Finite Group Databasebeta

← #79881

Subgroups — #79881

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#5558C211yesmaximal, characteristic, complemented
2#5555C211yesmaximal, characteristic, complemented
3C3×#442C211yesmaximal, characteristic, complemented
4#5158C211yesmaximal, characteristic, complemented
5#5158C211yesmaximal, characteristic, complemented
6#5019C211yesmaximal, characteristic, complemented
7#5009C211yesmaximal, characteristic, complemented
8#4868C211yesmaximal, characteristic, complemented
9#4862C211yesmaximal, characteristic, complemented
10#4780C211yesmaximal, characteristic, complemented
11#4778C211yesmaximal, characteristic, complemented
12#4772C211yesmaximal, characteristic, complemented
13#4771C211yesmaximal, characteristic, complemented
14#4706C211yesmaximal, characteristic, complemented
15#4703C211yesmaximal, characteristic, complemented
16#3307—31nomaximal, Sylow
17C2×#237C2211yescharacteristic
18C2×#237C2211yescharacteristic
19C2×C3×D8C2211yescharacteristic
20C3×C4×D4C2211yescharacteristic
21C3×C4×D4C2211yescharacteristic
22#938C2211yescharacteristic
23#938C2211yescharacteristic
24C2×#214C2211yescharacteristic
25C2×#214C2211yescharacteristic
26#930—21no—
27#929—21no—
28C4×#67—21no—
29C2×C4⋊Dic3—21no—
30C2×ΓL(1,𝔽25)C2211yescharacteristic
31C2×D3×C8C2211yescharacteristic
32#897C2211yescharacteristic
33#897C2211yescharacteristic
34#892C2211yescharacteristic
35D3×C4⋊C4C2211yescharacteristic
36#886—21no—
37#886—21no—
38#884—21no—
39#879—21no—
40C4×D12C2211yescharacteristic
41#870C2211yescharacteristic
42#869C2211yescharacteristic
43C3×#106C2211yescharacteristic
44C3×#102C2211yescharacteristic
45C3×#102C2211yescharacteristic
46C3×#97C2211yescharacteristic
47#832C2211yescharacteristic
48#832C2211yescharacteristic
49(C2×D3)⋊C8C2211yescharacteristic
50(C2×D3)⋊C8C2211yescharacteristic
51#816C2211yescharacteristic
52#816C2211yescharacteristic
53#816C2211yescharacteristic
54#816C2211yescharacteristic
55#810C2211yescharacteristic
56#810C2211yescharacteristic
57#808C2211yescharacteristic
58#807C2211yescharacteristic
59C4⋊(C3⋊C8)C2211yescharacteristic
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#442D311yescharacteristic, complemented
72#435—31no—
73#417—31no—
74#416—31no—
75C2×C3×D4C2311yescharacteristic
76C2×C3×D4C2311yescharacteristic
77C22×C3×C4—21no—
78C22×C3×C4—21no—
79C2×#67—21no—
80C2×#67—21no—
81C2×#67—21no—
82C2×#67—21no—
83C22×Dic3—21no—
84C22×Dic3—21no—
85#237—22no—
86#237—22no—
87#237—41no—
88#237—41no—
89C2×D12D411yescharacteristic
90C2×C4×D3—21no—
91C2×C4×D3C2311yescharacteristic
92C2×C4×D3C2311yescharacteristic
93C2×Dic6C2311yescharacteristic
94C2×Dic6C2311yescharacteristic
95C3×D8—22no—
96C2×C3×C8C2311yescharacteristic
97C2×C3×C8C2311yescharacteristic
98C3×C4⋊C4C2311yescharacteristic
99C3×C4⋊C4C2311yescharacteristic
100C3×C22⋊C4—21no—
101C3×C22⋊C4—21no—
102C3×C42C2311yescharacteristic
103#217—21no—
104#217—21no—
105#214—41no—
106#214—41no—
107(C2×D3)⋊C4—21no—
108(C2×D3)⋊C4—21no—
109(C2×D3)⋊C4—21no—
110(C2×D3)⋊C4D411yescharacteristic
111(C2×D3)⋊C4D411yescharacteristic
112C4⋊Dic3—21no—
113C4⋊Dic3—21no—
114C4⋊Dic3—21no—
115C4⋊Dic3—21no—
116C4⋊Dic3D411yescharacteristic
117C4⋊Dic3C2311yescharacteristic
118C4⋊Dic3C2311yescharacteristic
119Dic3⋊C4—21no—
120Dic3⋊C4—21no—
121Dic3⋊C4—21no—
122C4×Dic3—21no—
123C2×C3⋊C8C2311yescharacteristic
124C2×C3⋊C8C2311yescharacteristic
125ΓL(1,𝔽25)—41no—
126D3×C8—41no—
127C2×#41—31no—
128C2×#41—31no—
129C2×SD16—31no—
130C2×SD16—31no—
131C2×D8C2×D311yescharacteristic
132C2×M16—31no—
133C22×C8—31no—
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—61no—
148C4×D4C2×D311yescharacteristic
149C4×D4C2×D311yescharacteristic
150#117—31no—
151C2×C4⋊C4—31no—
152C2×C4⋊C4—61no—
153#107—31no—
154#106—31no—
155#106C2×D311yescharacteristic
156C4⋊C8—31no—
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#102C2×D311yescharacteristic
166#102C2×D311yescharacteristic
167C22⋊C8—31no—
168C22⋊C8—31no—
169#97C2×D311yescharacteristic
170C23×C3—21no—
171C23×C3—21no—
172C22×D3C2×D411yescharacteristic
173C22×D3C2×D411yescharacteristic
174C3×D4—21no—
175C3×D4—21no—
176C3×D4—21no—
177C3×D4#4112yes—
178C2×C3×C4—21no—
179C2×C3×C4—21no—
180C2×C3×C4—42no—
181C2×C3×C4—81no—
182C2×C3×C4C2×D411yescharacteristic
183C2×C3×C4C2×D411yescharacteristic
184C2×C3×C4C2411yescharacteristic
185#67—42no—
186#67—42no—
187#67—42no—
188#67—81no—
189C2×Dic3—21no—
190C2×Dic3—21no—
191C2×Dic3—21no—
192C2×Dic3—21no—
193C2×Dic3—42no—
194C2×Dic3—42no—
195C2×Dic3C2×D411yescharacteristic
196C2×Dic3C2×D411yescharacteristic
197D12—41no—
198C4×D3—21no—
199C4×D3—21no—
200C4×D3—21no—
201C4×D3—21no—
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—61no—
219C2×D4—61no—
220C2×D4—61no—
221C2×D4—61no—
222C2×D4C22×D311yescharacteristic
223C2×D4C22×D311yescharacteristic
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—31no—
227C22×C4—31no—
228C22×C4—61no—
229C22×C4—61no—
230C22×C4—61no—
231SD16—121no—
232SD16—121no—
233D8—22no—
234M16—121no—
235C2×C8—31no—
236C2×C8—31no—
237C2×C8—121no—
238C2×C8C22×D311yescharacteristic
239C2×C8C22×D311yescharacteristic
240C4⋊C4—31no—
241C4⋊C4—31no—
242C4⋊C4—31no—
243C4⋊C4—61no—
244C4⋊C4—61no—
245C4⋊C4—61no—
246C4⋊C4—61no—
247C4⋊C4—61no—
248C4⋊C4—61no—
249C4⋊C4—61no—
250C4⋊C4C22×D311yescharacteristic
251C4⋊C4C22×D311yescharacteristic
252C22⋊C4—21no—
253C22⋊C4—21no—
254C22⋊C4—31no—
255C22⋊C4—31no—
256C22⋊C4—61no—
257C22⋊C4—61no—
258C22⋊C4—61no—
259C22⋊C4—61no—
260C22⋊C4—61no—
261C42—61no—
262C42C22×D311yescharacteristic
263C22×C3—22no—
264C22×C3—41no—
265C22×C3—41no—
266C22×C3—41no—
267C22×C3—41no—
268C22×C3—41no—
269C22×C3C22×D411yescharacteristic
270C2×D3—21no—
271C2×D3—21no—
272C2×D3—21no—
273C2×D3—21no—
274C2×D3—21no—
275C2×D3—21no—
276C3×C4—21no—
277C3×C4—21no—
278C3×C4—41no—
279C3×C4—41no—
280C3×C4C2×#4111yescharacteristic
281C3×C4H(5,𝔽2)11yescharacteristic
282Dic3—21no—
283Dic3—21no—
284Dic3—41no—
285Dic3—41no—
286Dic3—41no—
287Dic3—41no—
288C23—21no—
289C23—21no—
290C23—31no—
291C23—31no—
292Q8—61no—
293Q8—61no—
294Q8—61no—
295Q8—61no—
296D4—21no—
297D4—21no—
298D4—21no—
299D4—121no—
300D4—122no—
301D4—122no—
302D4—122no—
303D4—241no—
304D4#23512yes—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—31no—
308C2×C4—31no—
309C2×C4—42no—
310C2×C4—61no—
311C2×C4—61no—
312C2×C4—61no—
313C2×C4—61no—
314C2×C4—61no—
315C2×C4—61no—
316C2×C4—61no—
317C2×C4—61no—
318C2×C4—81no—
319C2×C4—122no—
320C2×C4—122no—
321C2×C4—241no—
322C2×C4D3×D411yescharacteristic
323C2×C4D3×D411yescharacteristic
324C2×C4C23×D311yescharacteristic
325C8—21no—
326C8—21no—
327C8—61no—
328C8—61no—
329C2×C3—42no—
330C2×C3—81no—
331C2×C3#54611yescharacteristic
332C2×C3#57511yescharacteristic
333C2×C3#57711yescharacteristic
334D3—41no—
335D3—41no—
336C22—22no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—61no—
343C22—61no—
344C22—61no—
345C22—61no—
346C22—61no—
347C22—61no—
348C22C2×D3×D411yescharacteristic
349C4—21no—
350C4—21no—
351C4—41no—
352C4—41no—
353C4—61no—
354C4—61no—
355C4—121no—
356C4—121no—
357C4—121no—
358C4—121no—
359C4C2×#23511yescharacteristic
360C4#100911yescharacteristic
361C3#330711yescharacteristic, complemented, Sylow
362C2—42no—
363C2—81no—
364C2—121no—
365C2—121no—
366C2#555011yescharacteristic
367C2#577311yescharacteristic
368C2#577511yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#442C2
socleC22×C3C22×D4
hypercenter#442D3
hypocenterC3#3307
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #5558C2semidirect
2. #5555C2semidirect
3. C3×#442C2semidirect
4. #5158C2semidirect
5. #5158C2semidirect
6. #5019C2semidirect
7. #5009C2semidirect
8. #4868C2semidirect
9. #4862C2semidirect
10. #4780C2semidirect
11. #4778C2semidirect
12. #4772C2semidirect
13. #4771C2semidirect
14. #4706C2semidirect
15. #4703C2semidirect
71. #442D3semidirect
361. C3#3307semidirect

Maximal subgroups

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

subgroupindex
#55582
#55552
C3×#4422
#51582
#50192
#50092
#48682
#48622
#47802
#47782
#47722
#47712
#47062
#47032
#33073