Finite Group Databasebeta

← #19144807

Subgroups — #19144807

Order 5504.

372 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583507C211yesmaximal, characteristic, complemented
2#14583381C211yesmaximal, characteristic
3#14583233C211yesmaximal, characteristic, complemented
4#14583231C211yesmaximal, characteristic, complemented
5#14583208C211yesmaximal, characteristic, complemented
6#14583198C211yesmaximal, characteristic, complemented
7#14583107C211yesmaximal, characteristic, complemented
8#14583103C211yesmaximal, characteristic, complemented
9#14583064C211yesmaximal, characteristic
10#14583060C211yesmaximal, characteristic
11#14583001C211yesmaximal, characteristic, complemented
12C4×#10621885C211yesmaximal, characteristic, complemented
13C4×#10621884C211yesmaximal, characteristic, complemented
14#14582961C211yesmaximal, characteristic, complemented
15C43×#441C211yesmaximal, characteristic, complemented
16C2×#10621902C2211yescharacteristic
17C2×#10621885C2211yescharacteristic
18C2×#10621873C2211yescharacteristic
19C2×#10621884C2211yescharacteristic
20#13063323C2211yescharacteristic
21#13063320—21no—
22#13063319—21no—
23#13063317—21no—
24#13063316C2211yescharacteristic
25#13063315—21no—
26#13063305C2211yescharacteristic
27#13063301C2211yescharacteristic
28Q8×Dic43C2211yescharacteristic
29C4×Dic86C2211yescharacteristic
30C4×D172—21no—
31C4×D172C2211yescharacteristic
32#13063287—21no—
33#13063287C2211yescharacteristic
34#13063282—21no—
35#13063282C2211yescharacteristic
36C4⋊C4×D43—21no—
37C4⋊C4×D43C2211yescharacteristic
38#13063259C2211yescharacteristic
39#13063258C2211yescharacteristic
40#13063256C2211yescharacteristic
41Dic43⋊C8C2211yescharacteristic
42Dic43⋊C8C2211yescharacteristic
43#13063250C2211yescharacteristic
44#13063249C2211yescharacteristic
45#13063249C2211yescharacteristic
46#13063248C2211yescharacteristic
47#13063247C2211yescharacteristic
48#13063245C2211yescharacteristic
49(C2×D43)⋊C8C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic
51C4×C43⋊C8C2211yescharacteristic
52C2×Q16×C43C2211yescharacteristic
53C4×Q8×C43C2211yescharacteristic
54C4×Q8×C43C2211yescharacteristic
55#106×C43C2211yescharacteristic
56#103×C43C2211yescharacteristic
57#103×C43C2211yescharacteristic
58#97×C43C2211yescharacteristic
59C2×Q8×C43C2311yescharacteristic
60C2×Q8×C43C2311yescharacteristic
61#10621902—22no—
62#10621902—22no—
63C2×D172—21no—
64C2×D172C2311yescharacteristic
65C2×C4×D43—21no—
66C2×C4×D43—21no—
67C2×C4×D43—21no—
68C2×C4×D43—21no—
69C2×C4×D43C2311yescharacteristic
70C2×Dic86C2311yescharacteristic
71Q16×C43—22no—
72C2×C8×C43C2311yescharacteristic
73C2×C8×C43C2311yescharacteristic
74C4⋊C4×C43—21no—
75C4⋊C4×C43—21no—
76C4⋊C4×C43C2311yescharacteristic
77C4⋊C4×C43C2311yescharacteristic
78C42×C43—21no—
79C42×C43—21no—
80C42×C43C2311yescharacteristic
81#10621885—22no—
82#10621884—22no—
83(C2×D43)⋊C4—21no—
84(C2×D43)⋊C4—21no—
85(C2×D43)⋊C4—21no—
86(C2×D43)⋊C4—21no—
87(C2×D43)⋊C4D411yescharacteristic
88(C2×D43)⋊C4D411yescharacteristic
89C4⋊Dic43—21no—
90C4⋊Dic43—21no—
91C4⋊Dic43—21no—
92C4⋊Dic43C2311yescharacteristic
93C4⋊Dic43C2311yescharacteristic
94Dic43⋊C4—21no—
95Dic43⋊C4—21no—
96Dic43⋊C4—21no—
97Dic43⋊C4—21no—
98Dic43⋊C4—21no—
99Dic43⋊C4—21no—
100Dic43⋊C4D411yescharacteristic
101Dic43⋊C4D411yescharacteristic
102C4×Dic43—21no—
103C4×Dic43—21no—
104C4×Dic43C2311yescharacteristic
105C2×C43⋊C8C2311yescharacteristic
106C2×C43⋊C8C2311yescharacteristic
107#10621873—22no—
108C22×D43—21no—
109C22×D43C2×D411yescharacteristic
110Q8×C43—21no—
111Q8×C43—21no—
112Q8×C43—21no—
113Q8×C43#4112yes—
114C2×C4×C43—21no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43C2×D411yescharacteristic
119C2×C4×C43C2×D411yescharacteristic
120C2×C4×C43C2411yescharacteristic
121C2×Dic43—21no—
122C2×Dic43—21no—
123C2×Dic43—21no—
124C2×Dic43C2×D411yescharacteristic
125C2×Dic43C2×D411yescharacteristic
126C2×Dic43C2×D411yescharacteristic
127D172—24no—
128D172—21no—
129D172#4112yes—
130C4×D43—24no—
131C4×D43—21no—
132C4×D43—21no—
133C4×D43—81no—
134C4×D43—81no—
135C4×D43—81no—
136Dic86—21no—
137Dic86—21no—
138C8×C43—21no—
139C8×C43—21no—
140C43⋊C8—21no—
141C43⋊C8—21no—
142C22×C43C22×D411yescharacteristic
143C2×D43—22no—
144C2×D43—21no—
145C2×D43—21no—
146C2×D43—21no—
147C2×D43—41no—
148C2×D43—41no—
149C4×C43—22no—
150C4×C43—21no—
151C4×C43—21no—
152C4×C43—41no—
153C4×C43—41no—
154C4×C43—41no—
155C4×C43C2×#4111yescharacteristic
156C4×C43C2×#4111yescharacteristic
157Dic43—21no—
158Dic43—21no—
159Dic43—21no—
160Dic43—41no—
161Dic43—41no—
162Dic43—41no—
163#3120—431nomaximal, Sylow
164C2×C43#52511yescharacteristic
165C2×C43#57711yescharacteristic
166C2×C43#57811yescharacteristic
167D43—41no—
168D43—42no—
169#541—431no—
170#520—431no—
171#484—431no—
172#483—431no—
173#479—431no—
174#478—431no—
175#462—431no—
176#461—431no—
177#452—431no—
178#452—431no—
179#441D4311yescharacteristic, complemented
180#440—431no—
181C4×Q16—431no—
182C4×SD16—431no—
183#433—431no—
184C43#312011yescharacteristic, complemented, Sylow
185C2×#41—431no—
186C2×Q16—431no—
187C2×Q16C2×D4311yescharacteristic
188C2×SD16—431no—
189C2×SD16—431no—
190C4⋊Q8—431no—
191#126—861no—
192#126—861no—
193#125—431no—
194#125—861no—
195#125—861no—
196C22⋊Q8—431no—
197C22⋊Q8—431no—
198C4×Q8—431no—
199C4×Q8—431no—
200C4×Q8C2×D4311yescharacteristic
201C4×Q8C2×D4311yescharacteristic
202C4×D4—431no—
203C4×D4—431no—
204C4×D4—861no—
205C4×D4—861no—
206#117—431no—
207#117—861no—
208C2×C4⋊C4—431no—
209C2×C4⋊C4—861no—
210#107—431no—
211#107—431no—
212#106—431no—
213#106C2×D4311yescharacteristic
214C4⋊C8—431no—
215C4⋊C8—431no—
216#103—431no—
217#103—431no—
218#103—431no—
219#103—431no—
220#103C2×D4311yescharacteristic
221#103C2×D4311yescharacteristic
222#102—431no—
223#102—431no—
224C22⋊C8—431no—
225C22⋊C8—431no—
226#97C2×D4311yescharacteristic
227C4×C8—431no—
228#41—862no—
229#41—862no—
230C2×Q8—431no—
231C2×Q8C22×D4311yescharacteristic
232C2×Q8C22×D4311yescharacteristic
233C2×D4—431no—
234C2×D4—861no—
235C22×C4—431no—
236C22×C4—861no—
237C22×C4—861no—
238C22×C4—861no—
239C22×C4—861no—
240Q16—22no—
241Q16—862no—
242SD16—862no—
243SD16—862no—
244C2×C8—431no—
245C2×C8—431no—
246C2×C8C22×D4311yescharacteristic
247C2×C8C22×D4311yescharacteristic
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—431no—
251C4⋊C4—431no—
252C4⋊C4—431no—
253C4⋊C4—431no—
254C4⋊C4—861no—
255C4⋊C4—861no—
256C4⋊C4—861no—
257C4⋊C4—861no—
258C4⋊C4—861no—
259C4⋊C4—861no—
260C4⋊C4—861no—
261C4⋊C4—861no—
262C4⋊C4—861no—
263C4⋊C4C22×D4311yescharacteristic
264C4⋊C4C22×D4311yescharacteristic
265C22⋊C4—431no—
266C22⋊C4—431no—
267C22⋊C4—861no—
268C22⋊C4—861no—
269C22⋊C4—861no—
270C22⋊C4—861no—
271C42—21no—
272C42—21no—
273C42—431no—
274C42—861no—
275C42—861no—
276C42C22×D4311yescharacteristic
277C23—431no—
278C23—861no—
279Q8—21no—
280Q8—21no—
281Q8—21no—
282Q8—861no—
283Q8—861no—
284Q8#1062189812yes—
285D4—432no—
286D4—864no—
287D4—861no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—431no—
293C2×C4—431no—
294C2×C4—431no—
295C2×C4—864no—
296C2×C4—861no—
297C2×C4—861no—
298C2×C4—861no—
299C2×C4—861no—
300C2×C4—861no—
301C2×C4—3441no—
302C2×C4—3441no—
303C2×C4—3441no—
304C2×C4D4×D4311yescharacteristic
305C2×C4D4×D4311yescharacteristic
306C2×C4C23×D4311yescharacteristic
307C8—21no—
308C8—21no—
309C8—861no—
310C8—861no—
311C22—862no—
312C22—861no—
313C22—861no—
314C22—861no—
315C22—1721no—
316C22—1721no—
317C22C2×D4×D4311yescharacteristic
318C4—22no—
319C4—21no—
320C4—21no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—861no—
325C4—861no—
326C4—861no—
327C4—1721no—
328C4—1721no—
329C4—1721no—
330C4#41×D4311yescharacteristic
331C4C2×#1062189811yescharacteristic
332C2—1721no—
333C2—1722no—
334C2#1458340811yescharacteristic
335C2#1458370811yescharacteristic
336C2#1458371511yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#441C2
socleC22×C43C22×D4
hypercenter#441D43
hypocenterC43#3120
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
1. #14583507C2semidirect
3. #14583233C2semidirect
4. #14583231C2semidirect
5. #14583208C2semidirect
6. #14583198C2semidirect
7. #14583107C2semidirect
8. #14583103C2semidirect
11. #14583001C2semidirect
12. C4×#10621885C2semidirect
13. C4×#10621884C2semidirect
14. #14582961C2semidirect
15. C43×#441C2semidirect
179. #441D43semidirect
184. C43#3120semidirect