Finite Group Databasebeta

← #79471

Subgroups — #79471

Order 384.

388 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#5565C211yesmaximal, characteristic, complemented
2#5555C211yesmaximal, characteristic, complemented
3C3×#435C211yesmaximal, characteristic, complemented
4#5135C211yesmaximal, characteristic, complemented
5#5121C211yesmaximal, characteristic, complemented
6#5115C211yesmaximal, characteristic, complemented
7C2×#817C211yesmaximal, characteristic, complemented
8#4847C211yesmaximal, characteristic, complemented
9#4842C211yesmaximal, characteristic, complemented
10#4737C211yesmaximal, characteristic, complemented
11#4736C211yesmaximal, characteristic, complemented
12#4735C211yesmaximal, characteristic, complemented
13#4735C211yesmaximal, characteristic, complemented
14#4711C211yesmaximal, characteristic, complemented
15#4702C211yesmaximal, characteristic, complemented
16#3345—31nomaximal, Sylow
17C2×#237—21no—
18C2×C3×M16C2211yescharacteristic
19C22×C3×C8C2211yescharacteristic
20C3×C4×D4C2211yescharacteristic
21#939—21no—
22#930C2211yescharacteristic
23#930C2211yescharacteristic
24#930C2211yescharacteristic
25#930C2211yescharacteristic
26#926C2211yescharacteristic
27C2×C4⋊Dic3C2211yescharacteristic
28C2×C4⋊Dic3C2211yescharacteristic
29C2×C4⋊Dic3C2211yescharacteristic
30C2×D24C2211yescharacteristic
31#898—21no—
32#897—21no—
33#886—21no—
34#886—21no—
35#883—21no—
36#67⋊C4—21no—
37C4×D12C2211yescharacteristic
38C4×D12C2211yescharacteristic
39#870C2211yescharacteristic
40#869C2211yescharacteristic
41C3×C4⋊C8C2211yescharacteristic
42C3×C22⋊C8C2211yescharacteristic
43C3×C22⋊C8C2211yescharacteristic
44C3×#97C2211yescharacteristic
45#821C2211yescharacteristic
46#821C2211yescharacteristic
47#821C2211yescharacteristic
48#821C2211yescharacteristic
49#821C2211yescharacteristic
50#821C2211yescharacteristic
51#818C2211yescharacteristic
52#818C2211yescharacteristic
53#818C2211yescharacteristic
54#817C2211yescharacteristic
55#817C2211yescharacteristic
56#817C2211yescharacteristic
57#817C2211yescharacteristic
58#817C2211yescharacteristic
59#817C2211yescharacteristic
60#553—31no—
61#547—31no—
62#501—31no—
63#482—31no—
64#481—31no—
65#481—31no—
66#480—31no—
67#478—31no—
68#476—31no—
69#469—31no—
70#466—31no—
71#442—31no—
72#435D311yescharacteristic, complemented
73#428—31no—
74C2×#106—31no—
75C2×C3×D4D411yescharacteristic
76C22×C3×C4C2311yescharacteristic
77C22×C3×C4C2311yescharacteristic
78C2×#67—21no—
79C2×#67—21no—
80C2×#67—21no—
81C2×#67—21no—
82C22×Dic3—21no—
83C22×Dic3—21no—
84C22×Dic3—21no—
85#237—44no—
86C2×D12C2311yescharacteristic
87C2×D12C2311yescharacteristic
88C2×C4×D3—21no—
89C2×C4×D3—21no—
90C2×Dic6—21no—
91C3×M16—22no—
92C2×C3×C8—22no—
93C2×C3×C8C2311yescharacteristic
94C2×C3×C8C2311yescharacteristic
95C2×C3×C8C2311yescharacteristic
96C2×C3×C8C2311yescharacteristic
97C3×C4⋊C4D411yescharacteristic
98C3×C22⋊C4D411yescharacteristic
99C3×C22⋊C4D411yescharacteristic
100C3×C42C2311yescharacteristic
101#217—21no—
102(C2×D3)⋊C4—21no—
103(C2×D3)⋊C4—21no—
104(C2×D3)⋊C4—21no—
105(C2×D3)⋊C4—21no—
106(C2×D3)⋊C4—21no—
107(C2×D3)⋊C4—21no—
108C4⋊Dic3—21no—
109C4⋊Dic3—21no—
110C4⋊Dic3—21no—
111C4⋊Dic3—21no—
112C4⋊Dic3C2311yescharacteristic
113C4⋊Dic3C2311yescharacteristic
114C4⋊Dic3C2311yescharacteristic
115C4⋊Dic3C2311yescharacteristic
116C4⋊Dic3C2311yescharacteristic
117C4⋊Dic3C2311yescharacteristic
118Dic3⋊C4—21no—
119Dic3⋊C4—21no—
120C4×Dic3—21no—
121D24—22no—
122C2×#41—61no—
123C2×D8—31no—
124C2×M16C2×D311yescharacteristic
125C22×C8C2×D311yescharacteristic
126C4⋊Q8—31no—
127#126—61no—
128#125—31no—
129#123—61no—
130#123—61no—
131#123—61no—
132C22⋊Q8—61no—
133#121—31no—
134#121—31no—
135#121—31no—
136#121—31no—
137#121—61no—
138C4×D4—31no—
139C4×D4—31no—
140C4×D4—61no—
141C4×D4C2×D311yescharacteristic
142#117—31no—
143C2×C4⋊C4—31no—
144C2×C4⋊C4—31no—
145C2×C4⋊C4—31no—
146#107—31no—
147#107—31no—
148#107—31no—
149#106—31no—
150#106—31no—
151#106—31no—
152#106—31no—
153#106—31no—
154#106—31no—
155C4⋊C8C2×D311yescharacteristic
156#102—31no—
157#102—31no—
158#102—31no—
159#102—31no—
160#102—31no—
161#102—31no—
162C22⋊C8C2×D311yescharacteristic
163C22⋊C8C2×D311yescharacteristic
164#97C2×D311yescharacteristic
165C23×C3C2×D411yescharacteristic
166C23×C3C2×D411yescharacteristic
167C22×D3—21no—
168C22×D3—21no—
169C3×D4—22no—
170C2×C3×C4—21no—
171C2×C3×C4—21no—
172C2×C3×C4—21no—
173C2×C3×C4—21no—
174C2×C3×C4C2×D411yescharacteristic
175C2×C3×C4C2×D411yescharacteristic
176C2×C3×C4C2×D411yescharacteristic
177C2×C3×C4C2×D411yescharacteristic
178C2×C3×C4C2411yescharacteristic
179#67—42no—
180#67—42no—
181#67—42no—
182#67—81no—
183C2×Dic3—21no—
184C2×Dic3—21no—
185C2×Dic3—21no—
186C2×Dic3—21no—
187C2×Dic3—21no—
188C2×Dic3—21no—
189C2×Dic3—42no—
190C2×Dic3—42no—
191C2×Dic3—81no—
192D12—21no—
193D12—21no—
194D12—21no—
195D12—21no—
196C4×D3—42no—
197C4×D3—81no—
198Dic6—42no—
199C3×C8—21no—
200C3×C8—21no—
201C3×C8—21no—
202C3×C8#4112yescomplemented
203#41—124no—
204C2×Q8—61no—
205C2×D4—31no—
206C2×D4—31no—
207C2×D4—61no—
208C2×D4—61no—
209C2×D4—61no—
210C2×D4—61no—
211C2×D4D1211yescharacteristic
212C22×C4—61no—
213C22×C4—61no—
214C22×C4—61no—
215C22×C4—61no—
216C22×C4—61no—
217C22×C4C22×D311yescharacteristic
218C22×C4C22×D311yescharacteristic
219D8—62no—
220M16—22no—
221C2×C8—22no—
222C2×C8C22×D311yescharacteristic
223C2×C8C22×D311yescharacteristic
224C2×C8C22×D311yescharacteristic
225C2×C8C22×D311yescharacteristic
226C4⋊C4—31no—
227C4⋊C4—31no—
228C4⋊C4—31no—
229C4⋊C4—31no—
230C4⋊C4—31no—
231C4⋊C4—31no—
232C4⋊C4—61no—
233C4⋊C4—61no—
234C4⋊C4—61no—
235C4⋊C4—61no—
236C4⋊C4—61no—
237C4⋊C4—61no—
238C4⋊C4D1211yescharacteristic
239C22⋊C4—61no—
240C22⋊C4—61no—
241C22⋊C4—61no—
242C22⋊C4—61no—
243C22⋊C4—61no—
244C22⋊C4—61no—
245C22⋊C4—61no—
246C22⋊C4D1211yescharacteristic
247C22⋊C4D1211yescharacteristic
248C42—61no—
249C42C22×D311yescharacteristic
250C22×C3—21no—
251C22×C3—21no—
252C22×C3—21no—
253C22×C3—21no—
254C22×C3—21no—
255C22×C3AGL(1,ℤ/8)12yes—
256C22×C3C22×D411yescharacteristic
257C2×D3—41no—
258C2×D3—41no—
259C2×D3—41no—
260C2×D3—41no—
261C2×D3—41no—
262C2×D3—41no—
263C3×C4—21no—
264C3×C4—21no—
265C3×C4—21no—
266C3×C4—21no—
267C3×C4C2×#4111yescharacteristic
268C3×C42−1+411yescharacteristic
269Dic3—41no—
270Dic3—41no—
271Dic3—41no—
272Dic3—41no—
273Dic3—41no—
274Dic3—41no—
275C23—61no—
276C23—61no—
277C23C2×D1211yescharacteristic
278C23C2×D1211yescharacteristic
279Q8—122no—
280D4—22no—
281D4—61no—
282D4—61no—
283D4—61no—
284D4—61no—
285D4—122no—
286D4—122no—
287D4—122no—
288D4—241no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—61no—
294C2×C4—61no—
295C2×C4—61no—
296C2×C4—61no—
297C2×C4—61no—
298C2×C4—61no—
299C2×C4—122no—
300C2×C4—122no—
301C2×C4—122no—
302C2×C4—241no—
303C2×C4—241no—
304C2×C4C2×D1211yescharacteristic
305C2×C4C2×D1211yescharacteristic
306C2×C4C2×D1211yescharacteristic
307C2×C4C2×D1211yescharacteristic
308C2×C4C23×D311yescharacteristic
309C8—21no—
310C8—21no—
311C8—21no—
312C8#23712yescomplemented
313C2×C3—22no—
314C2×C3—41no—
315C2×C3#54711yescharacteristic
316C2×C3C2×AGL(1,ℤ/8)11yescharacteristic
317C2×C3#57711yescharacteristic
318D3—81no—
319D3—81no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—121no—
326C22—121no—
327C22—121no—
328C22—121no—
329C22—121no—
330C22—121no—
331C22#90812yes—
332C22C22×D1211yescharacteristic
333C4—21no—
334C4—21no—
335C4—21no—
336C4—21no—
337C4—121no—
338C4—121no—
339C4—121no—
340C4—121no—
341C4—121no—
342C4—121no—
343C4C2×#23711yescharacteristic
344C4#101011yescharacteristic
345C3#334511yescharacteristic, complemented, Sylow
346C2—22no—
347C2—41no—
348C2—241no—
349C2—241no—
350C2#555511yescharacteristic
351C2C2×#90811yescharacteristic
352C2#575111yescharacteristic
subgroupG/H
centerC22C22×D12
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#435C2
socleC22×C3C22×D4
hypercenter#435D3
hypocenterC3#3345
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. #5555C2semidirect
3. C3×#435C2semidirect
4. #5135C2semidirect
5. #5121C2semidirect
6. #5115C2semidirect
7. C2×#817C2semidirect
8. #4847C2semidirect
9. #4842C2semidirect
10. #4737C2semidirect
11. #4736C2semidirect
12. #4735C2semidirect
13. #4735C2semidirect
14. #4711C2semidirect
15. #4702C2semidirect
72. #435D3semidirect
202. C3×C8#41semidirect
312. C8#237semidirect
345. C3#3345semidirect

Maximal subgroups

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

subgroupindex
#55652
#55552
C3×#4352
#51352
#51212
#51152
C2×#8172
#48472
#48422
#47372
#47362
#47352
#47112
#47022
#33453