Finite Group Databasebeta

← #11774249

Subgroups — #11774249

Order 1152.

593 conjugacy classes of subgroups.

The subgroup lattice has 477 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#3799C211yesmaximal, characteristic
2C3×C4×D3×C8C211yesmaximal, characteristic, complemented
3#10590248C211yesmaximal, characteristic, complemented
4#10589325C211yesmaximal, characteristic, complemented
5C3×#4456C211yesmaximal, characteristic, complemented
6#10589084C211yesmaximal, characteristic, complemented
7#10589082C211yesmaximal, characteristic, complemented
8#69734—31nomaximal
9#68229—31nomaximal
10C2×#3799C411yescharacteristic
11C4×C4⋊(C3⋊D3)C2211yescharacteristic
12C2×C3×D3×C8—21no—
13C3×C42×D3C2211yescharacteristic
14C3×C4×Dic6C2211yescharacteristic
15#63904—21no—
16C4×#626—21no—
17#63894C411yescharacteristic
18C4×#624—21no—
19Dic3×Dic6C411yescharacteristic
20#63841C411yescharacteristic
21#63836—21no—
22C32×C4×C8C2211yescharacteristic
23C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
24C3×C8×Dic3—21no—
25C3×C4⋊(C3⋊C8)C2211yescharacteristic
26C3×C4×C3⋊C8C2211yescharacteristic
27(C2×D3)⋊(C3⋊C8)—21no—
28Dic3×C3⋊C8—21no—
29C4×#239—31no—
30C4×#235—31no—
31C2×C3×C4×C8—31no—
32#4925—31no—
33#4833—31no—
34C4×D3×C8D311yescharacteristic, complemented
35C3×Q8⋊C8—31no—
36#4535—31no—
37#4483—31no—
38#4459—31no—
39#4459—31no—
40#4459—31no—
41#4459—61no—
42#4456—31no—
43#4456D311yescharacteristic, complemented
44C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
45C2×C4×C3⋊D3—21no—
46C2×C3×C4×D3C2×C411yescharacteristic
47C2×C3×C4×D3D411yescharacteristic
48C2×C3×C4×D3D411yescharacteristic
49C2×C3×Dic6C2×C411yescharacteristic
50C2×#626—21no—
51C2×#624—21no—
52C2×#624—21no—
53#3799—22no—
54#3799C814yescomplemented
55C2×C32×C8—21no—
56C32×C42C2311yescharacteristic
57#3752—21no—
58C4⋊(C3⋊Dic3)C2×C411yescharacteristic
59C2×C3⋊(C3⋊C8)—21no—
60C3×C4⋊Dic3C2×C411yescharacteristic
61C3×Dic3⋊C4—21no—
62C3×C4×Dic3—21no—
63C3×C4×Dic3C2×C411yescharacteristic
64C3×C4×Dic3D411yescharacteristic
65C3×C4×Dic3D411yescharacteristic
66C2×C3×C3⋊C8—21no—
67C2×C3×C3⋊C8—21no—
68C3×D3×C8—24no—
69Dic3⋊Dic3—21no—
70#3722—21no—
71(C2×D3)⋊Dic3—21no—
72Dic32—21no—
73Dic32—21no—
74#1476—91noSylow
75C2×#239—31no—
76C2×#235—31no—
77C22×C3×C8—61no—
78C3×C4×Q8—31no—
79C2×C3×C42—31no—
80Q8×Dic3—31no—
81C4×#67—61no—
82C4×#67—61no—
83#926—31no—
84C2×D3×C8—21no—
85#893—31no—
86#893—61no—
87#892—31no—
88#892—61no—
89C4×D12—31no—
90C4×D12—31no—
91C4×D12—31no—
92C4×D12—61no—
93C4×D12—61no—
94#872—61no—
95C42×D3—61no—
96C42×D3—61no—
97C42×D3C2×D311yescharacteristic
98C4×Dic6—31no—
99C4×Dic6C2×D311yescharacteristic
100C3×C4⋊C8—31no—
101C3×C4×C8—21no—
102C3×C4×C8—31no—
103C3×C4×C8—61no—
104C3×C4×C8C2×D311yescharacteristic
105C3×C4×C8C2×D311yescharacteristic
106#830—61no—
107(C2×D3)⋊C8—61no—
108C8×Dic3—21no—
109C8×Dic3—61no—
110C4⋊(C3⋊C8)—31no—
111C4⋊(C3⋊C8)—31no—
112C4⋊(C3⋊C8)—61no—
113C4⋊(C3⋊C8)C2×D311yescharacteristic
114C4×C3⋊C8—61no—
115C4×C3⋊C8C2×D311yescharacteristic
116C22×C3⋊D3—21no—
117C22×C3×D3C22⋊C411yescharacteristic
118C2×C32×C4C22×C411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C3⋊Dic3—21no—
122C4⋊(C3⋊D3)—21no—
123C4⋊(C3⋊D3)C2×C812yescomplemented
124C4×C3⋊D3—41no—
125C4×C3⋊D3—41no—
126C2×C3×Dic3—21no—
127C2×C3×Dic3—21no—
128C2×C3×Dic3C22⋊C411yescharacteristic
129C2×C3×Dic3C22⋊C411yescharacteristic
130C2×C3×Dic3C22⋊C411yescharacteristic
131C3×C4×D3—21no—
132C3×C4×D3—21no—
133C3×C4×D3—22no—
134C3×C4×D3C2×C812yes—
135C3×C4×D3M1612yes—
136C3×Dic6—21no—
137C3×Dic6C2×C812yescomplemented
138#626—24no—
139#624—24no—
140#624—42no—
141C32×C8—22no—
142C3⋊(C3⋊C8)—41no—
143C3×C3⋊C8—22no—
144C3×C3⋊C8—41no—
145C4×#41—91no—
146#431—91no—
147C2×C4×C8—31no—
148Q8⋊C8—31no—
149Q8⋊C8—91no—
150D4⋊C8—91no—
151D4⋊C8—91no—
152C2×C3×Q8—31no—
153C22×C3×C4—31no—
154C22×C3×C4—31no—
155C22×C3×C4—31no—
156C2×#67—61no—
157#239—34no—
158#239—62no—
159#235—34no—
160#235—62no—
161C2×D12—31no—
162C2×D12—31no—
163C2×D12—61no—
164C2×D12—61no—
165C2×C4×D3—61no—
166C2×C4×D3—61no—
167C2×C4×D3—61no—
168C2×C4×D3—61no—
169C2×C4×D3—61no—
170C2×C4×D3—61no—
171C2×C4×D3—121no—
172C2×C4×D3C4×D311yescharacteristic
173C2×C4×D3D1211yescharacteristic
174C2×C4×D3#6711yescharacteristic
175C2×Dic6C4×D311yescharacteristic
176C2×C3×C8—21no—
177C2×C3×C8—21no—
178C2×C3×C8—41no—
179C2×C3×C8—64no—
180C2×C3×C8—61no—
181C2×C3×C8—61no—
182C3×C4⋊C4—31no—
183C3×C4⋊C4—61no—
184C3×C42—21no—
185C3×C42—31no—
186C3×C42—31no—
187C3×C42—31no—
188C3×C42—61no—
189C3×C42C22×D311yescharacteristic
190C3×C42C22×D311yescharacteristic
191#217—61no—
192(C2×D3)⋊C4—61no—
193(C2×D3)⋊C4—61no—
194(C2×D3)⋊C4—61no—
195(C2×D3)⋊C4—61no—
196(C2×D3)⋊C4—61no—
197(C2×D3)⋊C4—121no—
198C4⋊Dic3—31no—
199C4⋊Dic3—31no—
200C4⋊Dic3—61no—
201C4⋊Dic3—61no—
202C4⋊Dic3C4×D311yescharacteristic
203Dic3⋊C4—21no—
204Dic3⋊C4—61no—
205C4×Dic3—21no—
206C4×Dic3—61no—
207C4×Dic3—61no—
208C4×Dic3—61no—
209C4×Dic3—61no—
210C4×Dic3C4×D311yescharacteristic
211C4×Dic3D1211yescharacteristic
212C4×Dic3#6711yescharacteristic
213C2×C3⋊C8—21no—
214C2×C3⋊C8—21no—
215C2×C3⋊C8—61no—
216C2×C3⋊C8—61no—
217C2×C3⋊C8—121no—
218D3×C8—24no—
219C22×C32C2×C22⋊C411yescharacteristic
220C2×C3⋊D3—22no—
221C2×C3⋊D3—41no—
222C2×C3⋊D3—41no—
223C2×C3×D3—21no—
224C2×C3×D3—21no—
225C2×C3×D3C22⋊C812yes—
226C32×C4—21no—
227C32×C4C22×C811yescharacteristic
228C32×C4C2×M1611yescharacteristic
229C32×C4#13511yescharacteristic
230C32×C4#13511yescharacteristic
231C3⋊Dic3—41no—
232C3×Dic3—22no—
233C3×Dic3—21no—
234C3×Dic3—41no—
235C3×Dic3C22⋊C812yes—
236C3×Dic3#10412yes—
237C2×#41—91no—
238C22×C8—61no—
239C4×Q8—31no—
240C4×Q8—91no—
241C4×D4—91no—
242C4×D4—91no—
243C4×D4—181no—
244C4×D4—181no—
245#117—91no—
246#117—181no—
247C2×C42—31no—
248C2×C42—181no—
249C4⋊C8—31no—
250C4⋊C8—91no—
251C22⋊C8—181no—
252C4×C8—31no—
253C4×C8—61no—
254C4×C8—181no—
255C4×C8D3211yescharacteristic
256C23×C3—31no—
257C22×D3—61no—
258C22×D3—61no—
259C22×D3—121no—
260C22×D3(C2×D3)⋊C411yescharacteristic
261C3×Q8—32no—
262C3×Q8—61no—
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—21no—
266C2×C3×C4—31no—
267C2×C3×C4—31no—
268C2×C3×C4—32no—
269C2×C3×C4—32no—
270C2×C3×C4—31no—
271C2×C3×C4—62no—
272C2×C3×C4—61no—
273C2×C3×C4—61no—
274C2×C3×C4—61no—
275C2×C3×C4—61no—
276C2×C3×C4C2×C4×D311yescharacteristic
277C2×C3×C4C2×C4×D311yescharacteristic
278C2×C3×C4C2×D1211yescharacteristic
279C2×C3×C4D3×D411yescharacteristic
280C2×C3×C4D3×D411yescharacteristic
281C2×C3×C4C2×#6711yescharacteristic
282#67—64no—
283C2×Dic3—21no—
284C2×Dic3—21no—
285C2×Dic3—61no—
286C2×Dic3—61no—
287C2×Dic3—121no—
288C2×Dic3(C2×D3)⋊C411yescharacteristic
289C2×Dic3(C2×D3)⋊C411yescharacteristic
290C2×Dic3(C2×D3)⋊C411yescharacteristic
291D12—32no—
292D12—32no—
293D12—62no—
294D12—64no—
295D12—61no—
296D12—61no—
297D12—121no—
298C4×D3—21no—
299C4×D3—21no—
300C4×D3—22no—
301C4×D3—64no—
302C4×D3—64no—
303C4×D3—122no—
304C4×D3—121no—
305C4×D3—121no—
306C4×D3—121no—
307C4×D3—121no—
308C4×D3—122no—
309C4×D3—241no—
310C4×D3—241no—
311C4×D3D3×C812yes—
312C4×D3ΓL(1,𝔽25)12yes—
313Dic6—21no—
314Dic6D3×C812yescomplemented
315C3×C8—22no—
316C3×C8—22no—
317C3×C8—42no—
318C3×C8—62no—
319C3×C8—121no—
320C3⋊C8—22no—
321C3⋊C8—41no—
322C3⋊C8—121no—
323C3⋊C8—121no—
324C3⋊C8—241no—
325C2×C32C2×C22⋊C811yescharacteristic
326C2×C32#41611yescharacteristic
327C2×C32C2×#10411yescharacteristic
328C3⋊D3—42no—
329C3×D3—22no—
330#41—94no—
331#41—182no—
332C2×Q8—31no—
333C2×D4—91no—
334C2×D4—181no—
335C22×C4—31no—
336C22×C4—31no—
337C22×C4—31no—
338C22×C4—181no—
339C22×C4—181no—
340C22×C4—181no—
341C2×C8—21no—
342C2×C8—64no—
343C2×C8—61no—
344C2×C8—61no—
345C2×C8—181no—
346C4⋊C4—31no—
347C4⋊C4—61no—
348C4⋊C4—91no—
349C4⋊C4—181no—
350C22⋊C4—181no—
351C22⋊C4—181no—
352C22⋊C4—181no—
353C42—31no—
354C42—31no—
355C42—31no—
356C42—61no—
357C42—181no—
358C42—181no—
359C42C2×D3211yescharacteristic
360C22×C3—21no—
361C22×C3—32no—
362C22×C3—61no—
363C22×C3—61no—
364C22×C3D3×C22⋊C411yescharacteristic
365C22×C3C2×(C2×D3)⋊C411yescharacteristic
366C2×D3—21no—
367C2×D3—21no—
368C2×D3—62no—
369C2×D3—62no—
370C2×D3—122no—
371C2×D3—121no—
372C2×D3—121no—
373C2×D3—121no—
374C2×D3—121no—
375C2×D3—241no—
376C2×D3—241no—
377C2×D3(C2×D3)⋊C812yes—
378C3×C4—21no—
379C3×C4—21no—
380C3×C4—21no—
381C3×C4—21no—
382C3×C4—21no—
383C3×C4—21no—
384C3×C4—32no—
385C3×C4—32no—
386C3×C4—41no—
387C3×C4—61no—
388C3×C4—62no—
389C3×C4—121no—
390C3×C4C2×D3×C811yescharacteristic
391C3×C4C2×D3×C811yescharacteristic
392C3×C4C2×ΓL(1,𝔽25)11yescharacteristic
393C3×C4#90411yescharacteristic
394C3×C4#90411yescharacteristic
395C3×C4D3×M1611yescharacteristic
396C3×C4#91611yescharacteristic
397C3×C4#91911yescharacteristic
398Dic3—22no—
399Dic3—21no—
400Dic3—41no—
401Dic3—121no—
402Dic3—121no—
403Dic3—241no—
404Dic3#80512yes—
405Dic3(C2×D3)⋊C812yes—
406C32#147611yescharacteristic, complemented, Sylow
407C23—31no—
408C23—181no—
409Q8—32no—
410Q8—61no—
411D4—92no—
412D4—184no—
413D4—181no—
414C2×C4—31no—
415C2×C4—31no—
416C2×C4—32no—
417C2×C4—32no—
418C2×C4—31no—
419C2×C4—62no—
420C2×C4—61no—
421C2×C4—61no—
422C2×C4—61no—
423C2×C4—61no—
424C2×C4—184no—
425C2×C4—181no—
426C2×C4—362no—
427C2×C4—361no—
428C2×C4—361no—
429C2×C4C4×D3211yescharacteristic
430C2×C4D3×D1211yescharacteristic
431C2×C4D3×#6711yescharacteristic
432C8—22no—
433C8—62no—
434C8—121no—
435C8—361no—
436C2×C3—21no—
437C2×C3—21no—
438C2×C3—21no—
439C2×C3—62no—
440C2×C3D3×C22⋊C811yescharacteristic
441C2×C3#480411yescharacteristic
442C2×C3D3×#10411yescharacteristic
443C2×C3C2×#80511yescharacteristic
444C2×C3C2×(C2×D3)⋊C811yescharacteristic
445C2×C3#511311yescharacteristic
446D3—22no—
447D3—122no—
448D3—122no—
449D3—242no—
450C22—32no—
451C22—61no—
452C22—61no—
453C22—182no—
454C22—361no—
455C22—361no—
456C22D3×(C2×D3)⋊C411yescharacteristic
457C4—21no—
458C4—32no—
459C4—32no—
460C4—62no—
461C4—61no—
462C4—121no—
463C4—361no—
464C4D32×C811yescharacteristic
465C4D3×ΓL(1,𝔽25)11yescharacteristic
466C4#6380611yescharacteristic
467C4#6380811yescharacteristic
468C3—21no—
469C3#6822911yescharacteristic, complemented
470C3#6973411yescharacteristic, complemented
471C2—62no—
472C2—362no—
473C2D3×#80511yescharacteristic
474C2#1059069011yescharacteristic
475C2D3×(C2×D3)⋊C811yescharacteristic
subgroupG/H
centerC2×C4D3×D12
commutatorC32×C4C22×C8
FrattiniC42C2×D32
FittingC32×C4×C8C22
socleC22×C32C2×C22⋊C4
prime radicalC2×#3799C4
cosocleC32×C42C23
hypercenterC4×C8D32
hypocenterC32#1476
LCSG ▷ 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×C4×D3×C8C2semidirect
3. #10590248C2semidirect
4. #10589325C2semidirect
5. C3×#4456C2semidirect
6. #10589084C2semidirect
7. #10589082C2semidirect
34. C4×D3×C8D3semidirect
43. #4456D3semidirect
54. #3799C8semidirect
123. C4⋊(C3⋊D3)C2×C8semidirect
137. C3×Dic6C2×C8semidirect
314. Dic6D3×C8semidirect
406. C32#1476semidirect
469. C3#68229semidirect
470. C3#69734semidirect

Maximal subgroups

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

subgroupindex
C4×#37992
C3×C4×D3×C82
#105902482
#105893252
C3×#44562
#105890842
#105890822
#697343
#682293