Finite Group Databasebeta

← #79515

Subgroups — #79515

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
1#5565C211yesmaximal, characteristic
2D4×Dic6C211yesmaximal, characteristic, complemented
3C3×#435C211yesmaximal, characteristic, complemented
4#5134C211yesmaximal, characteristic, complemented
5#5120C211yesmaximal, characteristic, complemented
6#5114C211yesmaximal, characteristic, complemented
7C2×#816C211yesmaximal, characteristic, complemented
8#4841C211yesmaximal, characteristic, complemented
9#4829C211yesmaximal, characteristic, complemented
10#4738C211yesmaximal, characteristic, complemented
11#4738C211yesmaximal, characteristic, complemented
12#4723C211yesmaximal, characteristic, complemented
13#4722C211yesmaximal, characteristic, complemented
14#4710C211yesmaximal, characteristic, complemented
15#4703C211yesmaximal, characteristic, complemented
16#3320—31nomaximal, Sylow
17C22×Dic6C2211yescharacteristic
18C22×Dic6C2211yescharacteristic
19C2×C3×M16C2211yescharacteristic
20C22×C3×C8C2211yescharacteristic
21C3×C4×D4C2211yescharacteristic
22#939—21no—
23D4×Dic3—21no—
24#930C2211yescharacteristic
25#930C2211yescharacteristic
26#926C2211yescharacteristic
27C2×C4⋊Dic3C2211yescharacteristic
28#924C2211yescharacteristic
29#924C2211yescharacteristic
30C2×#204C2211yescharacteristic
31C2×#204C2211yescharacteristic
32C2×#204C2211yescharacteristic
33#898—21no—
34#888—21no—
35#883—21no—
36#67⋊C4—21no—
37#878—21no—
38#878—21no—
39C4×D12C2211yescharacteristic
40#870C2211yescharacteristic
41#869C2211yescharacteristic
42C4×Dic6C2211yescharacteristic
43C3×C4⋊C8C2211yescharacteristic
44C3×C22⋊C8C2211yescharacteristic
45C3×C22⋊C8C2211yescharacteristic
46C3×#97C2211yescharacteristic
47#821C2211yescharacteristic
48#818C2211yescharacteristic
49#818C2211yescharacteristic
50#817C2211yescharacteristic
51#816C2211yescharacteristic
52#816C2211yescharacteristic
53#816C2211yescharacteristic
54#816C2211yescharacteristic
55#816C2211yescharacteristic
56#816C2211yescharacteristic
57#816C2211yescharacteristic
58#816C2211yescharacteristic
59#816C2211yescharacteristic
60#553—31no—
61D4×Q8—31no—
62#491—31no—
63#485—31no—
64#484—31no—
65#479—31no—
66#468—31no—
67#465—31no—
68#461—31no—
69#448—31no—
70#448—31no—
71#440—31no—
72#435D311yescharacteristic, complemented
73#419—31no—
74C2×#103—31no—
75C2×C3×D4D411yescharacteristic
76C22×C3×C4C2311yescharacteristic
77C22×C3×C4C2311yescharacteristic
78C2×#67—21no—
79C2×#67—21no—
80C22×Dic3—21no—
81C22×Dic3—21no—
82C22×Dic3—21no—
83C2×D12C2311yescharacteristic
84C2×C4×D3—21no—
85C2×Dic6—22no—
86C2×Dic6—22no—
87C2×Dic6—21no—
88C2×Dic6—21no—
89C2×Dic6—41no—
90C2×Dic6—41no—
91C2×Dic6C2311yescharacteristic
92C2×Dic6C2311yescharacteristic
93C2×Dic6C2311yescharacteristic
94C3×M16—41no—
95C2×C3×C8—41no—
96C2×C3×C8C2311yescharacteristic
97C2×C3×C8C2311yescharacteristic
98C2×C3×C8C2311yescharacteristic
99C2×C3×C8C2311yescharacteristic
100C3×C4⋊C4D411yescharacteristic
101C3×C22⋊C4D411yescharacteristic
102C3×C22⋊C4D411yescharacteristic
103C3×C42C2311yescharacteristic
104#217—21no—
105#217—21no—
106#217—21no—
107(C2×D3)⋊C4—21no—
108(C2×D3)⋊C4—21no—
109(C2×D3)⋊C4—21no—
110C4⋊Dic3—21no—
111C4⋊Dic3—21no—
112C4⋊Dic3—21no—
113C4⋊Dic3C2311yescharacteristic
114C4⋊Dic3C2311yescharacteristic
115C4⋊Dic3C2311yescharacteristic
116C4⋊Dic3C2311yescharacteristic
117Dic3⋊C4—21no—
118Dic3⋊C4—21no—
119Dic3⋊C4—21no—
120Dic3⋊C4—21no—
121Dic3⋊C4—21no—
122C4×Dic3—21no—
123C4×Dic3—21no—
124#204—22no—
125#204—41no—
126#204—41no—
127C22×Q8—31no—
128C22×Q8—31no—
129C2×SD16—31no—
130C2×SD16—31no—
131C2×SD16—31no—
132C2×M16C2×D311yescharacteristic
133C22×C8C2×D311yescharacteristic
134C4⋊Q8—31no—
135C4⋊Q8—61no—
136#126—61no—
137#125—31no—
138#123—61no—
139C22⋊Q8—31no—
140C22⋊Q8—31no—
141C22⋊Q8—61no—
142C22⋊Q8—61no—
143#121—31no—
144#121—31no—
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#103—31no—
161#103—31no—
162#103—31no—
163#103—31no—
164#103—31no—
165#103—31no—
166#102—31no—
167C22⋊C8C2×D311yescharacteristic
168C22⋊C8C2×D311yescharacteristic
169#97C2×D311yescharacteristic
170C23×C3C2×D411yescharacteristic
171C23×C3C2×D411yescharacteristic
172C22×D3—21no—
173C3×D4—22no—
174C2×C3×C4—21no—
175C2×C3×C4—21no—
176C2×C3×C4—21no—
177C2×C3×C4—21no—
178C2×C3×C4C2×D411yescharacteristic
179C2×C3×C4C2×D411yescharacteristic
180C2×C3×C4C2×D411yescharacteristic
181C2×C3×C4C2×D411yescharacteristic
182C2×C3×C4C2411yescharacteristic
183#67—42no—
184#67—81no—
185C2×Dic3—21no—
186C2×Dic3—21no—
187C2×Dic3—21no—
188C2×Dic3—21no—
189C2×Dic3—21no—
190C2×Dic3—21no—
191C2×Dic3—21no—
192C2×Dic3—42no—
193C2×Dic3—42no—
194C2×Dic3—81no—
195D12—21no—
196D12—21no—
197C4×D3—81no—
198Dic6—21no—
199Dic6—21no—
200Dic6—21no—
201Dic6—21no—
202Dic6—21no—
203Dic6—42no—
204Dic6—42no—
205Dic6#4112yes—
206C3×C8—21no—
207C3×C8—21no—
208C3×C8—21no—
209C3×C8—21no—
210C2×Q8—31no—
211C2×Q8—31no—
212C2×Q8—31no—
213C2×Q8—62no—
214C2×Q8—62no—
215C2×Q8—61no—
216C2×Q8—61no—
217C2×Q8—121no—
218C2×Q8—121no—
219C2×D4—31no—
220C2×D4—61no—
221C2×D4—61no—
222C2×D4D1211yescharacteristic
223C22×C4—61no—
224C22×C4—61no—
225C22×C4—61no—
226C22×C4—61no—
227C22×C4C22×D311yescharacteristic
228C22×C4C22×D311yescharacteristic
229SD16—62no—
230SD16—121no—
231SD16—121no—
232M16—41no—
233C2×C8—41no—
234C2×C8C22×D311yescharacteristic
235C2×C8C22×D311yescharacteristic
236C2×C8C22×D311yescharacteristic
237C2×C8C22×D311yescharacteristic
238C4⋊C4—31no—
239C4⋊C4—31no—
240C4⋊C4—31no—
241C4⋊C4—31no—
242C4⋊C4—61no—
243C4⋊C4—61no—
244C4⋊C4—61no—
245C4⋊C4—61no—
246C4⋊C4—61no—
247C4⋊C4—61no—
248C4⋊C4—61no—
249C4⋊C4—61no—
250C4⋊C4D1211yescharacteristic
251C22⋊C4—61no—
252C22⋊C4—61no—
253C22⋊C4—61no—
254C22⋊C4—61no—
255C22⋊C4—61no—
256C22⋊C4—61no—
257C22⋊C4D1211yescharacteristic
258C22⋊C4D1211yescharacteristic
259C42—61no—
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×C4C2×#4111yescharacteristic
277C3×C4H(5,𝔽2)11yescharacteristic
278Dic3—22no—
279Dic3—41no—
280Dic3—41no—
281Dic3—41no—
282Dic3—41no—
283Dic3—41no—
284Dic3—41no—
285C23—61no—
286C23C2×D1211yescharacteristic
287C23C2×D1211yescharacteristic
288Q8—32no—
289Q8—61no—
290Q8—61no—
291Q8—61no—
292Q8—61no—
293Q8—61no—
294Q8—122no—
295Q8—122no—
296D4—22no—
297D4—61no—
298D4—61no—
299D4—122no—
300D4—241no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—61no—
306C2×C4—61no—
307C2×C4—61no—
308C2×C4—61no—
309C2×C4—61no—
310C2×C4—61no—
311C2×C4—61no—
312C2×C4—122no—
313C2×C4—122no—
314C2×C4—241no—
315C2×C4—241no—
316C2×C4C2×D1211yescharacteristic
317C2×C4C2×D1211yescharacteristic
318C2×C4C2×D1211yescharacteristic
319C2×C4C2×D1211yescharacteristic
320C2×C4C23×D311yescharacteristic
321C8—21no—
322C8—21no—
323C8—21no—
324C8—21no—
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#90912yes—
340C22C22×D1211yescharacteristic
341C4—21no—
342C4—21no—
343C4—21no—
344C4—21no—
345C4—62no—
346C4—121no—
347C4—121no—
348C4—121no—
349C4—121no—
350C4—121no—
351C4—121no—
352C4#100411yescharacteristic
353C4D3×#4111yescharacteristic
354C3#332011yescharacteristic, complemented, Sylow
355C2—22no—
356C2—41no—
357C2—241no—
358C2#555411yescharacteristic
359C2C2×#90911yescharacteristic
360C2#575111yescharacteristic
subgroupG/H
centerC22C22×D12
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#435C2
socleC22×C3C22×D4
prime radical#5565C2
hypercenter#435D3
hypocenterC3#3320
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
2. D4×Dic6C2semidirect
3. C3×#435C2semidirect
4. #5134C2semidirect
5. #5120C2semidirect
6. #5114C2semidirect
7. C2×#816C2semidirect
8. #4841C2semidirect
9. #4829C2semidirect
10. #4738C2semidirect
11. #4738C2semidirect
12. #4723C2semidirect
13. #4722C2semidirect
14. #4710C2semidirect
15. #4703C2semidirect
72. #435D3semidirect
354. C3#3320semidirect

Maximal subgroups

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

subgroupindex
#55652
D4×Dic62
C3×#4352
#51342
#51202
#51142
C2×#8162
#48412
#48292
#47382
#47232
#47222
#47102
#47032
#33203