Finite Group Databasebeta

← #11807763

Subgroups — #11807763

Order 1152.

1365 conjugacy classes of subgroups.

The subgroup lattice has 551 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64104C211yesmaximal, characteristic
2C3×#4980C212yesmaximal, complemented
3#10591380C212yesmaximal, complemented
4#10591380C212yesmaximal, complemented
5#10591378C212yesmaximal, complemented
6#10591355C211yesmaximal, characteristic, complemented
7#10591320C212yesmaximal, complemented
8#10591219C211yesmaximal, characteristic, complemented
9#10591202C212yesmaximal, complemented
10#75313—32nomaximal
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C22×C4⋊(C3⋊D3)C2212yes—
13C22×C4×C3⋊D3C2211yescharacteristic
14C22×#624C2212yes—
15C2×C32×C4⋊C4C2211yescharacteristic
16C2×#3752C2212yes—
17#64104C418yescomplemented
18C2×C3×C4⋊Dic3C2212yes—
19C2×C3×C4×Dic3C2212yes—
20C2×#3724C2212yes—
21C2×#3722C2211yescharacteristic
22C2×#3722C2212yes—
23C2×#3722C2212yes—
24C2×#3722C2212yes—
25C2×#3722C2211yescharacteristic
26C2×#3722C2212yes—
27C3×C3⋊#95C2212yes—
28C3×C3⋊#95C2212yes—
29C3×C3⋊#95C2212yes—
30C3×C3⋊#95C2212yes—
31#63579C2211yescharacteristic
32#63579C2211yescharacteristic
33C2×#895—32no—
34C2×#895—61no—
35C3×#387—32no—
36#4989—32no—
37#4988—32no—
38#4980D312yescomplemented
39#4940—32no—
40#4939—32no—
41#4669—32no—
42#4668—32no—
43#4667—32no—
44#4665—32no—
45#4665—32no—
46#4665—32no—
47#4665—32no—
48#4664—32no—
49C23×C3⋊D3C2312yes—
50C23×C3⋊D3C2311yescharacteristic
51C22×C32×C4C2312yes—
52C22×C32×C4C2311yescharacteristic
53C22×C3⋊Dic3C2311yescharacteristic
54C2×C4⋊(C3⋊D3)—42no—
55C2×C4⋊(C3⋊D3)—42no—
56C2×C4⋊(C3⋊D3)—42no—
57C2×C4⋊(C3⋊D3)C2×C414yes—
58C2×C4⋊(C3⋊D3)C2×C418yescomplemented
59C2×C4×C3⋊D3—42no—
60C2×C4×C3⋊D3C2×C414yescomplemented
61C22×C3×Dic3C2312yes—
62C22×C3×Dic3C2312yes—
63C22×C3×Dic3C2312yes—
64C22×C3×Dic3C2312yes—
65C2×#624—42no—
66C2×#624—42no—
67C2×#624—42no—
68C32×C4⋊C4C2×C414yescomplemented
69#3752C2×C418yescomplemented
70C3×C4⋊Dic3—42no—
71C3×C4×Dic3—42no—
72#3724—42no—
73#3722—41no—
74#3722—42no—
75#3722—42no—
76#3722—42no—
77#3722—42no—
78#3722—41no—
79#2377—91noSylow
80C22×D12—32no—
81C22×D12—32no—
82C22×D12—32no—
83C22×D12—61no—
84C22×D12—62no—
85C22×C4×D3—32no—
86C22×C4×D3—32no—
87C22×C4×D3—32no—
88C22×C4×D3—61no—
89C2×C3×C4⋊C4—21no—
90C2×C3×C4⋊C4—32no—
91C2×C3×C4⋊C4C2×D312yes—
92C2×C3×C42—32no—
93C2×(C2×D3)⋊C4—32no—
94C2×(C2×D3)⋊C4—32no—
95C2×(C2×D3)⋊C4—32no—
96C2×(C2×D3)⋊C4—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—62no—
106C2×C4⋊Dic3C2×D312yes—
107C2×Dic3⋊C4—32no—
108C2×Dic3⋊C4—32no—
109C2×C4×Dic3C2×D312yes—
110#895—316no—
111#895—68no—
112C3×#95—32no—
113C3×#95—32no—
114C3×#95—32no—
115C3×#95—32no—
116C3⋊#95—32no—
117C3⋊#95—32no—
118C3⋊#95C2×D312yes—
119C3⋊#95C2×D312yes—
120C3⋊#95C2×D312yes—
121C3⋊#95C2×D312yes—
122C23×C32C2411yescharacteristic
123C22×C3⋊D3—22no—
124C22×C3⋊D3—21no—
125C22×C3⋊D3—22no—
126C22×C3⋊D3—22no—
127C22×C3⋊D3—22no—
128C22×C3⋊D3—22no—
129C22×C3⋊D3—22no—
130C22×C3⋊D3—22no—
131C22×C3⋊D3—21no—
132C22×C3⋊D3—22no—
133C22×C3⋊D3C22×C414yes—
134C22×C3⋊D3C22×C412yes—
135C2×C32×C4—22no—
136C2×C32×C4—22no—
137C2×C32×C4—22no—
138C2×C32×C4C22×C414yes—
139C2×C32×C4C22×C412yes—
140C2×C3⋊Dic3—22no—
141C2×C3⋊Dic3C22×C412yes—
142C4⋊(C3⋊D3)—44no—
143C4⋊(C3⋊D3)—48no—
144C4×C3⋊D3—44no—
145C2×C3×Dic3—22no—
146C2×C3×Dic3—22no—
147C2×C3×Dic3—22no—
148C2×C3×Dic3—22no—
149C2×C3×Dic3—22no—
150C2×C3×Dic3—22no—
151C2×C3×Dic3—22no—
152C2×C3×Dic3—22no—
153C2×C3×Dic3—22no—
154C2×C3×Dic3—22no—
155C2×C3×Dic3—22no—
156C2×C3×Dic3—22no—
157#624—48no—
158C2×#121—91no—
159#390—92no—
160#388—92no—
161#387—32no—
162#386—92no—
163#386—92no—
164#385—92no—
165#381—91no—
166#380—91no—
167C23×D3—32no—
168C23×D3—32no—
169C23×D3—32no—
170C23×D3—61no—
171C23×D3—62no—
172C22×C3×C4—21no—
173C22×C3×C4—22no—
174C22×C3×C4—32no—
175C22×C3×C4—32no—
176C22×C3×C4—32no—
177C22×C3×C4—32no—
178C22×C3×C4C22×D312yes—
179C22×C3×C4C22×D312yes—
180C22×C3×C4C22×D312yes—
181C22×Dic3—32no—
182C22×Dic3—61no—
183C22×Dic3C22×D312yes—
184C22×Dic3C22×D312yes—
185C22×Dic3C22×D312yes—
186C22×Dic3C22×D312yes—
187C2×D12—38no—
188C2×D12—38no—
189C2×D12—38no—
190C2×D12—64no—
191C2×D12—68no—
192C2×D12—122no—
193C2×D12—122no—
194C2×D12—122no—
195C2×D12—122no—
196C2×D12—122no—
197C2×D12—122no—
198C2×D12—124no—
199C2×D12—124no—
200C2×D12—124no—
201C2×C4×D3—38no—
202C2×C4×D3—64no—
203C2×C4×D3—122no—
204C2×C4×D3—122no—
205C2×C4×D3—122no—
206C2×C4×D3—122no—
207C2×C4×D3—122no—
208C2×C4×D3—122no—
209C2×C4×D3—122no—
210C2×C4×D3—122no—
211C2×C4×D3—124no—
212C3×C4⋊C4—24no—
213C3×C4⋊C4—122no—
214C3×C4⋊C4C4×D318yescomplemented
215C3×C42—122no—
216(C2×D3)⋊C4—38no—
217(C2×D3)⋊C4—38no—
218(C2×D3)⋊C4—68no—
219(C2×D3)⋊C4—122no—
220(C2×D3)⋊C4—122no—
221(C2×D3)⋊C4—122no—
222(C2×D3)⋊C4—122no—
223(C2×D3)⋊C4—122no—
224(C2×D3)⋊C4—122no—
225(C2×D3)⋊C4—122no—
226(C2×D3)⋊C4—122no—
227(C2×D3)⋊C4—122no—
228(C2×D3)⋊C4—122no—
229C4⋊Dic3—42no—
230Dic3⋊C4—122no—
231Dic3⋊C4—122no—
232C4×Dic3—42no—
233C22×C32C23×C411yescharacteristic
234C22×C32H(5,𝔽2)12yes—
235C22×C32H(5,𝔽2)12yes—
236C22×C32H(5,𝔽2)11yescharacteristic
237C22×C322−1+411yescharacteristic
238C2×C3⋊D3—22no—
239C2×C3⋊D3—22no—
240C2×C3⋊D3—24no—
241C2×C3⋊D3—24no—
242C2×C3⋊D3—22no—
243C2×C3⋊D3—24no—
244C2×C3⋊D3—42no—
245C2×C3⋊D3—42no—
246C2×C3⋊D3—42no—
247C2×C3⋊D3—42no—
248C2×C3⋊D3—42no—
249C2×C3⋊D3—42no—
250C32×C4—22no—
251C32×C4—24no—
252C3⋊Dic3—22no—
253C3×Dic3—42no—
254C3×Dic3—42no—
255C3×Dic3—42no—
256C3×Dic3—42no—
257C22×D4—91no—
258C22×D4—92no—
259C23×C4—92no—
260C23×C4—91no—
261#121—98no—
262C2×C4⋊C4—32no—
263C2×C4⋊C4—92no—
264C2×C4⋊C4D3211yescharacteristic
265C2×C22⋊C4—92no—
266C2×C22⋊C4—91no—
267C2×C22⋊C4—91no—
268C2×C22⋊C4—92no—
269C2×C22⋊C4—92no—
270C2×C22⋊C4—92no—
271C2×C22⋊C4—92no—
272C2×C42—32no—
273#95—32no—
274#95—32no—
275#95—32no—
276#95—32no—
277#95—91no—
278#95—91no—
279C23×C3—21no—
280C23×C3C23×D312yes—
281C22×D3—34no—
282C22×D3—34no—
283C22×D3—34no—
284C22×D3—62no—
285C22×D3—64no—
286C22×D3—64no—
287C22×D3—62no—
288C22×D3—62no—
289C22×D3—62no—
290C22×D3—62no—
291C22×D3—62no—
292C22×D3—62no—
293C22×D3—62no—
294C22×D3—62no—
295C22×D3—62no—
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—122no—
306C22×D3—121no—
307C22×D3—121no—
308C22×D3—122no—
309C22×D3—122no—
310C22×D3—122no—
311C22×D3—122no—
312C22×D3—122no—
313C22×D3—122no—
314C2×C3×C4—24no—
315C2×C3×C4—22no—
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—24no—
323C2×C3×C4—42no—
324C2×C3×C4—42no—
325C2×C3×C4—62no—
326C2×C3×C4—62no—
327C2×C3×C4—62no—
328C2×C3×C4—62no—
329C2×C3×C4—62no—
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×C4C2×C4×D314yes—
338C2×C3×C4C2×C4×D314yes—
339C2×C3×C4C2×C4×D314yes—
340C2×Dic3—22no—
341C2×Dic3—22no—
342C2×Dic3—22no—
343C2×Dic3—22no—
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—34no—
353C2×Dic3—62no—
354C2×Dic3—62no—
355C2×Dic3—62no—
356C2×Dic3—122no—
357D12—128no—
358D12—128no—
359D12—128no—
360D12—128no—
361D12—1216no—
362C4×D3—128no—
363C4×D3—128no—
364C4×D3—128no—
365C4×D3—128no—
366C2×C32#51811yescharacteristic
367C2×C32#51811yescharacteristic
368C2×C32#52011yescharacteristic
369C2×C32#56012yes—
370C2×C32#56212yes—
371C3⋊D3—42no—
372C3⋊D3—44no—
373C24—92no—
374C24—91no—
375C2×D4—98no—
376C2×D4—94no—
377C2×D4—362no—
378C2×D4—362no—
379C2×D4—362no—
380C22×C4—32no—
381C22×C4—32no—
382C22×C4—32no—
383C22×C4—32no—
384C22×C4—91no—
385C22×C4—94no—
386C22×C4—362no—
387C22×C4—362no—
388C22×C4—362no—
389C22×C4—362no—
390C22×C4C2×D3211yescharacteristic
391C22×C4C2×D3212yes—
392C4⋊C4—122no—
393C4⋊C4—362no—
394C4⋊C4#62414yescomplemented
395C22⋊C4—98no—
396C22⋊C4—362no—
397C22⋊C4—362no—
398C22⋊C4—362no—
399C22⋊C4—361no—
400C22⋊C4—362no—
401C22⋊C4—361no—
402C42—122no—
403C22×C3—22no—
404C22×C3—22no—
405C22×C3—21no—
406C22×C3—21no—
407C22×C3—21no—
408C22×C3C22×C4×D312yes—
409C22×C3#100412yes—
410C22×C3#100712yes—
411C22×C3#100912yes—
412C22×C3#100912yes—
413C22×C3#100912yes—
414C22×C3#100912yes—
415C2×D3—64no—
416C2×D3—64no—
417C2×D3—64no—
418C2×D3—64no—
419C2×D3—64no—
420C2×D3—64no—
421C2×D3—64no—
422C2×D3—64no—
423C2×D3—64no—
424C2×D3—64no—
425C2×D3—122no—
426C2×D3—122no—
427C2×D3—124no—
428C2×D3—124no—
429C2×D3—124no—
430C2×D3—124no—
431C2×D3—124no—
432C2×D3—122no—
433C2×D3—122no—
434C2×D3—122no—
435C2×D3—122no—
436C2×D3—122no—
437C2×D3—122no—
438C2×D3—122no—
439C2×D3—122no—
440C2×D3—122no—
441C2×D3—122no—
442C2×D3—122no—
443C2×D3—122no—
444C2×D3—242no—
445C2×D3—242no—
446C2×D3—242no—
447C2×D3—242no—
448C3×C4—24no—
449C3×C4—24no—
450C3×C4—24no—
451C3×C4—24no—
452C3×C4—44no—
453C3×C4—122no—
454C3×C4—122no—
455C3×C4—122no—
456C3×C4—122no—
457Dic3—42no—
458Dic3—42no—
459Dic3—42no—
460Dic3—42no—
461Dic3—64no—
462Dic3—122no—
463C32#237711yescharacteristic, complemented, Sylow
464C23—94no—
465C23—92no—
466C23—182no—
467C23—182no—
468C23—182no—
469C23—182no—
470C23—182no—
471C23—182no—
472C23—181no—
473C23—182no—
474C23—181no—
475C23—182no—
476C23C22×D3211yescharacteristic
477D4—368no—
478D4—364no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—62no—
483C2×C4—62no—
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—92no—
495C2×C4—182no—
496C2×C4—364no—
497C2×C4—368no—
498C2×C4C2×#62414yes—
499C2×C4C2×#62412yes—
500C2×C3—21no—
501C2×C3—22no—
502C2×C3—22no—
503C2×C3—21no—
504C2×C3—21no—
505C2×C3#552112yes—
506C2×C3#554512yes—
507C2×C3#557412yes—
508C2×C3#564712yes—
509C2×C3#566612yes—
510C2×C3#570012yes—
511C2×C3#571112yes—
512D3—124no—
513D3—124no—
514D3—124no—
515D3—124no—
516D3—244no—
517C22—182no—
518C22—184no—
519C22—182no—
520C22—184no—
521C22—182no—
522C22—184no—
523C22—362no—
524C22—362no—
525C22—362no—
526C22—362no—
527C22—362no—
528C22—362no—
529C22#6430812yes—
530C22#6431412yes—
531C22#6431611yescharacteristic
532C22#6432011yescharacteristic
533C22C22×#62411yescharacteristic
534C4—24no—
535C4—22no—
536C4—122no—
537C4—122no—
538C4—122no—
539C4—122no—
540C4—182no—
541C3—21no—
542C3#7531312yescomplemented
543C2—362no—
544C2—364no—
545C2#1059459312yes—
546C2#1059466312yes—
547C2#1059499611yescharacteristic
548C2#1059522311yescharacteristic
549C2#1059535311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, cosocleC23×C32C24
prime radicalC2×#64104C2
hypercenterC2×C4⋊C4D32
hypocenterC32#2377
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
3. #10591380C2semidirect
4. #10591380C2semidirect
5. #10591378C2semidirect
6. #10591355C2semidirect
7. #10591320C2semidirect
8. #10591219C2semidirect
9. #10591202C2semidirect
17. #64104C4semidirect
38. #4980D3semidirect
58. C2×C4⋊(C3⋊D3)C2×C4semidirect
60. C2×C4×C3⋊D3C2×C4semidirect
68. C32×C4⋊C4C2×C4semidirect
69. #3752C2×C4semidirect
214. C3×C4⋊C4C4×D3semidirect
394. C4⋊C4#624semidirect
463. C32#2377semidirect
542. C3#75313semidirect

Maximal subgroups

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

subgroupindex
C2×#641042
C3×#49802
#105913802
#105913782
#105913552
#105913202
#105912192
#105912022
#753133