Finite Group Databasebeta

← #19135661

Subgroups — #19135661

Order 5504.

394 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583697C211yesmaximal, characteristic, complemented
2#14583411C211yesmaximal, characteristic, complemented
3#14583406C211yesmaximal, characteristic, complemented
4#14582915C211yesmaximal, characteristic, complemented
5#14582862C211yesmaximal, characteristic, complemented
6#14582655C211yesmaximal, characteristic, complemented
7C43×#421C211yesmaximal, characteristic, complemented
8C2×#10621898C2211yescharacteristic
9C22×C4×D43C2211yescharacteristic
10#13063356—21no—
11#13063355—21no—
12#13063351—21no—
13#13063350—21no—
14#13063345—22no—
15C2×#10621877C2211yescharacteristic
16#13063309—21no—
17#13063306—21no—
18#13063305—21no—
19#13063301—21no—
20#13063300—21no—
21#13063296—21no—
22#13063295—21no—
23#13063293—21no—
24C4×D172—22no—
25C4×C22⋊D43—22no—
26#13063284C2211yescharacteristic
27#13063251—22no—
28(C2×D43)⋊C8—22no—
29C2×#41×C43C2211yescharacteristic
30C2×M16×C43C2211yescharacteristic
31#117×C43C2211yescharacteristic
32#104×C43—22no—
33C23×D43D411yescharacteristic
34#41×C43—21no—
35#41×C43—21no—
36#41×C43—21no—
37#41×C43—21no—
38C2×Q8×C43D411yescharacteristic, complemented
39C2×D4×C43—21no—
40C2×D4×C43D411yescharacteristic, complemented
41C22×C4×C43—21no—
42C22×C4×C43C2311yescharacteristic
43C2×C22⋊D43—22no—
44C2×C22⋊D43—21no—
45C22×Dic43D411yescharacteristic
46#10621898—21no—
47#10621898—21no—
48#10621898—21no—
49#10621898—21no—
50C2×D172—22no—
51C2×D172D411yescharacteristic, complemented
52C2×C4×D43—21no—
53C2×C4×D43—21no—
54C2×C4×D43—21no—
55C2×C4×D43—21no—
56C2×C4×D43—21no—
57C2×C4×D43—21no—
58C2×C4×D43—21no—
59C2×Dic86D411yescharacteristic, complemented
60M16×C43—21no—
61M16×C43—21no—
62C2×C8×C43—21no—
63C4⋊C4×C43—21no—
64C22⋊C4×C43—21no—
65C42×C43D412yescomplemented
66C22⋊Dic43—22no—
67C22⋊Dic43—21no—
68#10621885—22no—
69#10621884—22no—
70#10621883—22no—
71#10621882—22no—
72(C2×D43)⋊C4—22no—
73(C2×D43)⋊C4—22no—
74(C2×D43)⋊C4—22no—
75C4⋊Dic43—22no—
76C4⋊Dic43—21no—
77Dic43⋊C4—22no—
78C4×Dic43D412yescomplemented
79#10621877—21no—
80#10621877—21no—
81C2×C43⋊C8D412yescomplemented
82C23×C43—21no—
83C23×C43C2×D411yescharacteristic
84C22×D43—21no—
85C22×D43—21no—
86C22×D43—21no—
87C22×D43—21no—
88C22×D43—42no—
89Q8×C43—21no—
90Q8×C43—21no—
91D4×C43—21no—
92D4×C43—21no—
93D4×C43—41no—
94D4×C43—41no—
95C2×C4×C43—21no—
96C2×C4×C43—22no—
97C2×C4×C43—41no—
98C2×C4×C43—41no—
99C2×C4×C43C2×D411yescharacteristic
100C2×C4×C43C2×D411yescharacteristic
101C2×C4×C43C2×D411yescharacteristic
102C2×C4×C43C2×D411yescharacteristic
103C2×C4×C43C2×D411yescharacteristic
104C2×C4×C43#4111yescharacteristic
105C22⋊D43—44no—
106C22⋊D43—41no—
107C22⋊D43—41no—
108C2×Dic43—22no—
109C2×Dic43—21no—
110C2×Dic43—21no—
111C2×Dic43—21no—
112C2×Dic43—21no—
113D172—21no—
114D172—21no—
115D172—44no—
116C4×D43—41no—
117C4×D43—41no—
118C4×D43—41no—
119C4×D43—41no—
120C4×D43—41no—
121C4×D43—41no—
122Dic86—21no—
123Dic86—21no—
124C8×C43—41no—
125C43⋊C8—22no—
126C22×C43—41no—
127C22×C43—42no—
128C22×C43—41no—
129C22×C43#12011yescharacteristic
130C22×C43#12011yescharacteristic
131C22×C43#12111yescharacteristic
132C2×D43—22no—
133C2×D43—22no—
134C2×D43—22no—
135C2×D43—41no—
136C2×D43—41no—
137C2×D43—41no—
138C2×D43—41no—
139C2×D43—42no—
140C2×D43—41no—
141C4×C43—42no—
142C4×C43—41no—
143C4×C43#12011yescharacteristic
144C4×C43#12111yescharacteristic
145C4×C43#12111yescharacteristic
146C4×C43#12711yescharacteristic
147Dic43—42no—
148Dic43—41no—
149Dic43—41no—
150#2010—431nomaximal, Sylow
151C2×C43—21no—
152C2×C43—21no—
153C2×C43—21no—
154C2×C43—81no—
155C2×C43#39211yescharacteristic
156D43—42no—
157D43—81no—
158#575—431no—
159#525—431no—
160#525—431no—
161#421—431no—
162#421D4311yescharacteristic, complemented
163#407—431no—
164H(3,ℤ/4)—431no—
165C43#201011yescharacteristic, complemented, Sylow
166C2×#41—431no—
167C2×#41C2×D4311yescharacteristic
168C23×C4—431no—
169#137—861no—
170#137—861no—
171AGL(1,ℤ/8)—861no—
172AGL(1,ℤ/8)—861no—
173#135—862no—
174C2×M16—431no—
175C2×M16C2×D4311yescharacteristic
176#123—861no—
177#123—861no—
178C22⋊Q8—861no—
179C22⋊Q8—861no—
180#121—861no—
181#121—861no—
182#120—861no—
183#120—861no—
184C4×D4—862no—
185C4×D4—862no—
186#117—431no—
187#117C2×D4311yescharacteristic
188#104—22no—
189#104—862no—
190C22⋊C8—862no—
191C24—431no—
192#41—21no—
193#41—21no—
194#41—21no—
195#41—21no—
196#41—861no—
197#41—861no—
198#41—861no—
199#41—861no—
200C2×Q8—431no—
201C2×Q8D17211yescharacteristic, complemented
202C2×D4—21no—
203C2×D4—431no—
204C2×D4—862no—
205C2×D4—862no—
206C2×D4—861no—
207C2×D4D17211yescharacteristic, complemented
208C22×C4—21no—
209C22×C4—431no—
210C22×C4—861no—
211C22×C4—861no—
212C22×C4—861no—
213C22×C4—861no—
214C22×C4—861no—
215C22×C4—861no—
216C22×C4—861no—
217C22×C4C22×D4311yescharacteristic
218Q16—862no—
219SD16—862no—
220SD16—862no—
221D8—862no—
222M16—21no—
223M16—21no—
224M16—861no—
225M16—861no—
226C2×C8—21no—
227C2×C8—432no—
228C4⋊C4—21no—
229C4⋊C4—862no—
230C4⋊C4—862no—
231C4⋊C4—861no—
232C22⋊C4—21no—
233C22⋊C4—862no—
234C22⋊C4—862no—
235C22⋊C4—862no—
236C22⋊C4—862no—
237C22⋊C4—861no—
238C42—432no—
239C42C22⋊D4312yescomplemented
240C23—21no—
241C23—861no—
242C23—861no—
243C23—861no—
244C23—861no—
245C23—1722no—
246C23D4×D4311yescharacteristic
247Q8—21no—
248Q8—21no—
249Q8—861no—
250Q8—861no—
251D4—21no—
252D4—21no—
253D4—41no—
254D4—41no—
255D4—861no—
256D4—861no—
257D4—1724no—
258D4—1724no—
259D4—1721no—
260D4—1721no—
261C2×C4—22no—
262C2×C4—21no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—861no—
266C2×C4—861no—
267C2×C4—862no—
268C2×C4—861no—
269C2×C4—861no—
270C2×C4—1721no—
271C2×C4—1721no—
272C2×C4—1721no—
273C2×C4—1721no—
274C2×C4—1721no—
275C2×C4—1721no—
276C2×C4C2×D17211yescharacteristic
277C2×C4#1062189811yescharacteristic
278C2×C4D4×D4311yescharacteristic
279C2×C4D4×D4311yescharacteristic
280C2×C4D4×D4311yescharacteristic
281C2×C4C2×C22⋊D4311yescharacteristic
282C8—41no—
283C8—862no—
284C22—41no—
285C22—42no—
286C22—41no—
287C22—862no—
288C22—862no—
289C22—862no—
290C22—1722no—
291C22—1721no—
292C22—1721no—
293C22—1721no—
294C22—1721no—
295C22—1721no—
296C22#1306329311yescharacteristic
297C22#1306329511yescharacteristic
298C22#1306329811yescharacteristic
299C4—42no—
300C4—41no—
301C4—1722no—
302C4—1721no—
303C4—1721no—
304C4#1306329511yescharacteristic
305C4#1306329811yescharacteristic
306C4#1306329911yescharacteristic
307C4#1306332111yescharacteristic
308C2—21no—
309C2—21no—
310C2—21no—
311C2—81no—
312C2—3441no—
313C2—1722no—
314C2#1458280811yescharacteristic
subgroupG/H
centerC4#13063321
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC43×#421C2
socleC2×C43#392
hypercenter#421D43
hypocenterC43#2010
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
1. #14583697C2semidirect
2. #14583411C2semidirect
3. #14583406C2semidirect
4. #14582915C2semidirect
5. #14582862C2semidirect
6. #14582655C2semidirect
7. C43×#421C2semidirect
38. C2×Q8×C43D4semidirect
40. C2×D4×C43D4semidirect
51. C2×D172D4semidirect
59. C2×Dic86D4semidirect
65. C42×C43D4semidirect
78. C4×Dic43D4semidirect
81. C2×C43⋊C8D4semidirect
162. #421D43semidirect
165. C43#2010semidirect
201. C2×Q8D172semidirect
207. C2×D4D172semidirect
239. C42C22⋊D43semidirect