Finite Group Databasebeta

← #11774441

Subgroups — #11774441

Order 1152.

459 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593974C211yesmaximal, characteristic
2C3×#4685C211yesmaximal, characteristic, complemented
3#10590248C211yesmaximal, characteristic, complemented
4#10589322C211yesmaximal, characteristic, complemented
5C3×#4459C211yesmaximal, characteristic, complemented
6#10589085C211yesmaximal, characteristic, complemented
7#10589081C211yesmaximal, characteristic, complemented
8#70760—31nomaximal
9#68169—31nomaximal
10C4×#634C2211yescharacteristic
11C3×C4×D12C2211yescharacteristic
12C3×C42×D3C2211yescharacteristic
13#63908C411yescharacteristic
14#63905—21no—
15C4×#625—21no—
16#63869C411yescharacteristic
17#63860C411yescharacteristic
18#63859—21no—
19#63857C411yescharacteristic
20#63855—21no—
21C32×C4×C8C2211yescharacteristic
22C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
23C3×(C2×D3)⋊C8—21no—
24C3×Dic3⋊C8—21no—
25C3×C4⋊(C3⋊C8)C2211yescharacteristic
26C3×C4×C3⋊C8C2211yescharacteristic
27(C2×D3)⋊(C3⋊C8)—21no—
28Dic3×C3⋊C8—21no—
29#5557—31no—
30#5479—31no—
31C3×#431—31no—
32#4925—31no—
33#4833—31no—
34#4685D311yescharacteristic, complemented
35C3×D4⋊C8—31no—
36D4⋊(C3⋊C8)—31no—
37#4484—31no—
38#4459—31no—
39#4459D311yescharacteristic, complemented
40#4456—31no—
41#4456—31no—
42#4456—31no—
43#4456—61no—
44C2×#634C2×C411yescharacteristic
45C2×C3×D12C2×C411yescharacteristic
46C2×C3×C4×D3—21no—
47C2×C3×C4×D3C2×C411yescharacteristic
48C2×C3×C4×D3D411yescharacteristic
49C2×C3×C4×D3D411yescharacteristic
50C2×#625—21no—
51C2×C32×C8—21no—
52C32×C42C2311yescharacteristic
53C4⋊(C3⋊Dic3)C2×C411yescharacteristic
54#3750—21no—
55C4×C3⋊Dic3—21no—
56C2×C3⋊(C3⋊C8)—21no—
57C3×(C2×D3)⋊C4—21no—
58C3×C4⋊Dic3C2×C411yescharacteristic
59C3×C4×Dic3C2×C411yescharacteristic
60C3×C4×Dic3D411yescharacteristic
61C3×C4×Dic3D411yescharacteristic
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64#3724—21no—
65Dic3⋊Dic3—21no—
66Dic3⋊Dic3—21no—
67(C2×D3)⋊Dic3—21no—
68(C2×D3)⋊Dic3—21no—
69(C2×D3)⋊Dic3—21no—
70(C2×D3)⋊Dic3—21no—
71#1482—91noSylow
72C3×C4×D4—31no—
73C2×C3×C42—31no—
74#938—31no—
75#936—31no—
76#930—31no—
77#929—61no—
78C4×#67—61no—
79C4×#67—61no—
80#926—61no—
81#924—31no—
82#897—31no—
83#890—31no—
84#883—61no—
85#879—61no—
86#876—61no—
87#875—31no—
88C4×D12C2×D311yescharacteristic
89#872—61no—
90C42×D3C2×D311yescharacteristic
91#870—31no—
92C4×Dic6—31no—
93C4×Dic6—31no—
94C4×Dic6—61no—
95C3×C4⋊C8—31no—
96C3×C4⋊C8—61no—
97C3×C22⋊C8—61no—
98C3×C4×C8—21no—
99C3×C4×C8—31no—
100C3×C4×C8C2×D311yescharacteristic
101C3×C4×C8C2×D311yescharacteristic
102#830—61no—
103(C2×D3)⋊C8—21no—
104(C2×D3)⋊C8—61no—
105Dic3⋊C8—21no—
106C8×Dic3—61no—
107C4⋊(C3⋊C8)—31no—
108C4⋊(C3⋊C8)—31no—
109C4⋊(C3⋊C8)—61no—
110C4⋊(C3⋊C8)C2×D311yescharacteristic
111C4×C3⋊C8—61no—
112C4×C3⋊C8C2×D311yescharacteristic
113C22×C3×D3—21no—
114C22×C3×D3C22⋊C411yescharacteristic
115C2×C32×C4C22×C411yescharacteristic
116C2×C32×C4C2×D411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118C2×C3⋊Dic3—21no—
119C2×C3⋊Dic3—21no—
120#634—21no—
121#634—21no—
122C2×C3×Dic3—21no—
123C2×C3×Dic3C22⋊C411yescharacteristic
124C2×C3×Dic3C22⋊C411yescharacteristic
125C2×C3×Dic3C22⋊C411yescharacteristic
126C3×D12—21no—
127C3×D12—21no—
128C3×C4×D3—21no—
129C3×C4×D3—21no—
130C3×C4×D3—21no—
131C3×C4×D3—21no—
132C3×C4×D3—41no—
133C3×C4×D3—41no—
134C3×C4×D3—41no—
135#625—42no—
136C32×C8—41no—
137C3⋊(C3⋊C8)—41no—
138C3×C3⋊C8—41no—
139C3×C3⋊C8—41no—
140#529—91no—
141#431—31no—
142#431—91no—
143Q8⋊C8—91no—
144Q8⋊C8—91no—
145D4⋊C8—31no—
146D4⋊C8—91no—
147C2×C3×D4—31no—
148C22×C3×C4—31no—
149C22×C3×C4—31no—
150C22×C3×C4—31no—
151C22×C3×C4—61no—
152C2×#67—61no—
153C2×#67—61no—
154C2×D12C4×D311yescharacteristic
155C2×C4×D3—21no—
156C2×C4×D3C4×D311yescharacteristic
157C2×C4×D3D1211yescharacteristic
158C2×C4×D3#6711yescharacteristic
159C2×Dic6—31no—
160C2×Dic6—31no—
161C2×Dic6—61no—
162C2×C3×C8—21no—
163C2×C3×C8—21no—
164C2×C3×C8—41no—
165C2×C3×C8—61no—
166C2×C3×C8—61no—
167C3×C4⋊C4—31no—
168C3×C22⋊C4—61no—
169C3×C42—21no—
170C3×C42—31no—
171C3×C42—31no—
172C3×C42—31no—
173C3×C42C22×D311yescharacteristic
174C3×C42C22×D311yescharacteristic
175#217—61no—
176#217—61no—
177#217—61no—
178#217—61no—
179(C2×D3)⋊C4—21no—
180(C2×D3)⋊C4—61no—
181(C2×D3)⋊C4—61no—
182(C2×D3)⋊C4—61no—
183(C2×D3)⋊C4—61no—
184C4⋊Dic3—31no—
185C4⋊Dic3—31no—
186C4⋊Dic3—61no—
187C4⋊Dic3—61no—
188C4⋊Dic3—61no—
189C4⋊Dic3C4×D311yescharacteristic
190Dic3⋊C4—61no—
191Dic3⋊C4—61no—
192Dic3⋊C4—61no—
193Dic3⋊C4—61no—
194Dic3⋊C4—61no—
195Dic3⋊C4—61no—
196Dic3⋊C4—121no—
197C4×Dic3—61no—
198C4×Dic3—61no—
199C4×Dic3—121no—
200C4×Dic3C4×D311yescharacteristic
201C4×Dic3D1211yescharacteristic
202C4×Dic3#6711yescharacteristic
203C2×C3⋊C8—21no—
204C2×C3⋊C8—21no—
205C2×C3⋊C8—61no—
206C2×C3⋊C8—61no—
207C2×C3⋊C8—121no—
208C22×C32C2×C22⋊C411yescharacteristic
209C2×C3×D3—21no—
210C2×C3×D3—21no—
211C2×C3×D3—21no—
212C2×C3×D3—41no—
213C2×C3×D3—41no—
214C2×C3×D3—41no—
215C32×C4—21no—
216C32×C4#13111yescharacteristic
217C32×C4#13111yescharacteristic
218C32×C4#13511yescharacteristic
219C32×C4#13511yescharacteristic
220C3⋊Dic3—41no—
221C3⋊Dic3—41no—
222C3×Dic3—21no—
223C3×Dic3—21no—
224C3×Dic3—21no—
225C3×Dic3—41no—
226#126—181no—
227#125—91no—
228#124—91no—
229#123—181no—
230C22⋊Q8—91no—
231#121—91no—
232C4×Q8—91no—
233C4×D4—31no—
234C4×D4—181no—
235#117—181no—
236C2×C42—31no—
237C4⋊C8—31no—
238C4⋊C8—61no—
239C4⋊C8—91no—
240C22⋊C8—61no—
241C22⋊C8—181no—
242C4×C8—31no—
243C4×C8—181no—
244C4×C8D3211yescharacteristic
245C23×C3—31no—
246C23×C3—61no—
247C22×D3—21no—
248C22×D3(C2×D3)⋊C411yescharacteristic
249C3×D4—61no—
250C3×D4—61no—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—31no—
255C2×C3×C4—31no—
256C2×C3×C4—31no—
257C2×C3×C4—61no—
258C2×C3×C4—61no—
259C2×C3×C4—61no—
260C2×C3×C4—61no—
261C2×C3×C4—61no—
262C2×C3×C4—121no—
263C2×C3×C4—121no—
264C2×C3×C4—121no—
265C2×C3×C4C2×C4×D311yescharacteristic
266C2×C3×C4C2×C4×D311yescharacteristic
267C2×C3×C4C2×D1211yescharacteristic
268C2×C3×C4D3×D411yescharacteristic
269C2×C3×C4D3×D411yescharacteristic
270C2×C3×C4C2×#6711yescharacteristic
271#67—122no—
272#67—122no—
273C2×Dic3—21no—
274C2×Dic3—61no—
275C2×Dic3—61no—
276C2×Dic3—61no—
277C2×Dic3—61no—
278C2×Dic3—121no—
279C2×Dic3—121no—
280C2×Dic3(C2×D3)⋊C411yescharacteristic
281C2×Dic3(C2×D3)⋊C411yescharacteristic
282C2×Dic3(C2×D3)⋊C411yescharacteristic
283D12—21no—
284D12—21no—
285C4×D3—21no—
286C4×D3—21no—
287C4×D3—21no—
288C4×D3—21no—
289C4×D3—41no—
290C4×D3—41no—
291C4×D3—41no—
292Dic6—62no—
293Dic6—61no—
294Dic6—61no—
295Dic6—61no—
296Dic6—61no—
297Dic6—121no—
298C3×C8—41no—
299C3×C8—41no—
300C3×C8—42no—
301C3×C8—121no—
302C3×C8—121no—
303C3⋊C8—41no—
304C3⋊C8—41no—
305C3⋊C8—121no—
306C3⋊C8—121no—
307C3⋊C8—241no—
308C2×C32#40811yescharacteristic
309C2×C32#41611yescharacteristic
310C2×C32#42111yescharacteristic
311C3×D3—41no—
312C3×D3—81no—
313C2×Q8—91no—
314C2×D4—31no—
315C2×D4—181no—
316C22×C4—31no—
317C22×C4—31no—
318C22×C4—31no—
319C22×C4—61no—
320C2×C8—21no—
321C2×C8—61no—
322C2×C8—61no—
323C2×C8—181no—
324C4⋊C4—31no—
325C4⋊C4—91no—
326C4⋊C4—181no—
327C4⋊C4—181no—
328C4⋊C4—181no—
329C4⋊C4—181no—
330C22⋊C4—61no—
331C22⋊C4—181no—
332C22⋊C4—181no—
333C22⋊C4—181no—
334C22⋊C4—181no—
335C42—31no—
336C42—31no—
337C42—31no—
338C42—181no—
339C42C2×D3211yescharacteristic
340C22×C3—21no—
341C22×C3—61no—
342C22×C3—61no—
343C22×C3—61no—
344C22×C3—121no—
345C22×C3—121no—
346C22×C3—121no—
347C22×C3D3×C22⋊C411yescharacteristic
348C22×C3C2×(C2×D3)⋊C411yescharacteristic
349C2×D3—21no—
350C2×D3—21no—
351C2×D3—21no—
352C2×D3—41no—
353C2×D3—41no—
354C2×D3—41no—
355C3×C4—21no—
356C3×C4—21no—
357C3×C4—21no—
358C3×C4—21no—
359C3×C4—21no—
360C3×C4—21no—
361C3×C4—41no—
362C3×C4—61no—
363C3×C4—61no—
364C3×C4—61no—
365C3×C4—121no—
366C3×C4#90111yescharacteristic
367C3×C4#90411yescharacteristic
368C3×C4#90411yescharacteristic
369C3×C4#90711yescharacteristic
370C3×C4#90711yescharacteristic
371C3×C4#90711yescharacteristic
372C3×C4#91211yescharacteristic
373C3×C4#91611yescharacteristic
374Dic3—21no—
375Dic3—21no—
376Dic3—21no—
377Dic3—41no—
378Dic3—122no—
379Dic3—121no—
380Dic3—121no—
381Dic3—121no—
382Dic3—121no—
383Dic3—241no—
384C32#148211yescharacteristic, complemented, Sylow
385C23—31no—
386C23—61no—
387Q8—181no—
388Q8—181no—
389D4—61no—
390D4—61no—
391D4—362no—
392C2×C4—31no—
393C2×C4—31no—
394C2×C4—31no—
395C2×C4—61no—
396C2×C4—61no—
397C2×C4—61no—
398C2×C4—61no—
399C2×C4—61no—
400C2×C4—121no—
401C2×C4—121no—
402C2×C4—121no—
403C2×C4—181no—
404C2×C4—181no—
405C2×C4C4×D3211yescharacteristic
406C2×C4D3×D1211yescharacteristic
407C2×C4D3×#6711yescharacteristic
408C8—41no—
409C8—121no—
410C8—121no—
411C8—361no—
412C2×C3—21no—
413C2×C3—21no—
414C2×C3—21no—
415C2×C3—121no—
416C2×C3—241no—
417C2×C3#472711yescharacteristic
418C2×C3#477211yescharacteristic
419C2×C3#482111yescharacteristic
420C2×C3#500511yescharacteristic
421C2×C3#511311yescharacteristic
422C2×C3#512911yescharacteristic
423D3—41no—
424D3—81no—
425C22—61no—
426C22—61no—
427C22—61no—
428C22—121no—
429C22—121no—
430C22—121no—
431C22D3×(C2×D3)⋊C411yescharacteristic
432C4—21no—
433C4—61no—
434C4—61no—
435C4—61no—
436C4—121no—
437C4—361no—
438C4—361no—
439C4#6380411yescharacteristic
440C4#6380511yescharacteristic
441C4#6380611yescharacteristic
442C4#6380711yescharacteristic
443C3—21no—
444C3#6816911yescharacteristic, complemented
445C3#7076011yescharacteristic, complemented
446C2—121no—
447C2—241no—
448C2#1059039211yescharacteristic
449C2#1059095411yescharacteristic
450C2#1059095511yescharacteristic
subgroupG/H
centerC2×C4D3×D12
commutatorC2×C32×C4C22×C4
FrattiniC42C2×D32
FittingC32×C4×C8C22
socleC22×C32C2×C22⋊C4
prime radical#63908C4
cosocleC32×C42C23
hypercenterC4×C8D32
hypocenterC32#1482
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
2. C3×#4685C2semidirect
3. #10590248C2semidirect
4. #10589322C2semidirect
5. C3×#4459C2semidirect
6. #10589085C2semidirect
7. #10589081C2semidirect
34. #4685D3semidirect
39. #4459D3semidirect
384. C32#1482semidirect
444. C3#68169semidirect
445. C3#70760semidirect

Maximal subgroups

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

subgroupindex
#105939742
C3×#46852
#105902482
#105893222
C3×#44592
#105890852
#105890812
#707603
#681693