Finite Group Databasebeta

← #11800860

Subgroups — #11800860

Order 1152.

1953 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63921C211yesmaximal, characteristic
2C2×D3×(C2×D3)⋊C4C212yesmaximal
3C4×#3752C211yesmaximal, characteristic, complemented
4C3×C4×(C2×D3)⋊C4C212yesmaximal, complemented
5#10591368C212yesmaximal, complemented
6Dic3×(C2×D3)⋊C4C212yesmaximal, complemented
7#10591260C211yesmaximal, characteristic, complemented
8#10591237C212yesmaximal, complemented
9#10591233C212yesmaximal, complemented
10#73560—32nomaximal
11C23×D32C2211yescharacteristic
12C22×C4×C3⋊D3C2211yescharacteristic
13C22×C3×C4×D3C2212yes—
14C22×#624C2211yescharacteristic
15C22×D3×Dic3C2212yes—
16C2×C32×C42C2211yescharacteristic, complemented
17C2×#3752C2212yes—
18C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
19C2×C3×(C2×D3)⋊C4C2212yes—
20C2×C3×(C2×D3)⋊C4C2212yes—
21C2×C3×C4×Dic3C2212yescomplemented
22C2×#3722C2212yes—
23C2×(C2×D3)⋊Dic3C2212yes—
24C2×(C2×D3)⋊Dic3C2212yes—
25C2×Dic32C2212yescomplemented
26C2×Dic32C2211yescharacteristic, complemented
27C2×Dic32C2211yescharacteristic, complemented
28#63921C418yescomplemented
29D3×(C2×D3)⋊C4C4116yescomplemented
30#63658C2212yescomplemented
31C3×C3⋊#95C2212yescomplemented
32C3×C3⋊#95C2212yescomplemented
33#63579C2212yescomplemented
34C22×(C2×D3)⋊C4—32no—
35C2×D3×C22⋊C4—32no—
36C2×D3×C22⋊C4—32no—
37C3×C4×C22⋊C4—32no—
38C4×#217—32no—
39Dic3×C22⋊C4—32no—
40Dic3×C22⋊C4—32no—
41C4×(C2×D3)⋊C4—32no—
42C4×(C2×D3)⋊C4—32no—
43C4×(C2×D3)⋊C4—32no—
44C4×(C2×D3)⋊C4—61no—
45C4×(C2×D3)⋊C4D312yescomplemented
46#4666—32no—
47#4666—32no—
48#4666—32no—
49#4666—32no—
50C23×C3⋊D3C2311yescharacteristic
51C23×C3×D3C2312yes—
52C22×D32—41no—
53C22×D32—42no—
54C22×D32—41no—
55C22×D32C2×C418yes—
56C22×D32C2×C414yes—
57C22×C32×C4C2312yes—
58C22×C32×C4C2311yescharacteristic
59C22×C3⋊Dic3C2312yes—
60C22×C3⋊Dic3C2311yescharacteristic
61C2×C4×C3⋊D3—41no—
62C2×C4×C3⋊D3—41no—
63C2×C4×C3⋊D3C2×C414yescomplemented
64C22×C3×Dic3C2312yes—
65C22×C3×Dic3C2312yes—
66C22×C3×Dic3C2312yes—
67C2×C3×C4×D3—42no—
68C2×C3×C4×D3—42no—
69C2×C3×C4×D3C2×C418yescomplemented
70C2×#624—42no—
71C2×#624C2×C414yescomplemented
72C2×D3×Dic3—42no—
73C2×D3×Dic3—42no—
74C2×D3×Dic3C2×C418yescomplemented
75C32×C42—41no—
76#3752C2×C418yescomplemented
77C4×C3⋊Dic3—41no—
78C3×(C2×D3)⋊C4C2×C418yescomplemented
79C3×(C2×D3)⋊C4C2×C418yescomplemented
80C3×C4×Dic3—42no—
81#3722C2×C418yescomplemented
82(C2×D3)⋊Dic3C2×C418yescomplemented
83(C2×D3)⋊Dic3C2×C418yescomplemented
84Dic32—41no—
85Dic32—42no—
86Dic32—41no—
87#2273—91noSylow
88C24×D3—32no—
89C23×C3×C4—32no—
90C23×Dic3—32no—
91C22×C4×D3—32no—
92C22×C4×D3—32no—
93C22×C4×D3—32no—
94C22×C4×D3—61no—
95C22×C4×D3C2×D312yes—
96C2×C3×C22⋊C4—32no—
97C2×C3×C22⋊C4—32no—
98C2×C3×C42—21no—
99C2×C3×C42—32no—
100C2×C3×C42C2×D312yescomplemented
101C2×#217—32no—
102C2×#217—32no—
103C2×(C2×D3)⋊C4—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—316no—
110C2×(C2×D3)⋊C4—62no—
111C2×(C2×D3)⋊C4C2×D312yes—
112C2×(C2×D3)⋊C4C2×D312yes—
113C2×C4×Dic3—32no—
114C2×C4×Dic3—32no—
115C2×C4×Dic3—32no—
116C2×C4×Dic3—32no—
117C2×C4×Dic3—32no—
118C2×C4×Dic3—61no—
119C2×C4×Dic3C2×D312yescomplemented
120D3×C22⋊C4—316no—
121D3×C22⋊C4—316no—
122C3×#95—32no—
123C3×#95—32no—
124C3⋊#95—32no—
125C3⋊#95—32no—
126C3⋊#95—32no—
127C3⋊#95—32no—
128C3⋊#95—62no—
129C3⋊#95C2×D312yescomplemented
130C3⋊#95C2×D312yescomplemented
131C23×C32C2411yescharacteristic
132C22×C3⋊D3—22no—
133C22×C3⋊D3—21no—
134C22×C3⋊D3—21no—
135C22×C3⋊D3C22×C414yes—
136C22×C3⋊D3C22×C412yes—
137C22×C3×D3—22no—
138C22×C3×D3—22no—
139C22×C3×D3—22no—
140C22×C3×D3—22no—
141C22×C3×D3C22×C414yes—
142C22×C3×D3C22×C414yes—
143C22×C3×D3C22×C414yes—
144C2×D32—48no—
145C2×D32—48no—
146C2×D32—44no—
147C2×D32—44no—
148C2×D32C42116yescomplemented
149C2×C32×C4—21no—
150C2×C32×C4—21no—
151C2×C32×C4—22no—
152C2×C32×C4—22no—
153C2×C32×C4C22×C412yes—
154C2×C32×C4C22×C414yes—
155C2×C3⋊Dic3—22no—
156C2×C3⋊Dic3—21no—
157C2×C3⋊Dic3—21no—
158C2×C3⋊Dic3—22no—
159C2×C3⋊Dic3C22×C412yes—
160C2×C3⋊Dic3C22×C414yes—
161C4×C3⋊D3—44no—
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×Dic3C22×C414yes—
169C2×C3×Dic3C22×C414yes—
170C2×C3×Dic3C22×C414yes—
171C3×C4×D3—48no—
172#624—44no—
173D3×Dic3—48no—
174C22×C22⋊C4—91no—
175C22×C22⋊C4—92no—
176C4×C22⋊C4—32no—
177C4×C22⋊C4—91no—
178C4×C22⋊C4—92no—
179C4×C22⋊C4—92no—
180C4×C22⋊C4—92no—
181C4×C22⋊C4—92no—
182C4×C22⋊C4—91no—
183C24×C3—32no—
184C23×D3—32no—
185C23×D3—38no—
186C23×D3—38no—
187C23×D3—38no—
188C23×D3—61no—
189C23×D3—122no—
190C23×D3—122no—
191C23×D3—122no—
192C23×D3—122no—
193C23×D3C22×D312yes—
194C22×C3×C4—21no—
195C22×C3×C4—22no—
196C22×C3×C4—32no—
197C22×C3×C4—32no—
198C22×C3×C4—32no—
199C22×C3×C4—38no—
200C22×C3×C4—122no—
201C22×C3×C4—122no—
202C22×C3×C4C22×D312yes—
203C22×C3×C4C22×D312yes—
204C22×C3×C4C22×D312yes—
205C22×Dic3—32no—
206C22×Dic3—32no—
207C22×Dic3—32no—
208C22×Dic3—38no—
209C22×Dic3—61no—
210C22×Dic3—62no—
211C22×Dic3—122no—
212C22×Dic3—122no—
213C22×Dic3C22×D312yes—
214C22×Dic3C22×D312yes—
215C22×Dic3C22×D312yes—
216C2×C4×D3—38no—
217C2×C4×D3—38no—
218C2×C4×D3—38no—
219C2×C4×D3—42no—
220C2×C4×D3—42no—
221C2×C4×D3—64no—
222C2×C4×D3—122no—
223C2×C4×D3—122no—
224C2×C4×D3—122no—
225C2×C4×D3—122no—
226C2×C4×D3—122no—
227C2×C4×D3—122no—
228C2×C4×D3—122no—
229C2×C4×D3—122no—
230C2×C4×D3C4×D318yescomplemented
231C3×C22⋊C4—38no—
232C3×C22⋊C4—38no—
233C3×C42—42no—
234C3×C42—42no—
235C3×C42—122no—
236#217—38no—
237#217—38no—
238(C2×D3)⋊C4—38no—
239(C2×D3)⋊C4—38no—
240(C2×D3)⋊C4—38no—
241(C2×D3)⋊C4—38no—
242(C2×D3)⋊C4—38no—
243(C2×D3)⋊C4—38no—
244(C2×D3)⋊C4—68no—
245(C2×D3)⋊C4C4×D318yescomplemented
246(C2×D3)⋊C4C4×D318yescomplemented
247C4×Dic3—42no—
248C4×Dic3—122no—
249C4×Dic3—122no—
250C4×Dic3—122no—
251C4×Dic3—122no—
252C4×Dic3—122no—
253C4×Dic3—122no—
254C22×C32C23×C412yes—
255C22×C32C23×C411yescharacteristic
256C22×C32H(5,𝔽2)11yescharacteristic
257C22×C32H(5,𝔽2)12yes—
258C22×C32H(5,𝔽2)11yescharacteristic
259C2×C3⋊D3—22no—
260C2×C3⋊D3—22no—
261C2×C3⋊D3—24no—
262C2×C3⋊D3—24no—
263C2×C3⋊D3C2×C4214yes—
264C2×C3×D3—24no—
265C2×C3×D3—24no—
266C2×C3×D3—24no—
267C2×C3×D3—24no—
268C2×C3×D3—24no—
269C2×C3×D3—24no—
270C2×C3×D3C2×C4218yes—
271D32—416no—
272C32×C4—22no—
273C32×C4—24no—
274C3⋊Dic3—24no—
275C3⋊Dic3—22no—
276C3×Dic3—24no—
277C3×Dic3—24no—
278C3×Dic3—24no—
279C25—91no—
280C23×C4—32no—
281C23×C4—91no—
282C23×C4—92no—
283C23×C4—91no—
284C2×C22⋊C4—32no—
285C2×C22⋊C4—32no—
286C2×C22⋊C4—98no—
287C2×C22⋊C4—916no—
288C2×C22⋊C4—92no—
289C2×C22⋊C4—92no—
290C2×C22⋊C4—92no—
291C2×C22⋊C4—92no—
292C2×C42—32no—
293C2×C42—91no—
294C2×C42—92no—
295C2×C42—91no—
296C2×C42—91no—
297C2×C42D3211yescharacteristic, complemented
298#95—32no—
299#95—32no—
300#95—92no—
301#95—92no—
302C23×C3—21no—
303C23×C3—34no—
304C23×C3—34no—
305C23×C3—34no—
306C23×C3—62no—
307C23×C3—62no—
308C23×C3—62no—
309C23×C3—62no—
310C23×C3C23×D312yes—
311C22×D3—22no—
312C22×D3—22no—
313C22×D3—22no—
314C22×D3—22no—
315C22×D3—34no—
316C22×D3—34no—
317C22×D3—34no—
318C22×D3—332no—
319C22×D3—64no—
320C22×D3—62no—
321C22×D3—62no—
322C22×D3—62no—
323C22×D3—62no—
324C22×D3—62no—
325C22×D3—121no—
326C22×D3—121no—
327C22×D3—122no—
328C22×D3—128no—
329C22×D3—128no—
330C22×D3—128no—
331C22×D3—128no—
332C22×D3—128no—
333C22×D3—128no—
334C22×D3C2×C4×D314yes—
335C22×D3C2×C4×D314yes—
336C22×D3C2×C4×D314yes—
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—22no—
345C2×C3×C4—22no—
346C2×C3×C4—24no—
347C2×C3×C4—34no—
348C2×C3×C4—34no—
349C2×C3×C4—34no—
350C2×C3×C4—42no—
351C2×C3×C4—42no—
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—128no—
359C2×C3×C4C2×C4×D314yes—
360C2×C3×C4C2×C4×D314yes—
361C2×C3×C4C2×C4×D314yes—
362C2×Dic3—22no—
363C2×Dic3—22no—
364C2×Dic3—22no—
365C2×Dic3—22no—
366C2×Dic3—22no—
367C2×Dic3—22no—
368C2×Dic3—34no—
369C2×Dic3—34no—
370C2×Dic3—34no—
371C2×Dic3—64no—
372C2×Dic3—62no—
373C2×Dic3—62no—
374C2×Dic3—62no—
375C2×Dic3—62no—
376C2×Dic3—62no—
377C2×Dic3—62no—
378C2×Dic3—62no—
379C2×Dic3—122no—
380C2×Dic3—121no—
381C2×Dic3—121no—
382C2×Dic3—122no—
383C2×Dic3—128no—
384C2×Dic3C2×C4×D314yes—
385C2×Dic3C2×C4×D314yes—
386C2×Dic3C2×C4×D314yes—
387C4×D3—48no—
388C4×D3—128no—
389C4×D3—128no—
390C4×D3—128no—
391C4×D3—128no—
392C2×C32C22×C4211yescharacteristic
393C2×C32#51812yes—
394C2×C32#51812yes—
395C2×C32#51811yescharacteristic
396C2×C32#51811yescharacteristic
397C3⋊D3—24no—
398C3×D3—28no—
399C24—32no—
400C24—94no—
401C24—98no—
402C24—91no—
403C24—362no—
404C24—361no—
405C24—361no—
406C22×C4—32no—
407C22×C4—32no—
408C22×C4—32no—
409C22×C4—38no—
410C22×C4—94no—
411C22×C4—98no—
412C22×C4—92no—
413C22×C4—91no—
414C22×C4—94no—
415C22×C4—122no—
416C22×C4—122no—
417C22×C4—361no—
418C22×C4—361no—
419C22×C4—362no—
420C22×C4—362no—
421C22×C4—362no—
422C22×C4C2×D3211yescharacteristic
423C22×C4C2×D3212yes—
424C22⋊C4—38no—
425C22⋊C4—38no—
426C22⋊C4—98no—
427C22⋊C4—98no—
428C22⋊C4—98no—
429C22⋊C4—98no—
430C42—41no—
431C42—122no—
432C42—361no—
433C42—362no—
434C42—361no—
435C42—361no—
436C22×C3—22no—
437C22×C3—21no—
438C22×C3—22no—
439C22×C3—21no—
440C22×C3—21no—
441C22×C3—38no—
442C22×C3—64no—
443C22×C3—64no—
444C22×C3—64no—
445C22×C3—64no—
446C22×C3—64no—
447C22×C3—64no—
448C22×C3C22×C4×D312yes—
449C22×C3C22×C4×D312yes—
450C22×C3C22×C4×D312yes—
451C22×C3#100412yes—
452C22×C3#100412yes—
453C22×C3#100912yes—
454C22×C3#100912yes—
455C2×D3—24no—
456C2×D3—24no—
457C2×D3—24no—
458C2×D3—24no—
459C2×D3—24no—
460C2×D3—24no—
461C2×D3—38no—
462C2×D3—64no—
463C2×D3—64no—
464C2×D3—64no—
465C2×D3—64no—
466C2×D3—64no—
467C2×D3—64no—
468C2×D3—64no—
469C2×D3—122no—
470C2×D3—124no—
471C2×D3—122no—
472C2×D3—124no—
473C2×D3—1232no—
474C2×D3C42×D318yes—
475C3×C4—24no—
476C3×C4—24no—
477C3×C4—24no—
478C3×C4—24no—
479C3×C4—44no—
480C3×C4—64no—
481C3×C4—64no—
482C3×C4—64no—
483Dic3—24no—
484Dic3—24no—
485Dic3—24no—
486Dic3—64no—
487Dic3—64no—
488Dic3—64no—
489Dic3—122no—
490Dic3—124no—
491C32#227311yescharacteristic, complemented, Sylow
492C23—34no—
493C23—34no—
494C23—34no—
495C23—62no—
496C23—62no—
497C23—62no—
498C23—62no—
499C23—916no—
500C23—94no—
501C23—92no—
502C23—182no—
503C23—181no—
504C23—181no—
505C23—368no—
506C23—364no—
507C23—368no—
508C23—364no—
509C23C22×D3211yescharacteristic
510C2×C4—22no—
511C2×C4—21no—
512C2×C4—22no—
513C2×C4—21no—
514C2×C4—34no—
515C2×C4—34no—
516C2×C4—34no—
517C2×C4—62no—
518C2×C4—62no—
519C2×C4—62no—
520C2×C4—62no—
521C2×C4—62no—
522C2×C4—62no—
523C2×C4—94no—
524C2×C4—92no—
525C2×C4—128no—
526C2×C4—182no—
527C2×C4—182no—
528C2×C4—181no—
529C2×C4—181no—
530C2×C4—364no—
531C2×C4—364no—
532C2×C4—368no—
533C2×C4C4×D3212yes—
534C2×C4C4×D3214yes—
535C2×C3—21no—
536C2×C3—22no—
537C2×C3—21no—
538C2×C3—22no—
539C2×C3—21no—
540C2×C3—68no—
541C2×C3C2×C42×D312yes—
542C2×C3#548612yes—
543C2×C3#552112yes—
544C2×C3#554512yes—
545C2×C3#554512yes—
546C2×C3#554512yes—
547C2×C3#554512yes—
548D3—28no—
549D3—68no—
550D3—124no—
551C22—38no—
552C22—64no—
553C22—64no—
554C22—64no—
555C22—64no—
556C22—64no—
557C22—64no—
558C22—94no—
559C22—184no—
560C22—182no—
561C22—184no—
562C22—182no—
563C22—3616no—
564C22C2×C4×D3212yes—
565C22C2×C4×D3211yescharacteristic
566C22#6430712yes—
567C22#6430811yescharacteristic
568C22#6433011yescharacteristic
569C4—24no—
570C4—22no—
571C4—64no—
572C4—64no—
573C4—64no—
574C4—184no—
575C4—182no—
576C3—21no—
577C3#7356012yescomplemented
578C2—68no—
579C2—184no—
580C2C42×D3211yescharacteristic
581C2#1059399412yes—
582C2#1059399611yescharacteristic
583C2#1059505612yes—
584C2#1059505811yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC2×C32C22×C42
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC23×D32C22
hypercenterC2×C42D32
hypocenterC32#2273
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
3. C4×#3752C2semidirect
4. C3×C4×(C2×D3)⋊C4C2semidirect
5. #10591368C2semidirect
6. Dic3×(C2×D3)⋊C4C2semidirect
7. #10591260C2semidirect
8. #10591237C2semidirect
9. #10591233C2semidirect
16. C2×C32×C42C22semidirect
18. C2×C4×C3⋊Dic3C22semidirect
21. C2×C3×C4×Dic3C22semidirect
25. C2×Dic32C22semidirect
26. C2×Dic32C22semidirect
27. C2×Dic32C22semidirect
28. #63921C4semidirect
29. D3×(C2×D3)⋊C4C4semidirect
30. #63658C22semidirect
31. C3×C3⋊#95C22semidirect
32. C3×C3⋊#95C22semidirect
33. #63579C22semidirect
45. C4×(C2×D3)⋊C4D3semidirect
63. C2×C4×C3⋊D3C2×C4semidirect
69. C2×C3×C4×D3C2×C4semidirect
71. C2×#624C2×C4semidirect
74. C2×D3×Dic3C2×C4semidirect
76. #3752C2×C4semidirect
78. C3×(C2×D3)⋊C4C2×C4semidirect
79. C3×(C2×D3)⋊C4C2×C4semidirect
81. #3722C2×C4semidirect
82. (C2×D3)⋊Dic3C2×C4semidirect
83. (C2×D3)⋊Dic3C2×C4semidirect
100. C2×C3×C42C2×D3semidirect
119. C2×C4×Dic3C2×D3semidirect
129. C3⋊#95C2×D3semidirect
130. C3⋊#95C2×D3semidirect
148. C2×D32C42semidirect
230. C2×C4×D3C4×D3semidirect
245. (C2×D3)⋊C4C4×D3semidirect
246. (C2×D3)⋊C4C4×D3semidirect
297. C2×C42D32semidirect
491. C32#2273semidirect
577. C3#73560semidirect

Maximal subgroups

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

subgroupindex
C2×#639212
C2×D3×(C2×D3)⋊C42
C4×#37522
C3×C4×(C2×D3)⋊C42
#105913682
Dic3×(C2×D3)⋊C42
#105912602
#105912372
#105912332
#735603