Finite Group Databasebeta

← #19142616

Subgroups — #19142616

Order 5504.

644 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 644 conjugacy classes of subgroups — too many to draw. Only its 125 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
1C2×#13063298C211yesmaximal, characteristic, complemented
2C2×#13063296C211yesmaximal, characteristic, complemented
3#14582827C212yesmaximal, complemented
4#14582826C211yesmaximal, characteristic, complemented
5#14582824C211yesmaximal, characteristic, complemented
6#14582808C212yesmaximal, complemented
7#14582807C211yesmaximal, characteristic, complemented
8#14582807C212yesmaximal, complemented
9#14582807C212yesmaximal, complemented
10#14582761C211yesmaximal, characteristic, complemented
11C43×#392C211yesmaximal, characteristic, complemented
12C22×D172C2211yescharacteristic
13C22×C22⋊D43C2211yescharacteristic
14C22×C22⋊D43C2211yescharacteristic
15C22×C22⋊D43C2212yes—
16C22×C22⋊D43C2212yes—
17C22×C4×D43C2211yescharacteristic
18#13063298—24no—
19#13063296—24no—
20C2×C4⋊Dic43C2211yescharacteristic
21C2×Dic43⋊C4C2211yescharacteristic
22C2×C22⋊Dic43C2212yes—
23C2×C22⋊Dic43C2212yes—
24C2×C22⋊Dic43C2212yes—
25C2×(C2×D43)⋊C4C2211yescharacteristic
26C2×(C2×D43)⋊C4C2212yes—
27C2×(C2×D43)⋊C4C2212yes—
28C43⋊#95C2211yescharacteristic
29C43⋊#95C2212yes—
30C43⋊#95C2212yes—
31C43⋊#95C2212yes—
32C22×D4×C43C2211yescharacteristic
33C22×D4×C43C2212yes—
34C2×C22⋊C4×C43C2211yescharacteristic
35C2×C22⋊C4×C43C2212yes—
36#95×C43C2211yescharacteristic
37C24×C43C2312yes—
38C24×C43C2311yescharacteristic
39C23×D43C2311yescharacteristic
40C23×D43C2311yescharacteristic
41C2×D4×C43—22no—
42C2×D4×C43—42no—
43C2×D4×C43—42no—
44C2×D4×C43—42no—
45C2×D4×C43—42no—
46C22×C4×C43C2312yes—
47C22×C4×C43C2311yescharacteristic
48C22×C4×C43C2311yescharacteristic
49C2×C22⋊D43—22no—
50C2×C22⋊D43—24no—
51C2×C22⋊D43—22no—
52C2×C22⋊D43—42no—
53C2×C22⋊D43—42no—
54C2×C22⋊D43—42no—
55C2×C22⋊D43—42no—
56C2×C22⋊D43—42no—
57C2×C22⋊D43—42no—
58C2×C22⋊D43—42no—
59C22×Dic43C2312yes—
60C22×Dic43C2311yescharacteristic
61C22×Dic43C2312yes—
62C22×Dic43C2311yescharacteristic
63C2×D172—22no—
64C2×D172—42no—
65C2×C4×D43—42no—
66C2×C4×D43D414yescomplemented
67C22⋊C4×C43—22no—
68C22⋊C4×C43—42no—
69C22⋊Dic43—24no—
70C22⋊Dic43—42no—
71C22⋊Dic43—42no—
72(C2×D43)⋊C4—22no—
73(C2×D43)⋊C4—42no—
74(C2×D43)⋊C4—42no—
75C4⋊Dic43—22no—
76Dic43⋊C4—22no—
77C23×C43—22no—
78C23×C43—21no—
79C23×C43—21no—
80C23×C43—22no—
81C23×C43—22no—
82C23×C43—22no—
83C23×C43—22no—
84C23×C43—22no—
85C23×C43—22no—
86C23×C43—22no—
87C23×C43—22no—
88C23×C43—21no—
89C23×C43C2411yescharacteristic
90C22×D43—22no—
91C22×D43—22no—
92C22×D43—21no—
93C22×D43—21no—
94C22×D43—21no—
95C22×D43—21no—
96C22×D43—22no—
97C22×D43—22no—
98C22×D43—21no—
99C22×D43C2×D412yes—
100D4×C43—44no—
101D4×C43—48no—
102C2×C4×C43—22no—
103C2×C4×C43—21no—
104C2×C4×C43—22no—
105C2×C4×C43—22no—
106C2×C4×C43—22no—
107C2×C4×C43—22no—
108C2×C4×C43C2×D412yes—
109C22⋊D43—44no—
110C22⋊D43—44no—
111C22⋊D43—48no—
112C22⋊D43—48no—
113C2×Dic43—22no—
114C2×Dic43—21no—
115C2×Dic43—22no—
116C2×Dic43—22no—
117C2×Dic43—22no—
118C2×Dic43—22no—
119C2×Dic43—22no—
120C2×Dic43—22no—
121C2×Dic43—22no—
122C2×Dic43C2×D412yes—
123D172—44no—
124C4×D43—44no—
125C22×C43—41no—
126C22×C43—42no—
127C22×C43—42no—
128C22×C43—41no—
129C22×C43—41no—
130C22×C43—42no—
131C22×C43—42no—
132C22×C43—42no—
133C22×C43—42no—
134C22×C43—42no—
135C22×C43—42no—
136C22×C43—42no—
137C22×C43C22×D411yescharacteristic
138C22×C43H(5,𝔽2)12yes—
139C22×C43H(5,𝔽2)12yes—
140C22×C43H(5,𝔽2)11yescharacteristic
141C22×C43H(5,𝔽2)11yescharacteristic
142C2×D43—22no—
143C2×D43—22no—
144C2×D43—22no—
145C2×D43—42no—
146C2×D43—42no—
147C2×D43—41no—
148C2×D43—41no—
149C2×D43—41no—
150C2×D43—42no—
151C2×D43—42no—
152C4×C43—22no—
153C4×C43—41no—
154C4×C43—42no—
155Dic43—22no—
156Dic43—41no—
157Dic43—42no—
158Dic43—42no—
159#2815—431nomaximal, Sylow
160C2×C43—81no—
161C2×C43—82no—
162C2×C43#53411yescharacteristic
163C2×C43#53511yescharacteristic
164C2×C43#53511yescharacteristic
165C2×C43#56012yes—
166C2×C43#56012yes—
167D43—42no—
168D43—81no—
169C2×#121—431no—
170C2×#121—431no—
171#397—431no—
172#397—432no—
173#397—431no—
174#392—432no—
175#392—431no—
176#392—432no—
177#392—432no—
178#392D4311yescharacteristic, complemented
179#381—431no—
180C43#281511yescharacteristic, complemented, Sylow
181C22×D4—431no—
182C22×D4—432no—
183C22×D4—431no—
184C22×D4—432no—
185C22×D4—431no—
186C22×D4C2×D4311yescharacteristic
187C22×D4C2×D4312yes—
188C23×C4—431no—
189#121—864no—
190#121—864no—
191C2×C4⋊C4—431no—
192C2×C4⋊C4—431no—
193C2×C22⋊C4—432no—
194C2×C22⋊C4—431no—
195C2×C22⋊C4—432no—
196C2×C22⋊C4—432no—
197C2×C22⋊C4—432no—
198C2×C22⋊C4—432no—
199C2×C22⋊C4C2×D4311yescharacteristic
200C2×C22⋊C4C2×D4312yes—
201#95—432no—
202#95—431no—
203#95—432no—
204#95—432no—
205#95C2×D4311yescharacteristic
206C24—431no—
207C24—431no—
208C24C22×D4311yescharacteristic
209C24C22×D4312yes—
210C2×D4—22no—
211C2×D4—42no—
212C2×D4—42no—
213C2×D4—42no—
214C2×D4—42no—
215C2×D4—862no—
216C2×D4—862no—
217C2×D4—862no—
218C2×D4—864no—
219C2×D4—1722no—
220C2×D4—1722no—
221C2×D4—1722no—
222C2×D4—1722no—
223C2×D4—1722no—
224C2×D4—1722no—
225C2×D4—1722no—
226C2×D4—1722no—
227C22×C4—431no—
228C22×C4—434no—
229C22×C4—432no—
230C22×C4—431no—
231C22×C4—432no—
232C22×C4—1722no—
233C22×C4C22×D4312yes—
234C22×C4C22×D4311yescharacteristic
235C22×C4C22×D4311yescharacteristic
236C4⋊C4—862no—
237C4⋊C4—862no—
238C22⋊C4—22no—
239C22⋊C4—42no—
240C22⋊C4—864no—
241C22⋊C4—862no—
242C22⋊C4—1722no—
243C22⋊C4—1722no—
244C22⋊C4—1722no—
245C22⋊C4—1722no—
246C23—21no—
247C23—22no—
248C23—22no—
249C23—22no—
250C23—21no—
251C23—22no—
252C23—22no—
253C23—22no—
254C23—22no—
255C23—22no—
256C23—21no—
257C23—22no—
258C23—432no—
259C23—862no—
260C23—862no—
261C23—861no—
262C23—861no—
263C23—861no—
264C23—861no—
265C23—862no—
266C23—862no—
267C23—861no—
268C23C23×D4311yescharacteristic
269D4—44no—
270D4—48no—
271D4—1724no—
272D4—1724no—
273D4—1724no—
274D4—1728no—
275D4—1728no—
276C2×C4—22no—
277C2×C4—21no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—432no—
283C2×C4—862no—
284C2×C4—861no—
285C2×C4—862no—
286C2×C4—862no—
287C2×C4—862no—
288C2×C4—862no—
289C2×C4—862no—
290C2×C4—862no—
291C2×C4—862no—
292C2×C4—1724no—
293C2×C4D4×D4312yes—
294C22—42no—
295C22—42no—
296C22—42no—
297C22—42no—
298C22—42no—
299C22—42no—
300C22—42no—
301C22—41no—
302C22—41no—
303C22—42no—
304C22—42no—
305C22—41no—
306C22—862no—
307C22—862no—
308C22—862no—
309C22—1722no—
310C22—1722no—
311C22—1721no—
312C22—1721no—
313C22—1721no—
314C22—1722no—
315C22—1722no—
316C22C2×D4×D4311yescharacteristic
317C22#1306337012yes—
318C22#1306337012yes—
319C22#1306337011yescharacteristic
320C22#1306337111yescharacteristic
321C4—22no—
322C4—42no—
323C4—41no—
324C4—862no—
325C4—1722no—
326C4—1721no—
327C4—1722no—
328C2—82no—
329C2—81no—
330C2—3441no—
331C2—1722no—
332C2#1458345911yescharacteristic
333C2#1458346211yescharacteristic
334C2#1458346511yescharacteristic
335C2#1458363712yes—
336C2#1458363812yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#392C2
hypercenter#392D43
hypocenterC43#2815
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×#13063298C2semidirect
2. C2×#13063296C2semidirect
3. #14582827C2semidirect
4. #14582826C2semidirect
5. #14582824C2semidirect
6. #14582808C2semidirect
7. #14582807C2semidirect
8. #14582807C2semidirect
9. #14582807C2semidirect
10. #14582761C2semidirect
11. C43×#392C2semidirect
66. C2×C4×D43D4semidirect
178. #392D43semidirect
180. C43#2815semidirect