Finite Group Databasebeta

← #11774628

Subgroups — #11774628

Order 1152.

527 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×#239C211yesmaximal, characteristic
2#10590263C211yesmaximal, characteristic, complemented
3#10590261C211yesmaximal, characteristic, complemented
4#10589401C211yesmaximal, characteristic, complemented
5C3×#4535C211yesmaximal, characteristic, complemented
6#10589081C211yesmaximal, characteristic, complemented
7#10589080C211yesmaximal, characteristic, complemented
8#71640—31nomaximal
9#68237—31nomaximal
10C2×C3×#239C411yescharacteristic
11C32×C4×Q8C2211yescharacteristic
12C3×Q8×Dic3C411yescharacteristic
13C3×#893—21no—
14C3×#893C411yescharacteristic
15C3×#892—21no—
16C3×#892C411yescharacteristic
17C3×C4×D12—21no—
18C3×C4×D12C2211yescharacteristic
19C3×C42×D3—21no—
20C3×C42×D3C2211yescharacteristic
21C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
22C4×C3⋊(C3⋊C8)C2211yescharacteristic
23C3×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4×C3⋊C8C2211yescharacteristic
25Dic3⋊(C3⋊C8)—21no—
26(C2×D3)⋊(C3⋊C8)—21no—
27(C2×D3)⋊(C3⋊C8)—21no—
28#63554—21no—
29C3×C4×#41—31no—
30C4×#239D311yescharacteristic
31#4926—31no—
32#4925—31no—
33#4835—31no—
34#4685—31no—
35C3×Q8⋊C8—31no—
36#4535—31no—
37#4535—31no—
38#4535—61no—
39#4535D311yescharacteristic, complemented
40D4⋊(C3⋊C8)—31no—
41D4⋊(C3⋊C8)—31no—
42#4483—31no—
43#4459—31no—
44C2×C32×Q8C2×C411yescharacteristic
45C3×#239—22no—
46C3×#239—22no—
47C2×C3×D12—21no—
48C2×C3×D12C2×C411yescharacteristic
49C2×C3×C4×D3—21no—
50C2×C3×C4×D3—21no—
51C2×C3×C4×D3—21no—
52C2×C3×C4×D3C2×C411yescharacteristic
53C2×C3×C4×D3D411yescharacteristic
54C2×C3×C4×D3D411yescharacteristic
55C32×C4⋊C4—21no—
56C32×C4⋊C4C2×C411yescharacteristic
57C32×C42—21no—
58C32×C42C2311yescharacteristic
59C2×C3⋊(C3⋊C8)—21no—
60C2×C3⋊(C3⋊C8)—21no—
61C3×(C2×D3)⋊C4—21no—
62C3×(C2×D3)⋊C4—21no—
63C3×(C2×D3)⋊C4—21no—
64C3×C4⋊Dic3—21no—
65C3×C4⋊Dic3C2×C411yescharacteristic
66C3×C4×Dic3—21no—
67C3×C4×Dic3—21no—
68C3×C4×Dic3C2×C411yescharacteristic
69C3×C4×Dic3D411yescharacteristic
70C3×C4×Dic3D411yescharacteristic
71C2×C3×C3⋊C8—21no—
72C2×C3×C3⋊C8—21no—
73#1488—91noSylow
74C2×C3×#41—31no—
75C2×#239Dic311yescharacteristic
76C3×C4×Q8—21no—
77C3×C4×Q8—31no—
78C3×C4×Q8C2×D311yescharacteristic
79C3×C4×Q8C2×D311yescharacteristic
80C3×C4×D4—31no—
81C3×C4×D4—31no—
82C3×C4×D4—61no—
83C3×C4×D4—61no—
84C3×#117—31no—
85C3×#117—61no—
86C2×C3×C42—31no—
87C2×C3×C42—61no—
88Q8×Dic3Dic311yescharacteristic
89#893—21no—
90#893Dic311yescharacteristic
91#892—21no—
92#892Dic311yescharacteristic
93C4×D12—21no—
94C4×D12C2×D311yescharacteristic
95C42×D3—21no—
96C42×D3C2×D311yescharacteristic
97C3×C4⋊C8—31no—
98C3×C4×C8—31no—
99#830—61no—
100#830—61no—
101(C2×D3)⋊C8—61no—
102(C2×D3)⋊C8—61no—
103#815—61no—
104Dic3⋊C8—61no—
105C4⋊(C3⋊C8)—31no—
106C4⋊(C3⋊C8)—31no—
107C4⋊(C3⋊C8)—61no—
108C4⋊(C3⋊C8)—61no—
109C4⋊(C3⋊C8)C2×D311yescharacteristic
110#803—61no—
111C4×C3⋊C8—31no—
112C4×C3⋊C8—31no—
113C4×C3⋊C8—61no—
114C4×C3⋊C8C2×D311yescharacteristic
115C22×C3×D3—21no—
116C22×C3×D3C22⋊C411yescharacteristic
117C32×Q8—21no—
118C32×Q8M1612yes—
119C2×C32×C4—21no—
120C2×C32×C4—21no—
121C2×C32×C4C22×C411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C3×Dic3—21no—
125C2×C3×Dic3C22⋊C411yescharacteristic
126C2×C3×Dic3C22⋊C411yescharacteristic
127C2×C3×Dic3C22⋊C411yescharacteristic
128C3×D12—24no—
129C3×D12—21no—
130C3×D12M1612yes—
131C3×C4×D3—24no—
132C3×C4×D3—21no—
133C3×C4×D3—21no—
134C3×C4×D3—21no—
135C3×C4×D3—21no—
136C3×C4×D3—41no—
137C3×C4×D3—42no—
138C3×C4×D3—41no—
139C3×C4×D3—41no—
140C3⋊(C3⋊C8)—41no—
141C3⋊(C3⋊C8)—41no—
142C3×C3⋊C8—41no—
143C3×C3⋊C8—41no—
144C4×#41—31no—
145#432—91no—
146#431—91no—
147Q8⋊C8—31no—
148Q8⋊C8—91no—
149D4⋊C8—91no—
150D4⋊C8—91no—
151C3×#41—62no—
152C3×#41—62no—
153C2×C3×Q8—21no—
154C2×C3×Q8C4×D311yescharacteristic
155C2×C3×Q8C2×Dic311yescharacteristic
156C2×C3×D4—31no—
157C2×C3×D4—61no—
158C22×C3×C4—31no—
159C22×C3×C4—31no—
160C22×C3×C4—31no—
161C22×C3×C4—61no—
162C22×C3×C4—61no—
163C22×C3×C4—61no—
164#239—22no—
165#239—22no—
166C2×D12—21no—
167C2×D12C2×Dic311yescharacteristic
168C2×C4×D3—21no—
169C2×C4×D3—21no—
170C2×C4×D3—21no—
171C2×C4×D3C2×Dic311yescharacteristic
172C2×C4×D3#6711yescharacteristic
173C2×C4×D3#6711yescharacteristic
174C2×C3×C8—61no—
175C2×C3×C8—61no—
176C3×C4⋊C4—21no—
177C3×C4⋊C4—21no—
178C3×C4⋊C4—21no—
179C3×C4⋊C4—31no—
180C3×C4⋊C4—41no—
181C3×C4⋊C4—61no—
182C3×C4⋊C4C4×D311yescharacteristic
183C3×C4⋊C4C2×Dic311yescharacteristic
184C3×C22⋊C4—61no—
185C3×C22⋊C4—61no—
186C3×C22⋊C4—61no—
187C3×C42—21no—
188C3×C42—21no—
189C3×C42—21no—
190C3×C42—31no—
191C3×C42—31no—
192C3×C42—31no—
193C3×C42—41no—
194C3×C42—61no—
195C3×C42—61no—
196C3×C42C22×D311yescharacteristic
197C3×C42C22×D311yescharacteristic
198(C2×D3)⋊C4—21no—
199(C2×D3)⋊C4—21no—
200(C2×D3)⋊C4—21no—
201C4⋊Dic3—21no—
202C4⋊Dic3C2×Dic311yescharacteristic
203C4×Dic3—21no—
204C4×Dic3—21no—
205C4×Dic3C2×Dic311yescharacteristic
206C4×Dic3#6711yescharacteristic
207C4×Dic3#6711yescharacteristic
208C2×C3⋊C8—21no—
209C2×C3⋊C8—21no—
210C2×C3⋊C8—61no—
211C2×C3⋊C8—61no—
212C2×C3⋊C8—61no—
213C2×C3⋊C8—61no—
214C2×C3⋊C8—121no—
215C2×C3⋊C8—121no—
216C22×C32C2×C22⋊C411yescharacteristic
217C2×C3×D3—21no—
218C2×C3×D3—22no—
219C2×C3×D3—21no—
220C2×C3×D3—21no—
221C2×C3×D3—41no—
222C2×C3×D3—41no—
223C32×C4—22no—
224C32×C4—21no—
225C32×C4—41no—
226C32×C4C2×M1611yescharacteristic
227C32×C4C2×M1611yescharacteristic
228C32×C4#13511yescharacteristic
229C32×C4#13511yescharacteristic
230C3×Dic3—21no—
231C3×Dic3—21no—
232C3×Dic3—21no—
233C3×Dic3—41no—
234C2×#41—31no—
235C4×Q8—31no—
236C4×Q8D3211yescharacteristic
237C4×D4—31no—
238C4×D4—31no—
239C4×D4—61no—
240C4×D4—61no—
241#117—31no—
242#117—61no—
243C2×C42—31no—
244C2×C42—61no—
245C4⋊C8—31no—
246C4⋊C8—91no—
247C4⋊C8—181no—
248C22⋊C8—181no—
249C22⋊C8—181no—
250#97—181no—
251C4×C8—31no—
252C4×C8—91no—
253C23×C3—31no—
254C23×C3—61no—
255C22×D3—21no—
256C22×D3#21711yescharacteristic
257C3×Q8—21no—
258C3×Q8—21no—
259C3×Q8—22no—
260C3×Q8—41no—
261C3×Q8ΓL(1,𝔽25)12yes—
262C3×Q8#20812yes—
263C3×D4—32no—
264C3×D4—64no—
265C3×D4—61no—
266C2×C3×C4—21no—
267C2×C3×C4—21no—
268C2×C3×C4—21no—
269C2×C3×C4—21no—
270C2×C3×C4—21no—
271C2×C3×C4—21no—
272C2×C3×C4—21no—
273C2×C3×C4—31no—
274C2×C3×C4—31no—
275C2×C3×C4—31no—
276C2×C3×C4—41no—
277C2×C3×C4—41no—
278C2×C3×C4—64no—
279C2×C3×C4—61no—
280C2×C3×C4—61no—
281C2×C3×C4—61no—
282C2×C3×C4—61no—
283C2×C3×C4—61no—
284C2×C3×C4—121no—
285C2×C3×C4—122no—
286C2×C3×C4—121no—
287C2×C3×C4—121no—
288C2×C3×C4C2×C4×D311yescharacteristic
289C2×C3×C4D3×D411yescharacteristic
290C2×C3×C4D3×D411yescharacteristic
291C2×C3×C4C22×Dic311yescharacteristic
292C2×C3×C4C2×#6711yescharacteristic
293C2×C3×C4C2×#6711yescharacteristic
294C2×Dic3—21no—
295C2×Dic3#21711yescharacteristic
296C2×Dic3#21711yescharacteristic
297C2×Dic3#21711yescharacteristic
298D12—24no—
299D12—21no—
300D12#20812yes—
301C4×D3—24no—
302C4×D3—21no—
303C4×D3—21no—
304C4×D3—21no—
305C4×D3—21no—
306C4×D3—41no—
307C4×D3—42no—
308C4×D3—41no—
309C4×D3—41no—
310C3×C8—121no—
311C3×C8—121no—
312C3⋊C8—41no—
313C3⋊C8—41no—
314C3⋊C8—121no—
315C3⋊C8—121no—
316C3⋊C8—122no—
317C3⋊C8—121no—
318C3⋊C8—121no—
319C3⋊C8—241no—
320C2×C32#40711yescharacteristic
321C2×C32#41611yescharacteristic
322C2×C32#42111yescharacteristic
323C3×D3—41no—
324C3×D3—42no—
325#41—62no—
326#41—62no—
327C2×Q8D3×Dic311yescharacteristic
328C2×D4—31no—
329C2×D4—61no—
330C22×C4—31no—
331C22×C4—31no—
332C22×C4—31no—
333C22×C4—61no—
334C22×C4—61no—
335C22×C4—61no—
336C2×C8—61no—
337C2×C8—61no—
338C2×C8—181no—
339C2×C8—181no—
340C4⋊C4—21no—
341C4⋊C4—31no—
342C4⋊C4—61no—
343C4⋊C4D3×Dic311yescharacteristic
344C22⋊C4—61no—
345C22⋊C4—61no—
346C22⋊C4—61no—
347C42—21no—
348C42—31no—
349C42—31no—
350C42—31no—
351C42—61no—
352C42—61no—
353C42C2×D3211yescharacteristic
354C22×C3—21no—
355C22×C3—62no—
356C22×C3—61no—
357C22×C3—61no—
358C22×C3—61no—
359C22×C3—121no—
360C22×C3—121no—
361C22×C3D3×C22⋊C411yescharacteristic
362C22×C3C2×#21711yescharacteristic
363C2×D3—21no—
364C2×D3—22no—
365C2×D3—21no—
366C2×D3—21no—
367C2×D3—41no—
368C2×D3—41no—
369C3×C4—22no—
370C3×C4—21no—
371C3×C4—22no—
372C3×C4—21no—
373C3×C4—21no—
374C3×C4—21no—
375C3×C4—21no—
376C3×C4—21no—
377C3×C4—41no—
378C3×C4—42no—
379C3×C4—41no—
380C3×C4—41no—
381C3×C4—61no—
382C3×C4—61no—
383C3×C4—61no—
384C3×C4—81no—
385C3×C4—121no—
386C3×C4C2×ΓL(1,𝔽25)11yescharacteristic
387C3×C4D3×M1611yescharacteristic
388C3×C4#91611yescharacteristic
389C3×C4#91911yescharacteristic
390C3×C4C2×#20811yescharacteristic
391C3×C4C2×#20811yescharacteristic
392C3×C4#95011yescharacteristic
393C3×C4#95011yescharacteristic
394Dic3—21no—
395Dic3—21no—
396Dic3—21no—
397Dic3—41no—
398C32#148811yescharacteristic, complemented, Sylow
399C23—31no—
400C23—61no—
401Q8—21no—
402Q8#371112yes—
403D4—32no—
404D4—64no—
405D4—61no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—31no—
409C2×C4—31no—
410C2×C4—31no—
411C2×C4—64no—
412C2×C4—61no—
413C2×C4—61no—
414C2×C4—61no—
415C2×C4—61no—
416C2×C4—61no—
417C2×C4—121no—
418C2×C4—122no—
419C2×C4—121no—
420C2×C4—121no—
421C2×C4C2×D3×Dic311yescharacteristic
422C2×C4D3×#6711yescharacteristic
423C2×C4D3×#6711yescharacteristic
424C8—121no—
425C8—121no—
426C8—361no—
427C8—361no—
428C2×C3—21no—
429C2×C3—21no—
430C2×C3—21no—
431C2×C3—121no—
432C2×C3—122no—
433C2×C3#472611yescharacteristic
434C2×C3#480411yescharacteristic
435C2×C3#482111yescharacteristic
436C2×C3#520711yescharacteristic
437C2×C3#523311yescharacteristic
438C2×C3#523611yescharacteristic
439D3—41no—
440D3—42no—
441C22—61no—
442C22—62no—
443C22—61no—
444C22—61no—
445C22—121no—
446C22—121no—
447C22D3×#21711yescharacteristic
448C4—22no—
449C4—21no—
450C4—41no—
451C4—61no—
452C4—61no—
453C4—61no—
454C4—121no—
455C4D3×#20811yescharacteristic
456C4C2×#371111yescharacteristic
457C4#6394711yescharacteristic
458C4#6394911yescharacteristic
459C3—21no—
460C3#6823711yescharacteristic, complemented
461C3#7164011yescharacteristic, complemented
462C2—121no—
463C2—122no—
464C2#1059115411yescharacteristic
465C2#1059155611yescharacteristic
466C2#1059167011yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4×Q8C22
socleC22×C32C2×C22⋊C4
prime radicalC2×C3×#239C4
cosocleC32×C42C23
hypercenterC4×Q8D32
hypocenterC32#1488
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
2. #10590263C2semidirect
3. #10590261C2semidirect
4. #10589401C2semidirect
5. C3×#4535C2semidirect
6. #10589081C2semidirect
7. #10589080C2semidirect
39. #4535D3semidirect
398. C32#1488semidirect
460. C3#68237semidirect
461. C3#71640semidirect

Maximal subgroups

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

subgroupindex
C3×C4×#2392
#105902632
#105902612
#105894012
C3×#45352
#105890812
#105890802
#716403
#682373