Finite Group Databasebeta

← #19146766

Subgroups — #19146766

Order 5504.

388 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583595C211yesmaximal, characteristic
2#14583267C211yesmaximal, characteristic, complemented
3#14583237C211yesmaximal, characteristic, complemented
4#14583232C211yesmaximal, characteristic, complemented
5#14583206C211yesmaximal, characteristic, complemented
6#14583147C211yesmaximal, characteristic, complemented
7#14583130C211yesmaximal, characteristic, complemented
8#14583101C211yesmaximal, characteristic, complemented
9#14583038C211yesmaximal, characteristic, complemented
10#14583038C211yesmaximal, characteristic, complemented
11#14582997C211yesmaximal, characteristic, complemented
12#14582971C211yesmaximal, characteristic, complemented
13#14582908C211yesmaximal, characteristic, complemented
14C2×#13063249C211yesmaximal, characteristic, complemented
15D4×Q8×C43C211yesmaximal, characteristic, complemented
16C2×#10621884C2211yescharacteristic
17C2×#10621884C2211yescharacteristic
18C2×#10621884C2211yescharacteristic
19C2×#10621877C2211yescharacteristic
20C22×C43⋊C8C2211yescharacteristic
21#13063320—21no—
22#13063317C2211yescharacteristic
23#13063307—21no—
24#13063299C2211yescharacteristic
25#13063299C2211yescharacteristic
26#13063297—21no—
27C4×D172C2211yescharacteristic
28(C22⋊D43)⋊C4—21no—
29#13063284C2211yescharacteristic
30C2×C4⋊Dic43C2211yescharacteristic
31#13063258C2211yescharacteristic
32#13063258C2211yescharacteristic
33#13063256C2211yescharacteristic
34C4⋊(C43⋊C8)C2211yescharacteristic
35#13063249C2211yescharacteristic
36#13063249C2211yescharacteristic
37#13063249C2211yescharacteristic
38#13063249C2211yescharacteristic
39#13063249C2211yescharacteristic
40#13063249C2211yescharacteristic
41#13063249C2211yescharacteristic
42#13063249C2211yescharacteristic
43#13063249C2211yescharacteristic
44#13063245C2211yescharacteristic
45C22⋊(C43⋊C8)C2211yescharacteristic
46C22⋊(C43⋊C8)C2211yescharacteristic
47#13063236C2211yescharacteristic
48C22×Q8×C43C2211yescharacteristic
49C22×Q8×C43C2211yescharacteristic
50C4⋊Q8×C43—21no—
51C4⋊Q8×C43C2211yescharacteristic
52C22⋊Q8×C43—21no—
53C22⋊Q8×C43—21no—
54C22⋊Q8×C43C2211yescharacteristic
55C22⋊Q8×C43C2211yescharacteristic
56C4×Q8×C43C2211yescharacteristic
57C4×D4×C43—21no—
58C4×D4×C43C2211yescharacteristic
59C2×Q8×C43—21no—
60C2×Q8×C43—21no—
61C2×Q8×C43—22no—
62C2×Q8×C43—22no—
63C2×Q8×C43—41no—
64C2×Q8×C43—41no—
65C2×Q8×C43C2311yescharacteristic
66C2×Q8×C43C2311yescharacteristic
67C2×Q8×C43C2311yescharacteristic
68C2×D4×C43D411yescharacteristic
69C22×C4×C43—21no—
70C22×C4×C43—21no—
71C22×C4×C43C2311yescharacteristic
72C22×C4×C43C2311yescharacteristic
73C2×C22⋊D43—21no—
74C2×C22⋊D43—21no—
75C22×Dic43—21no—
76C2×D172C2311yescharacteristic
77C2×C4×D43—21no—
78C4⋊C4×C43—21no—
79C4⋊C4×C43—21no—
80C4⋊C4×C43—21no—
81C4⋊C4×C43—21no—
82C4⋊C4×C43—21no—
83C4⋊C4×C43D411yescharacteristic
84C4⋊C4×C43C2311yescharacteristic
85C22⋊C4×C43—21no—
86C22⋊C4×C43—21no—
87C22⋊C4×C43D411yescharacteristic
88C22⋊C4×C43D411yescharacteristic
89C42×C43—21no—
90C42×C43C2311yescharacteristic
91C22⋊Dic43—21no—
92#10621884—22no—
93#10621884—41no—
94#10621884—41no—
95(C2×D43)⋊C4—21no—
96(C2×D43)⋊C4—21no—
97(C2×D43)⋊C4—21no—
98C4⋊Dic43—21no—
99C4⋊Dic43C2311yescharacteristic
100C4⋊Dic43C2311yescharacteristic
101C4⋊Dic43C2311yescharacteristic
102Dic43⋊C4—21no—
103Dic43⋊C4—21no—
104C4×Dic43—21no—
105#10621877—41no—
106C2×C43⋊C8—41no—
107C2×C43⋊C8C2311yescharacteristic
108C2×C43⋊C8C2311yescharacteristic
109C2×C43⋊C8C2311yescharacteristic
110C2×C43⋊C8C2311yescharacteristic
111C23×C43C2×D411yescharacteristic
112C23×C43C2×D411yescharacteristic
113C22×D43—21no—
114Q8×C43—21no—
115Q8×C43—21no—
116Q8×C43—21no—
117Q8×C43—21no—
118Q8×C43—21no—
119Q8×C43—42no—
120Q8×C43—42no—
121Q8×C43#4112yes—
122D4×C43—22no—
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—42no—
132C2×C4×C43—42no—
133C2×C4×C43C2×D411yescharacteristic
134C2×C4×C43C2×D411yescharacteristic
135C2×C4×C43C2×D411yescharacteristic
136C2×C4×C43C2×D411yescharacteristic
137C2×C4×C43C2411yescharacteristic
138C22⋊D43—42no—
139C22⋊D43—81no—
140C2×Dic43—21no—
141C2×Dic43—21no—
142C2×Dic43—21no—
143C2×Dic43—81no—
144D172—21no—
145D172—21no—
146C4×D43—81no—
147C43⋊C8—21no—
148C43⋊C8—21no—
149C43⋊C8—21no—
150C43⋊C8—21no—
151C22×C43—21no—
152C22×C43—21no—
153C22×C43—21no—
154C22×C43—21no—
155C22×C43—21no—
156C22×C43#13712yes—
157C22×C43C22×D411yescharacteristic
158C2×D43—41no—
159C2×D43—41no—
160C2×D43—41no—
161C4×C43—21no—
162C4×C43—21no—
163C4×C43—22no—
164C4×C43—21no—
165C4×C43—21no—
166C4×C43—41no—
167C4×C43—41no—
168C4×C43—41no—
169C4×C43C2×#4111yescharacteristic
170C4×C43H(5,𝔽2)11yescharacteristic
171Dic43—41no—
172Dic43—41no—
173Dic43—41no—
174#3320—431nomaximal, Sylow
175C2×C43—22no—
176C2×C43—41no—
177C2×C43#54611yescharacteristic
178C2×C43C2×#13711yescharacteristic
179C2×C43#57711yescharacteristic
180D43—81no—
181#553—431no—
182D4×Q8D4311yescharacteristic, complemented
183#491—431no—
184#485—431no—
185#484—431no—
186#479—431no—
187#468—431no—
188#465—431no—
189#461—431no—
190#448—431no—
191#448—431no—
192#440—431no—
193#435—431no—
194#419—431no—
195C2×#103—431no—
196C43#332011yescharacteristic, complemented, Sylow
197C22×Q8C2×D4311yescharacteristic
198C22×Q8C2×D4311yescharacteristic
199C2×SD16—431no—
200C2×SD16—431no—
201C2×SD16—431no—
202C2×M16—431no—
203C22×C8—431no—
204C4⋊Q8—21no—
205C4⋊Q8C2×D4311yescharacteristic
206#126—861no—
207#125—431no—
208#123—861no—
209C22⋊Q8—21no—
210C22⋊Q8—21no—
211C22⋊Q8C2×D4311yescharacteristic
212C22⋊Q8C2×D4311yescharacteristic
213#121—431no—
214#121—431no—
215#121—861no—
216C4×Q8C2×D4311yescharacteristic
217C4×D4—21no—
218C4×D4—431no—
219C4×D4—861no—
220C4×D4C2×D4311yescharacteristic
221#117—431no—
222C2×C4⋊C4—431no—
223#107—431no—
224#107—431no—
225#106—431no—
226C4⋊C8—431no—
227#103—431no—
228#103—431no—
229#103—431no—
230#103—431no—
231#103—431no—
232#103—431no—
233#103—431no—
234#103—431no—
235#103—431no—
236#102—431no—
237C22⋊C8—431no—
238C22⋊C8—431no—
239#97—431no—
240C2×Q8—21no—
241C2×Q8—21no—
242C2×Q8—22no—
243C2×Q8—22no—
244C2×Q8—41no—
245C2×Q8—41no—
246C2×Q8C22×D4311yescharacteristic
247C2×Q8C22×D4311yescharacteristic
248C2×Q8C22×D4311yescharacteristic
249C2×D4—431no—
250C2×D4—861no—
251C2×D4—861no—
252C2×D4C22⋊D4311yescharacteristic
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—861no—
256C22×C4—861no—
257C22×C4C22×D4311yescharacteristic
258C22×C4C22×D4311yescharacteristic
259SD16—862no—
260SD16—1721no—
261SD16—1721no—
262M16—1721no—
263C2×C8—431no—
264C2×C8—431no—
265C2×C8—431no—
266C2×C8—431no—
267C2×C8—1721no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—431no—
274C4⋊C4—431no—
275C4⋊C4—431no—
276C4⋊C4—861no—
277C4⋊C4—861no—
278C4⋊C4—861no—
279C4⋊C4C22⋊D4311yescharacteristic
280C4⋊C4C22×D4311yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—861no—
284C22⋊C4—861no—
285C22⋊C4—861no—
286C22⋊C4—861no—
287C22⋊C4C22⋊D4311yescharacteristic
288C22⋊C4C22⋊D4311yescharacteristic
289C42—21no—
290C42—861no—
291C42C22×D4311yescharacteristic
292C23—861no—
293C23C2×C22⋊D4311yescharacteristic
294C23C2×C22⋊D4311yescharacteristic
295Q8—21no—
296Q8—21no—
297Q8—21no—
298Q8—21no—
299Q8—21no—
300Q8—42no—
301Q8—42no—
302Q8#1062190012yes—
303D4—22no—
304D4—861no—
305D4—861no—
306D4—3441no—
307D4—1722no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—861no—
319C2×C4—861no—
320C2×C4—861no—
321C2×C4—3441no—
322C2×C4—3441no—
323C2×C4C2×C22⋊D4311yescharacteristic
324C2×C4C2×C22⋊D4311yescharacteristic
325C2×C4C2×C22⋊D4311yescharacteristic
326C2×C4C2×C22⋊D4311yescharacteristic
327C2×C4C23×D4311yescharacteristic
328C8—861no—
329C8—861no—
330C8—861no—
331C8—861no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—1721no—
338C22—1721no—
339C22—1721no—
340C22#1306335612yes—
341C22C22×C22⋊D4311yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—22no—
347C4—41no—
348C4—41no—
349C4—41no—
350C4—1721no—
351C4—1721no—
352C4—1721no—
353C4C2×#1062190011yescharacteristic
354C4#1306337011yescharacteristic
355C2—22no—
356C2—41no—
357C2—3441no—
358C2#1458354311yescharacteristic
359C2C2×#1306335611yescharacteristic
360C2#1458370711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingD4×Q8×C43C2
socleC22×C43C22×D4
hypercenterD4×Q8D43
hypocenterC43#3320
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4 ◁ D4×Q8

Complements

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

NH ≅ G/Ntype
2. #14583267C2semidirect
3. #14583237C2semidirect
4. #14583232C2semidirect
5. #14583206C2semidirect
6. #14583147C2semidirect
7. #14583130C2semidirect
8. #14583101C2semidirect
9. #14583038C2semidirect
10. #14583038C2semidirect
11. #14582997C2semidirect
12. #14582971C2semidirect
13. #14582908C2semidirect
14. C2×#13063249C2semidirect
15. D4×Q8×C43C2semidirect
182. D4×Q8D43semidirect
196. C43#3320semidirect