Finite Group Databasebeta

← #83547

Subgroups — #83547

Order 384.

488 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#548C211yesmaximal, characteristic, complemented
2C2×#950C211yesmaximal, characteristic, complemented
3C2×#942C211yesmaximal, characteristic, complemented
4#5553C211yesmaximal, characteristic, complemented
5#5238C211yesmaximal, characteristic, complemented
6#5227C211yesmaximal, characteristic, complemented
7#5058C211yesmaximal, characteristic, complemented
8#5054C211yesmaximal, characteristic, complemented
9#5048C211yesmaximal, characteristic, complemented
10#5047C211yesmaximal, characteristic, complemented
11#5039C211yesmaximal, characteristic, complemented
12#5037C211yesmaximal, characteristic, complemented
13#5030C211yesmaximal, characteristic, complemented
14#5027C211yesmaximal, characteristic, complemented
15#5011C211yesmaximal, characteristic, complemented
16#3271—31nomaximal, Sylow
17C2×C3×#41C2211yescharacteristic
18C22×C3×Q8C2211yescharacteristic
19C2×#235C2211yescharacteristic
20C2×#235C2211yescharacteristic
21C3×#124—21no—
22C3×#124C2211yescharacteristic
23C3×C22⋊Q8—21no—
24C3×C22⋊Q8C2211yescharacteristic
25C3×#121—21no—
26C3×#121C2211yescharacteristic
27C3×C4×Q8C2211yescharacteristic
28C3×C4×D4—21no—
29C3×C4×D4C2211yescharacteristic
30#950—24no—
31C2×#216C2211yescharacteristic
32C2×#216C2211yescharacteristic
33#942—24no—
34C2×#215C2211yescharacteristic
35C2×#215C2211yescharacteristic
36C2×#215C2211yescharacteristic
37C2×#215C2211yescharacteristic
38#940—21no—
39C2×#214C2211yescharacteristic
40C2×#213C2211yescharacteristic
41C2×#213C2211yescharacteristic
42#930C2211yescharacteristic
43#930C2211yescharacteristic
44C2×#208C2211yescharacteristic
45C22×C3⋊C8C2211yescharacteristic
46#893—21no—
47#884—21no—
48#884—21no—
49#874C2211yescharacteristic
50C4×Dic6C2211yescharacteristic
51#835C2211yescharacteristic
52#835C2211yescharacteristic
53#832C2211yescharacteristic
54#830C2211yescharacteristic
55#830C2211yescharacteristic
56#810C2211yescharacteristic
57#809C2211yescharacteristic
58#809C2211yescharacteristic
59#808C2211yescharacteristic
60C4⋊(C3⋊C8)C2211yescharacteristic
61#803C2211yescharacteristic
62C2×#137—31no—
63C2×#135—31no—
64#550—31no—
65#548D311yescharacteristic, complemented
66#496—31no—
67#469—31no—
68#465—31no—
69#464—31no—
70#460—31no—
71#452—31no—
72#449—31no—
73#449—31no—
74#448—31no—
75#441—31no—
76#435—31no—
77C3×#41—22no—
78C3×#41—41no—
79C2×C3×Q8—21no—
80C2×C3×Q8—22no—
81C2×C3×Q8—41no—
82C2×C3×Q8C2311yescharacteristic
83C2×C3×Q8C2311yescharacteristic
84C2×C3×D4—21no—
85C2×C3×D4—21no—
86C2×C3×D4D411yescharacteristic
87C2×C3×D4C2311yescharacteristic
88C22×C3×C4—21no—
89C22×C3×C4—21no—
90C22×C3×C4C2311yescharacteristic
91C22×C3×C4C2311yescharacteristic
92C2×#67—21no—
93C2×#67—21no—
94C2×#67—21no—
95C2×#67—21no—
96#235—22no—
97#235—22no—
98#235—41no—
99#235—41no—
100C2×D12—21no—
101C2×D12—21no—
102C2×D12C2311yescharacteristic
103C2×D12C2311yescharacteristic
104C2×C4×D3—21no—
105C2×C4×D3—21no—
106C2×Dic6C2311yescharacteristic
107C3×C4⋊C4—21no—
108C3×C4⋊C4—21no—
109C3×C4⋊C4D411yescharacteristic
110C3×C4⋊C4C2311yescharacteristic
111C3×C22⋊C4—21no—
112C3×C22⋊C4—21no—
113C3×C22⋊C4—21no—
114C3×C22⋊C4—21no—
115C3×C22⋊C4D411yescharacteristic
116C3×C22⋊C4D411yescharacteristic
117C3×C42—21no—
118C3×C42C2311yescharacteristic
119#216—22no—
120#216D414yescomplemented
121#215—22no—
122#215—22no—
123#215—22no—
124#215—41no—
125#214—22no—
126#213—22no—
127#213—41no—
128(C2×D3)⋊C4—21no—
129(C2×D3)⋊C4—21no—
130C4⋊Dic3C2311yescharacteristic
131Dic3⋊C4—21no—
132C4×Dic3—21no—
133#208—22no—
134C2×C3⋊C8—22no—
135C2×C3⋊C8C2311yescharacteristic
136C2×C3⋊C8C2311yescharacteristic
137C2×C3⋊C8C2311yescharacteristic
138C2×C3⋊C8C2311yescharacteristic
139C2×#41—31no—
140C2×#41—31no—
141C2×#41C2×D311yescharacteristic
142C22×Q8C2×D311yescharacteristic
143#137—64no—
144#135—64no—
145C2×Q16—31no—
146C2×Q16—31no—
147C2×SD16—31no—
148C2×SD16—31no—
149C2×SD16—31no—
150C2×SD16—31no—
151C2×SD16—31no—
152C2×D8—31no—
153C2×D8—31no—
154C2×M16—31no—
155C22×C8—31no—
156#127—31no—
157#127—61no—
158#124—21no—
159#124C2×D311yescharacteristic
160C22⋊Q8—21no—
161C22⋊Q8C2×D311yescharacteristic
162#121—21no—
163#121—31no—
164#121—31no—
165#121—61no—
166#121—61no—
167#121C2×D311yescharacteristic
168C4×Q8—31no—
169C4×Q8C2×D311yescharacteristic
170C4×D4—21no—
171C4×D4—61no—
172C4×D4C2×D311yescharacteristic
173#106—31no—
174C4⋊C8—31no—
175#103—31no—
176#103—31no—
177#103—31no—
178#102—31no—
179#102—31no—
180#102—31no—
181C22⋊C8—31no—
182C22⋊C8—31no—
183#97—31no—
184C23×C3—21no—
185C23×C3C2×D411yescharacteristic
186C23×C3C2×D411yescharacteristic
187C22×D3—21no—
188C22×D3—21no—
189C3×Q8—21no—
190C3×Q8—21no—
191C3×Q8—21no—
192C3×Q8—42no—
193C3×Q8C2×D412yes—
194C3×D4—21no—
195C3×D4—21no—
196C3×D4—41no—
197C3×D4—42no—
198C3×D4—42no—
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—42no—
207C2×C3×C4—42no—
208C2×C3×C4C2×D411yescharacteristic
209C2×C3×C4C2×D411yescharacteristic
210C2×C3×C4C2×D411yescharacteristic
211C2×C3×C4C2×D411yescharacteristic
212C2×C3×C4C2411yescharacteristic
213#67—42no—
214#67—42no—
215#67—81no—
216#67—81no—
217C2×Dic3—21no—
218C2×Dic3—21no—
219D12—21no—
220D12—21no—
221D12—21no—
222D12—21no—
223D12—42no—
224D12—81no—
225C4×D3—42no—
226C4×D3—42no—
227Dic6—21no—
228Dic6C2×D412yes—
229C3⋊C8—21no—
230C3⋊C8—21no—
231C3⋊C8—21no—
232C3⋊C8C2×D412yes—
233#41—22no—
234#41—41no—
235#41—62no—
236#41—62no—
237#41—121no—
238#41—121no—
239C2×Q8—21no—
240C2×Q8—22no—
241C2×Q8—31no—
242C2×Q8—41no—
243C2×Q8C22×D311yescharacteristic
244C2×Q8C22×D311yescharacteristic
245C2×D4—21no—
246C2×D4—21no—
247C2×D4—31no—
248C2×D4—31no—
249C2×D4—61no—
250C2×D4—61no—
251C2×D4—61no—
252C2×D4—61no—
253C2×D4—61no—
254C2×D4—61no—
255C2×D4#6711yescharacteristic
256C2×D4C22×D311yescharacteristic
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—61no—
260C22×C4—61no—
261C22×C4C22×D311yescharacteristic
262C22×C4C22×D311yescharacteristic
263Q16—34no—
264Q16—62no—
265SD16—62no—
266SD16—62no—
267SD16—62no—
268SD16—62no—
269SD16—121no—
270D8—62no—
271D8—121no—
272M16—62no—
273C2×C8—31no—
274C2×C8—31no—
275C2×C8—31no—
276C2×C8—31no—
277C2×C8—62no—
278C4⋊C4—21no—
279C4⋊C4—21no—
280C4⋊C4—31no—
281C4⋊C4—61no—
282C4⋊C4#6711yescharacteristic
283C4⋊C4C22×D311yescharacteristic
284C22⋊C4—21no—
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—21no—
288C22⋊C4—61no—
289C22⋊C4—61no—
290C22⋊C4#6711yescharacteristic
291C22⋊C4#6711yescharacteristic
292C42—21no—
293C42—61no—
294C42C22×D311yescharacteristic
295C22×C3—21no—
296C22×C3—21no—
297C22×C3—21no—
298C22×C3—21no—
299C22×C3—21no—
300C22×C3—21no—
301C22×C3—41no—
302C22×C3—41no—
303C22×C3—41no—
304C22×C3C22×D411yescharacteristic
305C2×D3—41no—
306C2×D3—41no—
307C2×D3—41no—
308C2×D3—41no—
309C2×D3—41no—
310C2×D3—41no—
311C3×C4—21no—
312C3×C4—21no—
313C3×C4—22no—
314C3×C4—21no—
315C3×C4—21no—
316C3×C4—41no—
317C3×C4—41no—
318C3×C4C22×D411yescharacteristic
319C3×C4H(5,𝔽2)11yescharacteristic
320Dic3—22no—
321Dic3—41no—
322C23—21no—
323C23—61no—
324C23—61no—
325C23C2×#6711yescharacteristic
326C23C2×#6711yescharacteristic
327Q8—21no—
328Q8—21no—
329Q8—21no—
330Q8—32no—
331Q8—42no—
332Q8—61no—
333Q8D3×D412yes—
334D4—21no—
335D4—21no—
336D4—41no—
337D4—42no—
338D4—42no—
339D4—61no—
340D4—61no—
341D4—61no—
342D4—61no—
343D4—122no—
344D4—122no—
345D4—122no—
346D4—241no—
347D4—241no—
348D4—241no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—61no—
359C2×C4—61no—
360C2×C4—122no—
361C2×C4—122no—
362C2×C4C2×#6711yescharacteristic
363C2×C4C2×#6711yescharacteristic
364C2×C4C2×#6711yescharacteristic
365C2×C4C2×#6711yescharacteristic
366C2×C4C23×D311yescharacteristic
367C8—32no—
368C8—61no—
369C8—61no—
370C8—61no—
371C2×C3—41no—
372C2×C3—41no—
373C2×C3—81no—
374C2×C3D4211yescharacteristic
375C2×C3#57511yescharacteristic
376C2×C3#57711yescharacteristic
377D3—81no—
378D3—81no—
379C22—21no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—121no—
389C22—121no—
390C22—121no—
391C22—121no—
392C22—121no—
393C22—121no—
394C22C22×#6711yescharacteristic
395C4—21no—
396C4—21no—
397C4—22no—
398C4—21no—
399C4—21no—
400C4—41no—
401C4—41no—
402C4—62no—
403C4—121no—
404C4C2×D3×D411yescharacteristic
405C4#100411yescharacteristic
406C3#327111yescharacteristic, complemented, Sylow
407C2—41no—
408C2—41no—
409C2—81no—
410C2—241no—
411C2—241no—
412C2D4×#6711yescharacteristic
413C2#582211yescharacteristic
414C2#583711yescharacteristic
subgroupG/H
centerC22C22×#67
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#548C2
socleC22×C3C22×D4
hypercenter#548D3
hypocenterC3#3271
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C3×#548C2semidirect
2. C2×#950C2semidirect
3. C2×#942C2semidirect
4. #5553C2semidirect
5. #5238C2semidirect
6. #5227C2semidirect
7. #5058C2semidirect
8. #5054C2semidirect
9. #5048C2semidirect
10. #5047C2semidirect
11. #5039C2semidirect
12. #5037C2semidirect
13. #5030C2semidirect
14. #5027C2semidirect
15. #5011C2semidirect
65. #548D3semidirect
120. #216D4semidirect
406. C3#3271semidirect

Maximal subgroups

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

subgroupindex
C3×#5482
C2×#9502
C2×#9422
#55532
#52382
#52272
#50582
#50542
#50482
#50472
#50392
#50372
#50302
#50272
#50112
#32713