Finite Group Databasebeta

← #19146464

Subgroups — #19146464

Order 5504.

388 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583607C211yesmaximal, characteristic
2Q8×C22⋊D43C211yesmaximal, characteristic
3#14583248C211yesmaximal, characteristic, complemented
4#14583235C211yesmaximal, characteristic, complemented
5#14583233C211yesmaximal, characteristic, complemented
6#14583192C211yesmaximal, characteristic, complemented
7#14583138C211yesmaximal, characteristic, complemented
8#14583137C211yesmaximal, characteristic, complemented
9#14583107C211yesmaximal, characteristic, complemented
10#14583053C211yesmaximal, characteristic, complemented
11Q16×Dic43C211yesmaximal, characteristic, complemented
12(C22⋊D43)⋊C8C211yesmaximal, characteristic
13C2×#13063249C211yesmaximal, characteristic, complemented
14#103×D43C211yesmaximal, characteristic, complemented
15C43×#451C211yesmaximal, characteristic, complemented
16C2×Q8×D43C2211yescharacteristic
17C2×#10621885C2211yescharacteristic
18C22×C43⋊C8C2211yescharacteristic
19C2×C8×D43C2211yescharacteristic
20#13063324C2211yescharacteristic
21#13063323—21no—
22#13063323C2211yescharacteristic
23#13063315—21no—
24#13063305—21no—
25#13063304—21no—
26#13063304C2211yescharacteristic
27#13063302—21no—
28#13063301—21no—
29#13063301C2211yescharacteristic
30#13063301C2211yescharacteristic
31Q8×Dic43C2211yescharacteristic
32Q8×Dic43C2211yescharacteristic
33C4×C22⋊D43—21no—
34C4×C22⋊D43C2211yescharacteristic
35(C22⋊D43)⋊C4—21no—
36C2×C4⋊Dic43C2211yescharacteristic
37C4⋊C4×D43C2211yescharacteristic
38#13063259C2211yescharacteristic
39#13063259C2211yescharacteristic
40#13063258C2211yescharacteristic
41Dic43⋊C8C2211yescharacteristic
42#13063250C2211yescharacteristic
43#13063250C2211yescharacteristic
44#13063249C2211yescharacteristic
45#13063249C2211yescharacteristic
46#13063249C2211yescharacteristic
47#13063249C2211yescharacteristic
48#13063249C2211yescharacteristic
49#13063248C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic
51C8×Dic43C2211yescharacteristic
52C22×Q8×C43C2211yescharacteristic
53C2×Q16×C43C2211yescharacteristic
54C2×Q16×C43C2211yescharacteristic
55C22⋊Q8×C43C2211yescharacteristic
56#103×C43C2211yescharacteristic
57#103×C43C2211yescharacteristic
58C22⋊C8×C43C2211yescharacteristic
59C2×Q8×C43—21no—
60C2×Q8×C43—22no—
61C2×Q8×C43—41no—
62C2×Q8×C43C2311yescharacteristic
63C2×Q8×C43C2311yescharacteristic
64C2×Q8×C43C2311yescharacteristic
65C22×C4×C43—21no—
66C22×C4×C43C2311yescharacteristic
67C2×C22⋊D43D411yescharacteristic
68C22×Dic43—21no—
69Q8×D43—22no—
70Q8×D43—41no—
71C2×C4×D43—21no—
72C2×C4×D43—21no—
73C2×C4×D43C2311yescharacteristic
74C2×Dic86—21no—
75C2×Dic86—21no—
76C2×Dic86C2311yescharacteristic
77Q16×C43—22no—
78Q16×C43—41no—
79C2×C8×C43C2311yescharacteristic
80C2×C8×C43C2311yescharacteristic
81C4⋊C4×C43—21no—
82C4⋊C4×C43C2311yescharacteristic
83C22⋊C4×C43—21no—
84C22⋊Dic43—21no—
85C22⋊Dic43D411yescharacteristic
86#10621885—41no—
87(C2×D43)⋊C4—21no—
88(C2×D43)⋊C4—21no—
89(C2×D43)⋊C4D411yescharacteristic
90C4⋊Dic43—21no—
91C4⋊Dic43—21no—
92C4⋊Dic43—21no—
93C4⋊Dic43C2311yescharacteristic
94C4⋊Dic43C2311yescharacteristic
95C4⋊Dic43C2311yescharacteristic
96Dic43⋊C4—21no—
97Dic43⋊C4—21no—
98Dic43⋊C4—21no—
99Dic43⋊C4—21no—
100Dic43⋊C4—21no—
101Dic43⋊C4—21no—
102Dic43⋊C4—21no—
103Dic43⋊C4D411yescharacteristic
104C4×Dic43—21no—
105C4×Dic43—21no—
106C4×Dic43C2311yescharacteristic
107C2×C43⋊C8—41no—
108C2×C43⋊C8C2311yescharacteristic
109C2×C43⋊C8C2311yescharacteristic
110C8×D43—41no—
111C23×C43C2×D411yescharacteristic
112C22×D43C2×D411yescharacteristic
113Q8×C43—21no—
114Q8×C43—21no—
115Q8×C43—21no—
116Q8×C43—21no—
117Q8×C43—21no—
118Q8×C43—42no—
119Q8×C43#4112yes—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—42no—
127C2×C4×C43C2×D411yescharacteristic
128C2×C4×C43C2411yescharacteristic
129C22⋊D43Q1614yescomplemented
130C2×Dic43—21no—
131C2×Dic43—21no—
132C2×Dic43—21no—
133C2×Dic43—21no—
134C2×Dic43—81no—
135C2×Dic43C2×D411yescharacteristic
136C2×Dic43C2×D411yescharacteristic
137C2×Dic43C2×D411yescharacteristic
138C4×D43—21no—
139C4×D43—21no—
140C4×D43—42no—
141C4×D43—81no—
142Dic86—21no—
143Dic86—21no—
144Dic86—42no—
145Dic86—81no—
146C8×C43—21no—
147C8×C43—21no—
148C43⋊C8—21no—
149C43⋊C8—21no—
150C22×C43—21no—
151C22×C43—21no—
152C22×C43C2×Q1612yes—
153C22×C43C22×D411yescharacteristic
154C2×D43—21no—
155C2×D43—21no—
156C2×D43C2×Q1612yes—
157C4×C43—22no—
158C4×C43—21no—
159C4×C43—41no—
160C4×C43—41no—
161C4×C43—41no—
162C4×C43C2×#4111yescharacteristic
163C4×C43H(5,𝔽2)11yescharacteristic
164Dic43—21no—
165Dic43—21no—
166Dic43—41no—
167Dic43—41no—
168Dic43—41no—
169Dic43—41no—
170Dic43C2×Q1612yes—
171#3299—431nomaximal, Sylow
172C2×C43—22no—
173C2×C43#54611yescharacteristic
174C2×C43C22×Q1611yescharacteristic
175C2×C43#57711yescharacteristic
176D43—22no—
177#554—431no—
178D4×Q8—431no—
179#487—431no—
180#484—431no—
181#484—431no—
182#477—431no—
183#467—431no—
184#467—431no—
185#462—431no—
186#451—431no—
187#451D4311yescharacteristic, complemented
188C4×Q16—431no—
189C8×D4—431no—
190C2×#103—431no—
191C2×#103—431no—
192C43#329911yescharacteristic, complemented, Sylow
193C22×Q8—431no—
194C22×Q8C2×D4311yescharacteristic
195C2×Q16—431no—
196C2×Q16C2×D4311yescharacteristic
197C2×Q16C2×D4311yescharacteristic
198C22×C8—431no—
199C22×C8—431no—
200C4⋊Q8—431no—
201C4⋊Q8—431no—
202C4⋊Q8—861no—
203#125—861no—
204C22⋊Q8—431no—
205C22⋊Q8—431no—
206C22⋊Q8—431no—
207C22⋊Q8—861no—
208C22⋊Q8—861no—
209C22⋊Q8—861no—
210C22⋊Q8—861no—
211C22⋊Q8C2×D4311yescharacteristic
212C4×Q8—431no—
213C4×Q8—431no—
214C4×D4—431no—
215C4×D4—861no—
216C4×D4—861no—
217C2×C4⋊C4—431no—
218C2×C4⋊C4—431no—
219#107—431no—
220#107—431no—
221#107—431no—
222C4⋊C8—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—
231#103C2×D4311yescharacteristic
232#103C2×D4311yescharacteristic
233C22⋊C8—431no—
234C22⋊C8C2×D4311yescharacteristic
235C4×C8—431no—
236C2×Q8—21no—
237C2×Q8—22no—
238C2×Q8—41no—
239C2×Q8—431no—
240C2×Q8—861no—
241C2×Q8—861no—
242C2×Q8—862no—
243C2×Q8—1721no—
244C2×Q8C22×D4311yescharacteristic
245C2×Q8C22×D4311yescharacteristic
246C2×Q8C22×D4311yescharacteristic
247C2×D4—431no—
248C22×C4—21no—
249C22×C4—431no—
250C22×C4—861no—
251C22×C4—861no—
252C22×C4—861no—
253C22×C4C22×D4311yescharacteristic
254Q16—22no—
255Q16—41no—
256Q16—1721no—
257C2×C8—431no—
258C2×C8—431no—
259C2×C8—1721no—
260C2×C8—1721no—
261C2×C8C22×D4311yescharacteristic
262C2×C8C22×D4311yescharacteristic
263C4⋊C4—21no—
264C4⋊C4—431no—
265C4⋊C4—431no—
266C4⋊C4—431no—
267C4⋊C4—431no—
268C4⋊C4—861no—
269C4⋊C4—861no—
270C4⋊C4—861no—
271C4⋊C4—861no—
272C4⋊C4—861no—
273C4⋊C4—861no—
274C4⋊C4—861no—
275C4⋊C4—861no—
276C4⋊C4—861no—
277C4⋊C4—861no—
278C4⋊C4C22×D4311yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—431no—
281C22⋊C4—431no—
282C22⋊C4—861no—
283C22⋊C4—861no—
284C22⋊C4—861no—
285C42—431no—
286C42—861no—
287C42—861no—
288C23—431no—
289C23D4×D4311yescharacteristic
290Q8—21no—
291Q8—21no—
292Q8—21no—
293Q8—21no—
294Q8—21no—
295Q8—42no—
296Q8—861no—
297Q8—861no—
298Q8—3441no—
299Q8—1722no—
300Q8#1062190012yes—
301D4—434no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—42no—
309C2×C4—431no—
310C2×C4—431no—
311C2×C4—431no—
312C2×C4—861no—
313C2×C4—861no—
314C2×C4—861no—
315C2×C4—861no—
316C2×C4—861no—
317C2×C4—861no—
318C2×C4—3441no—
319C2×C4—3441no—
320C2×C4—1722no—
321C2×C4D4×D4311yescharacteristic
322C2×C4C23×D4311yescharacteristic
323C8—21no—
324C8—21no—
325C8—861no—
326C8—861no—
327C22—21no—
328C22—21no—
329C22—432no—
330C22—861no—
331C22—861no—
332C22Q16×D4312yes—
333C22C2×D4×D4311yescharacteristic
334C4—21no—
335C4—22no—
336C4—41no—
337C4—41no—
338C4—41no—
339C4—432no—
340C4—861no—
341C4—861no—
342C4—1721no—
343C4—1721no—
344C4—1721no—
345C4—1721no—
346C4C2×#1062190011yescharacteristic
347C4#1306337011yescharacteristic
348C2—22no—
349C2—862no—
350C2#1458353611yescharacteristic
351C2C2×Q16×D4311yescharacteristic
352C2#1458370811yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#451C2
socleC22×C43C22×D4
hypercenter#451D43
hypocenterC43#3299
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
3. #14583248C2semidirect
4. #14583235C2semidirect
5. #14583233C2semidirect
6. #14583192C2semidirect
7. #14583138C2semidirect
8. #14583137C2semidirect
9. #14583107C2semidirect
10. #14583053C2semidirect
11. Q16×Dic43C2semidirect
13. C2×#13063249C2semidirect
14. #103×D43C2semidirect
15. C43×#451C2semidirect
129. C22⋊D43Q16semidirect
187. #451D43semidirect
192. C43#3299semidirect