Finite Group Databasebeta

← #79993

Subgroups — #79993

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#5798C211yesmaximal, characteristic, complemented
2#5619C211yesmaximal, characteristic, complemented
3C3×#447C211yesmaximal, characteristic, complemented
4#5217C211yesmaximal, characteristic, complemented
5#5152C211yesmaximal, characteristic, complemented
6#5150C211yesmaximal, characteristic, complemented
7#5150C211yesmaximal, characteristic, complemented
8Dic3×D8C211yesmaximal, characteristic, complemented
9#5035C211yesmaximal, characteristic, complemented
10#4785C211yesmaximal, characteristic, complemented
11#4766C211yesmaximal, characteristic, complemented
12#4763C211yesmaximal, characteristic, complemented
13#4756C211yesmaximal, characteristic, complemented
14#4737C211yesmaximal, characteristic, complemented
15#4720C211yesmaximal, characteristic, complemented
16#3122—31nomaximal, Sylow
17C22×C3×D4C2211yescharacteristic
18C2×C3×D8C2211yescharacteristic
19C2×C3×D8C2211yescharacteristic
20C3×#121C2211yescharacteristic
21C2×#217—21no—
22C2×#217—21no—
23#940C2211yescharacteristic, complemented
24#939—21no—
25#938—21no—
26D4×Dic3—21no—
27D4×Dic3—21no—
28D4×Dic3C2211yescharacteristic
29D4×Dic3C2211yescharacteristic
30D4×Dic3C2211yescharacteristic
31D4×Dic3C2211yescharacteristic
32D4×Dic3C2211yescharacteristic, complemented
33C2×#213C2211yescharacteristic
34C2×#213C2211yescharacteristic
35#930C2211yescharacteristic
36#926C2211yescharacteristic
37#926C2211yescharacteristic
38#893C2211yescharacteristic, complemented
39#890C2211yescharacteristic, complemented
40#886—21no—
41#883—21no—
42C3×#102C2211yescharacteristic
43C3×#102C2211yescharacteristic
44C3×C22⋊C8C2211yescharacteristic
45#832C2211yescharacteristic
46#832C2211yescharacteristic
47#832C2211yescharacteristic, complemented
48#832C2211yescharacteristic, complemented
49#830C2211yescharacteristic
50#821C2211yescharacteristic, complemented
51#821C2211yescharacteristic, complemented
52#818C2211yescharacteristic, complemented
53#817C2211yescharacteristic, complemented
54#815C2211yescharacteristic, complemented
55Dic3⋊C8C2211yescharacteristic, complemented
56Dic3⋊C8C2211yescharacteristic, complemented
57C8×Dic3C2211yescharacteristic, complemented
58#808C2211yescharacteristic, complemented
59#807C2211yescharacteristic, 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#447D311yescharacteristic, complemented
70#442—31no—
71#442—31no—
72C4×D8—31no—
73C4×D8—31no—
74#433—31no—
75C24×C3—21no—
76C2×C3×D4—22no—
77C2×C3×D4—22no—
78C2×C3×D4—21no—
79C2×C3×D4—21no—
80C2×C3×D4C2311yescharacteristic
81C2×C3×D4C2311yescharacteristic
82C2×C3×D4C2311yescharacteristic
83C22×C3×C4C2311yescharacteristic
84C2×#67—21no—
85C2×#67—21no—
86C2×#67—21no—
87C22×Dic3—21no—
88C22×Dic3—21no—
89C22×Dic3—21no—
90C22×Dic3—21no—
91C22×Dic3—21no—
92C2×D12C2311yescharacteristic
93C2×C4×D3—21no—
94C3×D8—22no—
95C3×D8—22no—
96C2×C3×C8C2311yescharacteristic
97C2×C3×C8C2311yescharacteristic
98C3×C4⋊C4C2311yescharacteristic
99C3×C22⋊C4—21no—
100#217—21no—
101#217—21no—
102#217—21no—
103#217—21no—
104#217—21no—
105#217—21no—
106#217D411yescharacteristic
107#217D411yescharacteristic
108#213—22no—
109#213—22no—
110(C2×D3)⋊C4—21no—
111(C2×D3)⋊C4—21no—
112C4⋊Dic3—21no—
113C4⋊Dic3D411yescharacteristic
114C4⋊Dic3D411yescharacteristic
115C4⋊Dic3C2311yescharacteristic
116C4⋊Dic3C2311yescharacteristic
117C4⋊Dic3C2311yescharacteristic
118Dic3⋊C4—21no—
119C4×Dic3—21no—
120C4×Dic3C2311yescharacteristic
121C4×Dic3C2311yescharacteristic
122C2×C3⋊C8C2311yescharacteristic
123C2×C3⋊C8C2311yescharacteristic
124C22×D4C2×D311yescharacteristic
125C2×D8—31no—
126C2×D8—31no—
127C2×D8C2×D311yescharacteristic
128C2×D8C2×D311yescharacteristic
129#127—31no—
130#125—31no—
131#123—61no—
132#123—61no—
133#121—31no—
134#121—61no—
135#121—61no—
136#121C2×D311yescharacteristic
137C4×D4—31no—
138C4×D4—31no—
139C4×D4—31no—
140C4×D4—31no—
141C4×D4—31no—
142C4×D4—31no—
143C4×D4—61no—
144C4×D4—61no—
145#117—31no—
146#117—31no—
147C2×C22⋊C4—61no—
148C2×C22⋊C4—61no—
149#107—31no—
150#107—31no—
151#106—31no—
152#106—31no—
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
163C22⋊C8—31no—
164C22⋊C8C2×D311yescharacteristic
165#97—31no—
166C4×C8—31no—
167C23×C3—24no—
168C23×C3—21no—
169C23×C3—21no—
170C23×C3—21no—
171C23×C3—81no—
172C23×C3—81no—
173C23×C3C2×D411yescharacteristic
174C22×D3—21no—
175C3×D4—24no—
176C3×D4—21no—
177C3×D4—21no—
178C3×D4—21no—
179C3×D4—21no—
180C3×D4—81no—
181C3×D4#4112yes—
182C3×D4#4112yes—
183C2×C3×C4—21no—
184C2×C3×C4—21no—
185C2×C3×C4—21no—
186C2×C3×C4C2×D411yescharacteristic
187C2×C3×C4C2411yescharacteristic
188#67—81no—
189#67—81no—
190#67—81no—
191C2×Dic3—21no—
192C2×Dic3—21no—
193C2×Dic3—21no—
194C2×Dic3—81no—
195C2×Dic3—81no—
196C2×Dic3—81no—
197C2×Dic3—81no—
198C2×Dic3—81no—
199C2×Dic3C2×D411yescharacteristic
200C2×Dic3C2×D411yescharacteristic
201C2×Dic3C2×D411yescharacteristic
202C2×Dic3C2×D411yescharacteristic
203D12—21no—
204D12—21no—
205C4×D3—81no—
206C3×C8—21no—
207C3×C8—21no—
208C3⋊C8—21no—
209C3⋊C8—21no—
210C24—21no—
211C2×D4—22no—
212C2×D4—22no—
213C2×D4—21no—
214C2×D4—21no—
215C2×D4—31no—
216C2×D4—61no—
217C2×D4—61no—
218C2×D4—61no—
219C2×D4C22×D311yescharacteristic
220C2×D4C22×D311yescharacteristic
221C2×D4C22×D311yescharacteristic
222C22×C4—61no—
223C22×C4—61no—
224C22×C4—61no—
225C22×C4—61no—
226C22×C4—61no—
227C22×C4—61no—
228C22×C4C22×D311yescharacteristic
229D8—22no—
230D8—22no—
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—31no—
242C4⋊C4—61no—
243C4⋊C4—61no—
244C4⋊C4C22×D311yescharacteristic
245C22⋊C4—21no—
246C22⋊C4—31no—
247C22⋊C4—31no—
248C22⋊C4—61no—
249C22⋊C4—61no—
250C22⋊C4—61no—
251C22⋊C4—61no—
252C22⋊C4—61no—
253C22⋊C4—61no—
254C22⋊C4—61no—
255C22⋊C4—61no—
256C42—31no—
257C42—31no—
258C42—61no—
259C22×C3—21no—
260C22×C3—22no—
261C22×C3—22no—
262C22×C3—21no—
263C22×C3—21no—
264C22×C3—41no—
265C22×C3—41no—
266C22×C3—41no—
267C22×C3—41no—
268C22×C3—41no—
269C22×C3—41no—
270C22×C3—41no—
271C22×C3—84no—
272C22×C3C22×D411yescharacteristic
273C2×D3—41no—
274C2×D3—41no—
275C2×D3—41no—
276C3×C4—21no—
277C3×C4—41no—
278C3×C4C2×#4111yescharacteristic
279C3×C4C2×#4111yescharacteristic
280Dic3—21no—
281Dic3—21no—
282Dic3—21no—
283Dic3—21no—
284Dic3—41no—
285Dic3—41no—
286Dic3—41no—
287C23—24no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23—61no—
292C23—81no—
293C23—81no—
294C23D3×D411yescharacteristic
295D4—24no—
296D4—21no—
297D4—21no—
298D4—21no—
299D4—21no—
300D4—61no—
301D4—61no—
302D4—81no—
303D4—241no—
304D4—241no—
305D4—241no—
306D4#23712yes—
307D4#23712yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—31no—
312C2×C4—31no—
313C2×C4—31no—
314C2×C4—31no—
315C2×C4—61no—
316C2×C4—61no—
317C2×C4—61no—
318C2×C4—241no—
319C2×C4—241no—
320C2×C4—241no—
321C2×C4—241no—
322C2×C4—241no—
323C2×C4—241no—
324C2×C4D3×D411yescharacteristic
325C2×C4C23×D311yescharacteristic
326C8—21no—
327C8—21no—
328C8—61no—
329C8—61no—
330C2×C3—41no—
331C2×C3—42no—
332C2×C3—42no—
333C2×C3—81no—
334C2×C3#52511yescharacteristic
335C2×C3#57611yescharacteristic
336C2×C3#57611yescharacteristic
337D3—81no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—22no—
342C22—22no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—84no—
351C22—121no—
352C22—121no—
353C22—121no—
354C22C2×D3×D411yescharacteristic
355C4—21no—
356C4—41no—
357C4—61no—
358C4—61no—
359C4—61no—
360C4—61no—
361C4—121no—
362C4—121no—
363C4—121no—
364C4C2×#23711yescharacteristic
365C4C2×#23711yescharacteristic
366C3#312211yescharacteristic, complemented, Sylow
367C2—41no—
368C2—42no—
369C2—42no—
370C2—81no—
371C2—241no—
372C2#558611yescharacteristic
373C2#575711yescharacteristic
374C2#577411yescharacteristic
subgroupG/H
centerC22C2×D3×D4
commutator, cosocleC2×C3×C4C24
FrattiniC2×C4C23×D3
FittingC3×#447C2
socleC22×C3C22×D4
hypercenter#447D3
hypocenterC3#3122
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #5798C2semidirect
2. #5619C2semidirect
3. C3×#447C2semidirect
4. #5217C2semidirect
5. #5152C2semidirect
6. #5150C2semidirect
7. #5150C2semidirect
8. Dic3×D8C2semidirect
9. #5035C2semidirect
10. #4785C2semidirect
11. #4766C2semidirect
12. #4763C2semidirect
13. #4756C2semidirect
14. #4737C2semidirect
15. #4720C2semidirect
23. #940C22semidirect
32. D4×Dic3C22semidirect
38. #893C22semidirect
39. #890C22semidirect
47. #832C22semidirect
48. #832C22semidirect
50. #821C22semidirect
51. #821C22semidirect
52. #818C22semidirect
53. #817C22semidirect
54. #815C22semidirect
55. Dic3⋊C8C22semidirect
56. Dic3⋊C8C22semidirect
57. C8×Dic3C22semidirect
58. #808C22semidirect
59. #807C22semidirect
69. #447D3semidirect
366. C3#3122semidirect

Maximal subgroups

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

subgroupindex
#57982
#56192
C3×#4472
#52172
#51522
#51502
Dic3×D82
#50352
#47852
#47662
#47632
#47562
#47372
#47202
#31223