dic6C2314yes—
60C2×#627—22no—
61C2×#624—22no—
62#3797—24no—
63#3797—24no—
64C32×C4⋊C4—21no—
65C32×C4⋊C4C2311yescharacteristic
66C32×C42—21no—
67C32×C42C2311yescharacteristic
68C4⋊(C3⋊Dic3)—21no—
69C4⋊(C3⋊Dic3)C2311yescharacteristic
70#3750—21no—
71#3750—21no—
72#3750—21no—
73C4×C3⋊Dic3—21no—
74C4×C3⋊Dic3—21no—
75C4×C3⋊Dic3—21no—
76C4×C3⋊Dic3D411yescharacteristic
77C4×C3⋊Dic3D411yescharacteristic
78C4×C3⋊Dic3C2311yescharacteristic
79C3×#216—28no—
80C3×C4⋊Dic3—22no—
81C3×C4⋊Dic3—22no—
82C2×C3×C3⋊C8C2314yes—
83#3724—22no—
84#3724—22no—
85#3719—28no—
86#3710—24no—
87C2×#462—91noSylow
88C2×D3×Q8—32no—
89C2×D3×Q8—34no—
90C2×D3×Q8—61no—
91C2×C3×Q16—34no—
92C3×C4⋊Q8—32no—
93C3×C4×Q8—21no—
94C3×C4×Q8C2×D312yes—
95Q8×Dic3—32no—
96Q8×Dic3—61no—
97#944—34no—
98C2×#216—34no—
99C2×#216C2×D314yes—
100D3×Q16—616no—
101C2×Dic12—34no—
102C2×D3×C8—34no—
103D3×C4⋊C4—32no—
104D3×C4⋊C4—61no—
105D3×C4⋊C4—62no—
106D3×C4⋊C4—62no—
107D3×C4⋊C4—62no—
108D3×C4⋊C4—62no—
109#888—62no—
110#888—62no—
111#887—32no—
112#887—61no—
113#887—62no—
114#887—62no—
115C42×D3—32no—
116C42×D3—61no—
117C42×D3—62no—
118C42×D3—62no—
119#869C2×D312yes—
120C4×Dic6—32no—
121C4×Dic6—61no—
122C4×Dic6—62no—
123C4×Dic6—62no—
124C3×C4⋊C8—32no—
125C3×#103—34no—
126#835—34no—
127#816—34no—
128Dic3⋊C8—34no—
129#810C2×D314yes—
130C4⋊(C3⋊C8)C2×D312yes—
131C22×C3⋊D3C2×D411yescharacteristic
132C32×Q8—21no—
133C32×Q8C2×D412yes—
134C2×C32×C4—21no—
135C2×C32×C4—21no—
136C2×C32×C4C2×D411yescharacteristic
137C2×C32×C4C2×D411yescharacteristic
138C2×C32×C4C2411yescharacteristic
139C2×C3⋊Dic3—21no—
140C2×C3⋊Dic3—21no—
141C2×C3⋊Dic3C2×D411yescharacteristic
142C2×C3⋊Dic3C2×D411yescharacteristic
143C2×C3⋊Dic3C2×D411yescharacteristic
144C4×C3⋊D3—24no—
145C4×C3⋊D3—22no—
146C4×C3⋊D3—42no—
147C4×C3⋊D3Q1614yescomplemented
148C4×C3⋊D3C2×D412yes—
149C4×C3⋊D3#4112yes—
150#634—21no—
151#634—24no—
152#634C2×D412yes—
153C2×C3×Dic3—24no—
154C3×Dic6—24no—
155C3×Dic6—24no—
156#627—44no—
157#624—44no—
158C3×C3⋊C8—24no—
159C22×Q16—92no—
160C2×C4⋊Q8—91no—
161C2×C4×Q8—91no—
162#462—32no—
163#462—92no—
164#462—92no—
165#462—92no—
166C2×C4⋊C8—91no—
167C2×#103—92no—
168C2×C3×Q8—21no—
169C2×C3×Q8—34no—
170C2×C3×Q8C22×D312yes—
171D3×Q8—38no—
172D3×Q8—64no—
173D3×Q8—68no—
174D3×Q8—68no—
175D3×Q8—64no—
176D3×Q8—64no—
177C2×C4×D3—32no—
178C2×C4×D3—32no—
179C2×C4×D3—32no—
180C2×C4×D3—61no—
181C2×C4×D3—61no—
182C2×C4×D3—61no—
183C2×C4×D3—62no—
184C2×C4×D3—62no—
185C2×C4×D3—64no—
186C2×C4×D3—62no—
187C2×C4×D3—62no—
188C2×Dic6—32no—
189C2×Dic6—61no—
190C2×Dic6—62no—
191C2×Dic6—62no—
192C2×Dic6—64no—
193C2×Dic6C22×D314yes—
194C3×Q16—68no—
195C2×C3×C8—34no—
196C3×C4⋊C4—22no—
197C3×C4⋊C4—22no—
198C3×C4⋊C4—21no—
199C3×C4⋊C4—62no—
200C3×C4⋊C4—62no—
201C3×C4⋊C4C22×D312yes—
202C3×C42—22no—
203C3×C42—22no—
204C3×C42—21no—
205C3×C42C22×D312yes—
206#216—28no—
207#216—68no—
208C4⋊Dic3—22no—
209C4⋊Dic3—22no—
210C4⋊Dic3—32no—
211C4⋊Dic3—61no—
212C4⋊Dic3—62no—
213C4⋊Dic3—62no—
214Dic3⋊C4—64no—
215Dic3⋊C4—64no—
216Dic3⋊C4—62no—
217Dic3⋊C4—62no—
218Dic3⋊C4—62no—
219Dic3⋊C4—62no—
220Dic3⋊C4—62no—
221Dic3⋊C4—62no—
222C4×Dic3—32no—
223C4×Dic3—32no—
224C4×Dic3—32no—
225C4×Dic3—61no—
226C4×Dic3—61no—
227C4×Dic3—61no—
228C4×Dic3—62no—
229C4×Dic3—62no—
230C4×Dic3—62no—
231C4×Dic3—62no—
232C4×Dic3—62no—
233C4×Dic3—62no—
234C2×C3⋊C8C22×D314yes—
235Dic12—68no—
236D3×C8—68no—
237C22×C32C22×D411yescharacteristic
238C2×C3⋊D3#12112yes—
239C2×C3⋊D3C2×Q1612yes—
240C2×C3⋊D3#13712yes—
241C32×C4—22no—
242C32×C4—21no—
243C32×C4—41no—
244C32×C4C2×Q1612yescomplemented
245C32×C4C22×D411yescharacteristic
246C32×C4C2×#4111yescharacteristic
247C3⋊Dic3—22no—
248C3⋊Dic3—21no—
249C3⋊Dic3—41no—
250C3⋊Dic3#12112yes—
251C3⋊Dic3C2×Q1612yescomplemented
252C3×Dic3—44no—
253C22×Q8—92no—
254C22×Q8—91no—
255C2×Q16—34no—
256C2×Q16—94no—
257C2×Q16—188no—
258C22×C8—92no—
259C4⋊Q8—32no—
260C4⋊Q8—92no—
261C4⋊Q8—181no—
262C4⋊Q8—181no—
263C4×Q8—91no—
264C4×Q8—91no—
265C4×Q8—91no—
266C4×Q8—181no—
267C4×Q8—181no—
268C4×Q8D3211yescharacteristic
269C2×C4⋊C4—91no—
270C2×C4⋊C4—181no—
271C2×C4⋊C4—181no—
272C2×C4⋊C4—181no—
273C2×C42—91no—
274C2×C42—181no—
275C4⋊C8—32no—
276C4⋊C8—92no—
277#103—34no—
278#103—94no—
279C22×D3—32no—
280C22×D3—61no—
281C3×Q8—22no—
282C3×Q8—22no—
283C3×Q8—22no—
284C3×Q8—64no—
285C3×Q8—64no—
286C3×Q8D3×D414yes—
287C2×C3×C4—22no—
288C2×C3×C4—22no—
289C2×C3×C4—22no—
290C2×C3×C4—22no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—64no—
295C2×C3×C4D3×D412yes—
296C2×C3×C4D3×D412yes—
297C2×C3×C4C23×D312yes—
298C2×Dic3—24no—
299C2×Dic3—32no—
300C2×Dic3—32no—
301C2×Dic3—32no—
302C2×Dic3—61no—
303C2×Dic3—61no—
304C2×Dic3—61no—
305C2×Dic3—62no—
306C2×Dic3—62no—
307C2×Dic3—62no—
308C2×Dic3—62no—
309C4×D3—38no—
310C4×D3—34no—
311C4×D3—34no—
312C4×D3—64no—
313C4×D3—62no—
314C4×D3—62no—
315C4×D3—64no—
316C4×D3—68no—
317C4×D3—68no—
318C4×D3—122no—
319C4×D3—128no—
320C4×D3—124no—
321C4×D3—124no—
322Dic6—24no—
323Dic6—24no—
324Dic6—34no—
325Dic6—62no—
326Dic6—68no—
327Dic6—68no—
328Dic6—62no—
329Dic6—62no—
330Dic6—128no—
331C3×C8—64no—
332C3⋊C8—24no—
333C2×C32C2×#12111yescharacteristic
334C2×C32C22×Q1611yescharacteristic
335C2×C32C2×#13711yescharacteristic
336C3⋊D3#46214yescomplemented
337C2×Q8—34no—
338C2×Q8—94no—
339C2×Q8—91no—
340C2×Q8—181no—
341C2×Q8—182no—
342C2×Q8—182no—
343C2×Q8—184no—
344C2×Q8—184no—
345C2×Q8C2×D3211yescharacteristic
346C22×C4—91no—
347C22×C4—91no—
348C22×C4—91no—
349C22×C4—181no—
350C22×C4—181no—
351C22×C4—182no—
352Q16—68no—
353Q16—188no—
354C2×C8—34no—
355C2×C8—184no—
356C4⋊C4—21no—
357C4⋊C4—62no—
358C4⋊C4—62no—
359C4⋊C4—91no—
360C4⋊C4—181no—
361C4⋊C4—181no—
362C4⋊C4—181no—
363C4⋊C4—182no—
364C4⋊C4—182no—
365C4⋊C4—181no—
366C4⋊C4C2×D3211yescharacteristic
367C42—21no—
368C42—91no—
369C42—91no—
370C42—91no—
371C42—181no—
372C42—181no—
373C42—181no—
374C42C2×D3211yescharacteristic
375C22×C3—21no—
376C22×C3C2×D3×D412yes—
377C2×D3—34no—
378C2×D3—34no—
379C2×D3—34no—
380C2×D3—62no—
381C2×D3—62no—
382C2×D3—62no—
383C3×C4—24no—
384C3×C4—22no—
385C3×C4—24no—
386C3×C4—21no—
387C3×C4—21no—
388C3×C4—22no—
389C3×C4—41no—
390C3×C4—42no—
391C3×C4—42no—
392C3×C4—124no—
393C3×C4D3×Q1614yescomplemented
394C3×C4C2×D3×D412yes—
395C3×C4D3×#4112yes—
396Dic3—34no—
397Dic3—34no—
398Dic3—44no—
399Dic3—62no—
400Dic3—62no—
401Dic3—64no—
402Dic3—62no—
403Dic3—64no—
404Dic3—121no—
405Dic3—122no—
406Dic3—122no—
407C32C2×#46211yescharacteristic, complemented, Sylow
408C23—91no—
409Q8—21no—
410Q8—64no—
411Q8—64no—
412Q8—92no—
413Q8—184no—
414Q8—181no—
415Q8—364no—
416Q8#380212yes—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—64no—
420C2×C4—91no—
421C2×C4—91no—
422C2×C4—92no—
423C2×C4—92no—
424C2×C4—94no—
425C2×C4—91no—
426C2×C4—182no—
427C2×C4—184no—
428C2×C4—181no—
429C2×C4—181no—
430C2×C4—362no—
431C2×C4—364no—
432C2×C4#381111yescharacteristic
433C2×C4#381111yescharacteristic
434C2×C4C22×D3211yescharacteristic
435C8—64no—
436C2×C3—21no—
437C2×C3—21no—
438C2×C3—21no—
439C2×C3D3×#12112yes—
440C2×C3C2×D3×Q1612yes—
441C2×C3D3×#13712yes—
442D3—38no—
443D3—64no—
444C22—92no—
445C22—92no—
446C22—92no—
447C22C2×#381111yescharacteristic
448C4—22no—
449C4—21no—
450C4—41no—
451C4—92no—
452C4—92no—
453C4—124no—
454C4—182no—
455C4—181no—
456C4—361no—
457C4#6394412yescomplemented
458C4C2×#380211yescharacteristic
459C4#6430611yescharacteristic
460C3—21no—
461C3D3×#46212yescomplemented
462C2—94no—
463C2#1059508111yescharacteristic
464C2C2×#6394411yescharacteristic
465C2#1059546811yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
hypercenterC4×Q8D32
hypocenterC32C2×#462
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
4. C3×#5031C2semidirect
5. #10591633C2semidirect
7. #10590566C2semidirect
8. #10590388C2semidirect
44. #5031D3semidirect
147. C4×C3⋊D3Q16semidirect
244. C32×C4C2×Q16semidirect
251. C3⋊Dic3C2×Q16semidirect
336. C3⋊D3#462semidirect
393. C3×C4D3×Q16semidirect
407. C32C2×#462semidirect
457. C4#63944semidirect
461. C3D3×#462semidirect

Maximal subgroups

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

subgroupindex
C4×Q8×C3⋊D32
C2×#639442
#105939092
C3×#50312
#105916332
#105906012
#105905662
#105903882
#105903312
D3×#4623