Finite Group Databasebeta

← #11775362

Subgroups — #11775362

Order 1152.

489 conjugacy classes of subgroups.

The subgroup lattice has 479 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5600C211yesmaximal, characteristic
2#10591206C211yesmaximal, characteristic, complemented
3#10591063C211yesmaximal, characteristic, complemented
4#10589403C211yesmaximal, characteristic
5C3×#4537C211yesmaximal, characteristic
6#10589153C211yesmaximal, characteristic, complemented
7#10589152C211yesmaximal, characteristic, complemented
8#71756—31nomaximal
9#68280—31nomaximal
10C32×#121C2211yescharacteristic
11C3×#936C411yescharacteristic, complemented
12C3×#935—21no—
13C3×D4×Dic3—21no—
14C3×D4×Dic3C411yescharacteristic, complemented
15C3×#924C2211yescharacteristic
16C2×C3×C4×Dic3C2211yescharacteristic
17C3×#890C411yescharacteristic, complemented
18C3×#887C411yescharacteristic, complemented
19C3×#879—21no—
20C3×#877—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#5600D311yescharacteristic
31#4936—31no—
32#4926—31no—
33#4719—31no—
34#4650—31no—
35C3×#327—31no—
36#4538—31no—
37#4538—31no—
38#4537—31no—
39#4537—31no—
40#4537—61no—
41#4537D311yescharacteristic
42#4467—31no—
43#4452—31no—
44C2×C32×D4—21no—
45C2×C32×D4C2×C411yescharacteristic
46C22×C32×C4C2311yescharacteristic
47C22×C3⋊Dic3—21no—
48C22×C3×Dic3—21no—
49C22×C3×Dic3—21no—
50C22×C3×Dic3D411yescharacteristic
51C22×C3×Dic3D411yescharacteristic
52C2×C3×Dic6C2×C411yescharacteristic
53C32×C4⋊C4C2×C411yescharacteristic
54C32×C22⋊C4—21no—
55C2×C3⋊(C3⋊C8)—21no—
56C3×#217—21no—
57C3×#217—21no—
58C3×#217—21no—
59C3×#217—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×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—31no—
78C3×#121—21no—
79C3×#121C2×D311yescharacteristic
80C3×#121C2×D311yescharacteristic
81C3×C4×Q8—31no—
82C3×C4×D4—31no—
83C3×C4×D4—61no—
84C3×#117—61no—
85C2×C3×C42—31no—
86#936Dic311yescharacteristic, complemented
87#935—21no—
88D4×Dic3—21no—
89D4×Dic3Dic311yescharacteristic, complemented
90C2×C4⋊Dic3—61no—
91#924C2×D311yescharacteristic
92C2×Dic3⋊C4—61no—
93C2×C4×Dic3C2×D311yescharacteristic
94#890Dic311yescharacteristic, complemented
95#887Dic311yescharacteristic, complemented
96#879—21no—
97#877—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×C32—21no—
115C23×C32C2×D411yescharacteristic
116C32×D4—41no—
117C32×D4—41no—
118C32×D4—41no—
119C2×C32×C4—21no—
120C2×C32×C4—41no—
121C2×C32×C4C22×C411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C3⋊Dic3—41no—
124C2×C3⋊Dic3—41no—
125C2×C3⋊Dic3—41no—
126C2×C3×Dic3—21no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3—21no—
129C2×C3×Dic3—21no—
130C2×C3×Dic3—41no—
131C2×C3×Dic3—42no—
132C2×C3×Dic3—41no—
133C2×C3×Dic3—41no—
134C2×C3×Dic3—41no—
135C2×C3×Dic3C22⋊C411yescharacteristic
136C2×C3×Dic3C22⋊C411yescharacteristic
137C2×C3×Dic3C22⋊C411yescharacteristic
138C2×C3×Dic3C22⋊C411yescharacteristic
139C3×Dic6—41no—
140C3⋊(C3⋊C8)—41no—
141C3×C3⋊C8—41no—
142#529—31no—
143#432—91no—
144#382—91no—
145#328—91no—
146#328—91no—
147#327—31no—
148#327—91no—
149C2×C3×Q8—31no—
150C2×C3×D4—21no—
151C2×C3×D4—21no—
152C2×C3×D4—21no—
153C2×C3×D4—41no—
154C2×C3×D4C4×D311yescharacteristic
155C2×C3×D4C2×Dic311yescharacteristic
156C22×C3×C4—21no—
157C22×C3×C4—31no—
158C22×C3×C4—31no—
159C22×C3×C4—61no—
160C22×C3×C4—61no—
161C22×C3×C4C22×D311yescharacteristic
162C22×C3×C4C22×D311yescharacteristic
163C22×Dic3—21no—
164C22×Dic3—21no—
165C22×Dic3—61no—
166C22×Dic3—61no—
167C22×Dic3—121no—
168C22×Dic3#6711yescharacteristic
169C22×Dic3#6711yescharacteristic
170C2×Dic6C2×Dic311yescharacteristic
171C2×C3×C8—61no—
172C3×C4⋊C4—21no—
173C3×C4⋊C4—31no—
174C3×C4⋊C4—61no—
175C3×C4⋊C4—61no—
176C3×C4⋊C4—61no—
177C3×C4⋊C4—61no—
178C3×C4⋊C4C4×D311yescharacteristic
179C3×C4⋊C4C2×Dic311yescharacteristic
180C3×C22⋊C4—21no—
181C3×C22⋊C4—21no—
182C3×C22⋊C4—41no—
183C3×C22⋊C4—61no—
184C3×C22⋊C4—61no—
185C3×C22⋊C4—61no—
186C3×C22⋊C4—61no—
187C3×C42—31no—
188C3×C42—31no—
189C3×C42—31no—
190C3×C42—31no—
191C3×C42—61no—
192#217—21no—
193#217—21no—
194#217—21no—
195#217—21no—
196C4⋊Dic3—21no—
197C4⋊Dic3—122no—
198C4⋊Dic3C2×Dic311yescharacteristic
199Dic3⋊C4—21no—
200Dic3⋊C4—21no—
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×C32—41no—
215C22×C32—41no—
216C22×C32—41no—
217C22×C32C2×C22⋊C411yescharacteristic
218C22×C32AGL(1,ℤ/8)11yescharacteristic
219C22×C32#13711yescharacteristic
220C32×C4—21no—
221C32×C4—21no—
222C32×C4—41no—
223C3⋊Dic3—81no—
224C3×Dic3—21no—
225C3×Dic3—21no—
226C3×Dic3—21no—
227C3×Dic3—21no—
228C3×Dic3—41no—
229C3×Dic3—41no—
230C3×Dic3—81no—
231#126—61no—
232#125—31no—
233#124—31no—
234#123—61no—
235C22⋊Q8—31no—
236#121D3211yescharacteristic
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—21no—
252C23×C3—21no—
253C23×C3—41no—
254C23×C3D3×D411yescharacteristic
255C23×C3C2×#6711yescharacteristic
256C3×Q8—121no—
257C3×D4—41no—
258C3×D4—41no—
259C3×D4—41no—
260C3×D4—41no—
261C3×D4—41no—
262C3×D4—41no—
263C3×D4—81no—
264C3×D4—81no—
265C3×D4—81no—
266C2×C3×C4—21no—
267C2×C3×C4—21no—
268C2×C3×C4—21no—
269C2×C3×C4—21no—
270C2×C3×C4—31no—
271C2×C3×C4—31no—
272C2×C3×C4—31no—
273C2×C3×C4—31no—
274C2×C3×C4—41no—
275C2×C3×C4—41no—
276C2×C3×C4—41no—
277C2×C3×C4—61no—
278C2×C3×C4—61no—
279C2×C3×C4—61no—
280C2×C3×C4—61no—
281C2×C3×C4—81no—
282C2×C3×C4—121no—
283C2×C3×C4—122no—
284C2×C3×C4—121no—
285C2×C3×C4—121no—
286C2×C3×C4—121no—
287C2×C3×C4C2×C4×D311yescharacteristic
288C2×C3×C4D3×D411yescharacteristic
289C2×C3×C4C22×Dic311yescharacteristic
290C2×C3×C4C2×#6711yescharacteristic
291C2×Dic3—21no—
292C2×Dic3—21no—
293C2×Dic3—21no—
294C2×Dic3—21no—
295C2×Dic3—41no—
296C2×Dic3—42no—
297C2×Dic3—41no—
298C2×Dic3—41no—
299C2×Dic3—41no—
300C2×Dic3—121no—
301C2×Dic3—121no—
302C2×Dic3—121no—
303C2×Dic3—121no—
304C2×Dic3—122no—
305C2×Dic3—121no—
306C2×Dic3—121no—
307C2×Dic3—241no—
308C2×Dic3—241no—
309C2×Dic3#21711yescharacteristic
310C2×Dic3#21711yescharacteristic
311C2×Dic3#21711yescharacteristic
312C2×Dic3#21711yescharacteristic
313Dic6—41no—
314C3×C8—121no—
315C3⋊C8—41no—
316C3⋊C8—121no—
317C3⋊C8—121no—
318C3⋊C8—241no—
319C2×C32—21no—
320C2×C32—21no—
321C2×C32—81no—
322C2×C32#41011yescharacteristic
323C2×C32#41711yescharacteristic
324C2×C32#42111yescharacteristic
325C2×Q8—31no—
326C2×D4—21no—
327C2×D4D3×Dic311yescharacteristic
328C22×C4—31no—
329C22×C4—31no—
330C22×C4—61no—
331C22×C4—61no—
332C22×C4—181no—
333C22×C4C2×D3211yescharacteristic
334C2×C8—61no—
335C2×C8—181no—
336C4⋊C4—31no—
337C4⋊C4—61no—
338C4⋊C4—61no—
339C4⋊C4—61no—
340C4⋊C4—61no—
341C4⋊C4—362no—
342C4⋊C4D3×Dic311yescharacteristic
343C22⋊C4—21no—
344C22⋊C4—61no—
345C22⋊C4—61no—
346C22⋊C4—61no—
347C22⋊C4—61no—
348C42—31no—
349C42—31no—
350C42—31no—
351C42—31no—
352C42—61no—
353C22×C3—21no—
354C22×C3—21no—
355C22×C3—21no—
356C22×C3—21no—
357C22×C3—21no—
358C22×C3—21no—
359C22×C3—21no—
360C22×C3—41no—
361C22×C3—41no—
362C22×C3—41no—
363C22×C3—41no—
364C22×C3—41no—
365C22×C3—41no—
366C22×C3—41no—
367C22×C3—41no—
368C22×C3—81no—
369C22×C3—81no—
370C22×C3—81no—
371C22×C3D3×C22⋊C411yescharacteristic
372C22×C3#91111yescharacteristic
373C22×C3#91511yescharacteristic
374C22×C3#94911yescharacteristic
375C22×C3#95111yescharacteristic
376C22×C3C2×#21711yescharacteristic
377C3×C4—21no—
378C3×C4—21no—
379C3×C4—21no—
380C3×C4—21no—
381C3×C4—41no—
382C3×C4—41no—
383C3×C4—41no—
384C3×C4—41no—
385C3×C4—61no—
386C3×C4—61no—
387C3×C4—61no—
388C3×C4—61no—
389C3×C4—81no—
390C3×C4—121no—
391C3×C4—121no—
392C3×C4—241no—
393Dic3—21no—
394Dic3—21no—
395Dic3—21no—
396Dic3—21no—
397Dic3—41no—
398Dic3—41no—
399Dic3—81no—
400Dic3—241no—
401Dic3—241no—
402Dic3—242no—
403C32#151211yescharacteristic, complemented, Sylow
404C23—21no—
405C23D3×#6711yescharacteristic
406Q8—121no—
407D4—41no—
408D4—41no—
409D4—41no—
410C2×C4—21no—
411C2×C4—31no—
412C2×C4—31no—
413C2×C4—31no—
414C2×C4—31no—
415C2×C4—41no—
416C2×C4—61no—
417C2×C4—61no—
418C2×C4—61no—
419C2×C4—61no—
420C2×C4—121no—
421C2×C4—122no—
422C2×C4—121no—
423C2×C4—121no—
424C2×C4—121no—
425C2×C4—361no—
426C2×C4—361no—
427C2×C4—361no—
428C2×C4C2×D3×Dic311yescharacteristic
429C2×C4D3×#6711yescharacteristic
430C8—121no—
431C8—361no—
432C2×C3—21no—
433C2×C3—21no—
434C2×C3—21no—
435C2×C3—21no—
436C2×C3—21no—
437C2×C3—21no—
438C2×C3—21no—
439C2×C3—41no—
440C2×C3—41no—
441C2×C3—81no—
442C2×C3—81no—
443C2×C3—161no—
444C2×C3#474011yescharacteristic
445C2×C3#477111yescharacteristic
446C2×C3#482111yescharacteristic
447C2×C3#523211yescharacteristic
448C2×C3#523611yescharacteristic
449C2×C3#524011yescharacteristic
450C22—21no—
451C22—21no—
452C22—41no—
453C22—41no—
454C22—41no—
455C22#6392511yescharacteristic
456C22#6392911yescharacteristic
457C22D3×#21711yescharacteristic
458C4—21no—
459C4—21no—
460C4—41no—
461C4—61no—
462C4—61no—
463C4—61no—
464C4—61no—
465C4—121no—
466C4—121no—
467C4—241no—
468C4—721no—
469C3—21no—
470C3#6828011yescharacteristic, complemented
471C3#7175611yescharacteristic, complemented
472C2—21no—
473C2—21no—
474C2—81no—
475C2#1059141411yescharacteristic
476C2#1059152811yescharacteristic
477C2#1059167011yescharacteristic
subgroupG/H
centerC22D3×#217
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
Fitting, prime radicalC32×#121C22
socleC22×C32C2×C22⋊C4
cosocleC22×C32×C4C23
hypercenter#121D32
hypocenterC32#1512
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
2. #10591206C2semidirect
3. #10591063C2semidirect
6. #10589153C2semidirect
7. #10589152C2semidirect
11. C3×#936C4semidirect
14. C3×D4×Dic3C4semidirect
17. C3×#890C4semidirect
18. C3×#887C4semidirect
86. #936Dic3semidirect
89. D4×Dic3Dic3semidirect
94. #890Dic3semidirect
95. #887Dic3semidirect
403. C32#1512semidirect
470. C3#68280semidirect
471. C3#71756semidirect

Maximal subgroups

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

subgroupindex
C3×#56002
#105912062
#105910632
#105894032
C3×#45372
#105891532
#105891522
#717563
#682803