Finite Group Databasebeta

← #82909

Subgroups — #82909

Order 384.

612 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#123C211yesmaximal, characteristic, complemented
2C2×#884C211yesmaximal, characteristic, complemented
3#5223C211yesmaximal, characteristic, complemented
4#5223C211yesmaximal, characteristic, complemented
5#5213C211yesmaximal, characteristic, complemented
6#5213C211yesmaximal, characteristic, complemented
7#4992C211yesmaximal, characteristic, complemented
8#4988C211yesmaximal, characteristic, complemented
9#4987C211yesmaximal, characteristic, complemented
10#4985C211yesmaximal, characteristic, complemented
11#4961C211yesmaximal, characteristic, complemented
12#4960C211yesmaximal, characteristic, complemented
13#4956C211yesmaximal, characteristic, complemented
14#4951C211yesmaximal, characteristic, complemented
15#4945C211yesmaximal, characteristic, complemented
16#2703—31nomaximal, Sylow
17C22×C3×D4C2211yescharacteristic
18C23×C3×C4C2211yescharacteristic
19C22×#67C2211yescharacteristic
20C22×#67C2211yescharacteristic
21C22×#67C2211yescharacteristic
22C22×#67C2211yescharacteristic
23C22×D12C2211yescharacteristic
24C22×C4×D3C2211yescharacteristic
25C3×#123—24no—
26C2×C3×C4⋊C4C2211yescharacteristic
27C2×C3×C4⋊C4C2211yescharacteristic
28C2×C3×C22⋊C4C2211yescharacteristic
29C2×C3×C22⋊C4C2211yescharacteristic
30C2×C3×C22⋊C4C2211yescharacteristic
31C2×#217C2211yescharacteristic
32C2×#217C2211yescharacteristic
33C2×#217C2211yescharacteristic
34C2×#217C2211yescharacteristic
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×C4×Dic3C2211yescharacteristic
45#884—24no—
46C3⋊#95C2211yescharacteristic
47C3⋊#95C2211yescharacteristic
48C3⋊#95C2211yescharacteristic
49C3⋊#95C2211yescharacteristic
50C3⋊#95C2211yescharacteristic
51C3⋊#95C2211yescharacteristic
52C3⋊#95C2211yescharacteristic
53C3⋊#95C2211yescharacteristic
54C2×#123D311yescharacteristic, complemented
55C2×#121—31no—
56#400—31no—
57#397—31no—
58#394—31no—
59#392—31no—
60#392—31no—
61#392—31no—
62#390—31no—
63#388—31no—
64#388—31no—
65#386—31no—
66#386—31no—
67#386—31no—
68#380—31no—
69C24×C3C2311yescharacteristic
70C24×C3C2311yescharacteristic
71C23×D3C2311yescharacteristic
72C23×D3C2311yescharacteristic
73C2×C3×D4—22no—
74C2×C3×D4—41no—
75C2×C3×D4—41no—
76C22×C3×C4—22no—
77C22×C3×C4—41no—
78C22×C3×C4—41no—
79C22×C3×C4C2311yescharacteristic
80C22×C3×C4C2311yescharacteristic
81C22×C3×C4C2311yescharacteristic
82C22×C3×C4C2311yescharacteristic
83C22×C3×C4C2311yescharacteristic
84C2×#67—22no—
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×#67—41no—
94C2×#67—41no—
95C2×#67—41no—
96C22×Dic3C2311yescharacteristic
97C22×Dic3C2311yescharacteristic
98C22×Dic3C2311yescharacteristic
99C22×Dic3C2311yescharacteristic
100C22×Dic3C2311yescharacteristic
101C22×Dic3C2311yescharacteristic
102C2×D12—22no—
103C2×D12—22no—
104C2×D12—41no—
105C2×C4×D3—22no—
106C2×C4×D3—22no—
107C2×C4×D3—41no—
108C3×C4⋊C4—22no—
109C3×C4⋊C4—22no—
110C3×C22⋊C4—22no—
111C3×C22⋊C4—22no—
112C3×C22⋊C4D414yescomplemented
113#217—22no—
114#217—41no—
115#217—41no—
116#217—41no—
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—
122(C2×D3)⋊C4—41no—
123(C2×D3)⋊C4—41no—
124C4⋊Dic3—41no—
125Dic3⋊C4—22no—
126C4×Dic3—41no—
127C22×D4—31no—
128C22×D4—31no—
129C22×D4—31no—
130C22×D4—31no—
131C22×D4—31no—
132C22×D4C2×D311yescharacteristic
133C23×C4—31no—
134C23×C4C2×D311yescharacteristic
135#123—24no—
136#121—64no—
137C2×C4⋊C4—31no—
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
154C2×C22⋊C4C2×D311yescharacteristic
155C2×C42—31no—
156#95—31no—
157#95—31no—
158#95—31no—
159#95—31no—
160#95—31no—
161#95—31no—
162#95—31no—
163#95—31no—
164C23×C3—21no—
165C23×C3—21no—
166C23×C3—21no—
167C23×C3—21no—
168C23×C3—21no—
169C23×C3—21no—
170C23×C3—21no—
171C23×C3—21no—
172C23×C3—21no—
173C23×C3—21no—
174C23×C3—21no—
175C23×C3—21no—
176C23×C3—21no—
177C23×C3C2×D412yes—
178C23×C3C2411yescharacteristic
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#4112yes—
193C3×D4—44no—
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—44no—
208C2×C3×C4C2×D412yes—
209C2×C3×C4C2×D412yes—
210#67—44no—
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×Dic3—21no—
228C2×Dic3—21no—
229C2×Dic3—21no—
230C2×Dic3—21no—
231C2×Dic3#4112yes—
232D12—44no—
233C4×D3—44no—
234C24—31no—
235C24—31no—
236C24C22×D311yescharacteristic
237C24C22×D311yescharacteristic
238C2×D4—22no—
239C2×D4—41no—
240C2×D4—41no—
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—
256C22×C4—22no—
257C22×C4—31no—
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×C4C22×D311yescharacteristic
269C22×C4C22×D311yescharacteristic
270C22×C4C22×D311yescharacteristic
271C22×C4C22×D311yescharacteristic
272C22×C4C22×D311yescharacteristic
273C4⋊C4—22no—
274C4⋊C4—22no—
275C4⋊C4—62no—
276C4⋊C4—121no—
277C22⋊C4—22no—
278C22⋊C4—22no—
279C22⋊C4—62no—
280C22⋊C4—62no—
281C22⋊C4—121no—
282C22⋊C4—121no—
283C22⋊C4—121no—
284C22⋊C4—121no—
285C22⋊C4—121no—
286C22⋊C4—121no—
287C22⋊C4—121no—
288C22⋊C4—121no—
289C22⋊C4—121no—
290C22⋊C4#6714yescomplemented
291C42—121no—
292C22×C3—22no—
293C22×C3—22no—
294C22×C3—22no—
295C22×C3—41no—
296C22×C3—41no—
297C22×C3—41no—
298C22×C3—41no—
299C22×C3—41no—
300C22×C3—41no—
301C22×C3—41no—
302C22×C3—41no—
303C22×C3—41no—
304C22×C3—41no—
305C22×C3—41no—
306C22×C3C22×D411yescharacteristic
307C22×C3C2×#4111yescharacteristic
308C22×C3C2×#4111yescharacteristic
309C22×C3H(5,𝔽2)11yescharacteristic
310C22×C3H(5,𝔽2)11yescharacteristic
311C22×C3H(5,𝔽2)11yescharacteristic
312C22×C3H(5,𝔽2)11yescharacteristic
313C2×D3—22no—
314C2×D3—22no—
315C2×D3—22no—
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—
327C3×C4—22no—
328C3×C4—22no—
329C3×C4—41no—
330C3×C4—41no—
331C3×C4—41no—
332Dic3—22no—
333Dic3—41no—
334Dic3—41no—
335Dic3—41no—
336Dic3—41no—
337Dic3—41no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—21no—
347C23—21no—
348C23—21no—
349C23—21no—
350C23—21no—
351C23—32no—
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—
365C23C2×#6712yes—
366C23C23×D311yescharacteristic
367D4—44no—
368D4—124no—
369D4—124no—
370D4—124no—
371D4—124no—
372D4—124no—
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—32no—
387C2×C4—44no—
388C2×C4—61no—
389C2×C4—61no—
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—61no—
404C2×C4—61no—
405C2×C4—124no—
406C2×C4C2×#6712yes—
407C2×C4C2×#6712yes—
408C2×C3—42no—
409C2×C3—81no—
410C2×C3#53511yescharacteristic
411C2×C3#53811yescharacteristic
412C2×C3#54011yescharacteristic
413C2×C3#54611yescharacteristic
414C2×C3#54611yescharacteristic
415C2×C3#55311yescharacteristic
416C2×C3#56011yescharacteristic
417D3—42no—
418D3—81no—
419C22—22no—
420C22—22no—
421C22—22no—
422C22—41no—
423C22—41no—
424C22—41no—
425C22—41no—
426C22—41no—
427C22—41no—
428C22—41no—
429C22—41no—
430C22—41no—
431C22—41no—
432C22—41no—
433C22—62no—
434C22—62no—
435C22—62no—
436C22—121no—
437C22—121no—
438C22—121no—
439C22—121no—
440C22—121no—
441C22—121no—
442C22—121no—
443C22—121no—
444C22—121no—
445C22—121no—
446C22—121no—
447C22#100411yescharacteristic
448C22#100411yescharacteristic
449C22D3×#4111yescharacteristic
450C22D3×#4111yescharacteristic
451C22#100911yescharacteristic
452C22#100911yescharacteristic
453C22C22×#6711yescharacteristic
454C4—22no—
455C4—22no—
456C4—41no—
457C4—41no—
458C4—41no—
459C4—62no—
460C4—121no—
461C4—121no—
462C4—121no—
463C4—121no—
464C4—121no—
465C3#270311yescharacteristic, complemented, Sylow
466C2—42no—
467C2—81no—
468C2—122no—
469C2—241no—
470C2#565711yescharacteristic
471C2#566111yescharacteristic
472C2#566311yescharacteristic
473C2#566611yescharacteristic
474C2#580511yescharacteristic
475C2#582911yescharacteristic
476C2#582911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, cosocleC23×C3C24
FittingC2×C3×#123C2
hypercenterC2×#123D3
hypocenterC3#2703
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. C2×C3×#123C2semidirect
2. C2×#884C2semidirect
3. #5223C2semidirect
4. #5223C2semidirect
5. #5213C2semidirect
6. #5213C2semidirect
7. #4992C2semidirect
8. #4988C2semidirect
9. #4987C2semidirect
10. #4985C2semidirect
11. #4961C2semidirect
12. #4960C2semidirect
13. #4956C2semidirect
14. #4951C2semidirect
15. #4945C2semidirect
54. C2×#123D3semidirect
112. C3×C22⋊C4D4semidirect
290. C22⋊C4#67semidirect
465. C3#2703semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#1232
C2×#8842
#52232
#52132
#49922
#49882
#49872
#49852
#49612
#49602
#49562
#49512
#49452
#27033