Finite Group Databasebeta

← #80533

Subgroups — #80533

Order 384.

496 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#916C211yesmaximal, characteristic, complemented
2C2×#912C211yesmaximal, characteristic, complemented
3#5668C211yesmaximal, characteristic, complemented
4C4×#237C211yesmaximal, characteristic, complemented
5C3×#463C211yesmaximal, characteristic, complemented
6#5162C211yesmaximal, characteristic, complemented
7#5150C211yesmaximal, characteristic, complemented
8#5054C211yesmaximal, characteristic, complemented
9#5016C211yesmaximal, characteristic, complemented
10#4845C211yesmaximal, characteristic, complemented
11D3×C4⋊C8C211yesmaximal, characteristic, complemented
12#4804C211yesmaximal, characteristic, complemented
13#4795C211yesmaximal, characteristic, complemented
14#4772C211yesmaximal, characteristic, complemented
15#4762C211yesmaximal, characteristic, complemented
16#3035—31nomaximal, Sylow
17C2×#239C2211yescharacteristic
18C2×#237C2211yescharacteristic
19C2×#237C2211yescharacteristic
20C2×C3×SD16C2211yescharacteristic
21C2×C3×D8C2211yescharacteristic
22C3×#124C2211yescharacteristic
23C3×C4×D4C2211yescharacteristic
24#944C2211yescharacteristic
25C2×#216C2211yescharacteristic
26#940C2211yescharacteristic
27D4×Dic3C2211yescharacteristic
28C2×#214C2211yescharacteristic
29C2×#214C2211yescharacteristic
30C2×#213C2211yescharacteristic
31C4×#67—21no—
32C2×C4×Dic3—21no—
33#916—24no—
34#912—24no—
35C2×Dic12C2211yescharacteristic
36C2×#204C2211yescharacteristic
37C2×D3×C8C2211yescharacteristic
38C2×D3×C8C2211yescharacteristic
39#892C2211yescharacteristic
40#887C2211yescharacteristic
41#884—21no—
42#884—21no—
43#67⋊C4—21no—
44#67⋊C4—21no—
45#67⋊C4—21no—
46#877—21no—
47#875C2211yescharacteristic
48C42×D3C2211yescharacteristic
49C4×Dic6C2211yescharacteristic
50C3×C4⋊C8C2211yescharacteristic
51C3×#103C2211yescharacteristic
52C3×#102C2211yescharacteristic
53#835C2211yescharacteristic
54#832C2211yescharacteristic
55#821C2211yescharacteristic
56#816C2211yescharacteristic
57Dic3⋊C8C2211yescharacteristic
58Dic3⋊C8C2211yescharacteristic
59#810C2211yescharacteristic
60#809C2211yescharacteristic
61C4⋊(C3⋊C8)C2211yescharacteristic
62C2×#135—31no—
63C2×#135—31no—
64#532—31no—
65C4×#41—31no—
66#464—31no—
67#464—31no—
68#463—31no—
69#463D311yescharacteristic, complemented
70#462—31no—
71#461—31no—
72#460—31no—
73#459—31no—
74C2×C4⋊C8—31no—
75#416—31no—
76#416—31no—
77C2×C3×Q8C2311yescharacteristic
78C2×C3×D4C2311yescharacteristic
79C2×C3×D4C2311yescharacteristic
80C22×C3×C4—21no—
81C2×#67—21no—
82C2×#67—21no—
83C2×#67—21no—
84C2×#67—21no—
85C22×Dic3—21no—
86C22×Dic3—21no—
87C22×Dic3—21no—
88#239—22no—
89#239—22no—
90#237—22no—
91#237—22no—
92#237—22no—
93#237D414yescomplemented
94C2×D12—21no—
95C2×D12C2311yescharacteristic
96C2×C4×D3—21no—
97C2×C4×D3D411yescharacteristic
98C2×C4×D3D411yescharacteristic
99C2×C4×D3C2311yescharacteristic
100C2×Dic6C2311yescharacteristic
101C2×Dic6C2311yescharacteristic
102C3×SD16—22no—
103C3×D8—22no—
104C2×C3×C8C2311yescharacteristic
105C2×C3×C8C2311yescharacteristic
106C3×C4⋊C4C2311yescharacteristic
107C3×C22⋊C4—21no—
108C3×C22⋊C4—21no—
109C3×C22⋊C4—21no—
110C3×C42C2311yescharacteristic
111#217—21no—
112#216—22no—
113#214—22no—
114#214—22no—
115#213—22no—
116(C2×D3)⋊C4—21no—
117(C2×D3)⋊C4—21no—
118(C2×D3)⋊C4—21no—
119C4⋊Dic3C2311yescharacteristic
120Dic3⋊C4—21no—
121Dic3⋊C4—21no—
122Dic3⋊C4—21no—
123Dic3⋊C4—21no—
124C4×Dic3—21no—
125C4×Dic3—21no—
126C4×Dic3—21no—
127C4×Dic3D411yescharacteristic
128C4×Dic3D411yescharacteristic
129C4×Dic3C2311yescharacteristic
130C2×C3⋊C8C2311yescharacteristic
131C2×C3⋊C8C2311yescharacteristic
132Dic12—22no—
133#204—22no—
134D3×C8—22no—
135D3×C8—22no—
136C2×#41—31no—
137C2×#41—31no—
138C2×#41—31no—
139#135—64no—
140#135—64no—
141C2×Q16—31no—
142C2×Q16—31no—
143C2×SD16—31no—
144C2×SD16—31no—
145C2×SD16—31no—
146C2×SD16C2×D311yescharacteristic
147C2×D8—31no—
148C2×D8C2×D311yescharacteristic
149C22×C8—31no—
150C22×C8—31no—
151C4⋊Q8—31no—
152#127—31no—
153#124—31no—
154#124C2×D311yescharacteristic
155#121—61no—
156#121—61no—
157C4×Q8—31no—
158C4×Q8—31no—
159C4×D4—31no—
160C4×D4—61no—
161C4×D4—61no—
162C4×D4—61no—
163C4×D4—61no—
164C4×D4C2×D311yescharacteristic
165#117—31no—
166#117—61no—
167C2×C42—31no—
168C2×C42—61no—
169C4⋊C8—31no—
170C4⋊C8—31no—
171C4⋊C8—31no—
172C4⋊C8C2×D311yescharacteristic
173#103—31no—
174#103—31no—
175#103—31no—
176#103C2×D311yescharacteristic
177#102—31no—
178#102—31no—
179#102—31no—
180#102C2×D311yescharacteristic
181C23×C3—21no—
182C23×C3—21no—
183C22×D3—21no—
184C22×D3C2×D411yescharacteristic
185C3×Q8—21no—
186C3×Q8—21no—
187C3×D4—21no—
188C3×D4—21no—
189C3×D4—21no—
190C3×D4C2×D412yes—
191C2×C3×C4—21no—
192C2×C3×C4—21no—
193C2×C3×C4—42no—
194C2×C3×C4C2×D411yescharacteristic
195C2×C3×C4C2×D411yescharacteristic
196C2×C3×C4C2411yescharacteristic
197#67—24no—
198#67—42no—
199#67—42no—
200#67—42no—
201C2×Dic3—21no—
202C2×Dic3—24no—
203C2×Dic3—21no—
204C2×Dic3—21no—
205C2×Dic3—42no—
206C2×Dic3—42no—
207C2×Dic3C2×D411yescharacteristic
208C2×Dic3C2×D411yescharacteristic
209C2×Dic3C2×D411yescharacteristic
210D12—21no—
211D12—21no—
212D12—42no—
213C4×D3—22no—
214C4×D3—41no—
215C4×D3—42no—
216C4×D3C2×D412yes—
217C4×D3#4112yes—
218Dic6—21no—
219Dic6—21no—
220Dic6—21no—
221Dic6C2×D412yes—
222C3×C8—21no—
223C3×C8—21no—
224C3⋊C8—21no—
225C3⋊C8—21no—
226#41—34no—
227#41—62no—
228#41—62no—
229#41—62no—
230#41—62no—
231#41—62no—
232C2×Q8—31no—
233C2×Q8—31no—
234C2×Q8C22×D311yescharacteristic
235C2×D4—31no—
236C2×D4—61no—
237C2×D4—61no—
238C2×D4—61no—
239C2×D4—61no—
240C2×D4—61no—
241C2×D4C22×D311yescharacteristic
242C2×D4C22×D311yescharacteristic
243C22×C4—21no—
244C22×C4—31no—
245C22×C4—31no—
246C22×C4—31no—
247C22×C4—61no—
248C22×C4—61no—
249C22×C4—61no—
250C22×C4—61no—
251Q16—62no—
252Q16—62no—
253SD16—22no—
254SD16—62no—
255SD16—62no—
256SD16—62no—
257D8—22no—
258D8—62no—
259C2×C8—31no—
260C2×C8—31no—
261C2×C8—62no—
262C2×C8—62no—
263C2×C8C22×D311yescharacteristic
264C2×C8C22×D311yescharacteristic
265C4⋊C4—31no—
266C4⋊C4—61no—
267C4⋊C4—61no—
268C4⋊C4—61no—
269C4⋊C4—61no—
270C4⋊C4C22×D311yescharacteristic
271C22⋊C4—21no—
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—61no—
275C22⋊C4—61no—
276C22⋊C4—61no—
277C22⋊C4—61no—
278C42—31no—
279C42—31no—
280C42—31no—
281C42—61no—
282C42—61no—
283C42—61no—
284C42C22×D311yescharacteristic
285C22×C3—22no—
286C22×C3—41no—
287C22×C3—41no—
288C22×C3—41no—
289C22×C3—41no—
290C22×C3—41no—
291C22×C3C22×D411yescharacteristic
292C2×D3—21no—
293C2×D3—21no—
294C2×D3—41no—
295C2×D3—41no—
296C2×D3—41no—
297C2×D3#12112yes—
298C3×C4—21no—
299C3×C4—21no—
300C3×C4—41no—
301C3×C4—41no—
302C3×C4C22×D411yescharacteristic
303C3×C4C2×#4111yescharacteristic
304Dic3—22no—
305Dic3—21no—
306Dic3—41no—
307Dic3—41no—
308Dic3#12112yes—
309Dic3#13512yescomplemented
310C23—21no—
311C23—21no—
312C23—31no—
313C23—61no—
314Q8—21no—
315Q8—21no—
316Q8—32no—
317Q8—61no—
318Q8—61no—
319Q8—61no—
320D4—21no—
321D4—21no—
322D4—21no—
323D4—64no—
324D4—61no—
325D4—61no—
326D4—122no—
327D4—122no—
328D4—122no—
329D4—122no—
330D4D3×D412yes—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—31no—
334C2×C4—31no—
335C2×C4—32no—
336C2×C4—32no—
337C2×C4—31no—
338C2×C4—42no—
339C2×C4—62no—
340C2×C4—64no—
341C2×C4—61no—
342C2×C4—61no—
343C2×C4—61no—
344C2×C4—121no—
345C2×C4—122no—
346C2×C4—122no—
347C2×C4—122no—
348C2×C4D3×D411yescharacteristic
349C2×C4D3×D411yescharacteristic
350C2×C4C23×D311yescharacteristic
351C8—21no—
352C8—21no—
353C8—61no—
354C8—61no—
355C2×C3—42no—
356C2×C3—81no—
357C2×C3C2×#12111yescharacteristic
358C2×C3C2×#13511yescharacteristic
359C2×C3#57511yescharacteristic
360D3—22no—
361D3—81no—
362C22—22no—
363C22—32no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—61no—
370C22—61no—
371C22—121no—
372C22—121no—
373C22—121no—
374C22C2×D3×D411yescharacteristic
375C4—21no—
376C4—21no—
377C4—32no—
378C4—32no—
379C4—41no—
380C4—41no—
381C4—61no—
382C4—62no—
383C4—121no—
384C4—121no—
385C4C2×D3×D411yescharacteristic
386C4D3×#4111yescharacteristic
387C3#303511yescharacteristic, complemented, Sylow
388C2—42no—
389C2—62no—
390C2—81no—
391C2—241no—
392C2D3×#12111yescharacteristic
393C2D3×#13511yescharacteristic
394C2#577311yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#463C2
socleC22×C3C22×D4
hypercenter#463D3
hypocenterC3#3035
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×#916C2semidirect
2. C2×#912C2semidirect
3. #5668C2semidirect
4. C4×#237C2semidirect
5. C3×#463C2semidirect
6. #5162C2semidirect
7. #5150C2semidirect
8. #5054C2semidirect
9. #5016C2semidirect
10. #4845C2semidirect
11. D3×C4⋊C8C2semidirect
12. #4804C2semidirect
13. #4795C2semidirect
14. #4772C2semidirect
15. #4762C2semidirect
69. #463D3semidirect
93. #237D4semidirect
309. Dic3#135semidirect
387. C3#3035semidirect

Maximal subgroups

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

subgroupindex
C2×#9162
C2×#9122
#56682
C4×#2372
C3×#4632
#51622
#51502
#50542
#50162
#48452
D3×C4⋊C82
#48042
#47952
#47722
#47622
#30353