Finite Group Databasebeta

← #11774557

Subgroups — #11774557

Order 1152.

665 conjugacy classes of subgroups.

The subgroup lattice has 525 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×D3×D4C211yesmaximal, characteristic
2#10590336C211yesmaximal, characteristic, complemented
3#10590261C211yesmaximal, characteristic, complemented
4D4⋊(C3⋊(C3⋊C8))C211yesmaximal, characteristic, complemented
5C3×D4⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
6#10589081C211yesmaximal, characteristic, complemented
7#10589080C211yesmaximal, characteristic, complemented
8#71598—31nomaximal
9#68172—31nomaximal
10C2×C3×D3×D4C411yescharacteristic
11C22×C3×C4×D3—21no—
12C32×C4×D4C2211yescharacteristic
13C3×D4×Dic3C411yescharacteristic
14C3×C4×#67—21no—
15C3×#893C411yescharacteristic
16C3×D3×C4⋊C4C411yescharacteristic
17C3×#67⋊C4—21no—
18C3×D3×C22⋊C4—21no—
19C3×C4×D12C2211yescharacteristic
20C3×C42×D3C2211yescharacteristic
21C2×#3711—21no—
22C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
23C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
24C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
25C3×C4×C3⋊C8C2211yescharacteristic, complemented
26Dic3⋊(C3⋊C8)—21no—
27Dic3⋊(C3⋊C8)—21no—
28(C2×D3)⋊(C3⋊C8)—21no—
29C2×C3×C4×D4—31no—
30C4×D3×D4D311yescharacteristic
31#4925—31no—
32#4924—31no—
33#4837—31no—
34#4685—31no—
35C3×D4⋊C8—31no—
36D4⋊(C3⋊C8)—31no—
37D4⋊(C3⋊C8)—31no—
38D4⋊(C3⋊C8)—31no—
39D4⋊(C3⋊C8)—31no—
40D4⋊(C3⋊C8)—61no—
41D4⋊(C3⋊C8)D311yescharacteristic, complemented
42#4483—31no—
43#4459—31no—
44C23×C3×D3—21no—
45C2×C32×D4C2×C411yescharacteristic
46C22×C32×C4—21no—
47C2×C3×#67—21no—
48C22×C3×Dic3—21no—
49C3×D3×D4—22no—
50C3×D3×D4—22no—
51C2×C3×D12C2×C411yescharacteristic
52C2×C3×C4×D3—21no—
53C2×C3×C4×D3—21no—
54C2×C3×C4×D3—21no—
55C2×C3×C4×D3—42no—
56C2×C3×C4×D3—42no—
57C2×C3×C4×D3C2×C411yescharacteristic
58C2×C3×C4×D3D411yescharacteristic
59C2×C3×C4×D3D411yescharacteristic
60C32×C4⋊C4C2×C411yescharacteristic
61C32×C22⋊C4—21no—
62C32×C42C2311yescharacteristic
63C2×C3⋊(C3⋊C8)—21no—
64C2×C3⋊(C3⋊C8)—21no—
65C3×#217—21no—
66C3×(C2×D3)⋊C4—21no—
67C3×(C2×D3)⋊C4—21no—
68C3×C4⋊Dic3C2×C411yescharacteristic
69C3×Dic3⋊C4—21no—
70C3×C4×Dic3C2×C411yescharacteristic
71C3×C4×Dic3D411yescharacteristic
72C3×C4×Dic3D411yescharacteristic
73C2×C3×C3⋊C8—21no—
74C2×C3×C3⋊C8—21no—
75#3711—42no—
76#1486—91noSylow
77C22×C3×D4—31no—
78C23×C3×C4—61no—
79C2×D3×D4Dic311yescharacteristic
80C22×C4×D3—21no—
81C3×C4×D4—21no—
82C3×C4×D4—31no—
83C3×C4×D4—31no—
84C3×C4×D4—31no—
85C3×C4×D4—61no—
86C3×C4×D4—61no—
87C3×C4×D4C2×D311yescharacteristic
88C3×C4×D4C2×D311yescharacteristic
89C2×C3×C4⋊C4—31no—
90C2×C3×C22⋊C4—61no—
91C2×C3×C42—31no—
92D4×Dic3Dic311yescharacteristic
93C4×#67—21no—
94C2×#208—61no—
95C2×ΓL(1,𝔽25)—61no—
96#893Dic311yescharacteristic
97D3×C4⋊C4Dic311yescharacteristic
98#67⋊C4—21no—
99D3×C22⋊C4—21no—
100C4×D12C2×D311yescharacteristic
101C42×D3C2×D311yescharacteristic
102C3×C4⋊C8—31no—
103C3×C4×C8—31no—
104#830—61no—
105(C2×D3)⋊C8—61no—
106Dic3⋊C8—61no—
107Dic3⋊C8—61no—
108C4⋊(C3⋊C8)—31no—
109C4⋊(C3⋊C8)—31no—
110C4⋊(C3⋊C8)—61no—
111C4⋊(C3⋊C8)—61no—
112C4⋊(C3⋊C8)—61no—
113C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
114C4×C3⋊C8—31no—
115C4×C3⋊C8—31no—
116C4×C3⋊C8—61no—
117C4×C3⋊C8C2×D311yescharacteristic, complemented
118C23×C32—21no—
119C22×C3×D3—24no—
120C22×C3×D3—21no—
121C22×C3×D3—42no—
122C22×C3×D3—42no—
123C22×C3×D3C22⋊C411yescharacteristic
124C32×D4—21no—
125C32×D4M1612yescomplemented
126C2×C32×C4—21no—
127C2×C32×C4—41no—
128C2×C32×C4—41no—
129C2×C32×C4C22×C411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4C2×D411yescharacteristic
132C3×#67—24no—
133C2×C3×Dic3—21no—
134C2×C3×Dic3—42no—
135C2×C3×Dic3C22⋊C411yescharacteristic
136C2×C3×Dic3C22⋊C411yescharacteristic
137C2×C3×Dic3C22⋊C411yescharacteristic
138C3×D12—21no—
139C3×D12M1612yescomplemented
140C3×C4×D3—21no—
141C3×C4×D3—21no—
142C3×C4×D3—41no—
143C3×C4×D3—42no—
144C3×C4×D3—41no—
145C3×C4×D3—41no—
146C3×C4×D3—42no—
147C3×C4×D3D812yes—
148C3×C4×D3SD1612yes—
149C3⋊(C3⋊C8)—41no—
150C3⋊(C3⋊C8)—41no—
151C3×C3⋊C8—41no—
152C3×C3⋊C8—41no—
153C2×C4×D4—31no—
154#431—91no—
155#423—91no—
156D4⋊C8—31no—
157D4⋊C8—91no—
158D4⋊C8—91no—
159D4⋊C8—91no—
160C24×C3—61no—
161C23×D3—21no—
162C2×C3×D4—21no—
163C2×C3×D4—31no—
164C2×C3×D4—61no—
165C2×C3×D4—62no—
166C2×C3×D4—62no—
167C2×C3×D4C4×D311yescharacteristic
168C2×C3×D4C2×Dic311yescharacteristic
169C22×C3×C4—21no—
170C22×C3×C4—21no—
171C22×C3×C4—31no—
172C22×C3×C4—31no—
173C22×C3×C4—31no—
174C22×C3×C4—41no—
175C22×C3×C4—61no—
176C22×C3×C4—61no—
177C22×C3×C4—61no—
178C22×C3×C4—61no—
179C22×C3×C4—122no—
180C22×C3×C4—122no—
181C2×#67—21no—
182C22×Dic3—21no—
183D3×D4—22no—
184D3×D4—22no—
185C2×D12C2×Dic311yescharacteristic
186C2×C4×D3—21no—
187C2×C4×D3—21no—
188C2×C4×D3—21no—
189C2×C4×D3—42no—
190C2×C4×D3—42no—
191C2×C4×D3C2×Dic311yescharacteristic
192C2×C4×D3#6711yescharacteristic
193C2×C4×D3#6711yescharacteristic
194C2×C3×C8—61no—
195C2×C3×C8—61no—
196C3×C4⋊C4—21no—
197C3×C4⋊C4—31no—
198C3×C4⋊C4—61no—
199C3×C4⋊C4C4×D311yescharacteristic
200C3×C4⋊C4C2×Dic311yescharacteristic
201C3×C22⋊C4—21no—
202C3×C22⋊C4—21no—
203C3×C22⋊C4—41no—
204C3×C22⋊C4—61no—
205C3×C22⋊C4—61no—
206C3×C22⋊C4—61no—
207C3×C42—21no—
208C3×C42—31no—
209C3×C42—31no—
210C3×C42—31no—
211C3×C42C22×D311yescharacteristic
212C3×C42C22×D311yescharacteristic
213#217—21no—
214(C2×D3)⋊C4—21no—
215(C2×D3)⋊C4—21no—
216C4⋊Dic3C2×Dic311yescharacteristic
217Dic3⋊C4—21no—
218C4×Dic3C2×Dic311yescharacteristic
219C4×Dic3#6711yescharacteristic
220C4×Dic3#6711yescharacteristic
221#208—122no—
222C2×C3⋊C8—21no—
223C2×C3⋊C8—21no—
224C2×C3⋊C8—61no—
225C2×C3⋊C8—61no—
226C2×C3⋊C8—61no—
227C2×C3⋊C8—61no—
228C2×C3⋊C8—121no—
229C2×C3⋊C8—121no—
230ΓL(1,𝔽25)—122no—
231C22×C32—22no—
232C22×C32—41no—
233C22×C32—41no—
234C22×C32C2×C22⋊C411yescharacteristic
235C2×C3×D3—21no—
236C2×C3×D3—21no—
237C2×C3×D3—22no—
238C2×C3×D3—48no—
239C2×C3×D3—41no—
240C2×C3×D3—41no—
241C2×C3×D3#10212yes—
242C32×C4—21no—
243C32×C4—41no—
244C32×C4C2×M1611yescharacteristic
245C32×C4C2×M1611yescharacteristic
246C32×C4C2×D811yescharacteristic
247C32×C4C2×SD1611yescharacteristic
248C3×Dic3—21no—
249C3×Dic3—21no—
250C3×Dic3—41no—
251C3×Dic3#10212yes—
252C22×D4—31no—
253C23×C4—61no—
254C2×M16—181no—
255C4×D4—31no—
256C4×D4—31no—
257C4×D4—31no—
258C4×D4—61no—
259C4×D4—61no—
260C4×D4D3211yescharacteristic
261C2×C4⋊C4—31no—
262C2×C22⋊C4—61no—
263C2×C42—31no—
264C4⋊C8—31no—
265C4⋊C8—91no—
266C4⋊C8—181no—
267C4⋊C8—181no—
268C22⋊C8—181no—
269C4×C8—31no—
270C4×C8—91no—
271C23×C3—21no—
272C23×C3—21no—
273C23×C3—31no—
274C23×C3—41no—
275C23×C3—64no—
276C23×C3—61no—
277C23×C3—122no—
278C23×C3—122no—
279C22×D3—24no—
280C22×D3—21no—
281C22×D3—42no—
282C22×D3—42no—
283C22×D3#21711yescharacteristic
284C3×D4—21no—
285C3×D4—21no—
286C3×D4—22no—
287C3×D4—32no—
288C3×D4—41no—
289C3×D4—64no—
290C3×D4—61no—
291C3×D4ΓL(1,𝔽25)12yescomplemented
292C3×D4#20812yescomplemented
293C2×C3×C4—21no—
294C2×C3×C4—21no—
295C2×C3×C4—21no—
296C2×C3×C4—21no—
297C2×C3×C4—21no—
298C2×C3×C4—31no—
299C2×C3×C4—32no—
300C2×C3×C4—32no—
301C2×C3×C4—31no—
302C2×C3×C4—31no—
303C2×C3×C4—41no—
304C2×C3×C4—41no—
305C2×C3×C4—41no—
306C2×C3×C4—41no—
307C2×C3×C4—41no—
308C2×C3×C4—61no—
309C2×C3×C4—61no—
310C2×C3×C4—61no—
311C2×C3×C4—81no—
312C2×C3×C4—81no—
313C2×C3×C4—121no—
314C2×C3×C4—122no—
315C2×C3×C4—122no—
316C2×C3×C4—122no—
317C2×C3×C4—121no—
318C2×C3×C4—121no—
319C2×C3×C4C2×C4×D311yescharacteristic
320C2×C3×C4D3×D411yescharacteristic
321C2×C3×C4D3×D411yescharacteristic
322C2×C3×C4C22×Dic311yescharacteristic
323C2×C3×C4C2×#6711yescharacteristic
324C2×C3×C4C2×#6711yescharacteristic
325#67—24no—
326C2×Dic3—21no—
327C2×Dic3—42no—
328C2×Dic3#21711yescharacteristic
329C2×Dic3#21711yescharacteristic
330C2×Dic3#21711yescharacteristic
331D12—21no—
332D12#20812yescomplemented
333C4×D3—21no—
334C4×D3—21no—
335C4×D3—41no—
336C4×D3—42no—
337C4×D3—41no—
338C4×D3—41no—
339C4×D3—42no—
340C4×D3#21312yes—
341C4×D3#21412yes—
342C3×C8—121no—
343C3×C8—121no—
344C3⋊C8—41no—
345C3⋊C8—41no—
346C3⋊C8—121no—
347C3⋊C8—121no—
348C3⋊C8—122no—
349C3⋊C8—121no—
350C3⋊C8—121no—
351C3⋊C8—241no—
352C2×C32—42no—
353C2×C32#40711yescharacteristic
354C2×C32C2×#10211yescharacteristic
355C2×C32#42111yescharacteristic
356C3×D3—22no—
357C3×D3—42no—
358C24—61no—
359C2×D4—31no—
360C2×D4—61no—
361C2×D4—62no—
362C2×D4—62no—
363C2×D4D3×Dic311yescharacteristic
364C22×C4—21no—
365C22×C4—31no—
366C22×C4—31no—
367C22×C4—31no—
368C22×C4—61no—
369C22×C4—61no—
370C22×C4—61no—
371C22×C4—61no—
372C22×C4—122no—
373C22×C4—122no—
374M16—362no—
375C2×C8—61no—
376C2×C8—61no—
377C2×C8—181no—
378C2×C8—181no—
379C4⋊C4—31no—
380C4⋊C4—61no—
381C4⋊C4D3×Dic311yescharacteristic
382C22⋊C4—21no—
383C22⋊C4—61no—
384C22⋊C4—61no—
385C22⋊C4—61no—
386C42—31no—
387C42—31no—
388C42—31no—
389C42C2×D3211yescharacteristic
390C22×C3—22no—
391C22×C3—22no—
392C22×C3—21no—
393C22×C3—32no—
394C22×C3—42no—
395C22×C3—41no—
396C22×C3—41no—
397C22×C3—41no—
398C22×C3—41no—
399C22×C3—61no—
400C22×C3—61no—
401C22×C3—62no—
402C22×C3—81no—
403C22×C3—81no—
404C22×C3—128no—
405C22×C3—121no—
406C22×C3—121no—
407C22×C3D3×C22⋊C411yescharacteristic
408C22×C3C2×#21711yescharacteristic
409C2×D3—21no—
410C2×D3—21no—
411C2×D3—22no—
412C2×D3—48no—
413C2×D3—41no—
414C2×D3—41no—
415C2×D3#83212yes—
416C3×C4—21no—
417C3×C4—21no—
418C3×C4—21no—
419C3×C4—21no—
420C3×C4—21no—
421C3×C4—21no—
422C3×C4—32no—
423C3×C4—41no—
424C3×C4—41no—
425C3×C4—41no—
426C3×C4—61no—
427C3×C4—61no—
428C3×C4—81no—
429C3×C4—121no—
430C3×C4C2×ΓL(1,𝔽25)11yescharacteristic
431C3×C4D3×M1611yescharacteristic
432C3×C4D3×D811yescharacteristic
433C3×C4D3×SD1611yescharacteristic
434C3×C4C2×#20811yescharacteristic
435C3×C4C2×#20811yescharacteristic
436C3×C4C2×#21311yescharacteristic
437C3×C4C2×#21411yescharacteristic
438Dic3—21no—
439Dic3—21no—
440Dic3—41no—
441Dic3#83212yes—
442C32#148611yescharacteristic, complemented, Sylow
443C23—21no—
444C23—31no—
445C23—64no—
446C23—61no—
447C23—122no—
448C23—122no—
449D4—21no—
450D4—32no—
451D4—64no—
452D4—61no—
453D4#371112yescomplemented
454C2×C4—21no—
455C2×C4—31no—
456C2×C4—32no—
457C2×C4—32no—
458C2×C4—31no—
459C2×C4—31no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—61no—
463C2×C4—61no—
464C2×C4—61no—
465C2×C4—121no—
466C2×C4—122no—
467C2×C4—122no—
468C2×C4—122no—
469C2×C4—121no—
470C2×C4—121no—
471C2×C4C2×D3×Dic311yescharacteristic
472C2×C4D3×#6711yescharacteristic
473C2×C4D3×#6711yescharacteristic
474C8—121no—
475C8—121no—
476C8—361no—
477C8—361no—
478C2×C3—21no—
479C2×C3—21no—
480C2×C3—21no—
481C2×C3—42no—
482C2×C3—42no—
483C2×C3—62no—
484C2×C3—82no—
485C2×C3—122no—
486C2×C3#472611yescharacteristic
487C2×C3D3×#10211yescharacteristic
488C2×C3#482111yescharacteristic
489C2×C3#520711yescharacteristic
490C2×C3C2×#83211yescharacteristic
491C2×C3#523611yescharacteristic
492D3—22no—
493D3—42no—
494C22—22no—
495C22—32no—
496C22—41no—
497C22—41no—
498C22—61no—
499C22—61no—
500C22—62no—
501C22—128no—
502C22—121no—
503C22—121no—
504C22D3×#21711yescharacteristic
505C4—21no—
506C4—32no—
507C4—41no—
508C4—61no—
509C4—61no—
510C4—121no—
511C4D3×#20811yescharacteristic
512C4C2×#371111yescharacteristic
513C4D3×#21311yescharacteristic
514C4D3×#21411yescharacteristic
515C3—21no—
516C3#6817211yescharacteristic, complemented
517C3#7159811yescharacteristic, complemented
518C2—42no—
519C2—62no—
520C2—122no—
521C2#1059115411yescharacteristic
522C2D3×#83211yescharacteristic
523C2#1059167011yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4×D4C22
socleC22×C32C2×C22⋊C4
prime radicalC2×C3×D3×D4C4
cosocleC32×C42C23
hypercenterC4×D4D32
hypocenterC32#1486
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. #10590336C2semidirect
3. #10590261C2semidirect
4. D4⋊(C3⋊(C3⋊C8))C2semidirect
5. C3×D4⋊(C3⋊C8)C2semidirect
6. #10589081C2semidirect
7. #10589080C2semidirect
22. C4⋊(C3⋊(C3⋊C8))C22semidirect
23. C4×C3⋊(C3⋊C8)C22semidirect
24. C3×C4⋊(C3⋊C8)C22semidirect
25. C3×C4×C3⋊C8C22semidirect
41. D4⋊(C3⋊C8)D3semidirect
113. C4⋊(C3⋊C8)C2×D3semidirect
117. C4×C3⋊C8C2×D3semidirect
125. C32×D4M16semidirect
139. C3×D12M16semidirect
291. C3×D4ΓL(1,𝔽25)semidirect
292. C3×D4#208semidirect
332. D12#208semidirect
442. C32#1486semidirect
453. D4#3711semidirect
516. C3#68172semidirect
517. C3#71598semidirect

Maximal subgroups

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

subgroupindex
C3×C4×D3×D42
#105903362
#105902612
D4⋊(C3⋊(C3⋊C8))2
C3×D4⋊(C3⋊C8)2
#105890812
#105890802
#715983
#681723