Finite Group Databasebeta

← #79510

Subgroups — #79510

Order 384.

404 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#5565C211yesmaximal, characteristic, complemented
2#5553C211yesmaximal, characteristic, complemented
3C3×#435C211yesmaximal, characteristic, complemented
4#5135C211yesmaximal, characteristic, complemented
5#5133C211yesmaximal, characteristic, complemented
6#5115C211yesmaximal, characteristic, complemented
7#5113C211yesmaximal, characteristic, complemented
8#4843C211yesmaximal, characteristic, complemented
9#4829C211yesmaximal, characteristic, complemented
10#4737C211yesmaximal, characteristic, complemented
11#4736C211yesmaximal, characteristic, complemented
12#4734C211yesmaximal, characteristic, complemented
13#4734C211yesmaximal, characteristic, complemented
14#4713C211yesmaximal, characteristic, complemented
15#4710C211yesmaximal, characteristic, complemented
16#3309—31nomaximal, Sylow
17C2×#235C2211yescharacteristic
18C2×#235C2211yescharacteristic
19C2×C3×M16C2211yescharacteristic
20C22×C3×C8C2211yescharacteristic
21C3×C4×D4C2211yescharacteristic
22#940—21no—
23#939—21no—
24#930C2211yescharacteristic
25#930C2211yescharacteristic
26#930C2211yescharacteristic
27#930C2211yescharacteristic
28#926C2211yescharacteristic
29C2×C4⋊Dic3C2211yescharacteristic
30C2×D24C2211yescharacteristic
31C2×D24C2211yescharacteristic
32C2×#204C2211yescharacteristic
33#898—21no—
34#893—21no—
35#884—21no—
36#884—21no—
37#883—21no—
38#67⋊C4—21no—
39#874C2211yescharacteristic
40C4×D12C2211yescharacteristic
41#870C2211yescharacteristic
42C4×Dic6C2211yescharacteristic
43C3×C4⋊C8C2211yescharacteristic
44C3×C22⋊C8C2211yescharacteristic
45C3×C22⋊C8C2211yescharacteristic
46C3×#97C2211yescharacteristic
47#821C2211yescharacteristic
48#821C2211yescharacteristic
49#821C2211yescharacteristic
50#821C2211yescharacteristic
51#821C2211yescharacteristic
52#821C2211yescharacteristic
53#821C2211yescharacteristic
54#818C2211yescharacteristic
55#818C2211yescharacteristic
56#817C2211yescharacteristic
57#816C2211yescharacteristic
58#816C2211yescharacteristic
59#816C2211yescharacteristic
60#553—31no—
61#550—31no—
62#490—31no—
63#482—31no—
64#480—31no—
65#479—31no—
66#469—31no—
67#466—31no—
68#459—31no—
69#449—31no—
70#449—31no—
71#440—31no—
72#435D311yescharacteristic, complemented
73#417—31no—
74#416—31no—
75C2×C3×D4D411yescharacteristic
76C22×C3×C4C2311yescharacteristic
77C22×C3×C4C2311yescharacteristic
78C2×#67—21no—
79C2×#67—21no—
80C2×#67—21no—
81C2×#67—21no—
82C2×#67—21no—
83C2×#67—21no—
84C22×Dic3—21no—
85#235—22no—
86#235—22no—
87#235—41no—
88#235—41no—
89C2×D12—21no—
90C2×D12—21no—
91C2×D12C2311yescharacteristic
92C2×D12C2311yescharacteristic
93C2×D12C2311yescharacteristic
94C2×C4×D3—21no—
95C2×C4×D3—21no—
96C2×C4×D3—21no—
97C2×Dic6C2311yescharacteristic
98C3×M16—41no—
99C2×C3×C8—41no—
100C2×C3×C8C2311yescharacteristic
101C2×C3×C8C2311yescharacteristic
102C2×C3×C8C2311yescharacteristic
103C2×C3×C8C2311yescharacteristic
104C3×C4⋊C4D411yescharacteristic
105C3×C22⋊C4D411yescharacteristic
106C3×C22⋊C4D411yescharacteristic
107C3×C42C2311yescharacteristic
108#217—21no—
109(C2×D3)⋊C4—21no—
110(C2×D3)⋊C4—21no—
111(C2×D3)⋊C4—21no—
112(C2×D3)⋊C4—21no—
113(C2×D3)⋊C4—21no—
114C4⋊Dic3—21no—
115C4⋊Dic3C2311yescharacteristic
116C4⋊Dic3C2311yescharacteristic
117C4⋊Dic3C2311yescharacteristic
118C4⋊Dic3C2311yescharacteristic
119Dic3⋊C4—21no—
120Dic3⋊C4—21no—
121Dic3⋊C4—21no—
122C4×Dic3—21no—
123C4×Dic3—21no—
124D24—41no—
125D24—41no—
126#204—22no—
127C2×#41—31no—
128C2×#41—31no—
129C2×SD16—31no—
130C2×D8—31no—
131C2×D8—31no—
132C2×M16C2×D311yescharacteristic
133C22×C8C2×D311yescharacteristic
134#127—31no—
135#127—61no—
136#126—61no—
137#125—31no—
138#123—61no—
139#121—31no—
140#121—31no—
141#121—31no—
142#121—31no—
143#121—61no—
144#121—61no—
145#121—61no—
146C4×Q8—31no—
147C4×D4—31no—
148C4×D4—61no—
149C4×D4—61no—
150C4×D4C2×D311yescharacteristic
151#117—31no—
152C2×C4⋊C4—31no—
153#107—31no—
154#107—31no—
155#106—31no—
156C4⋊C8C2×D311yescharacteristic
157#103—31no—
158#103—31no—
159#103—31no—
160#102—31no—
161#102—31no—
162#102—31no—
163#102—31no—
164#102—31no—
165#102—31no—
166#102—31no—
167C22⋊C8C2×D311yescharacteristic
168C22⋊C8C2×D311yescharacteristic
169#97C2×D311yescharacteristic
170C23×C3C2×D411yescharacteristic
171C23×C3C2×D411yescharacteristic
172C22×D3—21no—
173C22×D3—21no—
174C22×D3—21no—
175C3×D4—41no—
176C2×C3×C4—21no—
177C2×C3×C4—21no—
178C2×C3×C4—21no—
179C2×C3×C4—21no—
180C2×C3×C4C2×D411yescharacteristic
181C2×C3×C4C2×D411yescharacteristic
182C2×C3×C4C2×D411yescharacteristic
183C2×C3×C4C2×D411yescharacteristic
184C2×C3×C4C2411yescharacteristic
185#67—42no—
186#67—42no—
187#67—42no—
188#67—81no—
189#67—81no—
190#67—81no—
191C2×Dic3—21no—
192C2×Dic3—21no—
193C2×Dic3—21no—
194C2×Dic3—21no—
195C2×Dic3—21no—
196C2×Dic3—81no—
197D12—21no—
198D12—21no—
199D12—21no—
200D12—21no—
201D12—21no—
202D12—21no—
203D12—42no—
204D12—81no—
205C4×D3—42no—
206C4×D3—42no—
207C4×D3—81no—
208Dic6—21no—
209Dic6#4112yes—
210C3×C8—21no—
211C3×C8—21no—
212C3×C8—21no—
213C3×C8—21no—
214#41—62no—
215#41—62no—
216#41—121no—
217#41—121no—
218C2×Q8—31no—
219C2×D4—31no—
220C2×D4—31no—
221C2×D4—31no—
222C2×D4—61no—
223C2×D4—61no—
224C2×D4—61no—
225C2×D4—61no—
226C2×D4—61no—
227C2×D4—61no—
228C2×D4—61no—
229C2×D4—61no—
230C2×D4D1211yescharacteristic
231C22×C4—61no—
232C22×C4—61no—
233C22×C4—61no—
234C22×C4—61no—
235C22×C4C22×D311yescharacteristic
236C22×C4C22×D311yescharacteristic
237SD16—62no—
238D8—121no—
239D8—121no—
240M16—41no—
241C2×C8—41no—
242C2×C8C22×D311yescharacteristic
243C2×C8C22×D311yescharacteristic
244C2×C8C22×D311yescharacteristic
245C2×C8C22×D311yescharacteristic
246C4⋊C4—31no—
247C4⋊C4—31no—
248C4⋊C4—31no—
249C4⋊C4—31no—
250C4⋊C4—61no—
251C4⋊C4—61no—
252C4⋊C4—61no—
253C4⋊C4—61no—
254C4⋊C4D1211yescharacteristic
255C22⋊C4—61no—
256C22⋊C4—61no—
257C22⋊C4—61no—
258C22⋊C4—61no—
259C22⋊C4—61no—
260C22⋊C4—61no—
261C22⋊C4D1211yescharacteristic
262C22⋊C4D1211yescharacteristic
263C42—61no—
264C42—61no—
265C42C22×D311yescharacteristic
266C22×C3—21no—
267C22×C3—21no—
268C22×C3—21no—
269C22×C3—21no—
270C22×C3—21no—
271C22×C3—21no—
272C22×C3C22×D411yescharacteristic
273C2×D3—41no—
274C2×D3—41no—
275C2×D3—41no—
276C2×D3—41no—
277C2×D3—41no—
278C2×D3—41no—
279C2×D3—41no—
280C2×D3—41no—
281C2×D3—41no—
282C3×C4—21no—
283C3×C4—21no—
284C3×C4—21no—
285C3×C4—21no—
286C3×C4C2×#4111yescharacteristic
287C3×C4H(5,𝔽2)11yescharacteristic
288Dic3—22no—
289Dic3—41no—
290Dic3—41no—
291Dic3—41no—
292Dic3—41no—
293C23—61no—
294C23—61no—
295C23—61no—
296C23C2×D1211yescharacteristic
297C23C2×D1211yescharacteristic
298Q8—32no—
299Q8—61no—
300D4—41no—
301D4—61no—
302D4—61no—
303D4—61no—
304D4—61no—
305D4—61no—
306D4—61no—
307D4—122no—
308D4—122no—
309D4—122no—
310D4—122no—
311D4—241no—
312D4—241no—
313D4—241no—
314D4—241no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—61no—
320C2×C4—61no—
321C2×C4—61no—
322C2×C4—61no—
323C2×C4—61no—
324C2×C4—122no—
325C2×C4—122no—
326C2×C4—241no—
327C2×C4—241no—
328C2×C4C2×D1211yescharacteristic
329C2×C4C2×D1211yescharacteristic
330C2×C4C2×D1211yescharacteristic
331C2×C4C2×D1211yescharacteristic
332C2×C4C23×D311yescharacteristic
333C8—21no—
334C8—21no—
335C8—21no—
336C8—21no—
337C2×C3—41no—
338C2×C3—41no—
339C2×C3#54611yescharacteristic
340C2×C3#57511yescharacteristic
341C2×C3#57611yescharacteristic
342D3—81no—
343D3—81no—
344D3—81no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—121no—
352C22—121no—
353C22—121no—
354C22—121no—
355C22—121no—
356C22—121no—
357C22—121no—
358C22—121no—
359C22—121no—
360C22C22×D1211yescharacteristic
361C4—21no—
362C4—21no—
363C4—21no—
364C4—21no—
365C4—62no—
366C4—121no—
367C4—121no—
368C4—121no—
369C4—121no—
370C4#100411yescharacteristic
371C4D3×#4111yescharacteristic
372C3#330911yescharacteristic, complemented, Sylow
373C2—41no—
374C2—41no—
375C2—241no—
376C2—241no—
377C2—241no—
378C2#555411yescharacteristic
379C2#574811yescharacteristic
380C2#575211yescharacteristic
subgroupG/H
centerC22C22×D12
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#435C2
socleC22×C3C22×D4
hypercenter#435D3
hypocenterC3#3309
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. #5565C2semidirect
2. #5553C2semidirect
3. C3×#435C2semidirect
4. #5135C2semidirect
5. #5133C2semidirect
6. #5115C2semidirect
7. #5113C2semidirect
8. #4843C2semidirect
9. #4829C2semidirect
10. #4737C2semidirect
11. #4736C2semidirect
12. #4734C2semidirect
13. #4734C2semidirect
14. #4713C2semidirect
15. #4710C2semidirect
72. #435D3semidirect
372. C3#3309semidirect

Maximal subgroups

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

subgroupindex
#55652
#55532
C3×#4352
#51352
#51332
#51152
#51132
#48432
#48292
#47372
#47362
#47342
#47132
#47102
#33093