Finite Group Databasebeta

← #77753

Subgroups — #77753

Order 384.

710 conjugacy classes of subgroups.

The subgroup lattice has 492 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×#893C211yesmaximal, characteristic, complemented
5C3×#398C211yesmaximal, characteristic, complemented
6#4991C211yesmaximal, characteristic, complemented
7#4990C211yesmaximal, characteristic, complemented
8#4989C211yesmaximal, characteristic, complemented
9#4988C211yesmaximal, characteristic, complemented
10#4671C211yesmaximal, characteristic, complemented
11#4671C211yesmaximal, characteristic, complemented
12#4669C211yesmaximal, characteristic, complemented
13#4666C211yesmaximal, characteristic, complemented
14#4665C211yesmaximal, characteristic, complemented
15#4665C211yesmaximal, characteristic, complemented
16#2464—31nomaximal, Sylow
17C22×D12C2211yescharacteristic
18C22×D12C2211yescharacteristic
19C22×D12C2211yescharacteristic
20C22×D12C2211yescharacteristic
21C22×D12C2211yescharacteristic
22C22×D12C2211yescharacteristic
23C22×C4×D3C2211yescharacteristic
24C22×C4×D3C2211yescharacteristic
25C22×C4×D3C2211yescharacteristic
26C2×C3×C4⋊C4C2211yescharacteristic
27C2×C3×C4⋊C4C2211yescharacteristic
28C2×C3×C4⋊C4C2211yescharacteristic
29C2×C3×C4⋊C4C2211yescharacteristic
30C2×(C2×D3)⋊C4C2211yescharacteristic
31C2×(C2×D3)⋊C4C2211yescharacteristic
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×Dic3⋊C4C2211yescharacteristic
44C2×C4×Dic3C2211yescharacteristic
45C2×C4×Dic3C2211yescharacteristic
46#895—24no—
47#895—24no—
48#894—24no—
49#893—24no—
50C3×#95C2211yescharacteristic
51C3×#95C2211yescharacteristic
52C3×#95C2211yescharacteristic
53C3⋊#95C2211yescharacteristic
54C3⋊#95C2211yescharacteristic
55C3⋊#95C2211yescharacteristic
56C2×#123—31no—
57C2×#121—31no—
58C2×#121—31no—
59C2×C4×D4—31no—
60#398D311yescharacteristic, complemented
61#394—31no—
62#392—31no—
63#392—31no—
64#390—31no—
65#388—31no—
66#388—31no—
67#386—31no—
68#386—31no—
69#385—31no—
70C4×C22⋊C4—31no—
71C23×D3C2311yescharacteristic
72C23×D3C2311yescharacteristic
73C23×D3C2311yescharacteristic
74C23×D3C2311yescharacteristic
75C22×C3×C4C2311yescharacteristic
76C22×C3×C4C2311yescharacteristic
77C22×C3×C4C2311yescharacteristic
78C22×C3×C4C2311yescharacteristic
79C22×C3×C4C2311yescharacteristic
80C22×C3×C4C2311yescharacteristic
81C22×C3×C4C2311yescharacteristic
82C22×Dic3C2311yescharacteristic
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×C4×D3—22no—
105C2×C4×D3—22no—
106C2×C4×D3—22no—
107C2×C4×D3—22no—
108C2×C4×D3—22no—
109C2×C4×D3—22no—
110C2×C4×D3—41no—
111C2×C4×D3—41no—
112C2×C4×D3—41no—
113C3×C4⋊C4—22no—
114C3×C4⋊C4—22no—
115C3×C4⋊C4—22no—
116C3×C4⋊C4—22no—
117(C2×D3)⋊C4—22no—
118(C2×D3)⋊C4—22no—
119(C2×D3)⋊C4—22no—
120(C2×D3)⋊C4—22no—
121(C2×D3)⋊C4—22no—
122(C2×D3)⋊C4—22no—
123(C2×D3)⋊C4—22no—
124(C2×D3)⋊C4—22no—
125(C2×D3)⋊C4—41no—
126(C2×D3)⋊C4—41no—
127(C2×D3)⋊C4—41no—
128(C2×D3)⋊C4D414yescomplemented
129(C2×D3)⋊C4D414yescomplemented
130Dic3⋊C4—22no—
131C4×Dic3—22no—
132C4×Dic3—41no—
133C22×D4—31no—
134C22×D4—31no—
135C22×D4—31no—
136C22×D4—31no—
137C22×D4—31no—
138C22×D4—31no—
139C23×C4—31no—
140C23×C4—31no—
141C23×C4—31no—
142#123—64no—
143#121—64no—
144#121—64no—
145C4×D4—64no—
146C2×C4⋊C4—31no—
147C2×C4⋊C4C2×D311yescharacteristic
148C2×C4⋊C4C2×D311yescharacteristic
149C2×C4⋊C4C2×D311yescharacteristic
150C2×C4⋊C4C2×D311yescharacteristic
151C2×C22⋊C4—31no—
152C2×C22⋊C4—31no—
153C2×C22⋊C4—31no—
154C2×C22⋊C4—31no—
155C2×C22⋊C4—31no—
156C2×C22⋊C4—31no—
157C2×C22⋊C4—31no—
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×C42—31no—
165C2×C42—31no—
166#95—31no—
167#95—31no—
168#95—31no—
169#95C2×D311yescharacteristic
170#95C2×D311yescharacteristic
171#95C2×D311yescharacteristic
172C23×C3C2411yescharacteristic
173C22×D3—21no—
174C22×D3—21no—
175C22×D3—21no—
176C22×D3—21no—
177C22×D3—21no—
178C22×D3—21no—
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×D3C2×D412yes—
199C22×D3C2×D412yes—
200C22×D3#4112yes—
201C2×C3×C4—21no—
202C2×C3×C4—21no—
203C2×C3×C4—21no—
204C2×C3×C4—21no—
205C2×C3×C4—21no—
206C2×C3×C4—21no—
207C2×C3×C4—21no—
208C2×C3×C4—21no—
209C2×C3×C4—21no—
210C2×C3×C4—21no—
211C2×C3×C4—21no—
212C2×C3×C4—21no—
213C2×C3×C4—21no—
214C2×C3×C4—21no—
215C2×C3×C4—21no—
216C2×C3×C4—21no—
217C2×C3×C4—21no—
218C2×C3×C4C2×D412yes—
219C2×C3×C4C2×D412yes—
220C2×C3×C4#4112yes—
221C2×C3×C4#4112yes—
222C2×Dic3—21no—
223C2×Dic3—21no—
224C2×Dic3—21no—
225C2×Dic3—21no—
226C2×Dic3—21no—
227C2×Dic3—21no—
228C2×Dic3—21no—
229C2×Dic3—21no—
230C2×Dic3—21no—
231C2×Dic3—21no—
232C2×Dic3C2×D412yes—
233C2×Dic3C2×D412yes—
234D12—28no—
235D12—44no—
236D12—44no—
237D12—44no—
238D12—44no—
239D12—44no—
240C4×D3—44no—
241C4×D3—44no—
242C4×D3—44no—
243C24—31no—
244C24—31no—
245C24—31no—
246C24—31no—
247C2×D4—62no—
248C2×D4—62no—
249C2×D4—62no—
250C2×D4—62no—
251C2×D4—62no—
252C2×D4—62no—
253C2×D4—62no—
254C2×D4—62no—
255C2×D4—62no—
256C2×D4—62no—
257C2×D4—62no—
258C2×D4—62no—
259C2×D4—62no—
260C2×D4—121no—
261C2×D4—121no—
262C2×D4—121no—
263C2×D4—121no—
264C2×D4—121no—
265C22×C4—31no—
266C22×C4—31no—
267C22×C4—31no—
268C22×C4—31no—
269C22×C4—62no—
270C22×C4—62no—
271C22×C4—62no—
272C22×C4—62no—
273C22×C4—62no—
274C22×C4—62no—
275C22×C4—121no—
276C22×C4—121no—
277C22×C4—121no—
278C22×C4C22×D311yescharacteristic
279C22×C4C22×D311yescharacteristic
280C22×C4C22×D311yescharacteristic
281C22×C4C22×D311yescharacteristic
282C22×C4C22×D311yescharacteristic
283C22×C4C22×D311yescharacteristic
284C22×C4C22×D311yescharacteristic
285C4⋊C4—22no—
286C4⋊C4—22no—
287C4⋊C4—22no—
288C4⋊C4—22no—
289C4⋊C4—62no—
290C22⋊C4—34no—
291C22⋊C4—34no—
292C22⋊C4—62no—
293C22⋊C4—62no—
294C22⋊C4—62no—
295C22⋊C4—62no—
296C22⋊C4—62no—
297C22⋊C4—62no—
298C22⋊C4—62no—
299C22⋊C4—62no—
300C22⋊C4—121no—
301C22⋊C4—121no—
302C22⋊C4—121no—
303C42—62no—
304C42—121no—
305C22×C3C22×D411yescharacteristic
306C22×C3C22×D411yescharacteristic
307C22×C3C2×#4111yescharacteristic
308C22×C3C2×#4111yescharacteristic
309C22×C3C2×#4111yescharacteristic
310C22×C3H(5,𝔽2)11yescharacteristic
311C22×C3H(5,𝔽2)11yescharacteristic
312C2×D3—22no—
313C2×D3—22no—
314C2×D3—22no—
315C2×D3—22no—
316C2×D3—22no—
317C2×D3—22no—
318C2×D3—22no—
319C2×D3—22no—
320C2×D3—22no—
321C2×D3—41no—
322C2×D3—41no—
323C2×D3—41no—
324C2×D3—41no—
325C2×D3—41no—
326C2×D3—41no—
327C2×D3—41no—
328C2×D3—41no—
329C2×D3—41no—
330C2×D3—41no—
331C2×D3—41no—
332C2×D3—41no—
333C2×D3—41no—
334C2×D3—41no—
335C2×D3—41no—
336C2×D3—41no—
337C2×D3—41no—
338C2×D3—41no—
339C2×D3—41no—
340C3×C4—22no—
341C3×C4—22no—
342C3×C4—22no—
343C3×C4—22no—
344C3×C4—41no—
345C3×C4—41no—
346C3×C4—41no—
347Dic3—22no—
348Dic3—22no—
349Dic3—41no—
350Dic3—41no—
351C23—32no—
352C23—32no—
353C23—32no—
354C23—61no—
355C23—61no—
356C23—61no—
357C23—61no—
358C23—61no—
359C23—61no—
360C23—61no—
361C23—61no—
362C23—61no—
363C23—61no—
364C23—61no—
365C23—61no—
366C23—61no—
367C23—61no—
368C23—61no—
369C23—61no—
370C23—61no—
371C23—61no—
372C23—61no—
373C23—61no—
374C23—61no—
375C23—61no—
376C23—61no—
377C23—61no—
378C23—61no—
379C23C23×D311yescharacteristic
380D4—68no—
381D4—124no—
382D4—124no—
383D4—124no—
384D4—124no—
385D4—124no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—32no—
404C2×C4—32no—
405C2×C4—61no—
406C2×C4—61no—
407C2×C4—61no—
408C2×C4—61no—
409C2×C4—61no—
410C2×C4—61no—
411C2×C4—61no—
412C2×C4—61no—
413C2×C4—61no—
414C2×C4—61no—
415C2×C4—124no—
416C2×C4—124no—
417C2×C4—124no—
418C2×C4D3×D412yes—
419C2×C4D3×D412yes—
420C2×C4#23912yes—
421C2×C4#23912yes—
422C2×C3#52511yescharacteristic
423C2×C3#53211yescharacteristic
424C2×C3#54011yescharacteristic
425C2×C3D4211yescharacteristic
426C2×C3#54611yescharacteristic
427C2×C3#54611yescharacteristic
428C2×C3#55311yescharacteristic
429D3—42no—
430D3—42no—
431D3—42no—
432D3—81no—
433C22—62no—
434C22—62no—
435C22—62no—
436C22—62no—
437C22—62no—
438C22—62no—
439C22—62no—
440C22—62no—
441C22—62no—
442C22—121no—
443C22—121no—
444C22—121no—
445C22—121no—
446C22—121no—
447C22—121no—
448C22—121no—
449C22—121no—
450C22—121no—
451C22—121no—
452C22—121no—
453C22—121no—
454C22—121no—
455C22—121no—
456C22—121no—
457C22—121no—
458C22—121no—
459C22—121no—
460C22—121no—
461C22C2×D3×D411yescharacteristic
462C22C2×D3×D411yescharacteristic
463C22C2×#23911yescharacteristic
464C22C2×#23911yescharacteristic
465C22D3×#4111yescharacteristic
466C22#100911yescharacteristic
467C22#100911yescharacteristic
468C4—22no—
469C4—22no—
470C4—22no—
471C4—22no—
472C4—41no—
473C4—41no—
474C4—41no—
475C4—62no—
476C4—62no—
477C4—121no—
478C4—121no—
479C3#246411yescharacteristic, complemented, Sylow
480C2—122no—
481C2—122no—
482C2—122no—
483C2—241no—
484C2#560911yescharacteristic
485C2#562711yescharacteristic
486C2#563011yescharacteristic
487C2#565411yescharacteristic
488C2#569511yescharacteristic
489C2#569711yescharacteristic
490C2#572511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, cosocleC23×C3C24
FittingC3×#398C2
hypercenter#398D3
hypocenterC3#2464
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #398

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×#893C2semidirect
5. C3×#398C2semidirect
6. #4991C2semidirect
7. #4990C2semidirect
8. #4989C2semidirect
9. #4988C2semidirect
10. #4671C2semidirect
11. #4671C2semidirect
12. #4669C2semidirect
13. #4666C2semidirect
14. #4665C2semidirect
15. #4665C2semidirect
60. #398D3semidirect
128. (C2×D3)⋊C4D4semidirect
129. (C2×D3)⋊C4D4semidirect
479. C3#2464semidirect

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×#8932
C3×#3982
#49912
#49902
#49892
#49882
#46712
#46692
#46662
#46652
#24643