Finite Group Databasebeta

← #11859276

Subgroups — #11859276

Order 1152.

1205 conjugacy classes of subgroups.

The subgroup lattice has 591 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#3811C211yesmaximal, characteristic
2C2×#63818C211yesmaximal, characteristic, complemented
3C2×#63791C211yesmaximal, characteristic, complemented
4C3⋊D3×C22⋊C8C211yesmaximal, characteristic, complemented
5C3×#4729C212yesmaximal, complemented
6#10591156C212yesmaximal, complemented
7#10590935C211yesmaximal, characteristic, complemented
8#10590731C212yesmaximal, complemented
9#10590730C212yesmaximal, complemented
10#10590658C211yesmaximal, characteristic, complemented
11C8×#624C211yesmaximal, characteristic, complemented
12D3×#436—32nomaximal
13C22×C4×C3⋊D3C2211yescharacteristic
14C2×#3811C411yescharacteristic
15C2×C4×D32C2211yescharacteristic
16C2×C8×C3⋊D3C2211yescharacteristic
17C2×C8×C3⋊D3C2211yescharacteristic
18C3×C4×#67C2212yes—
19C2×C3×#208C2212yescomplemented
20C2×C3×ΓL(1,𝔽25)C2212yescomplemented
21#63974C411yescharacteristic
22#67⋊Dic3C412yes—
23#63921C411yescharacteristic
24C4×#626C2212yes—
25#63883C411yescharacteristic
26C4×#624C2211yescharacteristic
27#63881C412yes—
28C2×#3712C2212yescomplemented
29C2×#3711C2212yescomplemented
30#63818—24no—
31C2×#3710C2211yescharacteristic
32C2×#3710C2211yescharacteristic
33#63791—24no—
34C32×C22⋊C8C2211yescharacteristic, complemented
35#63657C2211yescharacteristic, complemented
36#63647C2211yescharacteristic, complemented
37#63647C2211yescharacteristic, complemented
38C3×(C2×D3)⋊C8C2212yescomplemented
39C3×Dic3⋊C8C2212yescomplemented
40C3×C8×Dic3C2212yescomplemented
41Dic3⋊(C3⋊C8)C2212yescomplemented
42(C2×D3)⋊(C3⋊C8)C2212yescomplemented
43Dic3×C3⋊C8C2212yescomplemented
44C2×D3×M16—32no—
45C2×D3×M16—32no—
46C4×D3×D4—32no—
47C3×#436—32no—
48#5128—32no—
49#5128—32no—
50#5012—32no—
51#4838—32no—
52D3×C4⋊C8—32no—
53#4729—32no—
54#4729D312yescomplemented
55D3×C22⋊C8—32no—
56D3×C22⋊C8—32no—
57D3×C22⋊C8—61no—
58#4688—32no—
59C4×D3×C8—32no—
60C23×C3⋊D3C2×C411yescharacteristic
61C22×D32C2×C411yescharacteristic
62C22×C32×C4C2311yescharacteristic
63C22×C3⋊Dic3C2×C411yescharacteristic
64C2×C4×C3⋊D3—22no—
65C2×C4×C3⋊D3—22no—
66C2×C4×C3⋊D3C2×C411yescharacteristic
67C2×C4×C3⋊D3C2×C411yescharacteristic
68C2×C4×C3⋊D3C2311yescharacteristic
69C2×C4×C3⋊D3C2311yescharacteristic
70C2×C3×#67C2×C412yes—
71C2×C3×C4×D3C2312yes—
72#3811—24no—
73C2×#626C2×C412yes—
74C2×#624C2×C411yescharacteristic
75C2×#624C2×C411yescharacteristic
76C2×#624C2×C411yescharacteristic
77C2×D3×Dic3C2×C412yes—
78C4×D32—22no—
79C4×D32—22no—
80C2×C32×C8C2311yescharacteristic
81C2×C32×C8C2311yescharacteristic
82C2×C3⋊(C3⋊C8)C2311yescharacteristic
83C2×C3⋊(C3⋊C8)C2311yescharacteristic
84C8×C3⋊D3—22no—
85C8×C3⋊D3—22no—
86C3×#217C2×C412yes—
87C3×(C2×D3)⋊C4C2×C412yes—
88C3×Dic3⋊C4C2×C412yes—
89C3×C4×Dic3C2312yes—
90C3×#208—24no—
91C2×C3×C3⋊C8C2312yes—
92C2×C3×C3⋊C8C2312yes—
93C3×ΓL(1,𝔽25)—24no—
94Dic3⋊Dic3C2×C412yes—
95#3722C2×C412yes—
96(C2×D3)⋊Dic3C2×C412yes—
97Dic32C2×C412yes—
98#3712—24no—
99#3711—24no—
100#3710—22no—
101#3710D414yescomplemented
102C2×#436—91noSylow
103C2×D3×D4—32no—
104C22×C4×D3—32no—
105C22×C4×D3—32no—
106C22×C4×D3—61no—
107C2×C3×M16—32no—
108C2×C3×M16—32no—
109C3×C4×D4—32no—
110D4×Dic3—32no—
111C4×#67—32no—
112C4×#67C2×D312yes—
113C2×#208—32no—
114C2×#208C2×D312yescomplemented
115D3×M16—68no—
116D3×M16—68no—
117C2×ΓL(1,𝔽25)—32no—
118C2×ΓL(1,𝔽25)—32no—
119C2×ΓL(1,𝔽25)—32no—
120C2×ΓL(1,𝔽25)C2×D312yescomplemented
121C2×D3×C8—32no—
122C2×D3×C8—32no—
123C2×D3×C8—32no—
124C2×D3×C8—32no—
125C2×D3×C8—61no—
126C2×D3×C8—61no—
127#893—32no—
128D3×C4⋊C4—32no—
129#67⋊C4—32no—
130#67⋊C4—32no—
131D3×C22⋊C4—32no—
132D3×C22⋊C4—32no—
133C4×D12—32no—
134C42×D3—32no—
135C3×C4⋊C8—32no—
136C3×C22⋊C8—21no—
137C3×C22⋊C8—32no—
138C3×C22⋊C8C2×D312yescomplemented
139C3×C4×C8—32no—
140#830—32no—
141#830—32no—
142#830—61no—
143(C2×D3)⋊C8—32no—
144(C2×D3)⋊C8—32no—
145(C2×D3)⋊C8—32no—
146(C2×D3)⋊C8—61no—
147(C2×D3)⋊C8—61no—
148(C2×D3)⋊C8C2×D312yescomplemented
149Dic3⋊C8—32no—
150Dic3⋊C8C2×D312yescomplemented
151C8×Dic3—32no—
152C8×Dic3C2×D312yescomplemented
153C4⋊(C3⋊C8)—32no—
154C4×C3⋊C8—32no—
155C23×C32C22×C411yescharacteristic
156C22×C3⋊D3—22no—
157C22×C3⋊D3—22no—
158C22×C3⋊D3—22no—
159C22×C3⋊D3C22×C411yescharacteristic
160C22×C3⋊D3C22×C411yescharacteristic
161C22×C3×D3C22×C412yes—
162C2×D32—22no—
163C2×D32—22no—
164C2×D32—22no—
165C2×C32×C4—21no—
166C2×C32×C4—21no—
167C2×C32×C4C22×C411yescharacteristic
168C2×C32×C4C2411yescharacteristic
169C2×C3⋊Dic3—22no—
170C2×C3⋊Dic3C22×C411yescharacteristic
171C2×C3⋊Dic3C22×C411yescharacteristic
172C4×C3⋊D3—22no—
173C4×C3⋊D3—21no—
174C4×C3⋊D3—21no—
175C4×C3⋊D3—22no—
176C4×C3⋊D3C2×D412yes—
177C4×C3⋊D3#4112yes—
178C3×#67—24no—
179C2×C3×Dic3C22×C412yes—
180C2×C3×Dic3C22×C412yes—
181C2×C3×Dic3C22×C412yes—
182C3×C4×D3—22no—
183C3×C4×D3—22no—
184#626—24no—
185#624—22no—
186#624—22no—
187#624M1614yescomplemented
188D3×Dic3—24no—
189C32×C8—21no—
190C32×C8—21no—
191C3⋊(C3⋊C8)—21no—
192C3⋊(C3⋊C8)—21no—
193C3×C3⋊C8—22no—
194C3×C3⋊C8C2×D414yescomplemented
195C22×M16—91no—
196C22×M16—91no—
197C2×C4×D4—91no—
198#436—32no—
199#436—92no—
200#436—92no—
201#436—92no—
202C2×C4⋊C8—91no—
203C2×C22⋊C8—91no—
204C2×C22⋊C8—91no—
205C2×C4×C8—91no—
206C23×D3—32no—
207C23×D3—32no—
208C23×D3—61no—
209C2×C3×D4—32no—
210C22×C3×C4—21no—
211C22×C3×C4—32no—
212C22×C3×C4C22×D312yes—
213C2×#67—32no—
214C2×#67C4×D312yes—
215C22×Dic3—32no—
216C22×Dic3—32no—
217C22×Dic3—61no—
218D3×D4—68no—
219C2×D12—32no—
220C2×C4×D3—32no—
221C2×C4×D3—32no—
222C2×C4×D3—32no—
223C2×C4×D3—32no—
224C2×C4×D3—32no—
225C2×C4×D3—32no—
226C2×C4×D3—32no—
227C2×C4×D3—32no—
228C2×C4×D3—61no—
229C2×C4×D3—61no—
230C2×C4×D3—61no—
231C2×C4×D3—61no—
232C2×C4×D3—64no—
233C2×C4×D3—64no—
234C2×C4×D3—64no—
235C2×C4×D3—64no—
236C2×C4×D3—122no—
237C2×C4×D3—122no—
238C2×C4×D3C22×D312yes—
239C3×M16—64no—
240C3×M16—64no—
241C2×C3×C8—21no—
242C2×C3×C8—21no—
243C2×C3×C8—32no—
244C2×C3×C8—32no—
245C2×C3×C8C22×D312yes—
246C2×C3×C8C22×D312yes—
247C3×C4⋊C4—32no—
248C3×C22⋊C4—32no—
249C3×C22⋊C4—32no—
250C3×C42—32no—
251#217—32no—
252#217C4×D312yes—
253(C2×D3)⋊C4—32no—
254(C2×D3)⋊C4—32no—
255(C2×D3)⋊C4—32no—
256(C2×D3)⋊C4C4×D312yes—
257C4⋊Dic3—32no—
258Dic3⋊C4—32no—
259Dic3⋊C4C4×D312yes—
260C4×Dic3—32no—
261C4×Dic3—32no—
262C4×Dic3C22×D312yes—
263#208—24no—
264#208—64no—
265C2×C3⋊C8—32no—
266C2×C3⋊C8—32no—
267C2×C3⋊C8—61no—
268C2×C3⋊C8—61no—
269C2×C3⋊C8C22×D312yes—
270C2×C3⋊C8C22×D312yes—
271ΓL(1,𝔽25)—24no—
272ΓL(1,𝔽25)—64no—
273ΓL(1,𝔽25)—64no—
274ΓL(1,𝔽25)—64no—
275D3×C8—38no—
276D3×C8—64no—
277D3×C8—64no—
278D3×C8—64no—
279D3×C8—122no—
280D3×C8—122no—
281C22×C32—21no—
282C22×C32—21no—
283C22×C32—21no—
284C22×C32C23×C411yescharacteristic
285C2×C3⋊D3—21no—
286C2×C3⋊D3—21no—
287C2×C3⋊D3—21no—
288C2×C3⋊D3—44no—
289C2×C3⋊D3C4×D412yes—
290C2×C3⋊D3C2×M1612yes—
291C2×C3⋊D3#13112yes—
292C2×C3×D3—22no—
293C2×C3×D3—22no—
294C2×C3×D3—22no—
295D32—44no—
296C32×C4—21no—
297C32×C4C22×D411yescharacteristic
298C32×C4C2×#4111yescharacteristic
299C3⋊Dic3—21no—
300C3⋊Dic3C4×D412yes—
301C3×Dic3—22no—
302C3×Dic3—22no—
303C3×Dic3C2×M1614yescomplemented
304C22×D4—91no—
305C23×C4—91no—
306C23×C4—91no—
307C2×M16—32no—
308C2×M16—32no—
309C2×M16—92no—
310C2×M16—92no—
311C2×M16—184no—
312C2×M16—184no—
313C22×C8—91no—
314C22×C8—91no—
315C22×C8—91no—
316C22×C8—91no—
317C4×D4—32no—
318C4×D4—92no—
319C4×D4—92no—
320C4×D4—92no—
321C2×C4⋊C4—91no—
322C2×C22⋊C4—91no—
323C2×C22⋊C4—91no—
324C2×C42—91no—
325C4⋊C8—32no—
326C4⋊C8—92no—
327C22⋊C8—32no—
328C22⋊C8—92no—
329C22⋊C8—91no—
330C22⋊C8—91no—
331C22⋊C8—91no—
332C22⋊C8D3211yescharacteristic, complemented
333C4×C8—32no—
334C4×C8—92no—
335C23×C3—21no—
336C23×C3—32no—
337C23×C3C2×C4×D312yes—
338C22×D3—32no—
339C22×D3—32no—
340C22×D3—61no—
341C22×D3—61no—
342C22×D3—64no—
343C22×D3—64no—
344C22×D3—64no—
345C22×D3—64no—
346C22×D3—64no—
347C22×D3—64no—
348C22×D3—64no—
349C22×D3—122no—
350C22×D3—122no—
351C22×D3C2×C4×D312yes—
352C3×D4—64no—
353C2×C3×C4—22no—
354C2×C3×C4—22no—
355C2×C3×C4—21no—
356C2×C3×C4—21no—
357C2×C3×C4—32no—
358C2×C3×C4—32no—
359C2×C3×C4—32no—
360C2×C3×C4—41no—
361C2×C3×C4—41no—
362C2×C3×C4—62no—
363C2×C3×C4—62no—
364C2×C3×C4C2×C4×D312yes—
365C2×C3×C4C23×D312yes—
366#67—24no—
367#67—64no—
368C2×Dic3—32no—
369C2×Dic3—32no—
370C2×Dic3—61no—
371C2×Dic3—61no—
372C2×Dic3—64no—
373C2×Dic3—64no—
374C2×Dic3—122no—
375C2×Dic3C2×C4×D312yes—
376C2×Dic3C2×C4×D312yes—
377C2×Dic3C2×C4×D312yes—
378D12—64no—
379C4×D3—22no—
380C4×D3—22no—
381C4×D3—34no—
382C4×D3—34no—
383C4×D3—38no—
384C4×D3—62no—
385C4×D3—62no—
386C4×D3—64no—
387C4×D3—64no—
388C4×D3—64no—
389C4×D3—64no—
390C4×D3—64no—
391C4×D3—62no—
392C4×D3—62no—
393C4×D3—122no—
394C4×D3—121no—
395C4×D3—121no—
396C4×D3—122no—
397C3×C8—22no—
398C3×C8—22no—
399C3×C8—34no—
400C3×C8—41no—
401C3×C8—41no—
402C3×C8—62no—
403C3⋊C8—22no—
404C3⋊C8—62no—
405C3⋊C8—62no—
406C3⋊C8—121no—
407C3⋊C8—121no—
408C3⋊C8D3×D414yescomplemented
409C2×C32—41no—
410C2×C32C2×C4×D411yescharacteristic
411C2×C32C22×M1611yescharacteristic
412C2×C32C2×#13111yescharacteristic
413C3⋊D3—41no—
414C3⋊D3#43614yescomplemented
415C3×D3—42no—
416C24—91no—
417C24—91no—
418C2×D4—32no—
419C2×D4—92no—
420C2×D4—184no—
421C22×C4—32no—
422C22×C4—91no—
423C22×C4—91no—
424C22×C4—91no—
425C22×C4—92no—
426C22×C4—91no—
427C22×C4—91no—
428C22×C4—91no—
429C22×C4—91no—
430C22×C4—91no—
431C22×C4—182no—
432C22×C4—182no—
433C22×C4—182no—
434C22×C4—182no—
435C22×C4C2×D3211yescharacteristic
436M16—64no—
437M16—64no—
438M16—184no—
439M16—184no—
440C2×C8—32no—
441C2×C8—32no—
442C2×C8—94no—
443C2×C8—91no—
444C2×C8—91no—
445C2×C8—182no—
446C2×C8—182no—
447C2×C8—182no—
448C2×C8C2×D3211yescharacteristic
449C2×C8C2×D3211yescharacteristic
450C4⋊C4—32no—
451C4⋊C4—92no—
452C22⋊C4—32no—
453C22⋊C4—32no—
454C22⋊C4—92no—
455C22⋊C4—92no—
456C42—32no—
457C42—92no—
458C22×C3—22no—
459C22×C3—22no—
460C22×C3—22no—
461C22×C3—22no—
462C22×C3—21no—
463C22×C3—41no—
464C22×C3—41no—
465C22×C3—62no—
466C22×C3—62no—
467C22×C3—62no—
468C22×C3C22×C4×D312yes—
469C2×D3—22no—
470C2×D3—22no—
471C2×D3—22no—
472C2×D3—34no—
473C2×D3—34no—
474C2×D3—34no—
475C2×D3—62no—
476C2×D3—62no—
477C2×D3—62no—
478C2×D3—62no—
479C2×D3—62no—
480C2×D3—62no—
481C2×D3—62no—
482C2×D3—121no—
483C2×D3—121no—
484C2×D3—128no—
485C2×D3—128no—
486C2×D3—128no—
487C3×C4—22no—
488C3×C4—21no—
489C3×C4—21no—
490C3×C4—34no—
491C3×C4—41no—
492C3×C4—62no—
493C3×C4—62no—
494C3×C4C2×D3×D412yes—
495C3×C4D3×#4112yes—
496Dic3—22no—
497Dic3—22no—
498Dic3—34no—
499Dic3—62no—
500Dic3—62no—
501Dic3—121no—
502Dic3D3×M1614yescomplemented
503C32C2×#43611yescharacteristic, complemented, Sylow
504C23—32no—
505C23—91no—
506C23—91no—
507C23—182no—
508C23—182no—
509C23—182no—
510C23—182no—
511C23—182no—
512C23—182no—
513C23C4×D3211yescharacteristic
514D4—64no—
515D4—184no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—32no—
519C2×C4—32no—
520C2×C4—32no—
521C2×C4—62no—
522C2×C4—62no—
523C2×C4—94no—
524C2×C4—91no—
525C2×C4—92no—
526C2×C4—92no—
527C2×C4—91no—
528C2×C4—182no—
529C2×C4—182no—
530C2×C4—182no—
531C2×C4—182no—
532C2×C4—184no—
533C2×C4—182no—
534C2×C4—181no—
535C2×C4—181no—
536C2×C4C4×D3211yescharacteristic
537C2×C4C22×D3211yescharacteristic
538C8—21no—
539C8—21no—
540C8—34no—
541C8—62no—
542C8—181no—
543C8—181no—
544C2×C3—21no—
545C2×C3—21no—
546C2×C3—21no—
547C2×C3—42no—
548C2×C3—42no—
549C2×C3—122no—
550C2×C3C4×D3×D412yes—
551C2×C3C2×D3×M1612yes—
552C2×C3D3×#13112yes—
553D3—38no—
554D3—42no—
555D3—64no—
556D3—122no—
557D3—122no—
558C22—21no—
559C22—21no—
560C22—21no—
561C22—62no—
562C22—62no—
563C22—62no—
564C22—92no—
565C22—92no—
566C22—92no—
567C22—181no—
568C22—181no—
569C22—181no—
570C22—364no—
571C22—364no—
572C22C2×C4×D3211yescharacteristic
573C4—21no—
574C4—34no—
575C4—62no—
576C4—62no—
577C4—92no—
578C4—181no—
579C4D32×D411yescharacteristic
580C4#6431211yescharacteristic
581C3—21no—
582C3D3×#43612yescomplemented
583C2—41no—
584C2—94no—
585C2—122no—
586C2—361no—
587C2#1059425511yescharacteristic
588C2#1059466911yescharacteristic
589C2D32×M1611yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC32×C22⋊C8C22
prime radicalC2×#3811C4
cosocleC2×C32×C4C24
hypercenterC22⋊C8D32
hypocenterC32C2×#436
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#63818C2semidirect
3. C2×#63791C2semidirect
4. C3⋊D3×C22⋊C8C2semidirect
5. C3×#4729C2semidirect
6. #10591156C2semidirect
7. #10590935C2semidirect
8. #10590731C2semidirect
9. #10590730C2semidirect
10. #10590658C2semidirect
11. C8×#624C2semidirect
19. C2×C3×#208C22semidirect
20. C2×C3×ΓL(1,𝔽25)C22semidirect
28. C2×#3712C22semidirect
29. C2×#3711C22semidirect
34. C32×C22⋊C8C22semidirect
35. #63657C22semidirect
36. #63647C22semidirect
37. #63647C22semidirect
38. C3×(C2×D3)⋊C8C22semidirect
39. C3×Dic3⋊C8C22semidirect
40. C3×C8×Dic3C22semidirect
41. Dic3⋊(C3⋊C8)C22semidirect
42. (C2×D3)⋊(C3⋊C8)C22semidirect
43. Dic3×C3⋊C8C22semidirect
54. #4729D3semidirect
101. #3710D4semidirect
114. C2×#208C2×D3semidirect
120. C2×ΓL(1,𝔽25)C2×D3semidirect
138. C3×C22⋊C8C2×D3semidirect
148. (C2×D3)⋊C8C2×D3semidirect
150. Dic3⋊C8C2×D3semidirect
152. C8×Dic3C2×D3semidirect
187. #624M16semidirect
194. C3×C3⋊C8C2×D4semidirect
303. C3×Dic3C2×M16semidirect
332. C22⋊C8D32semidirect
408. C3⋊C8D3×D4semidirect
414. C3⋊D3#436semidirect
502. Dic3D3×M16semidirect
503. C32C2×#436semidirect
582. C3D3×#436semidirect

Maximal subgroups

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

subgroupindex
C4×#38112
C2×#638182
C2×#637912
C3⋊D3×C22⋊C82
C3×#47292
#105911562
#105909352
#105907312
#105907302
#105906582
C8×#6242
D3×#4363