Finite Group Databasebeta

← #76387

Subgroups — #76387

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×#939C211yesmaximal, characteristic, complemented
2C2×#894C211yesmaximal, characteristic, complemented
3C3×#390C211yesmaximal, characteristic, complemented
4#5223C211yesmaximal, characteristic, complemented
5#4985C211yesmaximal, characteristic, complemented
6#4960C211yesmaximal, characteristic, complemented
7#4960C211yesmaximal, characteristic, complemented
8#4959C211yesmaximal, characteristic, complemented
9#4958C211yesmaximal, characteristic, complemented
10#4956C211yesmaximal, characteristic, complemented
11#4956C211yesmaximal, characteristic, complemented
12#4952C211yesmaximal, characteristic, complemented
13#4942C211yesmaximal, characteristic, complemented
14#4940C211yesmaximal, characteristic, complemented
15#4940C211yesmaximal, characteristic, complemented
16#2703—31nomaximal, Sylow
17C22×C3×D4C2211yescharacteristic
18C22×#67C2211yescharacteristic
19C22×#67C2211yescharacteristic
20C22×#67C2211yescharacteristic
21C22×#67C2211yescharacteristic
22C23×Dic3C2211yescharacteristic
23C22×D12C2211yescharacteristic
24C22×C4×D3C2211yescharacteristic
25C2×C3×C4⋊C4C2211yescharacteristic
26C2×C3×C22⋊C4C2211yescharacteristic
27C2×C3×C22⋊C4C2211yescharacteristic
28C2×C3×C22⋊C4C2211yescharacteristic
29C2×C3×C22⋊C4C2211yescharacteristic
30C2×C3×C42C2211yescharacteristic
31C2×#217C2211yescharacteristic
32C2×#217C2211yescharacteristic
33C2×#217C2211yescharacteristic
34#939—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×Dic3⋊C4C2211yescharacteristic
43C2×Dic3⋊C4C2211yescharacteristic
44C2×Dic3⋊C4C2211yescharacteristic
45#894—24no—
46C3⋊#95C2211yescharacteristic
47C3⋊#95C2211yescharacteristic
48C3⋊#95C2211yescharacteristic
49C3⋊#95C2211yescharacteristic
50C3⋊#95C2211yescharacteristic
51C3⋊#95C2211yescharacteristic
52C3⋊#95C2211yescharacteristic
53C3⋊#95C2211yescharacteristic
54C2×#123—31no—
55C2×#121—31no—
56#400—31no—
57#397—31no—
58#394—31no—
59#392—31no—
60#392—31no—
61#392—31no—
62#390D311yescharacteristic, complemented
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—22no—
75C2×C3×D4—41no—
76C22×C3×C4C2311yescharacteristic
77C22×C3×C4C2311yescharacteristic
78C22×C3×C4C2311yescharacteristic
79C22×C3×C4C2311yescharacteristic
80C22×C3×C4C2311yescharacteristic
81C2×#67—22no—
82C2×#67—22no—
83C2×#67—22no—
84C2×#67—22no—
85C2×#67—22no—
86C2×#67—41no—
87C2×#67—41no—
88C2×#67—41no—
89C2×#67—41no—
90C2×#67—41no—
91C2×#67—41no—
92C2×#67—41no—
93C22×Dic3—22no—
94C22×Dic3—22no—
95C22×Dic3—41no—
96C22×Dic3C2311yescharacteristic
97C22×Dic3C2311yescharacteristic
98C22×Dic3C2311yescharacteristic
99C22×Dic3C2311yescharacteristic
100C22×Dic3C2311yescharacteristic
101C22×Dic3C2311yescharacteristic
102C2×D12—22no—
103C2×D12—41no—
104C2×D12—41no—
105C2×C4×D3—22no—
106C2×C4×D3—41no—
107C2×C4×D3—41no—
108C3×C4⋊C4—22no—
109C3×C22⋊C4—41no—
110C3×C22⋊C4—41no—
111C3×C22⋊C4—41no—
112C3×C22⋊C4—41no—
113C3×C42—41no—
114#217—22no—
115#217—41no—
116#217—41no—
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)⋊C4D414yescomplemented
124Dic3⋊C4—22no—
125Dic3⋊C4—22no—
126Dic3⋊C4—41no—
127C22×D4—31no—
128C22×D4—31no—
129C22×D4—31no—
130C22×D4—31no—
131C22×D4—31no—
132C22×D4C2×D311yescharacteristic
133C23×C4—31no—
134C23×C4—31no—
135#123—64no—
136#121—64no—
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⋊C4C2×D311yescharacteristic
152C2×C22⋊C4C2×D311yescharacteristic
153C2×C22⋊C4C2×D311yescharacteristic
154C2×C22⋊C4C2×D311yescharacteristic
155C2×C42C2×D311yescharacteristic
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×C3#4112yes—
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×D3C2×D412yes—
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—21no—
208C2×C3×C4C2×D412yes—
209#67—44no—
210#67—44no—
211#67—44no—
212#67—44no—
213C2×Dic3—21no—
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—44no—
230C2×Dic3C2×D412yes—
231C2×Dic3#4112yes—
232D12—44no—
233C4×D3—44no—
234C24—31no—
235C24—31no—
236C24C22×D311yescharacteristic
237C24C22×D311yescharacteristic
238C2×D4—22no—
239C2×D4—22no—
240C2×D4—41no—
241C2×D4—62no—
242C2×D4—62no—
243C2×D4—62no—
244C2×D4—62no—
245C2×D4—62no—
246C2×D4—62no—
247C2×D4—121no—
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—31no—
257C22×C4—31no—
258C22×C4—31no—
259C22×C4—31no—
260C22×C4—31no—
261C22×C4—31no—
262C22×C4—62no—
263C22×C4—62no—
264C22×C4—62no—
265C22×C4—121no—
266C22×C4—121no—
267C22×C4—121no—
268C22×C4C22×D311yescharacteristic
269C22×C4C22×D311yescharacteristic
270C22×C4C22×D311yescharacteristic
271C22×C4C22×D311yescharacteristic
272C22×C4C22×D311yescharacteristic
273C4⋊C4—22no—
274C4⋊C4—62no—
275C4⋊C4—62no—
276C4⋊C4—121no—
277C22⋊C4—34no—
278C22⋊C4—41no—
279C22⋊C4—41no—
280C22⋊C4—41no—
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—
291C42—41no—
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—41no—
329C3×C4—41no—
330C3×C4—41no—
331C3×C4—41no—
332Dic3—22no—
333Dic3—22no—
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—
365C23#23512yes—
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—21no—
387C2×C4—32no—
388C2×C4—32no—
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×C4—124no—
407C2×C4D3×D412yes—
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—
447C22C2×#23511yescharacteristic
448C22C2×D3×D411yescharacteristic
449C22#100411yescharacteristic
450C22#100411yescharacteristic
451C22#100411yescharacteristic
452C22D3×#4111yescharacteristic
453C22#100911yescharacteristic
454C4—22no—
455C4—41no—
456C4—41no—
457C4—41no—
458C4—41no—
459C4—62no—
460C4—62no—
461C4—121no—
462C4—121no—
463C4—121no—
464C4—121no—
465C3#270311yescharacteristic, complemented, Sylow
466C2—42no—
467C2—81no—
468C2—122no—
469C2—241no—
470C2#549011yescharacteristic
471C2#554011yescharacteristic
472C2#556011yescharacteristic
473C2#561511yescharacteristic
474C2#562011yescharacteristic
475C2#567611yescharacteristic
476C2#571511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutator, socle, cosocleC23×C3C24
FittingC3×#390C2
hypercenter#390D3
hypocenterC3#2703
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#939C2semidirect
2. C2×#894C2semidirect
3. C3×#390C2semidirect
4. #5223C2semidirect
5. #4985C2semidirect
6. #4960C2semidirect
7. #4960C2semidirect
8. #4959C2semidirect
9. #4958C2semidirect
10. #4956C2semidirect
11. #4956C2semidirect
12. #4952C2semidirect
13. #4942C2semidirect
14. #4940C2semidirect
15. #4940C2semidirect
62. #390D3semidirect
123. (C2×D3)⋊C4D4semidirect
465. C3#2703semidirect

Maximal subgroups

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

subgroupindex
C2×#9392
C2×#8942
C3×#3902
#52232
#49852
#49602
#49592
#49582
#49562
#49522
#49422
#49402
#27033