Finite Group Databasebeta

← #11775370

Subgroups — #11775370

Order 1152.

484 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5624C211yesmaximal, characteristic
2#10591206C211yesmaximal, characteristic, complemented
3#10591063C211yesmaximal, characteristic, complemented
4#10589404C211yesmaximal, characteristic, complemented
5C3×#4538C211yesmaximal, characteristic, complemented
6#10589150C211yesmaximal, characteristic
7#10589149C211yesmaximal, characteristic
8#71756—31nomaximal
9#68312—31nomaximal
10C32×C22⋊Q8C2211yescharacteristic
11C3×#947C411yescharacteristic, complemented
12C3×Q8×Dic3C411yescharacteristic, complemented
13C3×#930C2211yescharacteristic
14C2×C3×C4×Dic3C2211yescharacteristic
15C3×#898—21no—
16C3×#893C411yescharacteristic, complemented
17C3×#892—21no—
18C3×#890C411yescharacteristic, complemented
19C3×#886—21no—
20C3×#67⋊C4—21no—
21C2×Dic3⋊Dic3—21no—
22#63658C2211yescharacteristic
23#63657C2211yescharacteristic
24C3×C3⋊#95C2211yescharacteristic
25C3×#830C2211yescharacteristic
26#63579—21no—
27Dic3⋊(C3⋊C8)—21no—
28#63554—21no—
29C3×#529—31no—
30#5624D311yescharacteristic
31#4936—31no—
32#4926—31no—
33#4719—31no—
34#4650—31no—
35C3×#328—31no—
36#4538—31no—
37#4538—31no—
38#4538—61no—
39#4538D311yescharacteristic, complemented
40#4537—31no—
41#4537—31no—
42#4470—31no—
43#4451—31no—
44C2×C32×Q8C2×C411yescharacteristic
45C22×C32×C4C2311yescharacteristic
46C22×C3⋊Dic3—21no—
47C2×C3×#67—21no—
48C22×C3×Dic3—21no—
49C22×C3×Dic3D411yescharacteristic
50C22×C3×Dic3D411yescharacteristic
51C2×C3×D12C2×C411yescharacteristic
52C2×C3×C4×D3—21no—
53C32×C4⋊C4—21no—
54C32×C4⋊C4C2×C411yescharacteristic
55C32×C22⋊C4—21no—
56C2×C3⋊(C3⋊C8)—21no—
57C3×(C2×D3)⋊C4—21no—
58C3×(C2×D3)⋊C4—21no—
59C3×(C2×D3)⋊C4—21no—
60C3×(C2×D3)⋊C4—21no—
61C3×C4⋊Dic3—21no—
62C3×C4⋊Dic3—21no—
63C3×C4⋊Dic3C2×C411yescharacteristic
64C3×Dic3⋊C4—21no—
65C3×C4×Dic3—21no—
66C3×C4×Dic3C2×C411yescharacteristic
67C3×C4×Dic3C2×C411yescharacteristic
68C3×C4×Dic3D411yescharacteristic
69C3×C4×Dic3D411yescharacteristic
70C2×C3×C3⋊C8—21no—
71Dic3⋊Dic3—42no—
72#1512—91noSylow
73C3×#126—61no—
74C3×#125—31no—
75C3×#124—31no—
76C3×#123—61no—
77C3×C22⋊Q8—21no—
78C3×C22⋊Q8C2×D311yescharacteristic
79C3×C22⋊Q8C2×D311yescharacteristic
80C3×#121—31no—
81C3×C4×Q8—31no—
82C3×C4×D4—31no—
83C3×C4×D4—61no—
84C3×#117—61no—
85C2×C3×C42—31no—
86#947Dic311yescharacteristic, complemented
87Q8×Dic3Dic311yescharacteristic, complemented
88#930C2×D311yescharacteristic
89C2×C4⋊Dic3—61no—
90C2×Dic3⋊C4—61no—
91C2×C4×Dic3C2×D311yescharacteristic
92#898—21no—
93#893Dic311yescharacteristic, complemented
94#892—21no—
95#890Dic311yescharacteristic, complemented
96#886—21no—
97#67⋊C4—21no—
98C3×C22⋊C8—31no—
99C3×#95—31no—
100C3⋊#95—31no—
101C3⋊#95—31no—
102C3⋊#95—61no—
103C3⋊#95—61no—
104C3⋊#95—61no—
105C3⋊#95C2×D311yescharacteristic
106#830—31no—
107#830—31no—
108#830—61no—
109#830C2×D311yescharacteristic
110#815—61no—
111Dic3⋊C8—61no—
112C4⋊(C3⋊C8)—61no—
113#803—61no—
114C23×C32C2×D411yescharacteristic
115C22×C3×D3—21no—
116C32×Q8—41no—
117C2×C32×C4—21no—
118C2×C32×C4—21no—
119C2×C32×C4—41no—
120C2×C32×C4C22×C411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C3⋊Dic3—41no—
123C2×C3⋊Dic3—41no—
124C2×C3⋊Dic3—41no—
125C3×#67—41no—
126C3×#67—41no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3—21no—
129C2×C3×Dic3—21no—
130C2×C3×Dic3—41no—
131C2×C3×Dic3—41no—
132C2×C3×Dic3—41no—
133C2×C3×Dic3—41no—
134C2×C3×Dic3C22⋊C411yescharacteristic
135C2×C3×Dic3C22⋊C411yescharacteristic
136C2×C3×Dic3C22⋊C411yescharacteristic
137C2×C3×Dic3C22⋊C411yescharacteristic
138C3×D12—41no—
139C3×C4×D3—42no—
140C3⋊(C3⋊C8)—41no—
141C3×C3⋊C8—41no—
142#529—31no—
143#432—91no—
144#382—91no—
145#328—31no—
146#328—91no—
147#327—91no—
148#327—91no—
149C2×C3×Q8—21no—
150C2×C3×Q8C4×D311yescharacteristic
151C2×C3×Q8C2×Dic311yescharacteristic
152C2×C3×D4—31no—
153C2×C3×D4—61no—
154C22×C3×C4—21no—
155C22×C3×C4—31no—
156C22×C3×C4—31no—
157C22×C3×C4—61no—
158C22×C3×C4—61no—
159C22×C3×C4C22×D311yescharacteristic
160C22×C3×C4C22×D311yescharacteristic
161C2×#67—21no—
162C22×Dic3—21no—
163C22×Dic3—61no—
164C22×Dic3—61no—
165C22×Dic3—121no—
166C22×Dic3#6711yescharacteristic
167C22×Dic3#6711yescharacteristic
168C2×D12C2×Dic311yescharacteristic
169C2×C4×D3—21no—
170C2×C3×C8—61no—
171C3×C4⋊C4—21no—
172C3×C4⋊C4—21no—
173C3×C4⋊C4—21no—
174C3×C4⋊C4—31no—
175C3×C4⋊C4—41no—
176C3×C4⋊C4—61no—
177C3×C4⋊C4—61no—
178C3×C4⋊C4—61no—
179C3×C4⋊C4C4×D311yescharacteristic
180C3×C4⋊C4C2×Dic311yescharacteristic
181C3×C22⋊C4—21no—
182C3×C22⋊C4—21no—
183C3×C22⋊C4—41no—
184C3×C22⋊C4—61no—
185C3×C22⋊C4—61no—
186C3×C22⋊C4—61no—
187C3×C22⋊C4—61no—
188C3×C42—31no—
189C3×C42—31no—
190C3×C42—31no—
191C3×C42—31no—
192C3×C42—61no—
193(C2×D3)⋊C4—21no—
194(C2×D3)⋊C4—21no—
195(C2×D3)⋊C4—21no—
196(C2×D3)⋊C4—21no—
197C4⋊Dic3—21no—
198C4⋊Dic3—21no—
199C4⋊Dic3—122no—
200C4⋊Dic3C2×Dic311yescharacteristic
201Dic3⋊C4—21no—
202Dic3⋊C4—122no—
203C4×Dic3—21no—
204C4×Dic3C2×Dic311yescharacteristic
205C4×Dic3C2×Dic311yescharacteristic
206C4×Dic3#6711yescharacteristic
207C4×Dic3#6711yescharacteristic
208C2×C3⋊C8—21no—
209C2×C3⋊C8—61no—
210C2×C3⋊C8—61no—
211C2×C3⋊C8—121no—
212C22×C32—21no—
213C22×C32—21no—
214C22×C32C2×C22⋊C411yescharacteristic
215C22×C32AGL(1,ℤ/8)11yescharacteristic
216C22×C32#13711yescharacteristic
217C2×C3×D3—41no—
218C2×C3×D3—41no—
219C2×C3×D3—41no—
220C32×C4—21no—
221C32×C4—21no—
222C32×C4—41no—
223C32×C4—41no—
224C3⋊Dic3—81no—
225C3×Dic3—21no—
226C3×Dic3—21no—
227C3×Dic3—21no—
228C3×Dic3—21no—
229C3×Dic3—41no—
230C3×Dic3—81no—
231#126—61no—
232#125—31no—
233#124—31no—
234#123—61no—
235C22⋊Q8D3211yescharacteristic
236#121—31no—
237C4×Q8—31no—
238C4×D4—31no—
239C4×D4—61no—
240#117—61no—
241C2×C4⋊C4—181no—
242C2×C42—31no—
243C4⋊C8—181no—
244C22⋊C8—31no—
245C22⋊C8—91no—
246#97—181no—
247#95—31no—
248#95—91no—
249#95—181no—
250C23×C3—21no—
251C23×C3—61no—
252C23×C3D3×D411yescharacteristic
253C23×C3C2×#6711yescharacteristic
254C22×D3—21no—
255C3×Q8—41no—
256C3×Q8—41no—
257C3×Q8—81no—
258C3×D4—121no—
259C3×D4—121no—
260C3×D4—121no—
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—31no—
269C2×C3×C4—31no—
270C2×C3×C4—31no—
271C2×C3×C4—41no—
272C2×C3×C4—41no—
273C2×C3×C4—41no—
274C2×C3×C4—41no—
275C2×C3×C4—61no—
276C2×C3×C4—61no—
277C2×C3×C4—61no—
278C2×C3×C4—81no—
279C2×C3×C4—122no—
280C2×C3×C4—121no—
281C2×C3×C4—121no—
282C2×C3×C4—121no—
283C2×C3×C4—121no—
284C2×C3×C4C2×C4×D311yescharacteristic
285C2×C3×C4D3×D411yescharacteristic
286C2×C3×C4C22×Dic311yescharacteristic
287C2×C3×C4C2×#6711yescharacteristic
288#67—41no—
289#67—41no—
290C2×Dic3—21no—
291C2×Dic3—21no—
292C2×Dic3—21no—
293C2×Dic3—41no—
294C2×Dic3—41no—
295C2×Dic3—41no—
296C2×Dic3—41no—
297C2×Dic3—121no—
298C2×Dic3—121no—
299C2×Dic3—121no—
300C2×Dic3—121no—
301C2×Dic3—122no—
302C2×Dic3—121no—
303C2×Dic3—121no—
304C2×Dic3—241no—
305C2×Dic3—241no—
306C2×Dic3#21711yescharacteristic
307C2×Dic3#21711yescharacteristic
308C2×Dic3#21711yescharacteristic
309C2×Dic3#21711yescharacteristic
310D12—41no—
311C4×D3—42no—
312C3×C8—121no—
313C3⋊C8—41no—
314C3⋊C8—121no—
315C3⋊C8—121no—
316C3⋊C8—241no—
317C2×C32—21no—
318C2×C32—21no—
319C2×C32#41011yescharacteristic
320C2×C32#41711yescharacteristic
321C2×C32#42111yescharacteristic
322C3×D3—81no—
323C2×Q8D3×Dic311yescharacteristic
324C2×D4—31no—
325C2×D4—61no—
326C22×C4—31no—
327C22×C4—31no—
328C22×C4—61no—
329C22×C4—61no—
330C22×C4—181no—
331C22×C4C2×D3211yescharacteristic
332C2×C8—61no—
333C2×C8—181no—
334C4⋊C4—21no—
335C4⋊C4—31no—
336C4⋊C4—61no—
337C4⋊C4—61no—
338C4⋊C4—61no—
339C4⋊C4—362no—
340C4⋊C4D3×Dic311yescharacteristic
341C22⋊C4—21no—
342C22⋊C4—61no—
343C22⋊C4—61no—
344C22⋊C4—61no—
345C22⋊C4—61no—
346C42—31no—
347C42—31no—
348C42—31no—
349C42—31no—
350C42—61no—
351C22×C3—21no—
352C22×C3—21no—
353C22×C3—21no—
354C22×C3—21no—
355C22×C3—21no—
356C22×C3—21no—
357C22×C3—21no—
358C22×C3—41no—
359C22×C3—41no—
360C22×C3—121no—
361C22×C3—121no—
362C22×C3—121no—
363C22×C3D3×C22⋊C411yescharacteristic
364C22×C3#91411yescharacteristic
365C22×C3#91811yescharacteristic
366C22×C3#94911yescharacteristic
367C22×C3#95111yescharacteristic
368C22×C3C2×#21711yescharacteristic
369C2×D3—41no—
370C2×D3—41no—
371C2×D3—41no—
372C3×C4—21no—
373C3×C4—21no—
374C3×C4—21no—
375C3×C4—21no—
376C3×C4—41no—
377C3×C4—41no—
378C3×C4—41no—
379C3×C4—41no—
380C3×C4—41no—
381C3×C4—41no—
382C3×C4—61no—
383C3×C4—61no—
384C3×C4—61no—
385C3×C4—61no—
386C3×C4—81no—
387C3×C4—81no—
388C3×C4—121no—
389C3×C4—241no—
390Dic3—21no—
391Dic3—21no—
392Dic3—21no—
393Dic3—21no—
394Dic3—41no—
395Dic3—81no—
396Dic3—241no—
397Dic3—241no—
398Dic3—242no—
399C32#151211yescharacteristic, complemented, Sylow
400C23—61no—
401C23D3×#6711yescharacteristic
402Q8—41no—
403D4—121no—
404D4—121no—
405D4—121no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—31no—
409C2×C4—31no—
410C2×C4—31no—
411C2×C4—31no—
412C2×C4—41no—
413C2×C4—61no—
414C2×C4—61no—
415C2×C4—61no—
416C2×C4—122no—
417C2×C4—121no—
418C2×C4—121no—
419C2×C4—121no—
420C2×C4—121no—
421C2×C4—361no—
422C2×C4—361no—
423C2×C4—361no—
424C2×C4C2×D3×Dic311yescharacteristic
425C2×C4D3×#6711yescharacteristic
426C8—121no—
427C8—361no—
428C2×C3—21no—
429C2×C3—21no—
430C2×C3—21no—
431C2×C3—21no—
432C2×C3—21no—
433C2×C3—21no—
434C2×C3—21no—
435C2×C3—41no—
436C2×C3—41no—
437C2×C3—241no—
438C2×C3#474011yescharacteristic
439C2×C3#480311yescharacteristic
440C2×C3#482111yescharacteristic
441C2×C3#523211yescharacteristic
442C2×C3#523611yescharacteristic
443C2×C3#524011yescharacteristic
444D3—81no—
445C22—21no—
446C22—21no—
447C22—121no—
448C22—121no—
449C22—121no—
450C22#6393911yescharacteristic
451C22#6394311yescharacteristic
452C22D3×#21711yescharacteristic
453C4—21no—
454C4—21no—
455C4—41no—
456C4—41no—
457C4—61no—
458C4—61no—
459C4—61no—
460C4—61no—
461C4—121no—
462C4—241no—
463C4—721no—
464C3—21no—
465C3#6831211yescharacteristic, complemented
466C3#7175611yescharacteristic, complemented
467C2—21no—
468C2—21no—
469C2—241no—
470C2#1059152811yescharacteristic
471C2#1059155011yescharacteristic
472C2#1059167011yescharacteristic
subgroupG/H
centerC22D3×#217
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×C22⋊Q8C22
socleC22×C32C2×C22⋊C4
prime radicalC3×#930C22
cosocleC22×C32×C4C23
hypercenterC22⋊Q8D32
hypocenterC32#1512
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #10591206C2semidirect
3. #10591063C2semidirect
4. #10589404C2semidirect
5. C3×#4538C2semidirect
11. C3×#947C4semidirect
12. C3×Q8×Dic3C4semidirect
16. C3×#893C4semidirect
18. C3×#890C4semidirect
39. #4538D3semidirect
86. #947Dic3semidirect
87. Q8×Dic3Dic3semidirect
93. #893Dic3semidirect
95. #890Dic3semidirect
399. C32#1512semidirect
465. C3#68312semidirect
466. C3#71756semidirect

Maximal subgroups

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

subgroupindex
C3×#56242
#105912062
#105910632
#105894042
C3×#45382
#105891502
#105891492
#717563
#683123