Finite Group Databasebeta

← #75481

Subgroups — #75481

Order 384.

632 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#887C211yesmaximal, characteristic, complemented
2C2×#885C211yesmaximal, characteristic
3C2×#67⋊C4C211yesmaximal, characteristic
4C3×#388C211yesmaximal, characteristic, complemented
5#4989C211yesmaximal, characteristic, complemented
6#4957C211yesmaximal, characteristic
7#4946C211yesmaximal, characteristic, complemented
8#4944C211yesmaximal, characteristic, complemented
9Dic3×C22⋊C4C211yesmaximal, characteristic, complemented
10C4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
11C4×Dic3⋊C4C211yesmaximal, characteristic, complemented
12#4669C211yesmaximal, characteristic, complemented
13#4669C211yesmaximal, characteristic, complemented
14#4649C211yesmaximal, characteristic, complemented
15#4646C211yesmaximal, characteristic, complemented
16#2367—31nomaximal, Sylow
17C22×#67C2211yescharacteristic
18C23×Dic3C2211yescharacteristic
19C22×C4×D3C2211yescharacteristic
20C22×Dic6C2211yescharacteristic
21C2×C3×C4⋊C4C2211yescharacteristic
22C2×C3×C22⋊C4C2211yescharacteristic
23C2×C3×C22⋊C4C2211yescharacteristic
24C2×C3×C22⋊C4C2211yescharacteristic
25C2×C3×C42C2211yescharacteristic
26C2×#217C2211yescharacteristic
27C2×#217C2211yescharacteristic
28C2×(C2×D3)⋊C4C2211yescharacteristic
29C2×(C2×D3)⋊C4C2211yescharacteristic
30C2×(C2×D3)⋊C4C2211yescharacteristic
31C2×(C2×D3)⋊C4C2211yescharacteristic
32C2×(C2×D3)⋊C4C2211yescharacteristic
33C2×Dic3⋊C4C2211yescharacteristic
34C2×Dic3⋊C4C2211yescharacteristic
35C2×Dic3⋊C4C2211yescharacteristic
36C2×Dic3⋊C4C2211yescharacteristic
37C2×Dic3⋊C4C2211yescharacteristic
38C2×C4×Dic3C2211yescharacteristic
39C2×C4×Dic3C2211yescharacteristic
40C2×C4×Dic3C2211yescharacteristic
41C2×C4×Dic3C2211yescharacteristic
42C2×C4×Dic3C2211yescharacteristic
43C2×C4×Dic3C2211yescharacteristic
44#887—24no—
45#885C418yescomplemented
46#67⋊C4—24no—
47C3×#95C2211yescharacteristic
48C3×#95C2211yescharacteristic
49C3⋊#95C2211yescharacteristic
50C3⋊#95C2211yescharacteristic
51C3⋊#95C2211yescharacteristic
52C3⋊#95C2211yescharacteristic
53C3⋊#95C2211yescharacteristic
54C3⋊#95C2211yescharacteristic
55C2×#124—31no—
56C2×C4×Q8—31no—
57C2×C4×D4—31no—
58#391—31no—
59#390—31no—
60#388—31no—
61#388—31no—
62#388—31no—
63#388D311yescharacteristic, complemented
64#385—31no—
65#385—31no—
66C4×C4⋊C4—31no—
67C4×C4⋊C4—31no—
68C4×C22⋊C4—31no—
69C4×C22⋊C4—31no—
70C24×C3C2311yescharacteristic
71C23×D3C2311yescharacteristic
72C22×C3×C4C2311yescharacteristic
73C22×C3×C4C2311yescharacteristic
74C22×C3×C4C2311yescharacteristic
75C22×C3×C4C2311yescharacteristic
76C22×C3×C4C2311yescharacteristic
77C22×C3×C4C2311yescharacteristic
78C2×#67—22no—
79C2×#67—22no—
80C2×#67C2×C414yes—
81C22×Dic3—22no—
82C22×Dic3—22no—
83C22×Dic3—41no—
84C22×Dic3C2311yescharacteristic
85C22×Dic3C2311yescharacteristic
86C22×Dic3C2311yescharacteristic
87C22×Dic3C2311yescharacteristic
88C22×Dic3C2311yescharacteristic
89C22×Dic3C2311yescharacteristic
90C22×Dic3C2311yescharacteristic
91C2×C4×D3—22no—
92C2×C4×D3—22no—
93C2×C4×D3—41no—
94C2×Dic6—22no—
95C2×Dic6—22no—
96C2×Dic6C2×C414yescomplemented
97C3×C4⋊C4—22no—
98C3×C22⋊C4—22no—
99C3×C22⋊C4—41no—
100C3×C22⋊C4C2×C414yescomplemented
101C3×C42—41no—
102#217—22no—
103#217C2×C414yescomplemented
104(C2×D3)⋊C4—22no—
105(C2×D3)⋊C4—22no—
106(C2×D3)⋊C4—41no—
107(C2×D3)⋊C4C2×C414yescomplemented
108(C2×D3)⋊C4C2×C414yescomplemented
109Dic3⋊C4—22no—
110Dic3⋊C4—22no—
111Dic3⋊C4—22no—
112Dic3⋊C4—22no—
113Dic3⋊C4D414yes—
114C4×Dic3—22no—
115C4×Dic3—22no—
116C4×Dic3—22no—
117C4×Dic3—22no—
118C4×Dic3—41no—
119C4×Dic3C2×C414yescomplemented
120C22×Q8—31no—
121C22×D4—31no—
122C23×C4—31no—
123C23×C4—31no—
124#124—38no—
125C4×Q8—64no—
126C4×D4—64no—
127C2×C4⋊C4—31no—
128C2×C4⋊C4—31no—
129C2×C4⋊C4—31no—
130C2×C4⋊C4—31no—
131C2×C4⋊C4—31no—
132C2×C4⋊C4C2×D311yescharacteristic
133C2×C22⋊C4—31no—
134C2×C22⋊C4—31no—
135C2×C22⋊C4—31no—
136C2×C22⋊C4—31no—
137C2×C22⋊C4—31no—
138C2×C22⋊C4—31no—
139C2×C22⋊C4—31no—
140C2×C22⋊C4C2×D311yescharacteristic
141C2×C22⋊C4C2×D311yescharacteristic
142C2×C22⋊C4C2×D311yescharacteristic
143C2×C42—31no—
144C2×C42—31no—
145C2×C42—31no—
146C2×C42—31no—
147C2×C42—31no—
148C2×C42—31no—
149C2×C42C2×D311yescharacteristic
150#95—31no—
151#95—31no—
152#95—31no—
153#95—31no—
154#95—31no—
155#95—31no—
156#95C2×D311yescharacteristic
157#95C2×D311yescharacteristic
158C23×C3—21no—
159C23×C3—21no—
160C23×C3—21no—
161C23×C3—21no—
162C23×C3—21no—
163C23×C3—21no—
164C23×C3C22×C412yes—
165C23×C3C2411yescharacteristic
166C22×D3—21no—
167C22×D3—21no—
168C22×D3—21no—
169C22×D3—21no—
170C22×D3—21no—
171C22×D3—21no—
172C22×D3C22×C412yes—
173C2×C3×C4—21no—
174C2×C3×C4—21no—
175C2×C3×C4—21no—
176C2×C3×C4—21no—
177C2×C3×C4—21no—
178C2×C3×C4—21no—
179C2×C3×C4—21no—
180C2×C3×C4—21no—
181C2×C3×C4—21no—
182C2×C3×C4—21no—
183C2×C3×C4—21no—
184C2×C3×C4—21no—
185C2×C3×C4—21no—
186C2×C3×C4—21no—
187C2×C3×C4—21no—
188C2×C3×C4C22×C412yes—
189C2×C3×C4C22×C412yes—
190C2×C3×C4C2×D412yes—
191#67—28no—
192C2×Dic3—21no—
193C2×Dic3—21no—
194C2×Dic3—21no—
195C2×Dic3—21no—
196C2×Dic3—21no—
197C2×Dic3—21no—
198C2×Dic3—21no—
199C2×Dic3—21no—
200C2×Dic3—21no—
201C2×Dic3—21no—
202C2×Dic3—21no—
203C2×Dic3—21no—
204C2×Dic3—21no—
205C2×Dic3—44no—
206C2×Dic3C22×C412yes—
207C2×Dic3C22×C412yes—
208C2×Dic3C22×C412yes—
209C2×Dic3C2×D412yes—
210C2×Dic3C2×D412yes—
211C2×Dic3#4112yes—
212C2×Dic3#4112yes—
213C2×Dic3#4112yes—
214C4×D3—44no—
215Dic6—28no—
216C24—31no—
217C24C22×D311yescharacteristic
218C2×Q8—34no—
219C2×Q8—62no—
220C2×Q8—62no—
221C2×D4—34no—
222C2×D4—62no—
223C2×D4—62no—
224C22×C4—31no—
225C22×C4—31no—
226C22×C4—31no—
227C22×C4—31no—
228C22×C4—31no—
229C22×C4—31no—
230C22×C4—31no—
231C22×C4—62no—
232C22×C4—62no—
233C22×C4—62no—
234C22×C4—62no—
235C22×C4—121no—
236C22×C4—121no—
237C22×C4C22×D311yescharacteristic
238C22×C4C22×D311yescharacteristic
239C22×C4C22×D311yescharacteristic
240C22×C4C22×D311yescharacteristic
241C22×C4C22×D311yescharacteristic
242C22×C4C22×D311yescharacteristic
243C4⋊C4—22no—
244C4⋊C4—34no—
245C4⋊C4—62no—
246C4⋊C4—62no—
247C4⋊C4—62no—
248C4⋊C4—62no—
249C22⋊C4—22no—
250C22⋊C4—34no—
251C22⋊C4—34no—
252C22⋊C4—34no—
253C22⋊C4—41no—
254C22⋊C4—62no—
255C22⋊C4—62no—
256C22⋊C4—62no—
257C22⋊C4—121no—
258C22⋊C4C4×D314yescomplemented
259C42—34no—
260C42—41no—
261C42—62no—
262C42—62no—
263C42—62no—
264C42—62no—
265C42—121no—
266C22×C3—22no—
267C22×C3—22no—
268C22×C3—22no—
269C22×C3—41no—
270C22×C3—41no—
271C22×C3—41no—
272C22×C3—41no—
273C22×C3C23×C411yescharacteristic
274C22×C3C22×D411yescharacteristic
275C22×C3C2×#4111yescharacteristic
276C22×C3C2×#4111yescharacteristic
277C22×C3C2×#4111yescharacteristic
278C22×C3H(5,𝔽2)11yescharacteristic
279C22×C32−1+411yescharacteristic
280C2×D3—22no—
281C2×D3—22no—
282C2×D3—22no—
283C2×D3—41no—
284C2×D3—41no—
285C2×D3—41no—
286C2×D3—41no—
287C3×C4—22no—
288C3×C4—22no—
289C3×C4—22no—
290C3×C4—41no—
291C3×C4—41no—
292C3×C4—41no—
293Dic3—22no—
294Dic3—22no—
295Dic3—22no—
296Dic3—22no—
297Dic3—22no—
298Dic3—41no—
299Dic3C4×D414yes—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—21no—
306C23—32no—
307C23—61no—
308C23—61no—
309C23—61no—
310C23—61no—
311C23—61no—
312C23—61no—
313C23C2×C4×D312yes—
314C23C23×D311yescharacteristic
315Q8—68no—
316D4—68no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—32no—
333C2×C4—32no—
334C2×C4—32no—
335C2×C4—32no—
336C2×C4—32no—
337C2×C4—32no—
338C2×C4—32no—
339C2×C4—32no—
340C2×C4—61no—
341C2×C4—61no—
342C2×C4—61no—
343C2×C4—61no—
344C2×C4—61no—
345C2×C4—61no—
346C2×C4—61no—
347C2×C4—61no—
348C2×C4—61no—
349C2×C4—61no—
350C2×C4—61no—
351C2×C4—61no—
352C2×C4—61no—
353C2×C4—124no—
354C2×C4—124no—
355C2×C4C2×C4×D312yes—
356C2×C4C2×C4×D312yes—
357C2×C4D3×D412yes—
358C2×C3—42no—
359C2×C3C2×C4×D411yescharacteristic
360C2×C3C4×#4111yescharacteristic
361C2×C3#52011yescharacteristic
362C2×C3#54611yescharacteristic
363C2×C3#54811yescharacteristic
364C2×C3#55611yescharacteristic
365C2×C3#55911yescharacteristic
366D3—42no—
367C22—22no—
368C22—22no—
369C22—22no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—62no—
375C22—62no—
376C22—62no—
377C22—121no—
378C22—121no—
379C22—121no—
380C22—121no—
381C22C22×C4×D311yescharacteristic
382C22C2×D3×D411yescharacteristic
383C22#100411yescharacteristic
384C22D3×#4111yescharacteristic
385C22D3×#4111yescharacteristic
386C22D3×#4111yescharacteristic
387C22#101011yescharacteristic
388C4—22no—
389C4—22no—
390C4—22no—
391C4—34no—
392C4—41no—
393C4—41no—
394C4—41no—
395C4—62no—
396C4—62no—
397C4—62no—
398C4—62no—
399C4—62no—
400C4—121no—
401C3#236711yescharacteristic, complemented, Sylow
402C2—42no—
403C2—122no—
404C2#552211yescharacteristic
405C2C4×D3×D411yescharacteristic
406C2#554611yescharacteristic
407C2#561011yescharacteristic
408C2#566411yescharacteristic
409C2#567711yescharacteristic
410C2#570211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutatorC22×C3C23×C4
FittingC3×#388C2
socle, cosocleC23×C3C24
prime radicalC22×#67C22
hypercenter#388D3
hypocenterC3#2367
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#887C2semidirect
4. C3×#388C2semidirect
5. #4989C2semidirect
7. #4946C2semidirect
8. #4944C2semidirect
9. Dic3×C22⋊C4C2semidirect
10. C4×(C2×D3)⋊C4C2semidirect
11. C4×Dic3⋊C4C2semidirect
12. #4669C2semidirect
13. #4669C2semidirect
14. #4649C2semidirect
15. #4646C2semidirect
45. #885C4semidirect
63. #388D3semidirect
96. C2×Dic6C2×C4semidirect
100. C3×C22⋊C4C2×C4semidirect
103. #217C2×C4semidirect
107. (C2×D3)⋊C4C2×C4semidirect
108. (C2×D3)⋊C4C2×C4semidirect
119. C4×Dic3C2×C4semidirect
258. C22⋊C4C4×D3semidirect
401. C3#2367semidirect

Maximal subgroups

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

subgroupindex
C2×#8872
C2×#8852
C2×#67⋊C42
C3×#3882
#49892
#49572
#49462
#49442
Dic3×C22⋊C42
C4×(C2×D3)⋊C42
C4×Dic3⋊C42
#46692
#46492
#46462
#23673