Finite Group Databasebeta

← #11805811

Subgroups — #11805811

Order 1152.

1389 conjugacy classes of subgroups.

The subgroup lattice has 555 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64102C211yesmaximal, characteristic
2C3×#4980C212yesmaximal, complemented
3#10591380C212yesmaximal
4#10591370C211yesmaximal, characteristic, complemented
5#10591325C211yesmaximal, characteristic, complemented
6C4×#3722C211yesmaximal, characteristic, complemented
7#10591266C212yesmaximal, complemented
8#10591252C211yesmaximal, characteristic, complemented
9#10591233C212yesmaximal, complemented
10#10591229C211yesmaximal, characteristic, complemented
11#10591219C211yesmaximal, characteristic, complemented
12#75306—32nomaximal
13C22×C4⋊(C3⋊D3)C2211yescharacteristic
14C22×C4×C3⋊D3C2211yescharacteristic
15C22×C4×C3⋊D3C2211yescharacteristic
16C22×#624C2212yes—
17C2×C32×C4⋊C4C2211yescharacteristic
18C2×#3752C2211yescharacteristic
19C2×#3752C2211yescharacteristic
20C2×C4×C3⋊Dic3C2211yescharacteristic
21#64102C418yescomplemented
22C2×C3×C4⋊Dic3C2212yes—
23C2×C3×C4×Dic3C2212yes—
24C2×#3722C2212yes—
25C2×#3722C2212yes—
26C2×#3722C2212yes—
27C2×Dic32C2212yes—
28C3×C3⋊#95C2212yes—
29C3×C3⋊#95C2212yes—
30C3×C3⋊#95C2212yes—
31C3×C3⋊#95C2212yes—
32#63579C2212yes—
33#63579C2211yescharacteristic
34#63579C2211yescharacteristic
35#63579C2211yescharacteristic
36#63579C2211yescharacteristic
37C2×#893—32no—
38C2×#893—61no—
39C3×#387—32no—
40#4990—32no—
41#4987—32no—
42#4980D312yescomplemented
43C4×(C2×D3)⋊C4—32no—
44C4×(C2×D3)⋊C4—32no—
45#4670—32no—
46#4666—32no—
47#4665—32no—
48#4665—32no—
49#4664—32no—
50D3×#95—32no—
51#4651—32no—
52#4648—32no—
53C23×C3⋊D3C2311yescharacteristic
54C23×C3⋊D3C2311yescharacteristic
55C22×C32×C4C2311yescharacteristic
56C22×C32×C4C2311yescharacteristic
57C22×C32×C4C2311yescharacteristic
58C22×C3⋊Dic3C2311yescharacteristic
59C22×C3⋊Dic3C2311yescharacteristic
60C2×C4⋊(C3⋊D3)—22no—
61C2×C4⋊(C3⋊D3)—22no—
62C2×C4⋊(C3⋊D3)C2×C414yes—
63C2×C4×C3⋊D3—42no—
64C2×C4×C3⋊D3—42no—
65C2×C4×C3⋊D3C2×C414yes—
66C2×C4×C3⋊D3C2×C414yescomplemented
67C22×C3×Dic3C2312yes—
68C22×C3×Dic3C2312yes—
69C22×C3×Dic3C2312yes—
70C22×C3×Dic3C2312yes—
71C2×#624—24no—
72C2×#624—24no—
73C2×#624—42no—
74C32×C4⋊C4C2×C414yescomplemented
75#3752C2×C414yes—
76#3752C2×C414yescomplemented
77C4×C3⋊Dic3C2×C414yescomplemented
78C3×C4⋊Dic3—42no—
79C3×C4×Dic3—42no—
80#3722—24no—
81#3722—24no—
82#3722—42no—
83Dic32—24no—
84#2353—91noSylow
85C22×D12—32no—
86C22×D12—61no—
87C22×C4×D3—32no—
88C22×C4×D3—32no—
89C22×C4×D3—32no—
90C22×C4×D3—32no—
91C22×C4×D3—61no—
92C22×C4×D3—61no—
93C2×C3×C4⋊C4—21no—
94C2×C3×C4⋊C4—32no—
95C2×C3×C4⋊C4C2×D312yes—
96C2×C3×C42—32no—
97C2×(C2×D3)⋊C4—32no—
98C2×(C2×D3)⋊C4—32no—
99C2×(C2×D3)⋊C4—32no—
100C2×(C2×D3)⋊C4—32no—
101C2×(C2×D3)⋊C4—32no—
102C2×(C2×D3)⋊C4—32no—
103C2×(C2×D3)⋊C4—32no—
104C2×(C2×D3)⋊C4—32no—
105C2×(C2×D3)⋊C4—61no—
106C2×(C2×D3)⋊C4—61no—
107C2×C4⋊Dic3C2×D312yes—
108C2×C4×Dic3—32no—
109C2×C4×Dic3—32no—
110C2×C4×Dic3—32no—
111C2×C4×Dic3—61no—
112C2×C4×Dic3C2×D312yes—
113#893—316no—
114#893—68no—
115C3×#95—32no—
116C3×#95—32no—
117C3×#95—32no—
118C3×#95—32no—
119C3⋊#95—32no—
120C3⋊#95—32no—
121C3⋊#95—32no—
122C3⋊#95—32no—
123C3⋊#95—32no—
124C3⋊#95—32no—
125C3⋊#95C2×D312yes—
126C3⋊#95C2×D312yes—
127C3⋊#95C2×D312yes—
128C3⋊#95C2×D312yes—
129C23×C32C2411yescharacteristic
130C22×C3⋊D3—21no—
131C22×C3⋊D3—21no—
132C22×C3⋊D3—22no—
133C22×C3⋊D3—22no—
134C22×C3⋊D3—22no—
135C22×C3⋊D3—22no—
136C22×C3⋊D3C22×C412yes—
137C22×C3⋊D3C22×C412yes—
138C22×C3⋊D3#4112yes—
139C22×C3⋊D3#4112yes—
140C2×C32×C4—21no—
141C2×C32×C4—21no—
142C2×C32×C4—22no—
143C2×C32×C4—22no—
144C2×C32×C4C22×C412yes—
145C2×C32×C4C22×C412yes—
146C2×C32×C4C22×C412yes—
147C2×C3⋊Dic3—22no—
148C2×C3⋊Dic3—22no—
149C2×C3⋊Dic3C22×C412yes—
150C2×C3⋊Dic3C22×C412yes—
151C4⋊(C3⋊D3)—28no—
152C4×C3⋊D3—44no—
153C4×C3⋊D3—44no—
154C2×C3×Dic3—22no—
155C2×C3×Dic3—22no—
156C2×C3×Dic3—22no—
157C2×C3×Dic3—22no—
158C2×C3×Dic3—22no—
159C2×C3×Dic3—22no—
160C2×C3×Dic3—22no—
161C2×C3×Dic3—22no—
162C2×C3×Dic3—22no—
163C2×C3×Dic3—22no—
164C2×C3×Dic3—22no—
165C2×C3×Dic3#4114yes—
166#624—48no—
167C2×C4×D4—91no—
168#388—92no—
169#387—32no—
170#386—92no—
171#383—91no—
172#381—91no—
173#380—91no—
174C4×C22⋊C4—92no—
175C4×C22⋊C4—91no—
176#376—91no—
177C2×#95—91no—
178C23×D3—32no—
179C23×D3—32no—
180C23×D3—61no—
181C23×D3—61no—
182C22×C3×C4—21no—
183C22×C3×C4—21no—
184C22×C3×C4—21no—
185C22×C3×C4—32no—
186C22×C3×C4—32no—
187C22×C3×C4—32no—
188C22×C3×C4—32no—
189C22×C3×C4C22×D312yes—
190C22×C3×C4C22×D312yes—
191C22×C3×C4C22×D312yes—
192C22×Dic3—32no—
193C22×Dic3—32no—
194C22×Dic3—61no—
195C22×Dic3—61no—
196C22×Dic3C22×D312yes—
197C22×Dic3C22×D312yes—
198C22×Dic3C22×D312yes—
199C22×Dic3C22×D312yes—
200C2×D12—38no—
201C2×D12—64no—
202C2×D12—64no—
203C2×D12—64no—
204C2×D12—64no—
205C2×D12—64no—
206C2×C4×D3—38no—
207C2×C4×D3—38no—
208C2×C4×D3—64no—
209C2×C4×D3—64no—
210C2×C4×D3—64no—
211C2×C4×D3—64no—
212C2×C4×D3—64no—
213C2×C4×D3—64no—
214C2×C4×D3—122no—
215C2×C4×D3—122no—
216C2×C4×D3—122no—
217C2×C4×D3—122no—
218C2×C4×D3—122no—
219C2×C4×D3—122no—
220C2×C4×D3—124no—
221C2×C4×D3—124no—
222C3×C4⋊C4—24no—
223C3×C4⋊C4—122no—
224C3×C4⋊C4C4×D318yescomplemented
225C3×C42—122no—
226(C2×D3)⋊C4—38no—
227(C2×D3)⋊C4—38no—
228(C2×D3)⋊C4—64no—
229(C2×D3)⋊C4—64no—
230(C2×D3)⋊C4—64no—
231(C2×D3)⋊C4—64no—
232(C2×D3)⋊C4—64no—
233(C2×D3)⋊C4—64no—
234(C2×D3)⋊C4—122no—
235(C2×D3)⋊C4—122no—
236C4⋊Dic3—42no—
237C4×Dic3—38no—
238C4×Dic3—42no—
239C4×Dic3—64no—
240C4×Dic3—64no—
241C4×Dic3—64no—
242C22×C32C23×C411yescharacteristic
243C22×C32C2×#4112yes—
244C22×C32C2×#4111yescharacteristic
245C22×C32C2×#4111yescharacteristic
246C22×C32H(5,𝔽2)12yes—
247C2×C3⋊D3—22no—
248C2×C3⋊D3—22no—
249C2×C3⋊D3—22no—
250C2×C3⋊D3—24no—
251C2×C3⋊D3—24no—
252C2×C3⋊D3—22no—
253C2×C3⋊D3—22no—
254C2×C3⋊D3—42no—
255C2×C3⋊D3—42no—
256C2×C3⋊D3#11714yes—
257C32×C4—22no—
258C32×C4—22no—
259C32×C4—22no—
260C3⋊Dic3—22no—
261C3⋊Dic3—22no—
262C3×Dic3—24no—
263C3×Dic3—42no—
264C3×Dic3—42no—
265C3×Dic3—42no—
266C22×D4—91no—
267C23×C4—92no—
268C23×C4—91no—
269C23×C4—91no—
270C4×D4—98no—
271C2×C4⋊C4—32no—
272C2×C4⋊C4D3211yescharacteristic
273C2×C22⋊C4—91no—
274C2×C22⋊C4—91no—
275C2×C22⋊C4—92no—
276C2×C22⋊C4—92no—
277C2×C22⋊C4—92no—
278C2×C42—32no—
279C2×C42—91no—
280C2×C42—92no—
281#95—32no—
282#95—32no—
283#95—32no—
284#95—32no—
285#95—91no—
286#95—91no—
287#95—91no—
288#95—91no—
289#95—92no—
290C23×C3—21no—
291C23×C3C23×D312yes—
292C22×D3—34no—
293C22×D3—34no—
294C22×D3—34no—
295C22×D3—34no—
296C22×D3—62no—
297C22×D3—62no—
298C22×D3—62no—
299C22×D3—62no—
300C22×D3—62no—
301C22×D3—62no—
302C22×D3—62no—
303C22×D3—62no—
304C22×D3—62no—
305C22×D3—62no—
306C22×D3—62no—
307C22×D3—62no—
308C22×D3—62no—
309C22×D3—62no—
310C22×D3—62no—
311C22×D3—62no—
312C22×D3—122no—
313C22×D3—122no—
314C22×D3—122no—
315C22×D3—122no—
316C2×C3×C4—22no—
317C2×C3×C4—22no—
318C2×C3×C4—22no—
319C2×C3×C4—22no—
320C2×C3×C4—22no—
321C2×C3×C4—22no—
322C2×C3×C4—22no—
323C2×C3×C4—22no—
324C2×C3×C4—22no—
325C2×C3×C4—22no—
326C2×C3×C4—22no—
327C2×C3×C4—34no—
328C2×C3×C4—42no—
329C2×C3×C4—42no—
330C2×C3×C4—62no—
331C2×C3×C4—62no—
332C2×C3×C4—62no—
333C2×C3×C4—62no—
334C2×C3×C4—62no—
335C2×C3×C4—62no—
336C2×C3×C4—62no—
337C2×C3×C4—62no—
338C2×C3×C4—62no—
339C2×C3×C4—62no—
340C2×C3×C4—62no—
341C2×C3×C4C2×C4×D314yes—
342C2×C3×C4C2×C4×D314yes—
343C2×C3×C4C2×C4×D314yes—
344C2×Dic3—22no—
345C2×Dic3—22no—
346C2×Dic3—22no—
347C2×Dic3—22no—
348C2×Dic3—22no—
349C2×Dic3—22no—
350C2×Dic3—22no—
351C2×Dic3—22no—
352C2×Dic3—22no—
353C2×Dic3—22no—
354C2×Dic3—22no—
355C2×Dic3—34no—
356C2×Dic3—34no—
357C2×Dic3—62no—
358C2×Dic3—62no—
359C2×Dic3—64no—
360C2×Dic3—62no—
361C2×Dic3—62no—
362C2×Dic3—62no—
363C2×Dic3—62no—
364C2×Dic3—122no—
365C2×Dic3#23914yes—
366D12—616no—
367D12—616no—
368C4×D3—128no—
369C4×D3—128no—
370C4×D3—128no—
371C4×D3—128no—
372C4×D3—128no—
373C4×D3—128no—
374C2×C32C2×#11711yescharacteristic
375C2×C32C4×#4111yescharacteristic
376C2×C32#51811yescharacteristic
377C2×C32#55112yes—
378C2×C32#55312yes—
379C3⋊D3—24no—
380C3⋊D3—42no—
381C24—91no—
382C24—91no—
383C2×D4—94no—
384C2×D4—182no—
385C2×D4—182no—
386C22×C4—32no—
387C22×C4—32no—
388C22×C4—32no—
389C22×C4—32no—
390C22×C4—91no—
391C22×C4—91no—
392C22×C4—94no—
393C22×C4—94no—
394C22×C4—184no—
395C22×C4—184no—
396C22×C4—362no—
397C22×C4—362no—
398C22×C4—362no—
399C22×C4C2×D3211yescharacteristic
400C22×C4C2×D3211yescharacteristic
401C22×C4C2×D3211yescharacteristic
402C4⋊C4—122no—
403C4⋊C4#62414yescomplemented
404C22⋊C4—94no—
405C22⋊C4—94no—
406C22⋊C4—184no—
407C22⋊C4—184no—
408C22⋊C4—362no—
409C42—94no—
410C42—122no—
411C42—184no—
412C22×C3—21no—
413C22×C3—21no—
414C22×C3—22no—
415C22×C3—22no—
416C22×C3—21no—
417C22×C3C22×C4×D312yes—
418C22×C3#100412yes—
419C22×C3C2×#23912yes—
420C22×C3D3×#4112yes—
421C22×C3D3×#4112yes—
422C22×C3D3×#4112yes—
423C22×C3#100912yes—
424C2×D3—38no—
425C2×D3—64no—
426C2×D3—64no—
427C2×D3—64no—
428C2×D3—64no—
429C2×D3—64no—
430C2×D3—64no—
431C2×D3—64no—
432C2×D3—64no—
433C2×D3—64no—
434C2×D3—64no—
435C2×D3—64no—
436C2×D3—122no—
437C2×D3—122no—
438C2×D3—122no—
439C2×D3—124no—
440C2×D3—124no—
441C2×D3—122no—
442C2×D3—124no—
443C2×D3—124no—
444C2×D3—122no—
445C2×D3—122no—
446C2×D3—122no—
447C2×D3—122no—
448C3×C4—24no—
449C3×C4—24no—
450C3×C4—24no—
451C3×C4—24no—
452C3×C4—42no—
453C3×C4—42no—
454C3×C4—64no—
455C3×C4—122no—
456C3×C4—122no—
457C3×C4—122no—
458Dic3—24no—
459Dic3—42no—
460Dic3—42no—
461Dic3—42no—
462Dic3—64no—
463Dic3—64no—
464Dic3—64no—
465Dic3—122no—
466C32#235311yescharacteristic, complemented, Sylow
467C23—92no—
468C23—92no—
469C23—92no—
470C23—92no—
471C23—182no—
472C23—182no—
473C23—181no—
474C23—181no—
475C23—182no—
476C23—182no—
477C23C22×D3211yescharacteristic
478D4—188no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—34no—
484C2×C4—62no—
485C2×C4—62no—
486C2×C4—62no—
487C2×C4—62no—
488C2×C4—62no—
489C2×C4—62no—
490C2×C4—62no—
491C2×C4—62no—
492C2×C4—62no—
493C2×C4—62no—
494C2×C4—62no—
495C2×C4—92no—
496C2×C4—92no—
497C2×C4—182no—
498C2×C4—182no—
499C2×C4—364no—
500C2×C4—364no—
501C2×C4—368no—
502C2×C4C2×#62412yes—
503C2×C4C2×#62412yes—
504C2×C4C2×#62412yes—
505C2×C3—21no—
506C2×C3—22no—
507C2×C3—21no—
508C2×C3—21no—
509C2×C3—22no—
510C2×C3D3×#11712yes—
511C2×C3#554512yes—
512C2×C3C4×#23912yes—
513C2×C3#563712yes—
514C2×C3#566112yes—
515C2×C3#569512yes—
516C2×C3#570512yes—
517D3—68no—
518D3—124no—
519D3—124no—
520D3—124no—
521C22—94no—
522C22—182no—
523C22—184no—
524C22—182no—
525C22—184no—
526C22—182no—
527C22—182no—
528C22—182no—
529C22—362no—
530C22—362no—
531C22#6430611yescharacteristic
532C22#6430611yescharacteristic
533C22#6431412yes—
534C22D3×#23912yes—
535C22C22×#62411yescharacteristic
536C4—22no—
537C4—22no—
538C4—22no—
539C4—64no—
540C4—122no—
541C4—122no—
542C4—122no—
543C4—182no—
544C4—182no—
545C3—21no—
546C3#7530612yescomplemented
547C2—184no—
548C2—362no—
549C2#1059446112yes—
550C2#1059465512yes—
551C2#1059496911yescharacteristic
552C2#1059522311yescharacteristic
553C2#1059538611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, cosocleC23×C32C24
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenterC2×C4⋊C4D32
hypocenterC32#2353
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C3×#4980C2semidirect
4. #10591370C2semidirect
5. #10591325C2semidirect
6. C4×#3722C2semidirect
7. #10591266C2semidirect
8. #10591252C2semidirect
9. #10591233C2semidirect
10. #10591229C2semidirect
11. #10591219C2semidirect
21. #64102C4semidirect
42. #4980D3semidirect
66. C2×C4×C3⋊D3C2×C4semidirect
74. C32×C4⋊C4C2×C4semidirect
76. #3752C2×C4semidirect
77. C4×C3⋊Dic3C2×C4semidirect
224. C3×C4⋊C4C4×D3semidirect
403. C4⋊C4#624semidirect
466. C32#2353semidirect
546. C3#75306semidirect

Maximal subgroups

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

subgroupindex
C2×#641022
C3×#49802
#105913802
#105913702
#105913252
C4×#37222
#105912662
#105912522
#105912332
#105912292
#105912192
#753063