Finite Group Databasebeta

← #79500

Subgroups — #79500

Order 384.

394 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#5565C211yesmaximal, characteristic, complemented
2#5551C211yesmaximal, characteristic, complemented
3C3×#435C211yesmaximal, characteristic, complemented
4#5134C211yesmaximal, characteristic, complemented
5#5133C211yesmaximal, characteristic, complemented
6#5114C211yesmaximal, characteristic, complemented
7#5113C211yesmaximal, characteristic, complemented
8#4847C211yesmaximal, characteristic, complemented
9#4841C211yesmaximal, characteristic, complemented
10#4734C211yesmaximal, characteristic, complemented
11#4734C211yesmaximal, characteristic, complemented
12#4723C211yesmaximal, characteristic, complemented
13#4721C211yesmaximal, characteristic, complemented
14#4711C211yesmaximal, characteristic, complemented
15#4703C211yesmaximal, characteristic, complemented
16#3307—31nomaximal, Sylow
17C2×#235C2211yescharacteristic
18C2×#235C2211yescharacteristic
19C2×C3×M16C2211yescharacteristic
20C22×C3×C8C2211yescharacteristic
21C3×C4×D4C2211yescharacteristic
22#939—21no—
23#938—21no—
24#930C2211yescharacteristic
25#930C2211yescharacteristic
26#926C2211yescharacteristic
27C2×C4⋊Dic3C2211yescharacteristic
28#924C2211yescharacteristic
29#924C2211yescharacteristic
30C2×D24C2211yescharacteristic
31C2×#204C2211yescharacteristic
32C2×#204C2211yescharacteristic
33#898—21no—
34D3×C4⋊C4—21no—
35#883—21no—
36#883—21no—
37#883—21no—
38#67⋊C4—21no—
39C4×D12C2211yescharacteristic
40C4×D12C2211yescharacteristic
41#870C2211yescharacteristic
42#869C2211yescharacteristic
43C3×C4⋊C8C2211yescharacteristic
44C3×C22⋊C8C2211yescharacteristic
45C3×C22⋊C8C2211yescharacteristic
46C3×#97C2211yescharacteristic
47#821C2211yescharacteristic
48#821C2211yescharacteristic
49#821C2211yescharacteristic
50#821C2211yescharacteristic
51#818C2211yescharacteristic
52#817C2211yescharacteristic
53#817C2211yescharacteristic
54#816C2211yescharacteristic
55#816C2211yescharacteristic
56#816C2211yescharacteristic
57#816C2211yescharacteristic
58#816C2211yescharacteristic
59#816C2211yescharacteristic
60#553—31no—
61#547—31no—
62#491—31no—
63#485—31no—
64#483—31no—
65#478—31no—
66#468—31no—
67#465—31no—
68#461—31no—
69#449—31no—
70#449—31no—
71#442—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—
82C22×Dic3—21no—
83#235—22no—
84#235—22no—
85#235—41no—
86#235—41no—
87C2×D12C2311yescharacteristic
88C2×D12C2311yescharacteristic
89C2×C4×D3—21no—
90C2×C4×D3—21no—
91C2×C4×D3—21no—
92C2×C4×D3—21no—
93C2×Dic6C2311yescharacteristic
94C2×Dic6C2311yescharacteristic
95C3×M16—41no—
96C2×C3×C8—41no—
97C2×C3×C8C2311yescharacteristic
98C2×C3×C8C2311yescharacteristic
99C2×C3×C8C2311yescharacteristic
100C2×C3×C8C2311yescharacteristic
101C3×C4⋊C4D411yescharacteristic
102C3×C22⋊C4D411yescharacteristic
103C3×C22⋊C4D411yescharacteristic
104C3×C42C2311yescharacteristic
105#217—21no—
106#217—21no—
107#217—21no—
108(C2×D3)⋊C4—21no—
109(C2×D3)⋊C4—21no—
110(C2×D3)⋊C4—21no—
111(C2×D3)⋊C4—21no—
112C4⋊Dic3—21no—
113C4⋊Dic3—21no—
114C4⋊Dic3—21no—
115C4⋊Dic3C2311yescharacteristic
116C4⋊Dic3C2311yescharacteristic
117C4⋊Dic3C2311yescharacteristic
118C4⋊Dic3C2311yescharacteristic
119Dic3⋊C4—21no—
120Dic3⋊C4—21no—
121Dic3⋊C4—21no—
122Dic3⋊C4—21no—
123C4×Dic3—21no—
124D24—22no—
125#204—41no—
126#204—41no—
127C2×#41—31no—
128C2×#41—31no—
129C2×SD16—31no—
130C2×SD16—31no—
131C2×D8—31no—
132C2×M16C2×D311yescharacteristic
133C22×C8C2×D311yescharacteristic
134C4⋊Q8—31no—
135#126—61no—
136#125—31no—
137#123—61no—
138#123—61no—
139#123—61no—
140C22⋊Q8—31no—
141C22⋊Q8—31no—
142#121—31no—
143#121—31no—
144#121—61no—
145#121—61no—
146C4×D4—31no—
147C4×D4—31no—
148C4×D4—61no—
149C4×D4C2×D311yescharacteristic
150#117—31no—
151C2×C4⋊C4—31no—
152C2×C4⋊C4—61no—
153#107—31no—
154#106—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#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—
174C3×D4—41no—
175C2×C3×C4—21no—
176C2×C3×C4—21no—
177C2×C3×C4—21no—
178C2×C3×C4—21no—
179C2×C3×C4C2×D411yescharacteristic
180C2×C3×C4C2×D411yescharacteristic
181C2×C3×C4C2×D411yescharacteristic
182C2×C3×C4C2×D411yescharacteristic
183C2×C3×C4C2411yescharacteristic
184#67—42no—
185#67—42no—
186#67—42no—
187#67—81no—
188C2×Dic3—21no—
189C2×Dic3—21no—
190C2×Dic3—21no—
191C2×Dic3—21no—
192C2×Dic3—21no—
193C2×Dic3—21no—
194C2×Dic3—81no—
195D12—21no—
196D12—21no—
197D12—21no—
198D12#4112yes—
199C4×D3—42no—
200C4×D3—42no—
201C4×D3—42no—
202C4×D3—81no—
203Dic6—21no—
204Dic6—21no—
205Dic6—21no—
206Dic6—21no—
207C3×C8—21no—
208C3×C8—21no—
209C3×C8—21no—
210C3×C8—21no—
211#41—62no—
212#41—62no—
213#41—121no—
214#41—121no—
215C2×Q8—31no—
216C2×Q8—31no—
217C2×D4—31no—
218C2×D4—31no—
219C2×D4—61no—
220C2×D4—61no—
221C2×D4—61no—
222C2×D4—61no—
223C2×D4D1211yescharacteristic
224C22×C4—61no—
225C22×C4—61no—
226C22×C4—61no—
227C22×C4—61no—
228C22×C4—61no—
229C22×C4C22×D311yescharacteristic
230C22×C4C22×D311yescharacteristic
231SD16—121no—
232SD16—121no—
233D8—62no—
234M16—41no—
235C2×C8—41no—
236C2×C8C22×D311yescharacteristic
237C2×C8C22×D311yescharacteristic
238C2×C8C22×D311yescharacteristic
239C2×C8C22×D311yescharacteristic
240C4⋊C4—31no—
241C4⋊C4—31no—
242C4⋊C4—31no—
243C4⋊C4—31no—
244C4⋊C4—61no—
245C4⋊C4—61no—
246C4⋊C4—61no—
247C4⋊C4—61no—
248C4⋊C4—61no—
249C4⋊C4—61no—
250C4⋊C4—61no—
251C4⋊C4D1211yescharacteristic
252C22⋊C4—61no—
253C22⋊C4—61no—
254C22⋊C4—61no—
255C22⋊C4—61no—
256C22⋊C4—61no—
257C22⋊C4—61no—
258C22⋊C4—61no—
259C22⋊C4D1211yescharacteristic
260C22⋊C4D1211yescharacteristic
261C42—61no—
262C42C22×D311yescharacteristic
263C22×C3—21no—
264C22×C3—21no—
265C22×C3—21no—
266C22×C3—21no—
267C22×C3—21no—
268C22×C3—21no—
269C22×C3C22×D411yescharacteristic
270C2×D3—22no—
271C2×D3—41no—
272C2×D3—41no—
273C2×D3—41no—
274C2×D3—41no—
275C2×D3—41no—
276C3×C4—21no—
277C3×C4—21no—
278C3×C4—21no—
279C3×C4—21no—
280C3×C4C2×#4111yescharacteristic
281C3×C4H(5,𝔽2)11yescharacteristic
282Dic3—41no—
283Dic3—41no—
284Dic3—41no—
285Dic3—41no—
286Dic3—41no—
287Dic3—41no—
288C23—61no—
289C23—61no—
290C23C2×D1211yescharacteristic
291C23C2×D1211yescharacteristic
292Q8—61no—
293Q8—61no—
294Q8—61no—
295Q8—61no—
296D4—32no—
297D4—41no—
298D4—61no—
299D4—61no—
300D4—61no—
301D4—122no—
302D4—122no—
303D4—122no—
304D4—241no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—61no—
310C2×C4—61no—
311C2×C4—61no—
312C2×C4—61no—
313C2×C4—61no—
314C2×C4—61no—
315C2×C4—122no—
316C2×C4—122no—
317C2×C4—122no—
318C2×C4—241no—
319C2×C4—241no—
320C2×C4C2×D1211yescharacteristic
321C2×C4C2×D1211yescharacteristic
322C2×C4C2×D1211yescharacteristic
323C2×C4C2×D1211yescharacteristic
324C2×C4C23×D311yescharacteristic
325C8—21no—
326C8—21no—
327C8—21no—
328C8—21no—
329C2×C3—41no—
330C2×C3—41no—
331C2×C3#54611yescharacteristic
332C2×C3#57511yescharacteristic
333C2×C3#57711yescharacteristic
334D3—42no—
335D3—81no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—62no—
343C22—121no—
344C22—121no—
345C22—121no—
346C22—121no—
347C22—121no—
348C22C22×D1211yescharacteristic
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—121no—
354C4—121no—
355C4—121no—
356C4—121no—
357C4—121no—
358C4—121no—
359C4#100411yescharacteristic
360C4D3×#4111yescharacteristic
361C3#330711yescharacteristic, complemented, Sylow
362C2—41no—
363C2—41no—
364C2—122no—
365C2—241no—
366C2#555411yescharacteristic
367C2#574811yescharacteristic
368C2#575111yescharacteristic
subgroupG/H
centerC22C22×D12
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#435C2
socleC22×C3C22×D4
hypercenter#435D3
hypocenterC3#3307
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. #5551C2semidirect
3. C3×#435C2semidirect
4. #5134C2semidirect
5. #5133C2semidirect
6. #5114C2semidirect
7. #5113C2semidirect
8. #4847C2semidirect
9. #4841C2semidirect
10. #4734C2semidirect
11. #4734C2semidirect
12. #4723C2semidirect
13. #4721C2semidirect
14. #4711C2semidirect
15. #4703C2semidirect
72. #435D3semidirect
361. C3#3307semidirect

Maximal subgroups

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

subgroupindex
#55652
#55512
C3×#4352
#51342
#51332
#51142
#51132
#48472
#48412
#47342
#47232
#47212
#47112
#47032
#33073