Finite Group Databasebeta

← #75910

Subgroups — #75910

Order 384.

598 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#894C211yesmaximal, characteristic, complemented
2C2×#884C211yesmaximal, characteristic, complemented
3C3×#388C211yesmaximal, characteristic, complemented
4#4990C211yesmaximal, characteristic, complemented
5#4961C211yesmaximal, characteristic, complemented
6#4960C211yesmaximal, characteristic, complemented
7#4960C211yesmaximal, characteristic, complemented
8#4959C211yesmaximal, characteristic, complemented
9#4957C211yesmaximal, characteristic, complemented
10#4939C211yesmaximal, characteristic, complemented
11C4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
12#4675C211yesmaximal, characteristic, complemented
13#4672C211yesmaximal, characteristic, complemented
14#4671C211yesmaximal, characteristic, complemented
15#4657C211yesmaximal, characteristic, complemented
16#2661—31nomaximal, Sylow
17C22×#67C2211yescharacteristic
18C22×#67C2211yescharacteristic
19C22×#67C2211yescharacteristic
20C22×D12C2211yescharacteristic
21C22×D12C2211yescharacteristic
22C22×D12C2211yescharacteristic
23C22×C4×D3C2211yescharacteristic
24C2×C3×C4⋊C4C2211yescharacteristic
25C2×C3×C22⋊C4C2211yescharacteristic
26C2×C3×C22⋊C4C2211yescharacteristic
27C2×C3×C22⋊C4C2211yescharacteristic
28C2×C3×C42C2211yescharacteristic
29C2×#217C2211yescharacteristic
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×C4⋊Dic3C2211yescharacteristic
42C2×Dic3⋊C4C2211yescharacteristic
43C2×Dic3⋊C4C2211yescharacteristic
44C2×Dic3⋊C4C2211yescharacteristic
45C2×C4×Dic3C2211yescharacteristic
46#894—24no—
47#884—24no—
48C3×#95C2211yescharacteristic
49C3×#95C2211yescharacteristic
50C3⋊#95C2211yescharacteristic
51C3⋊#95C2211yescharacteristic
52C3⋊#95C2211yescharacteristic
53C3⋊#95C2211yescharacteristic
54C2×#123—31no—
55C2×#121—31no—
56#398—31no—
57#397—31no—
58#394—31no—
59#394—31no—
60#394—31no—
61#392—31no—
62#392—31no—
63#392—31no—
64#390—31no—
65#390—31no—
66#388—31no—
67#388D311yescharacteristic, complemented
68C4×C22⋊C4—31no—
69C24×C3C2311yescharacteristic
70C23×D3C2311yescharacteristic
71C23×D3C2311yescharacteristic
72C23×D3C2311yescharacteristic
73C22×C3×C4C2311yescharacteristic
74C22×C3×C4C2311yescharacteristic
75C22×C3×C4C2311yescharacteristic
76C22×C3×C4C2311yescharacteristic
77C22×C3×C4C2311yescharacteristic
78C22×C3×C4C2311yescharacteristic
79C2×#67—22no—
80C2×#67—22no—
81C2×#67—22no—
82C2×#67—41no—
83C2×#67—41no—
84C2×#67—41no—
85C2×#67—41no—
86C2×#67—41no—
87C2×#67—41no—
88C22×Dic3C2311yescharacteristic
89C22×Dic3C2311yescharacteristic
90C22×Dic3C2311yescharacteristic
91C22×Dic3C2311yescharacteristic
92C22×Dic3C2311yescharacteristic
93C2×D12—22no—
94C2×D12—22no—
95C2×D12—22no—
96C2×D12—41no—
97C2×D12—41no—
98C2×D12—41no—
99C2×D12—41no—
100C2×D12—41no—
101C2×D12—41no—
102C2×C4×D3—41no—
103C2×C4×D3—41no—
104C2×C4×D3D414yescomplemented
105C3×C4⋊C4—22no—
106C3×C22⋊C4—22no—
107C3×C22⋊C4—22no—
108C3×C22⋊C4—41no—
109C3×C42—41no—
110#217—41no—
111(C2×D3)⋊C4—22no—
112(C2×D3)⋊C4—22no—
113(C2×D3)⋊C4—22no—
114(C2×D3)⋊C4—22no—
115(C2×D3)⋊C4—22no—
116(C2×D3)⋊C4—22no—
117(C2×D3)⋊C4—22no—
118(C2×D3)⋊C4—41no—
119(C2×D3)⋊C4—41no—
120(C2×D3)⋊C4—41no—
121(C2×D3)⋊C4—41no—
122C4⋊Dic3—41no—
123Dic3⋊C4—22no—
124Dic3⋊C4—22no—
125Dic3⋊C4—41no—
126C4×Dic3—41no—
127C22×D4—31no—
128C22×D4—31no—
129C22×D4—31no—
130C22×D4—31no—
131C22×D4—31no—
132C22×D4—31no—
133C23×C4—31no—
134#123—64no—
135#121—64no—
136C2×C4⋊C4—31no—
137C2×C4⋊C4—31no—
138C2×C4⋊C4—31no—
139C2×C4⋊C4—31no—
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⋊C4—31no—
153C2×C22⋊C4C2×D311yescharacteristic
154C2×C22⋊C4C2×D311yescharacteristic
155C2×C22⋊C4C2×D311yescharacteristic
156C2×C42—31no—
157C2×C42C2×D311yescharacteristic
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—21no—
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×D3—21no—
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×C4C2×D412yes—
210C2×C3×C4#4112yes—
211#67—44no—
212#67—44no—
213#67—44no—
214C2×Dic3—21no—
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×Dic3C2×D412yes—
228C2×Dic3#4112yes—
229D12—44no—
230D12—44no—
231D12—44no—
232C4×D3—44no—
233C24—31no—
234C24—31no—
235C24—31no—
236C24C22×D311yescharacteristic
237C2×D4—62no—
238C2×D4—62no—
239C2×D4—62no—
240C2×D4—62no—
241C2×D4—62no—
242C2×D4—62no—
243C2×D4—121no—
244C2×D4—121no—
245C2×D4—121no—
246C2×D4—121no—
247C2×D4—121no—
248C2×D4—121no—
249C2×D4—121no—
250C2×D4—121no—
251C2×D4—121no—
252C2×D4—121no—
253C2×D4—121no—
254C2×D4—121no—
255C22×C4—31no—
256C22×C4—31no—
257C22×C4—34no—
258C22×C4—31no—
259C22×C4—31no—
260C22×C4—31no—
261C22×C4—121no—
262C22×C4—121no—
263C22×C4C22×D311yescharacteristic
264C22×C4C22×D311yescharacteristic
265C22×C4C22×D311yescharacteristic
266C22×C4C22×D311yescharacteristic
267C22×C4C22×D311yescharacteristic
268C22×C4C22×D311yescharacteristic
269C4⋊C4—22no—
270C4⋊C4—62no—
271C4⋊C4—62no—
272C4⋊C4—121no—
273C4⋊C4—121no—
274C22⋊C4—22no—
275C22⋊C4—22no—
276C22⋊C4—41no—
277C22⋊C4—62no—
278C22⋊C4—62no—
279C22⋊C4—62no—
280C22⋊C4—62no—
281C22⋊C4—62no—
282C22⋊C4—62no—
283C22⋊C4—62no—
284C22⋊C4—121no—
285C22⋊C4—121no—
286C22⋊C4—121no—
287C22⋊C4—121no—
288C22⋊C4—121no—
289C42—41no—
290C42—121no—
291C22×C3—41no—
292C22×C3—41no—
293C22×C3—41no—
294C22×C3—41no—
295C22×C3—41no—
296C22×C3—41no—
297C22×C3—41no—
298C22×C3C22×D411yescharacteristic
299C22×C3C2×#4111yescharacteristic
300C22×C3C2×#4111yescharacteristic
301C22×C3H(5,𝔽2)11yescharacteristic
302C22×C3H(5,𝔽2)11yescharacteristic
303C22×C3H(5,𝔽2)11yescharacteristic
304C22×C3H(5,𝔽2)11yescharacteristic
305C2×D3—22no—
306C2×D3—22no—
307C2×D3—22no—
308C2×D3—41no—
309C2×D3—41no—
310C2×D3—41no—
311C2×D3—41no—
312C2×D3—41no—
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—
326C3×C4—22no—
327C3×C4—22no—
328C3×C4—41no—
329C3×C4—41no—
330C3×C4—41no—
331C3×C4—41no—
332Dic3—22no—
333Dic3—22no—
334Dic3—41no—
335Dic3—41no—
336Dic3—41no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—32no—
345C23—61no—
346C23—61no—
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—
365C23C23×D311yescharacteristic
366D4—124no—
367D4—124no—
368D4—124no—
369D4—124no—
370D4—124no—
371D4—124no—
372C2×C4—21no—
373C2×C4—21no—
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—32no—
389C2×C4—32no—
390C2×C4—61no—
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—124no—
404C2×C4#23512yes—
405C2×C4D3×D412yes—
406C2×C3—81no—
407C2×C3#53211yescharacteristic
408C2×C3#53411yescharacteristic
409C2×C3#53511yescharacteristic
410C2×C3#53811yescharacteristic
411C2×C3#53811yescharacteristic
412C2×C3#54011yescharacteristic
413C2×C3#54011yescharacteristic
414D3—42no—
415D3—81no—
416D3—81no—
417C22—41no—
418C22—41no—
419C22—41no—
420C22—41no—
421C22—41no—
422C22—41no—
423C22—41no—
424C22—62no—
425C22—62no—
426C22—62no—
427C22—121no—
428C22—121no—
429C22—121no—
430C22—121no—
431C22—121no—
432C22—121no—
433C22—121no—
434C22—121no—
435C22—121no—
436C22—121no—
437C22—121no—
438C22—121no—
439C22—121no—
440C22—121no—
441C22—121no—
442C22—121no—
443C22—121no—
444C22—121no—
445C22C2×#23511yescharacteristic
446C22C2×D3×D411yescharacteristic
447C22#100411yescharacteristic
448C22D3×#4111yescharacteristic
449C22#100911yescharacteristic
450C22#100911yescharacteristic
451C22#100911yescharacteristic
452C4—22no—
453C4—22no—
454C4—41no—
455C4—41no—
456C4—41no—
457C4—41no—
458C4—62no—
459C4—62no—
460C4—121no—
461C4—121no—
462C4—121no—
463C3#266111yescharacteristic, complemented, Sylow
464C2—81no—
465C2—122no—
466C2—241no—
467C2—241no—
468C2#553511yescharacteristic
469C2#554811yescharacteristic
470C2#556011yescharacteristic
471C2#560511yescharacteristic
472C2#566311yescharacteristic
473C2#567411yescharacteristic
474C2#570411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, cosocleC23×C3C24
FittingC3×#388C2
hypercenter#388D3
hypocenterC3#2661
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#894C2semidirect
2. C2×#884C2semidirect
3. C3×#388C2semidirect
4. #4990C2semidirect
5. #4961C2semidirect
6. #4960C2semidirect
7. #4960C2semidirect
8. #4959C2semidirect
9. #4957C2semidirect
10. #4939C2semidirect
11. C4×(C2×D3)⋊C4C2semidirect
12. #4675C2semidirect
13. #4672C2semidirect
14. #4671C2semidirect
15. #4657C2semidirect
67. #388D3semidirect
104. C2×C4×D3D4semidirect
463. C3#2661semidirect

Maximal subgroups

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

subgroupindex
C2×#8942
C2×#8842
C3×#3882
#49902
#49612
#49602
#49592
#49572
#49392
C4×(C2×D3)⋊C42
#46752
#46722
#46712
#46572
#26613