Finite Group Databasebeta

← #11805752

Subgroups — #11805752

Order 1152.

1014 conjugacy classes of subgroups.

The subgroup lattice has 525 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
9C22⋊C4×#157C212yesmaximal, complemented
10#10593737C211yesmaximal, characteristic, complemented
11#10593733C211yesmaximal, 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—24no—
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—22no—
61D4×C3⋊D3—22no—
62C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
63C2×C4×C3⋊D3—42no—
64C2×C4×C3⋊D3—42no—
65C2×C4×C3⋊D3C2×C411yescharacteristic
66C2×C4×C3⋊D3C2×C411yescharacteristic
67C2×C4×C3⋊D3C2×C411yescharacteristic, complemented
68C2×C4×C3⋊D3C2×C411yescharacteristic, complemented
69C2×C4×C3⋊D3C2311yescharacteristic
70C2×C4×C3⋊D3C2311yescharacteristic
71C2×C4×C3⋊D3C2311yescharacteristic
72C2×C4×C3⋊D3C2311yescharacteristic
73C2×C4×C3⋊D3C2311yescharacteristic
74C22⋊#157—24no—
75C22⋊#157—24no—
76C22⋊#157—42no—
77C4⋊#157—42no—
78C4×#157—24no—
79C4×#157—42no—
80C32×C4⋊C4C2×C411yescharacteristic, complemented
81C32×C22⋊C4C2×C411yescharacteristic
82C32×C22⋊C4C2×C411yescharacteristic, complemented
83C32×C42C2×C411yescharacteristic, complemented
84#3757C2×C411yescharacteristic
85#3757C2×C411yescharacteristic, complemented
86#3752C2×C411yescharacteristic
87#3752C2×C411yescharacteristic
88#3752C2×C411yescharacteristic, complemented
89#3752C2×C411yescharacteristic, complemented
90C4⋊(C3⋊Dic3)C2×C411yescharacteristic, complemented
91#3750C2×C411yescharacteristic, complemented
92#3750C2×C411yescharacteristic, complemented
93C4×C3⋊Dic3C2×C411yescharacteristic, complemented
94C4×C3⋊Dic3C2×C411yescharacteristic, complemented
95C4×C3⋊Dic3C2×C411yescharacteristic, complemented
96#2353—91nomaximal, Sylow
97C2×D3×D4—62no—
98C22×C4×D3—62no—
99C22×C4×D3—62no—
100C3×C4×D4—22no—
101D4×Dic3—62no—
102C4×#67—62no—
103C4×#67—62no—
104#893—62no—
105D3×C4⋊C4—62no—
106#67⋊C4—62no—
107#67⋊C4—62no—
108D3×C22⋊C4—62no—
109D3×C22⋊C4—62no—
110C4×D12—62no—
111C42×D3—62no—
112C23×C32C22×C411yescharacteristic
113C23×C32C22×C411yescharacteristic
114C22×C3⋊D3—21no—
115C22×C3⋊D3—21no—
116C22×C3⋊D3—22no—
117C22×C3⋊D3—22no—
118C22×C3⋊D3—22no—
119C22×C3⋊D3—22no—
120C22×C3⋊D3C22×C411yescharacteristic
121C22×C3⋊D3C22×C411yescharacteristic
122C22×C3⋊D3#4112yes—
123C22×C3⋊D3#4112yes—
124C22×C3⋊D3C2411yescharacteristic
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—
137C2×#157#4114yes—
138C32×D4—22no—
139C2×C32×C4—41no—
140C2×C32×C4—41no—
141C2×C32×C4C22×C411yescharacteristic
142C2×C32×C4C22×C411yescharacteristic
143C2×C32×C4C22×C411yescharacteristic
144C2×C32×C4C22×C411yescharacteristic
145C2×C32×C4C22×C411yescharacteristic
146#638—22no—
147#638—22no—
148C2×C3⋊Dic3—41no—
149C2×C3⋊Dic3—41no—
150C2×C3⋊Dic3C22×C411yescharacteristic
151C2×C3⋊Dic3C22×C411yescharacteristic
152C2×C3⋊Dic3C22×C411yescharacteristic
153C2×C3⋊Dic3C22×C411yescharacteristic
154C2×C3⋊Dic3C22×C411yescharacteristic
155C4⋊(C3⋊D3)—22no—
156C4×C3⋊D3—21no—
157C4×C3⋊D3—21no—
158C4×C3⋊D3—22no—
159C4×C3⋊D3—22no—
160C4×C3⋊D3—22no—
161C4×C3⋊D3—22no—
162C4×C3⋊D3—41no—
163C4×C3⋊D3—41no—
164C4×C3⋊D3—41no—
165C4×C3⋊D3—41no—
166C2×C4×D4—91no—
167#388—92no—
168#387—92no—
169#386—92no—
170#383—91no—
171#381—91no—
172#380—91no—
173C4×C22⋊C4—91no—
174C4×C22⋊C4—92no—
175#376—91no—
176C2×#95—91no—
177C23×D3—62no—
178C23×D3—62no—
179C2×C3×D4—22no—
180C22×C3×C4—22no—
181C22×C3×C4—22no—
182C2×#67—62no—
183C2×#67—62no—
184C22×Dic3—62no—
185C22×Dic3—62no—
186D3×D4—68no—
187D3×D4—68no—
188C2×D12—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—62no—
197C2×C4×D3—62no—
198C2×C4×D3—128no—
199C2×C4×D3—128no—
200C3×C4⋊C4—22no—
201C3×C22⋊C4—22no—
202C3×C22⋊C4—22no—
203C3×C42—22no—
204#217—62no—
205#217—62no—
206(C2×D3)⋊C4—62no—
207(C2×D3)⋊C4—62no—
208(C2×D3)⋊C4—62no—
209(C2×D3)⋊C4—62no—
210C4⋊Dic3—62no—
211Dic3⋊C4—62no—
212Dic3⋊C4—62no—
213C4×Dic3—62no—
214C4×Dic3—62no—
215C4×Dic3—62no—
216C22×C32—21no—
217C22×C32—21no—
218C22×C32—21no—
219C22×C32—21no—
220C22×C32—21no—
221C22×C32#11712yes—
222C22×C32C23×C411yescharacteristic
223C2×C3⋊D3—21no—
224C2×C3⋊D3—21no—
225C2×C3⋊D3—21no—
226C2×C3⋊D3—24no—
227C2×C3⋊D3—24no—
228C2×C3⋊D3—21no—
229C2×C3⋊D3—21no—
230C2×C3⋊D3—42no—
231C2×C3⋊D3—42no—
232C2×C3⋊D3#11712yes—
233C2×C3⋊D3C2×#4111yescharacteristic
234C2×C3⋊D3C2×#4112yes—
235C2×C3⋊D3C2×#4111yescharacteristic
236C2×C3⋊D3H(5,𝔽2)12yes—
237#157—24no—
238#157—42no—
239#157—42no—
240#157—42no—
241C32×C4—21no—
242C32×C4—21no—
243C32×C4—21no—
244C32×C4—21no—
245C32×C4—21no—
246C3⋊Dic3—21no—
247C3⋊Dic3—21no—
248C3⋊Dic3—21no—
249C3⋊Dic3—21no—
250C3⋊Dic3—21no—
251C22×D4—91no—
252C23×C4—91no—
253C23×C4—91no—
254C23×C4—92no—
255C4×D4—91no—
256C4×D4—91no—
257C4×D4—91no—
258C4×D4—91no—
259C4×D4—91no—
260C4×D4—91no—
261C4×D4—91no—
262C4×D4#15711yescharacteristic, complemented
263C2×C4⋊C4—91no—
264C2×C4⋊C4—92no—
265C2×C22⋊C4—91no—
266C2×C22⋊C4—91no—
267C2×C22⋊C4—92no—
268C2×C22⋊C4—92no—
269C2×C22⋊C4—92no—
270C2×C42—91no—
271C2×C42—92no—
272C2×C42—92no—
273#95—91no—
274#95—91no—
275#95—92no—
276#95—91no—
277#95—92no—
278#95—91no—
279#95—92no—
280#95—92no—
281#95—92no—
282C23×C3—22no—
283C23×C3—22no—
284C22×D3—62no—
285C22×D3—62no—
286C22×D3—62no—
287C22×D3—64no—
288C22×D3—64no—
289C22×D3—64no—
290C22×D3—64no—
291C22×D3—124no—
292C22×D3—124no—
293C22×D3—124no—
294C22×D3—124no—
295C3×D4—28no—
296C2×C3×C4—22no—
297C2×C3×C4—22no—
298C2×C3×C4—22no—
299C2×C3×C4—22no—
300C2×C3×C4—22no—
301C2×C3×C4—44no—
302C2×C3×C4—44no—
303#67—68no—
304#67—68no—
305C2×Dic3—62no—
306C2×Dic3—62no—
307C2×Dic3—62no—
308C2×Dic3—62no—
309C2×Dic3—62no—
310C2×Dic3—124no—
311C2×Dic3—124no—
312D12—68no—
313C4×D3—68no—
314C4×D3—64no—
315C4×D3—64no—
316C4×D3—124no—
317C4×D3—124no—
318C4×D3—124no—
319C4×D3—124no—
320C4×D3—124no—
321C4×D3—124no—
322C4×D3—124no—
323C2×C32—22no—
324C2×C32—41no—
325C2×C32C2×#11711yescharacteristic
326C2×C32C4×#4111yescharacteristic
327C2×C32#51811yescharacteristic
328C3⋊D3—22no—
329C3⋊D3—41no—
330C3⋊D3#55112yes—
331C3⋊D3#55312yes—
332C24—91no—
333C24—91no—
334C2×D4—91no—
335C2×D4—91no—
336C2×D4—91no—
337C2×D4—182no—
338C2×D4—182no—
339C2×D4C2×#15711yescharacteristic
340C22×C4—92no—
341C22×C4—91no—
342C22×C4—91no—
343C22×C4—91no—
344C22×C4—91no—
345C22×C4—91no—
346C22×C4—91no—
347C22×C4—91no—
348C22×C4—91no—
349C22×C4—91no—
350C22×C4—91no—
351C22×C4—91no—
352C22×C4—92no—
353C22×C4—92no—
354C22×C4—92no—
355C22×C4—184no—
356C22×C4—184no—
357C22×C4—362no—
358C22×C4—362no—
359C22×C4—362no—
360C22×C4C2×#15711yescharacteristic
361C22×C4C2×#15711yescharacteristic, complemented
362C4⋊C4—91no—
363C4⋊C4—91no—
364C4⋊C4—91no—
365C4⋊C4—362no—
366C4⋊C4C2×#15711yescharacteristic, complemented
367C22⋊C4—91no—
368C22⋊C4—91no—
369C22⋊C4—91no—
370C22⋊C4—91no—
371C22⋊C4—91no—
372C22⋊C4—91no—
373C22⋊C4—184no—
374C22⋊C4—184no—
375C22⋊C4—362no—
376C22⋊C4C2×#15711yescharacteristic
377C22⋊C4C2×#15711yescharacteristic, complemented
378C42—91no—
379C42—91no—
380C42—91no—
381C42—184no—
382C42—362no—
383C42C2×#15711yescharacteristic, complemented
384C22×C3—24no—
385C22×C3—24no—
386C22×C3—22no—
387C22×C3—42no—
388C22×C3—42no—
389C22×C3—42no—
390C22×C3—42no—
391C2×D3—64no—
392C2×D3—62no—
393C2×D3—62no—
394C2×D3—64no—
395C2×D3—64no—
396C2×D3—64no—
397C2×D3—128no—
398C2×D3—128no—
399C2×D3—122no—
400C2×D3—122no—
401C2×D3—122no—
402C2×D3—122no—
403C2×D3—128no—
404C2×D3—128no—
405C3×C4—24no—
406C3×C4—24no—
407C3×C4—42no—
408C3×C4—42no—
409C3×C4—42no—
410Dic3—64no—
411Dic3—64no—
412Dic3—122no—
413Dic3—122no—
414Dic3—122no—
415C32#235311yescharacteristic, complemented, Sylow
416C23—91no—
417C23—92no—
418C23—92no—
419C23—91no—
420C23—91no—
421C23—182no—
422C23—182no—
423C23—182no—
424C23—182no—
425C23—181no—
426C23—181no—
427C23C22×#15711yescharacteristic
428C23C22×#15711yescharacteristic
429D4—22no—
430D4—182no—
431D4—182no—
432D4—182no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—94no—
436C2×C4—91no—
437C2×C4—91no—
438C2×C4—91no—
439C2×C4—91no—
440C2×C4—91no—
441C2×C4—182no—
442C2×C4—182no—
443C2×C4—182no—
444C2×C4—182no—
445C2×C4—181no—
446C2×C4—181no—
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—182no—
456C2×C4—182no—
457C2×C4—182no—
458C2×C4—361no—
459C2×C4—361no—
460C2×C4—361no—
461C2×C4—361no—
462C2×C4—361no—
463C2×C4—361no—
464C2×C4—368no—
465C2×C4C22×#15711yescharacteristic
466C2×C4C22×#15711yescharacteristic
467C2×C4C22×#15711yescharacteristic
468C2×C4C22×#15711yescharacteristic
469C2×C4C22×#15711yescharacteristic
470C2×C3—22no—
471C2×C3—22no—
472C2×C3—22no—
473C2×C3—44no—
474C2×C3—44no—
475D3—64no—
476D3—64no—
477D3—124no—
478D3—124no—
479C22—21no—
480C22—21no—
481C22—21no—
482C22—21no—
483C22—21no—
484C22—91no—
485C22—91no—
486C22—92no—
487C22—92no—
488C22—92no—
489C22—184no—
490C22—184no—
491C22—181no—
492C22—181no—
493C22—181no—
494C22—181no—
495C22—181no—
496C22—362no—
497C22—362no—
498C22#6428612yes—
499C22C23×#15711yescharacteristic
500C4—21no—
501C4—21no—
502C4—21no—
503C4—21no—
504C4—21no—
505C4—184no—
506C4—181no—
507C4—181no—
508C4—181no—
509C4—181no—
510C4—181no—
511C4—362no—
512C4—362no—
513C4—362no—
514C3—22no—
515C2—22no—
516C2—41no—
517C2—92no—
518C2—92no—
519C2—182no—
520C2—361no—
521C2C2×#6428611yescharacteristic
522C2#1059664211yescharacteristic
523C2#41×#15711yescharacteristic
subgroupG/H
center, FrattiniC22C23×#157
commutator, socleC22×C32C23×C4
FittingC32×C4×D4C4
prime radicalC2×D4×C3⋊D3C22
cosocleC22×C3⋊D3C24
hypercenterC4×D4#157
hypocenterC32#2353
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. C22⋊C4×#157C2semidirect
10. #10593737C2semidirect
11. #10593733C2semidirect
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
67. C2×C4×C3⋊D3C2×C4semidirect
68. C2×C4×C3⋊D3C2×C4semidirect
80. C32×C4⋊C4C2×C4semidirect
82. C32×C22⋊C4C2×C4semidirect
83. C32×C42C2×C4semidirect
85. #3757C2×C4semidirect
88. #3752C2×C4semidirect
89. #3752C2×C4semidirect
90. C4⋊(C3⋊Dic3)C2×C4semidirect
91. #3750C2×C4semidirect
92. #3750C2×C4semidirect
93. C4×C3⋊Dic3C2×C4semidirect
94. C4×C3⋊Dic3C2×C4semidirect
95. C4×C3⋊Dic3C2×C4semidirect
262. C4×D4#157semidirect
361. C22×C4C2×#157semidirect
366. C4⋊C4C2×#157semidirect
377. C22⋊C4C2×#157semidirect
383. C42C2×#157semidirect
415. C32#2353semidirect

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
C22⋊C4×#1572
#105937372
#105937332
#23539