Finite Group Databasebeta

← #11775365

Subgroups — #11775365

Order 1152.

561 conjugacy classes of subgroups.

The subgroup lattice has 471 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595950C211yesmaximal, characteristic
2C3×#4936C211yesmaximal, characteristic, complemented
3C3×#4926C211yesmaximal, characteristic, complemented
4#10589154C212yesmaximal, complemented
5#10589151C212yesmaximal
6#70834—31nomaximal
7#69544—31nomaximal
8C2×C32×C42C2211yescharacteristic
9#64139C2211yescharacteristic
10#64138—21no—
11C4×#638—21no—
12#64133C2211yescharacteristic
13#64085—21no—
14#64084C411yescharacteristic, complemented
15C4×C4⋊(C3⋊D3)C411yescharacteristic, complemented
16#64081—21no—
17#64079C411yescharacteristic, complemented
18C4×#634C411yescharacteristic, complemented
19C2×C3×C4⋊Dic3—21no—
20C3×C3⋊#95—21no—
21C3×C3⋊#95C2212yes—
22C3×#830C2212yes—
23C3×C4⋊(C3⋊C8)—21no—
24C3×#803—21no—
25#5479—31no—
26#5479—31no—
27#5479—61no—
28C3×#432—31no—
29C3×#382—31no—
30#4936D311yescharacteristic, complemented
31#4926D311yescharacteristic, complemented
32#4470—32no—
33#4467—32no—
34#4452—32no—
35#4451—32no—
36C22×C32×C4D411yescharacteristic
37C22×C32×C4D411yescharacteristic
38C22×C32×C4C2311yescharacteristic
39C2×#638—21no—
40C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
41C2×C4×C3⋊D3—21no—
42C2×#634C2×C411yescharacteristic
43C22×C3×Dic3—22no—
44C32×C42C2×C411yescharacteristic
45C32×C42C2×C411yescharacteristic
46C32×C42D411yescharacteristic
47C32×C42D411yescharacteristic
48#3757—21no—
49#3752—21no—
50#3752—21no—
51#3752—21no—
52#3752—21no—
53C4⋊(C3⋊Dic3)C2×C411yescharacteristic
54C4⋊(C3⋊Dic3)C2×C411yescharacteristic
55#3750—21no—
56#3750—21no—
57#3750—21no—
58#3750—21no—
59C4×C3⋊Dic3—21no—
60C3×C4⋊Dic3—42no—
61C2×C3×C3⋊C8—22no—
62#1512—91noSylow
63C2×C3×C4⋊C4—61no—
64C2×C3×C42—21no—
65C2×C3×C42C2×D311yescharacteristic
66C2×C3×C42C2×D311yescharacteristic
67#930—31no—
68#930—31no—
69#930—61no—
70#929—62no—
71#929—61no—
72#929—61no—
73C4×#67—62no—
74C4×#67—61no—
75C4×#67—61no—
76C2×C4⋊Dic3—21no—
77#924—31no—
78#924—31no—
79#924—61no—
80#876—62no—
81#876—61no—
82#876—61no—
83#875—31no—
84#875—31no—
85#875—61no—
86C4×D12—31no—
87C4×D12—31no—
88C4×D12—61no—
89#872—62no—
90#872—61no—
91#872—61no—
92#870—31no—
93#870—31no—
94#870—61no—
95C4×Dic6—31no—
96C4×Dic6—31no—
97C4×Dic6—61no—
98C3×C4⋊C8—61no—
99C3×C22⋊C8—32no—
100C3×#97—61no—
101C3×#95—32no—
102C3×#95—61no—
103C3⋊#95—21no—
104C3⋊#95C2×D312yes—
105#830C2×D312yes—
106C4⋊(C3⋊C8)—21no—
107#803—21no—
108C23×C32C2×D411yescharacteristic
109C22×C3⋊D3—21no—
110C2×C32×C4—21no—
111C2×C32×C4—21no—
112C2×C32×C4—41no—
113C2×C32×C4—41no—
114C2×C32×C4C22⋊C411yescharacteristic
115C2×C32×C4C22⋊C411yescharacteristic
116C2×C32×C4C22⋊C411yescharacteristic
117C2×C32×C4C22⋊C411yescharacteristic
118C2×C32×C4C22×C411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120#638—41no—
121#638—41no—
122C2×C3⋊Dic3—21no—
123C2×C3⋊Dic3—21no—
124C2×C3⋊Dic3—21no—
125C4⋊(C3⋊D3)—41no—
126C4×C3⋊D3—42no—
127#634—41no—
128C2×C3×Dic3—42no—
129C2×C3×Dic3—42no—
130C2×C3×Dic3—42no—
131C3×C3⋊C8—42no—
132#529—91no—
133#432—31no—
134#382—31no—
135#328—92no—
136#327—92no—
137C22×C3×C4—21no—
138C22×C3×C4—21no—
139C22×C3×C4—21no—
140C22×C3×C4—62no—
141C22×C3×C4D1211yescharacteristic
142C22×C3×C4D1211yescharacteristic
143C22×C3×C4#6711yescharacteristic
144C22×C3×C4#6711yescharacteristic
145C22×C3×C4C22×D311yescharacteristic
146C22×C3×C4C22×D311yescharacteristic
147C2×#67—62no—
148C2×#67—61no—
149C2×#67—61no—
150C22×Dic3—22no—
151C2×D12—31no—
152C2×D12—31no—
153C2×D12—61no—
154C2×C4×D3—62no—
155C2×C4×D3—61no—
156C2×C4×D3—61no—
157C2×Dic6—31no—
158C2×Dic6—31no—
159C2×Dic6—61no—
160C2×C3×C8—62no—
161C3×C4⋊C4—122no—
162C3×C42—21no—
163C3×C42—21no—
164C3×C42—21no—
165C3×C42—21no—
166C3×C42C4×D311yescharacteristic
167C3×C42C4×D311yescharacteristic
168C3×C42C4×D311yescharacteristic
169C3×C42C4×D311yescharacteristic
170C3×C42D1211yescharacteristic
171C3×C42D1211yescharacteristic
172C3×C42#6711yescharacteristic
173C3×C42#6711yescharacteristic
174#217—62no—
175#217—61no—
176#217—61no—
177(C2×D3)⋊C4—62no—
178(C2×D3)⋊C4—62no—
179(C2×D3)⋊C4—62no—
180(C2×D3)⋊C4—62no—
181(C2×D3)⋊C4—61no—
182(C2×D3)⋊C4—61no—
183(C2×D3)⋊C4—61no—
184(C2×D3)⋊C4—61no—
185(C2×D3)⋊C4—61no—
186(C2×D3)⋊C4—61no—
187(C2×D3)⋊C4—61no—
188(C2×D3)⋊C4—61no—
189C4⋊Dic3—31no—
190C4⋊Dic3—31no—
191C4⋊Dic3—31no—
192C4⋊Dic3—31no—
193C4⋊Dic3—42no—
194C4⋊Dic3—61no—
195C4⋊Dic3—61no—
196Dic3⋊C4—62no—
197Dic3⋊C4—62no—
198Dic3⋊C4—62no—
199Dic3⋊C4—62no—
200Dic3⋊C4—61no—
201Dic3⋊C4—61no—
202Dic3⋊C4—61no—
203Dic3⋊C4—61no—
204Dic3⋊C4—61no—
205Dic3⋊C4—61no—
206Dic3⋊C4—61no—
207Dic3⋊C4—61no—
208C4×Dic3—62no—
209C4×Dic3—61no—
210C4×Dic3—61no—
211C2×C3⋊C8—22no—
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—21no—
223C32×C4—21no—
224C32×C4—21no—
225C32×C4—21no—
226C3⋊Dic3—41no—
227C3⋊Dic3—41no—
228C3⋊Dic3—41no—
229C3×Dic3—82no—
230#126—181no—
231#125—91no—
232#124—91no—
233#123—181no—
234C22⋊Q8—91no—
235#121—91no—
236C4×Q8—91no—
237C4×D4—91no—
238C4×D4—181no—
239#117—181no—
240C2×C4⋊C4—61no—
241C2×C42D3211yescharacteristic
242C4⋊C8—61no—
243C22⋊C8—32no—
244#97—61no—
245#95—32no—
246#95—61no—
247C23×C3—21no—
248C23×C3C2×D1211yescharacteristic
249C23×C3C2×#6711yescharacteristic
250C22×D3—62no—
251C22×D3—61no—
252C22×D3—61no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—21no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—41no—
264C2×C3×C4—41no—
265C2×C3×C4—41no—
266C2×C3×C4—41no—
267C2×C3×C4—41no—
268C2×C3×C4—41no—
269C2×C3×C4—42no—
270C2×C3×C4—42no—
271C2×C3×C4—122no—
272C2×C3×C4—122no—
273C2×C3×C4—122no—
274C2×C3×C4(C2×D3)⋊C411yescharacteristic
275C2×C3×C4(C2×D3)⋊C411yescharacteristic
276C2×C3×C4(C2×D3)⋊C411yescharacteristic
277C2×C3×C4(C2×D3)⋊C411yescharacteristic
278C2×C3×C4(C2×D3)⋊C411yescharacteristic
279C2×C3×C4(C2×D3)⋊C411yescharacteristic
280C2×C3×C4(C2×D3)⋊C411yescharacteristic
281C2×C3×C4(C2×D3)⋊C411yescharacteristic
282C2×C3×C4C2×C4×D311yescharacteristic
283C2×C3×C4C2×C4×D311yescharacteristic
284C2×C3×C4C2×D1211yescharacteristic
285C2×C3×C4C2×#6711yescharacteristic
286#67—122no—
287#67—122no—
288#67—121no—
289#67—121no—
290#67—121no—
291#67—121no—
292C2×Dic3—42no—
293C2×Dic3—42no—
294C2×Dic3—42no—
295C2×Dic3—62no—
296C2×Dic3—62no—
297C2×Dic3—62no—
298C2×Dic3—61no—
299C2×Dic3—61no—
300C2×Dic3—61no—
301C2×Dic3—61no—
302C2×Dic3—61no—
303C2×Dic3—61no—
304D12—121no—
305D12—121no—
306D12—122no—
307C4×D3—124no—
308C4×D3—122no—
309C4×D3—122no—
310Dic6—122no—
311Dic6—121no—
312Dic6—121no—
313C3×C8—122no—
314C3⋊C8—42no—
315C2×C32—21no—
316C2×C32—21no—
317C2×C32#41011yescharacteristic
318C2×C32#41711yescharacteristic
319C2×C32#42111yescharacteristic
320C3⋊D3—81no—
321C2×Q8—91no—
322C2×D4—91no—
323C2×D4—181no—
324C22×C4—62no—
325C22×C4—181no—
326C22×C4#62611yescharacteristic
327C22×C4#62611yescharacteristic
328C22×C4C2×D3211yescharacteristic
329C2×C8—62no—
330C4⋊C4—91no—
331C4⋊C4—91no—
332C4⋊C4—122no—
333C4⋊C4—181no—
334C4⋊C4—181no—
335C4⋊C4—181no—
336C4⋊C4—181no—
337C22⋊C4—181no—
338C22⋊C4—181no—
339C22⋊C4—181no—
340C22⋊C4—181no—
341C22⋊C4—181no—
342C42—181no—
343C42#62411yescharacteristic
344C42#62411yescharacteristic
345C42#62611yescharacteristic
346C42#62611yescharacteristic
347C22×C3—21no—
348C22×C3—21no—
349C22×C3—21no—
350C22×C3—21no—
351C22×C3—21no—
352C22×C3—21no—
353C22×C3—21no—
354C22×C3—41no—
355C22×C3—41no—
356C22×C3#90811yescharacteristic
357C22×C3#90911yescharacteristic
358C22×C3C2×(C2×D3)⋊C411yescharacteristic
359C22×C3C2×(C2×D3)⋊C411yescharacteristic
360C22×C3#93211yescharacteristic
361C22×C3#94211yescharacteristic
362C2×D3—122no—
363C2×D3—122no—
364C2×D3—122no—
365C2×D3—121no—
366C2×D3—121no—
367C2×D3—121no—
368C2×D3—121no—
369C2×D3—121no—
370C2×D3—121no—
371C3×C4—22no—
372C3×C4—22no—
373C3×C4—21no—
374C3×C4—21no—
375C3×C4—21no—
376C3×C4—21no—
377C3×C4—21no—
378C3×C4—21no—
379C3×C4—21no—
380C3×C4—21no—
381C3×C4—21no—
382C3×C4—21no—
383C3×C4—21no—
384C3×C4—21no—
385C3×C4—41no—
386C3×C4—41no—
387C3×C4—41no—
388C3×C4—41no—
389C3×C4—242no—
390Dic3—82no—
391Dic3—122no—
392Dic3—122no—
393Dic3—122no—
394Dic3—121no—
395Dic3—121no—
396Dic3—121no—
397Dic3—121no—
398Dic3—121no—
399Dic3—121no—
400C32#151211yescharacteristic, complemented, Sylow
401C23—181no—
402C23C2×#62611yescharacteristic
403Q8—361no—
404D4—361no—
405D4—361no—
406D4—361no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—122no—
412C2×C4—122no—
413C2×C4—122no—
414C2×C4—181no—
415C2×C4—181no—
416C2×C4—181no—
417C2×C4—362no—
418C2×C4#372211yescharacteristic
419C2×C4#372211yescharacteristic
420C2×C4#372211yescharacteristic
421C2×C4#372211yescharacteristic
422C2×C4C2×#62411yescharacteristic
423C2×C4C2×#62611yescharacteristic
424C8—122no—
425C2×C3—21no—
426C2×C3—21no—
427C2×C3—21no—
428C2×C3—21no—
429C2×C3—21no—
430C2×C3—21no—
431C2×C3—21no—
432C2×C3—41no—
433C2×C3—41no—
434C2×C3#496611yescharacteristic
435C2×C3#500511yescharacteristic
436C2×C3#500611yescharacteristic
437C2×C3#500611yescharacteristic
438C2×C3#513311yescharacteristic
439C2×C3#513911yescharacteristic
440D3—242no—
441D3—241no—
442D3—241no—
443C22—21no—
444C22—21no—
445C22—361no—
446C22—361no—
447C22—361no—
448C22#6383011yescharacteristic
449C22#6383311yescharacteristic
450C22C2×#372211yescharacteristic
451C4—21no—
452C4—21no—
453C4—21no—
454C4—21no—
455C4—21no—
456C4—21no—
457C4—242no—
458C4—361no—
459C4—361no—
460C4—361no—
461C3—21no—
462C3#6954411yescharacteristic, complemented
463C3#7083411yescharacteristic, complemented
464C2—21no—
465C2—21no—
466C2—721no—
467C2#1059110611yescharacteristic
468C2#1059111311yescharacteristic
469C2#1059123211yescharacteristic
subgroupG/H
centerC22C2×#3722
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C42C22
socleC22×C32C2×C22⋊C4
prime radical#64139C22
cosocleC22×C32×C4C23
hypercenterC2×C42D32
hypocenterC32#1512
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C3×#4936C2semidirect
3. C3×#4926C2semidirect
4. #10589154C2semidirect
14. #64084C4semidirect
15. C4×C4⋊(C3⋊D3)C4semidirect
17. #64079C4semidirect
18. C4×#634C4semidirect
30. #4936D3semidirect
31. #4926D3semidirect
400. C32#1512semidirect
462. C3#69544semidirect
463. C3#70834semidirect

Maximal subgroups

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

subgroupindex
#105959502
C3×#49362
C3×#49262
#105891542
#105891512
#708343
#695443