Finite Group Databasebeta

← #19146646

Subgroups — #19146646

Order 5504.

376 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583589C211yesmaximal, characteristic
2#14583267C211yesmaximal, characteristic, complemented
3#14583237C211yesmaximal, characteristic, complemented
4#14583227C211yesmaximal, characteristic, complemented
5#14583206C211yesmaximal, characteristic, complemented
6#14583155C211yesmaximal, characteristic, complemented
7#14583138C211yesmaximal, characteristic, complemented
8#14583106C211yesmaximal, characteristic, complemented
9#14583055C211yesmaximal, characteristic, complemented
10#14583055C211yesmaximal, characteristic, complemented
11#14583004C211yesmaximal, characteristic, complemented
12#14582971C211yesmaximal, characteristic
13#14582908C211yesmaximal, characteristic, complemented
14C2×#13063249C211yesmaximal, characteristic, complemented
15D4×Q8×C43C211yesmaximal, characteristic
16C2×#10621885C2211yescharacteristic
17C2×#10621885C2211yescharacteristic
18C2×#10621885C2211yescharacteristic
19C2×#10621877C2211yescharacteristic
20C22×C43⋊C8C2211yescharacteristic
21#13063318—21no—
22#13063317C2211yescharacteristic
23#13063315—21no—
24#13063306—21no—
25#13063304C2211yescharacteristic
26#13063304C2211yescharacteristic
27C4×Dic86C2211yescharacteristic
28#13063284C2211yescharacteristic
29#13063281—21no—
30C2×C4⋊Dic43C2211yescharacteristic
31#13063258C2211yescharacteristic
32#13063256C2211yescharacteristic
33#13063256C2211yescharacteristic
34C4⋊(C43⋊C8)C2211yescharacteristic
35#13063249C2211yescharacteristic
36#13063249C2211yescharacteristic
37#13063249C2211yescharacteristic
38#13063249C2211yescharacteristic
39#13063249C2211yescharacteristic
40#13063249C2211yescharacteristic
41#13063249C2211yescharacteristic
42#13063249C2211yescharacteristic
43#13063249C2211yescharacteristic
44#13063248C2211yescharacteristic
45C22⋊(C43⋊C8)C2211yescharacteristic
46C22⋊(C43⋊C8)C2211yescharacteristic
47#13063236C2211yescharacteristic
48C22×Q8×C43C2211yescharacteristic
49C22×Q8×C43C2211yescharacteristic
50C4⋊Q8×C43—21no—
51C4⋊Q8×C43C2211yescharacteristic
52C22⋊Q8×C43—21no—
53C22⋊Q8×C43—21no—
54C22⋊Q8×C43C2211yescharacteristic
55C22⋊Q8×C43C2211yescharacteristic
56C4×Q8×C43C2211yescharacteristic
57C4×D4×C43—21no—
58C4×D4×C43C2211yescharacteristic
59C2×Q8×C43—21no—
60C2×Q8×C43—21no—
61C2×Q8×C43—22no—
62C2×Q8×C43—22no—
63C2×Q8×C43—41no—
64C2×Q8×C43—41no—
65C2×Q8×C43C2311yescharacteristic
66C2×Q8×C43C2311yescharacteristic
67C2×Q8×C43C2311yescharacteristic
68C2×D4×C43D411yescharacteristic
69C22×C4×C43—21no—
70C22×C4×C43—21no—
71C22×C4×C43C2311yescharacteristic
72C22×C4×C43C2311yescharacteristic
73C22×Dic43—21no—
74C2×Dic86C2311yescharacteristic
75C4⋊C4×C43—21no—
76C4⋊C4×C43—21no—
77C4⋊C4×C43—21no—
78C4⋊C4×C43—21no—
79C4⋊C4×C43—21no—
80C4⋊C4×C43D411yescharacteristic
81C4⋊C4×C43C2311yescharacteristic
82C22⋊C4×C43—21no—
83C22⋊C4×C43—21no—
84C22⋊C4×C43D411yescharacteristic
85C22⋊C4×C43D411yescharacteristic
86C42×C43—21no—
87C42×C43C2311yescharacteristic
88C22⋊Dic43—21no—
89C22⋊Dic43—21no—
90C22⋊Dic43—21no—
91#10621885—22no—
92#10621885—41no—
93#10621885—41no—
94C4⋊Dic43—21no—
95C4⋊Dic43C2311yescharacteristic
96C4⋊Dic43C2311yescharacteristic
97C4⋊Dic43C2311yescharacteristic
98Dic43⋊C4—21no—
99Dic43⋊C4—21no—
100Dic43⋊C4—21no—
101Dic43⋊C4—21no—
102Dic43⋊C4—21no—
103C4×Dic43—21no—
104C4×Dic43—21no—
105#10621877—41no—
106C2×C43⋊C8—41no—
107C2×C43⋊C8C2311yescharacteristic
108C2×C43⋊C8C2311yescharacteristic
109C2×C43⋊C8C2311yescharacteristic
110C2×C43⋊C8C2311yescharacteristic
111C23×C43C2×D411yescharacteristic
112C23×C43C2×D411yescharacteristic
113Q8×C43—21no—
114Q8×C43—21no—
115Q8×C43—21no—
116Q8×C43—21no—
117Q8×C43—21no—
118Q8×C43—42no—
119Q8×C43—42no—
120Q8×C43#4112yes—
121D4×C43—22no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43—21no—
129C2×C4×C43—21no—
130C2×C4×C43—42no—
131C2×C4×C43—42no—
132C2×C4×C43C2×D411yescharacteristic
133C2×C4×C43C2×D411yescharacteristic
134C2×C4×C43C2×D411yescharacteristic
135C2×C4×C43C2×D411yescharacteristic
136C2×C4×C43C2411yescharacteristic
137C2×Dic43—21no—
138C2×Dic43—21no—
139C2×Dic43—21no—
140C2×Dic43—21no—
141C2×Dic43—42no—
142Dic86—21no—
143Dic86—21no—
144C43⋊C8—21no—
145C43⋊C8—21no—
146C43⋊C8—21no—
147C43⋊C8—21no—
148C22×C43—21no—
149C22×C43—21no—
150C22×C43—21no—
151C22×C43—21no—
152C22×C43—21no—
153C22×C43#13712yes—
154C22×C43C22×D411yescharacteristic
155C4×C43—21no—
156C4×C43—21no—
157C4×C43—22no—
158C4×C43—21no—
159C4×C43—21no—
160C4×C43—41no—
161C4×C43—41no—
162C4×C43—41no—
163C4×C43C2×#4111yescharacteristic
164C4×C43H(5,𝔽2)11yescharacteristic
165Dic43—41no—
166Dic43—41no—
167Dic43—41no—
168Dic43—41no—
169#3312—431nomaximal, Sylow
170C2×C43—22no—
171C2×C43—41no—
172C2×C43#54611yescharacteristic
173C2×C43C2×#13711yescharacteristic
174C2×C43#57811yescharacteristic
175#552—431no—
176D4×Q8D4311yescharacteristic
177#491—431no—
178#485—431no—
179#483—431no—
180#479—431no—
181#470—431no—
182#467—431no—
183#462—431no—
184#451—431no—
185#451—431no—
186#441—431no—
187#435—431no—
188#419—431no—
189C2×#103—431no—
190C43#331211yescharacteristic, complemented, Sylow
191C22×Q8C2×D4311yescharacteristic
192C22×Q8C2×D4311yescharacteristic
193C2×Q16—431no—
194C2×Q16—431no—
195C2×Q16—431no—
196C2×M16—431no—
197C22×C8—431no—
198C4⋊Q8—21no—
199C4⋊Q8C2×D4311yescharacteristic
200#126—861no—
201#125—431no—
202#125—861no—
203#123—861no—
204C22⋊Q8—21no—
205C22⋊Q8—21no—
206C22⋊Q8—431no—
207C22⋊Q8—431no—
208C22⋊Q8C2×D4311yescharacteristic
209C22⋊Q8C2×D4311yescharacteristic
210C4×Q8—431no—
211C4×Q8C2×D4311yescharacteristic
212C4×D4—21no—
213C4×D4C2×D4311yescharacteristic
214#117—431no—
215#117—861no—
216C2×C4⋊C4—431no—
217#107—431no—
218#106—431no—
219#106—431no—
220C4⋊C8—431no—
221#103—431no—
222#103—431no—
223#103—431no—
224#103—431no—
225#103—431no—
226#103—431no—
227#103—431no—
228#103—431no—
229#103—431no—
230#103—431no—
231C22⋊C8—431no—
232C22⋊C8—431no—
233#97—431no—
234C2×Q8—21no—
235C2×Q8—21no—
236C2×Q8—22no—
237C2×Q8—22no—
238C2×Q8—41no—
239C2×Q8—41no—
240C2×Q8—431no—
241C2×Q8C22×D4311yescharacteristic
242C2×Q8C22×D4311yescharacteristic
243C2×Q8C22×D4311yescharacteristic
244C2×D4C22⋊D4311yescharacteristic
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—861no—
248C22×C4C22×D4311yescharacteristic
249C22×C4C22×D4311yescharacteristic
250Q16—862no—
251Q16—1721no—
252Q16—1721no—
253M16—1721no—
254C2×C8—431no—
255C2×C8—431no—
256C2×C8—431no—
257C2×C8—431no—
258C2×C8—1721no—
259C4⋊C4—21no—
260C4⋊C4—21no—
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—431no—
265C4⋊C4—431no—
266C4⋊C4—431no—
267C4⋊C4—861no—
268C4⋊C4—861no—
269C4⋊C4—861no—
270C4⋊C4—861no—
271C4⋊C4—861no—
272C4⋊C4—861no—
273C4⋊C4C22⋊D4311yescharacteristic
274C4⋊C4C22×D4311yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—861no—
278C22⋊C4—861no—
279C22⋊C4—861no—
280C22⋊C4C22⋊D4311yescharacteristic
281C22⋊C4C22⋊D4311yescharacteristic
282C42—21no—
283C42—861no—
284C42—861no—
285C42C22×D4311yescharacteristic
286C23C2×C22⋊D4311yescharacteristic
287C23C2×C22⋊D4311yescharacteristic
288Q8—21no—
289Q8—21no—
290Q8—21no—
291Q8—21no—
292Q8—21no—
293Q8—42no—
294Q8—42no—
295Q8—861no—
296Q8—861no—
297Q8#1062190012yes—
298D4—22no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—861no—
310C2×C4—861no—
311C2×C4—861no—
312C2×C4—861no—
313C2×C4—1722no—
314C2×C4C2×C22⋊D4311yescharacteristic
315C2×C4C2×C22⋊D4311yescharacteristic
316C2×C4C2×C22⋊D4311yescharacteristic
317C2×C4C2×C22⋊D4311yescharacteristic
318C2×C4C23×D4311yescharacteristic
319C8—861no—
320C8—861no—
321C8—861no—
322C8—861no—
323C22—21no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—21no—
328C22#1306335612yes—
329C22C22×C22⋊D4311yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—22no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—1721no—
339C4—1721no—
340C4—1721no—
341C4—1721no—
342C4C2×#1062190011yescharacteristic
343C4#1306337011yescharacteristic
344C2—22no—
345C2—41no—
346C2#1458354311yescharacteristic
347C2C2×#1306335611yescharacteristic
348C2#1458371411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingD4×Q8×C43C2
socleC22×C43C22×D4
hypercenterD4×Q8D43
hypocenterC43#3312
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4 ◁ D4×Q8

Complements

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

NH ≅ G/Ntype
2. #14583267C2semidirect
3. #14583237C2semidirect
4. #14583227C2semidirect
5. #14583206C2semidirect
6. #14583155C2semidirect
7. #14583138C2semidirect
8. #14583106C2semidirect
9. #14583055C2semidirect
10. #14583055C2semidirect
11. #14583004C2semidirect
13. #14582908C2semidirect
14. C2×#13063249C2semidirect
190. C43#3312semidirect