Finite Group Databasebeta

← #19148682

Subgroups — #19148682

Order 5504.

992 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#14583625C211yesmaximal, characteristic, complemented
2#14583624C213yesmaximal, complemented
3#14583620C213yesmaximal, complemented
4#14583591C213yesmaximal, complemented
5#14583589C213yesmaximal, complemented
6Q8×C22⋊D43C211yesmaximal, characteristic, complemented
7Q8×C22⋊D43C211yesmaximal, characteristic, complemented
8#14583510C213yesmaximal, complemented
9#14583509C213yesmaximal, complemented
10#14583451C213yesmaximal, complemented
11#14583429C213yesmaximal
12#14583377C211yesmaximal, characteristic, complemented
13#14583375C211yesmaximal, characteristic, complemented
14C2×Q8×Dic43C211yesmaximal, characteristic, complemented
15D4×Q8×C43C211yesmaximal, characteristic, complemented
16C2×Q8×D43C2211yescharacteristic
17#13063324C2213yes—
18#13063323C2213yes—
19#13063323C2213yes—
20#13063320C2216yes—
21#13063320C2213yes—
22#13063318C2216yes—
23#13063318C2213yes—
24#13063317C2213yes—
25#13063316C2216yes—
26#13063316C2213yes—
27#13063315C2216yes—
28#13063315C2213yes—
29#13063315C2216yes—
30#13063311C2213yes—
31#13063309C2213yes—
32#13063306C2213yes—
33#13063304C2213yes—
34#13063304C2213yes—
35#13063302C2213yes—
36#13063301C2213yes—
37#13063301C2213yes—
38#13063297C2211yescharacteristic
39Q8×Dic43C2211yescharacteristic
40Q8×Dic43C2211yescharacteristic
41Q8×Dic43C2213yes—
42Q8×Dic43C2213yes—
43Q8×Dic43C2211yescharacteristic
44Q8×Dic43C2213yes—
45Q8×Dic43C2213yes—
46C4×Dic86C2213yes—
47C4×Dic86C2213yes—
48#13063290C2216yes—
49#13063290C2213yes—
50C4×C22⋊D43C2213yes—
51C4×C22⋊D43C2213yes—
52#13063284C2213yes—
53#13063284C2213yes—
54#13063283C2213yes—
55#13063282C2213yes—
56#13063281C2216yes—
57C2×C4⋊Dic43C2213yes—
58C2×C4×Dic43C2213yes—
59C22×Q8×C43C2211yescharacteristic
60C22×Q8×C43C2211yescharacteristic
61C4⋊Q8×C43C2213yes—
62C22⋊Q8×C43C2213yes—
63C22⋊Q8×C43C2213yes—
64C4×Q8×C43C2211yescharacteristic
65C4×D4×C43C2213yes—
66C2×Q8×C43—24no—
67C2×Q8×C43—24no—
68C2×Q8×C43C2313yes—
69C2×Q8×C43C2313yes—
70C2×Q8×C43C2311yescharacteristic
71C2×D4×C43C2311yescharacteristic
72C22×C4×C43C2313yes—
73C22×C4×C43C2313yes—
74C2×C22⋊D43C2311yescharacteristic
75C2×C22⋊D43C2311yescharacteristic
76C22×Dic43C2311yescharacteristic
77C22×Dic43C2313yes—
78Q8×D43—24no—
79C2×C4×D43C2313yes—
80C2×Dic86C2313yes—
81C2×Dic86C2313yes—
82C4⋊C4×C43C2313yes—
83C4⋊C4×C43C2313yes—
84C4⋊C4×C43C2316yes—
85C22⋊C4×C43C2313yes—
86C22⋊C4×C43C2313yes—
87C42×C43C2313yes—
88C22⋊Dic43C2313yes—
89C22⋊Dic43C2311yescharacteristic
90C22⋊Dic43C2313yes—
91C22⋊Dic43C2313yes—
92(C2×D43)⋊C4C2311yescharacteristic
93(C2×D43)⋊C4C2313yes—
94(C2×D43)⋊C4C2313yes—
95(C2×D43)⋊C4C2313yes—
96C4⋊Dic43C2313yes—
97C4⋊Dic43C2313yes—
98C4⋊Dic43C2316yes—
99C4⋊Dic43C2313yes—
100C4⋊Dic43C2313yes—
101C4⋊Dic43C2313yes—
102C4⋊Dic43C2313yes—
103Dic43⋊C4C2316yes—
104Dic43⋊C4C2316yes—
105Dic43⋊C4C2313yes—
106Dic43⋊C4C2313yes—
107Dic43⋊C4C2313yes—
108Dic43⋊C4C2313yes—
109Dic43⋊C4C2316yes—
110Dic43⋊C4C2311yescharacteristic
111Dic43⋊C4C2313yes—
112C4×Dic43C2313yes—
113C4×Dic43C2313yes—
114C4×Dic43C2313yes—
115C4×Dic43C2313yes—
116C4×Dic43C2316yes—
117C4×Dic43C2316yes—
118C4×Dic43C2313yes—
119C23×C43C2411yescharacteristic
120C23×C43C2411yescharacteristic
121C22×D43C2411yescharacteristic
122Q8×C43—26no—
123Q8×C43—26no—
124Q8×C43#4114yes—
125D4×C43—22no—
126C2×C4×C43—26no—
127C2×C4×C43—26no—
128C2×C4×C43C2413yes—
129C2×C4×C43C2413yes—
130C2×C4×C43C2413yes—
131C2×C4×C43C2411yescharacteristic
132C2×C4×C43C2413yes—
133C22⋊D43—22no—
134C22⋊D43—22no—
135C2×Dic43—26no—
136C2×Dic43—22no—
137C2×Dic43C2411yescharacteristic
138C2×Dic43C2413yes—
139C2×Dic43C2413yes—
140C2×Dic43C2411yescharacteristic
141C2×Dic43C2413yes—
142C2×Dic43C2413yes—
143C2×Dic43C2411yescharacteristic
144C4×D43—26no—
145Dic86—26no—
146Dic86—26no—
147C22×C43—21no—
148C22×C43—21no—
149C22×C43—21no—
150C22×C43—21no—
151C22×C43—21no—
152C22×C432−1+412yes—
153C22×C43C2511yescharacteristic
154C2×D43—21no—
155C2×D43—21no—
156C2×D43—21no—
157C4×C43—23no—
158C4×C43—23no—
159C4×C43—23no—
160C4×C43—21no—
161C4×C43C2×#4116yes—
162Dic43—23no—
163Dic43—23no—
164Dic43—21no—
165Dic43—23no—
166Dic43—23no—
167Dic43—21no—
168Dic432−1+412yes—
169#3523—431nomaximal, Sylow
170C2×C43—22no—
171C2×C43—41no—
172C2×C43C22×#4111yescharacteristic
173C2×C43C2×2−1+411yescharacteristic
174C2×C43C2×2−1+411yescharacteristic
175D43—41no—
176#557—433no—
177#557—431no—
178#556—433no—
179#552—433no—
180#552—433no—
181D4×Q8—431no—
182D4×Q8—431no—
183D4×Q8D4311yescharacteristic, complemented
184#541—433no—
185#541—433no—
186#533—433no—
187#529—433no—
188#519—431no—
189#519—431no—
190C2×C4×Q8—431no—
191C43#352311yescharacteristic, complemented, Sylow
192C22×Q8—431no—
193C22×Q8C2×D4311yescharacteristic
194C22×Q8C2×D4311yescharacteristic
195C4⋊Q8—433no—
196C4⋊Q8—433no—
197C4⋊Q8—433no—
198C4⋊Q8C2×D4313yes—
199#126—433no—
200#126—436no—
201#126—433no—
202#126—436no—
203#125—433no—
204#125—436no—
205#125—436no—
206#125—436no—
207#125—433no—
208#125—433no—
209#124—433no—
210#123—433no—
211#123—433no—
212C22⋊Q8—433no—
213C22⋊Q8—433no—
214C22⋊Q8—433no—
215C22⋊Q8—433no—
216C22⋊Q8—433no—
217C22⋊Q8C2×D4313yes—
218C22⋊Q8C2×D4313yes—
219#121—431no—
220C4×Q8—431no—
221C4×Q8—433no—
222C4×Q8—431no—
223C4×Q8—433no—
224C4×Q8—433no—
225C4×Q8—431no—
226C4×Q8—433no—
227C4×Q8—433no—
228C4×Q8—436no—
229C4×Q8—433no—
230C4×Q8—433no—
231C4×Q8C2×D4311yescharacteristic
232C4×D4—433no—
233C4×D4—433no—
234C4×D4C2×D4313yes—
235#117—433no—
236#117—433no—
237#117—433no—
238#117—436no—
239#117—433no—
240C2×C4⋊C4—433no—
241C2×C42—433no—
242C2×Q8—24no—
243C2×Q8—24no—
244C2×Q8—433no—
245C2×Q8—433no—
246C2×Q8—864no—
247C2×Q8C22×D4313yes—
248C2×Q8C22×D4313yes—
249C2×Q8C22×D4311yescharacteristic
250C2×D4—431no—
251C2×D4—431no—
252C2×D4C22×D4311yescharacteristic
253C22×C4—431no—
254C22×C4—433no—
255C22×C4—433no—
256C22×C4C22×D4313yes—
257C22×C4C22×D4313yes—
258C4⋊C4—433no—
259C4⋊C4—433no—
260C4⋊C4—436no—
261C4⋊C4—433no—
262C4⋊C4—433no—
263C4⋊C4—433no—
264C4⋊C4—433no—
265C4⋊C4—433no—
266C4⋊C4—436no—
267C4⋊C4—436no—
268C4⋊C4—433no—
269C4⋊C4—433no—
270C4⋊C4—431no—
271C4⋊C4—436no—
272C4⋊C4—433no—
273C4⋊C4—433no—
274C4⋊C4C22×D4313yes—
275C4⋊C4C22×D4313yes—
276C4⋊C4C22×D4316yes—
277C22⋊C4—431no—
278C22⋊C4—433no—
279C22⋊C4—433no—
280C22⋊C4—433no—
281C22⋊C4—431no—
282C22⋊C4—433no—
283C22⋊C4—433no—
284C22⋊C4—433no—
285C22⋊C4C22×D4313yes—
286C22⋊C4C22×D4313yes—
287C42—433no—
288C42—433no—
289C42—433no—
290C42—433no—
291C42—436no—
292C42—436no—
293C42—433no—
294C42C22×D4313yes—
295C23—431no—
296C23C23×D4311yescharacteristic
297C23C23×D4311yescharacteristic
298Q8—26no—
299Q8—26no—
300Q8—866no—
301Q8—866no—
302Q8#1062190014yes—
303D4—22no—
304D4—862no—
305D4—862no—
306C2×C4—26no—
307C2×C4—26no—
308C2×C4—431no—
309C2×C4—431no—
310C2×C4—433no—
311C2×C4—433no—
312C2×C4—431no—
313C2×C4—433no—
314C2×C4—433no—
315C2×C4—862no—
316C2×C4—866no—
317C2×C4—866no—
318C2×C4C23×D4313yes—
319C2×C4C23×D4313yes—
320C2×C4C23×D4313yes—
321C2×C4C23×D4311yescharacteristic
322C2×C4C23×D4313yes—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—861no—
329C22—861no—
330C22—861no—
331C22#1306337312yes—
332C22C24×D4311yescharacteristic
333C4—23no—
334C4—23no—
335C4—23no—
336C4—21no—
337C4—432no—
338C4—863no—
339C4—861no—
340C4—863no—
341C4—863no—
342C4—863no—
343C4—861no—
344C4C2×#1062190016yes—
345C2—22no—
346C2—41no—
347C2—1721no—
348C2C22×#1062190011yescharacteristic
349C22−1+4×D4311yescharacteristic
350C2C2×#1306337311yescharacteristic
subgroupG/H
center, FrattiniC22C24×D43
commutator, socleC22×C43C25
FittingD4×Q8×C43C2
hypercenterD4×Q8D43
hypocenterC43#3523
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ D4×Q8

Complements

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

NH ≅ G/Ntype
1. #14583625C2semidirect
2. #14583624C2semidirect
3. #14583620C2semidirect
4. #14583591C2semidirect
5. #14583589C2semidirect
6. Q8×C22⋊D43C2semidirect
7. Q8×C22⋊D43C2semidirect
8. #14583510C2semidirect
9. #14583509C2semidirect
10. #14583451C2semidirect
12. #14583377C2semidirect
13. #14583375C2semidirect
14. C2×Q8×Dic43C2semidirect
15. D4×Q8×C43C2semidirect
183. D4×Q8D43semidirect
191. C43#3523semidirect