Finite Group Databasebeta

← #73648

Subgroups — #73648

Order 384.

576 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#896C211yesmaximal, characteristic
2C2×#872C211yesmaximal, characteristic
3C2×C4×Dic6C211yesmaximal, characteristic, complemented
4C3×C4×C4⋊C4C211yesmaximal, characteristic, complemented
5#4990C211yesmaximal, characteristic
6#4980C211yesmaximal, characteristic, complemented
7#4976C211yesmaximal, characteristic, complemented
8#4940C211yesmaximal, characteristic
9#4940C211yesmaximal, characteristic
10#4933C211yesmaximal, characteristic, complemented
11C4×Dic3⋊C4C211yesmaximal, characteristic, complemented
12#4670C211yesmaximal, characteristic
13#4666C211yesmaximal, characteristic
14#4649C211yesmaximal, characteristic, complemented
15#4646C211yesmaximal, characteristic, complemented
16#2362—31nomaximal, Sylow
17C22×C4×D3C2211yescharacteristic
18C22×Dic6C2211yescharacteristic
19C2×C3×C4⋊C4C2211yescharacteristic
20C2×C3×C4⋊C4C2211yescharacteristic
21C2×C3×C42C2211yescharacteristic
22C2×C3×C42C2211yescharacteristic
23C2×C3×C42C2211yescharacteristic
24C2×(C2×D3)⋊C4C2211yescharacteristic
25C2×(C2×D3)⋊C4C2211yescharacteristic
26C2×(C2×D3)⋊C4C2211yescharacteristic
27C2×(C2×D3)⋊C4C2211yescharacteristic
28C2×(C2×D3)⋊C4C2211yescharacteristic
29C2×(C2×D3)⋊C4C2211yescharacteristic
30C2×C4⋊Dic3C2211yescharacteristic
31C2×Dic3⋊C4C2211yescharacteristic
32C2×Dic3⋊C4C2211yescharacteristic
33C2×Dic3⋊C4C2211yescharacteristic
34C2×Dic3⋊C4C2211yescharacteristic
35C2×Dic3⋊C4C2211yescharacteristic
36C2×Dic3⋊C4C2211yescharacteristic
37C2×C4×Dic3C2211yescharacteristic
38C2×C4×Dic3C2211yescharacteristic
39C2×C4×Dic3C2211yescharacteristic
40C2×C4×Dic3C2211yescharacteristic
41C2×C4×Dic3C2211yescharacteristic
42#896C418yescomplemented
43#872—24no—
44C4×Dic6—24no—
45C3×#95C2211yescharacteristic
46C3×#95C2211yescharacteristic
47C3⋊#95C2211yescharacteristic
48C3⋊#95C2211yescharacteristic
49C3⋊#95C2211yescharacteristic
50C3⋊#95C2211yescharacteristic
51C3⋊#95C2211yescharacteristic
52C3⋊#95C2211yescharacteristic
53C3⋊#95C2211yescharacteristic
54C3⋊#95C2211yescharacteristic
55C2×C22⋊Q8—31no—
56C2×C4×Q8—31no—
57C2×#117—31no—
58#391—31no—
59#389—31no—
60#388—31no—
61#388—31no—
62#388—31no—
63#388—31no—
64#387—31no—
65#387—31no—
66C4×C4⋊C4—31no—
67C4×C4⋊C4—31no—
68C4×C4⋊C4D311yescharacteristic, complemented
69C4×C22⋊C4—31no—
70C23×D3C2311yescharacteristic
71C22×C3×C4C2311yescharacteristic
72C22×C3×C4C2311yescharacteristic
73C22×C3×C4C2311yescharacteristic
74C22×C3×C4C2311yescharacteristic
75C22×C3×C4C2311yescharacteristic
76C22×C3×C4C2311yescharacteristic
77C22×C3×C4C2311yescharacteristic
78C22×Dic3C2311yescharacteristic
79C22×Dic3C2311yescharacteristic
80C22×Dic3C2311yescharacteristic
81C22×Dic3C2311yescharacteristic
82C22×Dic3C2311yescharacteristic
83C22×Dic3C2311yescharacteristic
84C22×Dic3C2311yescharacteristic
85C2×C4×D3—22no—
86C2×C4×D3—22no—
87C2×C4×D3C2×C414yes—
88C2×Dic6—22no—
89C2×Dic6—22no—
90C2×Dic6C2×C414yes—
91C3×C4⋊C4—22no—
92C3×C4⋊C4C2×C414yes—
93C3×C42—22no—
94C3×C42—22no—
95C3×C42—22no—
96(C2×D3)⋊C4—22no—
97(C2×D3)⋊C4—22no—
98(C2×D3)⋊C4—22no—
99(C2×D3)⋊C4—22no—
100(C2×D3)⋊C4C2×C414yes—
101(C2×D3)⋊C4C2×C414yes—
102C4⋊Dic3—22no—
103Dic3⋊C4—22no—
104Dic3⋊C4—22no—
105Dic3⋊C4—22no—
106Dic3⋊C4C2×C414yes—
107Dic3⋊C4C2×C414yes—
108Dic3⋊C4D414yes—
109C4×Dic3—22no—
110C4×Dic3—22no—
111C4×Dic3—22no—
112C4×Dic3—22no—
113C4×Dic3—22no—
114C22×Q8—31no—
115C23×C4—31no—
116C22⋊Q8—38no—
117C4×Q8—64no—
118#117—64no—
119C2×C4⋊C4—31no—
120C2×C4⋊C4—31no—
121C2×C4⋊C4—31no—
122C2×C4⋊C4—31no—
123C2×C4⋊C4—31no—
124C2×C4⋊C4—31no—
125C2×C4⋊C4—31no—
126C2×C4⋊C4C2×D311yescharacteristic
127C2×C4⋊C4C2×D311yescharacteristic
128C2×C22⋊C4—31no—
129C2×C22⋊C4—31no—
130C2×C22⋊C4—31no—
131C2×C22⋊C4—31no—
132C2×C22⋊C4—31no—
133C2×C22⋊C4—31no—
134C2×C42—31no—
135C2×C42—31no—
136C2×C42—31no—
137C2×C42—31no—
138C2×C42—31no—
139C2×C42C2×D311yescharacteristic
140C2×C42C2×D311yescharacteristic
141C2×C42C2×D311yescharacteristic
142#95—31no—
143#95—31no—
144#95—31no—
145#95—31no—
146#95—31no—
147#95—31no—
148#95—31no—
149#95—31no—
150#95C2×D311yescharacteristic
151#95C2×D311yescharacteristic
152C23×C3C2411yescharacteristic
153C22×D3—21no—
154C22×D3—21no—
155C22×D3—21no—
156C22×D3—21no—
157C22×D3—21no—
158C22×D3—21no—
159C22×D3C22×C412yes—
160C2×C3×C4—21no—
161C2×C3×C4—21no—
162C2×C3×C4—21no—
163C2×C3×C4—21no—
164C2×C3×C4—21no—
165C2×C3×C4—21no—
166C2×C3×C4—21no—
167C2×C3×C4—21no—
168C2×C3×C4—21no—
169C2×C3×C4—21no—
170C2×C3×C4—21no—
171C2×C3×C4—21no—
172C2×C3×C4—21no—
173C2×C3×C4—21no—
174C2×C3×C4—21no—
175C2×C3×C4C22×C412yes—
176C2×C3×C4C22×C412yes—
177C2×C3×C4C22×C412yes—
178C2×C3×C4C2×D412yes—
179C2×C3×C4#4112yes—
180C2×C3×C4#4112yes—
181C2×Dic3—21no—
182C2×Dic3—21no—
183C2×Dic3—21no—
184C2×Dic3—21no—
185C2×Dic3—21no—
186C2×Dic3—21no—
187C2×Dic3—21no—
188C2×Dic3—21no—
189C2×Dic3—21no—
190C2×Dic3—21no—
191C2×Dic3—21no—
192C2×Dic3—21no—
193C2×Dic3—21no—
194C2×Dic3—21no—
195C2×Dic3—21no—
196C2×Dic3C22×C412yes—
197C2×Dic3C22×C412yes—
198C2×Dic3C22×C412yes—
199C2×Dic3C2×D412yes—
200C2×Dic3C2×D412yes—
201C2×Dic3#4112yes—
202C4×D3—28no—
203Dic6—28no—
204C24—31no—
205C2×Q8—34no—
206C2×Q8—62no—
207C2×Q8—62no—
208C22×C4—31no—
209C22×C4—31no—
210C22×C4—31no—
211C22×C4—31no—
212C22×C4—34no—
213C22×C4—31no—
214C22×C4—31no—
215C22×C4—31no—
216C22×C4—62no—
217C22×C4—62no—
218C22×C4C22×D311yescharacteristic
219C22×C4C22×D311yescharacteristic
220C22×C4C22×D311yescharacteristic
221C22×C4C22×D311yescharacteristic
222C22×C4C22×D311yescharacteristic
223C22×C4C22×D311yescharacteristic
224C22×C4C22×D311yescharacteristic
225C4⋊C4—22no—
226C4⋊C4—34no—
227C4⋊C4—34no—
228C4⋊C4—34no—
229C4⋊C4—62no—
230C4⋊C4—62no—
231C4⋊C4—62no—
232C4⋊C4—62no—
233C4⋊C4C4×D314yes—
234C22⋊C4—34no—
235C22⋊C4—34no—
236C22⋊C4—62no—
237C22⋊C4—62no—
238C22⋊C4—62no—
239C22⋊C4—62no—
240C42—22no—
241C42—22no—
242C42—22no—
243C42—62no—
244C42—62no—
245C42—62no—
246C42—62no—
247C42—62no—
248C22×C3C23×C411yescharacteristic
249C22×C3C22×D411yescharacteristic
250C22×C3C2×#4111yescharacteristic
251C22×C3C2×#4111yescharacteristic
252C22×C3C2×#4111yescharacteristic
253C22×C32−1+411yescharacteristic
254C22×C32−1+411yescharacteristic
255C2×D3—22no—
256C2×D3—22no—
257C2×D3—22no—
258C2×D3—41no—
259C2×D3—41no—
260C2×D3—41no—
261C2×D3—41no—
262C3×C4—22no—
263C3×C4—22no—
264C3×C4—22no—
265C3×C4—22no—
266C3×C4—22no—
267C3×C4—22no—
268C3×C4—41no—
269Dic3—22no—
270Dic3—22no—
271Dic3—22no—
272Dic3—41no—
273Dic3—41no—
274Dic3—41no—
275Dic3C4×D414yes—
276C23—32no—
277C23—61no—
278C23—61no—
279C23—61no—
280C23—61no—
281C23—61no—
282C23—61no—
283C23C23×D311yescharacteristic
284Q8—68no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—32no—
301C2×C4—32no—
302C2×C4—32no—
303C2×C4—32no—
304C2×C4—32no—
305C2×C4—32no—
306C2×C4—68no—
307C2×C4—61no—
308C2×C4—61no—
309C2×C4—61no—
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—61no—
319C2×C4—61no—
320C2×C4—61no—
321C2×C4—61no—
322C2×C4C2×C4×D312yes—
323C2×C4C2×C4×D312yes—
324C2×C4C2×C4×D312yes—
325C2×C4#23512yes—
326C2×C4#23512yes—
327C2×C4D3×D412yes—
328C2×C3C2×C4×D411yescharacteristic
329C2×C3C4×#4111yescharacteristic
330C2×C3#51911yescharacteristic
331C2×C3#54711yescharacteristic
332C2×C3#54811yescharacteristic
333C2×C3#55211yescharacteristic
334C2×C3#55611yescharacteristic
335D3—42no—
336C22—62no—
337C22—62no—
338C22—62no—
339C22—121no—
340C22—121no—
341C22—121no—
342C22—121no—
343C22C22×C4×D311yescharacteristic
344C22C2×#23511yescharacteristic
345C22C2×#23511yescharacteristic
346C22C2×D3×D411yescharacteristic
347C22#100711yescharacteristic
348C22D3×#4111yescharacteristic
349C22#101011yescharacteristic
350C4—22no—
351C4—22no—
352C4—22no—
353C4—22no—
354C4—22no—
355C4—22no—
356C4—34no—
357C4—41no—
358C4—62no—
359C4—62no—
360C4—62no—
361C4—121no—
362C4—121no—
363C4—121no—
364C3#236211yescharacteristic, complemented, Sylow
365C2—122no—
366C2C4×#23511yescharacteristic
367C2#550711yescharacteristic
368C2#553111yescharacteristic
369C2C4×D3×D411yescharacteristic
370C2#555211yescharacteristic
371C2#556811yescharacteristic
372C2#557211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutatorC22×C3C23×C4
FittingC3×C4×C4⋊C4C2
socle, cosocleC23×C3C24
prime radicalC23×D3C23
hypercenterC4×C4⋊C4D3
hypocenterC3#2362
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×C4×Dic6C2semidirect
4. C3×C4×C4⋊C4C2semidirect
6. #4980C2semidirect
7. #4976C2semidirect
10. #4933C2semidirect
11. C4×Dic3⋊C4C2semidirect
14. #4649C2semidirect
15. #4646C2semidirect
42. #896C4semidirect
68. C4×C4⋊C4D3semidirect
364. C3#2362semidirect

Maximal subgroups

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

subgroupindex
C2×#8962
C2×#8722
C2×C4×Dic62
C3×C4×C4⋊C42
#49902
#49802
#49762
#49402
#49332
C4×Dic3⋊C42
#46702
#46662
#46492
#46462
#23623