Finite Group Databasebeta

← #74886

Subgroups — #74886

Order 384.

1056 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#235C211yesmaximal, characteristic, complemented
2C2×#937C211yesmaximal, characteristic, complemented
3C2×#882C211yesmaximal, characteristic, complemented
4C2×D3×C22⋊C4C211yesmaximal, characteristic, complemented
5C3×#386C211yesmaximal, characteristic, complemented
6#5223C211yesmaximal, characteristic, complemented
7#5213C211yesmaximal, characteristic, complemented
8#4960C211yesmaximal, characteristic, complemented
9#4956C211yesmaximal, characteristic, complemented
10#4956C211yesmaximal, characteristic, complemented
11#4947C211yesmaximal, characteristic, complemented
12#4673C211yesmaximal, characteristic, complemented
13#4665C211yesmaximal, characteristic, complemented
14#4665C211yesmaximal, characteristic, complemented
15#4664C211yesmaximal, characteristic, complemented
16#2404—31nomaximal, Sylow
17C24×D3C2211yescharacteristic
18C22×C3×D4C2211yescharacteristic
19C23×C3×C4C2211yescharacteristic, complemented
20C22×#67C2211yescharacteristic
21C22×#67C2211yescharacteristic
22C22×#67C2211yescharacteristic
23C22×#67C2211yescharacteristic, complemented
24C2×#235—24no—
25C2×#235—24no—
26C2×#235—24no—
27C22×D12C2211yescharacteristic
28C22×D12C2211yescharacteristic
29C22×C4×D3C2211yescharacteristic
30C22×C4×D3C2211yescharacteristic
31C22×C4×D3C2211yescharacteristic, complemented
32C22×Dic6C2211yescharacteristic, complemented
33C2×C3×C22⋊C4C2211yescharacteristic
34C2×C3×C22⋊C4C2211yescharacteristic
35C2×C3×C22⋊C4C2211yescharacteristic, complemented
36C2×#217C2211yescharacteristic
37C2×#217C2211yescharacteristic
38C2×#217C2211yescharacteristic, complemented
39#937—24no—
40C2×(C2×D3)⋊C4C2211yescharacteristic
41C2×(C2×D3)⋊C4C2211yescharacteristic
42C2×(C2×D3)⋊C4C2211yescharacteristic
43C2×(C2×D3)⋊C4C2211yescharacteristic
44C2×(C2×D3)⋊C4C2211yescharacteristic
45C2×(C2×D3)⋊C4C2211yescharacteristic
46C2×(C2×D3)⋊C4C2211yescharacteristic, complemented
47C2×(C2×D3)⋊C4C2211yescharacteristic, complemented
48#882—24no—
49D3×C22⋊C4—24no—
50C3×#95C2211yescharacteristic, complemented
51C3×#95C2211yescharacteristic, complemented
52C3⋊#95C2211yescharacteristic, complemented
53C3⋊#95C2211yescharacteristic, complemented
54C3⋊#95C2211yescharacteristic, complemented
55C3⋊#95C2211yescharacteristic, complemented
56C3⋊#95C2211yescharacteristic, complemented
57C3⋊#95C2211yescharacteristic, complemented
58C22×#41—31no—
59C2×#120—31no—
60C2×#120—31no—
61C22×C22⋊C4—31no—
62#393—31no—
63#393—31no—
64#392—31no—
65#392—31no—
66#386—31no—
67#386—31no—
68#386—31no—
69#386—31no—
70#386—31no—
71#386D311yescharacteristic, complemented
72#381—31no—
73C24×C3C2311yescharacteristic
74C24×C3C2311yescharacteristic
75C23×D3—22no—
76C23×D3—22no—
77C23×D3—22no—
78C23×D3—22no—
79C23×D3—22no—
80C23×D3—41no—
81C23×D3—41no—
82C23×D3C2311yescharacteristic
83C23×D3C2311yescharacteristic
84C23×D3C2311yescharacteristic
85C2×C3×D4—22no—
86C2×C3×D4—22no—
87C2×C3×D4—41no—
88C22×C3×C4—22no—
89C22×C3×C4—22no—
90C22×C3×C4—22no—
91C22×C3×C4C2311yescharacteristic
92C22×C3×C4C2311yescharacteristic
93C22×C3×C4C2311yescharacteristic
94C22×C3×C4C2311yescharacteristic
95C22×C3×C4C2311yescharacteristic
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—41no—
106C2×#67—41no—
107C2×#67D414yescomplemented
108C22×Dic3C2311yescharacteristic
109C22×Dic3C2311yescharacteristic
110C22×Dic3C2311yescharacteristic
111C22×Dic3C2311yescharacteristic
112C22×Dic3C2311yescharacteristic
113#235—232no—
114C2×D12—22no—
115C2×D12—22no—
116C2×D12—22no—
117C2×D12—22no—
118C2×D12—41no—
119C2×D12D414yescomplemented
120C2×C4×D3—22no—
121C2×C4×D3—22no—
122C2×C4×D3—22no—
123C2×C4×D3—22no—
124C2×C4×D3—22no—
125C2×C4×D3—22no—
126C2×C4×D3—41no—
127C2×C4×D3—41no—
128C2×C4×D3D414yescomplemented
129C2×Dic6—22no—
130C2×Dic6—22no—
131C2×Dic6—22no—
132C3×C22⋊C4—22no—
133C3×C22⋊C4—22no—
134C3×C22⋊C4—41no—
135#217—22no—
136#217—22no—
137#217—41no—
138(C2×D3)⋊C4—22no—
139(C2×D3)⋊C4—22no—
140(C2×D3)⋊C4—22no—
141(C2×D3)⋊C4—22no—
142(C2×D3)⋊C4—22no—
143(C2×D3)⋊C4—22no—
144(C2×D3)⋊C4—41no—
145(C2×D3)⋊C4—41no—
146C25—31no—
147C2×#41—64no—
148C2×#41—64no—
149C2×#41—64no—
150C22×Q8—31no—
151C22×D4—31no—
152C22×D4—31no—
153C22×D4—31no—
154C22×D4—31no—
155C22×D4—31no—
156C22×D4—31no—
157C22×D4C2×D311yescharacteristic
158C23×C4—31no—
159C23×C4—31no—
160C23×C4—31no—
161C23×C4C2×D311yescharacteristic, complemented
162#120—64no—
163#120—64no—
164C2×C22⋊C4—31no—
165C2×C22⋊C4—31no—
166C2×C22⋊C4—31no—
167C2×C22⋊C4—31no—
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—64no—
176C2×C22⋊C4C2×D311yescharacteristic
177C2×C22⋊C4C2×D311yescharacteristic
178C2×C22⋊C4C2×D311yescharacteristic, complemented
179#95—31no—
180#95—31no—
181#95—31no—
182#95—31no—
183#95—31no—
184#95—31no—
185#95C2×D311yescharacteristic, complemented
186#95C2×D311yescharacteristic, complemented
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×C3C2×D412yes—
200C23×C3#4112yescomplemented
201C23×C3C2411yescharacteristic
202C22×D3—21no—
203C22×D3—21no—
204C22×D3—21no—
205C22×D3—21no—
206C22×D3—28no—
207C22×D3—21no—
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—44no—
220C22×D3—44no—
221C22×D3—44no—
222C22×D3—44no—
223C22×D3—44no—
224C22×D3—44no—
225C22×D3C2×D412yes—
226C22×D3C2×D412yes—
227C22×D3C2×D412yes—
228C22×D3C2×D412yes—
229C22×D3#4112yescomplemented
230C3×D4—44no—
231C2×C3×C4—28no—
232C2×C3×C4—21no—
233C2×C3×C4—21no—
234C2×C3×C4—21no—
235C2×C3×C4—21no—
236C2×C3×C4—21no—
237C2×C3×C4—21no—
238C2×C3×C4—21no—
239C2×C3×C4—21no—
240C2×C3×C4—21no—
241C2×C3×C4—21no—
242C2×C3×C4—21no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4C2×D412yes—
246C2×C3×C4C2×D412yes—
247#67—28no—
248#67—28no—
249#67—44no—
250#67—44no—
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—21no—
260C2×Dic3—21no—
261C2×Dic3—21no—
262C2×Dic3—21no—
263C2×Dic3—21no—
264C2×Dic3C2×D412yes—
265C2×Dic3C2×D412yes—
266D12—28no—
267D12—44no—
268C4×D3—28no—
269C4×D3—28no—
270C4×D3—44no—
271Dic6—28no—
272C24—31no—
273C24—31no—
274C24—31no—
275C24—62no—
276C24—62no—
277C24—62no—
278C24—62no—
279C24—62no—
280C24—121no—
281C24—121no—
282C24C22×D311yescharacteristic
283C24C22×D311yescharacteristic
284#41—632no—
285C2×Q8—62no—
286C2×Q8—62no—
287C2×Q8—62no—
288C2×D4—22no—
289C2×D4—22no—
290C2×D4—34no—
291C2×D4—34no—
292C2×D4—41no—
293C2×D4—62no—
294C2×D4—62no—
295C2×D4—62no—
296C2×D4—62no—
297C2×D4—62no—
298C2×D4—62no—
299C2×D4—62no—
300C2×D4—62no—
301C2×D4—62no—
302C2×D4—62no—
303C2×D4—62no—
304C2×D4—62no—
305C2×D4—62no—
306C2×D4—121no—
307C2×D4—121no—
308C2×D4—121no—
309C22×C4—22no—
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—31no—
313C22×C4—31no—
314C22×C4—34no—
315C22×C4—31no—
316C22×C4—31no—
317C22×C4—31no—
318C22×C4—62no—
319C22×C4—62no—
320C22×C4—62no—
321C22×C4—62no—
322C22×C4—62no—
323C22×C4—62no—
324C22×C4—121no—
325C22×C4—121no—
326C22×C4C22×D311yescharacteristic
327C22×C4C22×D311yescharacteristic
328C22×C4C22×D311yescharacteristic
329C22×C4C22×D311yescharacteristic
330C22×C4C22×D311yescharacteristic
331C22⋊C4—22no—
332C22⋊C4—22no—
333C22⋊C4—41no—
334C22⋊C4—62no—
335C22⋊C4—62no—
336C22⋊C4—62no—
337C22⋊C4—62no—
338C22⋊C4—62no—
339C22⋊C4—62no—
340C22⋊C4—62no—
341C22⋊C4—62no—
342C22⋊C4—121no—
343C22⋊C4—121no—
344C22⋊C4—121no—
345C22×C3—22no—
346C22×C3—22no—
347C22×C3—22no—
348C22×C3—22no—
349C22×C3—22no—
350C22×C3—22no—
351C22×C3—41no—
352C22×C3—41no—
353C22×C3—41no—
354C22×C3—41no—
355C22×C3—41no—
356C22×C3—41no—
357C22×C3—41no—
358C22×C3—41no—
359C22×C3C22×D411yescharacteristic
360C22×C3C22×D411yescharacteristic
361C22×C3C22×D411yescharacteristic
362C22×C3C2×#4111yescharacteristic
363C22×C3C2×#4111yescharacteristic
364C22×C3H(5,𝔽2)11yescharacteristic
365C22×C3H(5,𝔽2)11yescharacteristic
366C2×D3—22no—
367C2×D3—22no—
368C2×D3—22no—
369C2×D3—22no—
370C2×D3—22no—
371C2×D3—22no—
372C2×D3—22no—
373C2×D3—22no—
374C2×D3—22no—
375C2×D3—22no—
376C2×D3—22no—
377C2×D3—22no—
378C2×D3—416no—
379C2×D3—41no—
380C2×D3—41no—
381C2×D3—41no—
382C2×D3—41no—
383C2×D3—41no—
384C2×D3—41no—
385C2×D3—41no—
386C2×D3—41no—
387C2×D3#12014yes—
388C3×C4—22no—
389C3×C4—22no—
390C3×C4—41no—
391C3×C4—41no—
392C3×C4—41no—
393Dic3—22no—
394Dic3—22no—
395Dic3—41no—
396Dic3—41no—
397Dic3—41no—
398C23—21no—
399C23—21no—
400C23—21no—
401C23—21no—
402C23—21no—
403C23—21no—
404C23—21no—
405C23—21no—
406C23—21no—
407C23—21no—
408C23—21no—
409C23—21no—
410C23—32no—
411C23—32no—
412C23—32no—
413C23—32no—
414C23—32no—
415C23—68no—
416C23—61no—
417C23—61no—
418C23—61no—
419C23—61no—
420C23—61no—
421C23—61no—
422C23—61no—
423C23—61no—
424C23—61no—
425C23—61no—
426C23—61no—
427C23—61no—
428C23—61no—
429C23—61no—
430C23—61no—
431C23—61no—
432C23—124no—
433C23—124no—
434C23—124no—
435C23—124no—
436C23—124no—
437C23—124no—
438C23#23512yescomplemented
439C23D3×D412yes—
440C23C23×D311yescharacteristic
441Q8—68no—
442D4—44no—
443D4—68no—
444D4—68no—
445D4—68no—
446D4—124no—
447D4—124no—
448D4—124no—
449C2×C4—28no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—32no—
464C2×C4—32no—
465C2×C4—68no—
466C2×C4—68no—
467C2×C4—61no—
468C2×C4—61no—
469C2×C4—61no—
470C2×C4—61no—
471C2×C4—61no—
472C2×C4—61no—
473C2×C4—61no—
474C2×C4—61no—
475C2×C4—61no—
476C2×C4—61no—
477C2×C4—61no—
478C2×C4—61no—
479C2×C4—61no—
480C2×C4—124no—
481C2×C4D3×D412yes—
482C2×C4D3×D412yes—
483C2×C3—42no—
484C2×C3—42no—
485C2×C3C2×#12011yescharacteristic
486C2×C3#52511yescharacteristic
487C2×C3#53511yescharacteristic
488C2×C3#54611yescharacteristic
489C2×C3#54611yescharacteristic
490C2×C3#54611yescharacteristic
491C2×C3#54611yescharacteristic
492D3—24no—
493D3—42no—
494D3—42no—
495C22—22no—
496C22—22no—
497C22—22no—
498C22—22no—
499C22—22no—
500C22—22no—
501C22—34no—
502C22—41no—
503C22—41no—
504C22—41no—
505C22—41no—
506C22—41no—
507C22—41no—
508C22—41no—
509C22—41no—
510C22—62no—
511C22—62no—
512C22—62no—
513C22—62no—
514C22—62no—
515C22—62no—
516C22—62no—
517C22—62no—
518C22—62no—
519C22—62no—
520C22—62no—
521C22—62no—
522C22—1216no—
523C22—121no—
524C22—121no—
525C22—121no—
526C22—121no—
527C22—121no—
528C22—121no—
529C22—121no—
530C22—121no—
531C22C2×#23511yescharacteristic
532C22C2×D3×D411yescharacteristic
533C22C2×D3×D411yescharacteristic
534C22C2×D3×D411yescharacteristic
535C22#100411yescharacteristic
536C22D3×#4111yescharacteristic
537C22#100911yescharacteristic
538C4—22no—
539C4—22no—
540C4—41no—
541C4—41no—
542C4—41no—
543C4—62no—
544C4—62no—
545C4—121no—
546C4—121no—
547C4—121no—
548C3#240411yescharacteristic, complemented, Sylow
549C2—42no—
550C2—42no—
551C2—64no—
552C2—122no—
553C2—122no—
554C2#549011yescharacteristic
555C2#554711yescharacteristic
556C2#555011yescharacteristic
557C2D3×#12011yescharacteristic
558C2#560711yescharacteristic
559C2#561211yescharacteristic
560C2#565411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, cosocleC23×C3C24
FittingC3×#386C2
hypercenter#386D3
hypocenterC3#2404
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C22×#235C2semidirect
2. C2×#937C2semidirect
3. C2×#882C2semidirect
4. C2×D3×C22⋊C4C2semidirect
5. C3×#386C2semidirect
6. #5223C2semidirect
7. #5213C2semidirect
8. #4960C2semidirect
9. #4956C2semidirect
10. #4956C2semidirect
11. #4947C2semidirect
12. #4673C2semidirect
13. #4665C2semidirect
14. #4665C2semidirect
15. #4664C2semidirect
19. C23×C3×C4C22semidirect
23. C22×#67C22semidirect
31. C22×C4×D3C22semidirect
32. C22×Dic6C22semidirect
35. C2×C3×C22⋊C4C22semidirect
38. C2×#217C22semidirect
46. C2×(C2×D3)⋊C4C22semidirect
47. C2×(C2×D3)⋊C4C22semidirect
50. C3×#95C22semidirect
51. C3×#95C22semidirect
52. C3⋊#95C22semidirect
53. C3⋊#95C22semidirect
54. C3⋊#95C22semidirect
55. C3⋊#95C22semidirect
56. C3⋊#95C22semidirect
57. C3⋊#95C22semidirect
71. #386D3semidirect
107. C2×#67D4semidirect
119. C2×D12D4semidirect
128. C2×C4×D3D4semidirect
161. C23×C4C2×D3semidirect
178. C2×C22⋊C4C2×D3semidirect
185. #95C2×D3semidirect
186. #95C2×D3semidirect
200. C23×C3#41semidirect
229. C22×D3#41semidirect
438. C23#235semidirect
548. C3#2404semidirect

Maximal subgroups

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

subgroupindex
C22×#2352
C2×#9372
C2×#8822
C2×D3×C22⋊C42
C3×#3862
#52232
#52132
#49602
#49562
#49472
#46732
#46652
#46642
#24043