Finite Group Databasebeta

← #19142534

Subgroups — #19142534

Order 5504.

470 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14582827C211yesmaximal, characteristic, complemented
2#14582813C211yesmaximal, characteristic, complemented
3#14582813C211yesmaximal, characteristic, complemented
4#14582813C211yesmaximal, characteristic, complemented
5#14582813C211yesmaximal, characteristic, complemented
6#14582802C211yesmaximal, characteristic, complemented
7#14582802C211yesmaximal, characteristic, complemented
8#14582796C211yesmaximal, characteristic, complemented
9#14582793C211yesmaximal, characteristic, complemented
10#14582793C211yesmaximal, characteristic, complemented
11#14582792C211yesmaximal, characteristic, complemented
12#14582792C211yesmaximal, characteristic, complemented
13#14582787C211yesmaximal, characteristic, complemented
14#14582786C211yesmaximal, characteristic, complemented
15C43×#392C211yesmaximal, characteristic
16C2×C4⋊Dic43C2211yescharacteristic
17C2×C4⋊Dic43C2211yescharacteristic
18C2×Dic43⋊C4C2211yescharacteristic
19C2×Dic43⋊C4C2211yescharacteristic
20C2×Dic43⋊C4C2211yescharacteristic
21C2×Dic43⋊C4C2211yescharacteristic
22C2×C22⋊Dic43C2211yescharacteristic
23C2×C22⋊Dic43C2211yescharacteristic
24C2×C22⋊Dic43C2211yescharacteristic
25C2×C22⋊Dic43C2211yescharacteristic
26C2×C22⋊Dic43C2211yescharacteristic
27C2×C22⋊Dic43C2211yescharacteristic
28C2×C22⋊Dic43C2211yescharacteristic
29C2×C22⋊Dic43C2211yescharacteristic
30C2×C22⋊Dic43C2211yescharacteristic
31C2×C22⋊Dic43C2211yescharacteristic
32C2×C22⋊Dic43C2211yescharacteristic
33C2×C22⋊Dic43C2211yescharacteristic
34C2×C4×Dic43C2211yescharacteristic
35C2×C4×Dic43C2211yescharacteristic
36C2×C4×Dic43C2211yescharacteristic
37C43⋊#95C2211yescharacteristic
38C43⋊#95C2211yescharacteristic
39C43⋊#95C2211yescharacteristic
40C43⋊#95C2211yescharacteristic
41C43⋊#95C2211yescharacteristic
42C43⋊#95C2211yescharacteristic
43C43⋊#95C2211yescharacteristic
44C22×D4×C43C2211yescharacteristic
45C22×D4×C43C2211yescharacteristic
46C22×D4×C43C2211yescharacteristic
47C2×C22⋊C4×C43C2211yescharacteristic
48C2×C22⋊C4×C43C2211yescharacteristic
49C2×C22⋊C4×C43C2211yescharacteristic
50#95×C43C2211yescharacteristic
51C24×C43C2311yescharacteristic
52C24×C43C2311yescharacteristic
53C24×C43C2311yescharacteristic
54C2×D4×C43—22no—
55C2×D4×C43—22no—
56C2×D4×C43—41no—
57C2×D4×C43—41no—
58C2×D4×C43—41no—
59C2×D4×C43—41no—
60C2×D4×C43—41no—
61C2×D4×C43—41no—
62C2×D4×C43—41no—
63C22×C4×C43C2311yescharacteristic
64C22×C4×C43C2311yescharacteristic
65C22×C4×C43C2311yescharacteristic
66C22×C4×C43C2311yescharacteristic
67C22×Dic43C2311yescharacteristic
68C22×Dic43C2311yescharacteristic
69C22×Dic43C2311yescharacteristic
70C22×Dic43C2311yescharacteristic
71C22×Dic43C2311yescharacteristic
72C22×Dic43C2311yescharacteristic
73C22×Dic43C2311yescharacteristic
74C22×Dic43C2311yescharacteristic
75C22⋊C4×C43—22no—
76C22⋊C4×C43—22no—
77C22⋊C4×C43—41no—
78C22⋊Dic43—22no—
79C22⋊Dic43—22no—
80C22⋊Dic43—22no—
81C22⋊Dic43—41no—
82C22⋊Dic43—41no—
83C22⋊Dic43—41no—
84C22⋊Dic43—41no—
85C22⋊Dic43—41no—
86C22⋊Dic43—41no—
87C22⋊Dic43—41no—
88C22⋊Dic43—41no—
89C22⋊Dic43—41no—
90C4⋊Dic43—41no—
91C4⋊Dic43—41no—
92Dic43⋊C4—22no—
93Dic43⋊C4—22no—
94Dic43⋊C4—41no—
95Dic43⋊C4—41no—
96C4×Dic43—41no—
97C4×Dic43—41no—
98C4×Dic43—41no—
99C23×C43—21no—
100C23×C43—21no—
101C23×C43—21no—
102C23×C43—21no—
103C23×C43—21no—
104C23×C43—21no—
105C23×C43—21no—
106C23×C43—21no—
107C23×C43—21no—
108C23×C43—21no—
109C23×C43—21no—
110C23×C43—21no—
111C23×C43—21no—
112C23×C43—21no—
113C23×C43—21no—
114C23×C43—21no—
115C23×C43—21no—
116C23×C43—21no—
117C23×C43—21no—
118C23×C43—21no—
119C23×C43—21no—
120C23×C43C2411yescharacteristic
121D4×C43—44no—
122D4×C43—44no—
123D4×C43—44no—
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#4112yes—
135C2×C4×C43#4112yes—
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×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#4112yes—
160C22×C43—41no—
161C22×C43—41no—
162C22×C43—41no—
163C22×C43—41no—
164C22×C43—41no—
165C22×C43—41no—
166C22×C43—41no—
167C22×C43—41no—
168C22×C43—41no—
169C22×C43—41no—
170C22×C43—41no—
171C22×C43—41no—
172C22×C43—41no—
173C22×C43—41no—
174C22×C43—41no—
175C22×C43—41no—
176C22×C43—41no—
177C22×C43—41no—
178C22×C43—41no—
179C22×C43—41no—
180C22×C43—41no—
181C22×C43C2×#4111yescharacteristic
182C22×C43C2×#4111yescharacteristic
183C22×C43C2×#4111yescharacteristic
184C22×C43H(5,𝔽2)11yescharacteristic
185C22×C43H(5,𝔽2)11yescharacteristic
186C22×C43H(5,𝔽2)11yescharacteristic
187C22×C43H(5,𝔽2)11yescharacteristic
188C4×C43—22no—
189C4×C43—22no—
190C4×C43—41no—
191C4×C43—41no—
192Dic43—22no—
193Dic43—41no—
194Dic43—41no—
195Dic43—41no—
196Dic43—41no—
197Dic43—41no—
198Dic43—41no—
199Dic43—41no—
200#2803—431nomaximal, Sylow
201C2×C43—81no—
202C2×C43—81no—
203C2×C43—81no—
204C2×C43#53811yescharacteristic
205C2×C43#53811yescharacteristic
206C2×C43#54011yescharacteristic
207C2×C43#55311yescharacteristic
208C2×C43#55511yescharacteristic
209C2×C43#55911yescharacteristic
210C2×C43#56011yescharacteristic
211#397—431no—
212#394—431no—
213#394—431no—
214#394—431no—
215#394—431no—
216#392D4311yescharacteristic
217#390—431no—
218#390—431no—
219#389—431no—
220#388—431no—
221#388—431no—
222#388—431no—
223#388—431no—
224#388—431no—
225#387—431no—
226C43#280311yescharacteristic, complemented, Sylow
227C22×D4C2×D4311yescharacteristic
228C22×D4C2×D4311yescharacteristic
229C22×D4C2×D4311yescharacteristic
230C2×C4⋊C4—431no—
231C2×C4⋊C4—431no—
232C2×C4⋊C4—431no—
233C2×C4⋊C4—431no—
234C2×C4⋊C4—431no—
235C2×C4⋊C4—431no—
236C2×C22⋊C4—431no—
237C2×C22⋊C4—431no—
238C2×C22⋊C4—431no—
239C2×C22⋊C4—431no—
240C2×C22⋊C4—431no—
241C2×C22⋊C4—431no—
242C2×C22⋊C4—431no—
243C2×C22⋊C4—431no—
244C2×C22⋊C4—431no—
245C2×C22⋊C4—431no—
246C2×C22⋊C4—431no—
247C2×C22⋊C4—431no—
248C2×C22⋊C4C2×D4311yescharacteristic
249C2×C22⋊C4C2×D4311yescharacteristic
250C2×C22⋊C4C2×D4311yescharacteristic
251C2×C42—431no—
252C2×C42—431no—
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#95C2×D4311yescharacteristic
262C24C22×D4311yescharacteristic
263C24C22×D4311yescharacteristic
264C24C22×D4311yescharacteristic
265C2×D4—22no—
266C2×D4—22no—
267C2×D4—41no—
268C2×D4—41no—
269C2×D4—41no—
270C2×D4—41no—
271C2×D4—41no—
272C2×D4—41no—
273C2×D4—41no—
274C22×C4—431no—
275C22×C4—431no—
276C22×C4—431no—
277C22×C4—431no—
278C22×C4—431no—
279C22×C4—431no—
280C22×C4—431no—
281C22×C4—431no—
282C22×C4C22×D4311yescharacteristic
283C22×C4C22×D4311yescharacteristic
284C22×C4C22×D4311yescharacteristic
285C22×C4C22×D4311yescharacteristic
286C4⋊C4—862no—
287C4⋊C4—862no—
288C4⋊C4—1721no—
289C4⋊C4—1721no—
290C4⋊C4—1721no—
291C4⋊C4—1721no—
292C22⋊C4—22no—
293C22⋊C4—22no—
294C22⋊C4—41no—
295C22⋊C4—862no—
296C22⋊C4—862no—
297C22⋊C4—862no—
298C22⋊C4—1721no—
299C22⋊C4—1721no—
300C22⋊C4—1721no—
301C22⋊C4—1721no—
302C22⋊C4—1721no—
303C22⋊C4—1721no—
304C22⋊C4—1721no—
305C22⋊C4—1721no—
306C22⋊C4—1721no—
307C42—1721no—
308C42—1721no—
309C42—1721no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23—21no—
322C23—21no—
323C23—21no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23C23×D4311yescharacteristic
332D4—44no—
333D4—44no—
334D4—44no—
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—21no—
345C2×C4—432no—
346C2×C4—861no—
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—861no—
367C2×C4—861no—
368C2×C4—861no—
369C2×C4#1062190012yes—
370C2×C4#1062190012yes—
371C22—41no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22#41×D4311yescharacteristic
393C22C2×#1062190011yescharacteristic
394C22C2×#1062190011yescharacteristic
395C22#1306337011yescharacteristic
396C22#1306337011yescharacteristic
397C22#1306337011yescharacteristic
398C22#1306337011yescharacteristic
399C4—22no—
400C4—22no—
401C4—41no—
402C4—41no—
403C4—862no—
404C4—1721no—
405C4—1721no—
406C4—1721no—
407C4—1721no—
408C4—1721no—
409C4—1721no—
410C4—1721no—
411C2—81no—
412C2—81no—
413C2—81no—
414C2#1458348411yescharacteristic
415C2#1458348411yescharacteristic
416C2#1458349911yescharacteristic
417C2#1458359611yescharacteristic
418C2#1458361311yescharacteristic
419C2#1458363511yescharacteristic
420C2#1458363811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#392C2
hypercenter#392D43
hypocenterC43#2803
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. #14582827C2semidirect
2. #14582813C2semidirect
3. #14582813C2semidirect
4. #14582813C2semidirect
5. #14582813C2semidirect
6. #14582802C2semidirect
7. #14582802C2semidirect
8. #14582796C2semidirect
9. #14582793C2semidirect
10. #14582793C2semidirect
11. #14582792C2semidirect
12. #14582792C2semidirect
13. #14582787C2semidirect
14. #14582786C2semidirect
226. C43#2803semidirect