Finite Group Databasebeta

← #387×D43 #19137015

Subgroups — #387×D43 #19137015

Order 5504.

712 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C4×D43C211yesmaximal, characteristic
2C2×C4⋊C4×D43C211yesmaximal, characteristic
3C2×C42×D43C211yesmaximal, characteristic
4#14582786C211yesmaximal, characteristic, complemented
5#14582785C211yesmaximal, characteristic, complemented
6#14582784C211yesmaximal, characteristic, complemented
7#14582783C211yesmaximal, characteristic, complemented
8#14582782C211yesmaximal, characteristic, complemented
9#14582781C211yesmaximal, characteristic, complemented
10#14582780C211yesmaximal, characteristic, complemented
11#95×D43C211yesmaximal, characteristic
12#95×D43C211yesmaximal, characteristic
13#95×D43C211yesmaximal, characteristic
14#95×D43C211yesmaximal, characteristic
15C43×#387C211yesmaximal, characteristic, complemented
16C22×C4×D43C2211yescharacteristic
17C22×C4×D43C2211yescharacteristic
18C22×C4×D43C2211yescharacteristic
19C22×C4×D43C2211yescharacteristic
20C22×C4×D43C2211yescharacteristic
21C22×C4×D43C2211yescharacteristic
22C22×C4×D43C2211yescharacteristic
23C2×C4⋊Dic43C2211yescharacteristic
24C2×C4⋊Dic43C2211yescharacteristic
25C2×Dic43⋊C4C2211yescharacteristic
26C2×Dic43⋊C4C2211yescharacteristic
27C2×Dic43⋊C4C2211yescharacteristic
28C2×Dic43⋊C4C2211yescharacteristic
29C4⋊C4×D43—24no—
30C4⋊C4×D43C418yescomplemented
31C2×C4×Dic43C2211yescharacteristic
32C2×C4×Dic43C2211yescharacteristic
33C2×C4×Dic43C2211yescharacteristic
34C42×D43—24no—
35C43⋊#95C2211yescharacteristic
36C43⋊#95C2211yescharacteristic
37C43⋊#95C2211yescharacteristic
38C43⋊#95C2211yescharacteristic
39C43⋊#95C2211yescharacteristic
40C43⋊#95C2211yescharacteristic
41C43⋊#95C2211yescharacteristic
42C43⋊#95C2211yescharacteristic
43C43⋊#95C2211yescharacteristic
44C43⋊#95C2211yescharacteristic
45C43⋊#95C2211yescharacteristic
46C43⋊#95C2211yescharacteristic
47C2×C4⋊C4×C43C2211yescharacteristic
48C2×C4⋊C4×C43C2211yescharacteristic
49C2×C42×C43C2211yescharacteristic
50#95×C43C2211yescharacteristic
51#95×C43C2211yescharacteristic
52#95×C43C2211yescharacteristic
53#95×C43C2211yescharacteristic
54C23×D43C2311yescharacteristic
55C22×C4×C43C2311yescharacteristic
56C22×C4×C43C2311yescharacteristic
57C22×C4×C43C2311yescharacteristic
58C22×C4×C43C2311yescharacteristic
59C22×C4×C43C2311yescharacteristic
60C22×C4×C43C2311yescharacteristic
61C22×C4×C43C2311yescharacteristic
62C22×Dic43C2311yescharacteristic
63C22×Dic43C2311yescharacteristic
64C22×Dic43C2311yescharacteristic
65C22×Dic43C2311yescharacteristic
66C22×Dic43C2311yescharacteristic
67C22×Dic43C2311yescharacteristic
68C22×Dic43C2311yescharacteristic
69C2×C4×D43—22no—
70C2×C4×D43—22no—
71C2×C4×D43—22no—
72C2×C4×D43—22no—
73C2×C4×D43—22no—
74C2×C4×D43—22no—
75C2×C4×D43—22no—
76C2×C4×D43—22no—
77C2×C4×D43—22no—
78C2×C4×D43—22no—
79C2×C4×D43—22no—
80C2×C4×D43—22no—
81C2×C4×D43—22no—
82C2×C4×D43—22no—
83C2×C4×D43—22no—
84C2×C4×D43—22no—
85C2×C4×D43C2×C414yes—
86C2×C4×D43C2×C414yes—
87C2×C4×D43C2×C414yes—
88C2×C4×D43D414yes—
89C2×C4×D43Q814yes—
90C4⋊C4×C43—22no—
91C4⋊C4×C43C2×C414yescomplemented
92C42×C43—22no—
93C4⋊Dic43—22no—
94C4⋊Dic43C2×C414yescomplemented
95Dic43⋊C4—22no—
96Dic43⋊C4—22no—
97Dic43⋊C4C2×C414yescomplemented
98Dic43⋊C4C2×C414yescomplemented
99C4×Dic43—22no—
100C4×Dic43—22no—
101C4×Dic43—22no—
102C23×C43C2411yescharacteristic
103C22×D43C22×C412yes—
104C22×D43C2×D412yes—
105C22×D43C2×Q812yes—
106C22×D43#4112yes—
107C22×D43#4112yes—
108C22×D43#4112yes—
109C22×D43#4112yes—
110C2×C4×C43—21no—
111C2×C4×C43—21no—
112C2×C4×C43—21no—
113C2×C4×C43—21no—
114C2×C4×C43—21no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43C22×C412yes—
127C2×C4×C43C22×C412yes—
128C2×C4×C43C22×C412yes—
129C2×C4×C43C2×D412yes—
130C2×C4×C43C2×Q812yes—
131C2×Dic43—21no—
132C2×Dic43—21no—
133C2×Dic43—21no—
134C2×Dic43—21no—
135C2×Dic43—21no—
136C2×Dic43—21no—
137C2×Dic43—21no—
138C2×Dic43—21no—
139C2×Dic43—21no—
140C2×Dic43—21no—
141C2×Dic43—21no—
142C2×Dic43—21no—
143C2×Dic43—21no—
144C2×Dic43—21no—
145C2×Dic43—21no—
146C2×Dic43—21no—
147C2×Dic43C22×C412yes—
148C2×Dic43C22×C412yes—
149C2×Dic43C22×C412yes—
150C2×Dic43C2×D412yes—
151C2×Dic43C2×Q812yes—
152C4×D43—28no—
153C4×D43—28no—
154C4×D43—28no—
155C4×D43—28no—
156C4×D43—28no—
157C4×D43—44no—
158C4×D43—44no—
159C22×C43C23×C411yescharacteristic
160C22×C43C22×D411yescharacteristic
161C22×C43C22×Q811yescharacteristic
162C22×C43C2×#4111yescharacteristic
163C22×C43C2×#4111yescharacteristic
164C22×C43C2×#4111yescharacteristic
165C22×C43C2×#4111yescharacteristic
166C2×D43#11714yes—
167C2×D43C4×D414yes—
168C2×D43C4×Q814yes—
169C2×D43C22⋊Q814yes—
170C2×D43#12314yes—
171C2×D43#12514yes—
172C2×D43#12614yes—
173C4×C43—22no—
174C4×C43—22no—
175C4×C43—22no—
176C4×C43—22no—
177C4×C43—22no—
178C4×C43—41no—
179C4×C43—41no—
180Dic43—22no—
181Dic43—22no—
182Dic43—22no—
183Dic43—22no—
184Dic43—22no—
185Dic43—41no—
186Dic43—41no—
187C2×#387—431nomaximal, Sylow
188C2×C43C2×#11711yescharacteristic
189C2×C43C2×C4×D411yescharacteristic
190C2×C43C2×C4×Q811yescharacteristic
191C2×C43C2×C22⋊Q811yescharacteristic
192C2×C43C2×#12311yescharacteristic
193C2×C43C2×#12511yescharacteristic
194C2×C43C2×#12611yescharacteristic
195D43#38718yesdirect product factor
196C22×C4⋊C4—431no—
197C22×C4⋊C4—431no—
198C22×C42—431no—
199#387—431no—
200#387—431no—
201#387—431no—
202#387—431no—
203#387—431no—
204#387—431no—
205#387—431no—
206#387D4311yescharacteristic, direct product factor
207C2×#95—431no—
208C2×#95—431no—
209C2×#95—431no—
210C2×#95—431no—
211C43C2×#38711yescharacteristic, complemented, Sylow
212C23×C4—431no—
213C23×C4—431no—
214C23×C4—431no—
215C23×C4—431no—
216C23×C4—431no—
217C23×C4—431no—
218C23×C4—431no—
219C2×C4⋊C4—431no—
220C2×C4⋊C4—431no—
221C2×C4⋊C4—431no—
222C2×C4⋊C4—438no—
223C2×C4⋊C4—431no—
224C2×C4⋊C4—431no—
225C2×C4⋊C4—431no—
226C2×C4⋊C4—864no—
227C2×C4⋊C4C2×D4311yescharacteristic
228C2×C4⋊C4C2×D4311yescharacteristic
229C2×C42—431no—
230C2×C42—431no—
231C2×C42—431no—
232C2×C42—864no—
233C2×C42C2×D4311yescharacteristic
234#95—431no—
235#95—431no—
236#95—431no—
237#95—431no—
238#95—431no—
239#95—431no—
240#95—431no—
241#95—431no—
242#95—431no—
243#95—431no—
244#95—431no—
245#95—431no—
246#95C2×D4311yescharacteristic
247#95C2×D4311yescharacteristic
248#95C2×D4311yescharacteristic
249#95C2×D4311yescharacteristic
250C24—431no—
251C22×C4—431no—
252C22×C4—431no—
253C22×C4—431no—
254C22×C4—431no—
255C22×C4—431no—
256C22×C4—434no—
257C22×C4—434no—
258C22×C4—434no—
259C22×C4—434no—
260C22×C4—434no—
261C22×C4—431no—
262C22×C4—431no—
263C22×C4—862no—
264C22×C4—862no—
265C22×C4—862no—
266C22×C4—862no—
267C22×C4—862no—
268C22×C4—862no—
269C22×C4—862no—
270C22×C4—862no—
271C22×C4—862no—
272C22×C4—862no—
273C22×C4—862no—
274C22×C4—862no—
275C22×C4—862no—
276C22×C4—862no—
277C22×C4—862no—
278C22×C4—862no—
279C22×C4C22×D4311yescharacteristic
280C22×C4C22×D4311yescharacteristic
281C22×C4C22×D4311yescharacteristic
282C22×C4C22×D4311yescharacteristic
283C22×C4C22×D4311yescharacteristic
284C22×C4C22×D4311yescharacteristic
285C22×C4C22×D4311yescharacteristic
286C4⋊C4—22no—
287C4⋊C4—434no—
288C4⋊C4—434no—
289C4⋊C4—434no—
290C4⋊C4—862no—
291C4⋊C4—862no—
292C4⋊C4—862no—
293C4⋊C4C4×D4314yescomplemented
294C42—22no—
295C42—862no—
296C42—862no—
297C42—862no—
298C23—432no—
299C23—432no—
300C23—432no—
301C23—432no—
302C23—432no—
303C23—432no—
304C23—432no—
305C23C23×D4311yescharacteristic
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—432no—
323C2×C4—432no—
324C2×C4—432no—
325C2×C4—432no—
326C2×C4—432no—
327C2×C4—868no—
328C2×C4—868no—
329C2×C4—868no—
330C2×C4—868no—
331C2×C4—868no—
332C2×C4—861no—
333C2×C4—861no—
334C2×C4—861no—
335C2×C4—861no—
336C2×C4—861no—
337C2×C4—861no—
338C2×C4—861no—
339C2×C4—861no—
340C2×C4—861no—
341C2×C4—861no—
342C2×C4—861no—
343C2×C4—861no—
344C2×C4—861no—
345C2×C4—861no—
346C2×C4—861no—
347C2×C4—861no—
348C2×C4—1724no—
349C2×C4—1724no—
350C2×C4C2×C4×D4312yes—
351C2×C4C2×C4×D4312yes—
352C2×C4C2×C4×D4312yes—
353C2×C4D4×D4312yes—
354C2×C4Q8×D4312yes—
355C22—434no—
356C22—434no—
357C22—434no—
358C22—434no—
359C22—434no—
360C22—434no—
361C22—434no—
362C22C22×C4×D4311yescharacteristic
363C22C2×D4×D4311yescharacteristic
364C22C2×Q8×D4311yescharacteristic
365C22#41×D4311yescharacteristic
366C22#41×D4311yescharacteristic
367C22#41×D4311yescharacteristic
368C22#41×D4311yescharacteristic
369C4—22no—
370C4—22no—
371C4—22no—
372C4—22no—
373C4—22no—
374C4—41no—
375C4—41no—
376C4—862no—
377C4—862no—
378C4—862no—
379C4—862no—
380C4—862no—
381C4—1721no—
382C4—1721no—
383C2—438no—
384C2#117×D4311yescharacteristic
385C2C4×D4×D4311yescharacteristic
386C2C4×Q8×D4311yescharacteristic
387C2C22⋊Q8×D4311yescharacteristic
388C2#123×D4311yescharacteristic
389C2#125×D4311yescharacteristic
390C2#126×D4311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutatorC22×C43C23×C4
FittingC43×#387C2
socleC23×C43C24
hypercenter#387D43
hypocenterC43C2×#387
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
4. #14582786C2semidirect
5. #14582785C2semidirect
6. #14582784C2semidirect
7. #14582783C2semidirect
8. #14582782C2semidirect
9. #14582781C2semidirect
10. #14582780C2semidirect
15. C43×#387C2semidirect
30. C4⋊C4×D43C4semidirect
91. C4⋊C4×C43C2×C4semidirect
94. C4⋊Dic43C2×C4semidirect
97. Dic43⋊C4C2×C4semidirect
98. Dic43⋊C4C2×C4semidirect
195. D43#387direct (N × H)
206. #387D43direct (N × H)
211. C43C2×#387semidirect
293. C4⋊C4C4×D43semidirect