Finite Group Databasebeta

← #79874

Subgroups — #79874

Order 384.

418 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#5562C211yesmaximal, characteristic, complemented
2#5545C211yesmaximal, characteristic, complemented
3C3×#442C211yesmaximal, characteristic, complemented
4#5156C211yesmaximal, characteristic, complemented
5#5150C211yesmaximal, characteristic, complemented
6C4×#213C211yesmaximal, characteristic, complemented
7C4×#213C211yesmaximal, characteristic, complemented
8#4871C211yesmaximal, characteristic, complemented
9#4866C211yesmaximal, characteristic, complemented
10#4786C211yesmaximal, characteristic, complemented
11#4779C211yesmaximal, characteristic, complemented
12#4773C211yesmaximal, characteristic, complemented
13#4763C211yesmaximal, characteristic, complemented
14#4711C211yesmaximal, characteristic, complemented
15#4709C211yesmaximal, characteristic, complemented
16#3122—31nomaximal, Sylow
17C2×D3×D4C2211yescharacteristic
18C2×C3×D8C2211yescharacteristic
19C3×C4×D4C2211yescharacteristic
20C3×C4×D4C2211yescharacteristic, complemented
21#940C2211yescharacteristic, complemented
22#938C2211yescharacteristic
23D4×Dic3C2211yescharacteristic
24C2×#213C2211yescharacteristic
25C2×#213C2211yescharacteristic
26#930—21no—
27#929—21no—
28C4×#67—21no—
29C2×(C2×D3)⋊C4—21no—
30C2×D24C2211yescharacteristic
31#895C2211yescharacteristic
32#893C2211yescharacteristic
33#892C2211yescharacteristic
34#890C2211yescharacteristic, complemented
35#884—21no—
36#883—21no—
37#67⋊C4—21no—
38D3×C22⋊C4—21no—
39C4×D12C2211yescharacteristic
40C4×D12C2211yescharacteristic, complemented
41#872C2211yescharacteristic
42C3×#106C2211yescharacteristic, complemented
43C3×#102C2211yescharacteristic
44C3×#102C2211yescharacteristic, complemented
45C3×#97C2211yescharacteristic, complemented
46#832C2211yescharacteristic
47#832C2211yescharacteristic, complemented
48#821C2211yescharacteristic
49#821C2211yescharacteristic, complemented
50(C2×D3)⋊C8C2211yescharacteristic
51(C2×D3)⋊C8C2211yescharacteristic
52#817C2211yescharacteristic, complemented
53Dic3⋊C8C2211yescharacteristic, complemented
54Dic3⋊C8C2211yescharacteristic, complemented
55#809C2211yescharacteristic
56#809C2211yescharacteristic, complemented
57#807C2211yescharacteristic, complemented
58#807C2211yescharacteristic, complemented
59C4×C3⋊C8C2211yescharacteristic, complemented
60#540—31no—
61#518—31no—
62#482—31no—
63#482—31no—
64#478—31no—
65#478—31no—
66#459—31no—
67#459—31no—
68#447—31no—
69#447—31no—
70#442—31no—
71#442D311yescharacteristic, complemented
72C4×D8—31no—
73C4×D8—31no—
74#433—31no—
75C23×D3—21no—
76C2×C3×D4C2311yescharacteristic
77C2×C3×D4C2311yescharacteristic
78C22×C3×C4—21no—
79C22×C3×C4—21no—
80C2×#67—21no—
81C2×#67—21no—
82C2×#67—21no—
83C2×#67—21no—
84C22×Dic3—21no—
85D3×D4—22no—
86D3×D4—22no—
87C2×D12—21no—
88C2×D12C2311yescharacteristic
89C2×D12C2311yescharacteristic
90C2×C4×D3—21no—
91C2×C4×D3—21no—
92C2×C4×D3—21no—
93C2×C4×D3C2311yescharacteristic
94C3×D8—22no—
95C2×C3×C8C2311yescharacteristic
96C2×C3×C8C2311yescharacteristic
97C3×C4⋊C4C2311yescharacteristic
98C3×C4⋊C4C2311yescharacteristic
99C3×C22⋊C4—21no—
100C3×C22⋊C4—21no—
101C3×C42C2311yescharacteristic
102#217—21no—
103#217—21no—
104#213—22no—
105#213—22no—
106(C2×D3)⋊C4—21no—
107(C2×D3)⋊C4—21no—
108(C2×D3)⋊C4—21no—
109(C2×D3)⋊C4—21no—
110(C2×D3)⋊C4—21no—
111(C2×D3)⋊C4D411yescharacteristic
112(C2×D3)⋊C4D411yescharacteristic
113C4⋊Dic3—21no—
114C4⋊Dic3C2311yescharacteristic
115C4⋊Dic3C2311yescharacteristic
116Dic3⋊C4—21no—
117Dic3⋊C4D411yescharacteristic
118Dic3⋊C4D411yescharacteristic
119C4×Dic3—21no—
120C4×Dic3C2311yescharacteristic
121C2×C3⋊C8C2311yescharacteristic
122C2×C3⋊C8C2311yescharacteristic
123D24—22no—
124C22×D4—31no—
125C2×D8—31no—
126C2×D8—31no—
127C2×D8—31no—
128C2×D8C2×D311yescharacteristic
129#127—31no—
130#125—31no—
131#123—61no—
132#123—61no—
133#121—31no—
134#121—31no—
135#121—61no—
136#121—61no—
137C4×D4—31no—
138C4×D4—31no—
139C4×D4—31no—
140C4×D4—31no—
141C4×D4—61no—
142C4×D4—61no—
143C4×D4C2×D311yescharacteristic
144C4×D4C2×D311yescharacteristic, complemented
145#117—31no—
146#117—31no—
147C2×C22⋊C4—61no—
148C2×C22⋊C4—61no—
149#107—31no—
150#107—31no—
151#106—31no—
152#106C2×D311yescharacteristic, complemented
153C4⋊C8—31no—
154C4⋊C8—31no—
155#102—31no—
156#102—31no—
157#102—31no—
158#102—31no—
159#102—31no—
160#102—31no—
161#102C2×D311yescharacteristic
162#102C2×D311yescharacteristic, complemented
163C22⋊C8—31no—
164C22⋊C8—31no—
165#97C2×D311yescharacteristic, complemented
166C4×C8—31no—
167C23×C3—21no—
168C23×C3—21no—
169C22×D3—21no—
170C22×D3—24no—
171C22×D3—21no—
172C22×D3—81no—
173C22×D3—81no—
174C22×D3C2×D411yescharacteristic
175C3×D4—21no—
176C3×D4—21no—
177C3×D4—21no—
178C3×D4#4112yes—
179C2×C3×C4—21no—
180C2×C3×C4—21no—
181C2×C3×C4—81no—
182C2×C3×C4—81no—
183C2×C3×C4C2×D411yescharacteristic
184C2×C3×C4C2×D411yescharacteristic
185C2×C3×C4C2411yescharacteristic
186#67—24no—
187#67—81no—
188#67—81no—
189#67—81no—
190C2×Dic3—21no—
191C2×Dic3—21no—
192C2×Dic3—81no—
193C2×Dic3C2×D411yescharacteristic
194C2×Dic3C2×D411yescharacteristic
195C2×Dic3C2×D411yescharacteristic
196D12—21no—
197D12—21no—
198D12—21no—
199D12—81no—
200D12#4112yes—
201C4×D3—21no—
202C4×D3—21no—
203C4×D3—81no—
204C4×D3—81no—
205C4×D3—81no—
206C3×C8—21no—
207C3×C8—21no—
208C3⋊C8—21no—
209C3⋊C8—21no—
210C24—61no—
211C2×D4—31no—
212C2×D4—31no—
213C2×D4—61no—
214C2×D4—61no—
215C2×D4—61no—
216C2×D4—61no—
217C2×D4—62no—
218C2×D4—62no—
219C2×D4—61no—
220C2×D4C22×D311yescharacteristic
221C2×D4C22×D311yescharacteristic
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—31no—
225C22×C4—61no—
226C22×C4—61no—
227C22×C4—61no—
228C22×C4—61no—
229D8—22no—
230D8—62no—
231D8—62no—
232D8—62no—
233C2×C8—31no—
234C2×C8—31no—
235C2×C8C22×D311yescharacteristic
236C2×C8C22×D311yescharacteristic
237C4⋊C4—31no—
238C4⋊C4—31no—
239C4⋊C4—31no—
240C4⋊C4—31no—
241C4⋊C4—61no—
242C4⋊C4—61no—
243C4⋊C4C22×D311yescharacteristic
244C4⋊C4C22×D311yescharacteristic
245C22⋊C4—21no—
246C22⋊C4—21no—
247C22⋊C4—31no—
248C22⋊C4—31no—
249C22⋊C4—61no—
250C22⋊C4—61no—
251C22⋊C4—61no—
252C22⋊C4—61no—
253C22⋊C4—61no—
254C22⋊C4—61no—
255C22⋊C4—61no—
256C42—31no—
257C42—61no—
258C42C22×D311yescharacteristic
259C22×C3—22no—
260C22×C3—41no—
261C22×C3—41no—
262C22×C3—41no—
263C22×C3—41no—
264C22×C3—41no—
265C22×C3C22×D411yescharacteristic
266C2×D3—21no—
267C2×D3—22no—
268C2×D3—21no—
269C2×D3—21no—
270C2×D3—41no—
271C2×D3—41no—
272C2×D3—41no—
273C2×D3—41no—
274C2×D3—41no—
275C2×D3—84no—
276C3×C4—21no—
277C3×C4—21no—
278C3×C4—41no—
279C3×C4—41no—
280C3×C4C2×#4111yescharacteristic
281C3×C4C2×#4111yescharacteristic
282Dic3—21no—
283Dic3—21no—
284Dic3—21no—
285Dic3—41no—
286Dic3—41no—
287C23—21no—
288C23—21no—
289C23—31no—
290C23—64no—
291C23—61no—
292C23—61no—
293C23—241no—
294C23—241no—
295D4—21no—
296D4—21no—
297D4—21no—
298D4—32no—
299D4—64no—
300D4—61no—
301D4—61no—
302D4—61no—
303D4—241no—
304D4—241no—
305D4—241no—
306D4—241no—
307D4#23512yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—31no—
311C2×C4—31no—
312C2×C4—31no—
313C2×C4—61no—
314C2×C4—61no—
315C2×C4—61no—
316C2×C4—61no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4—241no—
320C2×C4—241no—
321C2×C4—241no—
322C2×C4—241no—
323C2×C4D3×D411yescharacteristic
324C2×C4D3×D411yescharacteristic
325C2×C4C23×D311yescharacteristic
326C8—21no—
327C8—21no—
328C8—61no—
329C8—61no—
330C2×C3—42no—
331C2×C3—81no—
332C2×C3#52511yescharacteristic
333C2×C3#57611yescharacteristic
334C2×C3#57611yescharacteristic
335D3—41no—
336D3—42no—
337D3—81no—
338C22—22no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—61no—
345C22—61no—
346C22—61no—
347C22—62no—
348C22—121no—
349C22—121no—
350C22—121no—
351C22—121no—
352C22—121no—
353C22—244no—
354C22C2×D3×D411yescharacteristic
355C4—21no—
356C4—21no—
357C4—41no—
358C4—41no—
359C4—61no—
360C4—61no—
361C4—61no—
362C4—121no—
363C4—121no—
364C4C2×#23511yescharacteristic
365C4D3×#4111yescharacteristic
366C3#312211yescharacteristic, complemented, Sylow
367C2—42no—
368C2—81no—
369C2—121no—
370C2—122no—
371C2—241no—
372C2#554711yescharacteristic
373C2#577411yescharacteristic
374C2#577411yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#442C2
socleC22×C3C22×D4
hypercenter#442D3
hypocenterC3#3122
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. #5562C2semidirect
2. #5545C2semidirect
3. C3×#442C2semidirect
4. #5156C2semidirect
5. #5150C2semidirect
6. C4×#213C2semidirect
7. C4×#213C2semidirect
8. #4871C2semidirect
9. #4866C2semidirect
10. #4786C2semidirect
11. #4779C2semidirect
12. #4773C2semidirect
13. #4763C2semidirect
14. #4711C2semidirect
15. #4709C2semidirect
20. C3×C4×D4C22semidirect
21. #940C22semidirect
34. #890C22semidirect
40. C4×D12C22semidirect
42. C3×#106C22semidirect
44. C3×#102C22semidirect
45. C3×#97C22semidirect
47. #832C22semidirect
49. #821C22semidirect
52. #817C22semidirect
53. Dic3⋊C8C22semidirect
54. Dic3⋊C8C22semidirect
56. #809C22semidirect
57. #807C22semidirect
58. #807C22semidirect
59. C4×C3⋊C8C22semidirect
71. #442D3semidirect
144. C4×D4C2×D3semidirect
152. #106C2×D3semidirect
162. #102C2×D3semidirect
165. #97C2×D3semidirect
366. C3#3122semidirect

Maximal subgroups

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

subgroupindex
#55622
#55452
C3×#4422
#51562
#51502
C4×#2132
#48712
#48662
#47862
#47792
#47732
#47632
#47112
#47092
#31223