Finite Group Databasebeta

← #11774313

Subgroups — #11774313

Order 1152.

665 conjugacy classes of subgroups.

The subgroup lattice has 521 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×D3×D4C211yesmaximal, characteristic
2#10590261C211yesmaximal, characteristic, complemented
3#10590248C211yesmaximal, 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#71597—31nomaximal
9#68167—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
21C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
22C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
23C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
24C3×C4×C3⋊C8C2211yescharacteristic, complemented
25Dic3⋊(C3⋊C8)—21no—
26(C2×D3)⋊(C3⋊C8)—21no—
27(C2×D3)⋊(C3⋊C8)—21no—
28Dic3×C3⋊C8—21no—
29C2×C3×C4×D4—31no—
30C4×D3×D4D311yescharacteristic
31#4925—31no—
32#4925—31no—
33#4833—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×D4C814yescomplemented
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#1478—91noSylow
76C22×C3×D4—31no—
77C23×C3×C4—61no—
78C2×D3×D4Dic311yescharacteristic
79C22×C4×D3—21no—
80C3×C4×D4—21no—
81C3×C4×D4—31no—
82C3×C4×D4—31no—
83C3×C4×D4—31no—
84C3×C4×D4—61no—
85C3×C4×D4—61no—
86C3×C4×D4C2×D311yescharacteristic
87C3×C4×D4C2×D311yescharacteristic
88C2×C3×C4⋊C4—31no—
89C2×C3×C22⋊C4—61no—
90C2×C3×C42—31no—
91D4×Dic3Dic311yescharacteristic
92C4×#67—21no—
93#893Dic311yescharacteristic
94D3×C4⋊C4Dic311yescharacteristic
95#67⋊C4—21no—
96D3×C22⋊C4—21no—
97C4×D12C2×D311yescharacteristic
98C42×D3C2×D311yescharacteristic
99C3×C4⋊C8—31no—
100C3×C4×C8—31no—
101#830—61no—
102#830—61no—
103(C2×D3)⋊C8—61no—
104(C2×D3)⋊C8—61no—
105Dic3⋊C8—61no—
106C8×Dic3—61no—
107C4⋊(C3⋊C8)—31no—
108C4⋊(C3⋊C8)—31no—
109C4⋊(C3⋊C8)—61no—
110C4⋊(C3⋊C8)—61no—
111C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
112C4×C3⋊C8—31no—
113C4×C3⋊C8—31no—
114C4×C3⋊C8—61no—
115C4×C3⋊C8—61no—
116C4×C3⋊C8C2×D311yescharacteristic, complemented
117C23×C32—21no—
118C22×C3×D3—21no—
119C22×C3×D3—24no—
120C22×C3×D3—42no—
121C22×C3×D3—42no—
122C22×C3×D3C22⋊C411yescharacteristic
123C32×D4—21no—
124C32×D4C2×C812yes—
125C2×C32×C4—21no—
126C2×C32×C4—41no—
127C2×C32×C4—41no—
128C2×C32×C4C22×C411yescharacteristic
129C2×C32×C4C2×D411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131C3×#67—24no—
132C2×C3×Dic3—21no—
133C2×C3×Dic3—42no—
134C2×C3×Dic3C22⋊C411yescharacteristic
135C2×C3×Dic3C22⋊C411yescharacteristic
136C2×C3×Dic3C22⋊C411yescharacteristic
137C3×D12—21no—
138C3×D12C2×C812yes—
139C3×C4×D3—21no—
140C3×C4×D3—21no—
141C3×C4×D3—41no—
142C3×C4×D3—42no—
143C3×C4×D3—42no—
144C3×C4×D3—41no—
145C3×C4×D3—41no—
146C3×C4×D3C2×C812yes—
147C3×C4×D3M1612yes—
148C3⋊(C3⋊C8)—41no—
149C3⋊(C3⋊C8)—41no—
150C3×C3⋊C8—41no—
151C3×C3⋊C8—41no—
152C2×C4×D4—31no—
153#431—91no—
154#431—91no—
155D4⋊C8—31no—
156D4⋊C8—91no—
157D4⋊C8—91no—
158D4⋊C8—91no—
159C24×C3—61no—
160C23×D3—21no—
161C2×C3×D4—21no—
162C2×C3×D4—34no—
163C2×C3×D4—31no—
164C2×C3×D4—62no—
165C2×C3×D4—61no—
166C2×C3×D4C4×D311yescharacteristic
167C2×C3×D4C2×Dic311yescharacteristic
168C22×C3×C4—21no—
169C22×C3×C4—21no—
170C22×C3×C4—31no—
171C22×C3×C4—31no—
172C22×C3×C4—31no—
173C22×C3×C4—41no—
174C22×C3×C4—61no—
175C22×C3×C4—61no—
176C22×C3×C4—61no—
177C22×C3×C4—61no—
178C22×C3×C4—122no—
179C22×C3×C4—122no—
180C2×#67—21no—
181C22×Dic3—21no—
182D3×D4—22no—
183D3×D4C3⋊C814yescomplemented
184C2×D12C2×Dic311yescharacteristic
185C2×C4×D3—21no—
186C2×C4×D3—21no—
187C2×C4×D3—21no—
188C2×C4×D3—42no—
189C2×C4×D3—42no—
190C2×C4×D3C2×Dic311yescharacteristic
191C2×C4×D3#6711yescharacteristic
192C2×C4×D3#6711yescharacteristic
193C2×C3×C8—61no—
194C2×C3×C8—61no—
195C3×C4⋊C4—21no—
196C3×C4⋊C4—31no—
197C3×C4⋊C4—61no—
198C3×C4⋊C4C4×D311yescharacteristic
199C3×C4⋊C4C2×Dic311yescharacteristic
200C3×C22⋊C4—21no—
201C3×C22⋊C4—21no—
202C3×C22⋊C4—41no—
203C3×C22⋊C4—61no—
204C3×C22⋊C4—61no—
205C3×C22⋊C4—61no—
206C3×C42—21no—
207C3×C42—31no—
208C3×C42—31no—
209C3×C42—31no—
210C3×C42C22×D311yescharacteristic
211C3×C42C22×D311yescharacteristic
212#217—21no—
213(C2×D3)⋊C4—21no—
214(C2×D3)⋊C4—21no—
215C4⋊Dic3C2×Dic311yescharacteristic
216Dic3⋊C4—21no—
217C4×Dic3C2×Dic311yescharacteristic
218C4×Dic3#6711yescharacteristic
219C4×Dic3#6711yescharacteristic
220C2×C3⋊C8—21no—
221C2×C3⋊C8—21no—
222C2×C3⋊C8—61no—
223C2×C3⋊C8—61no—
224C2×C3⋊C8—61no—
225C2×C3⋊C8—61no—
226C2×C3⋊C8—121no—
227C2×C3⋊C8—121no—
228C22×C32—22no—
229C22×C32—41no—
230C22×C32—41no—
231C22×C32C2×C22⋊C411yescharacteristic
232C2×C3×D3—21no—
233C2×C3×D3—21no—
234C2×C3×D3—22no—
235C2×C3×D3—48no—
236C2×C3×D3—41no—
237C2×C3×D3—41no—
238C2×C3×D3C22⋊C812yes—
239C32×C4—21no—
240C32×C4—41no—
241C32×C4C22×C811yescharacteristic
242C32×C4C2×M1611yescharacteristic
243C32×C4AGL(1,ℤ/8)11yescharacteristic
244C32×C4AGL(1,ℤ/8)11yescharacteristic
245C3×Dic3—21no—
246C3×Dic3—21no—
247C3×Dic3—41no—
248C3×Dic3C22⋊C812yes—
249C22×D4—31no—
250C23×C4—61no—
251C4×D4—31no—
252C4×D4—31no—
253C4×D4—31no—
254C4×D4—61no—
255C4×D4—61no—
256C4×D4D3211yescharacteristic
257C2×C4⋊C4—31no—
258C2×C22⋊C4—61no—
259C2×C42—31no—
260C4⋊C8—31no—
261C4⋊C8—91no—
262C4⋊C8—181no—
263C22⋊C8—181no—
264C22⋊C8—181no—
265C4×C8—31no—
266C4×C8—91no—
267C4×C8—181no—
268C23×C3—21no—
269C23×C3—21no—
270C23×C3—31no—
271C23×C3—41no—
272C23×C3—64no—
273C23×C3—61no—
274C23×C3—122no—
275C23×C3—122no—
276C22×D3—21no—
277C22×D3—24no—
278C22×D3—42no—
279C22×D3—42no—
280C22×D3#21711yescharacteristic
281C3×D4—21no—
282C3×D4—21no—
283C3×D4—22no—
284C3×D4—32no—
285C3×D4—41no—
286C3×D4—64no—
287C3×D4—61no—
288C3×D4D3×C812yes—
289C3×D4C2×C3⋊C812yes—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—21no—
295C2×C3×C4—31no—
296C2×C3×C4—32no—
297C2×C3×C4—32no—
298C2×C3×C4—31no—
299C2×C3×C4—31no—
300C2×C3×C4—41no—
301C2×C3×C4—41no—
302C2×C3×C4—41no—
303C2×C3×C4—41no—
304C2×C3×C4—41no—
305C2×C3×C4—61no—
306C2×C3×C4—61no—
307C2×C3×C4—61no—
308C2×C3×C4—81no—
309C2×C3×C4—81no—
310C2×C3×C4—121no—
311C2×C3×C4—122no—
312C2×C3×C4—122no—
313C2×C3×C4—122no—
314C2×C3×C4—121no—
315C2×C3×C4—121no—
316C2×C3×C4C2×C4×D311yescharacteristic
317C2×C3×C4D3×D411yescharacteristic
318C2×C3×C4D3×D411yescharacteristic
319C2×C3×C4C22×Dic311yescharacteristic
320C2×C3×C4C2×#6711yescharacteristic
321C2×C3×C4C2×#6711yescharacteristic
322#67—24no—
323C2×Dic3—21no—
324C2×Dic3—42no—
325C2×Dic3#21711yescharacteristic
326C2×Dic3#21711yescharacteristic
327C2×Dic3#21711yescharacteristic
328D12—21no—
329D12C2×C3⋊C812yes—
330C4×D3—21no—
331C4×D3—21no—
332C4×D3—41no—
333C4×D3—42no—
334C4×D3—42no—
335C4×D3—41no—
336C4×D3—41no—
337C4×D3C2×C3⋊C812yes—
338C4×D3#20812yes—
339C3×C8—121no—
340C3×C8—121no—
341C3⋊C8—41no—
342C3⋊C8—41no—
343C3⋊C8—121no—
344C3⋊C8—121no—
345C3⋊C8—122no—
346C3⋊C8—121no—
347C3⋊C8—121no—
348C3⋊C8—241no—
349C2×C32—42no—
350C2×C32C2×C22⋊C811yescharacteristic
351C2×C32#41811yescharacteristic
352C2×C32#42111yescharacteristic
353C3×D3—22no—
354C3×D3—42no—
355C24—61no—
356C2×D4—34no—
357C2×D4—31no—
358C2×D4—62no—
359C2×D4—61no—
360C2×D4D3×Dic311yescharacteristic
361C22×C4—21no—
362C22×C4—31no—
363C22×C4—31no—
364C22×C4—31no—
365C22×C4—61no—
366C22×C4—61no—
367C22×C4—61no—
368C22×C4—61no—
369C22×C4—122no—
370C22×C4—122no—
371C2×C8—61no—
372C2×C8—61no—
373C2×C8—181no—
374C2×C8—181no—
375C4⋊C4—31no—
376C4⋊C4—61no—
377C4⋊C4D3×Dic311yescharacteristic
378C22⋊C4—21no—
379C22⋊C4—61no—
380C22⋊C4—61no—
381C22⋊C4—61no—
382C42—31no—
383C42—31no—
384C42—31no—
385C42C2×D3211yescharacteristic
386C22×C3—22no—
387C22×C3—22no—
388C22×C3—21no—
389C22×C3—32no—
390C22×C3—42no—
391C22×C3—41no—
392C22×C3—41no—
393C22×C3—41no—
394C22×C3—41no—
395C22×C3—61no—
396C22×C3—61no—
397C22×C3—62no—
398C22×C3—81no—
399C22×C3—81no—
400C22×C3—128no—
401C22×C3—121no—
402C22×C3—121no—
403C22×C3D3×C22⋊C411yescharacteristic
404C22×C3C2×#21711yescharacteristic
405C2×D3—21no—
406C2×D3—21no—
407C2×D3—22no—
408C2×D3—48no—
409C2×D3—41no—
410C2×D3—41no—
411C2×D3#83012yes—
412C3×C4—21no—
413C3×C4—21no—
414C3×C4—21no—
415C3×C4—21no—
416C3×C4—21no—
417C3×C4—21no—
418C3×C4—32no—
419C3×C4—41no—
420C3×C4—41no—
421C3×C4—41no—
422C3×C4—61no—
423C3×C4—61no—
424C3×C4—81no—
425C3×C4—121no—
426C3×C4C2×D3×C811yescharacteristic
427C3×C4D3×M1611yescharacteristic
428C3×C4#91111yescharacteristic
429C3×C4#91411yescharacteristic
430C3×C4C22×C3⋊C811yescharacteristic
431C3×C4C2×#20811yescharacteristic
432C3×C4#93211yescharacteristic
433C3×C4#93211yescharacteristic
434Dic3—21no—
435Dic3—21no—
436Dic3—41no—
437Dic3#83012yes—
438C32#147811yescharacteristic, complemented, Sylow
439C23—21no—
440C23—31no—
441C23—64no—
442C23—61no—
443C23—122no—
444C23—122no—
445D4—21no—
446D4—32no—
447D4—64no—
448D4—61no—
449D4D3×C3⋊C812yes—
450C2×C4—21no—
451C2×C4—31no—
452C2×C4—32no—
453C2×C4—32no—
454C2×C4—31no—
455C2×C4—31no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—61no—
459C2×C4—61no—
460C2×C4—61no—
461C2×C4—121no—
462C2×C4—122no—
463C2×C4—122no—
464C2×C4—122no—
465C2×C4—121no—
466C2×C4—121no—
467C2×C4C2×D3×Dic311yescharacteristic
468C2×C4D3×#6711yescharacteristic
469C2×C4D3×#6711yescharacteristic
470C8—121no—
471C8—121no—
472C8—361no—
473C8—361no—
474C2×C3—21no—
475C2×C3—21no—
476C2×C3—21no—
477C2×C3—42no—
478C2×C3—42no—
479C2×C3—62no—
480C2×C3—82no—
481C2×C3—122no—
482C2×C3D3×C22⋊C811yescharacteristic
483C2×C3#477011yescharacteristic
484C2×C3#482111yescharacteristic
485C2×C3C2×#83011yescharacteristic
486C2×C3#521511yescharacteristic
487C2×C3#523611yescharacteristic
488D3—22no—
489D3—42no—
490C22—22no—
491C22—32no—
492C22—41no—
493C22—41no—
494C22—61no—
495C22—61no—
496C22—62no—
497C22—128no—
498C22—121no—
499C22—121no—
500C22D3×#21711yescharacteristic
501C4—21no—
502C4—32no—
503C4—41no—
504C4—61no—
505C4—61no—
506C4—121no—
507C4C2×D3×C3⋊C811yescharacteristic
508C4D3×#20811yescharacteristic
509C4#6393211yescharacteristic
510C4#6393411yescharacteristic
511C3—21no—
512C3#6816711yescharacteristic, complemented
513C3#7159711yescharacteristic, complemented
514C2—42no—
515C2—62no—
516C2—122no—
517C2D3×#83011yescharacteristic
518C2#1059142111yescharacteristic
519C2#1059167011yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC32×C4C22×C8
FrattiniC42C2×D32
FittingC32×C4×D4C22
socleC22×C32C2×C22⋊C4
prime radicalC2×C3×D3×D4C4
cosocleC32×C42C23
hypercenterC4×D4D32
hypocenterC32#1478
LCSG ▷ 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. #10590261C2semidirect
3. #10590248C2semidirect
4. D4⋊(C3⋊(C3⋊C8))C2semidirect
5. C3×D4⋊(C3⋊C8)C2semidirect
6. #10589081C2semidirect
7. #10589080C2semidirect
21. C4⋊(C3⋊(C3⋊C8))C22semidirect
22. C4×C3⋊(C3⋊C8)C22semidirect
23. C3×C4⋊(C3⋊C8)C22semidirect
24. C3×C4×C3⋊C8C22semidirect
41. D4⋊(C3⋊C8)D3semidirect
50. C3×D3×D4C8semidirect
111. C4⋊(C3⋊C8)C2×D3semidirect
116. C4×C3⋊C8C2×D3semidirect
183. D3×D4C3⋊C8semidirect
438. C32#1478semidirect
512. C3#68167semidirect
513. C3#71597semidirect

Maximal subgroups

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

subgroupindex
C3×C4×D3×D42
#105902612
#105902482
D4⋊(C3⋊(C3⋊C8))2
C3×D4⋊(C3⋊C8)2
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