Finite Group Databasebeta

← #11858360

Subgroups — #11858360

Order 1152.

1025 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5522C211yesmaximal, characteristic
2C2×#63815C211yesmaximal, characteristic
3C2×#63814C211yesmaximal, characteristic
4#10592698C211yesmaximal, characteristic, complemented
5C3×#4999C211yesmaximal, characteristic, complemented
6#10591115C211yesmaximal, characteristic, complemented
7C2×Dic3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
8#10590336C212yesmaximal, complemented
9#10590324C212yesmaximal, complemented
10#10590324C212yesmaximal, complemented
11D3×C4⋊(C3⋊C8)C212yesmaximal, complemented
12#82512—31nomaximal
13#79081—31nomaximal
14C2×C3×#235C2211yescharacteristic
15C32×#117C2211yescharacteristic
16C2×#3748C2211yescharacteristic
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18C2×C3×C4×Dic3C2211yescharacteristic
19C2×C3×#208C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C3×#893C411yescharacteristic
22C3×#893C411yescharacteristic
23C3×#887C411yescharacteristic
24C3×#887C411yescharacteristic
25C3×#67⋊C4C412yes—
26C3×#67⋊C4C412yes—
27C3×#872C2212yes—
28C3×C42×D3C2212yes—
29C2×#3711C2212yes—
30C2×#3711C2212yes—
31#63815—24no—
32#63814—24no—
33C2×D3×C3⋊C8C2212yes—
34C2×D3×C3⋊C8C2212yes—
35C4⋊(C3⋊(C3⋊C8))C2212yes—
36C4⋊(C3⋊(C3⋊C8))C2212yes—
37C3×C4⋊(C3⋊C8)C2212yes—
38C3×C4⋊(C3⋊C8)C2212yes—
39Dic3⋊(C3⋊C8)C2211yescharacteristic
40Dic3⋊(C3⋊C8)C2212yes—
41Dic3⋊(C3⋊C8)C2211yescharacteristic
42Dic3⋊(C3⋊C8)C2211yescharacteristic
43Dic3⋊(C3⋊C8)C2212yes—
44Dic3⋊(C3⋊C8)C2211yescharacteristic
45C3×C4×#41—31no—
46C2×#948—31no—
47C2×#948—31no—
48C2×#907—31no—
49C2×#901—31no—
50#5522D311yescharacteristic
51C3×#424—31no—
52#5118—31no—
53C2×Dic3⋊C8—31no—
54#4999—31no—
55#4999—31no—
56#4999—32no—
57#4999—32no—
58#4999—61no—
59#4999D311yescharacteristic, complemented
60#4924—31no—
61#4924—32no—
62C2×C4⋊(C3⋊C8)—31no—
63C2×C4⋊(C3⋊C8)—32no—
64#4839—32no—
65#4839—32no—
66#4837—32no—
67D3×C4⋊C8—32no—
68C22×C32×C4C2311yescharacteristic
69C2×C3×#67C2×C412yes—
70C22×C3×Dic3C2×C411yescharacteristic
71C22×C3×Dic3C2×C411yescharacteristic
72C3×#235D414yes—
73C3×#235Q814yes—
74C2×C3×D12C2×C411yescharacteristic
75C2×C3×C4×D3C2×C412yes—
76C2×C3×C4×D3C2×C412yes—
77C2×C3×C4×D3C2312yes—
78C2×C3×Dic6C2×C411yescharacteristic
79C32×C4⋊C4C2×C411yescharacteristic
80C32×C4⋊C4C2×C411yescharacteristic
81C32×C22⋊C4C2×C412yes—
82C32×C42C2312yes—
83#3748—22no—
84C2×C3⋊(C3⋊C8)—22no—
85C2×C3⋊(C3⋊C8)C2311yescharacteristic
86C2×C3⋊(C3⋊C8)C2312yes—
87C2×C3⋊(C3⋊C8)C2311yescharacteristic
88C3×(C2×D3)⋊C4C2×C412yes—
89C3×(C2×D3)⋊C4C2×C412yes—
90C3×Dic3⋊C4C2×C412yes—
91C3×Dic3⋊C4C2×C412yes—
92C3×C4×Dic3C2×C412yes—
93C3×C4×Dic3C2×C412yes—
94C3×C4×Dic3C2×C411yescharacteristic
95C3×C4×Dic3C2×C411yescharacteristic
96C3×C4×Dic3C2311yescharacteristic
97C3×C4×Dic3C2311yescharacteristic
98C3×#208—22no—
99C2×C3×C3⋊C8—22no—
100C2×C3×C3⋊C8C2311yescharacteristic
101C2×C3×C3⋊C8C2311yescharacteristic
102C2×C3×C3⋊C8C2312yes—
103#3711—24no—
104#3711—24no—
105D3×C3⋊C8—24no—
106D3×C3⋊C8—24no—
107#2906—91noSylow
108C2×C3×#41—31no—
109C2×#235C2×D311yescharacteristic
110C2×C3×M16—31no—
111C22×C3×C8—31no—
112C3×C4×Q8—31no—
113C3×C4×Q8—31no—
114C3×C4×D4—31no—
115C3×C4×D4—31no—
116C3×C4×D4—32no—
117C3×C4×D4—32no—
118C3×#117—21no—
119C3×#117—32no—
120C3×#117C2×D311yescharacteristic
121C3×#117C2×D311yescharacteristic
122C2×C3×C42—31no—
123C2×C3×C42—32no—
124#948—64no—
125#948—64no—
126C2×C4×Dic3C2×D311yescharacteristic
127C2×#208—31no—
128C2×#208—31no—
129C2×#208—32no—
130C2×#208—32no—
131C2×#208—61no—
132C2×#208C2×D311yescharacteristic
133C22×C3⋊C8—31no—
134C22×C3⋊C8—31no—
135C22×C3⋊C8—32no—
136C22×C3⋊C8—32no—
137C22×C3⋊C8—61no—
138C22×C3⋊C8C2×D311yescharacteristic
139#907—64no—
140#901—64no—
141C2×ΓL(1,𝔽25)—32no—
142C2×ΓL(1,𝔽25)—32no—
143C2×D3×C8—32no—
144C2×D3×C8—32no—
145#893Dic311yescharacteristic
146#893Dic311yescharacteristic
147#887Dic311yescharacteristic
148#887Dic311yescharacteristic
149#67⋊C4Dic312yes—
150#67⋊C4Dic312yes—
151#872C2×D312yes—
152C42×D3C2×D312yes—
153C3×C4⋊C8—32no—
154C3×C4⋊C8—32no—
155Dic3⋊C8—31no—
156Dic3⋊C8—32no—
157Dic3⋊C8—31no—
158Dic3⋊C8—31no—
159Dic3⋊C8—31no—
160Dic3⋊C8—32no—
161C4⋊(C3⋊C8)—32no—
162C4⋊(C3⋊C8)—32no—
163C4⋊(C3⋊C8)—32no—
164C4⋊(C3⋊C8)—32no—
165C4⋊(C3⋊C8)—31no—
166C4⋊(C3⋊C8)—32no—
167C4⋊(C3⋊C8)—31no—
168C4⋊(C3⋊C8)—31no—
169C4⋊(C3⋊C8)—31no—
170C4⋊(C3⋊C8)—32no—
171C4⋊(C3⋊C8)—62no—
172C4⋊(C3⋊C8)—62no—
173C4⋊(C3⋊C8)C2×D312yes—
174C4⋊(C3⋊C8)C2×D312yes—
175C23×C32C22×C411yescharacteristic
176C22×C3×D3C22×C412yes—
177C2×C32×C4C22×C412yes—
178C2×C32×C4C22×C412yes—
179C2×C32×C4C22×C411yescharacteristic
180C2×C32×C4C2×D412yes—
181C2×C32×C4C2×Q812yes—
182C2×C32×C4C2411yescharacteristic
183C3×#67C4⋊C418yes—
184C2×C3×Dic3—22no—
185C2×C3×Dic3—41no—
186C2×C3×Dic3C22×C411yescharacteristic
187C2×C3×Dic3C22×C411yescharacteristic
188C2×C3×Dic3C22×C411yescharacteristic
189C2×C3×Dic3C22×C412yes—
190C2×C3×Dic3C22×C411yescharacteristic
191C3×D12C4⋊C414yes—
192C3×C4×D3—24no—
193C3×C4×D3—42no—
194C3×C4×D3C2×D414yes—
195C3×C4×D3C2×Q814yes—
196C3×Dic6C4⋊C414yes—
197C3⋊(C3⋊C8)—21no—
198C3⋊(C3⋊C8)—22no—
199C3⋊(C3⋊C8)—21no—
200C3×C3⋊C8—21no—
201C3×C3⋊C8—22no—
202C3×C3⋊C8—21no—
203C2×#131—91no—
204C2×#131—91no—
205C4×#41—31no—
206#424—31no—
207#424—92no—
208#424—92no—
209#424—91no—
210#423—92no—
211#423—91no—
212C2×C4⋊C8—92no—
213C2×C4⋊C8—91no—
214C3×#41—34no—
215C3×#41—34no—
216C2×C3×Q8—31no—
217C2×C3×D4—32no—
218C2×C3×D4—31no—
219C22×C3×C4—21no—
220C22×C3×C4—32no—
221C22×C3×C4—31no—
222C22×C3×C4—31no—
223C22×C3×C4—32no—
224C22×C3×C4—32no—
225C22×C3×C4C22×D311yescharacteristic
226C22×C3×C4C22×D311yescharacteristic
227C2×#67C2×Dic312yes—
228C22×Dic3C2×Dic311yescharacteristic
229C22×Dic3C2×Dic311yescharacteristic
230#235Dic614yes—
231#235D1214yes—
232C2×D12C2×Dic311yescharacteristic
233C2×C4×D3C2×Dic312yes—
234C2×C4×D3C2×Dic312yes—
235C2×C4×D3C22×D312yes—
236C2×Dic6C2×Dic311yescharacteristic
237C3×M16—62no—
238C2×C3×C8—31no—
239C2×C3×C8—32no—
240C2×C3×C8—31no—
241C2×C3×C8—62no—
242C3×C4⋊C4—21no—
243C3×C4⋊C4—21no—
244C3×C4⋊C4—32no—
245C3×C4⋊C4—32no—
246C3×C4⋊C4C4×D311yescharacteristic
247C3×C4⋊C4C4×D311yescharacteristic
248C3×C4⋊C4C2×Dic311yescharacteristic
249C3×C4⋊C4C2×Dic311yescharacteristic
250C3×C22⋊C4—22no—
251C3×C22⋊C4—32no—
252C3×C22⋊C4—32no—
253C3×C22⋊C4C4×D312yes—
254C3×C22⋊C4C2×Dic312yes—
255C3×C42—22no—
256C3×C42—32no—
257C3×C42—31no—
258C3×C42—32no—
259C3×C42—31no—
260C3×C42—31no—
261C3×C42—31no—
262C3×C42C22×D312yes—
263C3×C42C22×D312yes—
264(C2×D3)⋊C4C2×Dic312yes—
265(C2×D3)⋊C4C2×Dic312yes—
266Dic3⋊C4C2×Dic312yes—
267Dic3⋊C4C2×Dic312yes—
268C4×Dic3C2×Dic312yes—
269C4×Dic3C2×Dic312yes—
270C4×Dic3C2×Dic311yescharacteristic
271C4×Dic3C2×Dic311yescharacteristic
272C4×Dic3C22×D311yescharacteristic
273C4×Dic3C22×D311yescharacteristic
274#208—22no—
275#208—64no—
276#208—64no—
277#208—62no—
278#208—62no—
279#208—122no—
280C2×C3⋊C8—22no—
281C2×C3⋊C8—31no—
282C2×C3⋊C8—32no—
283C2×C3⋊C8—31no—
284C2×C3⋊C8—31no—
285C2×C3⋊C8—32no—
286C2×C3⋊C8—31no—
287C2×C3⋊C8—61no—
288C2×C3⋊C8—61no—
289C2×C3⋊C8—62no—
290C2×C3⋊C8—64no—
291C2×C3⋊C8—64no—
292C2×C3⋊C8—62no—
293C2×C3⋊C8—62no—
294C2×C3⋊C8—122no—
295C2×C3⋊C8C22×D311yescharacteristic
296C2×C3⋊C8C22×D312yes—
297C2×C3⋊C8C22×D311yescharacteristic
298ΓL(1,𝔽25)—64no—
299ΓL(1,𝔽25)—64no—
300D3×C8—64no—
301D3×C8—64no—
302C22×C32—21no—
303C22×C32—21no—
304C22×C32C2×C4⋊C412yes—
305C22×C32C23×C411yescharacteristic
306C2×C3×D3—22no—
307C2×C3×D3—22no—
308C2×C3×D3C2×C4⋊C414yes—
309C32×C4—22no—
310C32×C4—22no—
311C32×C4C2×C4⋊C412yes—
312C32×C4C22×D411yescharacteristic
313C32×C4C22×Q811yescharacteristic
314C3×Dic3—21no—
315C3×Dic3—21no—
316C3×Dic3—21no—
317C3×Dic3C2×C4⋊C414yes—
318C3×Dic3#13112yescomplemented
319C2×#41—31no—
320#131—184no—
321#131—184no—
322C2×M16—31no—
323C2×M16—92no—
324C2×M16—92no—
325C2×M16—91no—
326C22×C8—31no—
327C22×C8—92no—
328C22×C8—92no—
329C22×C8—91no—
330C4×Q8—31no—
331C4×Q8—31no—
332C4×D4—31no—
333C4×D4—31no—
334C4×D4—32no—
335C4×D4—32no—
336#117—32no—
337#117D3211yescharacteristic
338C2×C42—31no—
339C2×C42—32no—
340C4⋊C8—32no—
341C4⋊C8—32no—
342C4⋊C8—91no—
343C4⋊C8—91no—
344C4⋊C8—92no—
345C4⋊C8—91no—
346C4⋊C8—91no—
347C4⋊C8—92no—
348C4⋊C8—92no—
349C4⋊C8—92no—
350C23×C3—21no—
351C23×C3—32no—
352C23×C3C2×C4×D311yescharacteristic
353C23×C3C22×Dic311yescharacteristic
354C22×D3C22×Dic312yes—
355C3×Q8—34no—
356C3×D4—38no—
357C3×D4—34no—
358C2×C3×C4—21no—
359C2×C3×C4—22no—
360C2×C3×C4—22no—
361C2×C3×C4—21no—
362C2×C3×C4—22no—
363C2×C3×C4—22no—
364C2×C3×C4—31no—
365C2×C3×C4—32no—
366C2×C3×C4—34no—
367C2×C3×C4—34no—
368C2×C3×C4—31no—
369C2×C3×C4—31no—
370C2×C3×C4—31no—
371C2×C3×C4—64no—
372C2×C3×C4—62no—
373C2×C3×C4—122no—
374C2×C3×C4—121no—
375C2×C3×C4C2×Dic612yes—
376C2×C3×C4C2×C4×D312yes—
377C2×C3×C4C2×C4×D312yes—
378C2×C3×C4C2×C4×D311yescharacteristic
379C2×C3×C4C2×D1212yes—
380C2×C3×C4D3×D412yes—
381C2×C3×C4D3×Q812yes—
382C2×C3×C4C22×Dic312yes—
383C2×C3×C4C22×Dic312yes—
384C2×C3×C4C22×Dic311yescharacteristic
385C2×C3×C4C23×D311yescharacteristic
386C2×C3×C4C23×D311yescharacteristic
387#67C4⋊Dic318yes—
388C2×Dic3—22no—
389C2×Dic3—41no—
390C2×Dic3C22×Dic311yescharacteristic
391C2×Dic3C22×Dic311yescharacteristic
392C2×Dic3C22×Dic311yescharacteristic
393C2×Dic3C22×Dic312yes—
394C2×Dic3C22×Dic311yescharacteristic
395D12C4⋊Dic314yes—
396C4×D3—24no—
397C4×D3—42no—
398C4×D3C2×Dic614yes—
399C4×D3C2×D1214yes—
400Dic6C4⋊Dic314yes—
401C3×C8—61no—
402C3×C8—62no—
403C3×C8—61no—
404C3⋊C8—21no—
405C3⋊C8—21no—
406C3⋊C8—22no—
407C3⋊C8—61no—
408C3⋊C8—62no—
409C3⋊C8—61no—
410C3⋊C8—61no—
411C3⋊C8—62no—
412C3⋊C8—61no—
413C3⋊C8—121no—
414C3⋊C8—121no—
415C3⋊C8—122no—
416C2×C32—22no—
417C2×C32C22×C4⋊C411yescharacteristic
418C2×C32C2×#13111yescharacteristic
419C2×C32#56811yescharacteristic
420C3×D3—24no—
421#41—34no—
422#41—34no—
423C2×Q8—31no—
424C2×D4—32no—
425C2×D4—31no—
426C22×C4—32no—
427C22×C4—31no—
428C22×C4—31no—
429C22×C4—32no—
430C22×C4—32no—
431C22×C4C2×D3211yescharacteristic
432M16—62no—
433M16—184no—
434M16—184no—
435M16—182no—
436C2×C8—31no—
437C2×C8—31no—
438C2×C8—32no—
439C2×C8—62no—
440C2×C8—91no—
441C2×C8—91no—
442C2×C8—92no—
443C2×C8—184no—
444C2×C8—184no—
445C2×C8—182no—
446C4⋊C4—32no—
447C4⋊C4—32no—
448C4⋊C4D3×Dic311yescharacteristic
449C4⋊C4D3×Dic311yescharacteristic
450C22⋊C4—32no—
451C22⋊C4—32no—
452C22⋊C4D3×Dic312yes—
453C42—31no—
454C42—31no—
455C42—32no—
456C42—31no—
457C42—32no—
458C42—31no—
459C42C2×D3212yes—
460C22×C3—21no—
461C22×C3—21no—
462C22×C3—21no—
463C22×C3—21no—
464C22×C3—21no—
465C22×C3—22no—
466C22×C3—34no—
467C22×C3—41no—
468C22×C3—41no—
469C22×C3—62no—
470C22×C3—62no—
471C22×C3D3×C4⋊C412yes—
472C22×C3C2×C4⋊Dic312yes—
473C22×C3C22×C4×D311yescharacteristic
474C22×C3C23×Dic311yescharacteristic
475C2×D3—22no—
476C2×D3—22no—
477C2×D3C2×C4⋊Dic314yes—
478C3×C4—22no—
479C3×C4—22no—
480C3×C4—22no—
481C3×C4—22no—
482C3×C4—21no—
483C3×C4—21no—
484C3×C4—22no—
485C3×C4—32no—
486C3×C4—34no—
487C3×C4—42no—
488C3×C4—42no—
489C3×C4—61no—
490C3×C4—61no—
491C3×C4—61no—
492C3×C4D3×C4⋊C412yes—
493C3×C4C2×C4⋊Dic312yes—
494C3×C4C22×Dic611yescharacteristic
495C3×C4C22×D1211yescharacteristic
496C3×C4C2×D3×D411yescharacteristic
497C3×C4C2×D3×Q811yescharacteristic
498Dic3—21no—
499Dic3—21no—
500Dic3—21no—
501Dic3C2×C4⋊Dic314yes—
502Dic3#94812yescomplemented
503C32#290611yescharacteristic, complemented, Sylow
504C23—32no—
505C23C2×D3×Dic311yescharacteristic
506Q8—34no—
507D4—38no—
508D4—34no—
509C2×C4—31no—
510C2×C4—32no—
511C2×C4—34no—
512C2×C4—34no—
513C2×C4—31no—
514C2×C4—31no—
515C2×C4—31no—
516C2×C4—64no—
517C2×C4—62no—
518C2×C4—122no—
519C2×C4—121no—
520C2×C4D3×Dic612yes—
521C2×C4D3×D1212yes—
522C2×C4C2×D3×Dic312yes—
523C2×C4C2×D3×Dic312yes—
524C2×C4C2×D3×Dic311yescharacteristic
525C2×C4C22×D3211yescharacteristic
526C8—61no—
527C8—61no—
528C8—62no—
529C8—181no—
530C8—182no—
531C8—181no—
532C2×C3—22no—
533C2×C3—22no—
534C2×C3—21no—
535C2×C3—21no—
536C2×C3—21no—
537C2×C3—42no—
538C2×C3—64no—
539C2×C3C2×D3×C4⋊C411yescharacteristic
540C2×C3D3×#13111yescharacteristic
541C2×C3#575011yescharacteristic
542C2×C3C22×C4⋊Dic311yescharacteristic
543C2×C3C2×#94811yescharacteristic
544C2×C3#581911yescharacteristic
545D3—24no—
546C22—21no—
547C22—21no—
548C22—34no—
549C22—62no—
550C22—62no—
551C22D3×C4⋊Dic312yes—
552C22C22×D3×Dic311yescharacteristic
553C4—22no—
554C4—22no—
555C4—34no—
556C4—32no—
557C4—61no—
558C4—61no—
559C4—61no—
560C4D3×C4⋊Dic312yes—
561C4C2×D3×Dic611yescharacteristic
562C4C2×D3×D1211yescharacteristic
563C3—21no—
564C3#7908111yescharacteristic, complemented
565C3#8251211yescharacteristic, complemented
566C2—22no—
567C2—64no—
568C2C2×D3×C4⋊Dic311yescharacteristic
569C2D3×#94811yescharacteristic
570C2#1059544111yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC32×#117C22
prime radicalC2×C3×#235C22
cosocleC2×C32×C4C24
hypercenter#117D32
hypocenterC32#2906
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
4. #10592698C2semidirect
5. C3×#4999C2semidirect
6. #10591115C2semidirect
7. C2×Dic3⋊(C3⋊C8)C2semidirect
8. #10590336C2semidirect
9. #10590324C2semidirect
10. #10590324C2semidirect
11. D3×C4⋊(C3⋊C8)C2semidirect
59. #4999D3semidirect
318. C3×Dic3#131semidirect
502. Dic3#948semidirect
503. C32#2906semidirect
564. C3#79081semidirect
565. C3#82512semidirect

Maximal subgroups

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

subgroupindex
C3×#55222
C2×#638152
C2×#638142
#105926982
C3×#49992
#105911152
C2×Dic3⋊(C3⋊C8)2
#105903362
#105903242
D3×C4⋊(C3⋊C8)2
#825123
#790813