Finite Group Databasebeta

← #74752

Subgroups — #74752

Order 384.

724 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#939C211yesmaximal, characteristic, complemented
2C2×#939C211yesmaximal, characteristic, complemented
3C2×#930C211yesmaximal, characteristic, complemented
4C2×#67⋊C4C211yesmaximal, characteristic, complemented
5C3×#386C211yesmaximal, characteristic, complemented
6C2×C3⋊#95C211yesmaximal, characteristic, complemented
7#4960C211yesmaximal, characteristic, complemented
8#4959C211yesmaximal, characteristic, complemented
9#4958C211yesmaximal, characteristic, complemented
10#4956C211yesmaximal, characteristic, complemented
11#4951C211yesmaximal, characteristic, complemented
12#4675C211yesmaximal, characteristic, complemented
13#4669C211yesmaximal, characteristic, complemented
14#4665C211yesmaximal, characteristic, complemented
15#4657C211yesmaximal, characteristic, complemented
16#2543—31nomaximal, Sylow
17C22×C3×D4C2211yescharacteristic
18C23×C3×C4C2211yescharacteristic
19C22×#67C2211yescharacteristic
20C22×#67C2211yescharacteristic
21C22×#67C2211yescharacteristic
22C22×#67C2211yescharacteristic
23C23×Dic3C2211yescharacteristic
24C23×Dic3C2211yescharacteristic
25C22×D12C2211yescharacteristic
26C22×C4×D3C2211yescharacteristic
27C2×C3×C22⋊C4C2211yescharacteristic
28C2×C3×C22⋊C4C2211yescharacteristic
29C2×C3×C22⋊C4C2211yescharacteristic
30C2×#217C2211yescharacteristic
31C2×#217C2211yescharacteristic
32#939—24no—
33#939—24no—
34#930—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×(C2×D3)⋊C4C2211yescharacteristic
42C2×C4⋊Dic3C2211yescharacteristic
43C2×Dic3⋊C4C2211yescharacteristic
44C2×Dic3⋊C4C2211yescharacteristic
45C2×Dic3⋊C4C2211yescharacteristic
46C2×C4×Dic3C2211yescharacteristic
47#67⋊C4—24no—
48C3×#95C2211yescharacteristic
49C3×#95C2211yescharacteristic
50C3⋊#95C2211yescharacteristic
51C3⋊#95C2211yescharacteristic
52C3⋊#95C2211yescharacteristic
53C3⋊#95C2211yescharacteristic
54C3⋊#95C2211yescharacteristic
55C3⋊#95C2211yescharacteristic
56C2×#121—31no—
57C2×#121—31no—
58C2×#121—31no—
59C2×C4×D4—31no—
60#398—31no—
61#397—31no—
62#394—31no—
63#392—31no—
64#388—31no—
65#388—31no—
66#386—31no—
67#386—31no—
68#386—31no—
69#386D311yescharacteristic, complemented
70C2×#95—31no—
71C24×C3C2311yescharacteristic
72C24×C3C2311yescharacteristic
73C23×D3C2311yescharacteristic
74C23×D3C2311yescharacteristic
75C2×C3×D4—22no—
76C2×C3×D4—22no—
77C2×C3×D4—22no—
78C22×C3×C4—22no—
79C22×C3×C4—22no—
80C22×C3×C4—41no—
81C22×C3×C4C2311yescharacteristic
82C22×C3×C4C2311yescharacteristic
83C22×C3×C4C2311yescharacteristic
84C22×C3×C4C2311yescharacteristic
85C22×C3×C4C2311yescharacteristic
86C2×#67—22no—
87C2×#67—22no—
88C2×#67—22no—
89C2×#67—22no—
90C2×#67—22no—
91C2×#67—22no—
92C2×#67—22no—
93C2×#67—22no—
94C2×#67—41no—
95C2×#67—41no—
96C2×#67—41no—
97C2×#67D414yescomplemented
98C22×Dic3—22no—
99C22×Dic3—22no—
100C22×Dic3—41no—
101C22×Dic3—41no—
102C22×Dic3—41no—
103C22×Dic3D414yescomplemented
104C22×Dic3C2311yescharacteristic
105C22×Dic3C2311yescharacteristic
106C22×Dic3C2311yescharacteristic
107C22×Dic3C2311yescharacteristic
108C22×Dic3C2311yescharacteristic
109C22×Dic3C2311yescharacteristic
110C2×D12—22no—
111C2×D12—22no—
112C2×D12—41no—
113C2×C4×D3—22no—
114C2×C4×D3—41no—
115C2×C4×D3—41no—
116C3×C22⋊C4—22no—
117C3×C22⋊C4—22no—
118C3×C22⋊C4—41no—
119#217—22no—
120#217—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—22no—
126(C2×D3)⋊C4—22no—
127(C2×D3)⋊C4—41no—
128C4⋊Dic3—22no—
129Dic3⋊C4—22no—
130Dic3⋊C4—22no—
131Dic3⋊C4—22no—
132C4×Dic3—22no—
133C22×D4—31no—
134C22×D4—31no—
135C22×D4—31no—
136C22×D4—31no—
137C22×D4—31no—
138C22×D4C2×D311yescharacteristic
139C23×C4—31no—
140C23×C4—31no—
141C23×C4—31no—
142C23×C4C2×D311yescharacteristic
143#121—64no—
144#121—64no—
145#121—64no—
146C4×D4—64no—
147C2×C4⋊C4—31no—
148C2×C4⋊C4—31no—
149C2×C4⋊C4—31no—
150C2×C4⋊C4—31no—
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⋊C4C2×D311yescharacteristic
161C2×C22⋊C4C2×D311yescharacteristic
162C2×C22⋊C4C2×D311yescharacteristic
163C2×C42—31no—
164#95—31no—
165#95—31no—
166#95—31no—
167#95—31no—
168#95—31no—
169#95—31no—
170#95C2×D311yescharacteristic
171#95C2×D311yescharacteristic
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×C3—21no—
183C23×C3C2×D412yes—
184C23×C3C2×D412yes—
185C23×C3#4112yes—
186C23×C3C2411yescharacteristic
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×D3C2×D412yes—
201C3×D4—44no—
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—44no—
217C2×C3×C4#4112yes—
218#67—28no—
219#67—44no—
220#67—44no—
221#67—44no—
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—21no—
234C2×Dic3—21no—
235C2×Dic3—21no—
236C2×Dic3—44no—
237C2×Dic3—44no—
238C2×Dic3C2×D412yes—
239C2×Dic3C2×D412yes—
240C2×Dic3C2×D412yes—
241C2×Dic3#4112yes—
242D12—44no—
243C4×D3—44no—
244C24—31no—
245C24—31no—
246C24C22×D311yescharacteristic
247C24C22×D311yescharacteristic
248C2×D4—22no—
249C2×D4—22no—
250C2×D4—22no—
251C2×D4—34no—
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—62no—
261C2×D4—62no—
262C2×D4—121no—
263C2×D4—121no—
264C2×D4—121no—
265C2×D4—121no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—31no—
269C22×C4—31no—
270C22×C4—31no—
271C22×C4—31no—
272C22×C4—34no—
273C22×C4—31no—
274C22×C4—31no—
275C22×C4—41no—
276C22×C4—62no—
277C22×C4—62no—
278C22×C4—62no—
279C22×C4—121no—
280C22×C4—121no—
281C22×C4—121no—
282C22×C4—121no—
283C22×C4—121no—
284C22×C4C22×D311yescharacteristic
285C22×C4C22×D311yescharacteristic
286C22×C4C22×D311yescharacteristic
287C22×C4C22×D311yescharacteristic
288C22×C4C22×D311yescharacteristic
289C4⋊C4—62no—
290C4⋊C4—62no—
291C4⋊C4—62no—
292C4⋊C4—62no—
293C22⋊C4—22no—
294C22⋊C4—22no—
295C22⋊C4—41no—
296C22⋊C4—62no—
297C22⋊C4—62no—
298C22⋊C4—62no—
299C22⋊C4—62no—
300C22⋊C4—62no—
301C22⋊C4—62no—
302C22⋊C4—62no—
303C22⋊C4—62no—
304C22⋊C4—121no—
305C42—62no—
306C22×C3—22no—
307C22×C3—22no—
308C22×C3—22no—
309C22×C3—22no—
310C22×C3—22no—
311C22×C3—22no—
312C22×C3—41no—
313C22×C3—41no—
314C22×C3—41no—
315C22×C3—41no—
316C22×C3—41no—
317C22×C3—41no—
318C22×C3—41no—
319C22×C3#12114yes—
320C22×C3C22×D411yescharacteristic
321C22×C3C22×D411yescharacteristic
322C22×C3C2×#4111yescharacteristic
323C22×C3C2×#4111yescharacteristic
324C22×C3C2×#4111yescharacteristic
325C22×C3H(5,𝔽2)11yescharacteristic
326C22×C3H(5,𝔽2)11yescharacteristic
327C2×D3—22no—
328C2×D3—22no—
329C2×D3—22no—
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—
340C2×D3—41no—
341C3×C4—22no—
342C3×C4—41no—
343C3×C4—41no—
344C3×C4—41no—
345C3×C4—41no—
346Dic3—22no—
347Dic3—22no—
348Dic3—22no—
349Dic3—22no—
350Dic3—41no—
351Dic3—41no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—21no—
362C23—21no—
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—
376C23—61no—
377C23#23512yes—
378C23D3×D412yes—
379C23D3×D412yes—
380C23C23×D311yescharacteristic
381D4—44no—
382D4—68no—
383D4—124no—
384D4—124no—
385D4—124no—
386D4—124no—
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—32no—
402C2×C4—32no—
403C2×C4—32no—
404C2×C4—32no—
405C2×C4—44no—
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—61no—
418C2×C4—61no—
419C2×C4—61no—
420C2×C4—124no—
421C2×C4—124no—
422C2×C4—124no—
423C2×C4#23712yes—
424C2×C3—24no—
425C2×C3—81no—
426C2×C3C2×#12111yescharacteristic
427C2×C3#53211yescharacteristic
428C2×C3#53411yescharacteristic
429C2×C3#54611yescharacteristic
430C2×C3#54611yescharacteristic
431C2×C3#55311yescharacteristic
432C2×C3#55311yescharacteristic
433D3—42no—
434D3—81no—
435C22—22no—
436C22—22no—
437C22—22no—
438C22—22no—
439C22—22no—
440C22—22no—
441C22—41no—
442C22—41no—
443C22—41no—
444C22—41no—
445C22—41no—
446C22—41no—
447C22—41no—
448C22—62no—
449C22—62no—
450C22—62no—
451C22—121no—
452C22—121no—
453C22—121no—
454C22—121no—
455C22—121no—
456C22—121no—
457C22—121no—
458C22—121no—
459C22—121no—
460C22—121no—
461C22—121no—
462C22#88414yes—
463C22C2×#23511yescharacteristic
464C22C2×D3×D411yescharacteristic
465C22C2×D3×D411yescharacteristic
466C22C2×#23711yescharacteristic
467C22#100411yescharacteristic
468C22D3×#4111yescharacteristic
469C22#100911yescharacteristic
470C4—22no—
471C4—41no—
472C4—41no—
473C4—41no—
474C4—41no—
475C4—62no—
476C4—62no—
477C4—62no—
478C4—62no—
479C4—121no—
480C4—121no—
481C3#254311yescharacteristic, complemented, Sylow
482C2—24no—
483C2—81no—
484C2—122no—
485C2—241no—
486C2C2×#88411yescharacteristic
487C2#554011yescharacteristic
488C2#556511yescharacteristic
489C2#559111yescharacteristic
490C2#559611yescharacteristic
491C2#560511yescharacteristic
492C2#565411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, cosocleC23×C3C24
FittingC3×#386C2
hypercenter#386D3
hypocenterC3#2543
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C2×#939C2semidirect
2. C2×#939C2semidirect
3. C2×#930C2semidirect
4. C2×#67⋊C4C2semidirect
5. C3×#386C2semidirect
6. C2×C3⋊#95C2semidirect
7. #4960C2semidirect
8. #4959C2semidirect
9. #4958C2semidirect
10. #4956C2semidirect
11. #4951C2semidirect
12. #4675C2semidirect
13. #4669C2semidirect
14. #4665C2semidirect
15. #4657C2semidirect
69. #386D3semidirect
97. C2×#67D4semidirect
103. C22×Dic3D4semidirect
481. C3#2543semidirect

Maximal subgroups

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

subgroupindex
C2×#9392
C2×#9302
C2×#67⋊C42
C3×#3862
C2×C3⋊#952
#49602
#49592
#49582
#49562
#49512
#46752
#46692
#46652
#46572
#25433