Finite Group Databasebeta

← #83600

Subgroups — #83600

Order 384.

382 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#552C211yesmaximal, characteristic, complemented
2#5551C211yesmaximal, characteristic
3#5069C211yesmaximal, characteristic, complemented
4#5066C211yesmaximal, characteristic, complemented
5#5052C211yesmaximal, characteristic, complemented
6#5051C211yesmaximal, characteristic, complemented
7#5047C211yesmaximal, characteristic, complemented
8#5047C211yesmaximal, characteristic, complemented
9#5031C211yesmaximal, characteristic, complemented
10#5026C211yesmaximal, characteristic, complemented
11#5011C211yesmaximal, characteristic, complemented
12#5002C211yesmaximal, characteristic, complemented
13#4996C211yesmaximal, characteristic, complemented
14#4970C211yesmaximal, characteristic, complemented
15#4966C211yesmaximal, characteristic, complemented
16#3315—31nomaximal, Sylow
17C2×#235C2211yescharacteristic
18C2×#235C2211yescharacteristic
19C3×#126—21no—
20C3×#125—21no—
21C3×#125C2211yescharacteristic
22C3×#123—21no—
23C3×C22⋊Q8C2211yescharacteristic
24C3×C22⋊Q8C2211yescharacteristic
25C3×C4×Q8C2211yescharacteristic
26C3×C4×D4C2211yescharacteristic
27C3×#117—21no—
28C3×#117C2211yescharacteristic
29C2×C3×C4⋊C4C2211yescharacteristic
30C2×#216C2211yescharacteristic
31C2×#216C2211yescharacteristic
32C2×#215C2211yescharacteristic
33#938—21no—
34#924C2211yescharacteristic
35#924C2211yescharacteristic
36C2×#208C2211yescharacteristic
37C22×C3⋊C8C2211yescharacteristic
38D3×C4⋊C4—21no—
39#883—21no—
40#883—21no—
41C4×D12C2211yescharacteristic
42#869C2211yescharacteristic
43#835C2211yescharacteristic
44#830C2211yescharacteristic
45#830C2211yescharacteristic
46#810C2211yescharacteristic
47#810C2211yescharacteristic
48#810C2211yescharacteristic
49#810C2211yescharacteristic
50#810C2211yescharacteristic
51#810C2211yescharacteristic
52#809C2211yescharacteristic
53#809C2211yescharacteristic
54#809C2211yescharacteristic
55#808C2211yescharacteristic
56#807C2211yescharacteristic
57#807C2211yescharacteristic
58C4⋊(C3⋊C8)C2211yescharacteristic
59#803C2211yescharacteristic
60#552D311yescharacteristic, complemented
61#547—31no—
62#491—31no—
63#485—31no—
64#484—31no—
65#478—31no—
66#470—31no—
67#467—31no—
68#462—31no—
69#452—31no—
70#452—31no—
71#440—31no—
72#435—31no—
73#417—31no—
74#416—31no—
75C2×C3×Q8C2311yescharacteristic
76C2×C3×D4D411yescharacteristic
77C22×C3×C4—21no—
78C22×C3×C4C2311yescharacteristic
79C22×C3×C4C2311yescharacteristic
80C2×#67—21no—
81C2×#67—21no—
82#235—22no—
83#235—22no—
84#235—41no—
85#235—41no—
86C2×D12C2311yescharacteristic
87C2×C4×D3—21no—
88C2×C4×D3—21no—
89C2×C4×D3—21no—
90C2×Dic6C2311yescharacteristic
91C2×Dic6C2311yescharacteristic
92C3×C4⋊C4—21no—
93C3×C4⋊C4—21no—
94C3×C4⋊C4—21no—
95C3×C4⋊C4—21no—
96C3×C4⋊C4—21no—
97C3×C4⋊C4—21no—
98C3×C4⋊C4D411yescharacteristic
99C3×C4⋊C4C2311yescharacteristic
100C3×C4⋊C4C2311yescharacteristic
101C3×C4⋊C4C2311yescharacteristic
102C3×C22⋊C4—21no—
103C3×C22⋊C4—21no—
104C3×C22⋊C4—21no—
105C3×C22⋊C4D411yescharacteristic
106C3×C22⋊C4D411yescharacteristic
107C3×C42—21no—
108C3×C42—21no—
109C3×C42C2311yescharacteristic
110#217—21no—
111#217—21no—
112#216—41no—
113#216—41no—
114#215—22no—
115(C2×D3)⋊C4—21no—
116C4⋊Dic3—21no—
117C4⋊Dic3—21no—
118C4⋊Dic3C2311yescharacteristic
119Dic3⋊C4—21no—
120Dic3⋊C4—21no—
121#208—41no—
122C2×C3⋊C8—41no—
123C2×C3⋊C8C2311yescharacteristic
124C2×C3⋊C8C2311yescharacteristic
125C2×C3⋊C8C2311yescharacteristic
126C2×C3⋊C8C2311yescharacteristic
127C2×#41—31no—
128C2×#41—31no—
129C2×Q16—31no—
130C2×Q16—31no—
131C2×SD16—31no—
132C2×M16—31no—
133C22×C8—31no—
134C4⋊Q8—31no—
135#126—21no—
136#125—21no—
137#125C2×D311yescharacteristic
138#123—21no—
139#123—61no—
140#123—61no—
141C22⋊Q8—31no—
142C22⋊Q8—31no—
143C22⋊Q8C2×D311yescharacteristic
144C22⋊Q8C2×D311yescharacteristic
145#121—61no—
146C4×Q8C2×D311yescharacteristic
147C4×D4—31no—
148C4×D4C2×D311yescharacteristic
149#117—21no—
150#117C2×D311yescharacteristic
151C2×C4⋊C4—61no—
152C2×C4⋊C4C2×D311yescharacteristic
153#107—31no—
154#107—31no—
155#106—31no—
156C4⋊C8—31no—
157#103—31no—
158#103—31no—
159#103—31no—
160#103—31no—
161#103—31no—
162#103—31no—
163#103—31no—
164#102—31no—
165#102—31no—
166#102—31no—
167C22⋊C8—31no—
168C22⋊C8—31no—
169#97—31no—
170C23×C3C2×D411yescharacteristic
171C23×C3C2×D411yescharacteristic
172C22×D3—21no—
173C3×Q8—21no—
174C3×Q8—21no—
175C3×D4—41no—
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—42no—
185C2×C3×C4C2×D411yescharacteristic
186C2×C3×C4C2×D411yescharacteristic
187C2×C3×C4C2×D411yescharacteristic
188C2×C3×C4C2×D411yescharacteristic
189C2×C3×C4C2411yescharacteristic
190#67—42no—
191#67—42no—
192C2×Dic3—21no—
193C2×Dic3—21no—
194C2×Dic3—21no—
195D12—21no—
196D12#4112yes—
197C4×D3—42no—
198C4×D3—42no—
199C4×D3—42no—
200Dic6—21no—
201Dic6—21no—
202Dic6—21no—
203Dic6—21no—
204C3⋊C8—21no—
205C3⋊C8—21no—
206C3⋊C8—21no—
207C3⋊C8—21no—
208#41—62no—
209#41—62no—
210#41—121no—
211#41—121no—
212C2×Q8—31no—
213C2×Q8—31no—
214C2×Q8C22×D311yescharacteristic
215C2×D4—31no—
216C2×D4—61no—
217C2×D4—61no—
218C2×D4#6711yescharacteristic
219C22×C4—21no—
220C22×C4—61no—
221C22×C4—61no—
222C22×C4—61no—
223C22×C4C22×D311yescharacteristic
224C22×C4C22×D311yescharacteristic
225Q16—121no—
226Q16—121no—
227SD16—62no—
228M16—121no—
229C2×C8—31no—
230C2×C8—31no—
231C2×C8—31no—
232C2×C8—31no—
233C2×C8—121no—
234C4⋊C4—21no—
235C4⋊C4—21no—
236C4⋊C4—21no—
237C4⋊C4—21no—
238C4⋊C4—21no—
239C4⋊C4—21no—
240C4⋊C4—31no—
241C4⋊C4—61no—
242C4⋊C4—61no—
243C4⋊C4—61no—
244C4⋊C4—61no—
245C4⋊C4#6711yescharacteristic
246C4⋊C4C22×D311yescharacteristic
247C4⋊C4C22×D311yescharacteristic
248C4⋊C4C22×D311yescharacteristic
249C22⋊C4—21no—
250C22⋊C4—21no—
251C22⋊C4—21no—
252C22⋊C4—61no—
253C22⋊C4—61no—
254C22⋊C4—61no—
255C22⋊C4#6711yescharacteristic
256C22⋊C4#6711yescharacteristic
257C42—21no—
258C42—21no—
259C42C22×D311yescharacteristic
260C22×C3—21no—
261C22×C3—21no—
262C22×C3—21no—
263C22×C3—21no—
264C22×C3—21no—
265C22×C3—21no—
266C22×C3C22×D411yescharacteristic
267C2×D3—22no—
268C2×D3—41no—
269C2×D3—41no—
270C3×C4—21no—
271C3×C4—21no—
272C3×C4—21no—
273C3×C4—21no—
274C3×C4—41no—
275C3×C4—41no—
276C3×C4—41no—
277C3×C4—41no—
278C3×C4C2×#4111yescharacteristic
279C3×C4H(5,𝔽2)11yescharacteristic
280Dic3—41no—
281Dic3—41no—
282Dic3—41no—
283C23—61no—
284C23C2×#6711yescharacteristic
285C23C2×#6711yescharacteristic
286Q8—21no—
287Q8—21no—
288Q8—61no—
289Q8—61no—
290Q8—61no—
291Q8—61no—
292D4—32no—
293D4—41no—
294D4—61no—
295D4—122no—
296D4—122no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—42no—
306C2×C4—61no—
307C2×C4—61no—
308C2×C4—61no—
309C2×C4—122no—
310C2×C4—122no—
311C2×C4—122no—
312C2×C4C2×#6711yescharacteristic
313C2×C4C2×#6711yescharacteristic
314C2×C4C2×#6711yescharacteristic
315C2×C4C2×#6711yescharacteristic
316C2×C4C23×D311yescharacteristic
317C8—61no—
318C8—61no—
319C8—61no—
320C8—61no—
321C2×C3—41no—
322C2×C3—41no—
323C2×C3#54611yescharacteristic
324C2×C3#57511yescharacteristic
325C2×C3#57811yescharacteristic
326D3—42no—
327C22—21no—
328C22—21no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—62no—
334C22—121no—
335C22—121no—
336C22C22×#6711yescharacteristic
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—121no—
346C4—121no—
347C4—121no—
348C4D3×#4111yescharacteristic
349C4#100911yescharacteristic
350C3#331511yescharacteristic, complemented, Sylow
351C2—41no—
352C2—41no—
353C2—122no—
354C2#582211yescharacteristic
355C2#582911yescharacteristic
356C2#583811yescharacteristic
subgroupG/H
centerC22C22×#67
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#552C2
socleC22×C3C22×D4
prime radical#5551C2
hypercenter#552D3
hypocenterC3#3315
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C4×D4 ◁ #552

Complements

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

NH ≅ G/Ntype
1. C3×#552C2semidirect
3. #5069C2semidirect
4. #5066C2semidirect
5. #5052C2semidirect
6. #5051C2semidirect
7. #5047C2semidirect
8. #5047C2semidirect
9. #5031C2semidirect
10. #5026C2semidirect
11. #5011C2semidirect
12. #5002C2semidirect
13. #4996C2semidirect
14. #4970C2semidirect
15. #4966C2semidirect
60. #552D3semidirect
350. C3#3315semidirect

Maximal subgroups

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

subgroupindex
C3×#5522
#55512
#50692
#50662
#50522
#50512
#50472
#50312
#50262
#50112
#50022
#49962
#49702
#49662
#33153