Finite Group Databasebeta

← #75983

Subgroups — #75983

Order 384.

620 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#896C211yesmaximal, characteristic
2C2×D3×C4⋊C4C211yesmaximal, characteristic
3C2×#887C211yesmaximal, characteristic, complemented
4C3×#389C211yesmaximal, characteristic, complemented
5#4989C211yesmaximal, characteristic
6#4989C211yesmaximal, characteristic
7#4980C211yesmaximal, characteristic, complemented
8#4978C211yesmaximal, characteristic, complemented
9#4976C211yesmaximal, characteristic, complemented
10C4×(C2×D3)⋊C4C211yesmaximal, characteristic
11C4×Dic3⋊C4C211yesmaximal, characteristic, complemented
12#4666C211yesmaximal, characteristic
13#4666C211yesmaximal, characteristic
14#4647C211yesmaximal, characteristic, complemented
15#4646C211yesmaximal, characteristic, complemented
16#2360—31nomaximal, Sylow
17C22×C4×D3C2211yescharacteristic
18C22×C4×D3C2211yescharacteristic
19C22×C4×D3C2211yescharacteristic
20C22×Dic6C2211yescharacteristic
21C2×C3×C4⋊C4C2211yescharacteristic
22C2×C3×C4⋊C4C2211yescharacteristic
23C2×C3×C4⋊C4C2211yescharacteristic
24C2×C3×C4⋊C4C2211yescharacteristic
25C2×C3×C42C2211yescharacteristic
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
43D3×C4⋊C4—24no—
44#887—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—
57C22×C4⋊C4—31no—
58#391—31no—
59#389—31no—
60#389—31no—
61#389D311yescharacteristic, complemented
62#387—31no—
63#387—31no—
64#385—31no—
65#385—31no—
66C4×C4⋊C4—31no—
67C4×C22⋊C4—31no—
68C4×C22⋊C4—31no—
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×D3—22no—
88C2×C4×D3—22no—
89C2×C4×D3—22no—
90C2×C4×D3—22no—
91C2×C4×D3—41no—
92C2×C4×D3—41no—
93C2×C4×D3C2×C414yes—
94C2×Dic6—22no—
95C2×Dic6—22no—
96C2×Dic6C2×C414yescomplemented
97C3×C4⋊C4—22no—
98C3×C4⋊C4—22no—
99C3×C4⋊C4—41no—
100C3×C4⋊C4C2×C414yescomplemented
101C3×C42—41no—
102(C2×D3)⋊C4—22no—
103(C2×D3)⋊C4C2×C414yes—
104(C2×D3)⋊C4C2×C414yes—
105(C2×D3)⋊C4Q814yescomplemented
106C4⋊Dic3—22no—
107Dic3⋊C4—22no—
108Dic3⋊C4—22no—
109Dic3⋊C4—41no—
110Dic3⋊C4C2×C414yescomplemented
111Dic3⋊C4C2×C414yescomplemented
112Dic3⋊C4D414yes—
113C4×Dic3—22no—
114C4×Dic3—22no—
115C4×Dic3—22no—
116C4×Dic3—22no—
117C4×Dic3—41no—
118C22×Q8—31no—
119C23×C4—31no—
120C23×C4—31no—
121C23×C4—31no—
122C22⋊Q8—38no—
123C4×Q8—64no—
124C2×C4⋊C4—31no—
125C2×C4⋊C4—31no—
126C2×C4⋊C4—31no—
127C2×C4⋊C4—31no—
128C2×C4⋊C4—31no—
129C2×C4⋊C4—31no—
130C2×C4⋊C4—31no—
131C2×C4⋊C4—64no—
132C2×C4⋊C4C2×D311yescharacteristic
133C2×C4⋊C4C2×D311yescharacteristic
134C2×C4⋊C4C2×D311yescharacteristic
135C2×C4⋊C4C2×D311yescharacteristic
136C2×C22⋊C4—31no—
137C2×C22⋊C4—31no—
138C2×C22⋊C4—31no—
139C2×C22⋊C4—31no—
140C2×C42—31no—
141C2×C42—31no—
142C2×C42—31no—
143C2×C42—31no—
144C2×C42—31no—
145C2×C42C2×D311yescharacteristic
146#95—31no—
147#95—31no—
148#95—31no—
149#95—31no—
150#95—31no—
151#95—31no—
152#95—31no—
153#95—31no—
154#95C2×D311yescharacteristic
155#95C2×D311yescharacteristic
156C23×C3C2411yescharacteristic
157C22×D3—21no—
158C22×D3—21no—
159C22×D3—21no—
160C22×D3—21no—
161C22×D3C22×C412yes—
162C22×D3C2×Q812yes—
163C22×D3#4112yes—
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×C4—21no—
176C2×C3×C4—21no—
177C2×C3×C4—21no—
178C2×C3×C4—21no—
179C2×C3×C4—21no—
180C2×C3×C4C22×C412yes—
181C2×C3×C4C22×C412yes—
182C2×C3×C4C22×C412yes—
183C2×C3×C4C2×D412yes—
184C2×C3×C4C2×Q812yes—
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×Dic3—21no—
197C2×Dic3—21no—
198C2×Dic3—21no—
199C2×Dic3C22×C412yes—
200C2×Dic3C22×C412yes—
201C2×Dic3C22×C412yes—
202C2×Dic3C2×D412yes—
203C2×Dic3C2×D412yes—
204C2×Dic3C2×Q812yes—
205C2×Dic3#4112yes—
206C4×D3—28no—
207C4×D3—44no—
208C4×D3—44no—
209Dic6—28no—
210C24—31no—
211C2×Q8—34no—
212C2×Q8—62no—
213C2×Q8—62no—
214C22×C4—31no—
215C22×C4—31no—
216C22×C4—31no—
217C22×C4—31no—
218C22×C4—31no—
219C22×C4—34no—
220C22×C4—31no—
221C22×C4—31no—
222C22×C4—62no—
223C22×C4—62no—
224C22×C4—62no—
225C22×C4—62no—
226C22×C4—62no—
227C22×C4—62no—
228C22×C4—121no—
229C22×C4—121no—
230C22×C4C22×D311yescharacteristic
231C22×C4C22×D311yescharacteristic
232C22×C4C22×D311yescharacteristic
233C22×C4C22×D311yescharacteristic
234C22×C4C22×D311yescharacteristic
235C22×C4C22×D311yescharacteristic
236C22×C4C22×D311yescharacteristic
237C4⋊C4—22no—
238C4⋊C4—22no—
239C4⋊C4—34no—
240C4⋊C4—34no—
241C4⋊C4—34no—
242C4⋊C4—41no—
243C4⋊C4—62no—
244C4⋊C4—62no—
245C4⋊C4—62no—
246C4⋊C4—121no—
247C4⋊C4C4×D314yescomplemented
248C22⋊C4—34no—
249C22⋊C4—34no—
250C22⋊C4—34no—
251C22⋊C4—62no—
252C42—41no—
253C42—62no—
254C42—62no—
255C42—62no—
256C42—62no—
257C42—121no—
258C22×C3C23×C411yescharacteristic
259C22×C3C22×D411yescharacteristic
260C22×C3C22×Q811yescharacteristic
261C22×C3C2×#4111yescharacteristic
262C22×C3C2×#4111yescharacteristic
263C22×C3H(5,𝔽2)11yescharacteristic
264C22×C32−1+411yescharacteristic
265C2×D3—22no—
266C2×D3—22no—
267C2×D3—22no—
268C2×D3—22no—
269C2×D3—22no—
270C2×D3—22no—
271C2×D3C4×Q814yescomplemented
272C3×C4—22no—
273C3×C4—22no—
274C3×C4—22no—
275C3×C4—22no—
276C3×C4—22no—
277C3×C4—41no—
278C3×C4—41no—
279Dic3—22no—
280Dic3—22no—
281Dic3—22no—
282Dic3—22no—
283Dic3—41no—
284Dic3—41no—
285Dic3C4×D414yes—
286C23—32no—
287C23—32no—
288C23—32no—
289C23—61no—
290C23—61no—
291C23—61no—
292C23—61no—
293C23C23×D311yescharacteristic
294Q8—68no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—32no—
312C2×C4—32no—
313C2×C4—32no—
314C2×C4—32no—
315C2×C4—32no—
316C2×C4—32no—
317C2×C4—32no—
318C2×C4—68no—
319C2×C4—61no—
320C2×C4—61no—
321C2×C4—61no—
322C2×C4—61no—
323C2×C4—61no—
324C2×C4—61no—
325C2×C4—61no—
326C2×C4—61no—
327C2×C4—61no—
328C2×C4—61no—
329C2×C4—61no—
330C2×C4—61no—
331C2×C4—61no—
332C2×C4—61no—
333C2×C4—124no—
334C2×C4—124no—
335C2×C4C2×C4×D312yes—
336C2×C4C2×C4×D312yes—
337C2×C4C2×C4×D312yes—
338C2×C4D3×D412yes—
339C2×C4D3×Q812yes—
340C2×C3C2×C4×D411yescharacteristic
341C2×C3C2×C4×Q811yescharacteristic
342C2×C3#52011yescharacteristic
343C2×C3#54611yescharacteristic
344C2×C3D4×Q811yescharacteristic
345C2×C3#55211yescharacteristic
346C2×C3#55411yescharacteristic
347D3—24no—
348C22—34no—
349C22—62no—
350C22—62no—
351C22—62no—
352C22—62no—
353C22—62no—
354C22—62no—
355C22C22×C4×D311yescharacteristic
356C22C2×D3×D411yescharacteristic
357C22#100411yescharacteristic
358C22C2×D3×Q811yescharacteristic
359C22#100711yescharacteristic
360C22D3×#4111yescharacteristic
361C22D3×#4111yescharacteristic
362C4—22no—
363C4—22no—
364C4—22no—
365C4—22no—
366C4—22no—
367C4—34no—
368C4—41no—
369C4—41no—
370C4—62no—
371C4—62no—
372C4—62no—
373C4—62no—
374C4—121no—
375C4—121no—
376C3#236011yescharacteristic, complemented, Sylow
377C2—64no—
378C2#550411yescharacteristic
379C2C4×D3×D411yescharacteristic
380C2C4×D3×Q811yescharacteristic
381C2#561011yescharacteristic
382C2#563611yescharacteristic
383C2#569311yescharacteristic
384C2#572711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D3
commutatorC22×C3C23×C4
FittingC3×#389C2
socle, cosocleC23×C3C24
prime radicalC23×D3C23
hypercenter#389D3
hypocenterC3#2360
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
3. C2×#887C2semidirect
4. C3×#389C2semidirect
7. #4980C2semidirect
8. #4978C2semidirect
9. #4976C2semidirect
11. C4×Dic3⋊C4C2semidirect
14. #4647C2semidirect
15. #4646C2semidirect
42. #896C4semidirect
61. #389D3semidirect
96. C2×Dic6C2×C4semidirect
100. C3×C4⋊C4C2×C4semidirect
105. (C2×D3)⋊C4Q8semidirect
110. Dic3⋊C4C2×C4semidirect
111. Dic3⋊C4C2×C4semidirect
247. C4⋊C4C4×D3semidirect
271. C2×D3C4×Q8semidirect
376. C3#2360semidirect

Maximal subgroups

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

subgroupindex
C2×#8962
C2×D3×C4⋊C42
C2×#8872
C3×#3892
#49892
#49802
#49782
#49762
C4×(C2×D3)⋊C42
C4×Dic3⋊C42
#46662
#46472
#46462
#23603