Finite Group Databasebeta

← #11803034

Subgroups — #11803034

Order 1152.

994 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×D4×C3⋊D3C211yesmaximal, characteristic
2#10593826C212yesmaximal
3#10593812C211yesmaximal, characteristic, complemented
4#10593811C211yesmaximal, characteristic, complemented
5C4×C22⋊#157C211yesmaximal, characteristic, complemented
6C2×#63781C211yesmaximal, characteristic, complemented
7#10593758C212yesmaximal, complemented
8#10593747C212yesmaximal, complemented
9#10593746C212yesmaximal, complemented
10#10593737C211yesmaximal, characteristic, complemented
11#10593736C211yesmaximal, characteristic, complemented
12C23×#157C2212yes—
13C2×D4×C3⋊D3C2211yescharacteristic
14C22×C4×C3⋊D3C2211yescharacteristic
15C22×C4×C3⋊D3C2211yescharacteristic
16C2×C22⋊#157C2212yes—
17C2×C22⋊#157C2212yes—
18C2×C22⋊#157C2212yes—
19C2×C4⋊#157C2212yes—
20C2×C4⋊#157C2212yes—
21C2×C4×#157C2212yes—
22C32×C4×D4C411yescharacteristic, complemented
23D4×C3⋊Dic3C411yescharacteristic, complemented
24C4×#638C411yescharacteristic, complemented
25C4×#638C411yescharacteristic, complemented
26#64102C411yescharacteristic, complemented
27C4⋊C4×C3⋊D3C2211yescharacteristic
28#64090C411yescharacteristic, complemented
29#64090C411yescharacteristic, complemented
30C22⋊C4×C3⋊D3C2211yescharacteristic
31C22⋊C4×C3⋊D3C2211yescharacteristic
32C4×C4⋊(C3⋊D3)C411yescharacteristic, complemented
33C42×C3⋊D3C2211yescharacteristic
34#63781C2211yescharacteristic
35#63781C2211yescharacteristic
36#63781C2212yes—
37#63781C2211yescharacteristic
38#63781C2211yescharacteristic
39#63781C2212yes—
40#63781C2212yes—
41#63781C2212yes—
42#63781C2212yes—
43C4×D3×D4—62no—
44C23×C3⋊D3C2311yescharacteristic
45C23×C3⋊D3C2311yescharacteristic
46C22×#157—24no—
47C22×#157—42no—
48C22×#157—42no—
49C22×#157C2312yes—
50C22×#157C2312yes—
51C22×#157C2312yes—
52C22×#157C2312yes—
53C2×C32×D4C2×C411yescharacteristic
54C22×C32×C4C2×C411yescharacteristic
55C22×C32×C4C2×C411yescharacteristic, complemented
56C2×#638C2×C411yescharacteristic
57C2×#638C2×C411yescharacteristic
58C22×C3⋊Dic3C2×C411yescharacteristic
59C22×C3⋊Dic3C2×C411yescharacteristic, complemented
60D4×C3⋊D3—24no—
61C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
62C2×C4×C3⋊D3—42no—
63C2×C4×C3⋊D3—42no—
64C2×C4×C3⋊D3C2×C411yescharacteristic
65C2×C4×C3⋊D3C2×C411yescharacteristic
66C2×C4×C3⋊D3C2×C411yescharacteristic, complemented
67C2×C4×C3⋊D3C2×C411yescharacteristic, complemented
68C2×C4×C3⋊D3C2311yescharacteristic
69C2×C4×C3⋊D3C2311yescharacteristic
70C2×C4×C3⋊D3C2311yescharacteristic
71C2×C4×C3⋊D3C2311yescharacteristic
72C2×C4×C3⋊D3C2311yescharacteristic
73C22⋊#157—24no—
74C22⋊#157—42no—
75C22⋊#157—42no—
76C4⋊#157—42no—
77C4⋊#157—42no—
78C4×#157—42no—
79C32×C4⋊C4C2×C411yescharacteristic, complemented
80C32×C22⋊C4C2×C411yescharacteristic
81C32×C22⋊C4C2×C411yescharacteristic, complemented
82C32×C42C2×C411yescharacteristic, complemented
83#3757C2×C411yescharacteristic
84#3757C2×C411yescharacteristic, complemented
85#3752C2×C411yescharacteristic
86#3752C2×C411yescharacteristic
87#3752C2×C411yescharacteristic, complemented
88#3752C2×C411yescharacteristic, complemented
89C4⋊(C3⋊Dic3)C2×C411yescharacteristic, complemented
90#3750C2×C411yescharacteristic, complemented
91#3750C2×C411yescharacteristic, complemented
92C4×C3⋊Dic3C2×C411yescharacteristic, complemented
93C4×C3⋊Dic3C2×C411yescharacteristic, complemented
94C4×C3⋊Dic3C2×C411yescharacteristic, complemented
95#2318—91nomaximal, Sylow
96C2×D3×D4—62no—
97C22×C4×D3—62no—
98C22×C4×D3—62no—
99C3×C4×D4—22no—
100D4×Dic3—62no—
101C4×#67—62no—
102C4×#67—62no—
103#893—62no—
104D3×C4⋊C4—62no—
105#67⋊C4—62no—
106#67⋊C4—62no—
107D3×C22⋊C4—62no—
108D3×C22⋊C4—62no—
109C4×D12—62no—
110C42×D3—62no—
111C23×C32C22×C411yescharacteristic
112C23×C32C22×C411yescharacteristic
113C22×C3⋊D3—22no—
114C22×C3⋊D3—21no—
115C22×C3⋊D3—22no—
116C22×C3⋊D3—21no—
117C22×C3⋊D3—21no—
118C22×C3⋊D3—22no—
119C22×C3⋊D3—21no—
120C22×C3⋊D3C22×C411yescharacteristic
121C22×C3⋊D3C22×C411yescharacteristic
122C22×C3⋊D3#4114yes—
123C22×C3⋊D3C2411yescharacteristic
124C2×#157—22no—
125C2×#157—22no—
126C2×#157—22no—
127C2×#157—22no—
128C2×#157—22no—
129C2×#157—22no—
130C2×#157—22no—
131C2×#157—22no—
132C2×#157—22no—
133C2×#157—22no—
134C2×#157—22no—
135C2×#157—22no—
136C2×#157—48no—
137C32×D4—22no—
138C2×C32×C4—41no—
139C2×C32×C4—41no—
140C2×C32×C4C22×C411yescharacteristic
141C2×C32×C4C22×C411yescharacteristic
142C2×C32×C4C22×C411yescharacteristic
143C2×C32×C4C22×C411yescharacteristic
144C2×C32×C4C22×C411yescharacteristic
145#638—22no—
146#638—22no—
147C2×C3⋊Dic3—41no—
148C2×C3⋊Dic3—41no—
149C2×C3⋊Dic3C22×C411yescharacteristic
150C2×C3⋊Dic3C22×C411yescharacteristic
151C2×C3⋊Dic3C22×C411yescharacteristic
152C2×C3⋊Dic3C22×C411yescharacteristic
153C2×C3⋊Dic3C22×C411yescharacteristic
154C4⋊(C3⋊D3)—22no—
155C4×C3⋊D3—22no—
156C4×C3⋊D3—22no—
157C4×C3⋊D3—22no—
158C4×C3⋊D3—21no—
159C4×C3⋊D3—22no—
160C4×C3⋊D3—21no—
161C4×C3⋊D3—41no—
162C4×C3⋊D3—41no—
163C4×C3⋊D3—41no—
164C4×C3⋊D3—41no—
165C2×C4×D4—91no—
166#388—92no—
167#387—92no—
168#386—92no—
169#385—92no—
170#383—91no—
171#382—91no—
172#381—91no—
173#380—91no—
174C4×C22⋊C4—91no—
175C2×#95—91no—
176C23×D3—62no—
177C23×D3—62no—
178C2×C3×D4—22no—
179C22×C3×C4—22no—
180C22×C3×C4—22no—
181C2×#67—62no—
182C2×#67—62no—
183C22×Dic3—62no—
184C22×Dic3—62no—
185D3×D4—616no—
186C2×D12—62no—
187C2×C4×D3—62no—
188C2×C4×D3—62no—
189C2×C4×D3—62no—
190C2×C4×D3—62no—
191C2×C4×D3—62no—
192C2×C4×D3—62no—
193C2×C4×D3—62no—
194C2×C4×D3—62no—
195C2×C4×D3—62no—
196C2×C4×D3—128no—
197C2×C4×D3—128no—
198C3×C4⋊C4—22no—
199C3×C22⋊C4—22no—
200C3×C22⋊C4—22no—
201C3×C42—22no—
202#217—62no—
203#217—62no—
204(C2×D3)⋊C4—62no—
205(C2×D3)⋊C4—62no—
206(C2×D3)⋊C4—62no—
207(C2×D3)⋊C4—62no—
208C4⋊Dic3—62no—
209Dic3⋊C4—62no—
210Dic3⋊C4—62no—
211C4×Dic3—62no—
212C4×Dic3—62no—
213C4×Dic3—62no—
214C22×C32—21no—
215C22×C32—21no—
216C22×C32—21no—
217C22×C32—21no—
218C22×C32—21no—
219C22×C32#11712yes—
220C22×C32C23×C411yescharacteristic
221C2×C3⋊D3—21no—
222C2×C3⋊D3—21no—
223C2×C3⋊D3—21no—
224C2×C3⋊D3—24no—
225C2×C3⋊D3—24no—
226C2×C3⋊D3—21no—
227C2×C3⋊D3—21no—
228C2×C3⋊D3—42no—
229C2×C3⋊D3—42no—
230C2×C3⋊D3#11712yes—
231C2×C3⋊D3C2×#4112yes—
232C2×C3⋊D3H(5,𝔽2)11yescharacteristic
233C2×C3⋊D3H(5,𝔽2)12yes—
234C2×C3⋊D32−1+411yescharacteristic
235#157—42no—
236#157—42no—
237#157—42no—
238#157—42no—
239C32×C4—21no—
240C32×C4—21no—
241C32×C4—21no—
242C32×C4—21no—
243C32×C4—21no—
244C3⋊Dic3—21no—
245C3⋊Dic3—21no—
246C3⋊Dic3—21no—
247C3⋊Dic3—21no—
248C3⋊Dic3—21no—
249C22×D4—91no—
250C23×C4—91no—
251C23×C4—91no—
252C23×C4—92no—
253C4×D4—91no—
254C4×D4—91no—
255C4×D4—91no—
256C4×D4—91no—
257C4×D4—91no—
258C4×D4—91no—
259C4×D4—91no—
260C4×D4#15711yescharacteristic, complemented
261C2×C4⋊C4—91no—
262C2×C4⋊C4—92no—
263C2×C4⋊C4—92no—
264C2×C22⋊C4—91no—
265C2×C22⋊C4—91no—
266C2×C22⋊C4—92no—
267C2×C22⋊C4—92no—
268C2×C22⋊C4—92no—
269C2×C42—91no—
270C2×C42—92no—
271#95—91no—
272#95—91no—
273#95—92no—
274#95—91no—
275#95—91no—
276#95—92no—
277#95—92no—
278#95—92no—
279#95—92no—
280C23×C3—22no—
281C23×C3—22no—
282C22×D3—62no—
283C22×D3—62no—
284C22×D3—62no—
285C22×D3—68no—
286C22×D3—68no—
287C22×D3—124no—
288C22×D3—124no—
289C22×D3—122no—
290C22×D3—122no—
291C22×D3—122no—
292C22×D3—122no—
293C3×D4—28no—
294C2×C3×C4—22no—
295C2×C3×C4—22no—
296C2×C3×C4—22no—
297C2×C3×C4—22no—
298C2×C3×C4—22no—
299C2×C3×C4—44no—
300C2×C3×C4—44no—
301#67—68no—
302#67—68no—
303C2×Dic3—62no—
304C2×Dic3—62no—
305C2×Dic3—62no—
306C2×Dic3—62no—
307C2×Dic3—62no—
308C2×Dic3—124no—
309C2×Dic3—124no—
310D12—68no—
311C4×D3—68no—
312C4×D3—68no—
313C4×D3—122no—
314C4×D3—122no—
315C4×D3—124no—
316C4×D3—124no—
317C4×D3—124no—
318C4×D3—124no—
319C4×D3—124no—
320C4×D3—124no—
321C2×C32—22no—
322C2×C32—41no—
323C2×C32C2×#11711yescharacteristic
324C2×C32#51811yescharacteristic
325C2×C32#52011yescharacteristic
326C3⋊D3—22no—
327C3⋊D3—41no—
328C3⋊D3#53812yes—
329C3⋊D3#53912yes—
330C24—91no—
331C24—91no—
332C2×D4—91no—
333C2×D4—91no—
334C2×D4—91no—
335C2×D4—184no—
336C2×D4C2×#15711yescharacteristic
337C22×C4—91no—
338C22×C4—91no—
339C22×C4—91no—
340C22×C4—91no—
341C22×C4—91no—
342C22×C4—91no—
343C22×C4—91no—
344C22×C4—91no—
345C22×C4—91no—
346C22×C4—91no—
347C22×C4—91no—
348C22×C4—92no—
349C22×C4—92no—
350C22×C4—92no—
351C22×C4—92no—
352C22×C4—184no—
353C22×C4—362no—
354C22×C4—362no—
355C22×C4—362no—
356C22×C4—362no—
357C22×C4C2×#15711yescharacteristic
358C22×C4C2×#15711yescharacteristic, complemented
359C4⋊C4—91no—
360C4⋊C4—91no—
361C4⋊C4—91no—
362C4⋊C4—362no—
363C4⋊C4—362no—
364C4⋊C4C2×#15711yescharacteristic, complemented
365C22⋊C4—91no—
366C22⋊C4—91no—
367C22⋊C4—91no—
368C22⋊C4—91no—
369C22⋊C4—91no—
370C22⋊C4—91no—
371C22⋊C4—184no—
372C22⋊C4—362no—
373C22⋊C4—362no—
374C22⋊C4C2×#15711yescharacteristic
375C22⋊C4C2×#15711yescharacteristic, complemented
376C42—91no—
377C42—91no—
378C42—91no—
379C42—362no—
380C42C2×#15711yescharacteristic, complemented
381C22×C3—24no—
382C22×C3—24no—
383C22×C3—22no—
384C22×C3—42no—
385C22×C3—42no—
386C22×C3—42no—
387C22×C3—42no—
388C2×D3—64no—
389C2×D3—64no—
390C2×D3—62no—
391C2×D3—62no—
392C2×D3—64no—
393C2×D3—64no—
394C2×D3—128no—
395C2×D3—128no—
396C2×D3—122no—
397C2×D3—122no—
398C2×D3—122no—
399C2×D3—122no—
400C2×D3—128no—
401C2×D3—128no—
402C3×C4—24no—
403C3×C4—24no—
404C3×C4—42no—
405C3×C4—42no—
406C3×C4—42no—
407Dic3—64no—
408Dic3—64no—
409Dic3—122no—
410Dic3—122no—
411Dic3—122no—
412C32#231811yescharacteristic, complemented, Sylow
413C23—91no—
414C23—94no—
415C23—91no—
416C23—91no—
417C23—182no—
418C23—181no—
419C23—181no—
420C23—181no—
421C23—182no—
422C23—182no—
423C23—181no—
424C23C22×#15711yescharacteristic
425C23C22×#15711yescharacteristic
426D4—22no—
427D4—182no—
428D4—182no—
429D4—182no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—91no—
433C2×C4—91no—
434C2×C4—91no—
435C2×C4—91no—
436C2×C4—91no—
437C2×C4—182no—
438C2×C4—181no—
439C2×C4—182no—
440C2×C4—182no—
441C2×C4—182no—
442C2×C4—181no—
443C2×C4—182no—
444C2×C4—182no—
445C2×C4—182no—
446C2×C4—182no—
447C2×C4—182no—
448C2×C4—182no—
449C2×C4—182no—
450C2×C4—182no—
451C2×C4—182no—
452C2×C4—182no—
453C2×C4—182no—
454C2×C4—182no—
455C2×C4—361no—
456C2×C4—361no—
457C2×C4—361no—
458C2×C4—361no—
459C2×C4—361no—
460C2×C4—361no—
461C2×C4—368no—
462C2×C4C22×#15711yescharacteristic
463C2×C4C22×#15711yescharacteristic
464C2×C4C22×#15711yescharacteristic
465C2×C4C22×#15711yescharacteristic
466C2×C4C22×#15711yescharacteristic
467C2×C3—22no—
468C2×C3—22no—
469C2×C3—22no—
470C2×C3—44no—
471C2×C3—44no—
472D3—64no—
473D3—64no—
474D3—124no—
475D3—124no—
476C22—21no—
477C22—21no—
478C22—21no—
479C22—21no—
480C22—21no—
481C22—92no—
482C22—92no—
483C22—91no—
484C22—91no—
485C22—92no—
486C22—184no—
487C22—184no—
488C22—181no—
489C22—181no—
490C22—181no—
491C22—181no—
492C22—181no—
493C22—362no—
494C22—362no—
495C22#6428612yes—
496C22C23×#15711yescharacteristic
497C4—21no—
498C4—21no—
499C4—21no—
500C4—21no—
501C4—21no—
502C4—181no—
503C4—181no—
504C4—181no—
505C4—181no—
506C4—181no—
507C4—362no—
508C4—362no—
509C4—362no—
510C4—362no—
511C3—22no—
512C2—22no—
513C2—41no—
514C2—92no—
515C2—92no—
516C2—182no—
517C2—361no—
518C2C2×#6428611yescharacteristic
519C2#1059664211yescharacteristic
520C2#1059665011yescharacteristic
subgroupG/H
center, FrattiniC22C23×#157
commutator, socleC22×C32C23×C4
FittingC32×C4×D4C4
prime radicalC2×D4×C3⋊D3C22
cosocleC22×C3⋊D3C24
hypercenterC4×D4#157
hypocenterC32#2318
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
3. #10593812C2semidirect
4. #10593811C2semidirect
5. C4×C22⋊#157C2semidirect
6. C2×#63781C2semidirect
7. #10593758C2semidirect
8. #10593747C2semidirect
9. #10593746C2semidirect
10. #10593737C2semidirect
11. #10593736C2semidirect
22. C32×C4×D4C4semidirect
23. D4×C3⋊Dic3C4semidirect
24. C4×#638C4semidirect
25. C4×#638C4semidirect
26. #64102C4semidirect
28. #64090C4semidirect
29. #64090C4semidirect
32. C4×C4⋊(C3⋊D3)C4semidirect
55. C22×C32×C4C2×C4semidirect
59. C22×C3⋊Dic3C2×C4semidirect
66. C2×C4×C3⋊D3C2×C4semidirect
67. C2×C4×C3⋊D3C2×C4semidirect
79. C32×C4⋊C4C2×C4semidirect
81. C32×C22⋊C4C2×C4semidirect
82. C32×C42C2×C4semidirect
84. #3757C2×C4semidirect
87. #3752C2×C4semidirect
88. #3752C2×C4semidirect
89. C4⋊(C3⋊Dic3)C2×C4semidirect
90. #3750C2×C4semidirect
91. #3750C2×C4semidirect
92. C4×C3⋊Dic3C2×C4semidirect
93. C4×C3⋊Dic3C2×C4semidirect
94. C4×C3⋊Dic3C2×C4semidirect
260. C4×D4#157semidirect
358. C22×C4C2×#157semidirect
364. C4⋊C4C2×#157semidirect
375. C22⋊C4C2×#157semidirect
380. C42C2×#157semidirect
412. C32#2318semidirect

Maximal subgroups

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

subgroupindex
C4×D4×C3⋊D32
#105938262
#105938122
#105938112
C4×C22⋊#1572
C2×#637812
#105937582
#105937472
#105937462
#105937372
#105937362
#23189