Finite Group Databasebeta

← #82650

Subgroups — #82650

Order 384.

832 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#121C211yesmaximal, characteristic, complemented
2C2×#940C211yesmaximal, characteristic, complemented
3C2×#939C211yesmaximal, characteristic, complemented
4C2×#939C211yesmaximal, characteristic, complemented
5C2×C4×#67C211yesmaximal, characteristic, complemented
6C2×#884C211yesmaximal, characteristic, complemented
7#5223C211yesmaximal, characteristic, complemented
8#5223C211yesmaximal, characteristic, complemented
9#5222C211yesmaximal, characteristic, complemented
10#5213C211yesmaximal, characteristic, complemented
11#4991C211yesmaximal, characteristic, complemented
12#4976C211yesmaximal, characteristic, complemented
13#4957C211yesmaximal, characteristic, complemented
14#4956C211yesmaximal, characteristic, complemented
15Dic3×C22⋊C4C211yesmaximal, characteristic, complemented
16#2428—31nomaximal, Sylow
17C22×C3×D4C2211yescharacteristic
18C22×C3×D4C2211yescharacteristic
19C22×C3×D4C2211yescharacteristic
20C23×C3×C4C2211yescharacteristic
21C22×#67C2211yescharacteristic
22C22×#67C2211yescharacteristic
23C22×#67C2211yescharacteristic
24C22×#67C2211yescharacteristic
25C22×#67C2211yescharacteristic
26C22×#67C2211yescharacteristic
27C23×Dic3C2211yescharacteristic
28C22×D12C2211yescharacteristic
29C22×C4×D3C2211yescharacteristic
30C3×#121—24no—
31C2×C3×C4⋊C4C2211yescharacteristic
32C2×C3×C22⋊C4C2211yescharacteristic
33C2×C3×C22⋊C4C2211yescharacteristic
34C2×#217C2211yescharacteristic
35C2×#217C2211yescharacteristic
36C2×#217C2211yescharacteristic
37C2×#217C2211yescharacteristic
38C2×#217C2211yescharacteristic
39#940—24no—
40#939—24no—
41#939—24no—
42C4×#67—24no—
43C2×(C2×D3)⋊C4C2211yescharacteristic
44C2×(C2×D3)⋊C4C2211yescharacteristic
45C2×(C2×D3)⋊C4C2211yescharacteristic
46C2×(C2×D3)⋊C4C2211yescharacteristic
47C2×(C2×D3)⋊C4C2211yescharacteristic
48C2×Dic3⋊C4C2211yescharacteristic
49C2×Dic3⋊C4C2211yescharacteristic
50C2×Dic3⋊C4C2211yescharacteristic
51C2×C4×Dic3C2211yescharacteristic
52C2×C4×Dic3C2211yescharacteristic
53#884—24no—
54C3⋊#95C2211yescharacteristic
55C3⋊#95C2211yescharacteristic
56C3⋊#95C2211yescharacteristic
57C3⋊#95C2211yescharacteristic
58C2×#127—31no—
59C2×#121—31no—
60C2×#121—31no—
61C2×#121—31no—
62C2×#121D311yescharacteristic, complemented
63C2×C4×D4—31no—
64#394—31no—
65#394—31no—
66#392—31no—
67#392—31no—
68#390—31no—
69#389—31no—
70#386—31no—
71#386—31no—
72C4×C22⋊C4—31no—
73C24×C3C2311yescharacteristic
74C24×C3C2311yescharacteristic
75C24×C3C2311yescharacteristic
76C23×D3C2311yescharacteristic
77C23×D3C2311yescharacteristic
78C2×C3×D4—22no—
79C2×C3×D4—22no—
80C2×C3×D4—22no—
81C2×C3×D4—22no—
82C2×C3×D4—22no—
83C2×C3×D4—22no—
84C2×C3×D4—41no—
85C2×C3×D4—41no—
86C2×C3×D4—41no—
87C22×C3×C4—22no—
88C22×C3×C4—22no—
89C22×C3×C4—41no—
90C22×C3×C4C2311yescharacteristic
91C22×C3×C4C2311yescharacteristic
92C22×C3×C4C2311yescharacteristic
93C22×C3×C4C2311yescharacteristic
94C2×#67—22no—
95C2×#67—22no—
96C2×#67—22no—
97C2×#67—22no—
98C2×#67—22no—
99C2×#67—22no—
100C2×#67—22no—
101C2×#67—22no—
102C2×#67—22no—
103C2×#67—22no—
104C2×#67—22no—
105C2×#67—22no—
106C2×#67—22no—
107C2×#67—41no—
108C2×#67—41no—
109C2×#67—41no—
110C2×#67—41no—
111C2×#67D414yescomplemented
112C22×Dic3—22no—
113C22×Dic3—22no—
114C22×Dic3—22no—
115C22×Dic3C2311yescharacteristic
116C22×Dic3C2311yescharacteristic
117C22×Dic3C2311yescharacteristic
118C22×Dic3C2311yescharacteristic
119C22×Dic3C2311yescharacteristic
120C22×Dic3C2311yescharacteristic
121C2×D12—22no—
122C2×D12—22no—
123C2×D12—41no—
124C2×C4×D3—22no—
125C2×C4×D3—22no—
126C2×C4×D3—41no—
127C3×C4⋊C4—22no—
128C3×C22⋊C4—22no—
129C3×C22⋊C4D414yescomplemented
130#217—22no—
131#217—22no—
132#217—22no—
133#217—22no—
134#217—41no—
135(C2×D3)⋊C4—22no—
136(C2×D3)⋊C4—22no—
137(C2×D3)⋊C4—22no—
138(C2×D3)⋊C4—22no—
139(C2×D3)⋊C4—41no—
140Dic3⋊C4—22no—
141Dic3⋊C4—22no—
142Dic3⋊C4D414yescomplemented
143C4×Dic3—22no—
144C4×Dic3—22no—
145C22×D4—31no—
146C22×D4—31no—
147C22×D4—31no—
148C22×D4—31no—
149C22×D4—31no—
150C22×D4—31no—
151C22×D4—31no—
152C22×D4C2×D311yescharacteristic
153C22×D4C2×D311yescharacteristic
154C22×D4C2×D311yescharacteristic
155C23×C4—31no—
156C23×C4—31no—
157C23×C4C2×D311yescharacteristic
158#127—64no—
159#121—24no—
160#121—64no—
161#121—64no—
162#121—64no—
163C4×D4—64no—
164C2×C4⋊C4—31no—
165C2×C4⋊C4—31no—
166C2×C4⋊C4—31no—
167C2×C4⋊C4C2×D311yescharacteristic
168C2×C22⋊C4—31no—
169C2×C22⋊C4—31no—
170C2×C22⋊C4—31no—
171C2×C22⋊C4—31no—
172C2×C22⋊C4—31no—
173C2×C22⋊C4—31no—
174C2×C22⋊C4—31no—
175C2×C22⋊C4—31no—
176C2×C22⋊C4—31no—
177C2×C22⋊C4—31no—
178C2×C22⋊C4C2×D311yescharacteristic
179C2×C22⋊C4C2×D311yescharacteristic
180C2×C42—31no—
181C2×C42—31no—
182#95—31no—
183#95—31no—
184#95—31no—
185#95—31no—
186C23×C3—21no—
187C23×C3—21no—
188C23×C3—21no—
189C23×C3—21no—
190C23×C3—21no—
191C23×C3—21no—
192C23×C3—21no—
193C23×C3—21no—
194C23×C3—21no—
195C23×C3—21no—
196C23×C3—21no—
197C23×C3—21no—
198C23×C3—21no—
199C23×C3—21no—
200C23×C3—21no—
201C23×C3—21no—
202C23×C3—21no—
203C23×C3—21no—
204C23×C3—21no—
205C23×C3C2×D412yes—
206C23×C3C2×D412yes—
207C23×C3C2411yescharacteristic
208C22×D3—21no—
209C22×D3—21no—
210C22×D3—21no—
211C22×D3—21no—
212C22×D3—21no—
213C22×D3—21no—
214C22×D3—21no—
215C22×D3—21no—
216C22×D3—21no—
217C22×D3—21no—
218C22×D3—21no—
219C22×D3—21no—
220C22×D3—21no—
221C22×D3C2×D412yes—
222C3×D4—44no—
223C3×D4—44no—
224C3×D4—44no—
225C2×C3×C4—21no—
226C2×C3×C4—21no—
227C2×C3×C4—21no—
228C2×C3×C4—21no—
229C2×C3×C4—21no—
230C2×C3×C4—21no—
231C2×C3×C4—21no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—44no—
235C2×C3×C4C2×D412yes—
236C2×C3×C4C2×D412yes—
237C2×C3×C4C2×D412yes—
238#67—28no—
239#67—44no—
240#67—44no—
241#67—44no—
242#67—44no—
243#67—44no—
244C2×Dic3—21no—
245C2×Dic3—21no—
246C2×Dic3—21no—
247C2×Dic3—21no—
248C2×Dic3—21no—
249C2×Dic3—21no—
250C2×Dic3—21no—
251C2×Dic3—21no—
252C2×Dic3—21no—
253C2×Dic3—21no—
254C2×Dic3—21no—
255C2×Dic3—21no—
256C2×Dic3—21no—
257C2×Dic3—44no—
258C2×Dic3C2×D412yes—
259C2×Dic3C2×D412yes—
260C2×Dic3C2×D412yes—
261C2×Dic3#4112yes—
262C2×Dic3#4112yes—
263D12—44no—
264C4×D3—44no—
265C24—31no—
266C24—31no—
267C24C22×D311yescharacteristic
268C24C22×D311yescharacteristic
269C24C22×D311yescharacteristic
270C2×D4—22no—
271C2×D4—22no—
272C2×D4—22no—
273C2×D4—22no—
274C2×D4—22no—
275C2×D4—22no—
276C2×D4—34no—
277C2×D4—41no—
278C2×D4—41no—
279C2×D4—41no—
280C2×D4—62no—
281C2×D4—62no—
282C2×D4—62no—
283C2×D4—62no—
284C2×D4—62no—
285C2×D4—62no—
286C2×D4—62no—
287C2×D4—62no—
288C2×D4—62no—
289C2×D4—62no—
290C2×D4—62no—
291C2×D4—62no—
292C2×D4—62no—
293C2×D4—62no—
294C2×D4—62no—
295C2×D4—121no—
296C2×D4—121no—
297C2×D4—121no—
298C2×D4—121no—
299C2×D4—121no—
300C22×C4—22no—
301C22×C4—22no—
302C22×C4—31no—
303C22×C4—31no—
304C22×C4—31no—
305C22×C4—31no—
306C22×C4—31no—
307C22×C4—31no—
308C22×C4—41no—
309C22×C4—62no—
310C22×C4—62no—
311C22×C4—62no—
312C22×C4—62no—
313C22×C4—62no—
314C22×C4—121no—
315C22×C4C22×D311yescharacteristic
316C22×C4C22×D311yescharacteristic
317C22×C4C22×D311yescharacteristic
318C22×C4C22×D311yescharacteristic
319C4⋊C4—22no—
320C4⋊C4—34no—
321C4⋊C4—62no—
322C4⋊C4—62no—
323C22⋊C4—22no—
324C22⋊C4—62no—
325C22⋊C4—62no—
326C22⋊C4—62no—
327C22⋊C4—62no—
328C22⋊C4—62no—
329C22⋊C4—62no—
330C22⋊C4—62no—
331C22⋊C4—62no—
332C22⋊C4—121no—
333C22⋊C4—121no—
334C22⋊C4#6714yescomplemented
335C42—62no—
336C42—62no—
337C22×C3—22no—
338C22×C3—22no—
339C22×C3—22no—
340C22×C3—22no—
341C22×C3—22no—
342C22×C3—22no—
343C22×C3—41no—
344C22×C3—41no—
345C22×C3—41no—
346C22×C3—41no—
347C22×C3—41no—
348C22×C3—41no—
349C22×C3—41no—
350C22×C3—41no—
351C22×C3—41no—
352C22×C3—41no—
353C22×C3—41no—
354C22×C3—41no—
355C22×C3—41no—
356C22×C3—41no—
357C22×C3—41no—
358C22×C3C22×D411yescharacteristic
359C22×C3C22×D411yescharacteristic
360C22×C3C22×D411yescharacteristic
361C22×C3C2×#4111yescharacteristic
362C22×C3C2×#4111yescharacteristic
363C22×C3H(5,𝔽2)11yescharacteristic
364C22×C3H(5,𝔽2)11yescharacteristic
365C2×D3—22no—
366C2×D3—22no—
367C2×D3—22no—
368C2×D3—41no—
369C2×D3—41no—
370C2×D3—41no—
371C2×D3—41no—
372C2×D3—41no—
373C2×D3—41no—
374C2×D3—41no—
375C2×D3—41no—
376C2×D3—41no—
377C2×D3—41no—
378C2×D3—41no—
379C3×C4—22no—
380C3×C4—22no—
381C3×C4—22no—
382C3×C4—41no—
383Dic3—22no—
384Dic3—22no—
385Dic3—41no—
386Dic3—41no—
387Dic3—41no—
388Dic3#12114yescomplemented
389C23—21no—
390C23—21no—
391C23—21no—
392C23—21no—
393C23—21no—
394C23—21no—
395C23—21no—
396C23—21no—
397C23—21no—
398C23—21no—
399C23—21no—
400C23—21no—
401C23—21no—
402C23—21no—
403C23—21no—
404C23—21no—
405C23—21no—
406C23—21no—
407C23—21no—
408C23—32no—
409C23—61no—
410C23—61no—
411C23—61no—
412C23—61no—
413C23—61no—
414C23—61no—
415C23—61no—
416C23—61no—
417C23—61no—
418C23—61no—
419C23—61no—
420C23—61no—
421C23—61no—
422C23D3×D412yes—
423C23C2×#6712yes—
424C23C23×D311yescharacteristic
425D4—44no—
426D4—44no—
427D4—44no—
428D4—68no—
429D4—124no—
430D4—124no—
431D4—124no—
432D4—124no—
433D4—124no—
434D4—124no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—32no—
445C2×C4—32no—
446C2×C4—32no—
447C2×C4—32no—
448C2×C4—32no—
449C2×C4—44no—
450C2×C4—61no—
451C2×C4—61no—
452C2×C4—61no—
453C2×C4—61no—
454C2×C4—61no—
455C2×C4—61no—
456C2×C4—61no—
457C2×C4—61no—
458C2×C4—61no—
459C2×C4—61no—
460C2×C4—61no—
461C2×C4—61no—
462C2×C4—61no—
463C2×C4—124no—
464C2×C4—124no—
465C2×C4D3×D412yes—
466C2×C4C2×#6712yes—
467C2×C4C2×#6712yes—
468C2×C3—42no—
469C2×C3—42no—
470C2×C3—81no—
471C2×C3C2×#12111yescharacteristic
472C2×C3#53211yescharacteristic
473C2×C3#54011yescharacteristic
474C2×C3D4211yescharacteristic
475C2×C3D4211yescharacteristic
476C2×C3#54611yescharacteristic
477C2×C3#55011yescharacteristic
478D3—42no—
479D3—81no—
480C22—22no—
481C22—22no—
482C22—22no—
483C22—22no—
484C22—22no—
485C22—22no—
486C22—41no—
487C22—41no—
488C22—41no—
489C22—41no—
490C22—41no—
491C22—41no—
492C22—41no—
493C22—41no—
494C22—41no—
495C22—41no—
496C22—41no—
497C22—41no—
498C22—41no—
499C22—41no—
500C22—41no—
501C22—62no—
502C22—62no—
503C22—62no—
504C22—121no—
505C22—121no—
506C22—121no—
507C22—121no—
508C22—121no—
509C22—121no—
510C22—121no—
511C22—121no—
512C22—121no—
513C22—121no—
514C22—121no—
515C22C2×D3×D411yescharacteristic
516C22C2×D3×D411yescharacteristic
517C22#100411yescharacteristic
518C22#100411yescharacteristic
519C22D3×#4111yescharacteristic
520C22D3×#4111yescharacteristic
521C22C22×#6711yescharacteristic
522C4—22no—
523C4—22no—
524C4—22no—
525C4—34no—
526C4—41no—
527C4—62no—
528C4—62no—
529C4—121no—
530C4—121no—
531C4—121no—
532C3#242811yescharacteristic, complemented, Sylow
533C2—42no—
534C2—42no—
535C2—81no—
536C2—122no—
537C2—241no—
538C2#559911yescharacteristic
539C2D3×#12111yescharacteristic
540C2#561011yescharacteristic
541C2#561511yescharacteristic
542C2D4×#6711yescharacteristic
543C2D4×#6711yescharacteristic
544C2#583211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, cosocleC23×C3C24
FittingC2×C3×#121C2
hypercenterC2×#121D3
hypocenterC3#2428
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×C3×#121C2semidirect
2. C2×#940C2semidirect
3. C2×#939C2semidirect
4. C2×#939C2semidirect
5. C2×C4×#67C2semidirect
6. C2×#884C2semidirect
7. #5223C2semidirect
8. #5223C2semidirect
9. #5222C2semidirect
10. #5213C2semidirect
11. #4991C2semidirect
12. #4976C2semidirect
13. #4957C2semidirect
14. #4956C2semidirect
15. Dic3×C22⋊C4C2semidirect
62. C2×#121D3semidirect
111. C2×#67D4semidirect
129. C3×C22⋊C4D4semidirect
142. Dic3⋊C4D4semidirect
334. C22⋊C4#67semidirect
388. Dic3#121semidirect
532. C3#2428semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#1212
C2×#9402
C2×#9392
C2×C4×#672
C2×#8842
#52232
#52222
#52132
#49912
#49762
#49572
#49562
Dic3×C22⋊C42
#24283