Finite Group Databasebeta

← #83641

Subgroups — #83641

Order 384.

388 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#554C211yesmaximal, characteristic, complemented
2#5552C211yesmaximal, characteristic
3#5094C211yesmaximal, characteristic, complemented
4#5089C211yesmaximal, characteristic, complemented
5#5052C211yesmaximal, characteristic, complemented
6#5050C211yesmaximal, characteristic, complemented
7#5048C211yesmaximal, characteristic, complemented
8#5047C211yesmaximal, characteristic, complemented
9#5030C211yesmaximal, characteristic, complemented
10#5028C211yesmaximal, characteristic, complemented
11#5011C211yesmaximal, characteristic, complemented
12#4971C211yesmaximal, characteristic, complemented
13C2×#810C211yesmaximal, characteristic, complemented
14#4968C211yesmaximal, characteristic, complemented
15#4966C211yesmaximal, characteristic, complemented
16#3316—31nomaximal, Sylow
17C2×#235C2211yescharacteristic
18C22×Dic6C2211yescharacteristic
19C3×C4⋊Q8C2211yescharacteristic
20C3×#125—21no—
21C3×C22⋊Q8—21no—
22C3×C22⋊Q8—21no—
23C3×C22⋊Q8C2211yescharacteristic
24C3×C22⋊Q8C2211yescharacteristic
25C3×C4×Q8C2211yescharacteristic
26C3×C4×D4—21no—
27C3×C4×D4C2211yescharacteristic
28C2×C3×C4⋊C4C2211yescharacteristic
29C2×C3×C4⋊C4C2211yescharacteristic
30C2×#216C2211yescharacteristic
31C2×#216C2211yescharacteristic
32C2×#215C2211yescharacteristic
33#939—21no—
34#930C2211yescharacteristic
35#924C2211yescharacteristic
36C2×#208C2211yescharacteristic
37C22×C3⋊C8C2211yescharacteristic
38#896—21no—
39#885—21no—
40#67⋊C4—21no—
41#875C2211yescharacteristic
42C4×Dic6C2211yescharacteristic
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#808C2211yescharacteristic
57#808C2211yescharacteristic
58C4⋊(C3⋊C8)C2211yescharacteristic
59#803C2211yescharacteristic
60#554D311yescharacteristic, complemented
61#548—31no—
62#489—31no—
63#483—31no—
64#481—31no—
65#475—31no—
66#470—31no—
67#465—31no—
68#464—31no—
69#452—31no—
70#451—31no—
71#441—31no—
72#435—31no—
73#417—31no—
74C2×#103—31no—
75C2×C3×Q8—21no—
76C2×C3×Q8C2311yescharacteristic
77C2×C3×D4D411yescharacteristic
78C22×C3×C4—21no—
79C22×C3×C4—21no—
80C22×C3×C4C2311yescharacteristic
81C22×C3×C4C2311yescharacteristic
82C2×#67—21no—
83C2×#67—21no—
84C22×Dic3—21no—
85#235—22no—
86#235—41no—
87C2×D12C2311yescharacteristic
88C2×C4×D3—21no—
89C2×Dic6—22no—
90C2×Dic6—21no—
91C2×Dic6—41no—
92C2×Dic6C2311yescharacteristic
93C2×Dic6C2311yescharacteristic
94C3×C4⋊C4—21no—
95C3×C4⋊C4—21no—
96C3×C4⋊C4—21no—
97C3×C4⋊C4—21no—
98C3×C4⋊C4—21no—
99C3×C4⋊C4—21no—
100C3×C4⋊C4D411yescharacteristic
101C3×C4⋊C4C2311yescharacteristic
102C3×C4⋊C4C2311yescharacteristic
103C3×C4⋊C4C2311yescharacteristic
104C3×C22⋊C4—21no—
105C3×C22⋊C4—21no—
106C3×C22⋊C4D411yescharacteristic
107C3×C22⋊C4D411yescharacteristic
108C3×C42—21no—
109C3×C42C2311yescharacteristic
110#217—21no—
111#216—22no—
112#216—41no—
113#215—41no—
114(C2×D3)⋊C4—21no—
115(C2×D3)⋊C4—21no—
116(C2×D3)⋊C4—21no—
117C4⋊Dic3C2311yescharacteristic
118Dic3⋊C4—21no—
119Dic3⋊C4—21no—
120C4×Dic3—21no—
121#208—41no—
122C2×C3⋊C8—41no—
123C2×C3⋊C8C2311yescharacteristic
124C2×C3⋊C8C2311yescharacteristic
125C2×C3⋊C8C2311yescharacteristic
126C2×C3⋊C8C2311yescharacteristic
127C2×#41—31no—
128C22×Q8—31no—
129C2×Q16—31no—
130C2×Q16—31no—
131C2×SD16—31no—
132C2×M16—31no—
133C22×C8—31no—
134C4⋊Q8C2×D311yescharacteristic
135#125—21no—
136#124—31no—
137#124—61no—
138C22⋊Q8—21no—
139C22⋊Q8—21no—
140C22⋊Q8—31no—
141C22⋊Q8—61no—
142C22⋊Q8C2×D311yescharacteristic
143C22⋊Q8C2×D311yescharacteristic
144#121—31no—
145#121—61no—
146C4×Q8—31no—
147C4×Q8C2×D311yescharacteristic
148C4×D4—21no—
149C4×D4—61no—
150C4×D4C2×D311yescharacteristic
151C2×C4⋊C4C2×D311yescharacteristic
152C2×C4⋊C4C2×D311yescharacteristic
153#106—31no—
154#106—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×Q8—81no—
176C3×D4—22no—
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—81no—
186C2×C3×C4—81no—
187C2×C3×C4C2×D411yescharacteristic
188C2×C3×C4C2×D411yescharacteristic
189C2×C3×C4C2×D411yescharacteristic
190C2×C3×C4C2×D411yescharacteristic
191C2×C3×C4C2411yescharacteristic
192#67—42no—
193#67—42no—
194C2×Dic3—21no—
195C2×Dic3—21no—
196C2×Dic3—21no—
197C2×Dic3—42no—
198D12—21no—
199D12—21no—
200C4×D3—42no—
201Dic6—21no—
202Dic6—21no—
203Dic6—21no—
204Dic6—42no—
205Dic6#4112yes—
206C3⋊C8—21no—
207C3⋊C8—21no—
208C3⋊C8—21no—
209C3⋊C8—21no—
210#41—62no—
211#41—121no—
212C2×Q8—21no—
213C2×Q8—31no—
214C2×Q8—31no—
215C2×Q8—62no—
216C2×Q8—61no—
217C2×Q8—121no—
218C2×Q8C22×D311yescharacteristic
219C2×D4—31no—
220C2×D4—61no—
221C2×D4—61no—
222C2×D4#6711yescharacteristic
223C22×C4—21no—
224C22×C4—21no—
225C22×C4—61no—
226C22×C4—61no—
227C22×C4C22×D311yescharacteristic
228C22×C4C22×D311yescharacteristic
229Q16—62no—
230Q16—121no—
231SD16—121no—
232M16—121no—
233C2×C8—31no—
234C2×C8—31no—
235C2×C8—31no—
236C2×C8—31no—
237C2×C8—121no—
238C4⋊C4—21no—
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—31no—
245C4⋊C4—61no—
246C4⋊C4—61no—
247C4⋊C4#6711yescharacteristic
248C4⋊C4C22×D311yescharacteristic
249C4⋊C4C22×D311yescharacteristic
250C4⋊C4C22×D311yescharacteristic
251C22⋊C4—21no—
252C22⋊C4—21no—
253C22⋊C4—61no—
254C22⋊C4—61no—
255C22⋊C4—61no—
256C22⋊C4—61no—
257C22⋊C4#6711yescharacteristic
258C22⋊C4#6711yescharacteristic
259C42—21no—
260C42—61no—
261C42C22×D311yescharacteristic
262C22×C3—21no—
263C22×C3—21no—
264C22×C3—21no—
265C22×C3—21no—
266C22×C3—21no—
267C22×C3#13712yes—
268C22×C3C22×D411yescharacteristic
269C2×D3—41no—
270C2×D3—41no—
271C2×D3—41no—
272C3×C4—21no—
273C3×C4—21no—
274C3×C4—21no—
275C3×C4—21no—
276C3×C4—41no—
277C3×C4—41no—
278C3×C4—41no—
279C3×C4—41no—
280C3×C4C2×#4111yescharacteristic
281C3×C4H(5,𝔽2)11yescharacteristic
282Dic3—22no—
283Dic3—41no—
284Dic3—41no—
285C23—61no—
286C23C2×#6711yescharacteristic
287C23C2×#6711yescharacteristic
288Q8—21no—
289Q8—21no—
290Q8—32no—
291Q8—61no—
292Q8—61no—
293Q8—61no—
294Q8—81no—
295Q8—122no—
296D4—22no—
297D4—61no—
298D4—61no—
299D4—122no—
300D4—122no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—61no—
310C2×C4—61no—
311C2×C4—61no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—122no—
315C2×C4—122no—
316C2×C4C2×#6711yescharacteristic
317C2×C4C2×#6711yescharacteristic
318C2×C4C2×#6711yescharacteristic
319C2×C4C2×#6711yescharacteristic
320C2×C4C23×D311yescharacteristic
321C8—61no—
322C8—61no—
323C8—61no—
324C8—61no—
325C2×C3—22no—
326C2×C3—41no—
327C2×C3#54611yescharacteristic
328C2×C3C2×#13711yescharacteristic
329C2×C3#57711yescharacteristic
330D3—81no—
331C22—21no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—121no—
337C22—121no—
338C22—121no—
339C22#94212yes—
340C22C22×#6711yescharacteristic
341C4—21no—
342C4—21no—
343C4—21no—
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—62no—
350C4—121no—
351C4—121no—
352C4D3×#4111yescharacteristic
353C4#100911yescharacteristic
354C3#331611yescharacteristic, complemented, Sylow
355C2—22no—
356C2—41no—
357C2—241no—
358C2C2×#94211yescharacteristic
359C2#582911yescharacteristic
360C2#583611yescharacteristic
subgroupG/H
centerC22C22×#67
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#554C2
socleC22×C3C22×D4
prime radical#5552C2
hypercenter#554D3
hypocenterC3#3316
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C4×D4 ◁ #554

Complements

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

NH ≅ G/Ntype
1. C3×#554C2semidirect
3. #5094C2semidirect
4. #5089C2semidirect
5. #5052C2semidirect
6. #5050C2semidirect
7. #5048C2semidirect
8. #5047C2semidirect
9. #5030C2semidirect
10. #5028C2semidirect
11. #5011C2semidirect
12. #4971C2semidirect
13. C2×#810C2semidirect
14. #4968C2semidirect
15. #4966C2semidirect
60. #554D3semidirect
354. C3#3316semidirect

Maximal subgroups

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

subgroupindex
C3×#5542
#55522
#50942
#50892
#50522
#50502
#50482
#50472
#50302
#50282
#50112
#49712
C2×#8102
#49682
#49662
#33163