Finite Group Databasebeta

← #11865732

Subgroups — #11865732

Order 1152.

1488 conjugacy classes of subgroups.

The subgroup lattice has 453 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64125C212yesmaximal, complemented
2#10596187C211yesmaximal, characteristic, complemented
3C4×#3832C211yesmaximal, characteristic, complemented
4C32×#460C211yesmaximal, characteristic, complemented
5#10592865C212yesmaximal, complemented
6#10592771C211yesmaximal, characteristic, complemented
7#10592730C211yesmaximal, characteristic, complemented
8#10592540C211yesmaximal, characteristic, complemented
9C3⋊D3×C4⋊C8C211yesmaximal, characteristic, complemented
10#10592486C212yesmaximal, complemented
11#10592471C212yesmaximal, complemented
12#80382—34nomaximal
13C2×#3832C2211yescharacteristic
14C2×#3830C2212yes—
15C2×C32×SD16C2212yes—
16C32×#127C2211yescharacteristic
17C32×C4×Q8C2211yescharacteristic
18Q8×C3⋊Dic3C2211yescharacteristic
19C2×#3756C2212yes—
20#64147—21no—
21#64147—21no—
22#64145C2212yes—
23D4×C3⋊Dic3—21no—
24D4×C3⋊Dic3—21no—
25C2×#3753C2212yes—
26#64125—28no—
27C2×#3744C2212yes—
28C2×C8×C3⋊D3C2212yes—
29#64102—21no—
30#64102C2211yescharacteristic
31#64101—21no—
32#64101C2211yescharacteristic
33C4×C4⋊(C3⋊D3)—21no—
34C4×C4⋊(C3⋊D3)C2211yescharacteristic
35C42×C3⋊D3—21no—
36C42×C3⋊D3C2211yescharacteristic
37#64078C2211yescharacteristic
38C32×C4⋊C8C2211yescharacteristic
39C32×#102C2212yes—
40#63659C2212yes—
41#63643C2212yes—
42#63641C2212yes—
43#63637C2212yes—
44C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
45C2×#916—38no—
46#5716—34no—
47C4×#239—34no—
48C3×#460D314yescomplemented
49#5166—38no—
50#5072—34no—
51#5031—34no—
52#4841—34no—
53D3×C4⋊C8—34no—
54#4787—38no—
55#4772—38no—
56C2×C32×Q8C2311yescharacteristic
57C2×C32×D4—21no—
58C2×C32×D4—21no—
59C2×C32×D4C2312yes—
60C2×#638—22no—
61C22×C3⋊Dic3—22no—
62#3832—22no—
63#3832D414yescomplemented
64#3830—24no—
65#3830—24no—
66C2×C4⋊(C3⋊D3)—21no—
67C2×C4⋊(C3⋊D3)C2311yescharacteristic
68C2×C4×C3⋊D3—21no—
69C2×C4×C3⋊D3—21no—
70C2×C4×C3⋊D3—21no—
71C2×C4×C3⋊D3D411yescharacteristic
72C2×C4×C3⋊D3D411yescharacteristic
73C2×C4×C3⋊D3C2311yescharacteristic
74C2×#634C2312yes—
75C32×SD16—24no—
76C2×C32×C8C2312yes—
77C32×C4⋊C4—21no—
78C32×C4⋊C4C2311yescharacteristic
79C32×C42—21no—
80C32×C42C2311yescharacteristic
81#3757—22no—
82#3757—22no—
83#3756—24no—
84#3753—24no—
85#3752—21no—
86#3752—21no—
87#3752—21no—
88C4⋊(C3⋊Dic3)—21no—
89C4⋊(C3⋊Dic3)—21no—
90C4⋊(C3⋊Dic3)—21no—
91C4⋊(C3⋊Dic3)C2311yescharacteristic
92C4×C3⋊Dic3—21no—
93C4×C3⋊Dic3—21no—
94C4×C3⋊Dic3D411yescharacteristic
95C4×C3⋊Dic3D411yescharacteristic
96C4×C3⋊Dic3C2311yescharacteristic
97C2×C3⋊(C3⋊C8)C2312yes—
98#3744—24no—
99C8×C3⋊D3—24no—
100#3035—91noSylow
101C2×#239—34no—
102C2×#237—38no—
103C2×C3×SD16C2×D318yes—
104C3×#127C2×D314yes—
105C3×C4×Q8C2×D314yes—
106Q8×Dic3—34no—
107C2×#216—38no—
108#938—64no—
109#938—64no—
110#936—38no—
111D4×Dic3—64no—
112D4×Dic3—64no—
113C2×#213—38no—
114#916—632no—
115C2×#204—38no—
116C2×D3×C8—38no—
117#893—34no—
118#893—64no—
119#892—34no—
120#892—64no—
121C4×D12—34no—
122C4×D12—64no—
123C42×D3—34no—
124C42×D3—64no—
125#869—34no—
126C3×C4⋊C8C2×D314yes—
127C3×#102C2×D318yes—
128#832—38no—
129#816—38no—
130Dic3⋊C8—38no—
131#810—38no—
132C4⋊(C3⋊C8)—34no—
133C23×C32—22no—
134C22×C3⋊D3—21no—
135C22×C3⋊D3C2×D411yescharacteristic
136C32×Q8—21no—
137C32×Q8C2×D412yes—
138C32×D4—22no—
139C32×D4—22no—
140C32×D4—42no—
141C32×D4—42no—
142C2×C32×C4—21no—
143C2×C32×C4—21no—
144C2×C32×C4C2×D411yescharacteristic
145C2×C32×C4C2×D411yescharacteristic
146C2×C32×C4C2411yescharacteristic
147#638—44no—
148C2×C3⋊Dic3—21no—
149C2×C3⋊Dic3—22no—
150C2×C3⋊Dic3—44no—
151C2×C3⋊Dic3C2×D411yescharacteristic
152C2×C3⋊Dic3C2×D411yescharacteristic
153C2×C3⋊Dic3C2×D411yescharacteristic
154C4⋊(C3⋊D3)—24no—
155C4⋊(C3⋊D3)—21no—
156C4⋊(C3⋊D3)C2×D412yes—
157C4×C3⋊D3—22no—
158C4×C3⋊D3—24no—
159C4×C3⋊D3—41no—
160C4×C3⋊D3—42no—
161C4×C3⋊D3—42no—
162C4×C3⋊D3C2×D412yes—
163C4×C3⋊D3#4112yes—
164#634—22no—
165#634—22no—
166C32×C8—22no—
167C3⋊(C3⋊C8)—22no—
168C2×#135—92no—
169#532—91no—
170C4×#41—91no—
171#464—92no—
172#463—92no—
173#462—91no—
174#461—91no—
175#460C3⋊D311yescharacteristic, complemented
176#459—91no—
177C2×C4⋊C8—91no—
178#416—92no—
179C2×C3×Q8C22×D314yes—
180C2×C3×D4—24no—
181C2×C3×D4—24no—
182C2×C3×D4C22×D318yes—
183C2×#67—68no—
184C22×Dic3—68no—
185#239—316no—
186#239—68no—
187#237—616no—
188#237—616no—
189C2×D12—34no—
190C2×D12—64no—
191C2×C4×D3—34no—
192C2×C4×D3—34no—
193C2×C4×D3—34no—
194C2×C4×D3—64no—
195C2×C4×D3—64no—
196C2×C4×D3—64no—
197C2×Dic6—38no—
198C3×SD16—216no—
199C2×C3×C8C22×D318yes—
200C3×C4⋊C4—24no—
201C3×C4⋊C4C22×D314yes—
202C3×C42—24no—
203C3×C42C22×D314yes—
204#217—68no—
205#217—68no—
206#216—616no—
207#213—616no—
208(C2×D3)⋊C4—64no—
209(C2×D3)⋊C4—64no—
210(C2×D3)⋊C4—64no—
211C4⋊Dic3—34no—
212C4⋊Dic3—64no—
213C4⋊Dic3—64no—
214C4⋊Dic3—64no—
215C4×Dic3—34no—
216C4×Dic3—34no—
217C4×Dic3—34no—
218C4×Dic3—64no—
219C4×Dic3—64no—
220C2×C3⋊C8—38no—
221#204—616no—
222D3×C8—616no—
223C22×C32—42no—
224C22×C32—42no—
225C22×C32—42no—
226C22×C32C22×D411yescharacteristic
227C2×C3⋊D3—21no—
228C2×C3⋊D3—21no—
229C2×C3⋊D3—22no—
230C2×C3⋊D3—41no—
231C2×C3⋊D3—41no—
232C2×C3⋊D3#12112yes—
233C32×C4—22no—
234C32×C4—21no—
235C32×C4—41no—
236C32×C4#13512yescomplemented
237C32×C4C22×D411yescharacteristic
238C32×C4C2×#4111yescharacteristic
239C3⋊Dic3—21no—
240C3⋊Dic3—21no—
241C3⋊Dic3—42no—
242C3⋊Dic3—41no—
243C3⋊Dic3#12112yes—
244C2×#41—91no—
245C2×#41—92no—
246#135—188no—
247C2×Q16—92no—
248C2×SD16—92no—
249C2×SD16C2×C3⋊D312yes—
250C2×D8—92no—
251C22×C8—92no—
252C4⋊Q8—91no—
253#127C2×C3⋊D311yescharacteristic
254#124—92no—
255#121—181no—
256#121—181no—
257C4×Q8—91no—
258C4×Q8C2×C3⋊D311yescharacteristic
259C4×D4—91no—
260C4×D4—91no—
261C4×D4—181no—
262C4×D4—181no—
263C4×D4—181no—
264C4×D4—181no—
265#117—91no—
266#117—181no—
267C2×C42—91no—
268C2×C42—181no—
269C4⋊C8—92no—
270C4⋊C8—91no—
271C4⋊C8C2×C3⋊D311yescharacteristic
272#103—92no—
273#103—92no—
274#102—92no—
275#102C2×C3⋊D312yes—
276C23×C3—28no—
277C22×D3—34no—
278C22×D3—64no—
279C3×Q8—24no—
280C3×Q8D3×D418yes—
281C3×D4—28no—
282C3×D4—28no—
283C3×D4—48no—
284C3×D4—48no—
285C2×C3×C4—24no—
286C2×C3×C4—24no—
287C2×C3×C4D3×D414yes—
288C2×C3×C4D3×D414yes—
289C2×C3×C4C23×D314yes—
290#67—1216no—
291C2×Dic3—34no—
292C2×Dic3—34no—
293C2×Dic3—34no—
294C2×Dic3—64no—
295C2×Dic3—68no—
296C2×Dic3—1216no—
297D12—38no—
298D12—616no—
299D12—64no—
300C4×D3—38no—
301C4×D3—38no—
302C4×D3—616no—
303C4×D3—68no—
304C4×D3—124no—
305C4×D3—128no—
306C4×D3—128no—
307Dic6—68no—
308Dic6—68no—
309C3×C8—28no—
310C3⋊C8—68no—
311C2×C32—82no—
312C2×C32C2×#12111yescharacteristic
313C2×C32C2×#13511yescharacteristic
314C2×C32#57511yescharacteristic
315C3⋊D3—22no—
316C3⋊D3—42no—
317#41—94no—
318#41—182no—
319#41—184no—
320#41—184no—
321C2×Q8—92no—
322C2×Q8C22×C3⋊D311yescharacteristic
323C2×D4—21no—
324C2×D4—21no—
325C2×D4—91no—
326C2×D4—181no—
327C2×D4—182no—
328C2×D4C22×C3⋊D312yes—
329C22×C4—91no—
330C22×C4—91no—
331C22×C4—91no—
332C22×C4—181no—
333C22×C4—181no—
334C22×C4—182no—
335C22×C4—181no—
336Q16—184no—
337SD16—24no—
338SD16—184no—
339D8—184no—
340C2×C8—92no—
341C2×C8—184no—
342C2×C8C22×C3⋊D312yes—
343C4⋊C4—21no—
344C4⋊C4—91no—
345C4⋊C4—181no—
346C4⋊C4—181no—
347C4⋊C4—181no—
348C4⋊C4C22×C3⋊D311yescharacteristic
349C22⋊C4—181no—
350C22⋊C4—181no—
351C22⋊C4—182no—
352C22⋊C4—182no—
353C22⋊C4—181no—
354C42—21no—
355C42—91no—
356C42—91no—
357C42—91no—
358C42—181no—
359C42—181no—
360C42C22×C3⋊D311yescharacteristic
361C22×C3—48no—
362C22×C3—48no—
363C22×C3—48no—
364C22×C3C2×D3×D414yes—
365C2×D3—38no—
366C2×D3—64no—
367C2×D3—64no—
368C2×D3—68no—
369C2×D3—124no—
370C2×D3—124no—
371C3×C4—24no—
372C3×C4—28no—
373C3×C4—44no—
374C3×C4#91618yescomplemented
375C3×C4C2×D3×D414yes—
376C3×C4D3×#4114yes—
377Dic3—38no—
378Dic3—64no—
379Dic3—64no—
380Dic3—124no—
381Dic3—128no—
382C32#303511yescharacteristic, complemented, Sylow
383C23—22no—
384C23—91no—
385C23—181no—
386Q8—21no—
387Q8—182no—
388Q8—182no—
389Q8D4×C3⋊D312yes—
390D4—22no—
391D4—22no—
392D4—42no—
393D4—42no—
394D4—92no—
395D4—184no—
396D4—181no—
397D4—364no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—91no—
401C2×C4—92no—
402C2×C4—92no—
403C2×C4—91no—
404C2×C4—91no—
405C2×C4—184no—
406C2×C4—182no—
407C2×C4—181no—
408C2×C4—182no—
409C2×C4—361no—
410C2×C4—362no—
411C2×C4—364no—
412C2×C4—362no—
413C2×C4D4×C3⋊D311yescharacteristic
414C2×C4D4×C3⋊D311yescharacteristic
415C2×C4C23×C3⋊D311yescharacteristic
416C8—22no—
417C8—182no—
418C2×C3—88no—
419C2×C3D3×#12114yes—
420C2×C3C2×#91614yes—
421C2×C3#577314yes—
422D3—68no—
423D3—128no—
424C22—42no—
425C22—42no—
426C22—42no—
427C22—92no—
428C22—181no—
429C22—181no—
430C22—182no—
431C22—361no—
432C22—361no—
433C22C2×D4×C3⋊D311yescharacteristic
434C4—21no—
435C4—22no—
436C4—41no—
437C4—92no—
438C4—181no—
439C4—181no—
440C4—361no—
441C4—362no—
442C4#6412512yescomplemented
443C4C2×D4×C3⋊D311yescharacteristic
444C4#41×C3⋊D311yescharacteristic
445C3#8038214yescomplemented
446C2—82no—
447C2—182no—
448C2—362no—
449C2C3⋊D3×#12111yescharacteristic
450C2C2×#6412511yescharacteristic
451C2#1059624411yescharacteristic
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#460C2
socleC22×C32C22×D4
hypercenter#460C3⋊D3
hypocenterC32#3035
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. C2×#64125C2semidirect
2. #10596187C2semidirect
3. C4×#3832C2semidirect
4. C32×#460C2semidirect
5. #10592865C2semidirect
6. #10592771C2semidirect
7. #10592730C2semidirect
8. #10592540C2semidirect
9. C3⋊D3×C4⋊C8C2semidirect
10. #10592486C2semidirect
11. #10592471C2semidirect
48. C3×#460D3semidirect
63. #3832D4semidirect
175. #460C3⋊D3semidirect
236. C32×C4#135semidirect
374. C3×C4#916semidirect
382. C32#3035semidirect
442. C4#64125semidirect
445. C3#80382semidirect

Maximal subgroups

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

subgroupindex
C2×#641252
#105961872
C4×#38322
C32×#4602
#105928652
#105927712
#105927302
#105925402
C3⋊D3×C4⋊C82
#105924862
#105924712
#803823