Finite Group Databasebeta

← #11805521

Subgroups — #11805521

Order 1152.

1621 conjugacy classes of subgroups.

The subgroup lattice has 579 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64090C211yesmaximal, characteristic
2C2×#63952C212yesmaximal
3C3×#4950C212yesmaximal, complemented
4#10591720C211yesmaximal, characteristic, complemented
5C2×#63579C211yesmaximal, characteristic, complemented
6#10591378C212yesmaximal, complemented
7#10591370C211yesmaximal, characteristic, complemented
8#10591360C211yesmaximal, characteristic, complemented
9#10591325C211yesmaximal, characteristic, complemented
10#10591274C211yesmaximal, characteristic, complemented
11#10591264C212yesmaximal, complemented
12#74394—32nomaximal
13C22×#638C2211yescharacteristic
14C23×C3⋊Dic3C2211yescharacteristic
15C22×C4×C3⋊D3C2211yescharacteristic
16C23×C3×Dic3C2212yes—
17C22×#624C2212yes—
18C2×C32×C22⋊C4C2211yescharacteristic
19C2×#3752C2211yescharacteristic
20C2×#3750C2211yescharacteristic
21C2×C4×C3⋊Dic3C2211yescharacteristic
22#64090C418yescomplemented
23C2×C3×#217C2212yes—
24C2×C3×C4⋊Dic3C2212yes—
25C2×C3×C4⋊Dic3C2212yes—
26C2×#3724C2212yes—
27C2×#3724C2212yes—
28C2×#3722C2212yes—
29C2×Dic32C2212yes—
30#63952—28no—
31C3×C3⋊#95C2212yes—
32C3×C3⋊#95C2212yes—
33#63579C2212yes—
34#63579C2211yescharacteristic
35#63579C2211yescharacteristic
36#63579C2211yescharacteristic
37#63579C2211yescharacteristic
38C2×C4×#67—32no—
39C2×#67⋊C4—32no—
40C2×#67⋊C4—32no—
41C2×#67⋊C4—61no—
42C3×#385—32no—
43C2×C3⋊#95—32no—
44#4989—32no—
45#4987—32no—
46#4976—32no—
47Dic3×C4⋊C4—32no—
48#4950D312yescomplemented
49#4942—32no—
50#4668—32no—
51D3×#95—32no—
52#4650—32no—
53#4647—32no—
54C24×C32C2311yescharacteristic
55C23×C3⋊D3C2311yescharacteristic
56C22×C32×C4C2311yescharacteristic
57C22×C32×C4C2311yescharacteristic
58C2×#638C2×C414yes—
59C2×#638D414yes—
60C2×#638Q814yes—
61C22×C3⋊Dic3—42no—
62C22×C3⋊Dic3C2×C414yescomplemented
63C22×C3⋊Dic3C2311yescharacteristic
64C22×C3⋊Dic3C2311yescharacteristic
65C22×C3⋊Dic3C2311yescharacteristic
66C2×C4×C3⋊D3—42no—
67C2×C4×C3⋊D3C2×C414yescomplemented
68C22×C3×Dic3—24no—
69C22×C3×Dic3—24no—
70C22×C3×Dic3—42no—
71C22×C3×Dic3C2312yes—
72C22×C3×Dic3C2312yes—
73C22×C3×Dic3C2312yes—
74C22×C3×Dic3C2312yes—
75C2×#624—24no—
76C2×#624—24no—
77C2×#624—42no—
78C32×C22⋊C4C2×C414yescomplemented
79#3752C2×C414yescomplemented
80#3750C2×C414yescomplemented
81C4×C3⋊Dic3C2×C414yescomplemented
82C3×#217—24no—
83C3×C4⋊Dic3—24no—
84C3×C4⋊Dic3—42no—
85#3724—24no—
86#3724—42no—
87#3722—24no—
88Dic32—24no—
89#2349—91noSylow
90C23×C3×C4—32no—
91C22×#67—32no—
92C22×#67—61no—
93C23×Dic3—32no—
94C23×Dic3—61no—
95C23×Dic3C2×D312yes—
96C22×C4×D3—32no—
97C22×C4×D3—32no—
98C22×C4×D3—32no—
99C22×C4×D3—61no—
100C2×C3×C4⋊C4—32no—
101C2×C3×C4⋊C4—32no—
102C2×C3×C22⋊C4—21no—
103C2×C3×C22⋊C4—32no—
104C2×C3×C22⋊C4C2×D312yes—
105C2×#217C2×D312yes—
106C4×#67—68no—
107C2×(C2×D3)⋊C4—32no—
108C2×(C2×D3)⋊C4—32no—
109C2×(C2×D3)⋊C4—32no—
110C2×(C2×D3)⋊C4—61no—
111C2×C4⋊Dic3C2×D312yes—
112C2×C4⋊Dic3C2×D312yes—
113C2×Dic3⋊C4—32no—
114C2×Dic3⋊C4—32no—
115C2×Dic3⋊C4—32no—
116C2×Dic3⋊C4—32no—
117C2×Dic3⋊C4—32no—
118C2×Dic3⋊C4—61no—
119C2×C4×Dic3—32no—
120C2×C4×Dic3—32no—
121C2×C4×Dic3—32no—
122C2×C4×Dic3—61no—
123#67⋊C4—316no—
124#67⋊C4—68no—
125#67⋊C4—68no—
126C3×#95—32no—
127C3×#95—32no—
128C3⋊#95—32no—
129C3⋊#95—32no—
130C3⋊#95—32no—
131C3⋊#95—32no—
132C3⋊#95—32no—
133C3⋊#95—32no—
134C3⋊#95C2×D312yes—
135C3⋊#95C2×D312yes—
136C23×C32—22no—
137C23×C32—22no—
138C23×C32C22×C412yes—
139C23×C32C2×D412yes—
140C23×C32C2×Q812yes—
141C23×C32C2411yescharacteristic
142C22×C3⋊D3—22no—
143C22×C3⋊D3—22no—
144C22×C3⋊D3C22×C412yes—
145C22×C3⋊D3C2×D412yes—
146C22×C3⋊D3C2×Q812yes—
147C2×C32×C4—22no—
148C2×C32×C4—22no—
149C2×C32×C4C22×C412yes—
150C2×C32×C4C22×C412yes—
151#638C4⋊C4116yescomplemented
152C2×C3⋊Dic3—22no—
153C2×C3⋊Dic3—22no—
154C2×C3⋊Dic3—44no—
155C2×C3⋊Dic3C22×C412yes—
156C2×C3⋊Dic3C22×C412yes—
157C2×C3⋊Dic3C22×C412yes—
158C2×C3⋊Dic3C2×D412yes—
159C2×C3⋊Dic3C2×Q812yes—
160C4×C3⋊D3—44no—
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—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3—48no—
173C2×C3×Dic3#4114yes—
174#624—48no—
175C2×C4×D4—92no—
176C2×C4×D4—91no—
177#389—92no—
178#385—32no—
179#385—92no—
180#382—91no—
181#380—91no—
182#380—91no—
183C4×C4⋊C4—91no—
184C2×#95—91no—
185C2×#95—91no—
186C24×C3—21no—
187C24×C3C22×D312yes—
188C23×D3—32no—
189C23×D3—61no—
190C22×C3×C4—21no—
191C22×C3×C4—21no—
192C22×C3×C4—32no—
193C22×C3×C4—32no—
194C22×C3×C4—32no—
195C22×C3×C4—32no—
196C22×C3×C4—64no—
197C22×C3×C4—64no—
198C22×C3×C4—122no—
199C22×C3×C4C22×D312yes—
200C22×C3×C4C22×D312yes—
201C2×#67—38no—
202C2×#67—38no—
203C2×#67—38no—
204C2×#67—64no—
205C2×#67—64no—
206C2×#67—64no—
207C22×Dic3—24no—
208C22×Dic3—24no—
209C22×Dic3—32no—
210C22×Dic3—32no—
211C22×Dic3—32no—
212C22×Dic3—38no—
213C22×Dic3—42no—
214C22×Dic3—61no—
215C22×Dic3—61no—
216C22×Dic3—64no—
217C22×Dic3—61no—
218C22×Dic3—122no—
219C22×Dic3—122no—
220C22×Dic3—124no—
221C22×Dic3C22×D312yes—
222C22×Dic3C22×D312yes—
223C22×Dic3C22×D312yes—
224C22×Dic3C22×D312yes—
225C2×C4×D3—38no—
226C2×C4×D3—64no—
227C2×C4×D3—64no—
228C2×C4×D3—64no—
229C2×C4×D3—64no—
230C2×C4×D3—64no—
231C2×C4×D3—122no—
232C2×C4×D3—122no—
233C2×C4×D3—122no—
234C2×C4×D3—122no—
235C2×C4×D3—124no—
236C3×C4⋊C4—64no—
237C3×C4⋊C4—122no—
238C3×C22⋊C4—24no—
239C3×C22⋊C4—64no—
240C3×C22⋊C4C4×D318yescomplemented
241#217—24no—
242(C2×D3)⋊C4—38no—
243(C2×D3)⋊C4—64no—
244(C2×D3)⋊C4—64no—
245(C2×D3)⋊C4—64no—
246C4⋊Dic3—24no—
247C4⋊Dic3—42no—
248Dic3⋊C4—38no—
249Dic3⋊C4—64no—
250Dic3⋊C4—64no—
251Dic3⋊C4—64no—
252Dic3⋊C4—122no—
253Dic3⋊C4—122no—
254C4×Dic3—38no—
255C4×Dic3—64no—
256C4×Dic3—64no—
257C4×Dic3—64no—
258C22×C32—22no—
259C22×C32—22no—
260C22×C32—24no—
261C22×C32—24no—
262C22×C32C2×C4⋊C414yes—
263C22×C32C23×C411yescharacteristic
264C22×C32C22×D411yescharacteristic
265C22×C32C22×Q811yescharacteristic
266C22×C32C2×#4112yes—
267C22×C32H(5,𝔽2)12yes—
268C2×C3⋊D3—22no—
269C2×C3⋊D3—22no—
270C2×C3⋊D3—24no—
271C2×C3⋊D3—24no—
272C2×C3⋊D3C2×C4⋊C414yes—
273C32×C4—22no—
274C32×C4—22no—
275C3⋊Dic3—22no—
276C3⋊Dic3—22no—
277C3⋊Dic3C2×C4⋊C414yes—
278C3×Dic3—24no—
279C3×Dic3—42no—
280C3×Dic3—42no—
281C3×Dic3—42no—
282C22×D4—91no—
283C23×C4—32no—
284C23×C4—92no—
285C23×C4—91no—
286C23×C4—91no—
287C4×D4—98no—
288C4×D4—188no—
289C2×C4⋊C4—32no—
290C2×C4⋊C4—32no—
291C2×C4⋊C4—91no—
292C2×C4⋊C4—92no—
293C2×C4⋊C4—92no—
294C2×C22⋊C4—32no—
295C2×C22⋊C4—91no—
296C2×C22⋊C4—92no—
297C2×C22⋊C4D3211yescharacteristic
298C2×C42—91no—
299C2×C42—92no—
300#95—32no—
301#95—32no—
302#95—91no—
303#95—91no—
304#95—91no—
305#95—92no—
306#95—91no—
307C23×C3—22no—
308C23×C3—22no—
309C23×C3—22no—
310C23×C3—22no—
311C23×C3—21no—
312C23×C3—22no—
313C23×C3—22no—
314C23×C3—22no—
315C23×C3—42no—
316C23×C3—42no—
317C23×C3C2×C4×D314yes—
318C23×C3D3×D414yes—
319C23×C3D3×Q814yes—
320C23×C3C23×D312yes—
321C22×D3—34no—
322C22×D3—34no—
323C22×D3—34no—
324C22×D3—62no—
325C22×D3—62no—
326C22×D3—62no—
327C22×D3—62no—
328C22×D3—62no—
329C22×D3—62no—
330C22×D3—62no—
331C22×D3—122no—
332C22×D3—122no—
333C2×C3×C4—22no—
334C2×C3×C4—22no—
335C2×C3×C4—22no—
336C2×C3×C4—22no—
337C2×C3×C4—22no—
338C2×C3×C4—22no—
339C2×C3×C4—34no—
340C2×C3×C4—42no—
341C2×C3×C4—42no—
342C2×C3×C4—62no—
343C2×C3×C4—62no—
344C2×C3×C4—62no—
345C2×C3×C4—62no—
346C2×C3×C4—62no—
347C2×C3×C4—62no—
348C2×C3×C4—62no—
349C2×C3×C4—62no—
350C2×C3×C4—62no—
351C2×C3×C4—62no—
352C2×C3×C4—62no—
353C2×C3×C4—128no—
354C2×C3×C4C2×C4×D314yes—
355C2×C3×C4C2×C4×D314yes—
356#67—332no—
357#67—616no—
358C2×Dic3—22no—
359C2×Dic3—22no—
360C2×Dic3—22no—
361C2×Dic3—22no—
362C2×Dic3—22no—
363C2×Dic3—22no—
364C2×Dic3—22no—
365C2×Dic3—22no—
366C2×Dic3—22no—
367C2×Dic3—22no—
368C2×Dic3—22no—
369C2×Dic3—34no—
370C2×Dic3—34no—
371C2×Dic3—34no—
372C2×Dic3—34no—
373C2×Dic3—34no—
374C2×Dic3—48no—
375C2×Dic3—62no—
376C2×Dic3—62no—
377C2×Dic3—62no—
378C2×Dic3—62no—
379C2×Dic3—62no—
380C2×Dic3—64no—
381C2×Dic3—62no—
382C2×Dic3—62no—
383C2×Dic3—62no—
384C2×Dic3—62no—
385C2×Dic3—122no—
386C2×Dic3—128no—
387C2×Dic3—128no—
388C2×Dic3#23714yes—
389C4×D3—128no—
390C4×D3—128no—
391C4×D3—128no—
392C4×D3—128no—
393C2×C32—24no—
394C2×C32C22×C4⋊C411yescharacteristic
395C2×C32C4×#4111yescharacteristic
396C2×C32#51811yescharacteristic
397C2×C32#54612yes—
398C2×C32#55412yes—
399C3⋊D3—24no—
400C24—91no—
401C24C2×D3211yescharacteristic
402C2×D4—94no—
403C2×D4—94no—
404C2×D4—94no—
405C22×C4—32no—
406C22×C4—32no—
407C22×C4—32no—
408C22×C4—32no—
409C22×C4—64no—
410C22×C4—64no—
411C22×C4—91no—
412C22×C4—91no—
413C22×C4—91no—
414C22×C4—94no—
415C22×C4—94no—
416C22×C4—122no—
417C22×C4—184no—
418C22×C4—184no—
419C22×C4—362no—
420C22×C4—362no—
421C22×C4—362no—
422C22×C4C2×D3211yescharacteristic
423C22×C4C2×D3211yescharacteristic
424C4⋊C4—64no—
425C4⋊C4—94no—
426C4⋊C4—122no—
427C4⋊C4—184no—
428C4⋊C4—362no—
429C22⋊C4—64no—
430C22⋊C4—94no—
431C22⋊C4—184no—
432C22⋊C4#62414yescomplemented
433C42—94no—
434C42—184no—
435C22×C3—24no—
436C22×C3—24no—
437C22×C3—24no—
438C22×C3—24no—
439C22×C3—24no—
440C22×C3—24no—
441C22×C3—21no—
442C22×C3—21no—
443C22×C3—22no—
444C22×C3—22no—
445C22×C3—21no—
446C22×C3—24no—
447C22×C3—42no—
448C22×C3—44no—
449C22×C3—42no—
450C22×C3—44no—
451C22×C3D3×C4⋊C418yes—
452C22×C3C22×C4×D312yes—
453C22×C3C2×D3×D412yes—
454C22×C3C2×#23712yes—
455C22×C3#100412yes—
456C22×C3C2×D3×Q812yes—
457C22×C3D3×#4112yes—
458C22×C3#100912yes—
459C2×D3—38no—
460C2×D3—64no—
461C2×D3—64no—
462C2×D3—64no—
463C2×D3—64no—
464C2×D3—64no—
465C2×D3—64no—
466C2×D3—64no—
467C2×D3—122no—
468C2×D3—124no—
469C2×D3—122no—
470C2×D3—124no—
471C3×C4—24no—
472C3×C4—24no—
473C3×C4—42no—
474C3×C4—42no—
475C3×C4—64no—
476C3×C4—122no—
477C3×C4—122no—
478C3×C4—122no—
479Dic3—24no—
480Dic3—38no—
481Dic3—42no—
482Dic3—42no—
483Dic3—42no—
484Dic3—64no—
485Dic3—64no—
486Dic3—64no—
487Dic3—64no—
488Dic3—122no—
489C32#234911yescharacteristic, complemented, Sylow
490C23—22no—
491C23—22no—
492C23—92no—
493C23—92no—
494C23—92no—
495C23—182no—
496C23—182no—
497C23#379712yes—
498C23#380212yes—
499C23C2×#62412yes—
500C23C22×D3211yescharacteristic
501D4—916no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—34no—
505C2×C4—62no—
506C2×C4—62no—
507C2×C4—62no—
508C2×C4—62no—
509C2×C4—62no—
510C2×C4—62no—
511C2×C4—62no—
512C2×C4—62no—
513C2×C4—62no—
514C2×C4—62no—
515C2×C4—62no—
516C2×C4—92no—
517C2×C4—92no—
518C2×C4—92no—
519C2×C4—92no—
520C2×C4—92no—
521C2×C4—128no—
522C2×C4—182no—
523C2×C4—182no—
524C2×C4—364no—
525C2×C4—368no—
526C2×C4—364no—
527C2×C4C2×#62412yes—
528C2×C4C2×#62412yes—
529C2×C3—28no—
530C2×C3—22no—
531C2×C3—21no—
532C2×C3—21no—
533C2×C3—21no—
534C2×C3—22no—
535C2×C3—44no—
536C2×C3C2×D3×C4⋊C412yes—
537C2×C3C4×#23712yes—
538C2×C3#554512yes—
539C2×C3#559112yes—
540C2×C3#563512yes—
541C2×C3#563612yes—
542C2×C3#565412yes—
543D3—68no—
544D3—124no—
545C22—24no—
546C22—22no—
547C22—22no—
548C22—24no—
549C22—94no—
550C22—184no—
551C22—182no—
552C22—182no—
553C22—184no—
554C22#6390014yes—
555C22C2×#379711yescharacteristic
556C22C2×#380211yescharacteristic
557C22D3×#23712yes—
558C22#6431412yes—
559C22C22×#62411yescharacteristic
560C4—22no—
561C4—22no—
562C4—64no—
563C4—94no—
564C4—122no—
565C4—122no—
566C4—122no—
567C4—182no—
568C4—182no—
569C3—21no—
570C3#7439412yescomplemented
571C2—24no—
572C2—184no—
573C2#1059414112yes—
574C2#1059429412yes—
575C2C2×#6390011yescharacteristic
576C2#1059519011yescharacteristic
577C2#1059522311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC22×#638C22
hypercenterC2×C22⋊C4D32
hypocenterC32#2349
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C3×#4950C2semidirect
4. #10591720C2semidirect
5. C2×#63579C2semidirect
6. #10591378C2semidirect
7. #10591370C2semidirect
8. #10591360C2semidirect
9. #10591325C2semidirect
10. #10591274C2semidirect
11. #10591264C2semidirect
22. #64090C4semidirect
48. #4950D3semidirect
62. C22×C3⋊Dic3C2×C4semidirect
67. C2×C4×C3⋊D3C2×C4semidirect
78. C32×C22⋊C4C2×C4semidirect
79. #3752C2×C4semidirect
80. #3750C2×C4semidirect
81. C4×C3⋊Dic3C2×C4semidirect
151. #638C4⋊C4semidirect
240. C3×C22⋊C4C4×D3semidirect
432. C22⋊C4#624semidirect
489. C32#2349semidirect
570. C3#74394semidirect

Maximal subgroups

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

subgroupindex
C2×#640902
C2×#639522
C3×#49502
#105917202
C2×#635792
#105913782
#105913702
#105913602
#105913252
#105912742
#105912642
#743943