Finite Group Databasebeta

← #11807757

Subgroups — #11807757

Order 1152.

1365 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64139C211yesmaximal, characteristic
2C3×#5212C211yesmaximal, characteristic, complemented
3C3×#5211C211yesmaximal, characteristic, complemented
4#10591722C212yesmaximal, complemented
5#10591704C212yesmaximal, complemented
6#10591380C212yesmaximal, complemented
7#10591378C212yesmaximal, complemented
8#10591271C212yesmaximal, complemented
9#10591266C212yesmaximal, complemented
10#74124—31nomaximal
11#74014—31nomaximal
12C23×C32×C4C2211yescharacteristic
13C22×#638C2212yes—
14C22×C4⋊(C3⋊D3)C2211yescharacteristic
15C22×#624C2212yes—
16#64139C418yescomplemented
17C2×#3752C2212yes—
18C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
19C2×C3×#217C2212yes—
20C2×C3×#217C2211yescharacteristic
21C2×C3×#217C2211yescharacteristic
22C2×C3×C4⋊Dic3C2212yes—
23C2×#3724C2212yes—
24C2×#3722C2212yes—
25C2×#3722C2212yes—
26C2×#3722C2212yes—
27C2×Dic32C2212yes—
28C3×C3⋊#95C2211yescharacteristic
29C3×C3⋊#95C2212yes—
30C3×C3⋊#95C2212yes—
31C3×C3⋊#95C2211yescharacteristic
32#63579C2212yes—
33#63579C2212yes—
34C2×#930—31no—
35C2×#930—31no—
36C2×#930—61no—
37C3×#381—31no—
38C3×#380—31no—
39#5212D311yescharacteristic, complemented
40#5211D311yescharacteristic, complemented
41#4990—32no—
42#4989—32no—
43#4957—32no—
44#4957—32no—
45#4956—32no—
46#4956—32no—
47#4670—32no—
48#4668—32no—
49#4665—32no—
50#4665—32no—
51#4654—32no—
52#4653—32no—
53C24×C32C2311yescharacteristic
54C23×C3⋊D3C2312yes—
55C22×C32×C4—42no—
56C22×C32×C4C2×C414yescomplemented
57C22×C32×C4C2311yescharacteristic
58C22×C32×C4C2311yescharacteristic
59C2×#638—42no—
60C2×#638—42no—
61C2×#638C2×C418yescomplemented
62C22×C3⋊Dic3C2312yes—
63C2×C4⋊(C3⋊D3)—42no—
64C2×C4⋊(C3⋊D3)C2×C414yes—
65C22×C3×Dic3C2312yes—
66C22×C3×Dic3C2312yes—
67C22×C3×Dic3C2312yes—
68C22×C3×Dic3C2312yes—
69C2×#624—42no—
70C2×#624—42no—
71C2×#624—42no—
72#3752C2×C418yescomplemented
73C4⋊(C3⋊Dic3)C2×C414yescomplemented
74C3×#217—41no—
75C3×#217—42no—
76C3×#217—41no—
77C3×C4⋊Dic3—42no—
78#3724—42no—
79#3722—42no—
80#3722—42no—
81#3722—42no—
82Dic32—42no—
83#2377—91noSylow
84C23×C3×C4—21no—
85C23×C3×C4C2×D311yescharacteristic
86C23×C3×C4C2×D311yescharacteristic
87C22×#67—32no—
88C22×#67—32no—
89C22×#67—62no—
90C22×D12—31no—
91C22×D12—31no—
92C22×D12—61no—
93C22×C4×D3—32no—
94C22×C4×D3—32no—
95C2×C3×C4⋊C4—32no—
96C2×C3×C22⋊C4—31no—
97C2×C3×C22⋊C4—32no—
98C2×C3×C22⋊C4—31no—
99C2×#217C2×D312yes—
100C2×#217C2×D311yescharacteristic
101C2×#217C2×D311yescharacteristic
102#930—38no—
103#930—38no—
104#930—68no—
105C2×(C2×D3)⋊C4—32no—
106C2×(C2×D3)⋊C4—32no—
107C2×(C2×D3)⋊C4—32no—
108C2×(C2×D3)⋊C4—32no—
109C2×(C2×D3)⋊C4—32no—
110C2×(C2×D3)⋊C4—32no—
111C2×(C2×D3)⋊C4—32no—
112C2×(C2×D3)⋊C4—32no—
113C2×(C2×D3)⋊C4—62no—
114C2×C4⋊Dic3—31no—
115C2×C4⋊Dic3—31no—
116C2×C4⋊Dic3—61no—
117C2×C4⋊Dic3C2×D312yes—
118C2×Dic3⋊C4—32no—
119C2×Dic3⋊C4—32no—
120C2×C4×Dic3—32no—
121C2×C4×Dic3—32no—
122C3×#95—32no—
123C3×#95—32no—
124C3×#95—31no—
125C3×#95—31no—
126C3⋊#95—32no—
127C3⋊#95—32no—
128C3⋊#95—32no—
129C3⋊#95—32no—
130C3⋊#95C2×D312yes—
131C3⋊#95C2×D312yes—
132C3⋊#95C2×D311yescharacteristic
133C3⋊#95C2×D311yescharacteristic
134C23×C32—22no—
135C23×C32—21no—
136C23×C32—22no—
137C23×C32—21no—
138C23×C32C22×C412yes—
139C23×C32C2411yescharacteristic
140C22×C3⋊D3—22no—
141C22×C3⋊D3—22no—
142C22×C3⋊D3—22no—
143C22×C3⋊D3—22no—
144C22×C3⋊D3—22no—
145C22×C3⋊D3—22no—
146C22×C3⋊D3C22×C414yes—
147C2×C32×C4—22no—
148C2×C32×C4—22no—
149C2×C32×C4—44no—
150C2×C32×C4C22×C412yes—
151C2×C32×C4C22×C412yes—
152#638—48no—
153C2×C3⋊Dic3—22no—
154C2×C3⋊Dic3—22no—
155C2×C3⋊Dic3C22×C414yes—
156C4⋊(C3⋊D3)—44no—
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—22no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3—22no—
169#624—48no—
170C2×#121—91no—
171#390—92no—
172#388—92no—
173#387—92no—
174#386—92no—
175#386—92no—
176#385—92no—
177#381—31no—
178#380—31no—
179C24×C3—21no—
180C24×C3C22×D311yescharacteristic
181C24×C3C22×D311yescharacteristic
182C23×D3—32no—
183C23×D3—32no—
184C23×D3—62no—
185C22×C3×C4—24no—
186C22×C3×C4—21no—
187C22×C3×C4—21no—
188C22×C3×C4—32no—
189C22×C3×C4—32no—
190C22×C3×C4—32no—
191C22×C3×C4—32no—
192C22×C3×C4—42no—
193C22×C3×C4—42no—
194C22×C3×C4—44no—
195C22×C3×C4C4×D314yescomplemented
196C22×C3×C4C4×D314yescomplemented
197C22×C3×C4C22×D311yescharacteristic
198C22×C3×C4C22×D311yescharacteristic
199C22×C3×C4C22×D311yescharacteristic
200C22×C3×C4C22×D311yescharacteristic
201C2×#67—38no—
202C2×#67—38no—
203C2×#67—68no—
204C2×#67—122no—
205C2×#67—122no—
206C2×#67—122no—
207C2×#67—122no—
208C2×#67—124no—
209C2×#67—124no—
210C22×Dic3—32no—
211C22×Dic3—32no—
212C22×Dic3—62no—
213C22×Dic3C22×D312yes—
214C22×Dic3C22×D312yes—
215C22×Dic3C22×D312yes—
216C22×Dic3C22×D312yes—
217C2×D12—34no—
218C2×D12—34no—
219C2×D12—64no—
220C2×D12—122no—
221C2×D12—122no—
222C2×D12—124no—
223C2×C4×D3—122no—
224C2×C4×D3—122no—
225C2×C4×D3—122no—
226C2×C4×D3—122no—
227C2×C4×D3—122no—
228C2×C4×D3—122no—
229C3×C4⋊C4—122no—
230C3×C22⋊C4—122no—
231C3×C22⋊C4—121no—
232C3×C22⋊C4—121no—
233#217—41no—
234#217—42no—
235#217—41no—
236(C2×D3)⋊C4—38no—
237(C2×D3)⋊C4—38no—
238(C2×D3)⋊C4—68no—
239(C2×D3)⋊C4—122no—
240(C2×D3)⋊C4—122no—
241(C2×D3)⋊C4—122no—
242(C2×D3)⋊C4—122no—
243(C2×D3)⋊C4—122no—
244(C2×D3)⋊C4—122no—
245C4⋊Dic3—34no—
246C4⋊Dic3—34no—
247C4⋊Dic3—42no—
248C4⋊Dic3—64no—
249Dic3⋊C4—122no—
250Dic3⋊C4—122no—
251C4×Dic3—122no—
252C4×Dic3—122no—
253C22×C32—22no—
254C22×C32—22no—
255C22×C32—22no—
256C22×C32—42no—
257C22×C32—42no—
258C22×C32C23×C411yescharacteristic
259C22×C32H(5,𝔽2)12yes—
260C22×C32H(5,𝔽2)11yescharacteristic
261C22×C32H(5,𝔽2)12yes—
262C22×C322−1+411yescharacteristic
263C2×C3⋊D3—24no—
264C2×C3⋊D3—24no—
265C2×C3⋊D3—24no—
266C2×C3⋊D3—42no—
267C2×C3⋊D3—42no—
268C2×C3⋊D3—42no—
269C2×C3⋊D3—42no—
270C32×C4—22no—
271C32×C4—22no—
272C3⋊Dic3—24no—
273C3×Dic3—42no—
274C3×Dic3—42no—
275C3×Dic3—42no—
276C3×Dic3—42no—
277C22×D4—92no—
278C22×D4—91no—
279C23×C4—92no—
280C23×C4D3211yescharacteristic
281#121—98no—
282C2×C4⋊C4—32no—
283C2×C4⋊C4—91no—
284C2×C4⋊C4—92no—
285C2×C22⋊C4—31no—
286C2×C22⋊C4—31no—
287C2×C22⋊C4—32no—
288C2×C22⋊C4—92no—
289C2×C22⋊C4—92no—
290C2×C22⋊C4—92no—
291C2×C22⋊C4—92no—
292C2×C42—92no—
293#95—32no—
294#95—31no—
295#95—32no—
296#95—31no—
297#95—92no—
298#95—92no—
299C23×C3—24no—
300C23×C3—21no—
301C23×C3—22no—
302C23×C3—22no—
303C23×C3—21no—
304C23×C3—21no—
305C23×C3—22no—
306C23×C3—22no—
307C23×C3—21no—
308C23×C3—21no—
309C23×C3—22no—
310C23×C3—42no—
311C23×C3—41no—
312C23×C3—41no—
313C23×C3C2×C4×D312yes—
314C23×C3C2×C4×D312yes—
315C23×C3C23×D311yescharacteristic
316C23×C3C23×D311yescharacteristic
317C22×D3—34no—
318C22×D3—34no—
319C22×D3—64no—
320C22×D3—62no—
321C22×D3—62no—
322C22×D3—62no—
323C22×D3—62no—
324C22×D3—62no—
325C22×D3—62no—
326C22×D3—62no—
327C22×D3—62no—
328C22×D3—62no—
329C22×D3—62no—
330C22×D3—62no—
331C22×D3—62no—
332C22×D3—122no—
333C22×D3—122no—
334C22×D3—122no—
335C22×D3—122no—
336C22×D3—122no—
337C22×D3—122no—
338C2×C3×C4—24no—
339C2×C3×C4—22no—
340C2×C3×C4—22no—
341C2×C3×C4—22no—
342C2×C3×C4—22no—
343C2×C3×C4—22no—
344C2×C3×C4—22no—
345C2×C3×C4—42no—
346C2×C3×C4—44no—
347C2×C3×C4—44no—
348C2×C3×C4—48no—
349C2×C3×C4—62no—
350C2×C3×C4—62no—
351C2×C3×C4—62no—
352C2×C3×C4—62no—
353C2×C3×C4—62no—
354C2×C3×C4—62no—
355C2×C3×C4—62no—
356C2×C3×C4—62no—
357C2×C3×C4—62no—
358C2×C3×C4—62no—
359C2×C3×C4—62no—
360C2×C3×C4—62no—
361C2×C3×C4C2×C4×D312yes—
362C2×C3×C4C2×C4×D312yes—
363C2×C3×C4C2×C4×D312yes—
364C2×C3×C4C2×C4×D312yes—
365#67—128no—
366#67—128no—
367#67—1216no—
368C2×Dic3—22no—
369C2×Dic3—22no—
370C2×Dic3—22no—
371C2×Dic3—22no—
372C2×Dic3—22no—
373C2×Dic3—22no—
374C2×Dic3—22no—
375C2×Dic3—22no—
376C2×Dic3—22no—
377C2×Dic3—22no—
378C2×Dic3—22no—
379C2×Dic3—22no—
380C2×Dic3—34no—
381C2×Dic3—34no—
382C2×Dic3—64no—
383C2×Dic3—62no—
384C2×Dic3—62no—
385C2×Dic3—62no—
386C2×Dic3—62no—
387C2×Dic3—122no—
388C2×Dic3—122no—
389D12—124no—
390D12—124no—
391D12—128no—
392C4×D3—128no—
393C4×D3—128no—
394C2×C32—42no—
395C2×C32#51811yescharacteristic
396C2×C32#51811yescharacteristic
397C2×C32#52011yescharacteristic
398C2×C32#56012yes—
399C2×C32#56212yes—
400C3⋊D3—44no—
401C24—92no—
402C24C2×D3211yescharacteristic
403C2×D4—98no—
404C2×D4—94no—
405C2×D4—362no—
406C2×D4—362no—
407C2×D4—362no—
408C22×C4—32no—
409C22×C4—32no—
410C22×C4—32no—
411C22×C4—32no—
412C22×C4—42no—
413C22×C4—92no—
414C22×C4—362no—
415C22×C4—362no—
416C22×C4—362no—
417C22×C4#62414yescomplemented
418C22×C4C2×D3211yescharacteristic
419C22×C4C2×D3211yescharacteristic
420C4⋊C4—94no—
421C4⋊C4—122no—
422C4⋊C4—362no—
423C22⋊C4—98no—
424C22⋊C4—121no—
425C22⋊C4—121no—
426C22⋊C4—122no—
427C22⋊C4—362no—
428C22⋊C4—362no—
429C22⋊C4—362no—
430C42—362no—
431C22×C3—24no—
432C22×C3—22no—
433C22×C3—22no—
434C22×C3—22no—
435C22×C3—22no—
436C22×C3—22no—
437C22×C3—22no—
438C22×C3—21no—
439C22×C3—21no—
440C22×C3—22no—
441C22×C3—21no—
442C22×C3—22no—
443C22×C3—42no—
444C22×C3—42no—
445C22×C3—44no—
446C22×C3—44no—
447C22×C3—42no—
448C22×C3—42no—
449C22×C3—42no—
450C22×C3—42no—
451C22×C3C22×C4×D311yescharacteristic
452C22×C3C22×C4×D311yescharacteristic
453C22×C3#100411yescharacteristic
454C22×C3#100412yes—
455C22×C3#100412yes—
456C22×C3#100711yescharacteristic
457C22×C3#100911yescharacteristic
458C22×C3#100912yes—
459C22×C3#100912yes—
460C22×C3#101011yescharacteristic
461C2×D3—64no—
462C2×D3—64no—
463C2×D3—64no—
464C2×D3—64no—
465C2×D3—64no—
466C2×D3—64no—
467C2×D3—124no—
468C2×D3—124no—
469C2×D3—124no—
470C2×D3—122no—
471C2×D3—122no—
472C2×D3—122no—
473C2×D3—122no—
474C2×D3—122no—
475C2×D3—122no—
476C2×D3—122no—
477C2×D3—122no—
478C2×D3—242no—
479C2×D3—242no—
480C2×D3—242no—
481C2×D3—242no—
482C3×C4—24no—
483C3×C4—22no—
484C3×C4—22no—
485C3×C4—22no—
486C3×C4—22no—
487C3×C4—42no—
488C3×C4—122no—
489C3×C4—122no—
490C3×C4—122no—
491C3×C4—122no—
492Dic3—42no—
493Dic3—42no—
494Dic3—42no—
495Dic3—42no—
496Dic3—64no—
497Dic3—64no—
498Dic3—124no—
499C32#237711yescharacteristic, complemented, Sylow
500C23—21no—
501C23—21no—
502C23—22no—
503C23—22no—
504C23—94no—
505C23—182no—
506C23—182no—
507C23—182no—
508C23—182no—
509C23—182no—
510C23—182no—
511C23C2×#62412yes—
512C23C22×D3211yescharacteristic
513D4—364no—
514D4—368no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—44no—
518C2×C4—62no—
519C2×C4—62no—
520C2×C4—62no—
521C2×C4—62no—
522C2×C4—62no—
523C2×C4—62no—
524C2×C4—62no—
525C2×C4—62no—
526C2×C4—62no—
527C2×C4—62no—
528C2×C4—62no—
529C2×C4—62no—
530C2×C4—94no—
531C2×C4—182no—
532C2×C4—182no—
533C2×C4—368no—
534C2×C4C2×#62412yes—
535C2×C4C2×#62412yes—
536C2×C3—22no—
537C2×C3—22no—
538C2×C3—21no—
539C2×C3—21no—
540C2×C3—21no—
541C2×C3—44no—
542C2×C3—42no—
543C2×C3—42no—
544C2×C3#548611yescharacteristic
545C2×C3#548611yescharacteristic
546C2×C3#550411yescharacteristic
547C2×C3#552111yescharacteristic
548C2×C3#552111yescharacteristic
549C2×C3#552311yescharacteristic
550C2×C3#562012yes—
551C2×C3#564712yes—
552C2×C3#566612yes—
553C2×C3#566712yes—
554D3—124no—
555D3—124no—
556D3—244no—
557C22—22no—
558C22—22no—
559C22—22no—
560C22—42no—
561C22—42no—
562C22—184no—
563C22—184no—
564C22—184no—
565C22—362no—
566C22—362no—
567C22—362no—
568C22—362no—
569C22#6429711yescharacteristic
570C22#6430711yescharacteristic
571C22#6430812yes—
572C22C22×#62411yescharacteristic
573C22#6433012yes—
574C4—22no—
575C4—22no—
576C4—122no—
577C4—122no—
578C4—122no—
579C4—122no—
580C4—184no—
581C3—21no—
582C3#7401411yescharacteristic, complemented
583C3#7412411yescharacteristic, complemented
584C2—42no—
585C2—364no—
586C2#1059497812yes—
587C2#1059499011yescharacteristic
588C2#1059499611yescharacteristic
589C2#1059509012yes—
590C2#1059551011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC23×C32×C4C22
socle, cosocleC23×C32C24
prime radicalC2×#64139C2
hypercenterC23×C4D32
hypocenterC32#2377
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C3×#5212C2semidirect
3. C3×#5211C2semidirect
4. #10591722C2semidirect
5. #10591704C2semidirect
6. #10591380C2semidirect
7. #10591378C2semidirect
8. #10591271C2semidirect
9. #10591266C2semidirect
16. #64139C4semidirect
39. #5212D3semidirect
40. #5211D3semidirect
56. C22×C32×C4C2×C4semidirect
61. C2×#638C2×C4semidirect
72. #3752C2×C4semidirect
73. C4⋊(C3⋊Dic3)C2×C4semidirect
195. C22×C3×C4C4×D3semidirect
196. C22×C3×C4C4×D3semidirect
417. C22×C4#624semidirect
499. C32#2377semidirect
582. C3#74014semidirect
583. C3#74124semidirect

Maximal subgroups

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

subgroupindex
C2×#641392
C3×#52122
C3×#52112
#105917222
#105917042
#105913802
#105913782
#105912712
#105912662
#741243
#740143