Finite Group Databasebeta

← C4×#63804 #11857267

Subgroups — C4×#63804 #11857267

Order 1152.

1215 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63804C212yesmaximal
2C4×#3798C211yesmaximal, characteristic
3C4×#3743C211yesmaximal, characteristic, complemented
4C3×C4×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
5C3×C4×D3×C8C211yesmaximal, characteristic, complemented
6#10590910C212yesmaximal, complemented
7#10590908C212yesmaximal, complemented
8#10590693C212yesmaximal, complemented
9C4×#3711C211yesmaximal, characteristic, complemented
10C4×#3710C211yesmaximal, characteristic, complemented
11C4×D3×C3⋊C8C211yesmaximal, characteristic, complemented
12C4×#907—31nomaximal
13C4×#901—31nomaximal
14C2×#3798C2211yescharacteristic
15C2×#3743C2212yes—
16C42×C3⋊D3C2211yescharacteristic
17C2×C3×ΓL(1,𝔽25)C2212yes—
18C2×C3×D3×C8C2212yes—
19C3×C42×D3C2211yescharacteristic
20C3×C42×D3C2211yescharacteristic
21C4×#627C412yes—
22C4×#626C412yes—
23C4×#626C412yes—
24C4×#625C412yes—
25#63874C2211yescharacteristic
26#63855C2211yescharacteristic
27#63855C2211yescharacteristic
28C2×#3711C2212yes—
29C2×#3710C2212yes—
30C2×D3×C3⋊C8C2212yes—
31#63804C4116yesdirect product factor
32C32×C4×C8C2211yescharacteristic
33#63642C2212yes—
34C4×C3⋊(C3⋊C8)C2211yescharacteristic
35C3×#815C2212yes—
36C3×C8×Dic3C2212yes—
37C3×C4×C3⋊C8C2211yescharacteristic
38C3×C4×C3⋊C8C2211yescharacteristic
39#63554C2212yes—
40#63553C2212yes—
41Dic3×C3⋊C8C2212yes—
42C2×#907—32no—
43C2×#901—32no—
44C4×#235—31no—
45C4×#235—31no—
46C3×C4×M16—31no—
47C2×C3×C4×C8—31no—
48#5122—32no—
49#5101—32no—
50C4×#208—31no—
51C2×C4×C3⋊C8—31no—
52#4708—32no—
53#4708—32no—
54#4689—32no—
55#4689—32no—
56C4×ΓL(1,𝔽25)—31no—
57C4×ΓL(1,𝔽25)—31no—
58C4×ΓL(1,𝔽25)—31no—
59C4×ΓL(1,𝔽25)—61no—
60C4×ΓL(1,𝔽25)D311yescharacteristic, complemented
61C4×D3×C8—31no—
62C4×D3×C8—31no—
63C4×D3×C8—31no—
64C4×D3×C8D311yescharacteristic, complemented
65C2×C4×C3⋊D3C2×C412yes—
66C2×C4×C3⋊D3C2311yescharacteristic
67C2×C3×C4×D3C2×C412yes—
68C2×C3×C4×D3C2×C412yes—
69C2×C3×C4×D3C2311yescharacteristic
70C2×C3×C4×D3C2311yescharacteristic
71C2×#627C2×C411yescharacteristic
72C2×#626C2×C411yescharacteristic
73C2×#626C2×C411yescharacteristic
74C2×#625C2×C411yescharacteristic
75#3798C2×C418yes—
76C2×C32×C8C2312yes—
77C32×C42C2311yescharacteristic
78C4×C3⋊Dic3C2×C412yes—
79C4×C3⋊Dic3C2311yescharacteristic
80C2×C3⋊(C3⋊C8)C2312yes—
81#3743C2×C418yescomplemented
82C3×C4×Dic3C2×C412yes—
83C3×C4×Dic3C2×C412yes—
84C3×C4×Dic3C2311yescharacteristic
85C3×C4×Dic3C2311yescharacteristic
86C2×C3×C3⋊C8C2312yes—
87C2×C3×C3⋊C8C2312yes—
88C3×ΓL(1,𝔽25)C2×C418yescomplemented
89C3×D3×C8C2×C418yescomplemented
90#3724C2×C412yes—
91Dic3⋊Dic3C2×C412yes—
92Dic3⋊Dic3C2×C412yes—
93#3722C2×C412yes—
94(C2×D3)⋊Dic3C2×C412yes—
95(C2×D3)⋊Dic3C2×C412yes—
96#3711C2×C418yescomplemented
97#3710C2×C418yescomplemented
98D3×C3⋊C8C2×C418yescomplemented
99C4×#131—91noSylow
100C2×#235—31no—
101C2×#235—31no—
102C2×C3×M16—32no—
103C22×C3×C8—32no—
104C2×C3×C42—31no—
105C2×C3×C42—31no—
106C4×#67—32no—
107C4×#67—32no—
108C4×#67—32no—
109C4×#67—32no—
110#926—31no—
111#926—31no—
112C2×#208—32no—
113C22×C3⋊C8—32no—
114#907—316no—
115#901—316no—
116C2×ΓL(1,𝔽25)—32no—
117C2×ΓL(1,𝔽25)—32no—
118C2×ΓL(1,𝔽25)—32no—
119C2×ΓL(1,𝔽25)—62no—
120C2×ΓL(1,𝔽25)C2×D312yes—
121C2×D3×C8—32no—
122C2×D3×C8—32no—
123C2×D3×C8—32no—
124C2×D3×C8C2×D312yes—
125C4×D12—32no—
126C4×D12—32no—
127#872—31no—
128#872—31no—
129#872—31no—
130#872—31no—
131C42×D3—31no—
132C42×D3—31no—
133C42×D3—61no—
134C42×D3C2×D311yescharacteristic
135C42×D3C2×D311yescharacteristic
136C4×Dic6—32no—
137C4×Dic6—32no—
138C3×#97—32no—
139C3×C4×C8—21no—
140C3×C4×C8—32no—
141C3×C4×C8—31no—
142C3×C4×C8—31no—
143C3×C4×C8C2×D311yescharacteristic
144C3×C4×C8C2×D311yescharacteristic
145#815—32no—
146#815—32no—
147#815—32no—
148#815—62no—
149#815C2×D312yes—
150C8×Dic3—32no—
151C8×Dic3—32no—
152C8×Dic3—32no—
153C8×Dic3C2×D312yes—
154#803—32no—
155C4×C3⋊C8—31no—
156C4×C3⋊C8—31no—
157C4×C3⋊C8—32no—
158C4×C3⋊C8—61no—
159C4×C3⋊C8C2×D311yescharacteristic
160C4×C3⋊C8C2×D311yescharacteristic
161C22×C3⋊D3C22×C411yescharacteristic
162C22×C3×D3C22×C411yescharacteristic
163C22×C3×D3C22×C411yescharacteristic
164C2×C32×C4C22×C412yes—
165C2×C32×C4C2411yescharacteristic
166C2×C3⋊Dic3C22×C412yes—
167C2×C3⋊Dic3C22×C411yescharacteristic
168C4×C3⋊D3—24no—
169C4×C3⋊D3C22×C414yes—
170C2×C3×Dic3C22×C412yes—
171C2×C3×Dic3C22×C412yes—
172C2×C3×Dic3C22×C411yescharacteristic
173C2×C3×Dic3C22×C411yescharacteristic
174C3×C4×D3—24no—
175C3×C4×D3—24no—
176C3×C4×D3C22×C414yes—
177C3×C4×D3C22×C414yes—
178#627C4214yes—
179#626C4214yes—
180#626C4214yes—
181#625C4214yes—
182C32×C8C22×C414yes—
183C3⋊(C3⋊C8)C22×C414yes—
184C3×C3⋊C8C22×C414yes—
185C3×C3⋊C8C22×C414yes—
186C2×#131—92no—
187C4×#41—91no—
188#405—92no—
189#405—92no—
190#405—92no—
191C4×M16—31no—
192C4×M16—91no—
193C4×M16—91no—
194C2×C4×C8—31no—
195C2×C4×C8—91no—
196C2×C4×C8—91no—
197C22×C3×C4—31no—
198C22×C3×C4—31no—
199C22×C3×C4—32no—
200C22×C3×C4—32no—
201C2×#67—31no—
202C2×#67—31no—
203C2×#67—31no—
204C2×#67—31no—
205#235—38no—
206#235—38no—
207C2×D12—31no—
208C2×D12—31no—
209C2×C4×D3—31no—
210C2×C4×D3—31no—
211C2×C4×D3—32no—
212C2×C4×D3—32no—
213C2×C4×D3—61no—
214C2×C4×D3—62no—
215C2×C4×D3C4×D312yes—
216C2×C4×D3C4×D312yes—
217C2×C4×D3C22×D311yescharacteristic
218C2×C4×D3C22×D311yescharacteristic
219C2×Dic6—31no—
220C2×Dic6—31no—
221C3×M16—38no—
222C2×C3×C8—22no—
223C2×C3×C8—32no—
224C2×C3×C8—32no—
225C2×C3×C8—38no—
226C2×C3×C8C22×D312yes—
227C2×C3×C8C22×D312yes—
228C3×C42—21no—
229C3×C42—32no—
230C3×C42—32no—
231C3×C42—31no—
232C3×C42—31no—
233C3×C42C22×D311yescharacteristic
234C3×C42C22×D311yescharacteristic
235#217—32no—
236#217—32no—
237(C2×D3)⋊C4—32no—
238(C2×D3)⋊C4—32no—
239(C2×D3)⋊C4—32no—
240(C2×D3)⋊C4—32no—
241C4⋊Dic3—32no—
242C4⋊Dic3—32no—
243Dic3⋊C4—32no—
244Dic3⋊C4—32no—
245Dic3⋊C4—32no—
246Dic3⋊C4—32no—
247C4×Dic3—32no—
248C4×Dic3—32no—
249C4×Dic3—31no—
250C4×Dic3—31no—
251C4×Dic3—61no—
252C4×Dic3—62no—
253C4×Dic3C4×D312yes—
254C4×Dic3C4×D312yes—
255C4×Dic3C22×D311yescharacteristic
256C4×Dic3C22×D311yescharacteristic
257#208—38no—
258C2×C3⋊C8—32no—
259C2×C3⋊C8—32no—
260C2×C3⋊C8—38no—
261C2×C3⋊C8—62no—
262C2×C3⋊C8C22×D312yes—
263C2×C3⋊C8C22×D312yes—
264ΓL(1,𝔽25)—38no—
265ΓL(1,𝔽25)—38no—
266ΓL(1,𝔽25)—38no—
267ΓL(1,𝔽25)—68no—
268ΓL(1,𝔽25)C4×D318yescomplemented
269D3×C8—38no—
270D3×C8—38no—
271D3×C8—38no—
272D3×C8C4×D318yescomplemented
273C22×C32C23×C411yescharacteristic
274C2×C3⋊D3—22no—
275C2×C3⋊D3C2×C4212yes—
276C2×C3×D3—22no—
277C2×C3×D3—22no—
278C2×C3×D3C2×C4212yes—
279C2×C3×D3C2×C4212yes—
280C32×C4#13114yescomplemented
281C32×C4C23×C412yes—
282C3⋊Dic3—22no—
283C3⋊Dic3C2×C4212yes—
284C3×Dic3—22no—
285C3×Dic3—22no—
286C3×Dic3C2×C4212yes—
287C3×Dic3C2×C4212yes—
288C2×#41—91no—
289#131—916no—
290C2×M16—32no—
291C2×M16—92no—
292C2×M16—92no—
293C22×C8—32no—
294C22×C8—92no—
295C22×C8—92no—
296C4×Q8—92no—
297C4×D4—92no—
298C4×D4—92no—
299C4×D4—92no—
300#117—91no—
301#117—91no—
302#117—91no—
303C2×C42—31no—
304C2×C42—31no—
305C2×C42—91no—
306#97—32no—
307#97—92no—
308#97—92no—
309C4×C8—32no—
310C4×C8—31no—
311C4×C8—31no—
312C4×C8—92no—
313C4×C8—92no—
314C4×C8—91no—
315C4×C8D3211yescharacteristic
316C23×C3—31no—
317C23×C3—31no—
318C22×D3—31no—
319C22×D3—31no—
320C22×D3—61no—
321C22×D3C2×C4×D311yescharacteristic
322C22×D3C2×C4×D311yescharacteristic
323C2×C3×C4—21no—
324C2×C3×C4—22no—
325C2×C3×C4—31no—
326C2×C3×C4—31no—
327C2×C3×C4—34no—
328C2×C3×C4—34no—
329C2×C3×C4—32no—
330C2×C3×C4—32no—
331C2×C3×C4—64no—
332C2×C3×C4—64no—
333C2×C3×C4C2×C4×D312yes—
334C2×C3×C4C2×C4×D312yes—
335C2×C3×C4C23×D311yescharacteristic
336C2×C3×C4C23×D311yescharacteristic
337#67—34no—
338#67—34no—
339#67—34no—
340#67—34no—
341C2×Dic3—31no—
342C2×Dic3—31no—
343C2×Dic3—32no—
344C2×Dic3—32no—
345C2×Dic3—61no—
346C2×Dic3—62no—
347C2×Dic3C2×C4×D312yes—
348C2×Dic3C2×C4×D312yes—
349C2×Dic3C2×C4×D311yescharacteristic
350C2×Dic3C2×C4×D311yescharacteristic
351D12—34no—
352D12—34no—
353C4×D3—24no—
354C4×D3—24no—
355C4×D3—34no—
356C4×D3—34no—
357C4×D3—64no—
358C4×D3—64no—
359C4×D3—64no—
360C4×D3—124no—
361C4×D3C2×C4×D314yes—
362C4×D3C2×C4×D314yes—
363Dic6—34no—
364Dic6—34no—
365C3×C8—24no—
366C3×C8—34no—
367C3×C8—34no—
368C3×C8C2×C4×D314yes—
369C3×C8C2×C4×D314yes—
370C3⋊C8—34no—
371C3⋊C8—34no—
372C3⋊C8—64no—
373C3⋊C8C2×C4×D314yes—
374C3⋊C8C2×C4×D314yes—
375C2×C32C22×C4211yescharacteristic
376C2×C32C2×#13112yes—
377C3⋊D3—22no—
378C3×D3—22no—
379C3×D3—22no—
380#41—98no—
381C2×Q8—91no—
382C2×D4—91no—
383C2×D4—91no—
384C2×D4—91no—
385C22×C4—31no—
386C22×C4—31no—
387C22×C4—32no—
388C22×C4—32no—
389C22×C4—91no—
390C22×C4—92no—
391M16—38no—
392M16—98no—
393M16—98no—
394C2×C8—32no—
395C2×C8—32no—
396C2×C8—38no—
397C2×C8—98no—
398C2×C8—98no—
399C2×C8—92no—
400C2×C8C2×D3212yes—
401C4⋊C4—92no—
402C4⋊C4—92no—
403C4⋊C4—92no—
404C22⋊C4—92no—
405C22⋊C4—92no—
406C22⋊C4—92no—
407C42—31no—
408C42—31no—
409C42—32no—
410C42—32no—
411C42—91no—
412C42—92no—
413C42C2×D3211yescharacteristic
414C22×C3—21no—
415C22×C3—32no—
416C22×C3—32no—
417C22×C3—62no—
418C22×C3—62no—
419C22×C3C22×C4×D311yescharacteristic
420C22×C3C22×C4×D311yescharacteristic
421C2×D3—22no—
422C2×D3—22no—
423C2×D3—32no—
424C2×D3—32no—
425C2×D3—62no—
426C2×D3—62no—
427C2×D3—62no—
428C2×D3—122no—
429C2×D3C42×D312yes—
430C2×D3C42×D312yes—
431C3×C4—22no—
432C3×C4—24no—
433C3×C4—32no—
434C3×C4—32no—
435C3×C4—62no—
436C3×C4—62no—
437C3×C4#90114yescomplemented
438C3×C4#90714yescomplemented
439C3×C4C22×C4×D312yes—
440C3×C4C22×C4×D312yes—
441Dic3—22no—
442Dic3—22no—
443Dic3—32no—
444Dic3—32no—
445Dic3—62no—
446Dic3—62no—
447Dic3—62no—
448Dic3—122no—
449Dic3C42×D312yes—
450Dic3C42×D312yes—
451C32C4×#13111yescharacteristic, complemented, Sylow
452C23—31no—
453C23—31no—
454C23—91no—
455Q8—94no—
456D4—94no—
457D4—94no—
458D4—94no—
459C2×C4—31no—
460C2×C4—31no—
461C2×C4—34no—
462C2×C4—34no—
463C2×C4—32no—
464C2×C4—32no—
465C2×C4—64no—
466C2×C4—64no—
467C2×C4—91no—
468C2×C4—94no—
469C2×C4—92no—
470C2×C4—184no—
471C2×C4C4×D3212yes—
472C2×C4C22×D3211yescharacteristic
473C8—34no—
474C8—34no—
475C8—94no—
476C8C4×D3214yes—
477C2×C3—22no—
478C2×C3—21no—
479C2×C3—62no—
480C2×C3—62no—
481C2×C3C2×C42×D311yescharacteristic
482C2×C3C2×C42×D311yescharacteristic
483C2×C3C2×#90112yes—
484C2×C3C2×#90712yes—
485D3—22no—
486D3—22no—
487D3—62no—
488D3—62no—
489D3—122no—
490C22—32no—
491C22—32no—
492C22—62no—
493C22—62no—
494C22—92no—
495C22—182no—
496C22C2×C4×D3211yescharacteristic
497C4—32no—
498C4—32no—
499C4—62no—
500C4—62no—
501C4—92no—
502C4—182no—
503C4#6380414yesdirect product factor
504C4C2×C4×D3212yes—
505C3—21no—
506C3C4×#90111yescharacteristic, complemented
507C3C4×#90711yescharacteristic, complemented
508C2—62no—
509C2—62no—
510C2—182no—
511C2C42×D3211yescharacteristic
512C2C2×#6380412yes—
subgroupG/H
centerC42C2×D32
commutatorC2×C32C22×C42
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C23×C4
prime radicalC2×#3798C22
cosocleC2×C32×C4C24
hypercenterC4×C8D32
hypocenterC32C4×#131
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
3. C4×#3743C2semidirect
4. C3×C4×ΓL(1,𝔽25)C2semidirect
5. C3×C4×D3×C8C2semidirect
6. #10590910C2semidirect
7. #10590908C2semidirect
8. #10590693C2semidirect
9. C4×#3711C2semidirect
10. C4×#3710C2semidirect
11. C4×D3×C3⋊C8C2semidirect
31. #63804C4direct (N × H)
60. C4×ΓL(1,𝔽25)D3semidirect
64. C4×D3×C8D3semidirect
81. #3743C2×C4semidirect
88. C3×ΓL(1,𝔽25)C2×C4semidirect
89. C3×D3×C8C2×C4semidirect
96. #3711C2×C4semidirect
97. #3710C2×C4semidirect
98. D3×C3⋊C8C2×C4semidirect
268. ΓL(1,𝔽25)C4×D3semidirect
272. D3×C8C4×D3semidirect
280. C32×C4#131semidirect
437. C3×C4#901semidirect
438. C3×C4#907semidirect
451. C32C4×#131semidirect
503. C4#63804direct (N × H)
506. C3C4×#901semidirect
507. C3C4×#907semidirect

Maximal subgroups

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

subgroupindex
C2×#638042
C4×#37982
C4×#37432
C3×C4×ΓL(1,𝔽25)2
C3×C4×D3×C82
#105909102
#105909082
#105906932
C4×#37112
C4×#37102
C4×D3×C3⋊C82
C4×#9073
C4×#9013