Finite Group Databasebeta

← #19137227

Subgroups — #19137227

Order 5504.

568 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13063287C211yesmaximal, characteristic
2#14582790C211yesmaximal, characteristic, complemented
3#14582788C211yesmaximal, characteristic, complemented
4#14582785C211yesmaximal, characteristic, complemented
5#14582777C211yesmaximal, characteristic
6#14582777C211yesmaximal, characteristic
7#14582773C211yesmaximal, characteristic, complemented
8#14582770C211yesmaximal, characteristic, complemented
9#14582766C211yesmaximal, characteristic, complemented
10#14582763C211yesmaximal, characteristic, complemented
11#14582761C211yesmaximal, characteristic, complemented
12#14582756C211yesmaximal, characteristic, complemented
13C4×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
14#95×D43C211yesmaximal, characteristic, complemented
15C43×#387C211yesmaximal, characteristic, complemented
16C22×D172C2211yescharacteristic
17C22×C4×D43C2211yescharacteristic
18C22×C4×D43C2211yescharacteristic
19C22×C4×D43C2211yescharacteristic
20C22×C4×D43C2211yescharacteristic
21#13063287C418yescomplemented
22C2×C4⋊Dic43C2211yescharacteristic
23C2×Dic43⋊C4C2211yescharacteristic
24C2×Dic43⋊C4C2211yescharacteristic
25C2×(C2×D43)⋊C4C2211yescharacteristic
26C2×(C2×D43)⋊C4C2211yescharacteristic
27C2×(C2×D43)⋊C4C2211yescharacteristic
28C2×(C2×D43)⋊C4C2211yescharacteristic
29C2×(C2×D43)⋊C4C2211yescharacteristic
30C2×(C2×D43)⋊C4C2211yescharacteristic
31C2×(C2×D43)⋊C4C2211yescharacteristic
32C2×(C2×D43)⋊C4C2211yescharacteristic
33C2×C4×Dic43C2211yescharacteristic
34C2×C4×Dic43C2211yescharacteristic
35C43⋊#95C2211yescharacteristic
36C43⋊#95C2211yescharacteristic
37C43⋊#95C2211yescharacteristic
38C43⋊#95C2211yescharacteristic
39C43⋊#95C2211yescharacteristic
40C43⋊#95C2211yescharacteristic
41C43⋊#95C2211yescharacteristic
42C43⋊#95C2211yescharacteristic
43C43⋊#95C2211yescharacteristic
44C43⋊#95C2211yescharacteristic
45C2×C4⋊C4×C43C2211yescharacteristic
46C2×C4⋊C4×C43C2211yescharacteristic
47C2×C42×C43C2211yescharacteristic
48#95×C43C2211yescharacteristic
49#95×C43C2211yescharacteristic
50#95×C43C2211yescharacteristic
51#95×C43C2211yescharacteristic
52C23×D43C2311yescharacteristic
53C23×D43C2311yescharacteristic
54C22×C4×C43C2311yescharacteristic
55C22×C4×C43C2311yescharacteristic
56C22×C4×C43C2311yescharacteristic
57C22×C4×C43C2311yescharacteristic
58C22×C4×C43C2311yescharacteristic
59C22×C4×C43C2311yescharacteristic
60C22×C4×C43C2311yescharacteristic
61C22×Dic43C2311yescharacteristic
62C22×Dic43C2311yescharacteristic
63C22×Dic43C2311yescharacteristic
64C22×Dic43C2311yescharacteristic
65C22×Dic43C2311yescharacteristic
66C22×Dic43C2311yescharacteristic
67C2×D172—22no—
68C2×D172—22no—
69C2×D172C2×C414yes—
70C2×C4×D43—22no—
71C2×C4×D43—22no—
72C2×C4×D43—41no—
73C2×C4×D43—41no—
74C2×C4×D43—41no—
75C2×C4×D43—41no—
76C2×C4×D43—41no—
77C2×C4×D43—41no—
78C2×C4×D43—41no—
79C2×C4×D43—41no—
80C2×C4×D43C2×C414yes—
81C2×C4×D43C2×C414yescomplemented
82C4⋊C4×C43—41no—
83C4⋊C4×C43C2×C414yescomplemented
84C42×C43—41no—
85(C2×D43)⋊C4—22no—
86(C2×D43)⋊C4—22no—
87(C2×D43)⋊C4—41no—
88(C2×D43)⋊C4—41no—
89(C2×D43)⋊C4—41no—
90(C2×D43)⋊C4—41no—
91(C2×D43)⋊C4C2×C414yes—
92(C2×D43)⋊C4C2×C414yescomplemented
93C4⋊Dic43—41no—
94Dic43⋊C4—41no—
95Dic43⋊C4—41no—
96C4×Dic43—41no—
97C4×Dic43C2×C414yescomplemented
98C23×C43C2411yescharacteristic
99C22×D43—21no—
100C22×D43—21no—
101C22×D43—21no—
102C22×D43—21no—
103C22×D43—21no—
104C22×D43—21no—
105C22×D43—21no—
106C22×D43—21no—
107C22×D43—21no—
108C22×D43—21no—
109C22×D43C22×C412yes—
110C22×D43C22×C412yes—
111C22×D43#4112yes—
112C22×D43#4112yes—
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×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43—21no—
129C2×C4×C43—21no—
130C2×C4×C43—21no—
131C2×C4×C43C22×C412yes—
132C2×C4×C43C22×C412yes—
133C2×C4×C43C22×C412yes—
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×Dic43—21no—
148C2×Dic43—21no—
149C2×Dic43—21no—
150C2×Dic43C22×C412yes—
151C2×Dic43C22×C412yes—
152D172—28no—
153C4×D43—44no—
154C4×D43—44no—
155C4×D43—44no—
156C4×D43—44no—
157C22×C43C23×C411yescharacteristic
158C22×C43C2×#4111yescharacteristic
159C22×C43C2×#4111yescharacteristic
160C22×C43H(5,𝔽2)11yescharacteristic
161C22×C43H(5,𝔽2)11yescharacteristic
162C22×C43H(5,𝔽2)11yescharacteristic
163C22×C432−1+411yescharacteristic
164C2×D43—22no—
165C2×D43—22no—
166C2×D43—22no—
167C2×D43—22no—
168C2×D43—22no—
169C2×D43—22no—
170C2×D43—22no—
171C2×D43—22no—
172C2×D43—22no—
173C2×D43—41no—
174C2×D43—41no—
175C2×D43—41no—
176C2×D43—41no—
177C2×D43#11714yes—
178C4×C43—22no—
179C4×C43—22no—
180C4×C43—22no—
181C4×C43—41no—
182C4×C43—41no—
183C4×C43—41no—
184C4×C43—41no—
185Dic43—22no—
186Dic43—22no—
187Dic43—41no—
188Dic43—41no—
189Dic43—41no—
190Dic43—41no—
191#2318—431nomaximal, Sylow
192C2×C43C2×#11711yescharacteristic
193C2×C43#51811yescharacteristic
194C2×C43#52011yescharacteristic
195C2×C43#53811yescharacteristic
196C2×C43#53811yescharacteristic
197C2×C43#53911yescharacteristic
198C2×C43#53911yescharacteristic
199D43—24no—
200D43—42no—
201C2×C4×D4—431no—
202#388—431no—
203#388—431no—
204#387—431no—
205#387D4311yescharacteristic, complemented
206#386—431no—
207#386—431no—
208#385—431no—
209#385—431no—
210#383—431no—
211#382—431no—
212#381—431no—
213#380—431no—
214C4×C22⋊C4—431no—
215C2×#95—431no—
216C43#231811yescharacteristic, complemented, Sylow
217C22×D4—431no—
218C23×C4—431no—
219C23×C4—431no—
220C23×C4—431no—
221C23×C4—431no—
222C4×D4—438no—
223C2×C4⋊C4—431no—
224C2×C4⋊C4—431no—
225C2×C4⋊C4—431no—
226C2×C4⋊C4C2×D4311yescharacteristic
227C2×C4⋊C4C2×D4311yescharacteristic
228C2×C22⋊C4—431no—
229C2×C22⋊C4—431no—
230C2×C22⋊C4—431no—
231C2×C22⋊C4—431no—
232C2×C22⋊C4—431no—
233C2×C22⋊C4—431no—
234C2×C22⋊C4—431no—
235C2×C22⋊C4—431no—
236C2×C42—431no—
237C2×C42—431no—
238C2×C42C2×D4311yescharacteristic
239#95—431no—
240#95—431no—
241#95—431no—
242#95—431no—
243#95—431no—
244#95—431no—
245#95—431no—
246#95—431no—
247#95—431no—
248#95—431no—
249#95C2×D4311yescharacteristic
250#95C2×D4311yescharacteristic
251#95C2×D4311yescharacteristic
252#95C2×D4311yescharacteristic
253C24—431no—
254C24—431no—
255C2×D4—434no—
256C2×D4—862no—
257C2×D4—862no—
258C22×C4—431no—
259C22×C4—431no—
260C22×C4—434no—
261C22×C4—434no—
262C22×C4—431no—
263C22×C4—431no—
264C22×C4—431no—
265C22×C4—431no—
266C22×C4—862no—
267C22×C4—862no—
268C22×C4—1721no—
269C22×C4—1721no—
270C22×C4—1721no—
271C22×C4—1721no—
272C22×C4—1721no—
273C22×C4—1721no—
274C22×C4—1721no—
275C22×C4—1721no—
276C22×C4C22×D4311yescharacteristic
277C22×C4C22×D4311yescharacteristic
278C22×C4C22×D4311yescharacteristic
279C22×C4C22×D4311yescharacteristic
280C22×C4C22×D4311yescharacteristic
281C22×C4C22×D4311yescharacteristic
282C22×C4C22×D4311yescharacteristic
283C4⋊C4—41no—
284C4⋊C4—1721no—
285C4⋊C4—1721no—
286C4⋊C4—1721no—
287C4⋊C4C4×D4314yescomplemented
288C22⋊C4—434no—
289C22⋊C4—434no—
290C22⋊C4—862no—
291C22⋊C4—862no—
292C22⋊C4—1721no—
293C22⋊C4—1721no—
294C22⋊C4—1721no—
295C22⋊C4—1721no—
296C42—41no—
297C42—434no—
298C42—1721no—
299C23—432no—
300C23—432no—
301C23—432no—
302C23—432no—
303C23—861no—
304C23—861no—
305C23—861no—
306C23—861no—
307C23—861no—
308C23—861no—
309C23—861no—
310C23—861no—
311C23—861no—
312C23—861no—
313C23C23×D4311yescharacteristic
314D4—868no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—432no—
334C2×C4—432no—
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—861no—
349C2×C4—861no—
350C2×C4—861no—
351C2×C4—1724no—
352C2×C4—1724no—
353C2×C4—1724no—
354C2×C4—1724no—
355C2×C4C2×C4×D4312yes—
356C2×C4C2×C4×D4312yes—
357C2×C4C2×C4×D4312yes—
358C22—434no—
359C22—862no—
360C22—862no—
361C22—862no—
362C22—862no—
363C22—862no—
364C22—862no—
365C22—862no—
366C22—862no—
367C22—862no—
368C22—1721no—
369C22—1721no—
370C22—1721no—
371C22—1721no—
372C22C22×C4×D4311yescharacteristic
373C22#41×D4311yescharacteristic
374C22#41×D4311yescharacteristic
375C22#1306337011yescharacteristic
376C22#1306337111yescharacteristic
377C22#1306337111yescharacteristic
378C22#1306337311yescharacteristic
379C4—22no—
380C4—22no—
381C4—22no—
382C4—41no—
383C4—41no—
384C4—41no—
385C4—41no—
386C4—862no—
387C4—862no—
388C4—1721no—
389C4—1721no—
390C4—1721no—
391C4—1721no—
392C2—864no—
393C2—1722no—
394C2#117×D4311yescharacteristic
395C2#1458337111yescharacteristic
396C2#1458338111yescharacteristic
397C2#1458348511yescharacteristic
398C2#1458348811yescharacteristic
399C2#1458349511yescharacteristic
400C2#1458349711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutatorC22×C43C23×C4
FittingC43×#387C2
socleC23×C43C24
hypercenter#387D43
hypocenterC43#2318
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
2. #14582790C2semidirect
3. #14582788C2semidirect
4. #14582785C2semidirect
7. #14582773C2semidirect
8. #14582770C2semidirect
9. #14582766C2semidirect
10. #14582763C2semidirect
11. #14582761C2semidirect
12. #14582756C2semidirect
13. C4×(C2×D43)⋊C4C2semidirect
14. #95×D43C2semidirect
15. C43×#387C2semidirect
21. #13063287C4semidirect
81. C2×C4×D43C2×C4semidirect
83. C4⋊C4×C43C2×C4semidirect
92. (C2×D43)⋊C4C2×C4semidirect
97. C4×Dic43C2×C4semidirect
205. #387D43semidirect
216. C43#2318semidirect
287. C4⋊C4C4×D43semidirect