Finite Group Databasebeta

← #11803565

Subgroups — #11803565

Order 1152.

1094 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×#157C211yesmaximal, characteristic, complemented
2C2×#64286C211yesmaximal, characteristic, complemented
3C3⋊D3×#121C211yesmaximal, characteristic
4#10593827C211yesmaximal, characteristic, complemented
5#10593827C212yesmaximal, complemented
6#10593826C212yesmaximal, complemented
7#10593812C211yesmaximal, characteristic, complemented
8#10593759C211yesmaximal, characteristic, complemented
9C4⋊C4×#157C211yesmaximal, characteristic, complemented
10#10593747C212yesmaximal, complemented
11#10593746C212yesmaximal, complemented
12C23×#157C2212yes—
13C2×D4×C3⋊D3C2211yescharacteristic
14C2×D4×C3⋊D3C2212yes—
15C22×C4×C3⋊D3C2211yescharacteristic
16C2×C22⋊#157C2211yescharacteristic
17C2×C22⋊#157C2211yescharacteristic
18C2×C22⋊#157C2212yes—
19C2×C22⋊#157C2212yes—
20C2×C22⋊#157C2212yes—
21C2×C22⋊#157C2212yes—
22D4×#157—24no—
23#64286—24no—
24C2×C4⋊#157C2211yescharacteristic
25C2×C4⋊#157C2211yescharacteristic
26C2×C4⋊#157C2211yescharacteristic
27C2×C4⋊#157C2211yescharacteristic
28C2×C4⋊#157C2212yes—
29C2×C4×#157C2211yescharacteristic
30C2×C4×#157C2212yes—
31C2×C4×#157C2211yescharacteristic
32C32×#121C411yescharacteristic, complemented
33#64148C412yescomplemented
34#64147C411yescharacteristic, complemented
35#64139C411yescharacteristic, complemented
36#64104C411yescharacteristic, complemented
37C4⋊C4×C3⋊D3C2211yescharacteristic
38#64093C412yescomplemented
39C22⋊C4×C3⋊D3C2212yes—
40#63781C2212yes—
41#63781C2212yes—
42#63781C2212yes—
43D3×#121—62no—
44C23×C3⋊D3C2311yescharacteristic
45C23×C3⋊D3C2312yes—
46C22×#157—24no—
47C22×#157—42no—
48C22×#157—42no—
49C22×#157C2311yescharacteristic
50C22×#157C2311yescharacteristic
51C22×#157C2312yes—
52C22×#157C2312yes—
53C22×#157C2311yescharacteristic
54C22×#157C2311yescharacteristic
55C2×C32×D4C2×C411yescharacteristic
56C2×C32×D4C2×C412yescomplemented
57C22×C32×C4C2×C411yescharacteristic, complemented
58C2×#638C2×C412yes—
59C2×#638C2×C412yescomplemented
60C2×#638C2×C412yescomplemented
61C22×C3⋊Dic3C2×C411yescharacteristic, complemented
62D4×C3⋊D3—22no—
63D4×C3⋊D3—22no—
64D4×C3⋊D3—42no—
65D4×C3⋊D3—42no—
66C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
67C2×C4⋊(C3⋊D3)C2×C412yescomplemented
68C2×C4×C3⋊D3—22no—
69C2×C4×C3⋊D3—22no—
70C2×C4×C3⋊D3C2×C411yescharacteristic, complemented
71C2×C4×C3⋊D3C2×C411yescharacteristic, complemented
72C2×C4×C3⋊D3C2312yes—
73C2×C4×C3⋊D3C2311yescharacteristic
74C2×C4×C3⋊D3C2311yescharacteristic
75C22⋊#157—22no—
76C22⋊#157—22no—
77C22⋊#157—24no—
78C22⋊#157—42no—
79C22⋊#157—42no—
80C22⋊#157—42no—
81C4⋊#157—22no—
82C4⋊#157—22no—
83C4⋊#157—22no—
84C4⋊#157—22no—
85C4⋊#157—42no—
86C4×#157—22no—
87C4×#157—42no—
88C4×#157D414yescomplemented
89C32×C4⋊C4C2×C411yescharacteristic, complemented
90C32×C22⋊C4C2×C412yescomplemented
91#3757C2×C412yescomplemented
92#3752C2×C412yescomplemented
93#3752C2×C412yescomplemented
94C4⋊(C3⋊Dic3)C2×C411yescharacteristic, complemented
95#3750C2×C412yescomplemented
96#2324—91nomaximal, Sylow
97C2×D3×D4—62no—
98C2×D3×D4—64no—
99C22×C4×D3—62no—
100C3×#121—22no—
101#939—64no—
102#938—62no—
103#930—62no—
104#895—62no—
105D3×C4⋊C4—62no—
106#884—64no—
107D3×C22⋊C4—64no—
108C23×C32C22×C412yes—
109C23×C32C22×C411yescharacteristic
110C22×C3⋊D3—21no—
111C22×C3⋊D3—21no—
112C22×C3⋊D3—22no—
113C22×C3⋊D3—21no—
114C22×C3⋊D3—21no—
115C22×C3⋊D3—22no—
116C22×C3⋊D3—22no—
117C22×C3⋊D3—22no—
118C22×C3⋊D3—21no—
119C22×C3⋊D3—22no—
120C22×C3⋊D3—21no—
121C22×C3⋊D3—22no—
122C22×C3⋊D3C22×C412yes—
123C22×C3⋊D3C22×C411yescharacteristic
124C22×C3⋊D3C2411yescharacteristic
125C2×#157—21no—
126C2×#157—21no—
127C2×#157—21no—
128C2×#157—21no—
129C2×#157—22no—
130C2×#157—21no—
131C2×#157—21no—
132C2×#157—22no—
133C2×#157—22no—
134C2×#157—22no—
135C2×#157—22no—
136C2×#157—21no—
137C2×#157—21no—
138C2×#157—21no—
139C2×#157—22no—
140C2×#157—21no—
141C2×#157—48no—
142C2×#157C2×D412yes—
143C2×#157C2×D412yes—
144C32×D4—22no—
145C32×D4—42no—
146C2×C32×C4—22no—
147C2×C32×C4C22×C412yes—
148C2×C32×C4C22×C411yescharacteristic
149C2×C32×C4C22×C411yescharacteristic
150#638—24no—
151#638—42no—
152#638—42no—
153C2×C3⋊Dic3—22no—
154C2×C3⋊Dic3C22×C412yes—
155C2×C3⋊Dic3C22×C411yescharacteristic
156C2×C3⋊Dic3C22×C411yescharacteristic
157C4⋊(C3⋊D3)—22no—
158C4⋊(C3⋊D3)—42no—
159C4×C3⋊D3—21no—
160C4×C3⋊D3—21no—
161C4×C3⋊D3—22no—
162C4×C3⋊D3—22no—
163C4×C3⋊D3—22no—
164C4×C3⋊D3—22no—
165C4×C3⋊D3C2×D412yes—
166C4×C3⋊D3#4112yes—
167C2×#121—91no—
168C2×C4×D4—91no—
169C2×#117—91no—
170#390—91no—
171#390—92no—
172#389—91no—
173#388—92no—
174#386—92no—
175#385—92no—
176#380—91no—
177C4×C4⋊C4—91no—
178C23×D3—62no—
179C23×D3—64no—
180C2×C3×D4—22no—
181C2×C3×D4—24no—
182C22×C3×C4—22no—
183C2×#67—64no—
184C2×#67—64no—
185C2×#67—64no—
186C22×Dic3—62no—
187D3×D4—124no—
188D3×D4—124no—
189D3×D4—128no—
190D3×D4—128no—
191C2×D12—64no—
192C2×D12—62no—
193C2×C4×D3—62no—
194C2×C4×D3—62no—
195C2×C4×D3—64no—
196C2×C4×D3—62no—
197C2×C4×D3—62no—
198C2×C4×D3—124no—
199C2×C4×D3—124no—
200C3×C4⋊C4—22no—
201C3×C22⋊C4—24no—
202#217—64no—
203(C2×D3)⋊C4—64no—
204(C2×D3)⋊C4—64no—
205C4⋊Dic3—62no—
206Dic3⋊C4—64no—
207C22×C32—21no—
208C22×C32—21no—
209C22×C32—22no—
210C22×C32—22no—
211C22×C32—21no—
212C22×C32—22no—
213C22×C32C23×C411yescharacteristic
214C2×C3⋊D3—21no—
215C2×C3⋊D3—21no—
216C2×C3⋊D3—22no—
217C2×C3⋊D3—22no—
218C2×C3⋊D3—21no—
219C2×C3⋊D3—22no—
220C2×C3⋊D3—41no—
221C2×C3⋊D3—41no—
222C2×C3⋊D3—41no—
223C2×C3⋊D3—41no—
224C2×C3⋊D3—42no—
225C2×C3⋊D3—42no—
226C2×C3⋊D3—42no—
227C2×C3⋊D3—42no—
228C2×C3⋊D3C22×D411yescharacteristic
229C2×C3⋊D3C2×#4111yescharacteristic
230C2×C3⋊D3H(5,𝔽2)11yescharacteristic
231C2×C3⋊D3H(5,𝔽2)11yescharacteristic
232C2×C3⋊D3H(5,𝔽2)11yescharacteristic
233C2×C3⋊D32−1+411yescharacteristic
234#157—22no—
235#157—22no—
236#157—41no—
237#157—42no—
238#157—41no—
239#157—42no—
240C32×C4—21no—
241C32×C4—22no—
242C32×C4C4×D412yes—
243C3⋊Dic3—21no—
244C3⋊Dic3—22no—
245C3⋊Dic3C4×D412yes—
246C22×D4—91no—
247C22×D4—92no—
248C23×C4—91no—
249C23×C4—92no—
250#121—91no—
251#121—92no—
252#121—91no—
253#121—91no—
254#121—92no—
255#121#15711yescharacteristic, complemented
256C4×D4—184no—
257#117—184no—
258C2×C4⋊C4—91no—
259C2×C4⋊C4—91no—
260C2×C4⋊C4—91no—
261C2×C4⋊C4—91no—
262C2×C4⋊C4—91no—
263C2×C4⋊C4—92no—
264C2×C22⋊C4—92no—
265C2×C22⋊C4—91no—
266C2×C22⋊C4—91no—
267C2×C22⋊C4—92no—
268C2×C22⋊C4—92no—
269C2×C22⋊C4—92no—
270C2×C22⋊C4—92no—
271C2×C42—91no—
272C2×C42—91no—
273C2×C42—92no—
274#95—92no—
275#95—92no—
276#95—92no—
277C23×C3—22no—
278C23×C3—24no—
279C22×D3—62no—
280C22×D3—62no—
281C22×D3—64no—
282C22×D3—64no—
283C22×D3—64no—
284C22×D3—122no—
285C22×D3—122no—
286C22×D3—122no—
287C22×D3—122no—
288C22×D3—124no—
289C22×D3—124no—
290C22×D3—124no—
291C22×D3—124no—
292C22×D3—124no—
293C22×D3—124no—
294C3×D4—44no—
295C3×D4—48no—
296C2×C3×C4—22no—
297C2×C3×C4—24no—
298C2×C3×C4—22no—
299C2×C3×C4—44no—
300#67—128no—
301#67—128no—
302#67—128no—
303C2×Dic3—62no—
304C2×Dic3—64no—
305C2×Dic3—62no—
306C2×Dic3—124no—
307D12—124no—
308D12—128no—
309C4×D3—64no—
310C4×D3—64no—
311C4×D3—124no—
312C4×D3—124no—
313C4×D3—122no—
314C4×D3—122no—
315C4×D3—124no—
316C4×D3—124no—
317C2×C32—41no—
318C2×C32—42no—
319C2×C32C2×C4×D411yescharacteristic
320C2×C32#51811yescharacteristic
321C2×C32#52011yescharacteristic
322C3⋊D3—41no—
323C3⋊D3—42no—
324C3⋊D3#53511yescharacteristic
325C3⋊D3#53711yescharacteristic
326C3⋊D3#54011yescharacteristic
327C3⋊D3#54211yescharacteristic
328C24—92no—
329C24—91no—
330C2×D4—92no—
331C2×D4—92no—
332C2×D4—92no—
333C2×D4—91no—
334C2×D4—92no—
335C2×D4—182no—
336C2×D4—182no—
337C2×D4—362no—
338C2×D4—362no—
339C2×D4C2×#15711yescharacteristic
340C2×D4C2×#15712yescomplemented
341C22×C4—91no—
342C22×C4—91no—
343C22×C4—91no—
344C22×C4—91no—
345C22×C4—92no—
346C22×C4—91no—
347C22×C4—91no—
348C22×C4—91no—
349C22×C4—91no—
350C22×C4—92no—
351C22×C4—92no—
352C22×C4—91no—
353C22×C4—182no—
354C22×C4—182no—
355C22×C4—184no—
356C22×C4—362no—
357C22×C4—362no—
358C22×C4C2×#15711yescharacteristic, complemented
359C4⋊C4—92no—
360C4⋊C4—91no—
361C4⋊C4—182no—
362C4⋊C4—182no—
363C4⋊C4—182no—
364C4⋊C4—182no—
365C4⋊C4—362no—
366C4⋊C4C2×#15711yescharacteristic, complemented
367C22⋊C4—92no—
368C22⋊C4—92no—
369C22⋊C4—92no—
370C22⋊C4—182no—
371C22⋊C4—182no—
372C22⋊C4—184no—
373C22⋊C4—362no—
374C22⋊C4—362no—
375C22⋊C4—362no—
376C22⋊C4C2×#15712yescomplemented
377C42—94no—
378C42—182no—
379C42—362no—
380C22×C3—24no—
381C22×C3—22no—
382C22×C3—42no—
383C22×C3—42no—
384C22×C3—44no—
385C22×C3—44no—
386C22×C3—44no—
387C2×D3—62no—
388C2×D3—62no—
389C2×D3—62no—
390C2×D3—62no—
391C2×D3—62no—
392C2×D3—62no—
393C2×D3—64no—
394C2×D3—122no—
395C2×D3—122no—
396C2×D3—124no—
397C2×D3—124no—
398C2×D3—124no—
399C2×D3—124no—
400C2×D3—124no—
401C2×D3—124no—
402C2×D3—124no—
403C2×D3—244no—
404C2×D3—244no—
405C2×D3—244no—
406C2×D3—244no—
407C3×C4—24no—
408C3×C4—42no—
409C3×C4—44no—
410Dic3—64no—
411Dic3—122no—
412Dic3—124no—
413C32#232411yescharacteristic, complemented, Sylow
414C23—91no—
415C23—92no—
416C23—91no—
417C23—181no—
418C23—182no—
419C23—181no—
420C23—182no—
421C23—182no—
422C23—181no—
423C23—182no—
424C23—182no—
425C23—181no—
426C23—181no—
427C23—181no—
428C23—182no—
429C23C22×#15712yes—
430C23C22×#15711yescharacteristic
431D4—22no—
432D4—42no—
433D4—184no—
434D4—182no—
435D4—362no—
436D4—362no—
437D4—362no—
438C2×C4—22no—
439C2×C4—91no—
440C2×C4—92no—
441C2×C4—92no—
442C2×C4—92no—
443C2×C4—92no—
444C2×C4—91no—
445C2×C4—92no—
446C2×C4—182no—
447C2×C4—182no—
448C2×C4—181no—
449C2×C4—182no—
450C2×C4—181no—
451C2×C4—182no—
452C2×C4—181no—
453C2×C4—181no—
454C2×C4—181no—
455C2×C4—181no—
456C2×C4—182no—
457C2×C4—181no—
458C2×C4—181no—
459C2×C4—182no—
460C2×C4—182no—
461C2×C4—181no—
462C2×C4—182no—
463C2×C4—181no—
464C2×C4—182no—
465C2×C4—182no—
466C2×C4—181no—
467C2×C4—182no—
468C2×C4—181no—
469C2×C4—368no—
470C2×C4C22×#15711yescharacteristic
471C2×C4C22×#15712yes—
472C2×C4C22×#15711yescharacteristic
473C2×C3—22no—
474C2×C3—22no—
475C2×C3—22no—
476C2×C3—44no—
477C2×C3—84no—
478D3—62no—
479D3—62no—
480D3—62no—
481D3—62no—
482D3—124no—
483D3—244no—
484C22—21no—
485C22—22no—
486C22—21no—
487C22—22no—
488C22—21no—
489C22—22no—
490C22—91no—
491C22—91no—
492C22—91no—
493C22—91no—
494C22—91no—
495C22—91no—
496C22—181no—
497C22—182no—
498C22—181no—
499C22—182no—
500C22—181no—
501C22—182no—
502C22—362no—
503C22—361no—
504C22—361no—
505C22—361no—
506C22—361no—
507C22—362no—
508C22—362no—
509C22—362no—
510C22C23×#15711yescharacteristic
511C4—21no—
512C4—22no—
513C4—92no—
514C4—182no—
515C4—182no—
516C4—181no—
517C4—182no—
518C4—362no—
519C4—361no—
520C4—361no—
521C4—362no—
522C4D4×#15712yes—
523C3—22no—
524C2—41no—
525C2—42no—
526C2—91no—
527C2—91no—
528C2—91no—
529C2—91no—
530C2—361no—
531C2—362no—
532C2C2×D4×#15711yescharacteristic
533C2#1059664211yescharacteristic
534C2#1059665011yescharacteristic
subgroupG/H
center, FrattiniC22C23×#157
commutator, socleC22×C32C23×C4
FittingC32×#121C4
prime radicalC3⋊D3×#121C2
cosocleC22×C3⋊D3C24
hypercenter#121#157
hypocenterC32#2324
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×D4×#157C2semidirect
2. C2×#64286C2semidirect
4. #10593827C2semidirect
5. #10593827C2semidirect
6. #10593826C2semidirect
7. #10593812C2semidirect
8. #10593759C2semidirect
9. C4⋊C4×#157C2semidirect
10. #10593747C2semidirect
11. #10593746C2semidirect
32. C32×#121C4semidirect
33. #64148C4semidirect
34. #64147C4semidirect
35. #64139C4semidirect
36. #64104C4semidirect
38. #64093C4semidirect
56. C2×C32×D4C2×C4semidirect
57. C22×C32×C4C2×C4semidirect
59. C2×#638C2×C4semidirect
60. C2×#638C2×C4semidirect
61. C22×C3⋊Dic3C2×C4semidirect
67. C2×C4⋊(C3⋊D3)C2×C4semidirect
70. C2×C4×C3⋊D3C2×C4semidirect
71. C2×C4×C3⋊D3C2×C4semidirect
88. C4×#157D4semidirect
89. C32×C4⋊C4C2×C4semidirect
90. C32×C22⋊C4C2×C4semidirect
91. #3757C2×C4semidirect
92. #3752C2×C4semidirect
93. #3752C2×C4semidirect
94. C4⋊(C3⋊Dic3)C2×C4semidirect
95. #3750C2×C4semidirect
255. #121#157semidirect
340. C2×D4C2×#157semidirect
358. C22×C4C2×#157semidirect
366. C4⋊C4C2×#157semidirect
376. C22⋊C4C2×#157semidirect
413. C32#2324semidirect

Maximal subgroups

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

subgroupindex
C2×D4×#1572
C2×#642862
C3⋊D3×#1212
#105938272
#105938262
#105938122
#105937592
C4⋊C4×#1572
#105937472
#105937462
#23249