Finite Group Databasebeta

← #11801552

Subgroups — #11801552

Order 1152.

1605 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64102C211yesmaximal, characteristic
2C2×C4×#624C211yesmaximal, characteristic, complemented
3C2×#63849C211yesmaximal, characteristic, complemented
4C3×#4980C212yesmaximal, complemented
5#10591380C212yesmaximal
6#10591378C212yesmaximal, complemented
7#10591260C211yesmaximal, characteristic, complemented
8#10591260C211yesmaximal, characteristic, complemented
9#10591257C211yesmaximal, characteristic, complemented
10#10591252C211yesmaximal, characteristic, complemented
11#10591202C212yesmaximal, complemented
12#74937—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×#3724C2212yes—
25C2×#3722C2212yes—
26C2×#3722C2212yes—
27C2×#3722C2212yes—
28C2×Dic32C2211yescharacteristic
29C2×Dic32C2211yescharacteristic
30C2×Dic32C2211yescharacteristic
31C2×Dic32C2211yescharacteristic
32C4×#624—24no—
33#63849—24no—
34C3×C3⋊#95C2212yes—
35C3×C3⋊#95C2212yes—
36C3×C3⋊#95C2212yes—
37C3×C3⋊#95C2212yes—
38#63579C2212yes—
39C2×#893—32no—
40C2×#893—61no—
41C2×#892—32no—
42C2×C42×D3—32no—
43C3×#387—32no—
44#4989—32no—
45#4980D312yescomplemented
46#4940—32no—
47#4669—32no—
48#4668—32no—
49#4666—32no—
50#4666—32no—
51#4665—32no—
52#4665—32no—
53#4649—32no—
54#4648—32no—
55C23×C3⋊D3C2311yescharacteristic
56C23×C3⋊D3C2311yescharacteristic
57C22×C32×C4C2311yescharacteristic
58C22×C32×C4C2311yescharacteristic
59C22×C32×C4C2311yescharacteristic
60C22×C3⋊Dic3C2311yescharacteristic
61C22×C3⋊Dic3C2311yescharacteristic
62C2×C4⋊(C3⋊D3)—24no—
63C2×C4⋊(C3⋊D3)C2×C414yes—
64C2×C4×C3⋊D3—22no—
65C2×C4×C3⋊D3—22no—
66C2×C4×C3⋊D3—22no—
67C2×C4×C3⋊D3—22no—
68C2×C4×C3⋊D3C2×C414yes—
69C2×C4×C3⋊D3C2×C414yescomplemented
70C22×C3×Dic3C2312yes—
71C22×C3×Dic3C2312yes—
72C22×C3×Dic3C2312yes—
73C22×C3×Dic3C2312yes—
74C2×#624—24no—
75C2×#624—24no—
76C2×#624—24no—
77C32×C4⋊C4C2×C414yescomplemented
78#3752C2×C414yes—
79#3752C2×C414yescomplemented
80C4×C3⋊Dic3C2×C414yescomplemented
81C3×C4⋊Dic3—24no—
82C3×C4×Dic3—24no—
83#3724—24no—
84#3722—24no—
85#3722—24no—
86#3722—24no—
87Dic32—22no—
88Dic32—22no—
89Dic32—22no—
90Dic32D414yescomplemented
91#2290—91noSylow
92C22×D12—32no—
93C22×D12—61no—
94C22×C4×D3—32no—
95C22×C4×D3—32no—
96C22×C4×D3—32no—
97C22×C4×D3—32no—
98C22×C4×D3—61no—
99C22×C4×D3—61no—
100C2×C3×C4⋊C4—21no—
101C2×C3×C4⋊C4—32no—
102C2×C3×C4⋊C4C2×D312yes—
103C2×C3×C42—32no—
104C2×(C2×D3)⋊C4—32no—
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—61no—
113C2×(C2×D3)⋊C4—61no—
114C2×C4⋊Dic3C2×D312yes—
115C2×Dic3⋊C4—32no—
116C2×Dic3⋊C4—32no—
117C2×C4×Dic3—32no—
118C2×C4×Dic3—32no—
119C2×C4×Dic3—32no—
120C2×C4×Dic3—32no—
121C2×C4×Dic3—32no—
122C2×C4×Dic3—61no—
123C2×C4×Dic3C2×D312yes—
124#893—316no—
125#893—68no—
126#892—68no—
127C42×D3—68no—
128C3×#95—32no—
129C3×#95—32no—
130C3×#95—32no—
131C3×#95—32no—
132C3⋊#95—32no—
133C3⋊#95—32no—
134C3⋊#95C2×D312yes—
135C3⋊#95C2×D312yes—
136C3⋊#95C2×D312yes—
137C3⋊#95C2×D312yes—
138C23×C32C2411yescharacteristic
139C22×C3⋊D3—22no—
140C22×C3⋊D3—21no—
141C22×C3⋊D3—22no—
142C22×C3⋊D3—21no—
143C22×C3⋊D3—21no—
144C22×C3⋊D3—22no—
145C22×C3⋊D3—21no—
146C22×C3⋊D3C22×C412yes—
147C22×C3⋊D3C22×C412yes—
148C22×C3⋊D3#4114yes—
149C2×C32×C4—22no—
150C2×C32×C4—21no—
151C2×C32×C4—21no—
152C2×C32×C4—21no—
153C2×C32×C4—21no—
154C2×C32×C4C22×C412yes—
155C2×C32×C4C22×C412yes—
156C2×C32×C4C22×C412yes—
157C2×C3⋊Dic3—22no—
158C2×C3⋊Dic3C22×C412yes—
159C2×C3⋊Dic3C22×C412yes—
160C2×C3⋊Dic3C2×D412yes—
161C2×C3⋊Dic3#4112yes—
162C4⋊(C3⋊D3)—28no—
163C4×C3⋊D3—28no—
164C4×C3⋊D3—28no—
165C2×C3×Dic3—22no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3—22no—
168C2×C3×Dic3—22no—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3C2×D414yes—
176C2×C3×Dic3#4114yes—
177#624—216no—
178C2×C4×D4—91no—
179C2×#117—91no—
180C22×C42—91no—
181#388—92no—
182#387—32no—
183#386—92no—
184#385—92no—
185C4×C4⋊C4—91no—
186C4×C22⋊C4—91no—
187C4×C22⋊C4—91no—
188#376—91no—
189C23×D3—32no—
190C23×D3—32no—
191C23×D3—61no—
192C23×D3—61no—
193C22×C3×C4—21no—
194C22×C3×C4—21no—
195C22×C3×C4—21no—
196C22×C3×C4—32no—
197C22×C3×C4—32no—
198C22×C3×C4—32no—
199C22×C3×C4—32no—
200C22×C3×C4C22×D312yes—
201C22×C3×C4C22×D312yes—
202C22×C3×C4C22×D312yes—
203C22×Dic3—32no—
204C22×Dic3—32no—
205C22×Dic3—61no—
206C22×Dic3—61no—
207C22×Dic3C22×D312yes—
208C22×Dic3C22×D312yes—
209C22×Dic3C22×D312yes—
210C22×Dic3C22×D312yes—
211C2×D12—38no—
212C2×D12—64no—
213C2×D12—64no—
214C2×D12—64no—
215C2×D12—68no—
216C2×C4×D3—38no—
217C2×C4×D3—38no—
218C2×C4×D3—64no—
219C2×C4×D3—64no—
220C2×C4×D3—64no—
221C2×C4×D3—64no—
222C2×C4×D3—64no—
223C2×C4×D3—64no—
224C2×C4×D3—64no—
225C2×C4×D3—64no—
226C2×C4×D3—64no—
227C2×C4×D3—64no—
228C2×C4×D3—64no—
229C2×C4×D3—64no—
230C2×C4×D3—122no—
231C2×C4×D3—122no—
232C2×C4×D3—122no—
233C2×C4×D3—122no—
234C3×C4⋊C4—24no—
235C3×C4⋊C4—64no—
236C3×C4⋊C4C4×D318yescomplemented
237C3×C42—64no—
238(C2×D3)⋊C4—38no—
239(C2×D3)⋊C4—38no—
240(C2×D3)⋊C4—64no—
241(C2×D3)⋊C4—64no—
242(C2×D3)⋊C4—64no—
243(C2×D3)⋊C4—64no—
244(C2×D3)⋊C4—64no—
245(C2×D3)⋊C4—64no—
246(C2×D3)⋊C4—64no—
247(C2×D3)⋊C4—64no—
248C4⋊Dic3—24no—
249Dic3⋊C4—64no—
250Dic3⋊C4—64no—
251C4×Dic3—24no—
252C4×Dic3—38no—
253C4×Dic3—38no—
254C4×Dic3—64no—
255C4×Dic3—64no—
256C4×Dic3—64no—
257C4×Dic3—64no—
258C22×C32C23×C411yescharacteristic
259C22×C32C22×D411yescharacteristic
260C22×C32C2×#4112yes—
261C22×C32C2×#4112yes—
262C22×C32C2×#4111yescharacteristic
263C2×C3⋊D3—22no—
264C2×C3⋊D3—22no—
265C2×C3⋊D3—22no—
266C2×C3⋊D3—24no—
267C2×C3⋊D3—24no—
268C2×C3⋊D3—22no—
269C2×C3⋊D3—22no—
270C2×C3⋊D3—42no—
271C2×C3⋊D3—42no—
272C2×C3⋊D3#11714yescomplemented
273C32×C4—22no—
274C32×C4—22no—
275C32×C4—22no—
276C3⋊Dic3—22no—
277C3⋊Dic3C4×D414yes—
278C3×Dic3—24no—
279C3×Dic3—24no—
280C3×Dic3—42no—
281C3×Dic3—42no—
282C22×D4—91no—
283C23×C4—92no—
284C23×C4—91no—
285C23×C4—91no—
286C4×D4—98no—
287#117—184no—
288C2×C4⋊C4—32no—
289C2×C4⋊C4—92no—
290C2×C4⋊C4D3211yescharacteristic
291C2×C22⋊C4—91no—
292C2×C22⋊C4—91no—
293C2×C22⋊C4—92no—
294C2×C22⋊C4—92no—
295C2×C22⋊C4—92no—
296C2×C42—32no—
297C2×C42—91no—
298C2×C42—91no—
299C2×C42—91no—
300C2×C42—91no—
301C2×C42—91no—
302C2×C42—184no—
303#95—32no—
304#95—32no—
305#95—32no—
306#95—32no—
307#95—92no—
308C23×C3—21no—
309C23×C3C23×D312yes—
310C22×D3—34no—
311C22×D3—34no—
312C22×D3—34no—
313C22×D3—34no—
314C22×D3—62no—
315C22×D3—62no—
316C22×D3—64no—
317C22×D3—62no—
318C22×D3—62no—
319C22×D3—62no—
320C22×D3—62no—
321C22×D3—64no—
322C22×D3—62no—
323C22×D3—62no—
324C22×D3—62no—
325C22×D3—62no—
326C22×D3—62no—
327C22×D3—62no—
328C22×D3—121no—
329C22×D3—121no—
330C22×D3—121no—
331C22×D3—121no—
332C22×D3—122no—
333C22×D3—122no—
334C2×C3×C4—24no—
335C2×C3×C4—22no—
336C2×C3×C4—22no—
337C2×C3×C4—22no—
338C2×C3×C4—22no—
339C2×C3×C4—22no—
340C2×C3×C4—22no—
341C2×C3×C4—22no—
342C2×C3×C4—22no—
343C2×C3×C4—22no—
344C2×C3×C4—34no—
345C2×C3×C4—34no—
346C2×C3×C4—41no—
347C2×C3×C4—41no—
348C2×C3×C4—41no—
349C2×C3×C4—41no—
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×C4C2×C4×D314yes—
361C2×C3×C4C2×C4×D314yes—
362C2×C3×C4C2×C4×D314yes—
363C2×Dic3—22no—
364C2×Dic3—22no—
365C2×Dic3—22no—
366C2×Dic3—22no—
367C2×Dic3—22no—
368C2×Dic3—22no—
369C2×Dic3—22no—
370C2×Dic3—22no—
371C2×Dic3—22no—
372C2×Dic3—22no—
373C2×Dic3—34no—
374C2×Dic3—34no—
375C2×Dic3—34no—
376C2×Dic3—34no—
377C2×Dic3—62no—
378C2×Dic3—62no—
379C2×Dic3—62no—
380C2×Dic3—62no—
381C2×Dic3—62no—
382C2×Dic3—62no—
383C2×Dic3—122no—
384C2×Dic3D3×D414yes—
385C2×Dic3#23914yes—
386D12—616no—
387D12—616no—
388C4×D3—616no—
389C4×D3—616no—
390C4×D3—616no—
391C4×D3—616no—
392C4×D3—128no—
393C4×D3—128no—
394C2×C32C2×#11711yescharacteristic
395C2×C32C2×C4×D411yescharacteristic
396C2×C32C4×#4111yescharacteristic
397C2×C32#52512yes—
398C2×C32#52912yes—
399C3⋊D3—24no—
400C3⋊D3—42no—
401C24—91no—
402C24—91no—
403C2×D4—94no—
404C2×D4—184no—
405C22×C4—32no—
406C22×C4—32no—
407C22×C4—32no—
408C22×C4—32no—
409C22×C4—91no—
410C22×C4—91no—
411C22×C4—94no—
412C22×C4—94no—
413C22×C4—182no—
414C22×C4—182no—
415C22×C4—182no—
416C22×C4—182no—
417C22×C4—184no—
418C22×C4—184no—
419C22×C4—184no—
420C22×C4C2×D3211yescharacteristic
421C22×C4C2×D3211yescharacteristic
422C22×C4C2×D3211yescharacteristic
423C4⋊C4—64no—
424C4⋊C4—184no—
425C4⋊C4#62414yescomplemented
426C22⋊C4—94no—
427C22⋊C4—94no—
428C22⋊C4—184no—
429C22⋊C4—184no—
430C22⋊C4—184no—
431C42—64no—
432C42—94no—
433C42—94no—
434C42—182no—
435C42—182no—
436C42—182no—
437C22×C3—22no—
438C22×C3—21no—
439C22×C3—21no—
440C22×C3—22no—
441C22×C3—21no—
442C22×C3C22×C4×D312yes—
443C22×C3C2×D3×D412yes—
444C22×C3C2×#23912yes—
445C22×C3D3×#4112yes—
446C22×C3D3×#4112yes—
447C22×C3D3×#4112yes—
448C22×C3D3×#4112yes—
449C2×D3—38no—
450C2×D3—64no—
451C2×D3—64no—
452C2×D3—64no—
453C2×D3—64no—
454C2×D3—64no—
455C2×D3—64no—
456C2×D3—64no—
457C2×D3—64no—
458C2×D3—64no—
459C2×D3—64no—
460C2×D3—64no—
461C2×D3—122no—
462C2×D3—122no—
463C2×D3—124no—
464C2×D3—122no—
465C2×D3—124no—
466C2×D3—122no—
467C2×D3—124no—
468C2×D3—124no—
469C2×D3—122no—
470C2×D3—122no—
471C2×D3—122no—
472C2×D3—122no—
473C3×C4—24no—
474C3×C4—24no—
475C3×C4—24no—
476C3×C4—24no—
477C3×C4—42no—
478C3×C4—42no—
479C3×C4—64no—
480C3×C4—64no—
481C3×C4—122no—
482C3×C4—122no—
483Dic3—24no—
484Dic3—24no—
485Dic3—38no—
486Dic3—42no—
487Dic3—42no—
488Dic3—64no—
489Dic3—64no—
490Dic3—122no—
491C32#229011yescharacteristic, complemented, Sylow
492C23—94no—
493C23—92no—
494C23—92no—
495C23—181no—
496C23—181no—
497C23—182no—
498C23—182no—
499C23—181no—
500C23—181no—
501C23—182no—
502C23C22×D3211yescharacteristic
503D4—188no—
504C2×C4—22no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—34no—
510C2×C4—34no—
511C2×C4—62no—
512C2×C4—62no—
513C2×C4—62no—
514C2×C4—62no—
515C2×C4—62no—
516C2×C4—62no—
517C2×C4—62no—
518C2×C4—62no—
519C2×C4—62no—
520C2×C4—62no—
521C2×C4—92no—
522C2×C4—92no—
523C2×C4—92no—
524C2×C4—92no—
525C2×C4—188no—
526C2×C4—188no—
527C2×C4—1816no—
528C2×C4—182no—
529C2×C4C2×#62412yes—
530C2×C4C2×#62412yes—
531C2×C4C2×#62412yes—
532C2×C3—22no—
533C2×C3—21no—
534C2×C3—21no—
535C2×C3—21no—
536C2×C3—22no—
537C2×C3D3×#11712yes—
538C2×C3C4×D3×D412yes—
539C2×C3C4×#23912yes—
540C2×C3#562712yes—
541C2×C3#565612yes—
542C2×C3#569112yes—
543C2×C3#570612yes—
544D3—68no—
545D3—124no—
546D3—124no—
547D3—124no—
548C22—94no—
549C22—184no—
550C22—182no—
551C22—182no—
552C22—184no—
553C22—182no—
554C22—182no—
555C22—182no—
556C22—362no—
557C22—362no—
558C22#6430612yes—
559C22D32×D411yescharacteristic
560C22#6431211yescharacteristic
561C22D3×#23912yes—
562C22C22×#62411yescharacteristic
563C4—22no—
564C4—22no—
565C4—22no—
566C4—64no—
567C4—64no—
568C4—94no—
569C4—122no—
570C4—122no—
571C4—182no—
572C3—21no—
573C3#7493712yescomplemented
574C2—184no—
575C2—362no—
576C2#1059446512yes—
577C2#1059461512yes—
578C2#1059496911yescharacteristic
579C2D4×#62411yescharacteristic
580C2#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#2290
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×#624C2semidirect
3. C2×#63849C2semidirect
4. C3×#4980C2semidirect
6. #10591378C2semidirect
7. #10591260C2semidirect
8. #10591260C2semidirect
9. #10591257C2semidirect
10. #10591252C2semidirect
11. #10591202C2semidirect
21. #64102C4semidirect
45. #4980D3semidirect
69. C2×C4×C3⋊D3C2×C4semidirect
77. C32×C4⋊C4C2×C4semidirect
79. #3752C2×C4semidirect
80. C4×C3⋊Dic3C2×C4semidirect
90. Dic32D4semidirect
236. C3×C4⋊C4C4×D3semidirect
272. C2×C3⋊D3#117semidirect
425. C4⋊C4#624semidirect
491. C32#2290semidirect
573. C3#74937semidirect

Maximal subgroups

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

subgroupindex
C2×#641022
C2×C4×#6242
C2×#638492
C3×#49802
#105913802
#105913782
#105912602
#105912572
#105912522
#105912022
#749373