Finite Group Databasebeta

← #19146006

Subgroups — #19146006

Order 5504.

358 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583504C211yesmaximal, characteristic, complemented
2#14583206C211yesmaximal, characteristic, complemented
3#14583199C211yesmaximal, characteristic, complemented
4#14583186C211yesmaximal, characteristic, complemented
5#14583176C211yesmaximal, characteristic, complemented
6#14583150C211yesmaximal, characteristic, complemented
7#14583147C211yesmaximal, characteristic, complemented
8#14583133C211yesmaximal, characteristic, complemented
9#14583130C211yesmaximal, characteristic, complemented
10#14583111C211yesmaximal, characteristic, complemented
11#14583111C211yesmaximal, characteristic, complemented
12#14583099C211yesmaximal, characteristic, complemented
13#14583094C211yesmaximal, characteristic, complemented
14#14582926C211yesmaximal, characteristic, complemented
15C43×#542C211yesmaximal, characteristic, complemented
16C2×#10621884C2211yescharacteristic
17C2×#10621884C2211yescharacteristic
18C2×#10621882C2211yescharacteristic
19C2×#10621882C2211yescharacteristic
20C2×#10621877C2211yescharacteristic
21C22×C43⋊C8C2211yescharacteristic
22#13063322C2211yescharacteristic
23#13063317C2211yescharacteristic
24#13063310—21no—
25#13063310—21no—
26#13063299C2211yescharacteristic
27#13063299C2211yescharacteristic
28#13063298—21no—
29#13063298—21no—
30C4×D172C2211yescharacteristic
31C4×D172C2211yescharacteristic
32#13063258C2211yescharacteristic
33#13063258C2211yescharacteristic
34#13063256C2211yescharacteristic
35#13063256C2211yescharacteristic
36C4⋊(C43⋊C8)C2211yescharacteristic
37C4⋊(C43⋊C8)C2211yescharacteristic
38C4⋊(C43⋊C8)C2211yescharacteristic
39C4⋊(C43⋊C8)C2211yescharacteristic
40#13063249C2211yescharacteristic
41#13063249C2211yescharacteristic
42#13063246C2211yescharacteristic
43#13063246C2211yescharacteristic
44#13063245C2211yescharacteristic
45#13063245C2211yescharacteristic
46#13063245C2211yescharacteristic
47#13063245C2211yescharacteristic
48C4⋊Q8×C43C2211yescharacteristic
49#126×C43—21no—
50#124×C43—21no—
51#124×C43C2211yescharacteristic
52#123×C43—21no—
53C22⋊Q8×C43—21no—
54C22⋊Q8×C43C2211yescharacteristic
55#121×C43C2211yescharacteristic
56C4×Q8×C43C2211yescharacteristic
57C4×D4×C43C2211yescharacteristic
58#117×C43C2211yescharacteristic
59C2×Q8×C43—21no—
60C2×Q8×C43C2311yescharacteristic
61C2×D4×C43—21no—
62C2×D4×C43C2311yescharacteristic
63C22×C4×C43—21no—
64C22×C4×C43C2311yescharacteristic
65C2×C22⋊D43—21no—
66C2×C22⋊D43—21no—
67C2×D172—21no—
68C2×D172—21no—
69C2×D172C2311yescharacteristic
70C2×D172C2311yescharacteristic
71C2×C4×D43—21no—
72C2×C4×D43—21no—
73C4⋊C4×C43—21no—
74C4⋊C4×C43—21no—
75C4⋊C4×C43—21no—
76C4⋊C4×C43D411yescharacteristic
77C4⋊C4×C43D411yescharacteristic
78C4⋊C4×C43C2311yescharacteristic
79C4⋊C4×C43C2311yescharacteristic
80C22⋊C4×C43—21no—
81C22⋊C4×C43—21no—
82C22⋊C4×C43—21no—
83C22⋊C4×C43—21no—
84C22⋊C4×C43—21no—
85C22⋊C4×C43D411yescharacteristic
86C22⋊C4×C43D411yescharacteristic
87C42×C43—21no—
88C42×C43C2311yescharacteristic
89C42×C43C2311yescharacteristic
90#10621884—41no—
91#10621884—41no—
92#10621882—41no—
93#10621882—41no—
94(C2×D43)⋊C4—21no—
95(C2×D43)⋊C4—21no—
96(C2×D43)⋊C4—21no—
97(C2×D43)⋊C4—21no—
98C4⋊Dic43C2311yescharacteristic
99C4⋊Dic43C2311yescharacteristic
100Dic43⋊C4—21no—
101Dic43⋊C4—21no—
102#10621877—41no—
103C2×C43⋊C8—41no—
104C2×C43⋊C8C2311yescharacteristic
105C2×C43⋊C8C2311yescharacteristic
106C2×C43⋊C8C2311yescharacteristic
107C2×C43⋊C8C2311yescharacteristic
108C23×C43—21no—
109C23×C43C2×D411yescharacteristic
110C22×D43—21no—
111C22×D43—21no—
112Q8×C43—21no—
113Q8×C43—21no—
114Q8×C43—81no—
115D4×C43—21no—
116D4×C43—21no—
117D4×C43—81no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—81no—
124C2×C4×C43C2×D411yescharacteristic
125C2×C4×C43C2×D411yescharacteristic
126C2×C4×C43C2×D411yescharacteristic
127C2×C4×C43C2×D411yescharacteristic
128C2×C4×C43C2×D411yescharacteristic
129C2×C4×C43C2411yescharacteristic
130C22⋊D43—81no—
131C22⋊D43—81no—
132C2×Dic43—21no—
133C2×Dic43—21no—
134D172—21no—
135D172—21no—
136D172—21no—
137D172—21no—
138D172—81no—
139D172—81no—
140C4×D43—81no—
141C4×D43—81no—
142C43⋊C8—21no—
143C43⋊C8—21no—
144C43⋊C8—21no—
145C43⋊C8—21no—
146C22×C43—21no—
147C22×C43—21no—
148C22×C43—21no—
149C22×C43—41no—
150C22×C43—41no—
151C22×C43—41no—
152C22×C43C22×D411yescharacteristic
153C2×D43—41no—
154C2×D43—41no—
155C2×D43—41no—
156C2×D43—41no—
157C2×D43—41no—
158C2×D43—41no—
159C4×C43—21no—
160C4×C43—21no—
161C4×C43—21no—
162C4×C43—21no—
163C4×C43—21no—
164C4×C43—41no—
165C4×C43—41no—
166C4×C43—41no—
167C4×C43H(5,𝔽2)11yescharacteristic
168C4×C432−1+411yescharacteristic
169Dic43—41no—
170Dic43—41no—
171#3257—431nomaximal, Sylow
172C2×C43—41no—
173C2×C43—81no—
174C2×C43#53711yescharacteristic
175C2×C43#57611yescharacteristic
176C2×C43#57711yescharacteristic
177D43—81no—
178D43—81no—
179#542D4311yescharacteristic, complemented
180#540—431no—
181#479—431no—
182#478—431no—
183#476—431no—
184#474—431no—
185#469—431no—
186#468—431no—
187#466—431no—
188#465—431no—
189#463—431no—
190#463—431no—
191#460—431no—
192#459—431no—
193#424—431no—
194C43#325711yescharacteristic, complemented, Sylow
195C2×SD16—431no—
196C2×SD16—431no—
197C2×D8—431no—
198C2×D8—431no—
199C2×M16—431no—
200C22×C8—431no—
201C4⋊Q8C2×D4311yescharacteristic
202#127—431no—
203#126—21no—
204#125—431no—
205#124—21no—
206#124C2×D4311yescharacteristic
207#123—21no—
208#123—861no—
209#123—861no—
210C22⋊Q8—21no—
211C22⋊Q8C2×D4311yescharacteristic
212#121—431no—
213#121—431no—
214#121—861no—
215#121—861no—
216#121C2×D4311yescharacteristic
217C4×Q8C2×D4311yescharacteristic
218C4×D4—431no—
219C4×D4—431no—
220C4×D4C2×D4311yescharacteristic
221#117C2×D4311yescharacteristic
222#107—431no—
223#107—431no—
224#106—431no—
225#106—431no—
226C4⋊C8—431no—
227C4⋊C8—431no—
228C4⋊C8—431no—
229C4⋊C8—431no—
230#103—431no—
231#103—431no—
232#102—431no—
233#102—431no—
234#102—431no—
235#102—431no—
236#102—431no—
237#102—431no—
238C2×Q8—21no—
239C2×Q8C22×D4311yescharacteristic
240C2×D4—21no—
241C2×D4—431no—
242C2×D4—431no—
243C2×D4—861no—
244C2×D4—861no—
245C2×D4—861no—
246C2×D4—861no—
247C2×D4C22×D4311yescharacteristic
248C22×C4—21no—
249C22×C4—861no—
250C22×C4—861no—
251C22×C4C22×D4311yescharacteristic
252SD16—1721no—
253SD16—1721no—
254D8—1721no—
255D8—1721no—
256M16—1721no—
257C2×C8—431no—
258C2×C8—431no—
259C2×C8—431no—
260C2×C8—431no—
261C2×C8—1721no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—431no—
266C4⋊C4—431no—
267C4⋊C4—861no—
268C4⋊C4—861no—
269C4⋊C4C22⋊D4311yescharacteristic
270C4⋊C4C22⋊D4311yescharacteristic
271C4⋊C4C22×D4311yescharacteristic
272C4⋊C4C22×D4311yescharacteristic
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—21no—
278C22⋊C4—861no—
279C22⋊C4—861no—
280C22⋊C4—861no—
281C22⋊C4—861no—
282C22⋊C4C22⋊D4311yescharacteristic
283C22⋊C4C22⋊D4311yescharacteristic
284C42—21no—
285C42C22×D4311yescharacteristic
286C42C22×D4311yescharacteristic
287C23—21no—
288C23—861no—
289C23—861no—
290C23C2×C22⋊D4311yescharacteristic
291Q8—21no—
292Q8—21no—
293Q8—81no—
294D4—21no—
295D4—21no—
296D4—81no—
297D4—861no—
298D4—861no—
299D4—861no—
300D4—861no—
301D4—3441no—
302D4—3441no—
303D4—3441no—
304D4—3441no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—81no—
311C2×C4—861no—
312C2×C4—861no—
313C2×C4—3441no—
314C2×C4—3441no—
315C2×C4C2×C22⋊D4311yescharacteristic
316C2×C4C2×C22⋊D4311yescharacteristic
317C2×C4C2×C22⋊D4311yescharacteristic
318C2×C4C2×C22⋊D4311yescharacteristic
319C2×C4C2×C22⋊D4311yescharacteristic
320C2×C4C23×D4311yescharacteristic
321C8—861no—
322C8—861no—
323C8—861no—
324C8—861no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—1721no—
332C22—1721no—
333C22—1721no—
334C22—1721no—
335C22—1721no—
336C22—1721no—
337C22C22×C22⋊D4311yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—1721no—
347C4—1721no—
348C4#1306337111yescharacteristic
349C4#1306337211yescharacteristic
350C2—41no—
351C2—81no—
352C2—3441no—
353C2—3441no—
354C2#1458347711yescharacteristic
355C2#1458370211yescharacteristic
356C2#1458370711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#542C2
socleC22×C43C22×D4
hypercenter#542D43
hypocenterC43#3257
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
1. #14583504C2semidirect
2. #14583206C2semidirect
3. #14583199C2semidirect
4. #14583186C2semidirect
5. #14583176C2semidirect
6. #14583150C2semidirect
7. #14583147C2semidirect
8. #14583133C2semidirect
9. #14583130C2semidirect
10. #14583111C2semidirect
11. #14583111C2semidirect
12. #14583099C2semidirect
13. #14583094C2semidirect
14. #14582926C2semidirect
15. C43×#542C2semidirect
179. #542D43semidirect
194. C43#3257semidirect