Finite Group Databasebeta

← #82718

Subgroups — #82718

Order 384.

804 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×#939C211yesmaximal, characteristic, complemented
3C2×#939C211yesmaximal, characteristic, complemented
4C2×#938C211yesmaximal, characteristic, complemented
5C2×#930C211yesmaximal, characteristic, complemented
6C2×#884C211yesmaximal, characteristic, complemented
7#5223C211yesmaximal, characteristic, complemented
8#5223C211yesmaximal, characteristic, complemented
9#5223C211yesmaximal, characteristic, complemented
10#5210C211yesmaximal, characteristic, complemented
11#4994C211yesmaximal, characteristic, complemented
12#4989C211yesmaximal, characteristic, complemented
13#4960C211yesmaximal, characteristic, complemented
14#4950C211yesmaximal, characteristic, complemented
15#4948C211yesmaximal, characteristic, complemented
16#2675—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#939—24no—
40#939—24no—
41#938—24no—
42#930—24no—
43C2×(C2×D3)⋊C4C2211yescharacteristic
44C2×(C2×D3)⋊C4C2211yescharacteristic
45C2×(C2×D3)⋊C4C2211yescharacteristic
46C2×(C2×D3)⋊C4C2211yescharacteristic
47C2×(C2×D3)⋊C4C2211yescharacteristic
48C2×C4⋊Dic3C2211yescharacteristic
49C2×C4⋊Dic3C2211yescharacteristic
50C2×Dic3⋊C4C2211yescharacteristic
51C2×Dic3⋊C4C2211yescharacteristic
52C2×Dic3⋊C4C2211yescharacteristic
53#884—24no—
54C3⋊#95C2211yescharacteristic
55C3⋊#95C2211yescharacteristic
56C3⋊#95C2211yescharacteristic
57C3⋊#95C2211yescharacteristic
58C2×#121—31no—
59C2×#121—31no—
60C2×#121—31no—
61C2×#121—31no—
62C2×#121—31no—
63C2×#121D311yescharacteristic, complemented
64#396—31no—
65#396—31no—
66#392—31no—
67#392—31no—
68#392—31no—
69#392—31no—
70#385—31no—
71#385—31no—
72#385—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—41no—
105C2×#67—41no—
106C2×#67—41no—
107C2×#67—41no—
108C2×#67—41no—
109C2×#67—41no—
110C2×#67—41no—
111C2×#67—41no—
112C22×Dic3—22no—
113C22×Dic3—22no—
114C22×Dic3—41no—
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—41no—
133#217—41no—
134#217D414yescomplemented
135(C2×D3)⋊C4—22no—
136(C2×D3)⋊C4—22no—
137(C2×D3)⋊C4—22no—
138(C2×D3)⋊C4—41no—
139(C2×D3)⋊C4D414yescomplemented
140C4⋊Dic3—22no—
141C4⋊Dic3—22no—
142Dic3⋊C4—22no—
143Dic3⋊C4—22no—
144Dic3⋊C4—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#121—24no—
159#121—64no—
160#121—64no—
161#121—64no—
162#121—64no—
163#121—64no—
164C2×C4⋊C4—31no—
165C2×C4⋊C4—31no—
166C2×C4⋊C4—31no—
167C2×C4⋊C4—31no—
168C2×C4⋊C4—31no—
169C2×C4⋊C4C2×D311yescharacteristic
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⋊C4—31no—
179C2×C22⋊C4—31no—
180C2×C22⋊C4C2×D311yescharacteristic
181C2×C22⋊C4C2×D311yescharacteristic
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—44no—
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—21no—
258C2×Dic3—21no—
259C2×Dic3—44no—
260C2×Dic3C2×D412yes—
261C2×Dic3C2×D412yes—
262C2×Dic3C2×D412yes—
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—41no—
277C2×D4—41no—
278C2×D4—41no—
279C2×D4—62no—
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—121no—
292C2×D4—121no—
293C2×D4—121no—
294C2×D4—121no—
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—121no—
314C22×C4—121no—
315C22×C4C22×D311yescharacteristic
316C22×C4C22×D311yescharacteristic
317C22×C4C22×D311yescharacteristic
318C22×C4C22×D311yescharacteristic
319C4⋊C4—22no—
320C4⋊C4—62no—
321C4⋊C4—62no—
322C4⋊C4—62no—
323C4⋊C4—62no—
324C4⋊C4—62no—
325C22⋊C4—22no—
326C22⋊C4—34no—
327C22⋊C4—34no—
328C22⋊C4—62no—
329C22⋊C4—62no—
330C22⋊C4—62no—
331C22⋊C4—62no—
332C22⋊C4—62no—
333C22⋊C4—121no—
334C22⋊C4—121no—
335C22⋊C4—121no—
336C22⋊C4#6714yescomplemented
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×C3H(5,𝔽2)11yescharacteristic
362C22×C3H(5,𝔽2)11yescharacteristic
363C22×C3H(5,𝔽2)11yescharacteristic
364C22×C32−1+411yescharacteristic
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—22no—
386Dic3—41no—
387Dic3—41no—
388Dic3—41no—
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—124no—
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—44no—
448C2×C4—61no—
449C2×C4—61no—
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×C3#53711yescharacteristic
472C2×C3#53711yescharacteristic
473C2×C3#53711yescharacteristic
474C2×C3D4211yescharacteristic
475C2×C3D4211yescharacteristic
476C2×C3D4211yescharacteristic
477C2×C3#56011yescharacteristic
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
519C22#100911yescharacteristic
520C22#101011yescharacteristic
521C22C22×#6711yescharacteristic
522C4—22no—
523C4—22no—
524C4—22no—
525C4—41no—
526C4—62no—
527C4—62no—
528C4—62no—
529C4—121no—
530C4—121no—
531C4—121no—
532C3#267511yescharacteristic, complemented, Sylow
533C2—42no—
534C2—42no—
535C2—81no—
536C2—122no—
537C2—241no—
538C2#559711yescharacteristic
539C2#560811yescharacteristic
540C2#560911yescharacteristic
541C2#562011yescharacteristic
542C2D4×#6711yescharacteristic
543C2D4×#6711yescharacteristic
544C2#583311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, cosocleC23×C3C24
FittingC2×C3×#121C2
hypercenterC2×#121D3
hypocenterC3#2675
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×#939C2semidirect
3. C2×#939C2semidirect
4. C2×#938C2semidirect
5. C2×#930C2semidirect
6. C2×#884C2semidirect
7. #5223C2semidirect
8. #5223C2semidirect
9. #5223C2semidirect
10. #5210C2semidirect
11. #4994C2semidirect
12. #4989C2semidirect
13. #4960C2semidirect
14. #4950C2semidirect
15. #4948C2semidirect
63. C2×#121D3semidirect
129. C3×C22⋊C4D4semidirect
134. #217D4semidirect
139. (C2×D3)⋊C4D4semidirect
336. C22⋊C4#67semidirect
532. C3#2675semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#1212
C2×#9392
C2×#9382
C2×#9302
C2×#8842
#52232
#52102
#49942
#49892
#49602
#49502
#49482
#26753