Finite Group Databasebeta

← #11786364

Subgroups — #11786364

Order 1152.

765 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D3×C8C211yesmaximal, characteristic
2C2×#63641C211yesmaximal, characteristic, complemented
3C4×(C2×D3)⋊Dic3C211yesmaximal, characteristic
4C2×Dic3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
5C2×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic
6C3×#4550C211yesmaximal, characteristic, complemented
7#10589156C211yesmaximal, characteristic, complemented
8#71974—31nomaximal
9#68666—31nomaximal
10C22×C3×C4×D3C2211yescharacteristic
11C22×C32×C8C2211yescharacteristic
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C2×C3×C4×Dic3C2211yescharacteristic
15C22×C3×C3⋊C8C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C2×C3×D3×C8—22no—
18C2×C3×D3×C8—22no—
19C2×C3×D3×C8—22no—
20C2×(C2×D3)⋊Dic3C411yescharacteristic
21C2×(C2×D3)⋊Dic3C411yescharacteristic
22#63641—22no—
23#63579C411yescharacteristic
24#63579C411yescharacteristic
25Dic3⋊(C3⋊C8)—22no—
26(C2×D3)⋊(C3⋊C8)—22no—
27C23×C3×C8—31no—
28C22×D3×C8D311yescharacteristic
29C4×#217—31no—
30C2×#830—31no—
31C2×(C2×D3)⋊C8—31no—
32C2×Dic3⋊C8—31no—
33C2×Dic3⋊C8—31no—
34C2×Dic3⋊C8—31no—
35C2×Dic3⋊C8—61no—
36C4×(C2×D3)⋊C4—31no—
37C2×C4⋊(C3⋊C8)—31no—
38C3×#336—31no—
39#4550—31no—
40#4550—31no—
41#4550D311yescharacteristic, complemented
42C23×C3×D3C2×C411yescharacteristic
43C22×C32×C4C2311yescharacteristic
44C22×C3⋊Dic3C2×C411yescharacteristic
45C22×C3⋊Dic3C2×C411yescharacteristic
46C22×C3×Dic3C2×C411yescharacteristic
47C22×C3×Dic3C2×C411yescharacteristic
48C22×C3×Dic3C2×C411yescharacteristic
49C2×C3×C4×D3—21no—
50C2×C3×C4×D3—21no—
51C2×C3×C4×D3—21no—
52C2×C3×C4×D3—21no—
53C2×C3×C4×D3D412yes—
54C2×C3×C4×D3Q812yes—
55C2×C32×C8—21no—
56C2×C32×C8—21no—
57C2×C32×C8D412yes—
58C4×C3⋊Dic3—21no—
59C4×C3⋊Dic3—21no—
60C2×C3⋊(C3⋊C8)—21no—
61C2×C3⋊(C3⋊C8)—21no—
62C2×C3⋊(C3⋊C8)—21no—
63C3×C4×Dic3—21no—
64C3×C4×Dic3—21no—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—21no—
67C2×C3×C3⋊C8—21no—
68C2×C3×C3⋊C8—21no—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8D412yes—
71C3×D3×C8—28no—
72(C2×D3)⋊Dic3—22no—
73(C2×D3)⋊Dic3C814yescomplemented
74#1850—91noSylow
75C23×C3×C4—31no—
76C22×C4×D3C2×D311yescharacteristic
77C22×C3×C8—21no—
78C22×C3×C8—31no—
79C22×C3×C8—31no—
80C22×C3×C8—62no—
81C22×C3×C8—62no—
82C22×C3×C8—62no—
83C22×C3×C8C2×D311yescharacteristic
84C22×C3×C8C2×D311yescharacteristic
85C2×C3×C42—31no—
86C2×#217—31no—
87C2×#217—31no—
88C2×(C2×D3)⋊C4—31no—
89C2×(C2×D3)⋊C4—31no—
90C2×C4×Dic3—31no—
91C2×C4×Dic3—31no—
92C2×C4×Dic3—61no—
93C2×C4×Dic3C2×D311yescharacteristic
94C22×C3⋊C8—31no—
95C22×C3⋊C8—31no—
96C22×C3⋊C8—61no—
97C22×C3⋊C8C2×D311yescharacteristic
98C22×C3⋊C8C2×D311yescharacteristic
99C2×D3×C8—22no—
100C2×D3×C8—22no—
101C2×D3×C8—22no—
102C3⋊#95—31no—
103C3⋊#95—31no—
104C3⋊#95—31no—
105C3⋊#95—31no—
106#830—62no—
107(C2×D3)⋊C8—62no—
108Dic3⋊C8—62no—
109Dic3⋊C8—64no—
110Dic3⋊C8—62no—
111Dic3⋊C8—62no—
112C4⋊(C3⋊C8)—62no—
113C23×C32C22×C411yescharacteristic
114C22×C3×D3—21no—
115C22×C3×D3—21no—
116C22×C3×D3—21no—
117C22×C3×D3—21no—
118C22×C3×D3C4⋊C412yes—
119C22×C3×D3C2×C812yes—
120C22×C3×D3M1612yes—
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4C2×Q811yescharacteristic
125C2×C32×C4#4111yescharacteristic
126C2×C32×C4#4111yescharacteristic
127C2×C3⋊Dic3—21no—
128C2×C3⋊Dic3—21no—
129C2×C3⋊Dic3—21no—
130C2×C3⋊Dic3—21no—
131C2×C3⋊Dic3—21no—
132C2×C3⋊Dic3C2×C812yescomplemented
133C2×C3×Dic3—21no—
134C2×C3×Dic3—21no—
135C2×C3×Dic3—21no—
136C2×C3×Dic3—21no—
137C2×C3×Dic3—21no—
138C2×C3×Dic3—21no—
139C2×C3×Dic3—21no—
140C2×C3×Dic3C4⋊C412yes—
141C2×C3×Dic3C2×C812yescomplemented
142C3×C4×D3—22no—
143C3×C4×D3—22no—
144C3×C4×D3—22no—
145C3×C4×D3—22no—
146C32×C8—22no—
147C3⋊(C3⋊C8)—41no—
148C3×C3⋊C8—22no—
149C3×C3⋊C8—41no—
150C23×C8—31no—
151C2×C4⋊C8—91no—
152C2×C4⋊C8—91no—
153C2×C22⋊C8—91no—
154C4×C22⋊C4—91no—
155#336—31no—
156#336—91no—
157C24×C3—31no—
158C23×D3C4×D311yescharacteristic
159C22×C3×C4—21no—
160C22×C3×C4—31no—
161C22×C3×C4—31no—
162C22×C3×C4—32no—
163C22×C3×C4—32no—
164C22×C3×C4—31no—
165C22×C3×C4—61no—
166C22×C3×C4—61no—
167C22×C3×C4—61no—
168C22×C3×C4—61no—
169C22×C3×C4C22×D311yescharacteristic
170C22×C3×C4C22×D311yescharacteristic
171C22×Dic3—31no—
172C22×Dic3—31no—
173C22×Dic3—31no—
174C22×Dic3—31no—
175C22×Dic3—61no—
176C22×Dic3—61no—
177C22×Dic3C4×D311yescharacteristic
178C22×Dic3C4×D311yescharacteristic
179C22×Dic3C4×D311yescharacteristic
180C2×C4×D3—21no—
181C2×C4×D3—21no—
182C2×C4×D3—21no—
183C2×C4×D3—21no—
184C2×C4×D3Dic612yes—
185C2×C4×D3#6712yes—
186C2×C3×C8—21no—
187C2×C3×C8—21no—
188C2×C3×C8—21no—
189C2×C3×C8—21no—
190C2×C3×C8—22no—
191C2×C3×C8—32no—
192C2×C3×C8—41no—
193C2×C3×C8—41no—
194C2×C3×C8—68no—
195C2×C3×C8—61no—
196C2×C3×C8—61no—
197C2×C3×C8—61no—
198C2×C3×C8—61no—
199C2×C3×C8—61no—
200C2×C3×C8D1212yes—
201C2×C3×C8#6712yes—
202C3×C42—61no—
203C3×C42—61no—
204#217—34no—
205#217—62no—
206(C2×D3)⋊C4—34no—
207(C2×D3)⋊C4—62no—
208C4×Dic3—21no—
209C4×Dic3—21no—
210C4×Dic3—62no—
211C4×Dic3—62no—
212C4×Dic3—61no—
213C4×Dic3—61no—
214C4×Dic3—61no—
215C4×Dic3—61no—
216C2×C3⋊C8—21no—
217C2×C3⋊C8—21no—
218C2×C3⋊C8—21no—
219C2×C3⋊C8—21no—
220C2×C3⋊C8—21no—
221C2×C3⋊C8—62no—
222C2×C3⋊C8—61no—
223C2×C3⋊C8—61no—
224C2×C3⋊C8—61no—
225C2×C3⋊C8—61no—
226C2×C3⋊C8—61no—
227C2×C3⋊C8—61no—
228C2×C3⋊C8—121no—
229C2×C3⋊C8—121no—
230C2×C3⋊C8#6712yes—
231D3×C8—28no—
232C22×C32C2×C4⋊C411yescharacteristic
233C22×C32C4×D411yescharacteristic
234C22×C32C4×D411yescharacteristic
235C22×C32C22×C811yescharacteristic
236C22×C32C2×M1611yescharacteristic
237C22×C32#13111yescharacteristic
238C22×C32#13111yescharacteristic
239C2×C3×D3—22no—
240C2×C3×D3—22no—
241C2×C3×D3—22no—
242C2×C3×D3—22no—
243C2×C3×D3—22no—
244C2×C3×D3—22no—
245C2×C3×D3C4⋊C814yescomplemented
246C32×C4#12011yescharacteristic
247C32×C4C22⋊Q811yescharacteristic
248C32×C4C22⋊Q811yescharacteristic
249C32×C4#12311yescharacteristic
250C3⋊Dic3—22no—
251C3⋊Dic3—41no—
252C3×Dic3—22no—
253C3×Dic3—22no—
254C3×Dic3—41no—
255C23×C4—31no—
256C22×C8—31no—
257C22×C8—31no—
258C22×C8—62no—
259C22×C8—62no—
260C22×C8—62no—
261C22×C8—91no—
262C22×C8D3211yescharacteristic
263C2×C22⋊C4—91no—
264C2×C22⋊C4—91no—
265C2×C42—31no—
266C2×C42—91no—
267C4⋊C8—182no—
268C4⋊C8—182no—
269C22⋊C8—182no—
270#95—91no—
271#95—91no—
272C23×C3—21no—
273C23×C3—32no—
274C23×C3—32no—
275C23×C3—32no—
276C23×C3—61no—
277C23×C3—61no—
278C23×C3—61no—
279C23×C3—61no—
280C23×C3C2×C4×D311yescharacteristic
281C23×C3C2×C4×D311yescharacteristic
282C22×D3—21no—
283C22×D3—21no—
284C22×D3—21no—
285C22×D3—21no—
286C22×D3D3×C812yes—
287C22×D3ΓL(1,𝔽25)12yes—
288C22×D3Dic3⋊C412yes—
289C2×C3×C4—21no—
290C2×C3×C4—21no—
291C2×C3×C4—21no—
292C2×C3×C4—21no—
293C2×C3×C4—21no—
294C2×C3×C4—21no—
295C2×C3×C4—32no—
296C2×C3×C4—32no—
297C2×C3×C4—61no—
298C2×C3×C4—61no—
299C2×C3×C4—61no—
300C2×C3×C4—61no—
301C2×C3×C4—62no—
302C2×C3×C4—62no—
303C2×C3×C4—62no—
304C2×C3×C4—62no—
305C2×C3×C4—61no—
306C2×C3×C4—61no—
307C2×C3×C4—61no—
308C2×C3×C4C2×Dic611yescharacteristic
309C2×C3×C4C2×D1211yescharacteristic
310C2×C3×C4#23511yescharacteristic
311C2×C3×C4#23511yescharacteristic
312C2×C3×C4#23511yescharacteristic
313C2×C3×C4D3×D411yescharacteristic
314C2×C3×C4D3×D411yescharacteristic
315C2×C3×C4#23711yescharacteristic
316C2×C3×C4D3×Q811yescharacteristic
317C2×C3×C4C2×#6711yescharacteristic
318C2×C3×C4C2×#6711yescharacteristic
319C2×C3×C4C2×#6711yescharacteristic
320C2×Dic3—21no—
321C2×Dic3—21no—
322C2×Dic3—21no—
323C2×Dic3—21no—
324C2×Dic3—21no—
325C2×Dic3—21no—
326C2×Dic3—21no—
327C2×Dic3—32no—
328C2×Dic3—32no—
329C2×Dic3—62no—
330C2×Dic3—62no—
331C2×Dic3—62no—
332C2×Dic3—61no—
333C2×Dic3—61no—
334C2×Dic3—61no—
335C2×Dic3—61no—
336C2×Dic3—62no—
337C2×Dic3—61no—
338C2×Dic3—61no—
339C2×Dic3—61no—
340C2×Dic3—61no—
341C2×Dic3—61no—
342C2×Dic3—61no—
343C2×Dic3—121no—
344C2×Dic3—121no—
345C2×Dic3D3×C812yescomplemented
346C2×Dic3Dic3⋊C412yes—
347C4×D3—22no—
348C4×D3—22no—
349C4×D3—22no—
350C4×D3—22no—
351C3×C8—22no—
352C3×C8—22no—
353C3×C8—42no—
354C3×C8—62no—
355C3×C8—121no—
356C3⋊C8—22no—
357C3⋊C8—41no—
358C3⋊C8—122no—
359C3⋊C8—121no—
360C3⋊C8—121no—
361C2×C32#38511yescharacteristic
362C2×C32C2×C4⋊C811yescharacteristic
363C2×C32#42411yescharacteristic
364C2×C32C8×D411yescharacteristic
365C2×C32C8×D411yescharacteristic
366C2×C32#43511yescharacteristic
367C2×C32#43511yescharacteristic
368C3×D3—24no—
369C24—31no—
370C22×C4—31no—
371C22×C4—31no—
372C22×C4—32no—
373C22×C4—32no—
374C22×C4—31no—
375C22×C4—61no—
376C22×C4—61no—
377C22×C4—61no—
378C22×C4—61no—
379C22×C4—91no—
380C22×C4—91no—
381C22×C4C2×D3211yescharacteristic
382C2×C8—21no—
383C2×C8—21no—
384C2×C8—32no—
385C2×C8—68no—
386C2×C8—61no—
387C2×C8—61no—
388C2×C8—61no—
389C2×C8—61no—
390C2×C8—61no—
391C2×C8—181no—
392C2×C8—181no—
393C2×C8—181no—
394C2×C8#62612yes—
395C22⋊C4—94no—
396C22⋊C4—182no—
397C42—61no—
398C42—61no—
399C42—181no—
400C42—181no—
401C22×C3—21no—
402C22×C3—21no—
403C22×C3—21no—
404C22×C3—21no—
405C22×C3—21no—
406C22×C3—21no—
407C22×C3—21no—
408C22×C3—34no—
409C22×C3—62no—
410C22×C3—62no—
411C22×C3—62no—
412C22×C3—62no—
413C22×C3—62no—
414C22×C3—62no—
415C22×C3C4×D1211yescharacteristic
416C22×C3#67⋊C411yescharacteristic
417C22×C3D3×C4⋊C411yescharacteristic
418C22×C3C2×D3×C811yescharacteristic
419C22×C3C2×D3×C811yescharacteristic
420C22×C3C2×ΓL(1,𝔽25)11yescharacteristic
421C22×C3#90111yescharacteristic
422C22×C3#90111yescharacteristic
423C22×C3#90111yescharacteristic
424C22×C3D3×M1611yescharacteristic
425C22×C3#90711yescharacteristic
426C22×C3C2×Dic3⋊C411yescharacteristic
427C22×C3C4×#6711yescharacteristic
428C22×C3C4×#6711yescharacteristic
429C2×D3—22no—
430C2×D3—22no—
431C2×D3—22no—
432C2×D3—22no—
433C2×D3—22no—
434C2×D3—22no—
435C2×D3Dic3⋊C814yescomplemented
436C3×C4—21no—
437C3×C4—21no—
438C3×C4—21no—
439C3×C4—21no—
440C3×C4—62no—
441C3×C4—62no—
442C3×C4—121no—
443C3×C4#88211yescharacteristic
444C3×C4#88311yescharacteristic
445C3×C4#89611yescharacteristic
446C3×C4#89711yescharacteristic
447C3×C4#92411yescharacteristic
448C3×C4#92411yescharacteristic
449C3×C4#92911yescharacteristic
450C3×C4#95311yescharacteristic
451Dic3—22no—
452Dic3—22no—
453Dic3—41no—
454Dic3—64no—
455Dic3—62no—
456Dic3—62no—
457Dic3—122no—
458Dic3—121no—
459Dic3—121no—
460C32#185011yescharacteristic, complemented, Sylow
461C23—32no—
462C23—32no—
463C23—32no—
464C23—61no—
465C23—61no—
466C23—61no—
467C23—61no—
468C23C4×D3211yescharacteristic
469C2×C4—32no—
470C2×C4—32no—
471C2×C4—61no—
472C2×C4—61no—
473C2×C4—61no—
474C2×C4—61no—
475C2×C4—62no—
476C2×C4—62no—
477C2×C4—62no—
478C2×C4—62no—
479C2×C4—61no—
480C2×C4—61no—
481C2×C4—61no—
482C2×C4—92no—
483C2×C4—181no—
484C2×C4—181no—
485C2×C4—181no—
486C2×C4—181no—
487C2×C4—181no—
488C2×C4D3×Dic611yescharacteristic
489C2×C4#379511yescharacteristic
490C2×C4#379811yescharacteristic
491C2×C4C2×#62611yescharacteristic
492C2×C4D3×#6711yescharacteristic
493C2×C4D3×#6711yescharacteristic
494C8—22no—
495C8—62no—
496C8—121no—
497C8—361no—
498C2×C3—21no—
499C2×C3—21no—
500C2×C3—21no—
501C2×C3—21no—
502C2×C3—21no—
503C2×C3—21no—
504C2×C3—21no—
505C2×C3—64no—
506C2×C3#466811yescharacteristic
507C2×C3C8×D1211yescharacteristic
508C2×C3#470611yescharacteristic
509C2×C3#67⋊C811yescharacteristic
510C2×C3#472811yescharacteristic
511C2×C3D3×C4⋊C811yescharacteristic
512C2×C3#483911yescharacteristic
513C2×C3C2×Dic3⋊C811yescharacteristic
514C2×C3#510211yescharacteristic
515C2×C3C8×#6711yescharacteristic
516C2×C3C8×#6711yescharacteristic
517C2×C3#511111yescharacteristic
518C2×C3#511111yescharacteristic
519C2×C3#521011yescharacteristic
520D3—24no—
521C22—34no—
522C22—62no—
523C22—62no—
524C22—62no—
525C22—62no—
526C22—62no—
527C22—62no—
528C22D32×C811yescharacteristic
529C22D3×ΓL(1,𝔽25)11yescharacteristic
530C22#6380311yescharacteristic
531C22#6380411yescharacteristic
532C22D3×Dic3⋊C411yescharacteristic
533C22#6387911yescharacteristic
534C22C4×#62611yescharacteristic
535C4—62no—
536C4—62no—
537C4—121no—
538C4—182no—
539C4—361no—
540C4#6385111yescharacteristic
541C4#6385711yescharacteristic
542C4#6390511yescharacteristic
543C4#6397711yescharacteristic
544C3—21no—
545C3#6866611yescharacteristic, complemented
546C3#7197411yescharacteristic, complemented
547C2—64no—
548C2D3×Dic3⋊C811yescharacteristic
549C2#1059069411yescharacteristic
550C2#1059071711yescharacteristic
551C2C8×#62611yescharacteristic
552C2#1059072311yescharacteristic
553C2#1059072611yescharacteristic
554C2#1059127811yescharacteristic
subgroupG/H
center, FrattiniC22×C4C2×D32
commutatorC22×C32C22×C8
FittingC22×C32×C8C22
socleC23×C32C22×C4
prime radicalC23×C3×D3C2×C4
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32#1850
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C2×#63641C2semidirect
4. C2×Dic3⋊(C3⋊C8)C2semidirect
6. C3×#4550C2semidirect
7. #10589156C2semidirect
41. #4550D3semidirect
73. (C2×D3)⋊Dic3C8semidirect
132. C2×C3⋊Dic3C2×C8semidirect
141. C2×C3×Dic3C2×C8semidirect
245. C2×C3×D3C4⋊C8semidirect
345. C2×Dic3D3×C8semidirect
435. C2×D3Dic3⋊C8semidirect
460. C32#1850semidirect
545. C3#68666semidirect
546. C3#71974semidirect

Maximal subgroups

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

subgroupindex
C22×C3×D3×C82
C2×#636412
C4×(C2×D3)⋊Dic32
C2×Dic3⋊(C3⋊C8)2
C2×(C2×D3)⋊(C3⋊C8)2
C3×#45502
#105891562
#719743
#686663