Finite Group Databasebeta

← #74667

Subgroups — #74667

Order 384.

740 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×#940C211yesmaximal, characteristic
2C2×C4×#67C211yesmaximal, characteristic, complemented
3C2×#67⋊C4C211yesmaximal, characteristic, complemented
4C3×#386C211yesmaximal, characteristic, complemented
5#5220C211yesmaximal, characteristic, complemented
6#5213C211yesmaximal, characteristic, complemented
7#4958C211yesmaximal, characteristic, complemented
8#4957C211yesmaximal, characteristic, complemented
9#4957C211yesmaximal, characteristic, complemented
10#4956C211yesmaximal, characteristic, complemented
11#4956C211yesmaximal, characteristic, complemented
12#4665C211yesmaximal, characteristic, complemented
13#4665C211yesmaximal, characteristic, complemented
14#4650C211yesmaximal, characteristic, complemented
15#4648C211yesmaximal, characteristic, complemented
16#2328—31nomaximal, Sylow
17C22×C3×D4C2211yescharacteristic
18C23×C3×C4C2211yescharacteristic
19C22×#67C2211yescharacteristic
20C22×#67C2211yescharacteristic
21C22×#67C2211yescharacteristic
22C22×#67C2211yescharacteristic
23C23×Dic3C2211yescharacteristic
24C22×D12C2211yescharacteristic
25C22×C4×D3C2211yescharacteristic
26C22×C4×D3C2211yescharacteristic
27C2×C3×C22⋊C4C2211yescharacteristic
28C2×C3×C22⋊C4C2211yescharacteristic
29C2×C3×C22⋊C4C2211yescharacteristic
30C2×#217C2211yescharacteristic
31C2×#217C2211yescharacteristic
32C2×#217C2211yescharacteristic
33#940C418yescomplemented
34C4×#67—24no—
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×Dic3⋊C4C2211yescharacteristic
42C2×Dic3⋊C4C2211yescharacteristic
43C2×C4×Dic3C2211yescharacteristic
44C2×C4×Dic3C2211yescharacteristic
45C2×C4×Dic3C2211yescharacteristic
46#67⋊C4—24no—
47C3×#95C2211yescharacteristic
48C3×#95C2211yescharacteristic
49C3⋊#95C2211yescharacteristic
50C3⋊#95C2211yescharacteristic
51C3⋊#95C2211yescharacteristic
52C3⋊#95C2211yescharacteristic
53C3⋊#95C2211yescharacteristic
54C3⋊#95C2211yescharacteristic
55C2×#127—31no—
56C2×C4×D4—31no—
57C2×C4×D4—31no—
58#390—31no—
59#390—31no—
60#386—31no—
61#386—31no—
62#386—31no—
63#386—31no—
64#386—31no—
65#386—31no—
66#386—31no—
67#386D311yescharacteristic, complemented
68#382—31no—
69#376—31no—
70C24×C3C2311yescharacteristic
71C24×C3C2311yescharacteristic
72C23×D3C2311yescharacteristic
73C23×D3C2311yescharacteristic
74C2×C3×D4—41no—
75C2×C3×D4—41no—
76C2×C3×D4C2×C414yescomplemented
77C22×C3×C4—22no—
78C22×C3×C4—41no—
79C22×C3×C4—41no—
80C22×C3×C4C2311yescharacteristic
81C22×C3×C4C2311yescharacteristic
82C22×C3×C4C2311yescharacteristic
83C22×C3×C4C2311yescharacteristic
84C22×C3×C4C2311yescharacteristic
85C2×#67—22no—
86C2×#67—22no—
87C2×#67—22no—
88C2×#67—22no—
89C2×#67—41no—
90C2×#67—41no—
91C2×#67—41no—
92C2×#67—41no—
93C2×#67C2×C414yescomplemented
94C2×#67C2×C414yescomplemented
95C2×#67C2×C414yescomplemented
96C2×#67C2×C414yescomplemented
97C22×Dic3—22no—
98C22×Dic3—41no—
99C22×Dic3—41no—
100C22×Dic3C2311yescharacteristic
101C22×Dic3C2311yescharacteristic
102C22×Dic3C2311yescharacteristic
103C22×Dic3C2311yescharacteristic
104C22×Dic3C2311yescharacteristic
105C22×Dic3C2311yescharacteristic
106C2×D12—41no—
107C2×D12—41no—
108C2×D12C2×C414yescomplemented
109C2×C4×D3—22no—
110C2×C4×D3—22no—
111C2×C4×D3—41no—
112C2×C4×D3—41no—
113C2×C4×D3—41no—
114C2×C4×D3—41no—
115C3×C22⋊C4—22no—
116C3×C22⋊C4—41no—
117C3×C22⋊C4—41no—
118#217—22no—
119#217—41no—
120#217—41no—
121(C2×D3)⋊C4—22no—
122(C2×D3)⋊C4—22no—
123(C2×D3)⋊C4—41no—
124(C2×D3)⋊C4—41no—
125(C2×D3)⋊C4—41no—
126(C2×D3)⋊C4—41no—
127Dic3⋊C4—22no—
128Dic3⋊C4—22no—
129C4×Dic3—22no—
130C4×Dic3C2×C414yescomplemented
131C4×Dic3D414yescomplemented
132C22×D4—31no—
133C22×D4—31no—
134C22×D4—31no—
135C22×D4—31no—
136C22×D4—31no—
137C22×D4C2×D311yescharacteristic
138C23×C4—31no—
139C23×C4—31no—
140C23×C4—31no—
141C23×C4C2×D311yescharacteristic
142#127—38no—
143C4×D4—64no—
144C4×D4—64no—
145C2×C4⋊C4—31no—
146C2×C4⋊C4—31no—
147C2×C22⋊C4—31no—
148C2×C22⋊C4—31no—
149C2×C22⋊C4—31no—
150C2×C22⋊C4—31no—
151C2×C22⋊C4—31no—
152C2×C22⋊C4—31no—
153C2×C22⋊C4—31no—
154C2×C22⋊C4—31no—
155C2×C22⋊C4—31no—
156C2×C22⋊C4C2×D311yescharacteristic
157C2×C22⋊C4C2×D311yescharacteristic
158C2×C22⋊C4C2×D311yescharacteristic
159C2×C42—31no—
160C2×C42—31no—
161C2×C42—31no—
162#95—31no—
163#95—31no—
164#95—31no—
165#95—31no—
166#95—31no—
167#95—31no—
168#95C2×D311yescharacteristic
169#95C2×D311yescharacteristic
170C23×C3—21no—
171C23×C3—21no—
172C23×C3—21no—
173C23×C3—21no—
174C23×C3—21no—
175C23×C3—21no—
176C23×C3—21no—
177C23×C3—21no—
178C23×C3—21no—
179C23×C3—21no—
180C23×C3—21no—
181C23×C3—21no—
182C23×C3C22×C412yes—
183C23×C3C22×C412yes—
184C23×C3C2411yescharacteristic
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×D3C22×C412yes—
198C22×D3C22×C412yes—
199C3×D4—44no—
200C2×C3×C4—21no—
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—44no—
214C2×C3×C4C22×C412yes—
215C2×C3×C4C2×D412yes—
216#67—28no—
217#67—28no—
218#67—44no—
219#67—44no—
220C2×Dic3—21no—
221C2×Dic3—21no—
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×Dic3—21no—
233C2×Dic3—44no—
234C2×Dic3C22×C412yes—
235C2×Dic3C22×C412yes—
236C2×Dic3C2×D412yes—
237C2×Dic3C2×D412yes—
238C2×Dic3#4112yes—
239D12—44no—
240C4×D3—44no—
241C4×D3—44no—
242C24—31no—
243C24—31no—
244C24C22×D311yescharacteristic
245C24C22×D311yescharacteristic
246C2×D4—34no—
247C2×D4—34no—
248C2×D4—34no—
249C2×D4—34no—
250C2×D4—34no—
251C2×D4—41no—
252C2×D4—41no—
253C2×D4—62no—
254C2×D4—62no—
255C2×D4—62no—
256C2×D4—62no—
257C2×D4—121no—
258C2×D4—121no—
259C2×D4—121no—
260C2×D4—121no—
261C2×D4—121no—
262C2×D4—121no—
263C2×D4C4×D314yescomplemented
264C22×C4—22no—
265C22×C4—31no—
266C22×C4—31no—
267C22×C4—31no—
268C22×C4—31no—
269C22×C4—31no—
270C22×C4—31no—
271C22×C4—41no—
272C22×C4—41no—
273C22×C4—62no—
274C22×C4—62no—
275C22×C4—62no—
276C22×C4—121no—
277C22×C4—121no—
278C22×C4—121no—
279C22×C4—121no—
280C22×C4—121no—
281C22×C4—121no—
282C22×C4C22×D311yescharacteristic
283C22×C4C22×D311yescharacteristic
284C22×C4C22×D311yescharacteristic
285C22×C4C22×D311yescharacteristic
286C22×C4C22×D311yescharacteristic
287C4⋊C4—62no—
288C4⋊C4—62no—
289C22⋊C4—22no—
290C22⋊C4—41no—
291C22⋊C4—41no—
292C22⋊C4—62no—
293C22⋊C4—62no—
294C22⋊C4—62no—
295C22⋊C4—121no—
296C22⋊C4—121no—
297C22⋊C4—121no—
298C22⋊C4—121no—
299C22⋊C4—121no—
300C22⋊C4—121no—
301C42—34no—
302C42—34no—
303C42—62no—
304C22×C3—22no—
305C22×C3—22no—
306C22×C3—22no—
307C22×C3—22no—
308C22×C3—22no—
309C22×C3—22no—
310C22×C3—41no—
311C22×C3—41no—
312C22×C3—41no—
313C22×C3—41no—
314C22×C3—41no—
315C22×C3—41no—
316C22×C3—41no—
317C22×C3—41no—
318C22×C3C23×C411yescharacteristic
319C22×C3C22×D411yescharacteristic
320C22×C3C2×#4111yescharacteristic
321C22×C3H(5,𝔽2)11yescharacteristic
322C22×C3H(5,𝔽2)11yescharacteristic
323C22×C3H(5,𝔽2)11yescharacteristic
324C22×C3H(5,𝔽2)11yescharacteristic
325C2×D3—22no—
326C2×D3—22no—
327C2×D3—22no—
328C2×D3—22no—
329C2×D3—22no—
330C2×D3—22no—
331C2×D3—41no—
332C2×D3—41no—
333C2×D3—41no—
334C2×D3—41no—
335C2×D3—41no—
336C2×D3—41no—
337C2×D3—41no—
338C2×D3—41no—
339C3×C4—22no—
340C3×C4—22no—
341C3×C4—41no—
342C3×C4—41no—
343C3×C4—41no—
344Dic3—22no—
345Dic3—22no—
346Dic3—41no—
347Dic3—41no—
348Dic3—41no—
349Dic3C4×D414yes—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—21no—
362C23—32no—
363C23—32no—
364C23—61no—
365C23—61no—
366C23—61no—
367C23—61no—
368C23—61no—
369C23—61no—
370C23—61no—
371C23—61no—
372C23—61no—
373C23—61no—
374C23—61no—
375C23—61no—
376C23C2×C4×D312yes—
377C23C2×C4×D312yes—
378C23C23×D311yescharacteristic
379D4—44no—
380D4—68no—
381D4—68no—
382D4—124no—
383D4—124no—
384D4—124no—
385C2×C4—21no—
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—32no—
399C2×C4—32no—
400C2×C4—32no—
401C2×C4—32no—
402C2×C4—32no—
403C2×C4—44no—
404C2×C4—61no—
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—61no—
416C2×C4—61no—
417C2×C4—124no—
418C2×C4—124no—
419C2×C4—124no—
420C2×C4C2×C4×D312yes—
421C2×C4D3×D412yes—
422C2×C3—42no—
423C2×C3—42no—
424C2×C3C2×C4×D411yescharacteristic
425C2×C3#51811yescharacteristic
426C2×C3#51811yescharacteristic
427C2×C3#53511yescharacteristic
428C2×C3#53511yescharacteristic
429C2×C3#54011yescharacteristic
430C2×C3#54011yescharacteristic
431D3—42no—
432D3—42no—
433C22—22no—
434C22—22no—
435C22—22no—
436C22—22no—
437C22—22no—
438C22—22no—
439C22—41no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22—41no—
444C22—41no—
445C22—41no—
446C22—41no—
447C22—62no—
448C22—62no—
449C22—62no—
450C22—62no—
451C22—62no—
452C22—62no—
453C22—121no—
454C22—121no—
455C22—121no—
456C22—121no—
457C22—121no—
458C22—121no—
459C22—121no—
460C22—121no—
461C22C22×C4×D311yescharacteristic
462C22C2×D3×D411yescharacteristic
463C22#100411yescharacteristic
464C22#100411yescharacteristic
465C22#100411yescharacteristic
466C22D3×#4111yescharacteristic
467C22#100911yescharacteristic
468C4—22no—
469C4—22no—
470C4—34no—
471C4—41no—
472C4—41no—
473C4—41no—
474C4—62no—
475C4—62no—
476C4—121no—
477C4—121no—
478C4—121no—
479C3#232811yescharacteristic, complemented, Sylow
480C2—42no—
481C2—42no—
482C2—122no—
483C2—122no—
484C2#548611yescharacteristic
485C2C4×D3×D411yescharacteristic
486C2#554511yescharacteristic
487C2#559211yescharacteristic
488C2#560711yescharacteristic
489C2#561511yescharacteristic
490C2#566311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutatorC22×C3C23×C4
FittingC3×#386C2
socle, cosocleC23×C3C24
prime radicalC2×#940C2
hypercenter#386D3
hypocenterC3#2328
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C2×C4×#67C2semidirect
3. C2×#67⋊C4C2semidirect
4. C3×#386C2semidirect
5. #5220C2semidirect
6. #5213C2semidirect
7. #4958C2semidirect
8. #4957C2semidirect
9. #4957C2semidirect
10. #4956C2semidirect
11. #4956C2semidirect
12. #4665C2semidirect
13. #4665C2semidirect
14. #4650C2semidirect
15. #4648C2semidirect
33. #940C4semidirect
67. #386D3semidirect
76. C2×C3×D4C2×C4semidirect
93. C2×#67C2×C4semidirect
94. C2×#67C2×C4semidirect
95. C2×#67C2×C4semidirect
96. C2×#67C2×C4semidirect
108. C2×D12C2×C4semidirect
130. C4×Dic3C2×C4semidirect
131. C4×Dic3D4semidirect
263. C2×D4C4×D3semidirect
479. C3#2328semidirect

Maximal subgroups

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

subgroupindex
C2×#9402
C2×C4×#672
C2×#67⋊C42
C3×#3862
#52202
#52132
#49582
#49572
#49562
#46652
#46502
#46482
#23283