Finite Group Databasebeta

← #11868827

Subgroups — #11868827

Order 1152.

987 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595993C211yesmaximal, characteristic
2C2×#63919C211yesmaximal, characteristic, complemented
3C3×#4995C212yesmaximal, complemented
4#10591120C211yesmaximal, characteristic, complemented
5#10591106C212yesmaximal
6#10590433C212yesmaximal, complemented
7#10590432C212yesmaximal, complemented
8#10590431C212yesmaximal, complemented
9#10590430C212yesmaximal, complemented
10#79240—32nomaximal
11C2×#3828C2211yescharacteristic
12C22×#627—21no—
13C32×#117C2211yescharacteristic
14C2×C4×C3⋊Dic3C2211yescharacteristic
15#64102C2211yescharacteristic
16#64102C2211yescharacteristic
17#64096C2211yescharacteristic
18#64096C2211yescharacteristic
19#64090—21no—
20#64090—21no—
21#64081—21no—
22C42×C3⋊D3—21no—
23C2×C3×C4⋊Dic3C2212yes—
24C2×C3×#208C2212yes—
25C2×#3724—21no—
26#63919—21no—
27#63919—21no—
28#63919C2212yes—
29#63919C2212yes—
30C3×#808C2214yes—
31C3×#807C2214yes—
32#63572C2212yes—
33#63572C2212yes—
34#63567C2214yes—
35#63564C2214yes—
36#5522—32no—
37#5522—61no—
38C2×#888—32no—
39C3×#428—32no—
40#5133—32no—
41#5118—32no—
42#4995D312yescomplemented
43#4966—32no—
44#4890—34no—
45#4875—34no—
46#4870—34no—
47#4854—34no—
48C22×C32×C4C2311yescharacteristic
49C2×#638—21no—
50C22×C3⋊Dic3D411yescharacteristic
51C22×C3⋊Dic3D411yescharacteristic
52#3828—22no—
53#3828Q814yescomplemented
54C2×C4⋊(C3⋊D3)C2311yescharacteristic
55C2×C4×C3⋊D3—21no—
56C2×C4×C3⋊D3—21no—
57C2×C4×C3⋊D3—21no—
58C2×#634C2311yescharacteristic
59C22×C3×Dic3—22no—
60C2×#627—22no—
61C2×#627—22no—
62C2×#627—44no—
63C32×C4⋊C4C2311yescharacteristic
64C32×C4⋊C4C2311yescharacteristic
65C32×C22⋊C4—21no—
66C32×C42—21no—
67#3752—21no—
68#3752—21no—
69#3750—21no—
70#3750—21no—
71C4×C3⋊Dic3—21no—
72C4×C3⋊Dic3—21no—
73C4×C3⋊Dic3D411yescharacteristic
74C4×C3⋊Dic3D411yescharacteristic
75C4×C3⋊Dic3C2311yescharacteristic
76C4×C3⋊Dic3C2311yescharacteristic
77C3×C4⋊Dic3—22no—
78C3×C4⋊Dic3C2314yes—
79C3×#208—24no—
80C2×C3×C3⋊C8C2314yes—
81#3724—22no—
82#3724—22no—
83#3079—91noSylow
84C2×#235—32no—
85C2×#235—61no—
86C22×Dic6—62no—
87C2×C3×M16—32no—
88C3×#117—21no—
89C3×#117C2×D312yes—
90C2×C3×C4⋊C4—32no—
91C2×C4⋊Dic3C2×D312yes—
92C2×Dic3⋊C4—62no—
93C2×C4×Dic3—32no—
94C2×C4×Dic3—61no—
95C2×#208C2×D312yes—
96#893—32no—
97#893—32no—
98#893—61no—
99#893—61no—
100#888—34no—
101#888—34no—
102#888—62no—
103#888—62no—
104#887—32no—
105#887—32no—
106#887—61no—
107#887—61no—
108#67⋊C4—62no—
109#67⋊C4—62no—
110#67⋊C4—62no—
111#67⋊C4—62no—
112#872—62no—
113#872—62no—
114C42×D3—62no—
115C42×D3—62no—
116C3×#107—34no—
117C3×#106—34no—
118#821—34no—
119#816—34no—
120Dic3⋊C8—34no—
121Dic3⋊C8—34no—
122#810—34no—
123#809—34no—
124#808C2×D314yes—
125#807C2×D314yes—
126C23×C32C2×D411yescharacteristic
127C22×C3⋊D3—21no—
128C2×C32×C4—21no—
129C2×C32×C4—21no—
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4C2×Q812yes—
132C2×C32×C4#4112yes—
133C2×C32×C4C2411yescharacteristic
134#638—24no—
135C2×C3⋊Dic3—21no—
136C2×C3⋊Dic3—22no—
137C2×C3⋊Dic3—22no—
138C2×C3⋊Dic3C2×D411yescharacteristic
139C2×C3⋊Dic3C2×D411yescharacteristic
140C2×C3⋊Dic3C2×D411yescharacteristic
141C2×C3⋊Dic3C2×D411yescharacteristic
142C4⋊(C3⋊D3)—21no—
143C4⋊(C3⋊D3)C2×Q812yescomplemented
144C4×C3⋊D3—24no—
145C4×C3⋊D3—42no—
146C4×C3⋊D3—42no—
147#634—21no—
148#634C2×Q812yescomplemented
149C2×C3×Dic3—24no—
150C2×C3×Dic3—44no—
151#627—44no—
152#627—44no—
153C3×C3⋊C8—24no—
154C2×C4⋊Q8—91no—
155C4×#41—91no—
156#477—92no—
157#476—92no—
158#475—92no—
159#474—92no—
160#428—32no—
161#423—91no—
162#417—92no—
163C22×C3×C4—21no—
164C22×C3×C4—62no—
165C22×C3×C4C22×D312yes—
166C2×#67—62no—
167C2×#67—62no—
168C22×Dic3—22no—
169C22×Dic3—32no—
170C22×Dic3—32no—
171C22×Dic3—61no—
172C22×Dic3—61no—
173#235—38no—
174#235—64no—
175#235—64no—
176#235—64no—
177C2×D12—32no—
178C2×D12—61no—
179C2×C4×D3—62no—
180C2×C4×D3—62no—
181C2×C4×D3—62no—
182C2×C4×D3—62no—
183C2×C4×D3—62no—
184C2×C4×D3—62no—
185C2×Dic6—32no—
186C2×Dic6—61no—
187C2×Dic6—64no—
188C2×Dic6—64no—
189C2×Dic6—128no—
190C3×M16—64no—
191C2×C3×C8—34no—
192C3×C4⋊C4—21no—
193C3×C4⋊C4—21no—
194C3×C4⋊C4—34no—
195C3×C4⋊C4—62no—
196C3×C4⋊C4C22×D312yes—
197C3×C4⋊C4C22×D312yes—
198C3×C22⋊C4—22no—
199C3×C22⋊C4—22no—
200C3×C42—22no—
201C3×C42—22no—
202(C2×D3)⋊C4—62no—
203(C2×D3)⋊C4—62no—
204(C2×D3)⋊C4—62no—
205(C2×D3)⋊C4—62no—
206C4⋊Dic3—22no—
207C4⋊Dic3C22×D314yes—
208Dic3⋊C4—64no—
209Dic3⋊C4—64no—
210Dic3⋊C4—62no—
211Dic3⋊C4—62no—
212Dic3⋊C4—62no—
213Dic3⋊C4—62no—
214C4×Dic3—32no—
215C4×Dic3—32no—
216C4×Dic3—32no—
217C4×Dic3—32no—
218C4×Dic3—61no—
219C4×Dic3—61no—
220C4×Dic3—61no—
221C4×Dic3—61no—
222C4×Dic3—62no—
223C4×Dic3—62no—
224C4×Dic3—62no—
225C4×Dic3—62no—
226#208—24no—
227C2×C3⋊C8C22×D314yes—
228C22×C32—21no—
229C22×C32—21no—
230C22×C32C22⋊Q812yes—
231C22×C32C22×D411yescharacteristic
232C2×C3⋊D3—22no—
233C2×C3⋊D3—41no—
234C2×C3⋊D3—41no—
235C32×C4—41no—
236C32×C4—41no—
237C32×C4C22⋊Q812yes—
238C32×C4C22×Q811yescharacteristic
239C32×C4C2×#4111yescharacteristic
240C3⋊Dic3—22no—
241C3⋊Dic3—21no—
242C3⋊Dic3—21no—
243C3⋊Dic3AGL(1,ℤ/8)12yes—
244C3⋊Dic3#13712yes—
245C3×Dic3—44no—
246C2×#41—91no—
247C22×Q8—181no—
248C2×M16—32no—
249C4⋊Q8—92no—
250C4⋊Q8—92no—
251C4⋊Q8—181no—
252C4⋊Q8—181no—
253C4×Q8—91no—
254C4×Q8—91no—
255C4×D4—91no—
256C4×D4—91no—
257C4×D4—181no—
258C4×D4—181no—
259#117—181no—
260#117D3211yescharacteristic
261C2×C4⋊C4—32no—
262C2×C4⋊C4—181no—
263C2×C42—91no—
264C2×C42—181no—
265#107—34no—
266#106—34no—
267C4⋊C8—92no—
268C4⋊C8—92no—
269#103—94no—
270#102—94no—
271C23×C3—21no—
272C23×C3D3×D412yes—
273C22×D3—62no—
274C22×D3—62no—
275C2×C3×C4—22no—
276C2×C3×C4—22no—
277C2×C3×C4—22no—
278C2×C3×C4—22no—
279C2×C3×C4—21no—
280C2×C3×C4—22no—
281C2×C3×C4—22no—
282C2×C3×C4—21no—
283C2×C3×C4—64no—
284C2×C3×C4—124no—
285C2×C3×C4#23514yes—
286C2×C3×C4D3×D412yes—
287C2×C3×C4D3×Q814yes—
288C2×C3×C4C23×D312yes—
289#67—68no—
290#67—68no—
291C2×Dic3—24no—
292C2×Dic3—32no—
293C2×Dic3—32no—
294C2×Dic3—32no—
295C2×Dic3—32no—
296C2×Dic3—44no—
297C2×Dic3—61no—
298C2×Dic3—61no—
299C2×Dic3—61no—
300C2×Dic3—61no—
301C2×Dic3—64no—
302C2×Dic3—64no—
303C2×Dic3—62no—
304C2×Dic3—62no—
305C2×Dic3—122no—
306C2×Dic3—122no—
307D12—34no—
308D12—62no—
309D12—62no—
310D12—62no—
311C4×D3—68no—
312C4×D3—68no—
313C4×D3—124no—
314C4×D3—124no—
315C4×D3—124no—
316C4×D3—124no—
317Dic6—34no—
318Dic6—62no—
319Dic6—62no—
320Dic6—62no—
321Dic6—128no—
322Dic6—128no—
323C3×C8—64no—
324C3⋊C8—24no—
325C2×C32—22no—
326C2×C32C2×C22⋊Q811yescharacteristic
327C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
328C2×C32C2×#13711yescharacteristic
329C3⋊D3—42no—
330#41—94no—
331#41—182no—
332C2×Q8—91no—
333C2×Q8—182no—
334C2×Q8—182no—
335C2×Q8—364no—
336C2×D4—91no—
337C2×D4—181no—
338C22×C4—62no—
339C22×C4—91no—
340C22×C4—91no—
341C22×C4—181no—
342C22×C4—181no—
343C22×C4—181no—
344C22×C4C2×D3211yescharacteristic
345M16—64no—
346C2×C8—34no—
347C4⋊C4—34no—
348C4⋊C4—62no—
349C4⋊C4—181no—
350C4⋊C4—181no—
351C4⋊C4—182no—
352C4⋊C4—182no—
353C4⋊C4C2×D3211yescharacteristic
354C4⋊C4C2×D3211yescharacteristic
355C22⋊C4—21no—
356C22⋊C4—181no—
357C22⋊C4—181no—
358C42—21no—
359C42—91no—
360C42—91no—
361C42—91no—
362C42—91no—
363C42—181no—
364C42—181no—
365C22×C3—22no—
366C22×C3—22no—
367C22×C3—21no—
368C22×C3—22no—
369C22×C3—41no—
370C22×C3—41no—
371C22×C3#89614yes—
372C22×C3C2×D3×D412yes—
373C2×D3—64no—
374C2×D3—64no—
375C2×D3—122no—
376C2×D3—122no—
377C2×D3—122no—
378C2×D3—122no—
379C3×C4—21no—
380C3×C4—21no—
381C3×C4—22no—
382C3×C4—42no—
383C3×C4—42no—
384C3×C4—42no—
385C3×C4—42no—
386C3×C4—124no—
387C3×C4#89614yes—
388C3×C4C2×#23512yes—
389C3×C4C2×D3×Q812yes—
390Dic3—34no—
391Dic3—34no—
392Dic3—44no—
393Dic3—62no—
394Dic3—62no—
395Dic3—64no—
396Dic3—64no—
397Dic3—62no—
398Dic3—62no—
399Dic3—121no—
400Dic3—121no—
401C32#307911yescharacteristic, complemented, Sylow
402C23—181no—
403C23#381111yescharacteristic
404Q8—92no—
405Q8—181no—
406Q8—364no—
407Q8—364no—
408D4—92no—
409D4—184no—
410D4—181no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—64no—
414C2×C4—91no—
415C2×C4—91no—
416C2×C4—91no—
417C2×C4—91no—
418C2×C4—124no—
419C2×C4—182no—
420C2×C4—182no—
421C2×C4—181no—
422C2×C4—184no—
423C2×C4—362no—
424C2×C4—362no—
425C2×C4#379712yes—
426C2×C4#379812yes—
427C2×C4#381111yescharacteristic
428C2×C4C22×D3211yescharacteristic
429C8—64no—
430C2×C3—24no—
431C2×C3—21no—
432C2×C3—21no—
433C2×C3—21no—
434C2×C3—42no—
435C2×C3C2×#89612yes—
436C2×C3D3×AGL(1,ℤ/8)12yes—
437C2×C3D3×#13712yes—
438D3—124no—
439D3—124no—
440C22—21no—
441C22—21no—
442C22—182no—
443C22—361no—
444C22—361no—
445C22#6386512yes—
446C22C2×#381111yescharacteristic
447C4—41no—
448C4—41no—
449C4—92no—
450C4—92no—
451C4—124no—
452C4—182no—
453C4—181no—
454C4—181no—
455C4#6386512yes—
456C4C2×#379711yescharacteristic
457C4C2×#379811yescharacteristic
458C3—21no—
459C3#7924012yescomplemented
460C2—22no—
461C2—362no—
462C2C2×#6386511yescharacteristic
463C2#1059545811yescharacteristic
464C2#1059546811yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radicalC2×#3828C22
hypercenter#117D32
hypocenterC32#3079
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. C2×#63919C2semidirect
3. C3×#4995C2semidirect
4. #10591120C2semidirect
6. #10590433C2semidirect
7. #10590432C2semidirect
8. #10590431C2semidirect
9. #10590430C2semidirect
42. #4995D3semidirect
53. #3828Q8semidirect
143. C4⋊(C3⋊D3)C2×Q8semidirect
148. #634C2×Q8semidirect
401. C32#3079semidirect
459. C3#79240semidirect

Maximal subgroups

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

subgroupindex
#105959932
C2×#639192
C3×#49952
#105911202
#105911062
#105904332
#105904322
#105904312
#105904302
#792403