Finite Group Databasebeta

← #11861566

Subgroups — #11861566

Order 1152.

979 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#3799C211yesmaximal, characteristic
2#10592533C211yesmaximal, characteristic, complemented
3C3×#4833C211yesmaximal, characteristic, complemented
4C3×#4830C211yesmaximal, characteristic, complemented
5#10590906C212yesmaximal, complemented
6#10590721C212yesmaximal, complemented
7C8×#624C212yesmaximal, complemented
8#10590643C212yesmaximal, complemented
9#10590327C211yesmaximal, characteristic, complemented
10C4×D3×C3⋊C8C211yesmaximal, characteristic, complemented
11#10590250C211yesmaximal, characteristic, complemented
12C8×#239—31nomaximal
13#79276—31nomaximal
14C2×#3799C411yescharacteristic
15C2×C8×C3⋊D3C2212yes—
16C4×C4⋊(C3⋊D3)C2211yescharacteristic
17C3×C42×D3C2211yescharacteristic
18C3×C4×Dic6C2211yescharacteristic
19#63904C412yes—
20C4×#626C2212yes—
21#63894C411yescharacteristic
22C4×#624C2212yes—
23Dic3×Dic6C411yescharacteristic
24#63841C411yescharacteristic
25#63836C412yes—
26C2×#3710C2212yes—
27C2×D3×C3⋊C8C2211yescharacteristic
28C2×D3×C3⋊C8C2211yescharacteristic
29C32×C4⋊C8C2211yescharacteristic
30#63647C2212yes—
31C4×C3⋊(C3⋊C8)C2211yescharacteristic
32C3×(C2×D3)⋊C8C2212yes—
33C3×Dic3⋊C8C2212yes—
34C3×C8×Dic3C2212yes—
35C3×C8×Dic3C2212yes—
36C3×C4⋊(C3⋊C8)C2211yescharacteristic
37C3×C4×C3⋊C8C2211yescharacteristic
38Dic3⋊(C3⋊C8)C2212yes—
39#63557C2212yes—
40Dic3×C3⋊C8C2212yes—
41Dic3×C3⋊C8C2211yescharacteristic
42Dic3×C3⋊C8C2211yescharacteristic
43C4×#239—31no—
44C4×#235—31no—
45C3×C8×Q8—31no—
46C3×#431—31no—
47Q8×C3⋊C8—31no—
48C2×C4×C3⋊C8—31no—
49#4834—31no—
50#4834—31no—
51#4834—32no—
52#4834—31no—
53#4834—61no—
54#4833—32no—
55#4833D311yescharacteristic, complemented
56#4830—31no—
57#4830D311yescharacteristic, complemented
58#67⋊C8—32no—
59#67⋊C8—32no—
60C8×D12—32no—
61C8×D12—31no—
62#4685—32no—
63C4×D3×C8—31no—
64C4×D3×C8—32no—
65C4×D3×C8—32no—
66C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
67C2×C4×C3⋊D3C2312yes—
68C2×C3×C4×D3C2×C411yescharacteristic
69C2×C3×C4×D3C2×C411yescharacteristic
70C2×C3×C4×D3C2311yescharacteristic
71C2×C3×Dic6C2×C411yescharacteristic
72C2×#626C2×C412yes—
73C2×#624C2×C412yes—
74C2×#624C2×C412yes—
75#3799C818yescomplemented
76C2×C32×C8C2312yes—
77C32×C42C2311yescharacteristic
78#3752C2×C412yes—
79C4⋊(C3⋊Dic3)C2×C411yescharacteristic
80C2×C3⋊(C3⋊C8)C2311yescharacteristic
81C2×C3⋊(C3⋊C8)C2311yescharacteristic
82C8×C3⋊D3—24no—
83C3×C4⋊Dic3C2×C411yescharacteristic
84C3×Dic3⋊C4C2×C412yes—
85C3×C4×Dic3C2×C411yescharacteristic
86C3×C4×Dic3C2×C411yescharacteristic
87C3×C4×Dic3C2311yescharacteristic
88C3×C4×Dic3C2312yes—
89C2×C3×C3⋊C8C2311yescharacteristic
90C2×C3×C3⋊C8C2312yes—
91C2×C3×C3⋊C8C2311yescharacteristic
92Dic3⋊Dic3C2×C412yes—
93#3722C2×C412yes—
94(C2×D3)⋊Dic3C2×C412yes—
95Dic32C2×C412yes—
96Dic32C2×C412yes—
97#3710—24no—
98D3×C3⋊C8—22no—
99D3×C3⋊C8—22no—
100C8×#41—91noSylow
101C2×#239—31no—
102C2×#235—31no—
103C3×C4×Q8—31no—
104C2×C3×C42—31no—
105Q8×Dic3—31no—
106C4×#67—32no—
107C4×#67—32no—
108#926—31no—
109C22×C3⋊C8—31no—
110C22×C3⋊C8—31no—
111C2×D3×C8—31no—
112C2×D3×C8—31no—
113C2×D3×C8—32no—
114C2×D3×C8—32no—
115C2×D3×C8—32no—
116C2×D3×C8—32no—
117C2×D3×C8—62no—
118#893—32no—
119#893—31no—
120#892—31no—
121#892—32no—
122C4×D12—32no—
123C4×D12—31no—
124C4×D12—31no—
125C4×D12—31no—
126C4×D12—61no—
127#872—32no—
128C42×D3—32no—
129C42×D3—32no—
130C42×D3C2×D311yescharacteristic
131C4×Dic6—31no—
132C4×Dic6C2×D311yescharacteristic
133C3×C4⋊C8—21no—
134C3×C4⋊C8—32no—
135C3×C4⋊C8—31no—
136C3×C4⋊C8C2×D311yescharacteristic
137C3×C4⋊C8C2×D311yescharacteristic
138C3×C22⋊C8—32no—
139C3×C4×C8—32no—
140C3×C4×C8—32no—
141C3×C4×C8—31no—
142(C2×D3)⋊C8—32no—
143(C2×D3)⋊C8—32no—
144(C2×D3)⋊C8—32no—
145(C2×D3)⋊C8—32no—
146(C2×D3)⋊C8—62no—
147(C2×D3)⋊C8C2×D312yes—
148Dic3⋊C8—32no—
149Dic3⋊C8C2×D312yes—
150C8×Dic3—31no—
151C8×Dic3—32no—
152C8×Dic3—31no—
153C8×Dic3C2×D312yes—
154C8×Dic3C2×D312yes—
155C4⋊(C3⋊C8)—32no—
156C4⋊(C3⋊C8)C2×D311yescharacteristic
157C4×C3⋊C8—31no—
158C4×C3⋊C8—31no—
159C4×C3⋊C8—31no—
160C4×C3⋊C8—31no—
161C4×C3⋊C8—32no—
162C4×C3⋊C8—61no—
163C4×C3⋊C8C2×D311yescharacteristic
164C22×C3⋊D3C22×C412yes—
165C22×C3×D3C22×C411yescharacteristic
166C2×C32×C4C22×C411yescharacteristic
167C2×C32×C4C22×C411yescharacteristic
168C2×C32×C4C2411yescharacteristic
169C2×C3⋊Dic3C22×C412yes—
170C4⋊(C3⋊D3)C2×C814yescomplemented
171C4×C3⋊D3—22no—
172C4×C3⋊D3—22no—
173C2×C3×Dic3C22×C412yes—
174C2×C3×Dic3C22×C411yescharacteristic
175C2×C3×Dic3C22×C411yescharacteristic
176C2×C3×Dic3C22×C412yes—
177C2×C3×Dic3C22×C411yescharacteristic
178C3×C4×D3—21no—
179C3×C4×D3—21no—
180C3×C4×D3—22no—
181C3×C4×D3C2×C814yescomplemented
182C3×Dic6C2×C814yescomplemented
183#626C2×C818yescomplemented
184#624—24no—
185#624C2×C818yescomplemented
186C32×C8—22no—
187C3⋊(C3⋊C8)—21no—
188C3⋊(C3⋊C8)#4112yescomplemented
189C3×C3⋊C8—21no—
190C3×C3⋊C8—22no—
191C3×C3⋊C8#4112yescomplemented
192C4×#41—91no—
193C8×Q8—31no—
194C8×Q8—91no—
195C8×D4—92no—
196C8×D4—91no—
197C8×D4—92no—
198C8×D4—91no—
199#431—31no—
200#431—92no—
201C2×C4×C8—92no—
202C2×C4×C8—91no—
203C2×C3×Q8—31no—
204C22×C3×C4—31no—
205C22×C3×C4—31no—
206C22×C3×C4—31no—
207C2×#67—32no—
208#239—38no—
209#235—38no—
210C2×D12—32no—
211C2×D12—31no—
212C2×D12—31no—
213C2×D12—61no—
214C2×C4×D3—32no—
215C2×C4×D3—32no—
216C2×C4×D3—32no—
217C2×C4×D3—32no—
218C2×C4×D3—32no—
219C2×C4×D3—32no—
220C2×C4×D3—62no—
221C2×C4×D3C4×D311yescharacteristic
222C2×C4×D3C4×D311yescharacteristic
223C2×C4×D3C22×D311yescharacteristic
224C2×Dic6C4×D311yescharacteristic
225C2×C3×C8—22no—
226C2×C3×C8—31no—
227C2×C3×C8—32no—
228C2×C3×C8—31no—
229C2×C3×C8C22×D312yes—
230C2×C3×C8C22×D312yes—
231C3×C4⋊C4—32no—
232C3×C4⋊C4—31no—
233C3×C42—21no—
234C3×C42—31no—
235C3×C42—31no—
236C3×C42—31no—
237C3×C42—32no—
238C3×C42C22×D311yescharacteristic
239C3×C42C22×D311yescharacteristic
240#217—32no—
241(C2×D3)⋊C4—32no—
242(C2×D3)⋊C4—32no—
243(C2×D3)⋊C4—32no—
244(C2×D3)⋊C4—32no—
245(C2×D3)⋊C4—32no—
246(C2×D3)⋊C4—62no—
247C4⋊Dic3—31no—
248C4⋊Dic3—31no—
249C4⋊Dic3—32no—
250C4⋊Dic3—61no—
251C4⋊Dic3C4×D311yescharacteristic
252Dic3⋊C4—32no—
253Dic3⋊C4C4×D312yes—
254C4×Dic3—32no—
255C4×Dic3—32no—
256C4×Dic3—32no—
257C4×Dic3—32no—
258C4×Dic3C4×D311yescharacteristic
259C4×Dic3C4×D311yescharacteristic
260C4×Dic3C22×D311yescharacteristic
261C4×Dic3C22×D312yes—
262C2×C3⋊C8—31no—
263C2×C3⋊C8—31no—
264C2×C3⋊C8—31no—
265C2×C3⋊C8—31no—
266C2×C3⋊C8—61no—
267C2×C3⋊C8—61no—
268C2×C3⋊C8—62no—
269C2×C3⋊C8—62no—
270C2×C3⋊C8C22×D311yescharacteristic
271C2×C3⋊C8C22×D312yes—
272C2×C3⋊C8C22×D311yescharacteristic
273D3×C8—64no—
274D3×C8—64no—
275D3×C8—64no—
276D3×C8—62no—
277D3×C8—62no—
278D3×C8—64no—
279D3×C8—124no—
280C22×C32C23×C411yescharacteristic
281C2×C3⋊D3—22no—
282C2×C3⋊D3—22no—
283C2×C3⋊D3C22×C814yes—
284C2×C3×D3—21no—
285C2×C3×D3—21no—
286C2×C3×D3C22×C812yes—
287C32×C4—21no—
288C32×C4C22×C812yes—
289C32×C4C2×#4111yescharacteristic
290C32×C4C2×#4111yescharacteristic
291C3⋊Dic3—22no—
292C3×Dic3—21no—
293C3×Dic3—22no—
294C3×Dic3C22×C812yes—
295C3×Dic3C22×C814yes—
296C3×Dic3#13112yes—
297C2×#41—91no—
298C22×C8—92no—
299C22×C8—91no—
300C22×C8—91no—
301C22×C8—92no—
302C4×Q8—31no—
303C4×Q8—91no—
304C4×D4—91no—
305C4×D4—92no—
306C4×D4—92no—
307C4×D4—91no—
308#117—92no—
309#117—91no—
310C2×C42—31no—
311C2×C42—92no—
312C4⋊C8—32no—
313C4⋊C8—31no—
314C4⋊C8—92no—
315C4⋊C8D3211yescharacteristic
316C22⋊C8—32no—
317C22⋊C8—92no—
318C22⋊C8—92no—
319C4×C8—32no—
320C4×C8—32no—
321C4×C8—31no—
322C4×C8—91no—
323C4×C8—91no—
324C4×C8—92no—
325C4×C8—91no—
326C23×C3—31no—
327C22×D3—32no—
328C22×D3—32no—
329C22×D3—62no—
330C22×D3C2×C4×D311yescharacteristic
331C3×Q8—34no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4—21no—
335C2×C3×C4—31no—
336C2×C3×C4—31no—
337C2×C3×C4—32no—
338C2×C3×C4—34no—
339C2×C3×C4—32no—
340C2×C3×C4—31no—
341C2×C3×C4—62no—
342C2×C3×C4—61no—
343C2×C3×C4—61no—
344C2×C3×C4C2×C4×D311yescharacteristic
345C2×C3×C4C2×C4×D311yescharacteristic
346C2×C3×C4C2×C4×D311yescharacteristic
347C2×C3×C4C2×C4×D311yescharacteristic
348C2×C3×C4C23×D311yescharacteristic
349C2×C3×C4C23×D311yescharacteristic
350#67—38no—
351C2×Dic3—32no—
352C2×Dic3—32no—
353C2×Dic3—62no—
354C2×Dic3C2×C4×D312yes—
355C2×Dic3C2×C4×D311yescharacteristic
356C2×Dic3C2×C4×D311yescharacteristic
357C2×Dic3C2×C4×D312yes—
358C2×Dic3C2×C4×D311yescharacteristic
359D12—38no—
360D12—34no—
361D12—34no—
362D12—64no—
363C4×D3—21no—
364C4×D3—21no—
365C4×D3—22no—
366C4×D3—38no—
367C4×D3—38no—
368C4×D3—64no—
369C4×D3—62no—
370C4×D3—62no—
371C4×D3—62no—
372C4×D3—62no—
373C4×D3—64no—
374C4×D3—122no—
375C4×D3—122no—
376C4×D3D3×C814yescomplemented
377Dic6D3×C814yescomplemented
378C3×C8—22no—
379C3×C8—22no—
380C3×C8—32no—
381C3×C8—42no—
382C3×C8—62no—
383C3×C8—61no—
384C3⋊C8—22no—
385C3⋊C8—21no—
386C3⋊C8—32no—
387C3⋊C8—32no—
388C3⋊C8—62no—
389C3⋊C8—61no—
390C3⋊C8—61no—
391C3⋊C8—121no—
392C3⋊C8#23912yescomplemented
393C2×C32C4×#4111yescharacteristic
394C2×C32C23×C811yescharacteristic
395C2×C32C2×#13111yescharacteristic
396C3⋊D3—24no—
397C3×D3—22no—
398#41—98no—
399C2×Q8—31no—
400C2×D4—92no—
401C2×D4—91no—
402C22×C4—31no—
403C22×C4—31no—
404C22×C4—31no—
405C22×C4—92no—
406C22×C4—92no—
407C22×C4—92no—
408C2×C8—31no—
409C2×C8—32no—
410C2×C8—31no—
411C2×C8—91no—
412C2×C8—91no—
413C2×C8—184no—
414C2×C8—184no—
415C2×C8—182no—
416C2×C8—182no—
417C2×C8C2×D3212yes—
418C4⋊C4—32no—
419C4⋊C4—31no—
420C4⋊C4—92no—
421C4⋊C4—91no—
422C22⋊C4—92no—
423C22⋊C4—92no—
424C22⋊C4—92no—
425C42—31no—
426C42—32no—
427C42—31no—
428C42—31no—
429C42—92no—
430C42—92no—
431C42C2×D3211yescharacteristic
432C22×C3—21no—
433C22×C3—32no—
434C22×C3—61no—
435C22×C3—61no—
436C22×C3C22×C4×D311yescharacteristic
437C22×C3C22×C4×D311yescharacteristic
438C2×D3—21no—
439C2×D3—21no—
440C2×D3—34no—
441C2×D3—34no—
442C2×D3—64no—
443C2×D3—62no—
444C2×D3—62no—
445C2×D3—62no—
446C2×D3—62no—
447C2×D3—122no—
448C2×D3—122no—
449C2×D3C2×D3×C812yes—
450C3×C4—21no—
451C3×C4—21no—
452C3×C4—22no—
453C3×C4—21no—
454C3×C4—21no—
455C3×C4—32no—
456C3×C4—34no—
457C3×C4—32no—
458C3×C4—41no—
459C3×C4—62no—
460C3×C4—61no—
461C3×C4C2×D3×C812yes—
462C3×C4C2×D3×C812yes—
463C3×C4C2×#23911yescharacteristic
464C3×C4D3×#4111yescharacteristic
465C3×C4D3×#4111yescharacteristic
466C3×C4D3×#4111yescharacteristic
467Dic3—22no—
468Dic3—21no—
469Dic3—62no—
470Dic3—62no—
471Dic3—122no—
472Dic3C2×D3×C814yes—
473Dic3C2×D3×C812yes—
474Dic3#90712yes—
475C32C8×#4111yescharacteristic, complemented, Sylow
476C23—31no—
477C23—92no—
478Q8—34no—
479D4—98no—
480D4—94no—
481C2×C4—31no—
482C2×C4—31no—
483C2×C4—32no—
484C2×C4—34no—
485C2×C4—31no—
486C2×C4—32no—
487C2×C4—62no—
488C2×C4—61no—
489C2×C4—61no—
490C2×C4—98no—
491C2×C4—92no—
492C2×C4—184no—
493C2×C4—182no—
494C2×C4—182no—
495C2×C4C4×D3211yescharacteristic
496C2×C4C4×D3211yescharacteristic
497C2×C4C22×D3211yescharacteristic
498C8—22no—
499C8—32no—
500C8—61no—
501C8—62no—
502C8—92no—
503C8—181no—
504C2×C3—21no—
505C2×C3—21no—
506C2×C3—21no—
507C2×C3—62no—
508C2×C3#552211yescharacteristic
509C2×C3C4×#23911yescharacteristic
510C2×C3C22×D3×C811yescharacteristic
511C2×C3C22×D3×C811yescharacteristic
512C2×C3C2×#90711yescharacteristic
513C2×C3D3×#13111yescharacteristic
514D3—22no—
515D3—64no—
516D3—64no—
517D3—124no—
518C22—32no—
519C22—61no—
520C22—61no—
521C22—94no—
522C22—182no—
523C22—182no—
524C22C2×C4×D3211yescharacteristic
525C4—21no—
526C4—32no—
527C4—34no—
528C4—32no—
529C4—61no—
530C4—62no—
531C4—182no—
532C4D32×C812yes—
533C4#6431211yescharacteristic
534C4D3×#23911yescharacteristic
535C3—21no—
536C3#7927611yescharacteristic, complemented
537C3C8×#23911yescharacteristic, complemented
538C2—62no—
539C2—184no—
540C2#1059436211yescharacteristic
541C2C2×D32×C811yescharacteristic
542C2D3×#90711yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutatorC2×C32C23×C8
FittingC32×C4⋊C8C22
socleC22×C32C23×C4
prime radicalC2×#3799C4
cosocleC2×C32×C4C24
hypercenterC4⋊C8D32
hypocenterC32C8×#41
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #10592533C2semidirect
3. C3×#4833C2semidirect
4. C3×#4830C2semidirect
5. #10590906C2semidirect
6. #10590721C2semidirect
7. C8×#624C2semidirect
8. #10590643C2semidirect
9. #10590327C2semidirect
10. C4×D3×C3⋊C8C2semidirect
11. #10590250C2semidirect
55. #4833D3semidirect
57. #4830D3semidirect
75. #3799C8semidirect
170. C4⋊(C3⋊D3)C2×C8semidirect
181. C3×C4×D3C2×C8semidirect
182. C3×Dic6C2×C8semidirect
183. #626C2×C8semidirect
185. #624C2×C8semidirect
188. C3⋊(C3⋊C8)#41semidirect
191. C3×C3⋊C8#41semidirect
376. C4×D3D3×C8semidirect
377. Dic6D3×C8semidirect
392. C3⋊C8#239semidirect
475. C32C8×#41semidirect
536. C3#79276semidirect
537. C3C8×#239semidirect

Maximal subgroups

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

subgroupindex
C4×#37992
#105925332
C3×#48332
C3×#48302
#105909062
#105907212
C8×#6242
#105906432
#105903272
C4×D3×C3⋊C82
#105902502
C8×#2393
#792763