Finite Group Databasebeta

← #19142216

Subgroups — #19142216

Order 5504.

498 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43⋊#401C211yesmaximal, characteristic, complemented
2#14582840C211yesmaximal, characteristic, complemented
3#14582827C211yesmaximal, characteristic, complemented
4#14582814C211yesmaximal, characteristic, complemented
5#14582813C211yesmaximal, characteristic, complemented
6#14582807C211yesmaximal, characteristic
7#14582793C211yesmaximal, characteristic, complemented
8#14582788C211yesmaximal, characteristic, complemented
9#14582787C211yesmaximal, characteristic, complemented
10#14582778C211yesmaximal, characteristic, complemented
11#14582775C211yesmaximal, characteristic, complemented
12#14582775C211yesmaximal, characteristic, complemented
13#14582772C211yesmaximal, characteristic, complemented
14#14582758C211yesmaximal, characteristic, complemented
15C43×#386C211yesmaximal, characteristic, complemented
16C22×C22⋊D43C2211yescharacteristic
17C22×C22⋊D43C2211yescharacteristic
18C22×C4×D43C2211yescharacteristic
19C2×Dic43⋊C4C2211yescharacteristic
20C2×Dic43⋊C4C2211yescharacteristic
21C2×Dic43⋊C4C2211yescharacteristic
22C2×Dic43⋊C4C2211yescharacteristic
23C2×C22⋊Dic43C2211yescharacteristic
24C2×C22⋊Dic43C2211yescharacteristic
25C2×C22⋊Dic43C2211yescharacteristic
26C2×C22⋊Dic43C2211yescharacteristic
27C2×C22⋊Dic43C2211yescharacteristic
28C2×C22⋊Dic43C2211yescharacteristic
29C2×(C2×D43)⋊C4C2211yescharacteristic
30C2×(C2×D43)⋊C4C2211yescharacteristic
31C2×(C2×D43)⋊C4C2211yescharacteristic
32C2×(C2×D43)⋊C4C2211yescharacteristic
33C2×C4×Dic43C2211yescharacteristic
34C43⋊#95C2211yescharacteristic
35C43⋊#95C2211yescharacteristic
36C43⋊#95C2211yescharacteristic
37C43⋊#95C2211yescharacteristic
38C43⋊#95C2211yescharacteristic
39C43⋊#95C2211yescharacteristic
40C43⋊#95C2211yescharacteristic
41C43⋊#95C2211yescharacteristic
42C43⋊#95C2211yescharacteristic
43C43⋊#95C2211yescharacteristic
44C22×D4×C43C2211yescharacteristic
45C23×C4×C43C2211yescharacteristic
46C2×C22⋊C4×C43C2211yescharacteristic
47C2×C22⋊C4×C43C2211yescharacteristic
48C2×C22⋊C4×C43C2211yescharacteristic
49#95×C43C2211yescharacteristic
50#95×C43C2211yescharacteristic
51C24×C43C2311yescharacteristic
52C24×C43C2311yescharacteristic
53C23×D43C2311yescharacteristic
54C2×D4×C43—22no—
55C2×D4×C43—41no—
56C2×D4×C43—41no—
57C22×C4×C43—41no—
58C22×C4×C43—41no—
59C22×C4×C43—41no—
60C22×C4×C43C2311yescharacteristic
61C22×C4×C43C2311yescharacteristic
62C22×C4×C43C2311yescharacteristic
63C22×C4×C43C2311yescharacteristic
64C22×C4×C43C2311yescharacteristic
65C2×C22⋊D43—22no—
66C2×C22⋊D43—22no—
67C2×C22⋊D43—22no—
68C2×C22⋊D43—41no—
69C2×C22⋊D43—41no—
70C2×C22⋊D43—41no—
71C22×Dic43C2311yescharacteristic
72C22×Dic43C2311yescharacteristic
73C22×Dic43C2311yescharacteristic
74C22×Dic43C2311yescharacteristic
75C22×Dic43C2311yescharacteristic
76C22×Dic43C2311yescharacteristic
77C22×Dic43C2311yescharacteristic
78C2×C4×D43—22no—
79C2×C4×D43—41no—
80C2×C4×D43—41no—
81C22⋊C4×C43—41no—
82C22⋊C4×C43—41no—
83C22⋊C4×C43—41no—
84C22⋊Dic43—22no—
85C22⋊Dic43—22no—
86C22⋊Dic43—22no—
87C22⋊Dic43—41no—
88C22⋊Dic43—41no—
89C22⋊Dic43—41no—
90(C2×D43)⋊C4—22no—
91(C2×D43)⋊C4—41no—
92(C2×D43)⋊C4—41no—
93(C2×D43)⋊C4—41no—
94Dic43⋊C4—41no—
95Dic43⋊C4—41no—
96Dic43⋊C4—41no—
97Dic43⋊C4—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#4112yes—
113C23×C43C2411yescharacteristic
114C22×D43—21no—
115C22×D43—21no—
116C22×D43—21no—
117C22×D43—21no—
118C22×D43—21no—
119C22×D43—21no—
120C22×D43#4112yes—
121D4×C43—44no—
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—21no—
137C2×C4×C43—44no—
138C22⋊D43—44no—
139C22⋊D43—44no—
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—21no—
160C2×Dic43#4112yes—
161C4×D43—44no—
162C22×C43—22no—
163C22×C43—22no—
164C22×C43—22no—
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×C43C2×#4111yescharacteristic
177C22×C43C2×#4111yescharacteristic
178C22×C43C2×#4111yescharacteristic
179C22×C43H(5,𝔽2)11yescharacteristic
180C22×C43H(5,𝔽2)11yescharacteristic
181C22×C43H(5,𝔽2)11yescharacteristic
182C22×C43H(5,𝔽2)11yescharacteristic
183C2×D43—22no—
184C2×D43—22no—
185C2×D43—22no—
186C2×D43—41no—
187C2×D43—41no—
188C2×D43—41no—
189C2×D43—41no—
190C4×C43—41no—
191C4×C43—41no—
192C4×C43—41no—
193C4×C43—41no—
194C4×C43—41no—
195Dic43—22no—
196Dic43—41no—
197Dic43—41no—
198Dic43—41no—
199Dic43—41no—
200Dic43—41no—
201Dic43—41no—
202#2778—431nomaximal, Sylow
203C2×C43—42no—
204C2×C43—81no—
205C2×C43#53811yescharacteristic
206C2×C43#53811yescharacteristic
207C2×C43#53811yescharacteristic
208C2×C43#55111yescharacteristic
209C2×C43#55311yescharacteristic
210C2×C43#55311yescharacteristic
211C2×C43#56011yescharacteristic
212D43—42no—
213#401—431no—
214#400—431no—
215#397—431no—
216#394—431no—
217#394—431no—
218#392—431no—
219#388—431no—
220#388—431no—
221#388—431no—
222#386—431no—
223#386—431no—
224#386—431no—
225#386D4311yescharacteristic, complemented
226#385—431no—
227#380—431no—
228C43#277811yescharacteristic, complemented, Sylow
229C22×D4—431no—
230C22×D4—431no—
231C22×D4C2×D4311yescharacteristic
232C23×C4—431no—
233C23×C4C2×D4311yescharacteristic
234C2×C4⋊C4—431no—
235C2×C4⋊C4—431no—
236C2×C4⋊C4—431no—
237C2×C4⋊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—
252#95—431no—
253#95—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—
262#95C2×D4311yescharacteristic
263#95C2×D4311yescharacteristic
264C24—431no—
265C24C22×D4311yescharacteristic
266C24C22×D4311yescharacteristic
267C2×D4—22no—
268C2×D4—41no—
269C2×D4—41no—
270C2×D4—862no—
271C2×D4—862no—
272C2×D4—862no—
273C2×D4—1721no—
274C2×D4—1721no—
275C2×D4—1721no—
276C22×C4—41no—
277C22×C4—41no—
278C22×C4—41no—
279C22×C4—431no—
280C22×C4—431no—
281C22×C4—431no—
282C22×C4—431no—
283C22×C4—431no—
284C22×C4—431no—
285C22×C4—431no—
286C22×C4—862no—
287C22×C4—1721no—
288C22×C4—1721no—
289C22×C4C22×D4311yescharacteristic
290C22×C4C22×D4311yescharacteristic
291C22×C4C22×D4311yescharacteristic
292C22×C4C22×D4311yescharacteristic
293C22×C4C22×D4311yescharacteristic
294C4⋊C4—1721no—
295C4⋊C4—1721no—
296C4⋊C4—1721no—
297C4⋊C4—1721no—
298C22⋊C4—41no—
299C22⋊C4—41no—
300C22⋊C4—41no—
301C22⋊C4—862no—
302C22⋊C4—862no—
303C22⋊C4—862no—
304C22⋊C4—862no—
305C22⋊C4—1721no—
306C22⋊C4—1721no—
307C22⋊C4—1721no—
308C22⋊C4—1721no—
309C22⋊C4—1721no—
310C22⋊C4—1721no—
311C42—1721no—
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—432no—
326C23—861no—
327C23—861no—
328C23—861no—
329C23—861no—
330C23—861no—
331C23—861no—
332C23#1062189812yes—
333C23C23×D4311yescharacteristic
334D4—44no—
335D4—1724no—
336D4—1724no—
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—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—44no—
353C2×C4—432no—
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—861no—
370C2×C4—861no—
371C2×C4—861no—
372C2×C4—861no—
373C2×C4—861no—
374C2×C4—1724no—
375C22—22no—
376C22—22no—
377C22—22no—
378C22—41no—
379C22—41no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—862no—
390C22—862no—
391C22—862no—
392C22—1721no—
393C22—1721no—
394C22—1721no—
395C22—1721no—
396C22#41×D4311yescharacteristic
397C22#41×D4311yescharacteristic
398C22C2×#1062189811yescharacteristic
399C22#1306337011yescharacteristic
400C22#1306337011yescharacteristic
401C22#1306337011yescharacteristic
402C22#1306337011yescharacteristic
403C4—41no—
404C4—41no—
405C4—41no—
406C4—41no—
407C4—41no—
408C4—862no—
409C4—1721no—
410C4—1721no—
411C4—1721no—
412C4—1721no—
413C4—1721no—
414C4—1721no—
415C2—42no—
416C2—81no—
417C2—1722no—
418C2#1458348111yescharacteristic
419C2#1458348111yescharacteristic
420C2#1458348711yescharacteristic
421C2#1458357811yescharacteristic
422C2#1458359411yescharacteristic
423C2#1458359811yescharacteristic
424C2#1458363811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#386C2
hypercenter#386D43
hypocenterC43#2778
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C43⋊#401C2semidirect
2. #14582840C2semidirect
3. #14582827C2semidirect
4. #14582814C2semidirect
5. #14582813C2semidirect
7. #14582793C2semidirect
8. #14582788C2semidirect
9. #14582787C2semidirect
10. #14582778C2semidirect
11. #14582775C2semidirect
12. #14582775C2semidirect
13. #14582772C2semidirect
14. #14582758C2semidirect
15. C43×#386C2semidirect
225. #386D43semidirect
228. C43#2778semidirect