Finite Group Databasebeta

← #11774342

Subgroups — #11774342

Order 1152.

531 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×D3×Q8C211yesmaximal, characteristic
2#10590261C211yesmaximal, characteristic
3#10590248C211yesmaximal, characteristic
4#10589401C211yesmaximal, characteristic, complemented
5C3×#4535C211yesmaximal, characteristic, complemented
6#10589084C211yesmaximal, characteristic, complemented
7#10589083C211yesmaximal, characteristic, complemented
8#71621—31nomaximal
9#68231—31nomaximal
10C2×C3×D3×Q8C411yescharacteristic
11C32×C4×Q8C2211yescharacteristic
12C3×Q8×Dic3C411yescharacteristic
13C3×D3×C4⋊C4—21no—
14C3×D3×C4⋊C4C411yescharacteristic
15C3×#887—21no—
16C3×#887C411yescharacteristic
17C3×C42×D3—21no—
18C3×C42×D3C2211yescharacteristic
19C3×C4×Dic6—21no—
20C3×C4×Dic6C2211yescharacteristic
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—
28Dic3×C3⋊C8—21no—
29C2×C3×C4×Q8—31no—
30C4×D3×Q8D311yescharacteristic
31#4925—31no—
32#4925—31no—
33#4833—31no—
34#4685—31no—
35C3×Q8⋊C8—31no—
36#4535—31no—
37#4535—31no—
38#4535—31no—
39#4535—31no—
40#4535—61no—
41#4535D311yescharacteristic, complemented
42#4484—31no—
43#4456—31no—
44C2×C32×Q8C2×C411yescharacteristic
45C3×D3×Q8—22no—
46C3×D3×Q8C814yescomplemented
47C2×C3×C4×D3—21no—
48C2×C3×C4×D3—21no—
49C2×C3×C4×D3C2×C411yescharacteristic
50C2×C3×C4×D3D411yescharacteristic
51C2×C3×C4×D3D411yescharacteristic
52C2×C3×Dic6—21no—
53C2×C3×Dic6C2×C411yescharacteristic
54C32×C4⋊C4—21no—
55C32×C4⋊C4C2×C411yescharacteristic
56C32×C42—21no—
57C32×C42C2311yescharacteristic
58C2×C3⋊(C3⋊C8)—21no—
59C2×C3⋊(C3⋊C8)—21no—
60C3×C4⋊Dic3—21no—
61C3×C4⋊Dic3C2×C411yescharacteristic
62C3×Dic3⋊C4—21no—
63C3×Dic3⋊C4—21no—
64C3×Dic3⋊C4—21no—
65C3×C4×Dic3—21no—
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#1479—91noSylow
74C22×C3×Q8—31no—
75C2×D3×Q8Dic311yescharacteristic
76C3×C4×Q8—21no—
77C3×C4×Q8—31no—
78C3×C4×Q8—31no—
79C3×C4×Q8—31no—
80C3×C4×Q8—61no—
81C3×C4×Q8—61no—
82C3×C4×Q8C2×D311yescharacteristic
83C3×C4×Q8C2×D311yescharacteristic
84C2×C3×C4⋊C4—31no—
85C2×C3×C4⋊C4—61no—
86C2×C3×C42—31no—
87C2×C3×C42—61no—
88Q8×Dic3Dic311yescharacteristic
89D3×C4⋊C4—21no—
90D3×C4⋊C4Dic311yescharacteristic
91#887—21no—
92#887Dic311yescharacteristic
93C42×D3—21no—
94C42×D3C2×D311yescharacteristic
95C4×Dic6—21no—
96C4×Dic6C2×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—
103Dic3⋊C8—61no—
104C8×Dic3—61no—
105C4⋊(C3⋊C8)—31no—
106C4⋊(C3⋊C8)—31no—
107C4⋊(C3⋊C8)—61no—
108C4⋊(C3⋊C8)—61no—
109C4⋊(C3⋊C8)C2×D311yescharacteristic
110C4×C3⋊C8—31no—
111C4×C3⋊C8—31no—
112C4×C3⋊C8—61no—
113C4×C3⋊C8—61no—
114C4×C3⋊C8C2×D311yescharacteristic
115C22×C3×D3C22⋊C411yescharacteristic
116C32×Q8—21no—
117C32×Q8C2×C812yes—
118C2×C32×C4—21no—
119C2×C32×C4—21no—
120C2×C32×C4C22×C411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C3×Dic3—21no—
124C2×C3×Dic3—21no—
125C2×C3×Dic3C22⋊C411yescharacteristic
126C2×C3×Dic3C22⋊C411yescharacteristic
127C2×C3×Dic3C22⋊C411yescharacteristic
128C3×C4×D3—24no—
129C3×C4×D3—21no—
130C3×C4×D3—21no—
131C3×C4×D3—41no—
132C3×C4×D3—42no—
133C3×C4×D3C2×C812yes—
134C3×C4×D3M1612yes—
135C3×Dic6—21no—
136C3×Dic6—24no—
137C3×Dic6C2×C812yes—
138C3⋊(C3⋊C8)—41no—
139C3⋊(C3⋊C8)—41no—
140C3×C3⋊C8—41no—
141C3×C3⋊C8—41no—
142C2×C4×Q8—31no—
143#431—91no—
144#431—91no—
145Q8⋊C8—31no—
146Q8⋊C8—91no—
147Q8⋊C8—91no—
148Q8⋊C8—91no—
149C2×C3×Q8—21no—
150C2×C3×Q8—34no—
151C2×C3×Q8—31no—
152C2×C3×Q8—61no—
153C2×C3×Q8—62no—
154C2×C3×Q8C4×D311yescharacteristic
155C2×C3×Q8C2×Dic311yescharacteristic
156C22×C3×C4—31no—
157C22×C3×C4—31no—
158C22×C3×C4—31no—
159C22×C3×C4—61no—
160C22×C3×C4—61no—
161D3×Q8—22no—
162D3×Q8C3⋊C814yescomplemented
163C2×C4×D3—21no—
164C2×C4×D3—21no—
165C2×C4×D3C2×Dic311yescharacteristic
166C2×C4×D3#6711yescharacteristic
167C2×C4×D3#6711yescharacteristic
168C2×Dic6—21no—
169C2×Dic6C2×Dic311yescharacteristic
170C2×C3×C8—61no—
171C2×C3×C8—61no—
172C3×C4⋊C4—21no—
173C3×C4⋊C4—21no—
174C3×C4⋊C4—21no—
175C3×C4⋊C4—31no—
176C3×C4⋊C4—41no—
177C3×C4⋊C4—61no—
178C3×C4⋊C4—61no—
179C3×C4⋊C4—61no—
180C3×C4⋊C4—61no—
181C3×C4⋊C4C4×D311yescharacteristic
182C3×C4⋊C4C2×Dic311yescharacteristic
183C3×C42—21no—
184C3×C42—21no—
185C3×C42—21no—
186C3×C42—31no—
187C3×C42—31no—
188C3×C42—31no—
189C3×C42—41no—
190C3×C42—61no—
191C3×C42—61no—
192C3×C42—61no—
193C3×C42C22×D311yescharacteristic
194C3×C42C22×D311yescharacteristic
195C4⋊Dic3—21no—
196C4⋊Dic3C2×Dic311yescharacteristic
197Dic3⋊C4—21no—
198Dic3⋊C4—21no—
199Dic3⋊C4—21no—
200C4×Dic3—21no—
201C4×Dic3—21no—
202C4×Dic3—21no—
203C4×Dic3C2×Dic311yescharacteristic
204C4×Dic3#6711yescharacteristic
205C4×Dic3#6711yescharacteristic
206C2×C3⋊C8—21no—
207C2×C3⋊C8—21no—
208C2×C3⋊C8—61no—
209C2×C3⋊C8—61no—
210C2×C3⋊C8—61no—
211C2×C3⋊C8—61no—
212C2×C3⋊C8—121no—
213C2×C3⋊C8—121no—
214C22×C32C2×C22⋊C411yescharacteristic
215C2×C3×D3—21no—
216C2×C3×D3—21no—
217C2×C3×D3C22⋊C812yes—
218C32×C4—22no—
219C32×C4—21no—
220C32×C4—41no—
221C32×C4C22×C811yescharacteristic
222C32×C4C2×M1611yescharacteristic
223C32×C4#13711yescharacteristic
224C32×C4#13711yescharacteristic
225C3×Dic3—22no—
226C3×Dic3—21no—
227C3×Dic3—21no—
228C3×Dic3—41no—
229C3×Dic3C22⋊C812yes—
230C22×Q8—31no—
231C4×Q8—31no—
232C4×Q8—31no—
233C4×Q8—31no—
234C4×Q8—61no—
235C4×Q8—61no—
236C4×Q8D3211yescharacteristic
237C2×C4⋊C4—31no—
238C2×C4⋊C4—61no—
239C2×C42—31no—
240C2×C42—61no—
241C4⋊C8—31no—
242C4⋊C8—91no—
243C4⋊C8—181no—
244C22⋊C8—181no—
245C22⋊C8—181no—
246C4×C8—31no—
247C4×C8—91no—
248C4×C8—181no—
249C23×C3—31no—
250C22×D3#21711yescharacteristic
251C3×Q8—21no—
252C3×Q8—21no—
253C3×Q8—22no—
254C3×Q8—32no—
255C3×Q8—41no—
256C3×Q8—64no—
257C3×Q8—61no—
258C3×Q8D3×C812yes—
259C3×Q8C2×C3⋊C812yes—
260C2×C3×C4—21no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—21no—
266C2×C3×C4—21no—
267C2×C3×C4—31no—
268C2×C3×C4—32no—
269C2×C3×C4—32no—
270C2×C3×C4—31no—
271C2×C3×C4—31no—
272C2×C3×C4—41no—
273C2×C3×C4—41no—
274C2×C3×C4—64no—
275C2×C3×C4—61no—
276C2×C3×C4—61no—
277C2×C3×C4—61no—
278C2×C3×C4—61no—
279C2×C3×C4—121no—
280C2×C3×C4—122no—
281C2×C3×C4C2×C4×D311yescharacteristic
282C2×C3×C4D3×D411yescharacteristic
283C2×C3×C4D3×D411yescharacteristic
284C2×C3×C4C22×Dic311yescharacteristic
285C2×C3×C4C2×#6711yescharacteristic
286C2×C3×C4C2×#6711yescharacteristic
287C2×Dic3—21no—
288C2×Dic3—21no—
289C2×Dic3#21711yescharacteristic
290C2×Dic3#21711yescharacteristic
291C2×Dic3#21711yescharacteristic
292C4×D3—24no—
293C4×D3—21no—
294C4×D3—21no—
295C4×D3—41no—
296C4×D3—42no—
297C4×D3C2×C3⋊C812yes—
298C4×D3#20812yes—
299Dic6—21no—
300Dic6—24no—
301Dic6C2×C3⋊C812yes—
302C3×C8—121no—
303C3×C8—121no—
304C3⋊C8—41no—
305C3⋊C8—41no—
306C3⋊C8—121no—
307C3⋊C8—121no—
308C3⋊C8—122no—
309C3⋊C8—121no—
310C3⋊C8—121no—
311C3⋊C8—241no—
312C2×C32C2×C22⋊C811yescharacteristic
313C2×C32#41911yescharacteristic
314C2×C32#42111yescharacteristic
315C3×D3—22no—
316C2×Q8—34no—
317C2×Q8—31no—
318C2×Q8—61no—
319C2×Q8—62no—
320C2×Q8D3×Dic311yescharacteristic
321C22×C4—31no—
322C22×C4—31no—
323C22×C4—31no—
324C22×C4—61no—
325C22×C4—61no—
326C2×C8—61no—
327C2×C8—61no—
328C2×C8—181no—
329C2×C8—181no—
330C4⋊C4—21no—
331C4⋊C4—31no—
332C4⋊C4—61no—
333C4⋊C4—61no—
334C4⋊C4—61no—
335C4⋊C4—61no—
336C4⋊C4D3×Dic311yescharacteristic
337C42—21no—
338C42—31no—
339C42—31no—
340C42—31no—
341C42—61no—
342C42—61no—
343C42—61no—
344C42C2×D3211yescharacteristic
345C22×C3—21no—
346C22×C3—32no—
347C22×C3—61no—
348C22×C3—61no—
349C22×C3D3×C22⋊C411yescharacteristic
350C22×C3C2×#21711yescharacteristic
351C2×D3—21no—
352C2×D3—21no—
353C2×D3#83012yes—
354C3×C4—22no—
355C3×C4—22no—
356C3×C4—21no—
357C3×C4—21no—
358C3×C4—21no—
359C3×C4—21no—
360C3×C4—21no—
361C3×C4—21no—
362C3×C4—32no—
363C3×C4—41no—
364C3×C4—42no—
365C3×C4—41no—
366C3×C4—41no—
367C3×C4—62no—
368C3×C4—61no—
369C3×C4—61no—
370C3×C4—81no—
371C3×C4—121no—
372C3×C4C2×D3×C811yescharacteristic
373C3×C4D3×M1611yescharacteristic
374C3×C4#91511yescharacteristic
375C3×C4#91811yescharacteristic
376C3×C4C22×C3⋊C811yescharacteristic
377C3×C4C2×#20811yescharacteristic
378C3×C4#94211yescharacteristic
379C3×C4#94211yescharacteristic
380Dic3—22no—
381Dic3—21no—
382Dic3—21no—
383Dic3—41no—
384Dic3#83012yes—
385C32#147911yescharacteristic, complemented, Sylow
386C23—31no—
387Q8—21no—
388Q8—32no—
389Q8—64no—
390Q8—61no—
391Q8D3×C3⋊C812yes—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—31no—
395C2×C4—32no—
396C2×C4—32no—
397C2×C4—31no—
398C2×C4—31no—
399C2×C4—64no—
400C2×C4—61no—
401C2×C4—61no—
402C2×C4—61no—
403C2×C4—61no—
404C2×C4—121no—
405C2×C4—122no—
406C2×C4C2×D3×Dic311yescharacteristic
407C2×C4D3×#6711yescharacteristic
408C2×C4D3×#6711yescharacteristic
409C8—121no—
410C8—121no—
411C8—361no—
412C8—361no—
413C2×C3—21no—
414C2×C3—21no—
415C2×C3—21no—
416C2×C3—62no—
417C2×C3D3×C22⋊C811yescharacteristic
418C2×C3#480211yescharacteristic
419C2×C3#482111yescharacteristic
420C2×C3C2×#83011yescharacteristic
421C2×C3#522511yescharacteristic
422C2×C3#523611yescharacteristic
423D3—22no—
424C22—32no—
425C22—61no—
426C22—61no—
427C22D3×#21711yescharacteristic
428C4—22no—
429C4—21no—
430C4—32no—
431C4—41no—
432C4—61no—
433C4—62no—
434C4—61no—
435C4—121no—
436C4C2×D3×C3⋊C811yescharacteristic
437C4D3×#20811yescharacteristic
438C4#6394611yescharacteristic
439C4#6394811yescharacteristic
440C3—21no—
441C3#6823111yescharacteristic, complemented
442C3#7162111yescharacteristic, complemented
443C2—62no—
444C2D3×#83011yescharacteristic
445C2#1059155711yescharacteristic
446C2#1059167011yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC32×C4C22×C8
FrattiniC42C2×D32
FittingC32×C4×Q8C22
socleC22×C32C2×C22⋊C4
prime radicalC22×C3×D3C22⋊C4
cosocleC32×C42C23
hypercenterC4×Q8D32
hypocenterC32#1479
LCSG ▷ 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
4. #10589401C2semidirect
5. C3×#4535C2semidirect
6. #10589084C2semidirect
7. #10589083C2semidirect
41. #4535D3semidirect
46. C3×D3×Q8C8semidirect
162. D3×Q8C3⋊C8semidirect
385. C32#1479semidirect
441. C3#68231semidirect
442. C3#71621semidirect

Maximal subgroups

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

subgroupindex
C3×C4×D3×Q82
#105902612
#105902482
#105894012
C3×#45352
#105890842
#105890832
#716213
#682313