Finite Group Databasebeta

← #11874298

Subgroups — #11874298

Order 1152.

1215 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63806C214yesmaximal, complemented
2#10593970C211yesmaximal, characteristic, complemented
3#10593897C211yesmaximal, characteristic, complemented
4#10592392C211yesmaximal, characteristic, complemented
5C3×#4693C211yesmaximal, characteristic, complemented
6C3×C4×D3×C8C211yesmaximal, characteristic, complemented
7#10590862C214yesmaximal, complemented
8#10590386C211yesmaximal, characteristic, complemented
9#10590350C211yesmaximal, characteristic, complemented
10#81760—31nomaximal
11#78467—31nomaximal
12C2×#3799C2212yes—
13C2×#3795C2212yes—
14C2×#3744C2214yes—
15#64083C2211yescharacteristic
16#64078C2211yescharacteristic
17C2×C3×#204C2214yes—
18C2×C3×D3×C8C2212yes—
19C3×#874C2211yescharacteristic
20C3×C42×D3C2211yescharacteristic
21C3×#869C2211yescharacteristic
22#63909—22no—
23#63908—22no—
24#63894—22no—
25Dic3×D12—22no—
26#63864C2212yes—
27#63860C2212yes—
28C2×#3719C2214yes—
29C2×#3714C2214yes—
30#63806—216no—
31C32×C4×C8C2211yescharacteristic
32C3×C8×Dic3C2212yes—
33C3×C4×C3⋊C8C2211yescharacteristic
34C2×#916—34no—
35C2×#904—34no—
36#5725—31no—
37#5716—31no—
38#5477—31no—
39#5477—31no—
40C3×#492—31no—
41C2×C3×C4×C8—31no—
42#5168—34no—
43#5092—31no—
44#5073—31no—
45#4699—31no—
46#4696—34no—
47#4695—31no—
48#4693—31no—
49#4693—31no—
50#4693—61no—
51#4693D311yescharacteristic, complemented
52C4×D3×C8D311yescharacteristic, complemented
53C2×C4⋊(C3⋊D3)—22no—
54C2×C4⋊(C3⋊D3)C2312yes—
55C2×#634C2312yes—
56C2×C3×D12—22no—
57C2×C3×D12C2312yes—
58C2×C3×C4×D3D412yes—
59C2×C3×C4×D3C2311yescharacteristic
60C2×C3×Dic6C2312yes—
61C2×#626—22no—
62C2×#625—22no—
63C2×#624—22no—
64C2×D3×Dic3—22no—
65#3799—28no—
66#3795—28no—
67C2×C32×C8C2312yes—
68C32×C42C2311yescharacteristic
69C4⋊(C3⋊Dic3)—22no—
70#3744—28no—
71C3×C4⋊Dic3—22no—
72C3×C4×Dic3D412yes—
73C3×C4×Dic3C2311yescharacteristic
74C2×C3×C3⋊C8C2312yes—
75C3×#204—28no—
76C3×D3×C8D418yescomplemented
77#3722—24no—
78(C2×D3)⋊Dic3—24no—
79#3719—28no—
80#3714—28no—
81#3147—91noSylow
82C2×#239—32no—
83C2×#237—32no—
84C2×#235—32no—
85C2×#235—32no—
86C2×C3×SD16—34no—
87C22×C3×C8—32no—
88C3×C4⋊Q8—31no—
89C3×#127—31no—
90C2×C3×C42—31no—
91#947—32no—
92C2×#216—34no—
93#938—62no—
94#936—32no—
95D4×Dic3—62no—
96C2×#213—34no—
97#930—62no—
98#930—62no—
99#916—616no—
100C2×Dic12—34no—
101#904—616no—
102C2×D24—34no—
103C2×#204—34no—
104C2×#204—34no—
105C2×#204—64no—
106C2×#204C2×D314yes—
107C2×D3×C8C2×D312yes—
108#895—62no—
109#893—62no—
110#875—32no—
111#875—32no—
112#874—31no—
113#874—31no—
114#874—61no—
115#874C2×D311yescharacteristic
116C4×D12—62no—
117C4×D12—62no—
118C42×D3C2×D311yescharacteristic
119#869—31no—
120#869—31no—
121#869—61no—
122#869C2×D311yescharacteristic
123C3×C4×C8—21no—
124C3×C4×C8—32no—
125C3×C4×C8—31no—
126C3×C4×C8C2×D311yescharacteristic
127C3×C4×C8C2×D311yescharacteristic
128C8×Dic3C2×D312yes—
129C4×C3⋊C8C2×D311yescharacteristic
130C22×C3⋊D3—22no—
131C22×C3×D3—22no—
132C22×C3×D3C2×D411yescharacteristic
133C2×C32×C4C2×D412yes—
134C2×C32×C4C2411yescharacteristic
135C2×C3⋊Dic3—22no—
136C4⋊(C3⋊D3)—24no—
137C4⋊(C3⋊D3)—44no—
138#634—24no—
139C2×C3×Dic3—22no—
140C2×C3×Dic3C2×D412yes—
141C2×C3×Dic3C2×D411yescharacteristic
142C3×D12—24no—
143C3×D12—44no—
144C3×C4×D3—24no—
145C3×C4×D3C2×D414yes—
146C3×Dic6—24no—
147#626—44no—
148#625—44no—
149#624—44no—
150D3×Dic3—44no—
151C32×C8C2×D414yes—
152C3×C3⋊C8C2×D414yes—
153C2×#135—94no—
154#532—91no—
155#532—91no—
156#495—94no—
157#494—91no—
158#493—91no—
159#492—31no—
160#492—91no—
161C2×C4×C8—31no—
162C2×C3×Q8—32no—
163C2×C3×D4—32no—
164C2×C3×D4—62no—
165C22×C3×C4—31no—
166C22×C3×C4—32no—
167C2×#67—62no—
168C2×#67—62no—
169C2×#67—62no—
170C22×Dic3—62no—
171#239—68no—
172#237—68no—
173#235—68no—
174#235—68no—
175C2×D12—22no—
176C2×D12—32no—
177C2×D12—32no—
178C2×D12—62no—
179C2×D12—62no—
180C2×D12—62no—
181C2×D12—62no—
182C2×D12—122no—
183C2×D12C22×D312yes—
184C2×C4×D3—62no—
185C2×C4×D3—62no—
186C2×C4×D3—62no—
187C2×C4×D3D1212yes—
188C2×C4×D3C22×D311yescharacteristic
189C2×Dic6—32no—
190C2×Dic6—32no—
191C2×Dic6—62no—
192C2×Dic6C22×D312yes—
193C3×SD16—68no—
194C2×C3×C8—22no—
195C2×C3×C8—32no—
196C2×C3×C8—38no—
197C2×C3×C8C22×D312yes—
198C2×C3×C8C22×D312yes—
199C3×C4⋊C4—62no—
200C3×C42—21no—
201C3×C42—32no—
202C3×C42—31no—
203C3×C42C22×D311yescharacteristic
204C3×C42C22×D311yescharacteristic
205#217—64no—
206#216—68no—
207#213—68no—
208(C2×D3)⋊C4—64no—
209(C2×D3)⋊C4—64no—
210(C2×D3)⋊C4—64no—
211C4⋊Dic3—22no—
212C4⋊Dic3—62no—
213C4⋊Dic3—62no—
214C4⋊Dic3—122no—
215C4×Dic3D1212yes—
216C4×Dic3C22×D311yescharacteristic
217C2×C3⋊C8C22×D312yes—
218Dic12—68no—
219D24—68no—
220#204—28no—
221#204—68no—
222#204—68no—
223#204—128no—
224D3×C8D1218yescomplemented
225C22×C32C22×D411yescharacteristic
226C2×C3⋊D3—42no—
227C2×C3⋊D3—44no—
228C2×C3×D3—22no—
229C2×C3×D3—42no—
230C2×C3×D3—44no—
231C2×C3×D3#12712yes—
232C32×C4#13514yescomplemented
233C32×C4C22×D412yes—
234C3⋊Dic3—42no—
235C3×Dic3—22no—
236C3×Dic3—42no—
237C3×Dic3#12712yes—
238C2×#41—92no—
239C2×#41—92no—
240#135—1816no—
241C2×Q16—94no—
242C2×SD16—34no—
243C2×SD16—94no—
244C2×D8—94no—
245C22×C8—32no—
246C4⋊Q8—31no—
247C4⋊Q8—91no—
248#127—31no—
249#127—91no—
250#124—92no—
251#124—92no—
252#121—182no—
253#121—182no—
254C4×D4—182no—
255C4×D4—182no—
256C2×C42—31no—
257C4×C8—32no—
258C4×C8—31no—
259C4×C8D3211yescharacteristic
260C23×C3—31no—
261C23×C3—62no—
262C22×D3—22no—
263C22×D3—62no—
264C22×D3—62no—
265C22×D3—122no—
266C22×D3C2×D1211yescharacteristic
267C3×Q8—64no—
268C3×D4—64no—
269C3×D4—124no—
270C2×C3×C4—21no—
271C2×C3×C4—22no—
272C2×C3×C4—31no—
273C2×C3×C4—34no—
274C2×C3×C4—32no—
275C2×C3×C4—64no—
276C2×C3×C4—62no—
277C2×C3×C4C2×D1212yes—
278C2×C3×C4D3×D412yes—
279C2×C3×C4C23×D311yescharacteristic
280C2×C3×C4C23×D311yescharacteristic
281#67—124no—
282#67—124no—
283#67—124no—
284C2×Dic3—22no—
285C2×Dic3—62no—
286C2×Dic3—62no—
287C2×Dic3—122no—
288C2×Dic3—124no—
289C2×Dic3C2×D1212yes—
290C2×Dic3C2×D1211yescharacteristic
291D12—24no—
292D12—44no—
293D12—64no—
294D12—64no—
295D12—124no—
296D12—124no—
297D12—124no—
298D12—124no—
299D12—244no—
300C4×D3—24no—
301C4×D3—124no—
302C4×D3—124no—
303C4×D3—124no—
304C4×D3C2×D1214yes—
305Dic6—24no—
306Dic6—64no—
307Dic6—64no—
308Dic6—124no—
309C3×C8—24no—
310C3×C8—34no—
311C3×C8C2×D1214yes—
312C3×C8D3×D414yes—
313C3⋊C8C2×D1214yes—
314C2×C32C2×#12711yescharacteristic
315C2×C32C2×#13512yes—
316C3⋊D3—82no—
317C3×D3—22no—
318C3×D3—82no—
319#41—188no—
320#41—188no—
321C2×Q8—32no—
322C2×Q8—92no—
323C2×D4—32no—
324C2×D4—62no—
325C2×D4—92no—
326C2×D4—182no—
327C2×D4—182no—
328C2×D4—182no—
329C22×C4—31no—
330C22×C4—32no—
331C22×C4—182no—
332C22×C4—182no—
333Q16—188no—
334SD16—68no—
335SD16—188no—
336D8—188no—
337C2×C8—32no—
338C2×C8—38no—
339C2×C8C2×D3212yes—
340C4⋊C4—62no—
341C4⋊C4—182no—
342C22⋊C4—184no—
343C22⋊C4—184no—
344C42—31no—
345C42—32no—
346C42C2×D3211yescharacteristic
347C22×C3—21no—
348C22×C3—32no—
349C22×C3—62no—
350C22×C3—122no—
351C22×C3—124no—
352C22×C3C22×D1211yescharacteristic
353C22×C3C2×D3×D411yescharacteristic
354C2×D3—22no—
355C2×D3—42no—
356C2×D3—44no—
357C2×D3—122no—
358C2×D3—122no—
359C2×D3—124no—
360C2×D3—124no—
361C2×D3—242no—
362C2×D3—244no—
363C2×D3#87412yes—
364C3×C4—22no—
365C3×C4—24no—
366C3×C4—32no—
367C3×C4—62no—
368C3×C4—122no—
369C3×C4#90414yescomplemented
370C3×C4#91614yescomplemented
371C3×C4C22×D1212yes—
372C3×C4C2×D3×D412yes—
373Dic3—22no—
374Dic3—42no—
375Dic3—122no—
376Dic3—122no—
377Dic3—242no—
378Dic3#87412yes—
379C32#314711yescharacteristic, complemented, Sylow
380C23—31no—
381C23—62no—
382C23—182no—
383Q8—64no—
384Q8—184no—
385D4—64no—
386D4—124no—
387D4—184no—
388D4—364no—
389D4—364no—
390D4—364no—
391C2×C4—31no—
392C2×C4—34no—
393C2×C4—32no—
394C2×C4—64no—
395C2×C4—62no—
396C2×C4—182no—
397C2×C4—364no—
398C2×C4—364no—
399C2×C4D3×D1212yes—
400C2×C4C22×D3211yescharacteristic
401C8—34no—
402C8D3×D1214yes—
403C2×C3—22no—
404C2×C3—21no—
405C2×C3—62no—
406C2×C3—242no—
407C2×C3C2×#87411yescharacteristic
408C2×C3D3×#12711yescharacteristic
409C2×C3C2×#90412yes—
410C2×C3C2×#91612yes—
411D3—22no—
412D3—82no—
413D3—242no—
414D3—242no—
415D3—482no—
416C22—32no—
417C22—62no—
418C22—124no—
419C22—122no—
420C22—364no—
421C22—362no—
422C22C2×D3×D1211yescharacteristic
423C4—32no—
424C4—62no—
425C4—122no—
426C4—362no—
427C4#6380614yescomplemented
428C4C2×D3×D1212yes—
429C3—21no—
430C3#7846711yescharacteristic, complemented
431C3#8176011yescharacteristic, complemented
432C2—62no—
433C2—242no—
434C2—722no—
435C2D3×#87411yescharacteristic
436C2C2×#6380612yes—
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
hypercenterC4×C8D32
hypocenterC32#3147
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
1. C2×#63806C2semidirect
2. #10593970C2semidirect
3. #10593897C2semidirect
4. #10592392C2semidirect
5. C3×#4693C2semidirect
6. C3×C4×D3×C8C2semidirect
7. #10590862C2semidirect
8. #10590386C2semidirect
9. #10590350C2semidirect
51. #4693D3semidirect
52. C4×D3×C8D3semidirect
76. C3×D3×C8D4semidirect
224. D3×C8D12semidirect
232. C32×C4#135semidirect
369. C3×C4#904semidirect
370. C3×C4#916semidirect
379. C32#3147semidirect
427. C4#63806semidirect
430. C3#78467semidirect
431. C3#81760semidirect

Maximal subgroups

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

subgroupindex
C2×#638062
#105939702
#105938972
#105923922
C3×#46932
C3×C4×D3×C82
#105908622
#105903862
#105903502
#817603
#784673