Finite Group Databasebeta

← #19144561

Subgroups — #19144561

Order 5504.

386 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583472C211yesmaximal, characteristic
2#14583379C211yesmaximal, characteristic
3#14583243C211yesmaximal, characteristic, complemented
4#14583240C211yesmaximal, characteristic, complemented
5#14583238C211yesmaximal, characteristic, complemented
6#14583236C211yesmaximal, characteristic, complemented
7#14583232C211yesmaximal, characteristic, complemented
8#14583230C211yesmaximal, characteristic, complemented
9#14583228C211yesmaximal, characteristic, complemented
10#14582940C211yesmaximal, characteristic, complemented
11#14582934C211yesmaximal, characteristic, complemented
12#14582906C211yesmaximal, characteristic, complemented
13#103×D43C211yesmaximal, characteristic, complemented
14#14582864C211yesmaximal, characteristic
15C43×#485C211yesmaximal, characteristic, complemented
16C2×#10621898C2211yescharacteristic
17C2×Q8×D43C2211yescharacteristic
18C2×#10621872C2211yescharacteristic
19C2×C8×D43C2211yescharacteristic
20#13063324—21no—
21#13063311—21no—
22#13063310—21no—
23#13063307—21no—
24#13063305C2211yescharacteristic
25#13063304C2211yescharacteristic
26#13063301C2211yescharacteristic
27C4×Dic86—21no—
28C4×D172—21no—
29(C22⋊D43)⋊C4—21no—
30(C22⋊D43)⋊C4—21no—
31#13063283C2211yescharacteristic
32#13063283C2211yescharacteristic
33#13063283C2211yescharacteristic
34C2×C4⋊Dic43C2211yescharacteristic
35C4⋊C4×D43C2211yescharacteristic
36C4⋊C4×D43C2211yescharacteristic
37#13063258C2211yescharacteristic
38#13063258C2211yescharacteristic
39#13063258C2211yescharacteristic
40#13063257C2211yescharacteristic
41#13063257C2211yescharacteristic
42#13063256C2211yescharacteristic
43#13063250C2211yescharacteristic
44#13063250C2211yescharacteristic
45#13063249C2211yescharacteristic
46#13063249C2211yescharacteristic
47#13063248C2211yescharacteristic
48#13063248C2211yescharacteristic
49C22⋊(C43⋊C8)C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic
51(C2×D43)⋊C8C2211yescharacteristic
52C22⋊Q8×C43C2211yescharacteristic
53#117×C43C2211yescharacteristic
54#107×C43C2211yescharacteristic
55#106×C43C2211yescharacteristic
56#103×C43C2211yescharacteristic
57#103×C43C2211yescharacteristic
58C22⋊C8×C43C2211yescharacteristic
59C2×Q8×C43C2311yescharacteristic
60C22×C4×C43C2311yescharacteristic
61C2×C22⋊D43D411yescharacteristic
62C2×C22⋊D43D411yescharacteristic
63C22×Dic43—21no—
64Q8×D43—22no—
65Q8×D43—22no—
66#10621898—22no—
67#10621898—22no—
68C2×D172D411yescharacteristic
69C2×C4×D43—21no—
70C2×C4×D43—21no—
71C2×C4×D43—21no—
72C2×C4×D43C2311yescharacteristic
73C2×C4×D43C2311yescharacteristic
74C2×Dic86—21no—
75C2×Dic86D411yescharacteristic
76C2×Dic86C2311yescharacteristic
77C2×C8×C43C2311yescharacteristic
78C2×C8×C43C2311yescharacteristic
79C4⋊C4×C43—21no—
80C4⋊C4×C43C2311yescharacteristic
81C4⋊C4×C43C2311yescharacteristic
82C4⋊C4×C43C2311yescharacteristic
83C22⋊C4×C43—21no—
84C22⋊C4×C43—21no—
85C42×C43—21no—
86C22⋊Dic43—21no—
87(C2×D43)⋊C4—21no—
88(C2×D43)⋊C4—21no—
89(C2×D43)⋊C4—21no—
90(C2×D43)⋊C4—21no—
91(C2×D43)⋊C4—21no—
92C4⋊Dic43—21no—
93C4⋊Dic43—21no—
94C4⋊Dic43C2311yescharacteristic
95C4⋊Dic43C2311yescharacteristic
96C4⋊Dic43C2311yescharacteristic
97Dic43⋊C4—21no—
98Dic43⋊C4—21no—
99Dic43⋊C4—21no—
100Dic43⋊C4—21no—
101C4×Dic43—21no—
102C4×Dic43—21no—
103C4×Dic43—21no—
104C2×C43⋊C8C2311yescharacteristic
105C2×C43⋊C8C2311yescharacteristic
106#10621872—22no—
107C8×D43—22no—
108C23×C43C2×D411yescharacteristic
109C22×D43C2×D411yescharacteristic
110C22×D43C2×D411yescharacteristic
111Q8×C43—21no—
112Q8×C43—21no—
113C2×C4×C43—21no—
114C2×C4×C43—21no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43C2×D411yescharacteristic
120C2×C4×C43C2411yescharacteristic
121C22⋊D43—22no—
122C22⋊D43—22no—
123C2×Dic43—21no—
124C2×Dic43—21no—
125C2×Dic43—21no—
126C2×Dic43—21no—
127C2×Dic43—81no—
128C2×Dic43C2×D411yescharacteristic
129C2×Dic43C2×D411yescharacteristic
130D172—22no—
131C4×D43—21no—
132C4×D43—21no—
133C4×D43—42no—
134C4×D43—81no—
135C4×D43—81no—
136C4×D43#4112yes—
137C4×D43#4112yes—
138Dic86—22no—
139Dic86—21no—
140Dic86—21no—
141Dic86—42no—
142C8×C43—21no—
143C8×C43—21no—
144C43⋊C8—21no—
145C43⋊C8—21no—
146C22×C43—21no—
147C22×C43—21no—
148C22×C43—21no—
149C22×C43C22×D411yescharacteristic
150C2×D43—21no—
151C2×D43—21no—
152C2×D43—21no—
153C2×D43—21no—
154C2×D43—21no—
155C2×D43#12312yes—
156C4×C43—21no—
157C4×C43—41no—
158C4×C43—41no—
159C4×C43—41no—
160C4×C43—41no—
161C4×C43C2×#4111yescharacteristic
162C4×C43C2×#4111yescharacteristic
163Dic43—21no—
164Dic43—41no—
165Dic43—41no—
166Dic43—41no—
167Dic43—41no—
168Dic43#12312yes—
169#3097—431nomaximal, Sylow
170C2×C43—41no—
171C2×C43C2×#12311yescharacteristic
172C2×C43#57711yescharacteristic
173C2×C43#57811yescharacteristic
174D43—22no—
175D43—41no—
176#536—431no—
177#520—431no—
178#485—431no—
179#485—431no—
180#485—431no—
181#485D4311yescharacteristic, complemented
182#484—431no—
183#484—431no—
184#483—431no—
185#483—431no—
186#428—431no—
187#427—431no—
188#419—431no—
189C2×#103—431no—
190#408—431no—
191C43#309711yescharacteristic, complemented, Sylow
192C2×#41—431no—
193C22×Q8—431no—
194C2×M16—431no—
195C22×C8—431no—
196C4⋊Q8—861no—
197#124—861no—
198#123—861no—
199#123—861no—
200C22⋊Q8—431no—
201C22⋊Q8—431no—
202C22⋊Q8—431no—
203C22⋊Q8C2×D4311yescharacteristic
204C4×Q8—861no—
205C4×D4—861no—
206C4×D4—861no—
207C4×D4—861no—
208#117—431no—
209#117—431no—
210#117—431no—
211#117C2×D4311yescharacteristic
212C2×C4⋊C4—431no—
213C2×C4⋊C4—431no—
214C2×C4⋊C4—431no—
215#107—431no—
216#107—431no—
217#107—431no—
218#107C2×D4311yescharacteristic
219#106—431no—
220#106—431no—
221#106—431no—
222#106C2×D4311yescharacteristic
223#103—431no—
224#103—431no—
225#103—431no—
226#103—431no—
227#103—431no—
228#103—431no—
229#103C2×D4311yescharacteristic
230#103C2×D4311yescharacteristic
231C22⋊C8—431no—
232C22⋊C8—431no—
233C22⋊C8—431no—
234C22⋊C8C2×D4311yescharacteristic
235#41—862no—
236#41—862no—
237C2×Q8—431no—
238C2×Q8—431no—
239C2×Q8—861no—
240C2×Q8—862no—
241C2×Q8—862no—
242C2×Q8C22×D4311yescharacteristic
243C2×D4—431no—
244C2×D4—431no—
245C2×D4—431no—
246C22×C4—431no—
247C22×C4—431no—
248C22×C4—861no—
249C22×C4—861no—
250C22×C4—861no—
251C22×C4—861no—
252C22×C4C22×D4311yescharacteristic
253M16—862no—
254C2×C8—431no—
255C2×C8—431no—
256C2×C8—862no—
257C2×C8C22×D4311yescharacteristic
258C2×C8C22×D4311yescharacteristic
259C4⋊C4—21no—
260C4⋊C4—431no—
261C4⋊C4—431no—
262C4⋊C4—431no—
263C4⋊C4—861no—
264C4⋊C4—861no—
265C4⋊C4—861no—
266C4⋊C4—861no—
267C4⋊C4—861no—
268C4⋊C4—861no—
269C4⋊C4C22×D4311yescharacteristic
270C4⋊C4C22×D4311yescharacteristic
271C4⋊C4C22×D4311yescharacteristic
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—861no—
275C22⋊C4—861no—
276C22⋊C4—861no—
277C22⋊C4—861no—
278C22⋊C4—861no—
279C22⋊C4—861no—
280C42—21no—
281C42—861no—
282C42—861no—
283C42—861no—
284C23—431no—
285C23—431no—
286C23D4×D4311yescharacteristic
287Q8—21no—
288Q8—21no—
289Q8—862no—
290Q8—861no—
291Q8—861no—
292Q8—1722no—
293D4—862no—
294D4—862no—
295D4—862no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—431no—
303C2×C4—432no—
304C2×C4—432no—
305C2×C4—431no—
306C2×C4—861no—
307C2×C4—861no—
308C2×C4—861no—
309C2×C4—861no—
310C2×C4—861no—
311C2×C4—861no—
312C2×C4—3441no—
313C2×C4—3441no—
314C2×C4—3441no—
315C2×C4—1722no—
316C2×C4D4×D4311yescharacteristic
317C2×C4C23×D4311yescharacteristic
318C8—21no—
319C8—21no—
320C8—861no—
321C8—861no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—432no—
326C22—861no—
327C22—861no—
328C22—861no—
329C22—861no—
330C22—861no—
331C22C2×D4×D4311yescharacteristic
332C4—21no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—432no—
338C4—861no—
339C4—1721no—
340C4—1721no—
341C4—1721no—
342C4—1721no—
343C4#41×D4311yescharacteristic
344C4#41×D4311yescharacteristic
345C2—41no—
346C2—862no—
347C2—1721no—
348C2#123×D4311yescharacteristic
349C2#1458370611yescharacteristic
350C2#1458371511yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#485C2
socleC22×C43C22×D4
hypercenter#485D43
hypocenterC43#3097
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
3. #14583243C2semidirect
4. #14583240C2semidirect
5. #14583238C2semidirect
6. #14583236C2semidirect
7. #14583232C2semidirect
8. #14583230C2semidirect
9. #14583228C2semidirect
10. #14582940C2semidirect
11. #14582934C2semidirect
12. #14582906C2semidirect
13. #103×D43C2semidirect
15. C43×#485C2semidirect
181. #485D43semidirect
191. C43#3097semidirect