Finite Group Databasebeta

← #74634

Subgroups — #74634

Order 384.

626 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#930C211yesmaximal, characteristic, complemented
2C2×#895C211yesmaximal, characteristic, complemented
3C3×#385C211yesmaximal, characteristic, complemented
4#5213C211yesmaximal, characteristic, complemented
5#4992C211yesmaximal, characteristic, complemented
6#4991C211yesmaximal, characteristic, complemented
7#4986C211yesmaximal, characteristic, complemented
8#4960C211yesmaximal, characteristic, complemented
9#4960C211yesmaximal, characteristic, complemented
10#4956C211yesmaximal, characteristic, complemented
11#4956C211yesmaximal, characteristic, complemented
12#4674C211yesmaximal, characteristic, complemented
13#4665C211yesmaximal, characteristic, complemented
14#4665C211yesmaximal, characteristic, complemented
15#4664C211yesmaximal, characteristic, complemented
16#2688—31nomaximal, Sylow
17C23×C3×C4C2211yescharacteristic
18C22×#67C2211yescharacteristic
19C22×#67C2211yescharacteristic
20C22×#67C2211yescharacteristic
21C22×D12C2211yescharacteristic
22C22×D12C2211yescharacteristic
23C22×D12C2211yescharacteristic
24C22×C4×D3C2211yescharacteristic
25C22×C4×D3C2211yescharacteristic
26C2×C3×C4⋊C4C2211yescharacteristic
27C2×C3×C4⋊C4C2211yescharacteristic
28C2×C3×C22⋊C4C2211yescharacteristic
29C2×C3×C22⋊C4C2211yescharacteristic
30C2×#217C2211yescharacteristic
31#930—24no—
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×C4⋊Dic3C2211yescharacteristic
43#895—24no—
44C3×#95C2211yescharacteristic
45C3×#95C2211yescharacteristic
46C3⋊#95C2211yescharacteristic
47C3⋊#95C2211yescharacteristic
48C3⋊#95C2211yescharacteristic
49C3⋊#95C2211yescharacteristic
50C3⋊#95C2211yescharacteristic
51C3⋊#95C2211yescharacteristic
52C3⋊#95C2211yescharacteristic
53C3⋊#95C2211yescharacteristic
54C2×#121—31no—
55C2×#121—31no—
56#400—31no—
57#397—31no—
58#397—31no—
59#394—31no—
60#392—31no—
61#392—31no—
62#386—31no—
63#386—31no—
64#386—31no—
65#386—31no—
66#386—31no—
67#385D311yescharacteristic, complemented
68#381—31no—
69C24×C3C2311yescharacteristic
70C23×D3C2311yescharacteristic
71C23×D3C2311yescharacteristic
72C23×D3C2311yescharacteristic
73C22×C3×C4—22no—
74C22×C3×C4—41no—
75C22×C3×C4—41no—
76C22×C3×C4C2311yescharacteristic
77C22×C3×C4C2311yescharacteristic
78C22×C3×C4C2311yescharacteristic
79C22×C3×C4C2311yescharacteristic
80C22×C3×C4C2311yescharacteristic
81C22×C3×C4C2311yescharacteristic
82C2×#67—22no—
83C2×#67—22no—
84C2×#67—22no—
85C2×#67—22no—
86C2×#67—22no—
87C2×#67—41no—
88C2×#67—41no—
89C2×#67—41no—
90C2×#67—41no—
91C22×Dic3C2311yescharacteristic
92C22×Dic3C2311yescharacteristic
93C22×Dic3C2311yescharacteristic
94C22×Dic3C2311yescharacteristic
95C22×Dic3C2311yescharacteristic
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×D12D414yescomplemented
105C2×C4×D3—22no—
106C2×C4×D3—22no—
107C2×C4×D3—41no—
108C2×C4×D3—41no—
109C2×C4×D3—41no—
110C2×C4×D3—41no—
111C3×C4⋊C4—22no—
112C3×C4⋊C4—41no—
113C3×C22⋊C4—22no—
114C3×C22⋊C4—41no—
115#217—41no—
116(C2×D3)⋊C4—22no—
117(C2×D3)⋊C4—22no—
118(C2×D3)⋊C4—22no—
119(C2×D3)⋊C4—22no—
120(C2×D3)⋊C4—41no—
121(C2×D3)⋊C4—41no—
122(C2×D3)⋊C4—41no—
123(C2×D3)⋊C4—41no—
124(C2×D3)⋊C4—41no—
125(C2×D3)⋊C4—41no—
126C4⋊Dic3—22no—
127C22×D4—31no—
128C22×D4—31no—
129C22×D4—31no—
130C22×D4—31no—
131C22×D4—31no—
132C22×D4—31no—
133C23×C4—31no—
134C23×C4—31no—
135C23×C4C2×D311yescharacteristic
136#121—64no—
137#121—64no—
138C2×C4⋊C4—31no—
139C2×C4⋊C4C2×D311yescharacteristic
140C2×C4⋊C4C2×D311yescharacteristic
141C2×C22⋊C4—31no—
142C2×C22⋊C4—31no—
143C2×C22⋊C4—31no—
144C2×C22⋊C4—31no—
145C2×C22⋊C4—31no—
146C2×C22⋊C4—31no—
147C2×C22⋊C4—31no—
148C2×C22⋊C4—31no—
149C2×C22⋊C4—31no—
150C2×C22⋊C4—31no—
151C2×C22⋊C4—31no—
152C2×C22⋊C4C2×D311yescharacteristic
153C2×C22⋊C4C2×D311yescharacteristic
154#95—31no—
155#95—31no—
156#95—31no—
157#95—31no—
158#95—31no—
159#95—31no—
160#95—31no—
161#95—31no—
162#95C2×D311yescharacteristic
163#95C2×D311yescharacteristic
164C23×C3—21no—
165C23×C3—21no—
166C23×C3—21no—
167C23×C3—21no—
168C23×C3—21no—
169C23×C3—21no—
170C23×C3#4112yes—
171C23×C3C2411yescharacteristic
172C22×D3—21no—
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×D3C2×D412yes—
192C22×D3C2×D412yes—
193C2×C3×C4—21no—
194C2×C3×C4—21no—
195C2×C3×C4—21no—
196C2×C3×C4—21no—
197C2×C3×C4—21no—
198C2×C3×C4—21no—
199C2×C3×C4—21no—
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—44no—
210C2×C3×C4C2×D412yes—
211C2×C3×C4#4112yes—
212#67—44no—
213#67—44no—
214#67—44no—
215C2×Dic3—21no—
216C2×Dic3—21no—
217C2×Dic3—21no—
218C2×Dic3—21no—
219C2×Dic3—21no—
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—
230D12—44no—
231D12—44no—
232D12—44no—
233C4×D3—44no—
234C4×D3—44no—
235C24—31no—
236C24—31no—
237C24—31no—
238C24C22×D311yescharacteristic
239C2×D4—34no—
240C2×D4—62no—
241C2×D4—62no—
242C2×D4—62no—
243C2×D4—62no—
244C2×D4—62no—
245C2×D4—62no—
246C2×D4—62no—
247C2×D4—62no—
248C2×D4—121no—
249C2×D4—121no—
250C2×D4—121no—
251C2×D4—121no—
252C2×D4—121no—
253C2×D4—121no—
254C2×D4—121no—
255C2×D4—121no—
256C2×D4—121no—
257C22×C4—22no—
258C22×C4—31no—
259C22×C4—31no—
260C22×C4—31no—
261C22×C4—31no—
262C22×C4—31no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4—62no—
266C22×C4—62no—
267C22×C4—121no—
268C22×C4—121no—
269C22×C4—121no—
270C22×C4—121no—
271C22×C4C22×D311yescharacteristic
272C22×C4C22×D311yescharacteristic
273C22×C4C22×D311yescharacteristic
274C22×C4C22×D311yescharacteristic
275C22×C4C22×D311yescharacteristic
276C22×C4C22×D311yescharacteristic
277C4⋊C4—22no—
278C4⋊C4—41no—
279C4⋊C4—62no—
280C22⋊C4—22no—
281C22⋊C4—41no—
282C22⋊C4—62no—
283C22⋊C4—62no—
284C22⋊C4—62no—
285C22⋊C4—62no—
286C22⋊C4—121no—
287C22⋊C4—121no—
288C22⋊C4—121no—
289C22⋊C4—121no—
290C22⋊C4—121no—
291C22⋊C4—121no—
292C22⋊C4—121no—
293C22×C3—22no—
294C22×C3—22no—
295C22×C3—22no—
296C22×C3—41no—
297C22×C3—41no—
298C22×C3—41no—
299C22×C3—41no—
300C22×C3C22×D411yescharacteristic
301C22×C3C2×#4111yescharacteristic
302C22×C3C2×#4111yescharacteristic
303C22×C3H(5,𝔽2)11yescharacteristic
304C22×C3H(5,𝔽2)11yescharacteristic
305C22×C3H(5,𝔽2)11yescharacteristic
306C22×C3H(5,𝔽2)11yescharacteristic
307C2×D3—22no—
308C2×D3—22no—
309C2×D3—22no—
310C2×D3—22no—
311C2×D3—22no—
312C2×D3—22no—
313C2×D3—41no—
314C2×D3—41no—
315C2×D3—41no—
316C2×D3—41no—
317C2×D3—41no—
318C2×D3—41no—
319C2×D3—41no—
320C2×D3—41no—
321C2×D3—41no—
322C2×D3—41no—
323C2×D3—41no—
324C2×D3—41no—
325C2×D3—41no—
326C2×D3—41no—
327C2×D3—41no—
328C3×C4—22no—
329C3×C4—22no—
330C3×C4—41no—
331C3×C4—41no—
332C3×C4—41no—
333C3×C4—41no—
334Dic3—41no—
335Dic3—41no—
336Dic3—41no—
337Dic3—41no—
338Dic3—41no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—32no—
346C23—32no—
347C23—61no—
348C23—61no—
349C23—61no—
350C23—61no—
351C23—61no—
352C23—61no—
353C23—61no—
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#23912yes—
367C23C23×D311yescharacteristic
368D4—124no—
369D4—124no—
370D4—124no—
371D4—124no—
372D4—124no—
373D4—124no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—44no—
391C2×C4—61no—
392C2×C4—61no—
393C2×C4—61no—
394C2×C4—61no—
395C2×C4—61no—
396C2×C4—61no—
397C2×C4—61no—
398C2×C4—61no—
399C2×C4—61no—
400C2×C4—61no—
401C2×C4—61no—
402C2×C4—61no—
403C2×C4—61no—
404C2×C4—61no—
405C2×C4—61no—
406C2×C4—124no—
407C2×C4—124no—
408C2×C4#23512yes—
409C2×C4D3×D412yes—
410C2×C3—42no—
411C2×C3#53411yescharacteristic
412C2×C3#53811yescharacteristic
413C2×C3#54011yescharacteristic
414C2×C3#54611yescharacteristic
415C2×C3#54611yescharacteristic
416C2×C3#55311yescharacteristic
417C2×C3#56011yescharacteristic
418D3—42no—
419D3—42no—
420D3—81no—
421C22—22no—
422C22—22no—
423C22—22no—
424C22—41no—
425C22—41no—
426C22—41no—
427C22—41no—
428C22—62no—
429C22—62no—
430C22—62no—
431C22—62no—
432C22—62no—
433C22—62no—
434C22—121no—
435C22—121no—
436C22—121no—
437C22—121no—
438C22—121no—
439C22—121no—
440C22—121no—
441C22—121no—
442C22—121no—
443C22—121no—
444C22—121no—
445C22—121no—
446C22—121no—
447C22—121no—
448C22—121no—
449C22C2×#23511yescharacteristic
450C22C2×D3×D411yescharacteristic
451C22#100411yescharacteristic
452C22#100411yescharacteristic
453C22C2×#23911yescharacteristic
454C22#100911yescharacteristic
455C22#100911yescharacteristic
456C4—22no—
457C4—22no—
458C4—41no—
459C4—41no—
460C4—41no—
461C4—41no—
462C4—121no—
463C4—121no—
464C4—121no—
465C4—121no—
466C4—121no—
467C3#268811yescharacteristic, complemented, Sylow
468C2—42no—
469C2—122no—
470C2—122no—
471C2—241no—
472C2#551411yescharacteristic
473C2#555011yescharacteristic
474C2#556211yescharacteristic
475C2#558911yescharacteristic
476C2#563011yescharacteristic
477C2#564411yescharacteristic
478C2#566611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, cosocleC23×C3C24
FittingC3×#385C2
hypercenter#385D3
hypocenterC3#2688
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. C2×#930C2semidirect
2. C2×#895C2semidirect
3. C3×#385C2semidirect
4. #5213C2semidirect
5. #4992C2semidirect
6. #4991C2semidirect
7. #4986C2semidirect
8. #4960C2semidirect
9. #4960C2semidirect
10. #4956C2semidirect
11. #4956C2semidirect
12. #4674C2semidirect
13. #4665C2semidirect
14. #4665C2semidirect
15. #4664C2semidirect
67. #385D3semidirect
104. C2×D12D4semidirect
467. C3#2688semidirect

Maximal subgroups

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

subgroupindex
C2×#9302
C2×#8952
C3×#3852
#52132
#49922
#49912
#49862
#49602
#49562
#46742
#46652
#46642
#26883