Finite Group Databasebeta

← #79480

Subgroups — #79480

Order 384.

484 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#907C211yesmaximal, characteristic, complemented
2C2×#901C211yesmaximal, characteristic, complemented
3#5548C211yesmaximal, characteristic
4C3×#435C211yesmaximal, characteristic, complemented
5#5127C211yesmaximal, characteristic, complemented
6#5111C211yesmaximal, characteristic, complemented
7#5011C211yesmaximal, characteristic, complemented
8#4837C211yesmaximal, characteristic, complemented
9#4836C211yesmaximal, characteristic, complemented
10#4730C211yesmaximal, characteristic, complemented
11#4728C211yesmaximal, characteristic, complemented
12#4727C211yesmaximal, characteristic, complemented
13#4727C211yesmaximal, characteristic, complemented
14#4706C211yesmaximal, characteristic, complemented
15D3×#97C211yesmaximal, characteristic, complemented
16#2932—31nomaximal, Sylow
17C2×#235C2211yescharacteristic
18C2×#235C2211yescharacteristic
19C2×C3×M16C2211yescharacteristic
20C22×C3×C8C2211yescharacteristic
21C3×C4×D4C2211yescharacteristic
22#940C411yescharacteristic
23#938C411yescharacteristic
24C4×#67C2211yescharacteristic
25C4×#67C2211yescharacteristic
26C2×#208C2211yescharacteristic
27C22×C3⋊C8C2211yescharacteristic
28#907—24no—
29#901—24no—
30C2×ΓL(1,𝔽25)C2211yescharacteristic
31C2×ΓL(1,𝔽25)C2211yescharacteristic
32C2×ΓL(1,𝔽25)C2211yescharacteristic
33C2×ΓL(1,𝔽25)C2211yescharacteristic
34C2×D3×C8C2211yescharacteristic
35C2×D3×C8C2211yescharacteristic
36C2×D3×C8C2211yescharacteristic
37C2×D3×C8C2211yescharacteristic
38#895C411yescharacteristic
39#888C411yescharacteristic
40#885C411yescharacteristic
41#885C411yescharacteristic
42#884C411yescharacteristic
43#884C411yescharacteristic
44C4×D12C2211yescharacteristic
45C42×D3C2211yescharacteristic
46C3×C4⋊C8C2211yescharacteristic
47C3×C22⋊C8C2211yescharacteristic
48C3×C22⋊C8C2211yescharacteristic
49C3×#97C2211yescharacteristic
50#830C2211yescharacteristic
51#830C2211yescharacteristic
52(C2×D3)⋊C8C2211yescharacteristic
53(C2×D3)⋊C8C2211yescharacteristic
54(C2×D3)⋊C8C2211yescharacteristic
55(C2×D3)⋊C8C2211yescharacteristic
56#815C2211yescharacteristic
57#815C2211yescharacteristic
58Dic3⋊C8C2211yescharacteristic
59Dic3⋊C8C2211yescharacteristic
60C4⋊(C3⋊C8)C2211yescharacteristic
61#803C2211yescharacteristic
62C2×#131—31no—
63C2×#131—31no—
64#532—31no—
65#435—31no—
66#435—31no—
67#435—31no—
68#435—31no—
69#435—31no—
70#435—31no—
71#435—31no—
72#435D311yescharacteristic, complemented
73#423—31no—
74#408—31no—
75#408—31no—
76C2×#97—31no—
77C2×C3×D4C2×C411yescharacteristic
78C22×C3×C4C2311yescharacteristic
79C22×C3×C4C2311yescharacteristic
80C2×#67C2×C411yescharacteristic
81C2×#67C2×C411yescharacteristic
82C2×#67C2×C411yescharacteristic
83C2×#67C2×C411yescharacteristic
84C2×#67C2×C411yescharacteristic
85C2×#67C2×C411yescharacteristic
86#235—22no—
87#235—22no—
88#235—22no—
89#235—22no—
90C2×D12C2×C411yescharacteristic
91C2×D12C2×C411yescharacteristic
92C2×D12C2×C411yescharacteristic
93C2×C4×D3C2×C411yescharacteristic
94C2×C4×D3C2×C411yescharacteristic
95C2×C4×D3C2311yescharacteristic
96C2×C4×D3C2311yescharacteristic
97C2×C4×D3C2311yescharacteristic
98C2×Dic6C2×C411yescharacteristic
99C2×Dic6C2×C411yescharacteristic
100C3×M16—22no—
101C2×C3×C8—22no—
102C2×C3×C8C2311yescharacteristic
103C2×C3×C8C2311yescharacteristic
104C2×C3×C8C2311yescharacteristic
105C2×C3×C8C2311yescharacteristic
106C3×C4⋊C4C2×C411yescharacteristic
107C3×C22⋊C4C2×C411yescharacteristic
108C3×C22⋊C4C2×C411yescharacteristic
109C3×C42C2311yescharacteristic
110#217C2×C411yescharacteristic
111#217C2×C411yescharacteristic
112(C2×D3)⋊C4C2×C411yescharacteristic
113(C2×D3)⋊C4C2×C411yescharacteristic
114(C2×D3)⋊C4C2×C411yescharacteristic
115(C2×D3)⋊C4C2×C411yescharacteristic
116C4⋊Dic3C2×C411yescharacteristic
117Dic3⋊C4C2×C411yescharacteristic
118Dic3⋊C4C2×C411yescharacteristic
119C4×Dic3C2×C411yescharacteristic
120C4×Dic3C2×C411yescharacteristic
121C4×Dic3C2311yescharacteristic
122#208—22no—
123C2×C3⋊C8—22no—
124C2×C3⋊C8C2311yescharacteristic
125C2×C3⋊C8C2311yescharacteristic
126C2×C3⋊C8C2311yescharacteristic
127C2×C3⋊C8C2311yescharacteristic
128ΓL(1,𝔽25)—22no—
129ΓL(1,𝔽25)—22no—
130ΓL(1,𝔽25)—22no—
131ΓL(1,𝔽25)—22no—
132D3×C8—22no—
133D3×C8—22no—
134D3×C8—22no—
135D3×C8D414yescomplemented
136C2×#41—31no—
137C2×#41—31no—
138#131—64no—
139#131—64no—
140C2×M16—31no—
141C2×M16—31no—
142C2×M16—31no—
143C2×M16—31no—
144C2×M16—31no—
145C2×M16C2×D311yescharacteristic
146C22×C8—31no—
147C22×C8—31no—
148C22×C8—31no—
149C22×C8—31no—
150C22×C8—31no—
151C22×C8C2×D311yescharacteristic
152C4⋊Q8—31no—
153#127—31no—
154#124—31no—
155#124—31no—
156#121—31no—
157#121—31no—
158#121—31no—
159#121—31no—
160C4×D4—31no—
161C4×D4—31no—
162C4×D4—31no—
163C4×D4C2×D311yescharacteristic
164C2×C42—31no—
165C4⋊C8—31no—
166C4⋊C8—31no—
167C4⋊C8—31no—
168C4⋊C8C2×D311yescharacteristic
169C22⋊C8—31no—
170C22⋊C8—31no—
171C22⋊C8—31no—
172C22⋊C8—31no—
173C22⋊C8—31no—
174C22⋊C8—31no—
175C22⋊C8C2×D311yescharacteristic
176C22⋊C8C2×D311yescharacteristic
177#97—31no—
178#97—31no—
179#97—31no—
180#97C2×D311yescharacteristic
181C23×C3C22×C411yescharacteristic
182C23×C3C22×C411yescharacteristic
183C22×D3C22×C411yescharacteristic
184C22×D3C22×C411yescharacteristic
185C22×D3C22×C411yescharacteristic
186C3×D4—41no—
187C2×C3×C4—21no—
188C2×C3×C4—21no—
189C2×C3×C4—21no—
190C2×C3×C4—21no—
191C2×C3×C4C22×C411yescharacteristic
192C2×C3×C4C22×C411yescharacteristic
193C2×C3×C4C22×C411yescharacteristic
194C2×C3×C4C22×C411yescharacteristic
195C2×C3×C4C2411yescharacteristic
196#67—22no—
197#67—22no—
198#67—22no—
199#67—22no—
200#67—41no—
201#67—41no—
202C2×Dic3C22×C411yescharacteristic
203C2×Dic3C22×C411yescharacteristic
204C2×Dic3C22×C411yescharacteristic
205C2×Dic3C22×C411yescharacteristic
206C2×Dic3C22×C411yescharacteristic
207D12—22no—
208D12—22no—
209D12—41no—
210C4×D3—21no—
211C4×D3—21no—
212C4×D3—21no—
213C4×D3—21no—
214C4×D3—41no—
215C4×D3—41no—
216C4×D3C2×D412yes—
217C4×D3#4112yes—
218Dic6—22no—
219Dic6—22no—
220C3×C8—21no—
221C3×C8—21no—
222C3×C8—21no—
223C3×C8C2×D412yes—
224C3⋊C8—21no—
225C3⋊C8—21no—
226C3⋊C8—21no—
227C3⋊C8C2×D412yes—
228#41—62no—
229#41—62no—
230#41—62no—
231#41—62no—
232C2×Q8—31no—
233C2×Q8—31no—
234C2×D4—31no—
235C2×D4—31no—
236C2×D4—31no—
237C2×D4—31no—
238C2×D4—31no—
239C2×D4—31no—
240C2×D4—31no—
241C2×D4—31no—
242C2×D4—31no—
243C2×D4C4×D311yescharacteristic
244C22×C4—31no—
245C22×C4—31no—
246C22×C4—31no—
247C22×C4—31no—
248C22×C4—31no—
249C22×C4C22×D311yescharacteristic
250C22×C4C22×D311yescharacteristic
251M16—22no—
252M16—62no—
253M16—62no—
254M16—62no—
255M16—62no—
256M16—62no—
257C2×C8—22no—
258C2×C8—31no—
259C2×C8—34no—
260C2×C8—31no—
261C2×C8—31no—
262C2×C8—31no—
263C2×C8—62no—
264C2×C8—62no—
265C2×C8—62no—
266C2×C8—62no—
267C2×C8C22×D311yescharacteristic
268C2×C8C22×D311yescharacteristic
269C2×C8C22×D311yescharacteristic
270C2×C8C22×D311yescharacteristic
271C4⋊C4—31no—
272C4⋊C4—31no—
273C4⋊C4—31no—
274C4⋊C4C4×D311yescharacteristic
275C22⋊C4—31no—
276C22⋊C4—31no—
277C22⋊C4—31no—
278C22⋊C4—31no—
279C22⋊C4—31no—
280C22⋊C4—31no—
281C22⋊C4C4×D311yescharacteristic
282C22⋊C4C4×D311yescharacteristic
283C42—31no—
284C42—31no—
285C42—31no—
286C42C22×D311yescharacteristic
287C22×C3—21no—
288C22×C3—21no—
289C22×C3—21no—
290C22×C3—21no—
291C22×C3—21no—
292C22×C3—21no—
293C22×C3C23×C411yescharacteristic
294C2×D3—21no—
295C2×D3—21no—
296C2×D3—21no—
297C2×D3—21no—
298C2×D3—21no—
299C2×D3—21no—
300C2×D3—21no—
301C2×D3—21no—
302C2×D3C4×D412yes—
303C3×C4—21no—
304C3×C4—21no—
305C3×C4—21no—
306C3×C4—21no—
307C3×C4C22×D411yescharacteristic
308C3×C4C2×#4111yescharacteristic
309Dic3—21no—
310Dic3—21no—
311Dic3—21no—
312Dic3—21no—
313Dic3C4×D412yes—
314C23—31no—
315C23—31no—
316C23—31no—
317C23C2×C4×D311yescharacteristic
318C23C2×C4×D311yescharacteristic
319Q8—62no—
320Q8—62no—
321D4—41no—
322D4—62no—
323D4—62no—
324D4—62no—
325D4—62no—
326D4—62no—
327D4—62no—
328D4—121no—
329D4—121no—
330D4—121no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—31no—
336C2×C4—32no—
337C2×C4—32no—
338C2×C4—31no—
339C2×C4—31no—
340C2×C4—31no—
341C2×C4—31no—
342C2×C4—61no—
343C2×C4—61no—
344C2×C4—61no—
345C2×C4—61no—
346C2×C4—121no—
347C2×C4—121no—
348C2×C4C2×C4×D311yescharacteristic
349C2×C4C2×C4×D311yescharacteristic
350C2×C4C2×C4×D311yescharacteristic
351C2×C4C2×C4×D311yescharacteristic
352C2×C4C23×D311yescharacteristic
353C8—21no—
354C8—21no—
355C8—21no—
356C8—32no—
357C8—61no—
358C8—61no—
359C8—61no—
360C8D3×D412yes—
361C2×C3—41no—
362C2×C3—41no—
363C2×C3C2×C4×D411yescharacteristic
364C2×C3#56811yescharacteristic
365C2×C3#56811yescharacteristic
366D3—22no—
367D3—41no—
368D3—41no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—32no—
376C22—61no—
377C22—61no—
378C22—61no—
379C22—61no—
380C22—61no—
381C22—61no—
382C22—61no—
383C22—61no—
384C22C22×C4×D311yescharacteristic
385C4—21no—
386C4—21no—
387C4—21no—
388C4—21no—
389C4—32no—
390C4—61no—
391C4—61no—
392C4—61no—
393C4—61no—
394C4C2×D3×D411yescharacteristic
395C4D3×#4111yescharacteristic
396C3#293211yescharacteristic, complemented, Sylow
397C2—41no—
398C2—41no—
399C2—62no—
400C2—121no—
401C2—121no—
402C2C4×D3×D411yescharacteristic
403C2#574511yescharacteristic
404C2#575011yescharacteristic
subgroupG/H
center, FrattiniC2×C4C23×D3
commutator, socleC22×C3C23×C4
FittingC3×#435C2
prime radical#5548C2
cosocleC2×C3×C4C24
hypercenter#435D3
hypocenterC3#2932
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. C2×#907C2semidirect
2. C2×#901C2semidirect
4. C3×#435C2semidirect
5. #5127C2semidirect
6. #5111C2semidirect
7. #5011C2semidirect
8. #4837C2semidirect
9. #4836C2semidirect
10. #4730C2semidirect
11. #4728C2semidirect
12. #4727C2semidirect
13. #4727C2semidirect
14. #4706C2semidirect
15. D3×#97C2semidirect
72. #435D3semidirect
135. D3×C8D4semidirect
396. C3#2932semidirect

Maximal subgroups

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

subgroupindex
C2×#9072
C2×#9012
#55482
C3×#4352
#51272
#51112
#50112
#48372
#48362
#47302
#47282
#47272
#47062
D3×#972
#29323