Finite Group Databasebeta

← #19147550

Subgroups — #19147550

Order 5504.

348 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583610C211yesmaximal, characteristic, complemented
2#14583605C211yesmaximal, characteristic, complemented
3#14583307C211yesmaximal, characteristic, complemented
4#14583299C211yesmaximal, characteristic, complemented
5#14583202C211yesmaximal, characteristic, complemented
6#14583198C211yesmaximal, characteristic, complemented
7#14583198C211yesmaximal, characteristic, complemented
8#14583196C211yesmaximal, characteristic, complemented
9#14583178C211yesmaximal, characteristic, complemented
10#14583176C211yesmaximal, characteristic, complemented
11#14583027C211yesmaximal, characteristic, complemented
12#14583012C211yesmaximal, characteristic
13#14583010C211yesmaximal, characteristic
14#14582981C211yesmaximal, characteristic
15C43×#501C211yesmaximal, characteristic, complemented
16C2×D344C2211yescharacteristic
17#13063324C2211yescharacteristic
18#13063316C2211yescharacteristic
19#13063316C2211yescharacteristic
20#13063316C2211yescharacteristic
21#13063305—21no—
22#13063305—21no—
23#13063303—21no—
24#13063303—21no—
25#13063301—21no—
26#13063301—21no—
27C4×Dic86C2211yescharacteristic
28C4×D172C2211yescharacteristic
29C4×D172C2211yescharacteristic
30#13063287C2211yescharacteristic
31#13063287C2211yescharacteristic
32#13063287C2211yescharacteristic
33#13063287C2211yescharacteristic
34C4⋊C4×D43—21no—
35C4⋊C4×D43—21no—
36#13063258C2211yescharacteristic
37#13063258C2211yescharacteristic
38#13063258C2211yescharacteristic
39#13063257C2211yescharacteristic
40#13063256C2211yescharacteristic
41C4⋊(C43⋊C8)C2211yescharacteristic
42Dic43⋊C8C2211yescharacteristic
43Dic43⋊C8C2211yescharacteristic
44#13063247C2211yescharacteristic
45#13063247C2211yescharacteristic
46#13063245C2211yescharacteristic
47#13063245C2211yescharacteristic
48#13063245C2211yescharacteristic
49#13063245C2211yescharacteristic
50#13063235C2211yescharacteristic
51C8×Dic43C2211yescharacteristic
52C4⋊Q8×C43C2211yescharacteristic
53#125×C43C2211yescharacteristic
54#107×C43C2211yescharacteristic
55#107×C43C2211yescharacteristic
56#106×C43C2211yescharacteristic
57#106×C43C2211yescharacteristic
58#97×C43C2211yescharacteristic
59C2×Q8×C43—21no—
60C2×D172C2311yescharacteristic
61C2×D172C2311yescharacteristic
62C2×C4×D43—21no—
63C2×C4×D43—21no—
64C2×C4×D43—21no—
65C2×C4×D43—21no—
66C2×C4×D43—21no—
67C2×C4×D43—21no—
68C2×Dic86—21no—
69C2×Dic86D411yescharacteristic
70C2×C8×C43C2311yescharacteristic
71C2×C8×C43C2311yescharacteristic
72C4⋊C4×C43—21no—
73C4⋊C4×C43—21no—
74C4⋊C4×C43—21no—
75C4⋊C4×C43C2311yescharacteristic
76C4⋊C4×C43C2311yescharacteristic
77C4⋊C4×C43C2311yescharacteristic
78C4⋊C4×C43C2311yescharacteristic
79C42×C43C2311yescharacteristic
80(C2×D43)⋊C4—21no—
81(C2×D43)⋊C4—21no—
82(C2×D43)⋊C4—21no—
83(C2×D43)⋊C4—21no—
84(C2×D43)⋊C4—21no—
85(C2×D43)⋊C4—21no—
86C4⋊Dic43—21no—
87C4⋊Dic43—21no—
88C4⋊Dic43—21no—
89C4⋊Dic43D411yescharacteristic
90C4⋊Dic43C2311yescharacteristic
91C4⋊Dic43C2311yescharacteristic
92Dic43⋊C4—21no—
93Dic43⋊C4—21no—
94Dic43⋊C4—21no—
95Dic43⋊C4—21no—
96Dic43⋊C4D411yescharacteristic
97Dic43⋊C4D411yescharacteristic
98C4×Dic43C2311yescharacteristic
99C4×Dic43C2311yescharacteristic
100C2×C43⋊C8C2311yescharacteristic
101C2×C43⋊C8C2311yescharacteristic
102D344Q814yescomplemented
103C22×D43—21no—
104C22×D43—21no—
105Q8×C43—81no—
106C2×C4×C43—21no—
107C2×C4×C43—21no—
108C2×C4×C43—21no—
109C2×C4×C43—21no—
110C2×C4×C43C2×D411yescharacteristic
111C2×C4×C43C2×D411yescharacteristic
112C2×C4×C43C2411yescharacteristic
113C2×Dic43—21no—
114C2×Dic43—21no—
115C2×Dic43C2×D411yescharacteristic
116C2×Dic43C2×D411yescharacteristic
117C2×Dic43C2×D411yescharacteristic
118C2×Dic43C2×D411yescharacteristic
119D172—21no—
120D172—21no—
121D172C2×Q812yes—
122D172C2×Q812yes—
123C4×D43—42no—
124C4×D43—42no—
125C4×D43—81no—
126C4×D43—81no—
127C4×D43—81no—
128C4×D43—81no—
129Dic86—41no—
130Dic86—81no—
131C8×C43—21no—
132C8×C43C2×Q812yes—
133C43⋊C8—21no—
134C43⋊C8—21no—
135C22×C43C22×D411yescharacteristic
136C2×D43—22no—
137C2×D43—22no—
138C2×D43—41no—
139C2×D43—41no—
140C2×D43—41no—
141C2×D43—41no—
142C4×C43—21no—
143C4×C43—21no—
144C4×C43—41no—
145C4×C43—41no—
146C4×C43—41no—
147C4×C43—41no—
148C4×C43C22×Q811yescharacteristic
149C4×C432−1+411yescharacteristic
150Dic43—21no—
151Dic43—21no—
152Dic43—21no—
153Dic43—21no—
154Dic43—41no—
155Dic43—41no—
156#3389—431nomaximal, Sylow
157C2×C43D4×Q811yescharacteristic
158C2×C43#57511yescharacteristic
159C2×C43#57611yescharacteristic
160D43—42no—
161D43—42no—
162#554—431no—
163#554—431no—
164#501—431no—
165#501D4311yescharacteristic, complemented
166#499—431no—
167#478—431no—
168#478—431no—
169#478—431no—
170#478—431no—
171#474—431no—
172#474—431no—
173#446—431no—
174#442—431no—
175#442—431no—
176C4×D8—431no—
177C43#338911yescharacteristic, complemented, Sylow
178C2×D8—431no—
179C4⋊Q8—431no—
180C4⋊Q8C2×D4311yescharacteristic
181#125—431no—
182#125—431no—
183#125—431no—
184#125C2×D4311yescharacteristic
185C22⋊Q8—861no—
186C22⋊Q8—861no—
187C22⋊Q8—861no—
188C22⋊Q8—861no—
189C22⋊Q8—861no—
190C22⋊Q8—861no—
191C4×Q8—431no—
192C4×D4—431no—
193C4×D4—431no—
194C4×D4—431no—
195C4×D4—431no—
196C4×D4—431no—
197C4×D4—431no—
198C2×C4⋊C4—861no—
199C2×C4⋊C4—861no—
200#107—431no—
201#107—431no—
202#107—431no—
203#107C2×D4311yescharacteristic
204#107C2×D4311yescharacteristic
205#106—431no—
206#106—431no—
207#106C2×D4311yescharacteristic
208#106C2×D4311yescharacteristic
209C4⋊C8—431no—
210C4⋊C8—431no—
211C4⋊C8—431no—
212#102—431no—
213#102—431no—
214#102—431no—
215#102—431no—
216#102—431no—
217#102—431no—
218#97—431no—
219#97C2×D4311yescharacteristic
220C4×C8—431no—
221C2×Q8—21no—
222C2×Q8—431no—
223C2×Q8—861no—
224C2×D4—431no—
225C2×D4—431no—
226C22×C4—861no—
227C22×C4—861no—
228C22×C4—861no—
229C22×C4—861no—
230C22×C4—861no—
231C22×C4—861no—
232D8—434no—
233C2×C8—431no—
234C2×C8—431no—
235C2×C8C22×D4311yescharacteristic
236C2×C8C22×D4311yescharacteristic
237C4⋊C4—21no—
238C4⋊C4—21no—
239C4⋊C4—21no—
240C4⋊C4—431no—
241C4⋊C4—431no—
242C4⋊C4—431no—
243C4⋊C4—431no—
244C4⋊C4—431no—
245C4⋊C4—861no—
246C4⋊C4—861no—
247C4⋊C4—861no—
248C4⋊C4—861no—
249C4⋊C4—861no—
250C4⋊C4—861no—
251C4⋊C4—861no—
252C4⋊C4C22×D4311yescharacteristic
253C4⋊C4C22×D4311yescharacteristic
254C4⋊C4C22×D4311yescharacteristic
255C4⋊C4C22×D4311yescharacteristic
256C22⋊C4—861no—
257C22⋊C4—861no—
258C22⋊C4—861no—
259C22⋊C4—861no—
260C22⋊C4—861no—
261C22⋊C4—861no—
262C42—431no—
263C42—431no—
264C42C22×D4311yescharacteristic
265C23—861no—
266C23—861no—
267Q8—81no—
268Q8—3441no—
269Q8—1721no—
270D4—432no—
271D4—432no—
272D4—861no—
273D4—861no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—431no—
279C2×C4—431no—
280C2×C4—431no—
281C2×C4—431no—
282C2×C4—861no—
283C2×C4—861no—
284C2×C4—3441no—
285C2×C4—3441no—
286C2×C4—3441no—
287C2×C4—3441no—
288C2×C4—1722no—
289C2×C4—1722no—
290C2×C4D4×D4311yescharacteristic
291C2×C4D4×D4311yescharacteristic
292C2×C4C23×D4311yescharacteristic
293C8—21no—
294C8—861no—
295C8—861no—
296C8Q8×D4312yes—
297C22—862no—
298C22—862no—
299C22—1721no—
300C22—1721no—
301C22—1721no—
302C22—1721no—
303C22C2×D4×D4311yescharacteristic
304C4—21no—
305C4—21no—
306C4—41no—
307C4—41no—
308C4—41no—
309C4—41no—
310C4—861no—
311C4—861no—
312C4—861no—
313C4—861no—
314C4—1721no—
315C4—1721no—
316C4C2×Q8×D4311yescharacteristic
317C4#1306337311yescharacteristic
318C2—1722no—
319C2—1722no—
320C2#1458356411yescharacteristic
321C2#1458369811yescharacteristic
322C2#1458370311yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#501C2
socleC22×C43C22×D4
hypercenter#501D43
hypocenterC43#3389
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
1. #14583610C2semidirect
2. #14583605C2semidirect
3. #14583307C2semidirect
4. #14583299C2semidirect
5. #14583202C2semidirect
6. #14583198C2semidirect
7. #14583198C2semidirect
8. #14583196C2semidirect
9. #14583178C2semidirect
10. #14583176C2semidirect
11. #14583027C2semidirect
15. C43×#501C2semidirect
102. D344Q8semidirect
165. #501D43semidirect
177. C43#3389semidirect