Finite Group Databasebeta

← #75387

Subgroups — #75387

Order 384.

734 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#895C211yesmaximal, characteristic, complemented
2C2×#895C211yesmaximal, characteristic, complemented
3C2×#894C211yesmaximal, characteristic, complemented
4C2×#874C211yesmaximal, characteristic, complemented
5C3×#387C211yesmaximal, characteristic, complemented
6#4991C211yesmaximal, characteristic, complemented
7#4940C211yesmaximal, characteristic, complemented
8#4672C211yesmaximal, characteristic, complemented
9#4671C211yesmaximal, characteristic, complemented
10#4671C211yesmaximal, characteristic, complemented
11#4671C211yesmaximal, characteristic, complemented
12#4671C211yesmaximal, characteristic, complemented
13#4665C211yesmaximal, characteristic, complemented
14#4665C211yesmaximal, characteristic, complemented
15#4665C211yesmaximal, characteristic, complemented
16#2673—31nomaximal, Sylow
17C22×D12C2211yescharacteristic
18C22×D12C2211yescharacteristic
19C22×D12C2211yescharacteristic
20C22×D12C2211yescharacteristic
21C22×D12C2211yescharacteristic
22C22×D12C2211yescharacteristic
23C22×D12C2211yescharacteristic
24C22×D12C2211yescharacteristic
25C22×D12C2211yescharacteristic
26C22×D12C2211yescharacteristic
27C22×C4×D3C2211yescharacteristic
28C22×C4×D3C2211yescharacteristic
29C2×C3×C4⋊C4C2211yescharacteristic
30C2×C3×C4⋊C4C2211yescharacteristic
31C2×C3×C42C2211yescharacteristic
32C2×(C2×D3)⋊C4C2211yescharacteristic
33C2×(C2×D3)⋊C4C2211yescharacteristic
34C2×(C2×D3)⋊C4C2211yescharacteristic
35C2×(C2×D3)⋊C4C2211yescharacteristic
36C2×(C2×D3)⋊C4C2211yescharacteristic
37C2×(C2×D3)⋊C4C2211yescharacteristic
38C2×(C2×D3)⋊C4C2211yescharacteristic
39C2×(C2×D3)⋊C4C2211yescharacteristic
40C2×(C2×D3)⋊C4C2211yescharacteristic
41C2×(C2×D3)⋊C4C2211yescharacteristic
42C2×(C2×D3)⋊C4C2211yescharacteristic
43C2×(C2×D3)⋊C4C2211yescharacteristic
44C2×(C2×D3)⋊C4C2211yescharacteristic
45C2×Dic3⋊C4C2211yescharacteristic
46#895—24no—
47#895—24no—
48#894—24no—
49#874—24no—
50C3×#95C2211yescharacteristic
51C3×#95C2211yescharacteristic
52C3×#95C2211yescharacteristic
53C3×#95C2211yescharacteristic
54C3⋊#95C2211yescharacteristic
55C3⋊#95C2211yescharacteristic
56C2×#127—31no—
57C2×#123—31no—
58C2×#121—31no—
59C2×#121—31no—
60#394—31no—
61#394—31no—
62#392—31no—
63#392—31no—
64#392—31no—
65#392—31no—
66#388—31no—
67#387D311yescharacteristic, complemented
68#386—31no—
69#386—31no—
70#386—31no—
71C23×D3C2311yescharacteristic
72C23×D3C2311yescharacteristic
73C23×D3C2311yescharacteristic
74C23×D3C2311yescharacteristic
75C23×D3C2311yescharacteristic
76C22×C3×C4C2311yescharacteristic
77C22×C3×C4C2311yescharacteristic
78C22×C3×C4C2311yescharacteristic
79C22×C3×C4C2311yescharacteristic
80C22×C3×C4C2311yescharacteristic
81C22×C3×C4C2311yescharacteristic
82C22×C3×C4C2311yescharacteristic
83C22×Dic3C2311yescharacteristic
84C22×Dic3C2311yescharacteristic
85C22×Dic3C2311yescharacteristic
86C2×D12—22no—
87C2×D12—22no—
88C2×D12—22no—
89C2×D12—22no—
90C2×D12—22no—
91C2×D12—22no—
92C2×D12—22no—
93C2×D12—22no—
94C2×D12—22no—
95C2×D12—22no—
96C2×D12—22no—
97C2×D12—22no—
98C2×D12—22no—
99C2×D12—41no—
100C2×D12—41no—
101C2×D12—41no—
102C2×D12—41no—
103C2×D12—41no—
104C2×D12—41no—
105C2×D12—41no—
106C2×D12—41no—
107C2×D12—41no—
108C2×D12—41no—
109C2×D12—41no—
110C2×D12—41no—
111C2×D12—41no—
112C2×D12—41no—
113C2×D12—41no—
114C2×D12—41no—
115C2×D12D414yescomplemented
116C2×C4×D3—22no—
117C2×C4×D3—22no—
118C2×C4×D3—22no—
119C2×C4×D3—41no—
120C2×C4×D3—41no—
121C2×C4×D3—41no—
122C3×C4⋊C4—22no—
123C3×C4⋊C4D414yescomplemented
124C3×C42—22no—
125(C2×D3)⋊C4—22no—
126(C2×D3)⋊C4—22no—
127(C2×D3)⋊C4—22no—
128(C2×D3)⋊C4—22no—
129(C2×D3)⋊C4—22no—
130(C2×D3)⋊C4—22no—
131(C2×D3)⋊C4—22no—
132(C2×D3)⋊C4—22no—
133(C2×D3)⋊C4—41no—
134(C2×D3)⋊C4—41no—
135(C2×D3)⋊C4—41no—
136(C2×D3)⋊C4—41no—
137(C2×D3)⋊C4—41no—
138Dic3⋊C4—22no—
139C22×D4—31no—
140C22×D4—31no—
141C22×D4—31no—
142C22×D4—31no—
143C22×D4—31no—
144C22×D4—31no—
145C22×D4—31no—
146C22×D4—31no—
147C22×D4—31no—
148C22×D4—31no—
149C23×C4—31no—
150C23×C4—31no—
151#127—64no—
152#123—64no—
153#121—64no—
154#121—64no—
155C2×C4⋊C4—31no—
156C2×C4⋊C4C2×D311yescharacteristic
157C2×C4⋊C4C2×D311yescharacteristic
158C2×C22⋊C4—31no—
159C2×C22⋊C4—31no—
160C2×C22⋊C4—31no—
161C2×C22⋊C4—31no—
162C2×C22⋊C4—31no—
163C2×C22⋊C4—31no—
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×C42C2×D311yescharacteristic
172#95—31no—
173#95—31no—
174#95C2×D311yescharacteristic
175#95C2×D311yescharacteristic
176#95C2×D311yescharacteristic
177#95C2×D311yescharacteristic
178C23×C3C2411yescharacteristic
179C22×D3—21no—
180C22×D3—21no—
181C22×D3—21no—
182C22×D3—21no—
183C22×D3—21no—
184C22×D3—21no—
185C22×D3—21no—
186C22×D3—21no—
187C22×D3—21no—
188C22×D3—21no—
189C22×D3—21no—
190C22×D3—21no—
191C22×D3—21no—
192C22×D3—21no—
193C22×D3—21no—
194C22×D3—21no—
195C22×D3—21no—
196C22×D3—21no—
197C22×D3—21no—
198C22×D3—21no—
199C22×D3—21no—
200C22×D3—21no—
201C22×D3—21no—
202C22×D3—21no—
203C22×D3—21no—
204C22×D3—21no—
205C22×D3—21no—
206C22×D3—21no—
207C22×D3—21no—
208C22×D3—21no—
209C22×D3—21no—
210C22×D3—21no—
211C22×D3—21no—
212C22×D3C2×D412yes—
213C22×D3C2×D412yes—
214C2×C3×C4—21no—
215C2×C3×C4—21no—
216C2×C3×C4—21no—
217C2×C3×C4—21no—
218C2×C3×C4—21no—
219C2×C3×C4—21no—
220C2×C3×C4—21no—
221C2×C3×C4—21no—
222C2×C3×C4—21no—
223C2×C3×C4—21no—
224C2×C3×C4—21no—
225C2×C3×C4—21no—
226C2×C3×C4—21no—
227C2×C3×C4—21no—
228C2×C3×C4—21no—
229C2×C3×C4—21no—
230C2×C3×C4C2×D412yes—
231C2×C3×C4C2×D412yes—
232C2×C3×C4C2×D412yes—
233C2×C3×C4C2×D412yes—
234C2×C3×C4#4112yes—
235C2×Dic3—21no—
236C2×Dic3—21no—
237C2×Dic3—21no—
238C2×Dic3—21no—
239C2×Dic3—21no—
240C2×Dic3—21no—
241C2×Dic3—21no—
242C2×Dic3—21no—
243C2×Dic3—21no—
244D12—44no—
245D12—44no—
246D12—44no—
247D12—44no—
248D12—44no—
249D12—44no—
250D12—44no—
251D12—44no—
252D12—44no—
253D12—44no—
254C4×D3—44no—
255C4×D3—44no—
256C24—31no—
257C24—31no—
258C24—31no—
259C24—31no—
260C24—31no—
261C2×D4—34no—
262C2×D4—62no—
263C2×D4—62no—
264C2×D4—62no—
265C2×D4—62no—
266C2×D4—62no—
267C2×D4—62no—
268C2×D4—62no—
269C2×D4—62no—
270C2×D4—62no—
271C2×D4—62no—
272C2×D4—62no—
273C2×D4—62no—
274C2×D4—62no—
275C2×D4—121no—
276C2×D4—121no—
277C2×D4—121no—
278C2×D4—121no—
279C2×D4—121no—
280C2×D4—121no—
281C2×D4—121no—
282C2×D4—121no—
283C2×D4—121no—
284C2×D4—121no—
285C2×D4—121no—
286C2×D4—121no—
287C2×D4—121no—
288C2×D4—121no—
289C2×D4—121no—
290C2×D4—121no—
291C22×C4—31no—
292C22×C4—31no—
293C22×C4—31no—
294C22×C4—62no—
295C22×C4—62no—
296C22×C4—62no—
297C22×C4—121no—
298C22×C4—121no—
299C22×C4—121no—
300C22×C4C22×D311yescharacteristic
301C22×C4C22×D311yescharacteristic
302C22×C4C22×D311yescharacteristic
303C22×C4C22×D311yescharacteristic
304C22×C4C22×D311yescharacteristic
305C22×C4C22×D311yescharacteristic
306C22×C4C22×D311yescharacteristic
307C4⋊C4—22no—
308C4⋊C4—62no—
309C4⋊C4D1214yescomplemented
310C22⋊C4—62no—
311C22⋊C4—62no—
312C22⋊C4—62no—
313C22⋊C4—62no—
314C22⋊C4—62no—
315C22⋊C4—62no—
316C22⋊C4—62no—
317C22⋊C4—62no—
318C22⋊C4—121no—
319C22⋊C4—121no—
320C22⋊C4—121no—
321C22⋊C4—121no—
322C22⋊C4—121no—
323C42—22no—
324C22×C3C22×D411yescharacteristic
325C22×C3C22×D411yescharacteristic
326C22×C3C2×#4111yescharacteristic
327C22×C3H(5,𝔽2)11yescharacteristic
328C22×C3H(5,𝔽2)11yescharacteristic
329C22×C3H(5,𝔽2)11yescharacteristic
330C22×C3H(5,𝔽2)11yescharacteristic
331C2×D3—22no—
332C2×D3—22no—
333C2×D3—22no—
334C2×D3—22no—
335C2×D3—22no—
336C2×D3—22no—
337C2×D3—41no—
338C2×D3—41no—
339C2×D3—41no—
340C2×D3—41no—
341C2×D3—41no—
342C2×D3—41no—
343C2×D3—41no—
344C2×D3—41no—
345C2×D3—41no—
346C2×D3—41no—
347C2×D3—41no—
348C2×D3—41no—
349C2×D3—41no—
350C2×D3—41no—
351C2×D3—41no—
352C2×D3—41no—
353C2×D3—41no—
354C2×D3—41no—
355C2×D3—41no—
356C2×D3—41no—
357C2×D3—41no—
358C2×D3—41no—
359C2×D3—41no—
360C2×D3—41no—
361C2×D3—41no—
362C2×D3—41no—
363C2×D3—41no—
364C2×D3—41no—
365C2×D3—41no—
366C3×C4—22no—
367C3×C4—22no—
368C3×C4—22no—
369C3×C4—22no—
370C3×C4—22no—
371C3×C4—41no—
372C3×C4—41no—
373Dic3—41no—
374Dic3—41no—
375Dic3—41no—
376C23—32no—
377C23—32no—
378C23—61no—
379C23—61no—
380C23—61no—
381C23—61no—
382C23—61no—
383C23—61no—
384C23—61no—
385C23—61no—
386C23—61no—
387C23—61no—
388C23—61no—
389C23—61no—
390C23—61no—
391C23—61no—
392C23—61no—
393C23—61no—
394C23—61no—
395C23—61no—
396C23—61no—
397C23—61no—
398C23—61no—
399C23—61no—
400C23—61no—
401C23—61no—
402C23—61no—
403C23—61no—
404C23—61no—
405C23—61no—
406C23—61no—
407C23—61no—
408C23—61no—
409C23—61no—
410C23—61no—
411C23C23×D311yescharacteristic
412D4—124no—
413D4—124no—
414D4—124no—
415D4—124no—
416D4—124no—
417D4—124no—
418D4—124no—
419D4—124no—
420D4—124no—
421D4—124no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—61no—
439C2×C4—61no—
440C2×C4—61no—
441C2×C4—61no—
442C2×C4—61no—
443C2×C4—61no—
444C2×C4—61no—
445C2×C4—61no—
446C2×C4—61no—
447C2×C4—124no—
448C2×C4—124no—
449C2×C4C2×D1212yes—
450C2×C4C2×D1212yes—
451C2×C4C2×D1212yes—
452C2×C4D3×D412yes—
453C2×C4#23912yes—
454C2×C3#53411yescharacteristic
455C2×C3#53511yescharacteristic
456C2×C3#54011yescharacteristic
457C2×C3D4211yescharacteristic
458C2×C3#54611yescharacteristic
459C2×C3#55011yescharacteristic
460C2×C3#56011yescharacteristic
461D3—42no—
462D3—42no—
463D3—81no—
464D3—81no—
465D3—81no—
466C22—62no—
467C22—62no—
468C22—62no—
469C22—62no—
470C22—62no—
471C22—62no—
472C22—121no—
473C22—121no—
474C22—121no—
475C22—121no—
476C22—121no—
477C22—121no—
478C22—121no—
479C22—121no—
480C22—121no—
481C22—121no—
482C22—121no—
483C22—121no—
484C22—121no—
485C22—121no—
486C22—121no—
487C22—121no—
488C22—121no—
489C22—121no—
490C22—121no—
491C22—121no—
492C22—121no—
493C22—121no—
494C22—121no—
495C22—121no—
496C22—121no—
497C22—121no—
498C22—121no—
499C22—121no—
500C22—121no—
501C22C22×D1211yescharacteristic
502C22C2×D3×D411yescharacteristic
503C22C2×#23911yescharacteristic
504C22#100911yescharacteristic
505C22#100911yescharacteristic
506C22#100911yescharacteristic
507C22#100911yescharacteristic
508C4—22no—
509C4—22no—
510C4—22no—
511C4—22no—
512C4—22no—
513C4—41no—
514C4—41no—
515C4—121no—
516C4—121no—
517C4—121no—
518C3#267311yescharacteristic, complemented, Sylow
519C2—122no—
520C2—122no—
521C2—241no—
522C2—241no—
523C2—241no—
524C2#552511yescharacteristic
525C2D4×D1211yescharacteristic
526C2#557711yescharacteristic
527C2#563011yescharacteristic
528C2#565311yescharacteristic
529C2#569711yescharacteristic
530C2#571111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, cosocleC23×C3C24
FittingC3×#387C2
hypercenter#387D3
hypocenterC3#2673
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
1. C2×#895C2semidirect
2. C2×#895C2semidirect
3. C2×#894C2semidirect
4. C2×#874C2semidirect
5. C3×#387C2semidirect
6. #4991C2semidirect
7. #4940C2semidirect
8. #4672C2semidirect
9. #4671C2semidirect
10. #4671C2semidirect
11. #4671C2semidirect
12. #4671C2semidirect
13. #4665C2semidirect
14. #4665C2semidirect
15. #4665C2semidirect
67. #387D3semidirect
115. C2×D12D4semidirect
123. C3×C4⋊C4D4semidirect
309. C4⋊C4D12semidirect
518. C3#2673semidirect

Maximal subgroups

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

subgroupindex
C2×#8952
C2×#8942
C2×#8742
C3×#3872
#49912
#49402
#46722
#46712
#46652
#26733