Finite Group Databasebeta

← #11858351

Subgroups — #11858351

Order 1152.

1037 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#901C211yesmaximal, characteristic
2#10594958C211yesmaximal, characteristic
3C2×#63815C211yesmaximal, characteristic
4C2×#63641C211yesmaximal, characteristic, complemented
5C3×#5102C211yesmaximal, characteristic, complemented
6#10591120C211yesmaximal, characteristic, complemented
7#10591117C211yesmaximal, characteristic, complemented
8#10590695C212yesmaximal, complemented
9#10590694C212yesmaximal, complemented
10#10590663C212yesmaximal, complemented
11D3×Dic3⋊C8C212yesmaximal, complemented
12#83783—31nomaximal
13#79081—31nomaximal
14C2×C3×#235C2211yescharacteristic
15C22×C32×C8C2211yescharacteristic
16C2×C4×C3⋊Dic3C2211yescharacteristic
17C22×C3⋊(C3⋊C8)C2211yescharacteristic
18C3×#926C2211yescharacteristic
19C2×C3×#208C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21C3×#901—24no—
22C2×C3×ΓL(1,𝔽25)C2212yes—
23C2×C3×D3×C8C2212yes—
24#67⋊Dic3C412yes—
25#67⋊Dic3C412yes—
26#63898C411yescharacteristic
27#63898C411yescharacteristic
28C4×D3×Dic3C2212yes—
29#63855C2212yes—
30#63843C411yescharacteristic
31#63843C411yescharacteristic
32C2×#3711C2212yes—
33#63815—24no—
34C2×D3×C3⋊C8C2212yes—
35#63641C2211yescharacteristic
36#63641C2211yescharacteristic
37#63641C2211yescharacteristic
38#63641C2211yescharacteristic
39C3×Dic3⋊C8C2212yes—
40C3×Dic3⋊C8C2212yes—
41#63572C2212yes—
42#63572C2212yes—
43Dic3⋊(C3⋊C8)C2212yes—
44Dic3⋊(C3⋊C8)C2212yes—
45C2×C3×#131—31no—
46Dic3×#41—31no—
47C2×#948—31no—
48C2×#907—31no—
49C2×#901D311yescharacteristic
50#5522—31no—
51C3×#424—31no—
52#5119—31no—
53#5119—32no—
54#5118—31no—
55#5118—31no—
56#5118—32no—
57#5102—32no—
58#5102D311yescharacteristic, complemented
59C2×Dic3⋊C8—31no—
60C2×Dic3⋊C8—31no—
61C2×Dic3⋊C8—32no—
62C2×Dic3⋊C8—61no—
63#4999—31no—
64#4839—32no—
65#4839—32no—
66#4837—32no—
67D3×C4⋊C8—32no—
68C22×C32×C4C2311yescharacteristic
69C22×C3⋊Dic3C2×C411yescharacteristic
70C22×C3⋊Dic3C2×C411yescharacteristic
71C2×C3×#67C2×C412yes—
72C3×#235D414yes—
73C3×#235Q814yes—
74C2×C3×D12C2×C411yescharacteristic
75C2×C3×C4×D3C2312yes—
76C2×C3×Dic6C2×C411yescharacteristic
77C2×D3×Dic3C2×C412yes—
78C2×D3×Dic3C2×C412yes—
79C2×C32×C8—22no—
80C2×C32×C8C2311yescharacteristic
81C2×C32×C8C2311yescharacteristic
82C4×C3⋊Dic3C2×C411yescharacteristic
83C4×C3⋊Dic3C2×C411yescharacteristic
84C4×C3⋊Dic3C2311yescharacteristic
85C4×C3⋊Dic3C2311yescharacteristic
86C2×C3⋊(C3⋊C8)—22no—
87C2×C3⋊(C3⋊C8)C2311yescharacteristic
88C2×C3⋊(C3⋊C8)C2311yescharacteristic
89C3×#217C2×C412yes—
90C3×C4⋊Dic3C2×C411yescharacteristic
91C3×C4⋊Dic3C2×C411yescharacteristic
92C3×C4×Dic3C2312yes—
93C3×#208—22no—
94C3×#208—22no—
95C2×C3×C3⋊C8C2312yes—
96C2×C3×C3⋊C8C2312yes—
97C3×ΓL(1,𝔽25)—24no—
98C3×D3×C8—24no—
99Dic3⋊Dic3C2×C412yes—
100Dic3⋊Dic3C2×C412yes—
101(C2×D3)⋊Dic3C2×C412yes—
102(C2×D3)⋊Dic3C2×C412yes—
103Dic32C2×C412yes—
104Dic32C2×C412yes—
105#3711—24no—
106D3×C3⋊C8—24no—
107#2906—91noSylow
108C2×C3×#41—31no—
109C2×#235C2×D311yescharacteristic
110C3×#131—64no—
111C2×C3×M16—31no—
112C2×C3×M16—31no—
113C2×C3×M16—32no—
114C22×C3×C8—21no—
115C22×C3×C8—32no—
116C22×C3×C8C2×D311yescharacteristic
117C22×C3×C8C2×D311yescharacteristic
118C3×#117—31no—
119#948—64no—
120Q8×Dic3—31no—
121Q8×Dic3—31no—
122D4×Dic3—32no—
123D4×Dic3—32no—
124D4×Dic3—31no—
125D4×Dic3—31no—
126#926—32no—
127#926C2×D311yescharacteristic
128C2×C4×Dic3—31no—
129C2×C4×Dic3—31no—
130C2×C4×Dic3—32no—
131C2×C4×Dic3—61no—
132C2×#208—32no—
133C2×#208C2×D311yescharacteristic
134C2×#208C2×D311yescharacteristic
135C22×C3⋊C8—31no—
136C22×C3⋊C8—31no—
137C22×C3⋊C8—32no—
138C22×C3⋊C8—61no—
139#907—64no—
140#901—24no—
141C2×ΓL(1,𝔽25)—32no—
142C2×ΓL(1,𝔽25)C2×D312yes—
143C2×D3×C8—32no—
144C2×D3×C8C2×D312yes—
145#893—31no—
146#893—31no—
147#887—31no—
148#887—31no—
149#67⋊C4—32no—
150#67⋊C4—32no—
151#872—32no—
152C42×D3—32no—
153C3×C4⋊C8—32no—
154C3×C4⋊C8—32no—
155Dic3⋊C8—31no—
156Dic3⋊C8—31no—
157Dic3⋊C8—31no—
158Dic3⋊C8—31no—
159Dic3⋊C8—31no—
160Dic3⋊C8—31no—
161Dic3⋊C8—31no—
162Dic3⋊C8—31no—
163Dic3⋊C8—32no—
164Dic3⋊C8—32no—
165Dic3⋊C8—32no—
166Dic3⋊C8—32no—
167Dic3⋊C8—32no—
168Dic3⋊C8—32no—
169Dic3⋊C8—61no—
170Dic3⋊C8—61no—
171Dic3⋊C8—61no—
172Dic3⋊C8—61no—
173Dic3⋊C8C2×D312yes—
174Dic3⋊C8C2×D312yes—
175C4⋊(C3⋊C8)—32no—
176C4⋊(C3⋊C8)—32no—
177C23×C32C22×C411yescharacteristic
178C22×C3×D3C22×C412yes—
179C2×C32×C4C22×C411yescharacteristic
180C2×C32×C4C2×D412yes—
181C2×C32×C4C2×Q812yes—
182C2×C32×C4C2411yescharacteristic
183C2×C3⋊Dic3—22no—
184C2×C3⋊Dic3—41no—
185C2×C3⋊Dic3C22×C411yescharacteristic
186C2×C3⋊Dic3C22×C411yescharacteristic
187C2×C3⋊Dic3C22×C411yescharacteristic
188C2×C3⋊Dic3C22×C411yescharacteristic
189C3×#67C4⋊C418yes—
190C2×C3×Dic3C22×C412yes—
191C2×C3×Dic3C22×C412yes—
192C2×C3×Dic3C22×C412yes—
193C3×D12C4⋊C414yes—
194C3×C4×D3C2×D414yes—
195C3×C4×D3C2×Q814yes—
196C3×Dic6C4⋊C414yes—
197D3×Dic3—24no—
198D3×Dic3—42no—
199C32×C8—21no—
200C32×C8—21no—
201C3⋊(C3⋊C8)—21no—
202C3⋊(C3⋊C8)—21no—
203C3×C3⋊C8—22no—
204C3×C3⋊C8—22no—
205C2×#131—31no—
206C2×#131—91no—
207C4×#41—91no—
208#424—31no—
209#424—92no—
210#424—92no—
211#424—91no—
212#423—92no—
213#423—91no—
214C2×C4⋊C8—92no—
215C2×C4⋊C8—91no—
216C3×#41—34no—
217C3×#41—34no—
218C2×C3×Q8—31no—
219C2×C3×D4—32no—
220C2×C3×D4—31no—
221C22×C3×C4—21no—
222C22×C3×C4—32no—
223C22×C3×C4C22×D311yescharacteristic
224C22×C3×C4C22×D311yescharacteristic
225C2×#67C4×D312yes—
226C22×Dic3—31no—
227C22×Dic3—31no—
228C22×Dic3—31no—
229C22×Dic3—31no—
230C22×Dic3—32no—
231C22×Dic3—32no—
232C22×Dic3—61no—
233C22×Dic3—61no—
234#235Dic614yes—
235#235#6714yes—
236C2×D12C4×D311yescharacteristic
237C2×C4×D3—32no—
238C2×C4×D3—32no—
239C2×C4×D3C22×D312yes—
240C2×Dic6C4×D311yescharacteristic
241C3×M16—64no—
242C3×M16—62no—
243C3×M16—62no—
244C2×C3×C8—22no—
245C2×C3×C8—22no—
246C2×C3×C8—21no—
247C2×C3×C8—21no—
248C2×C3×C8—32no—
249C2×C3×C8—32no—
250C2×C3×C8—42no—
251C2×C3×C8—64no—
252C2×C3×C8C22×D311yescharacteristic
253C2×C3×C8C22×D311yescharacteristic
254C2×C3×C8C22×D311yescharacteristic
255C2×C3×C8C22×D311yescharacteristic
256C3×C4⋊C4—31no—
257C3×C4⋊C4—31no—
258C3×C22⋊C4—32no—
259C3×C42—32no—
260#217—32no—
261#217—32no—
262#217C4×D312yes—
263(C2×D3)⋊C4—32no—
264(C2×D3)⋊C4—32no—
265C4⋊Dic3—32no—
266C4⋊Dic3—32no—
267C4⋊Dic3C4×D311yescharacteristic
268C4⋊Dic3C4×D311yescharacteristic
269Dic3⋊C4—32no—
270Dic3⋊C4—32no—
271C4×Dic3—31no—
272C4×Dic3—31no—
273C4×Dic3—31no—
274C4×Dic3—31no—
275C4×Dic3—31no—
276C4×Dic3—31no—
277C4×Dic3—31no—
278C4×Dic3—31no—
279C4×Dic3—32no—
280C4×Dic3—32no—
281C4×Dic3—32no—
282C4×Dic3—32no—
283C4×Dic3—61no—
284C4×Dic3—61no—
285C4×Dic3—61no—
286C4×Dic3—61no—
287C4×Dic3C22×D312yes—
288#208—22no—
289#208—22no—
290#208—64no—
291C2×C3⋊C8—31no—
292C2×C3⋊C8—31no—
293C2×C3⋊C8—31no—
294C2×C3⋊C8—31no—
295C2×C3⋊C8—61no—
296C2×C3⋊C8—61no—
297C2×C3⋊C8—64no—
298C2×C3⋊C8—62no—
299C2×C3⋊C8—62no—
300C2×C3⋊C8—122no—
301C2×C3⋊C8C22×D312yes—
302C2×C3⋊C8C22×D312yes—
303ΓL(1,𝔽25)—24no—
304ΓL(1,𝔽25)—64no—
305D3×C8—24no—
306D3×C8—64no—
307C22×C32—21no—
308C22×C32—21no—
309C22×C32C2×C4⋊C412yes—
310C22×C32C23×C411yescharacteristic
311C2×C3×D3—22no—
312C2×C3×D3—22no—
313C2×C3×D3C2×C4⋊C414yes—
314C32×C4C2×C4⋊C412yes—
315C32×C4C22×D411yescharacteristic
316C32×C4C22×Q811yescharacteristic
317C3⋊Dic3—21no—
318C3⋊Dic3—21no—
319C3⋊Dic3—21no—
320C3⋊Dic3#13112yescomplemented
321C3×Dic3—22no—
322C3×Dic3—22no—
323C3×Dic3C2×C4⋊C414yes—
324C2×#41—31no—
325#131—64no—
326#131—184no—
327C2×M16—31no—
328C2×M16—31no—
329C2×M16—32no—
330C2×M16—92no—
331C22×C8—32no—
332C22×C8—92no—
333C22×C8—91no—
334C22×C8D3211yescharacteristic
335C4×Q8—91no—
336C4×Q8—91no—
337C4×D4—92no—
338C4×D4—92no—
339C4×D4—91no—
340C4×D4—91no—
341#117—31no—
342#117—92no—
343C2×C42—92no—
344C2×C42—91no—
345C4⋊C8—32no—
346C4⋊C8—32no—
347C4⋊C8—92no—
348C4⋊C8—92no—
349C4⋊C8—92no—
350C4⋊C8—92no—
351C4⋊C8—91no—
352C4⋊C8—91no—
353C4⋊C8—91no—
354C4⋊C8—91no—
355C23×C3—21no—
356C23×C3—32no—
357C23×C3C2×C4×D311yescharacteristic
358C23×C3C2×C4×D311yescharacteristic
359C22×D3C2×C4×D312yes—
360C3×Q8—34no—
361C3×D4—38no—
362C3×D4—34no—
363C2×C3×C4—21no—
364C2×C3×C4—22no—
365C2×C3×C4—21no—
366C2×C3×C4—22no—
367C2×C3×C4—32no—
368C2×C3×C4—34no—
369C2×C3×C4—34no—
370C2×C3×C4—32no—
371C2×C3×C4—32no—
372C2×C3×C4C2×Dic612yes—
373C2×C3×C4C2×C4×D311yescharacteristic
374C2×C3×C4C2×C4×D311yescharacteristic
375C2×C3×C4D3×D412yes—
376C2×C3×C4D3×Q812yes—
377C2×C3×C4C2×#6712yes—
378C2×C3×C4C23×D311yescharacteristic
379C2×C3×C4C23×D311yescharacteristic
380#67Dic3⋊C418yes—
381C2×Dic3—31no—
382C2×Dic3—31no—
383C2×Dic3—31no—
384C2×Dic3—31no—
385C2×Dic3—31no—
386C2×Dic3—31no—
387C2×Dic3—31no—
388C2×Dic3—31no—
389C2×Dic3—61no—
390C2×Dic3—61no—
391C2×Dic3—61no—
392C2×Dic3—61no—
393C2×Dic3—64no—
394C2×Dic3—62no—
395C2×Dic3—62no—
396C2×Dic3—64no—
397C2×Dic3—122no—
398C2×Dic3—121no—
399C2×Dic3—121no—
400C2×Dic3—122no—
401C2×Dic3C2×C4×D312yes—
402C2×Dic3C2×C4×D312yes—
403C2×Dic3C2×C4×D312yes—
404D12Dic3⋊C414yes—
405C4×D3—64no—
406C4×D3—122no—
407C4×D3C2×Dic614yes—
408C4×D3C2×#6714yes—
409Dic6Dic3⋊C414yes—
410C3×C8—21no—
411C3×C8—21no—
412C3×C8—21no—
413C3×C8—21no—
414C3×C8—41no—
415C3×C8—41no—
416C3×C8—62no—
417C3×C8—62no—
418C3⋊C8—22no—
419C3⋊C8—22no—
420C3⋊C8—61no—
421C3⋊C8—61no—
422C3⋊C8—61no—
423C3⋊C8—61no—
424C3⋊C8—121no—
425C3⋊C8—121no—
426C2×C32—22no—
427C2×C32C22×C4⋊C411yescharacteristic
428C2×C32C2×#13111yescharacteristic
429C2×C32#56811yescharacteristic
430C3×D3—24no—
431#41—34no—
432#41—34no—
433C2×Q8—31no—
434C2×D4—32no—
435C2×D4—31no—
436C22×C4—32no—
437C22×C4—92no—
438C22×C4—92no—
439C22×C4—91no—
440C22×C4—91no—
441C22×C4C2×D3211yescharacteristic
442M16—64no—
443M16—62no—
444M16—62no—
445M16—184no—
446C2×C8—22no—
447C2×C8—32no—
448C2×C8—32no—
449C2×C8—64no—
450C2×C8—91no—
451C2×C8—91no—
452C2×C8—184no—
453C2×C8—182no—
454C2×C8C2×D3211yescharacteristic
455C2×C8C2×D3211yescharacteristic
456C4⋊C4—31no—
457C4⋊C4—31no—
458C4⋊C4—92no—
459C4⋊C4—92no—
460C22⋊C4—32no—
461C22⋊C4—92no—
462C22⋊C4—92no—
463C42—32no—
464C42—92no—
465C42—92no—
466C42—91no—
467C42—91no—
468C42—91no—
469C42—91no—
470C22×C3—22no—
471C22×C3—22no—
472C22×C3—21no—
473C22×C3—21no—
474C22×C3—21no—
475C22×C3—21no—
476C22×C3—21no—
477C22×C3—22no—
478C22×C3—34no—
479C22×C3—62no—
480C22×C3—62no—
481C22×C3D3×C4⋊C412yes—
482C22×C3C2×Dic3⋊C412yes—
483C22×C3C22×C4×D311yescharacteristic
484C22×C3C22×C4×D311yescharacteristic
485C2×D3—22no—
486C2×D3—22no—
487C2×D3C2×Dic3⋊C414yes—
488C3×C4—21no—
489C3×C4—21no—
490C3×C4—22no—
491C3×C4—34no—
492C3×C4—62no—
493C3×C4—62no—
494C3×C4D3×C4⋊C412yes—
495C3×C4C2×Dic3⋊C412yes—
496C3×C4C22×Dic611yescharacteristic
497C3×C4C2×D3×D411yescharacteristic
498C3×C4C2×D3×Q811yescharacteristic
499C3×C4C22×#6711yescharacteristic
500Dic3—22no—
501Dic3—22no—
502Dic3—32no—
503Dic3—32no—
504Dic3—62no—
505Dic3—62no—
506Dic3—61no—
507Dic3—61no—
508Dic3—61no—
509Dic3—61no—
510Dic3—61no—
511Dic3—61no—
512Dic3—121no—
513Dic3—121no—
514Dic3C2×Dic3⋊C414yes—
515C32#290611yescharacteristic, complemented, Sylow
516C23—32no—
517C23C4×D3211yescharacteristic
518Q8—34no—
519D4—38no—
520D4—34no—
521C2×C4—32no—
522C2×C4—34no—
523C2×C4—34no—
524C2×C4—32no—
525C2×C4—32no—
526C2×C4—91no—
527C2×C4—91no—
528C2×C4—91no—
529C2×C4—91no—
530C2×C4—184no—
531C2×C4—182no—
532C2×C4—362no—
533C2×C4—361no—
534C2×C4D3×Dic612yes—
535C2×C4C4×D3211yescharacteristic
536C2×C4D3×#6712yes—
537C2×C4C22×D3211yescharacteristic
538C8—21no—
539C8—21no—
540C8—62no—
541C8—62no—
542C8—181no—
543C8—181no—
544C2×C3—24no—
545C2×C3—22no—
546C2×C3—22no—
547C2×C3—21no—
548C2×C3—21no—
549C2×C3—21no—
550C2×C3—64no—
551C2×C3C2×D3×C4⋊C411yescharacteristic
552C2×C3D3×#13111yescharacteristic
553C2×C3D3×#13111yescharacteristic
554C2×C3#575011yescharacteristic
555C2×C3#575011yescharacteristic
556C2×C3C22×Dic3⋊C411yescharacteristic
557D3—24no—
558C22—21no—
559C22—21no—
560C22—34no—
561C22—62no—
562C22—62no—
563C22D3×Dic3⋊C412yes—
564C22C2×C4×D3211yescharacteristic
565C4—34no—
566C4—62no—
567C4—62no—
568C4—92no—
569C4—181no—
570C4—181no—
571C4—181no—
572C4D3×Dic3⋊C412yes—
573C4C2×D3×Dic611yescharacteristic
574C4C2×D3×#6711yescharacteristic
575C3—21no—
576C3#7908111yescharacteristic, complemented
577C3#8378311yescharacteristic, complemented
578C2—22no—
579C2—64no—
580C2#1059466911yescharacteristic
581C2#1059467011yescharacteristic
582C2C2×D3×Dic3⋊C411yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC22×C32×C8C22
prime radicalC2×C3×#235C22
cosocleC2×C32×C4C24
hypercenterC22×C8D32
hypocenterC32#2906
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
4. C2×#63641C2semidirect
5. C3×#5102C2semidirect
6. #10591120C2semidirect
7. #10591117C2semidirect
8. #10590695C2semidirect
9. #10590694C2semidirect
10. #10590663C2semidirect
11. D3×Dic3⋊C8C2semidirect
58. #5102D3semidirect
320. C3⋊Dic3#131semidirect
515. C32#2906semidirect
576. C3#79081semidirect
577. C3#83783semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9012
#105949582
C2×#638152
C2×#636412
C3×#51022
#105911202
#105911172
#105906952
#105906942
#105906632
D3×Dic3⋊C82
#837833
#790813