Finite Group Databasebeta

← #19140934

Subgroups — #19140934

Order 5504.

568 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13063308C211yesmaximal, characteristic
2C2×#13063307C211yesmaximal, characteristic
3C2×#13063301C211yesmaximal, characteristic, complemented
4#14582832C211yesmaximal, characteristic, complemented
5#14582829C211yesmaximal, characteristic, complemented
6#14582827C211yesmaximal, characteristic, complemented
7#14582825C211yesmaximal, characteristic, complemented
8#14582818C211yesmaximal, characteristic, complemented
9#14582814C211yesmaximal, characteristic
10#14582792C211yesmaximal, characteristic, complemented
11#14582789C211yesmaximal, characteristic, complemented
12#14582772C211yesmaximal, characteristic, complemented
13#14582770C211yesmaximal, characteristic, complemented
14#14582768C211yesmaximal, characteristic, complemented
15C2×C22⋊Q8×C43C211yesmaximal, characteristic, complemented
16C22×C22⋊D43C2211yescharacteristic
17C22×C4×D43C2211yescharacteristic
18#13063308—24no—
19#13063307—24no—
20#13063301—24no—
21C2×C4⋊Dic43C2211yescharacteristic
22C2×C4⋊Dic43C2211yescharacteristic
23C2×Dic43⋊C4C2211yescharacteristic
24C2×Dic43⋊C4C2211yescharacteristic
25C2×Dic43⋊C4C2211yescharacteristic
26C2×Dic43⋊C4C2211yescharacteristic
27C2×Dic43⋊C4C2211yescharacteristic
28C2×Dic43⋊C4C2211yescharacteristic
29C2×Dic43⋊C4C2211yescharacteristic
30C2×C22⋊Dic43C2211yescharacteristic
31C2×C22⋊Dic43C2211yescharacteristic
32C2×C22⋊Dic43C2211yescharacteristic
33C2×(C2×D43)⋊C4C2211yescharacteristic
34C2×(C2×D43)⋊C4C2211yescharacteristic
35C2×(C2×D43)⋊C4C2211yescharacteristic
36C2×(C2×D43)⋊C4C2211yescharacteristic
37C2×(C2×D43)⋊C4C2211yescharacteristic
38C2×C4×Dic43C2211yescharacteristic
39C43⋊#95C2211yescharacteristic
40C43⋊#95C2211yescharacteristic
41C43⋊#95C2211yescharacteristic
42C43⋊#95C2211yescharacteristic
43C43⋊#95C2211yescharacteristic
44C43⋊#95C2211yescharacteristic
45C43⋊#95C2211yescharacteristic
46C43⋊#95C2211yescharacteristic
47C22×Q8×C43C2211yescharacteristic
48C23×C4×C43C2211yescharacteristic
49C22⋊Q8×C43—24no—
50C2×C4⋊C4×C43C2211yescharacteristic
51C2×C4⋊C4×C43C2211yescharacteristic
52C2×C4⋊C4×C43C2211yescharacteristic
53C2×C22⋊C4×C43C2211yescharacteristic
54C2×C22⋊C4×C43C2211yescharacteristic
55C24×C43C2311yescharacteristic
56C23×D43C2311yescharacteristic
57C2×Q8×C43—22no—
58C2×Q8×C43—22no—
59C2×Q8×C43—41no—
60C22×C4×C43—22no—
61C22×C4×C43—22no—
62C22×C4×C43—41no—
63C22×C4×C43C2311yescharacteristic
64C22×C4×C43C2311yescharacteristic
65C22×C4×C43C2311yescharacteristic
66C22×C4×C43C2311yescharacteristic
67C22×C4×C43C2311yescharacteristic
68C22×C4×C43C2311yescharacteristic
69C2×C22⋊D43—22no—
70C2×C22⋊D43—22no—
71C2×C22⋊D43—41no—
72C22×Dic43C2311yescharacteristic
73C22×Dic43C2311yescharacteristic
74C22×Dic43C2311yescharacteristic
75C22×Dic43C2311yescharacteristic
76C22×Dic43C2311yescharacteristic
77C22×Dic43C2311yescharacteristic
78C22×Dic43C2311yescharacteristic
79C2×C4×D43—22no—
80C2×C4×D43—22no—
81C2×C4×D43—41no—
82C4⋊C4×C43—22no—
83C4⋊C4×C43—22no—
84C4⋊C4×C43—22no—
85C22⋊C4×C43—22no—
86C22⋊C4×C43D414yes—
87C22⋊Dic43—22no—
88C22⋊Dic43—22no—
89C22⋊Dic43—22no—
90(C2×D43)⋊C4—22no—
91(C2×D43)⋊C4—22no—
92(C2×D43)⋊C4—22no—
93(C2×D43)⋊C4—22no—
94(C2×D43)⋊C4D414yes—
95C4⋊Dic43—22no—
96C4⋊Dic43—22no—
97Dic43⋊C4—22no—
98Dic43⋊C4—22no—
99Dic43⋊C4—22no—
100Dic43⋊C4—22no—
101Dic43⋊C4—22no—
102Dic43⋊C4—41no—
103Dic43⋊C4—41no—
104C4×Dic43—22no—
105C23×C43—21no—
106C23×C43—21no—
107C23×C43—21no—
108C23×C43—21no—
109C23×C43—21no—
110C23×C43—21no—
111C23×C43C2×D412yes—
112C23×C43C2411yescharacteristic
113C22×D43—21no—
114C22×D43—21no—
115C22×D43—21no—
116C22×D43—21no—
117C22×D43—21no—
118C22×D43—21no—
119C22×D43C2×D412yes—
120Q8×C43—44no—
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×C43—21no—
132C2×C4×C43—21no—
133C2×C4×C43—21no—
134C2×C4×C43—21no—
135C2×C4×C43—21no—
136C2×C4×C43—44no—
137C2×C4×C43C2×D412yes—
138C2×C4×C43C2×D412yes—
139C2×C4×C43C2×D412yes—
140C22⋊D43—44no—
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×Dic43—21no—
151C2×Dic43—21no—
152C2×Dic43—21no—
153C2×Dic43—21no—
154C2×Dic43—21no—
155C2×Dic43—21no—
156C2×Dic43—21no—
157C2×Dic43—21no—
158C2×Dic43—21no—
159C2×Dic43—21no—
160C2×Dic43C2×D412yes—
161C2×Dic43#4112yes—
162C4×D43—44no—
163C22×C43—22no—
164C22×C43—22no—
165C22×C43—22no—
166C22×C43—41no—
167C22×C43—41no—
168C22×C43—41no—
169C22×C43—41no—
170C22×C43C22×D411yescharacteristic
171C22×C43C22×D411yescharacteristic
172C22×C43C2×#4111yescharacteristic
173C22×C43H(5,𝔽2)11yescharacteristic
174C22×C432−1+411yescharacteristic
175C22×C432−1+411yescharacteristic
176C22×C432−1+411yescharacteristic
177C2×D43—22no—
178C2×D43—22no—
179C2×D43—22no—
180C2×D43—41no—
181C2×D43—41no—
182C2×D43—41no—
183C2×D43—41no—
184C4×C43—22no—
185C4×C43—22no—
186C4×C43—22no—
187C4×C43—41no—
188C4×C43—41no—
189C4×C43—41no—
190Dic43—22no—
191Dic43—22no—
192Dic43—41no—
193Dic43—41no—
194Dic43—41no—
195Dic43—41no—
196Dic43—41no—
197#2680—431nomaximal, Sylow
198C2×C43—42no—
199C2×C43#53611yescharacteristic
200C2×C43#53611yescharacteristic
201C2×C43#53911yescharacteristic
202C2×C43D4211yescharacteristic
203C2×C43#54711yescharacteristic
204C2×C43#54711yescharacteristic
205C2×C43#56311yescharacteristic
206D43—42no—
207C2×#123—431no—
208C2×#123—431no—
209C2×C22⋊Q8—431no—
210C2×C22⋊Q8D4311yescharacteristic, complemented
211#398—431no—
212#398—431no—
213#397—431no—
214#397—431no—
215#395—431no—
216#394—431no—
217#388—431no—
218#388—431no—
219#385—431no—
220#385—431no—
221#384—431no—
222C43#268011yescharacteristic, complemented, Sylow
223C22×Q8C2×D4311yescharacteristic
224C22×D4—431no—
225C23×C4—431no—
226C23×C4C2×D4311yescharacteristic
227#123—864no—
228#123—864no—
229C22⋊Q8—24no—
230C22⋊Q8—864no—
231C2×C4⋊C4—431no—
232C2×C4⋊C4—431no—
233C2×C4⋊C4—431no—
234C2×C4⋊C4—431no—
235C2×C4⋊C4—431no—
236C2×C4⋊C4—431no—
237C2×C4⋊C4—431no—
238C2×C4⋊C4—431no—
239C2×C4⋊C4—431no—
240C2×C4⋊C4C2×D4311yescharacteristic
241C2×C4⋊C4C2×D4311yescharacteristic
242C2×C4⋊C4C2×D4311yescharacteristic
243C2×C22⋊C4—431no—
244C2×C22⋊C4—431no—
245C2×C22⋊C4—431no—
246C2×C22⋊C4—431no—
247C2×C22⋊C4—431no—
248C2×C22⋊C4—431no—
249C2×C22⋊C4—431no—
250C2×C22⋊C4—431no—
251C2×C22⋊C4C2×D4311yescharacteristic
252C2×C22⋊C4C2×D4311yescharacteristic
253C2×C42—431no—
254#95—431no—
255#95—431no—
256#95—431no—
257#95—431no—
258#95—431no—
259#95—431no—
260#95—431no—
261#95—431no—
262C24—431no—
263C24C22×D4311yescharacteristic
264C2×Q8—22no—
265C2×Q8—22no—
266C2×Q8—41no—
267C2×D4—862no—
268C2×D4—862no—
269C2×D4—1721no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—41no—
273C22×C4—431no—
274C22×C4—431no—
275C22×C4—431no—
276C22×C4—431no—
277C22×C4—431no—
278C22×C4—431no—
279C22×C4—431no—
280C22×C4—862no—
281C22×C4—862no—
282C22×C4—1721no—
283C22×C4C22×D4311yescharacteristic
284C22×C4C22×D4311yescharacteristic
285C22×C4C22×D4311yescharacteristic
286C22×C4C22×D4311yescharacteristic
287C22×C4C22×D4311yescharacteristic
288C22×C4C22×D4311yescharacteristic
289C4⋊C4—22no—
290C4⋊C4—22no—
291C4⋊C4—22no—
292C4⋊C4—862no—
293C4⋊C4—862no—
294C4⋊C4—862no—
295C4⋊C4—862no—
296C4⋊C4—862no—
297C4⋊C4—862no—
298C4⋊C4—862no—
299C4⋊C4—1721no—
300C4⋊C4—1721no—
301C22⋊C4—22no—
302C22⋊C4—434no—
303C22⋊C4—862no—
304C22⋊C4—862no—
305C22⋊C4—862no—
306C22⋊C4—862no—
307C22⋊C4—862no—
308C22⋊C4—862no—
309C22⋊C4—862no—
310C22⋊C4C22⋊D4314yes—
311C42—862no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—432no—
319C23—861no—
320C23—861no—
321C23—861no—
322C23—861no—
323C23—861no—
324C23—861no—
325C23C2×C22⋊D4312yes—
326C23C23×D4311yescharacteristic
327Q8—44no—
328D4—1724no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—44no—
345C2×C4—432no—
346C2×C4—432no—
347C2×C4—861no—
348C2×C4—861no—
349C2×C4—861no—
350C2×C4—861no—
351C2×C4—861no—
352C2×C4—861no—
353C2×C4—861no—
354C2×C4—861no—
355C2×C4—861no—
356C2×C4—861no—
357C2×C4—861no—
358C2×C4—861no—
359C2×C4—861no—
360C2×C4—861no—
361C2×C4—861no—
362C2×C4—861no—
363C2×C4—861no—
364C2×C4—861no—
365C2×C4—861no—
366C2×C4—1724no—
367C2×C4D4×D4312yes—
368C2×C4C2×C22⋊D4312yes—
369C2×C4C2×C22⋊D4312yes—
370C22—22no—
371C22—22no—
372C22—22no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—862no—
378C22—862no—
379C22—862no—
380C22—1721no—
381C22—1721no—
382C22—1721no—
383C22—1721no—
384C22C2×D4×D4311yescharacteristic
385C22C22×C22⋊D4311yescharacteristic
386C22#41×D4311yescharacteristic
387C22#1306337011yescharacteristic
388C22#1306337211yescharacteristic
389C22#1306337311yescharacteristic
390C22#1306337311yescharacteristic
391C4—22no—
392C4—22no—
393C4—22no—
394C4—41no—
395C4—41no—
396C4—41no—
397C4—862no—
398C4—862no—
399C4—1721no—
400C4—1721no—
401C4—1721no—
402C4—1721no—
403C4—1721no—
404C2—42no—
405C2—1722no—
406C2#1458347211yescharacteristic
407C2#1458347311yescharacteristic
408C2#1458349511yescharacteristic
409C2D4×C22⋊D4311yescharacteristic
410C2#1458354811yescharacteristic
411C2#1458355111yescharacteristic
412C2#1458365011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC2×C22⋊Q8×C43C2
hypercenterC2×C22⋊Q8D43
hypocenterC43#2680
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. C2×#13063301C2semidirect
4. #14582832C2semidirect
5. #14582829C2semidirect
6. #14582827C2semidirect
7. #14582825C2semidirect
8. #14582818C2semidirect
10. #14582792C2semidirect
11. #14582789C2semidirect
12. #14582772C2semidirect
13. #14582770C2semidirect
14. #14582768C2semidirect
15. C2×C22⋊Q8×C43C2semidirect
210. C2×C22⋊Q8D43semidirect
222. C43#2680semidirect