Finite Group Databasebeta

← #19148185

Subgroups — #19148185

Order 5504.

1112 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583631C213yesmaximal, complemented
2#14583625C211yesmaximal, characteristic, complemented
3#14583620C213yesmaximal, complemented
4#14583601C213yesmaximal, complemented
5#14583595C213yesmaximal, complemented
6#14583568C211yesmaximal, characteristic, complemented
7#14583560C211yesmaximal, characteristic, complemented
8#14583444C213yesmaximal, complemented
9#14583435C213yesmaximal, complemented
10#14583428C213yesmaximal, complemented
11#41×Dic43C211yesmaximal, characteristic, complemented
12C4×#10621902C211yesmaximal, characteristic, complemented
13C4×#10621900C213yesmaximal, complemented
14C2×Q8×Dic43C211yesmaximal, characteristic, complemented
15C43×#548C211yesmaximal, characteristic, complemented
16C2×#10621902C2211yescharacteristic
17C2×#10621900C2213yes—
18#13063324C2213yes—
19#13063321C2213yes—
20#13063320C2216yes—
21#13063318C2216yes—
22#13063317C2213yes—
23#13063316C2213yes—
24#13063314C2213yes—
25#13063311C2216yes—
26#13063309C2216yes—
27#13063307C2216yes—
28#13063301C2213yes—
29#13063299C2213yes—
30#13063299C2213yes—
31#13063297C2216yes—
32#13063296C2213yes—
33Q8×Dic43C2211yescharacteristic
34Q8×Dic43C2211yescharacteristic
35Q8×Dic43C2213yes—
36Q8×Dic43C2211yescharacteristic
37Q8×Dic43C2213yes—
38C4×Dic86C2213yes—
39#13063290C2213yes—
40C4×D172C2213yes—
41D4×Dic43C2213yes—
42D4×Dic43C2213yes—
43D4×Dic43C2213yes—
44#13063287C2213yes—
45C4×C22⋊D43C2213yes—
46C4×C22⋊D43C2213yes—
47(C22⋊D43)⋊C4C2213yes—
48(C22⋊D43)⋊C4C2213yes—
49(C22⋊D43)⋊C4C2216yes—
50#13063284C2213yes—
51#13063283C2213yes—
52#13063283C2213yes—
53#13063281C2211yescharacteristic
54#13063281C2213yes—
55C2×C4⋊Dic43C2213yes—
56C2×C4×Dic43C2213yes—
57C2×C4×Dic43C2213yes—
58C42×D43C2213yes—
59C2×#41×C43C2211yescharacteristic
60C22×Q8×C43C2211yescharacteristic
61#124×C43C2213yes—
62C22⋊Q8×C43C2213yes—
63#121×C43C2213yes—
64C4×Q8×C43C2211yescharacteristic
65C4×D4×C43C2213yes—
66#41×C43—24no—
67C2×Q8×C43—24no—
68C2×Q8×C43C2313yes—
69C2×Q8×C43C2311yescharacteristic
70C2×D4×C43C2313yes—
71C2×D4×C43C2313yes—
72C22×C4×C43C2313yes—
73C22×C4×C43C2313yes—
74C2×C22⋊D43C2313yes—
75C2×C22⋊D43C2313yes—
76C2×C22⋊D43C2316yes—
77C22×Dic43C2313yes—
78C22×Dic43C2313yes—
79C22×Dic43C2313yes—
80C22×Dic43C2311yescharacteristic
81#10621902—24no—
82#10621900—212no—
83C2×D172C2313yes—
84C2×C4×D43C2313yes—
85C2×C4×D43C2313yes—
86C2×C4×D43C2313yes—
87C2×Dic86C2313yes—
88C4⋊C4×C43C2313yes—
89C4⋊C4×C43C2313yes—
90C22⋊C4×C43C2311yescharacteristic
91C22⋊C4×C43C2313yes—
92C22⋊C4×C43C2316yes—
93C42×C43C2313yes—
94C22⋊Dic43C2311yescharacteristic
95C22⋊Dic43C2313yes—
96C22⋊Dic43C2316yes—
97(C2×D43)⋊C4C2313yes—
98(C2×D43)⋊C4C2313yes—
99(C2×D43)⋊C4C2316yes—
100(C2×D43)⋊C4C2316yes—
101C4⋊Dic43C2313yes—
102C4⋊Dic43C2313yes—
103C4⋊Dic43C2316yes—
104C4⋊Dic43C2313yes—
105C4⋊Dic43C2313yes—
106Dic43⋊C4C2311yescharacteristic
107Dic43⋊C4C2313yes—
108Dic43⋊C4C2311yescharacteristic
109Dic43⋊C4C2313yes—
110Dic43⋊C4C2316yes—
111C4×Dic43C2311yescharacteristic
112C4×Dic43C2313yes—
113C4×Dic43C2313yes—
114C4×Dic43C2311yescharacteristic
115C4×Dic43C2313yes—
116C4×Dic43C2313yes—
117C4×Dic43C2313yes—
118C4×Dic43C2313yes—
119C4×Dic43C2313yes—
120C23×C43C2413yes—
121C23×C43C2411yescharacteristic
122C22×D43C2413yes—
123Q8×C43—26no—
124Q8×C43#4114yescomplemented
125D4×C43—26no—
126D4×C43—26no—
127C2×C4×C43—26no—
128C2×C4×C43—26no—
129C2×C4×C43C2411yescharacteristic
130C2×C4×C43C2413yes—
131C2×C4×C43C2411yescharacteristic
132C2×C4×C43C2413yes—
133C2×C4×C43C2413yes—
134C22⋊D43—26no—
135C22⋊D43—26no—
136C22⋊D43—46no—
137C2×Dic43—26no—
138C2×Dic43—43no—
139C2×Dic43—43no—
140C2×Dic43#4114yescomplemented
141C2×Dic43C2411yescharacteristic
142C2×Dic43C2411yescharacteristic
143C2×Dic43C2413yes—
144C2×Dic43C2413yes—
145C2×Dic43C2413yes—
146C2×Dic43C2411yescharacteristic
147C2×Dic43C2411yescharacteristic
148D172—26no—
149C4×D43—26no—
150C4×D43—26no—
151C4×D43—43no—
152Dic86—26no—
153C22×C43—21no—
154C22×C43—21no—
155C22×C43—23no—
156C22×C43—23no—
157C22×C43—23no—
158C22×C43C2×#4112yes—
159C22×C43C2511yescharacteristic
160C2×D43—23no—
161C2×D43—23no—
162C2×D43—23no—
163C4×C43—23no—
164C4×C43—21no—
165C4×C43—23no—
166C4×C43—21no—
167C4×C43C2×#4116yes—
168Dic43—23no—
169Dic43—21no—
170Dic43—23no—
171Dic43—21no—
172Dic43—23no—
173Dic43C2×#4112yes—
174Dic43C2×#4112yes—
175#3480—431nomaximal, Sylow
176C2×C43—22no—
177C2×C43—43no—
178C2×C43C22×#4111yescharacteristic
179C2×C43C22×#4111yescharacteristic
180C2×C43#58511yescharacteristic
181D43—43no—
182#559—433no—
183#557—431no—
184#556—433no—
185#553—433no—
186#553—433no—
187#550—431no—
188#548—431no—
189#548D4311yescharacteristic, complemented
190#532—433no—
191#529—433no—
192#529—433no—
193C4×#41—431no—
194C4×#41—431no—
195C4×#41—433no—
196C2×C4×Q8—431no—
197C43#348011yescharacteristic, complemented, Sylow
198C2×#41—431no—
199C2×#41—433no—
200C2×#41C2×D4311yescharacteristic
201C22×Q8C2×D4311yescharacteristic
202C4⋊Q8—433no—
203#127—433no—
204#126—436no—
205#126—436no—
206#125—433no—
207#125—433no—
208#124—433no—
209#124—436no—
210#124C2×D4313yes—
211#123—436no—
212#123—436no—
213C22⋊Q8—433no—
214C22⋊Q8C2×D4313yes—
215#121—433no—
216#121—436no—
217#121—433no—
218#121—433no—
219#121C2×D4313yes—
220C4×Q8—431no—
221C4×Q8—433no—
222C4×Q8—431no—
223C4×Q8—433no—
224C4×Q8—431no—
225C4×Q8—433no—
226C4×Q8—433no—
227C4×Q8C2×D4311yescharacteristic
228C4×D4—433no—
229C4×D4—433no—
230C4×D4—433no—
231C4×D4—433no—
232C4×D4—433no—
233C4×D4—433no—
234C4×D4—433no—
235C4×D4—433no—
236C4×D4—436no—
237C4×D4—433no—
238C4×D4C2×D4313yes—
239#117—433no—
240#117—433no—
241#117—433no—
242#117—431no—
243#117—433no—
244C2×C4⋊C4—433no—
245C2×C42—433no—
246C2×C42—433no—
247C2×C42—433no—
248#41—24no—
249#41—8612no—
250#41—864no—
251C2×Q8—24no—
252C2×Q8—433no—
253C2×Q8C22×D4313yes—
254C2×Q8C22×D4311yescharacteristic
255C2×D4—433no—
256C2×D4—433no—
257C2×D4—436no—
258C2×D4—433no—
259C2×D4C22×D4313yes—
260C2×D4C22×D4313yes—
261C22×C4—431no—
262C22×C4—433no—
263C22×C4—433no—
264C22×C4—433no—
265C22×C4—433no—
266C22×C4—433no—
267C22×C4—433no—
268C22×C4C22×D4313yes—
269C22×C4C22×D4313yes—
270C4⋊C4—433no—
271C4⋊C4—433no—
272C4⋊C4—436no—
273C4⋊C4—431no—
274C4⋊C4—431no—
275C4⋊C4—433no—
276C4⋊C4—433no—
277C4⋊C4—433no—
278C4⋊C4—433no—
279C4⋊C4—436no—
280C4⋊C4C22×D4313yes—
281C4⋊C4C22×D4313yes—
282C22⋊C4—431no—
283C22⋊C4—433no—
284C22⋊C4—436no—
285C22⋊C4—433no—
286C22⋊C4—436no—
287C22⋊C4—433no—
288C22⋊C4—436no—
289C22⋊C4C22×D4311yescharacteristic
290C22⋊C4C22×D4313yes—
291C22⋊C4C22×D4316yes—
292C42—431no—
293C42—431no—
294C42—433no—
295C42—433no—
296C42—433no—
297C42—433no—
298C42—433no—
299C42—433no—
300C42—433no—
301C42C22×D4313yes—
302C23—433no—
303C23C23×D4313yes—
304C23C23×D4311yescharacteristic
305Q8—26no—
306Q8—866no—
307Q8#1062190014yescomplemented
308D4—26no—
309D4—26no—
310D4—866no—
311D4—866no—
312D4—866no—
313D4—1726no—
314C2×C4—26no—
315C2×C4—26no—
316C2×C4—434no—
317C2×C4—431no—
318C2×C4—431no—
319C2×C4—431no—
320C2×C4—431no—
321C2×C4—433no—
322C2×C4—433no—
323C2×C4—433no—
324C2×C4—866no—
325C2×C4—866no—
326C2×C4—866no—
327C2×C4—1723no—
328C2×C4—1723no—
329C2×C4—1723no—
330C2×C4C23×D4311yescharacteristic
331C2×C4C23×D4313yes—
332C2×C4C23×D4311yescharacteristic
333C2×C4C23×D4313yes—
334C2×C4C23×D4313yes—
335C22—21no—
336C22—21no—
337C22—23no—
338C22—23no—
339C22—23no—
340C22—863no—
341C22—863no—
342C22—863no—
343C22#41×D4312yes—
344C22C24×D4311yescharacteristic
345C4—23no—
346C4—21no—
347C4—23no—
348C4—21no—
349C4—432no—
350C4—432no—
351C4—863no—
352C4—861no—
353C4—863no—
354C4—861no—
355C4—863no—
356C4C2×#1062190016yes—
357C2—22no—
358C2—43no—
359C2—1723no—
360C2C2×#41×D4311yescharacteristic
361C2C22×#1062190011yescharacteristic
362C2#1458373611yescharacteristic
subgroupG/H
center, FrattiniC22C24×D43
commutator, socleC22×C43C25
FittingC43×#548C2
hypercenter#548D43
hypocenterC43#3480
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ #548

Complements

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

NH ≅ G/Ntype
1. #14583631C2semidirect
2. #14583625C2semidirect
3. #14583620C2semidirect
4. #14583601C2semidirect
5. #14583595C2semidirect
6. #14583568C2semidirect
7. #14583560C2semidirect
8. #14583444C2semidirect
9. #14583435C2semidirect
10. #14583428C2semidirect
11. #41×Dic43C2semidirect
12. C4×#10621902C2semidirect
13. C4×#10621900C2semidirect
14. C2×Q8×Dic43C2semidirect
15. C43×#548C2semidirect
124. Q8×C43#41semidirect
140. C2×Dic43#41semidirect
189. #548D43semidirect
197. C43#3480semidirect
307. Q8#10621900semidirect