Finite Group Databasebeta

← #19147029

Subgroups — #19147029

Order 5504.

376 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583589C211yesmaximal, characteristic, complemented
2#14583305C211yesmaximal, characteristic, complemented
3#14583234C211yesmaximal, characteristic, complemented
4#14583229C211yesmaximal, characteristic, complemented
5#14583220C211yesmaximal, characteristic, complemented
6#14583210C211yesmaximal, characteristic, complemented
7#14583199C211yesmaximal, characteristic, complemented
8#14583191C211yesmaximal, characteristic, complemented
9#14583143C211yesmaximal, characteristic, complemented
10#14583126C211yesmaximal, characteristic, complemented
11#14582999C211yesmaximal, characteristic, complemented
12#14582971C211yesmaximal, characteristic, complemented
13#14582939C211yesmaximal, characteristic, complemented
14C2×#13063258C211yesmaximal, characteristic, complemented
15C43×#547C211yesmaximal, characteristic
16C2×#10621883C2211yescharacteristic
17C2×#10621877C2211yescharacteristic
18C22×C43⋊C8C2211yescharacteristic
19#13063318—21no—
20#13063317C2211yescharacteristic
21#13063315—21no—
22#13063306—21no—
23#13063304C2211yescharacteristic
24#13063304C2211yescharacteristic
25C4×Dic86C2211yescharacteristic
26#13063284C2211yescharacteristic
27#13063281—21no—
28C2×C4⋊Dic43C2211yescharacteristic
29#13063258C2211yescharacteristic
30#13063258C2211yescharacteristic
31#13063258C2211yescharacteristic
32#13063258C2211yescharacteristic
33#13063258C2211yescharacteristic
34#13063258C2211yescharacteristic
35#13063256C2211yescharacteristic
36#13063256C2211yescharacteristic
37#13063256C2211yescharacteristic
38C4⋊(C43⋊C8)C2211yescharacteristic
39#13063248C2211yescharacteristic
40#13063248C2211yescharacteristic
41#13063248C2211yescharacteristic
42#13063246C2211yescharacteristic
43#13063246C2211yescharacteristic
44#13063246C2211yescharacteristic
45C22⋊(C43⋊C8)C2211yescharacteristic
46C22⋊(C43⋊C8)C2211yescharacteristic
47#13063236C2211yescharacteristic
48C2×#41×C43—21no—
49C4⋊Q8×C43C2211yescharacteristic
50#123×C43—21no—
51#123×C43—21no—
52C22⋊Q8×C43—21no—
53#121×C43C2211yescharacteristic
54#121×C43C2211yescharacteristic
55C4×D4×C43C2211yescharacteristic
56C4×D4×C43C2211yescharacteristic
57C2×C4⋊C4×C43C2211yescharacteristic
58C2×C4⋊C4×C43C2211yescharacteristic
59#41×C43—44no—
60C2×Q8×C43—21no—
61C2×D4×C43—21no—
62C2×D4×C43—21no—
63C2×D4×C43D411yescharacteristic
64C2×D4×C43C2311yescharacteristic
65C22×C4×C43—21no—
66C22×C4×C43—21no—
67C22×C4×C43—21no—
68C22×C4×C43C2311yescharacteristic
69C22×C4×C43C2311yescharacteristic
70C22×Dic43—21no—
71C2×Dic86C2311yescharacteristic
72C4⋊C4×C43—21no—
73C4⋊C4×C43—21no—
74C4⋊C4×C43—21no—
75C4⋊C4×C43D411yescharacteristic
76C4⋊C4×C43C2311yescharacteristic
77C4⋊C4×C43C2311yescharacteristic
78C4⋊C4×C43C2311yescharacteristic
79C22⋊C4×C43—21no—
80C22⋊C4×C43—21no—
81C22⋊C4×C43—21no—
82C22⋊C4×C43D411yescharacteristic
83C22⋊C4×C43D411yescharacteristic
84C42×C43C2311yescharacteristic
85C22⋊Dic43—21no—
86C22⋊Dic43—21no—
87C22⋊Dic43—21no—
88#10621883—22no—
89C4⋊Dic43—21no—
90C4⋊Dic43C2311yescharacteristic
91C4⋊Dic43C2311yescharacteristic
92C4⋊Dic43C2311yescharacteristic
93Dic43⋊C4—21no—
94Dic43⋊C4—21no—
95Dic43⋊C4—21no—
96Dic43⋊C4—21no—
97Dic43⋊C4—21no—
98C4×Dic43—21no—
99C4×Dic43—21no—
100#10621877—22no—
101C2×C43⋊C8—22no—
102C2×C43⋊C8C2311yescharacteristic
103C2×C43⋊C8C2311yescharacteristic
104C2×C43⋊C8C2311yescharacteristic
105C2×C43⋊C8C2311yescharacteristic
106C23×C43—21no—
107C23×C43C2×D411yescharacteristic
108C23×C43C2×D411yescharacteristic
109Q8×C43—42no—
110D4×C43—22no—
111D4×C43—21no—
112D4×C43—21no—
113D4×C43—42no—
114D4×C43—42no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—42no—
123C2×C4×C43—42no—
124C2×C4×C43—42no—
125C2×C4×C43C2×D411yescharacteristic
126C2×C4×C43C2×D411yescharacteristic
127C2×C4×C43C2×D411yescharacteristic
128C2×C4×C43C2×D411yescharacteristic
129C2×C4×C43C2411yescharacteristic
130C2×Dic43—21no—
131C2×Dic43—21no—
132C2×Dic43—21no—
133C2×Dic43—21no—
134C2×Dic43—42no—
135Dic86—21no—
136Dic86—21no—
137C43⋊C8—21no—
138C43⋊C8—21no—
139C43⋊C8—21no—
140C43⋊C8#4112yescomplemented
141C22×C43—21no—
142C22×C43—21no—
143C22×C43—21no—
144C22×C43—21no—
145C22×C43—21no—
146C22×C43—41no—
147C22×C43—41no—
148C22×C43—41no—
149C22×C43AGL(1,ℤ/8)12yes—
150C22×C43C22×D411yescharacteristic
151C4×C43—21no—
152C4×C43—21no—
153C4×C43—21no—
154C4×C43—21no—
155C4×C43—41no—
156C4×C43—41no—
157C4×C43—41no—
158C4×C43C2×#4111yescharacteristic
159C4×C432−1+411yescharacteristic
160Dic43—41no—
161Dic43—41no—
162Dic43—41no—
163Dic43—41no—
164#3343—431nomaximal, Sylow
165C2×C43—22no—
166C2×C43—41no—
167C2×C43—81no—
168C2×C43#54711yescharacteristic
169C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
170C2×C43#57811yescharacteristic
171#552—431no—
172#547D4311yescharacteristic
173#501—431no—
174#484—431no—
175#483—431no—
176#482—431no—
177#480—431no—
178#478—431no—
179#477—431no—
180#468—431no—
181#465—431no—
182#440—431no—
183#435—431no—
184#428—431no—
185C2×#107—431no—
186C43#334311yescharacteristic, complemented, Sylow
187C2×#41—21no—
188C2×SD16—431no—
189C2×M16—431no—
190C22×C8—431no—
191C4⋊Q8C2×D4311yescharacteristic
192#126—861no—
193#125—431no—
194#125—861no—
195#123—21no—
196#123—21no—
197#123—861no—
198C22⋊Q8—21no—
199C22⋊Q8—431no—
200C22⋊Q8—431no—
201#121C2×D4311yescharacteristic
202#121C2×D4311yescharacteristic
203C4×Q8—431no—
204C4×D4C2×D4311yescharacteristic
205C4×D4C2×D4311yescharacteristic
206#117—431no—
207#117—861no—
208C2×C4⋊C4—431no—
209C2×C4⋊C4C2×D4311yescharacteristic
210C2×C4⋊C4C2×D4311yescharacteristic
211#107—431no—
212#107—431no—
213#107—431no—
214#107—431no—
215#107—431no—
216#107—431no—
217#106—431no—
218#106—431no—
219#106—431no—
220C4⋊C8—431no—
221#103—431no—
222#103—431no—
223#103—431no—
224#102—431no—
225#102—431no—
226#102—431no—
227C22⋊C8—431no—
228C22⋊C8—431no—
229#97—431no—
230#41—44no—
231C2×Q8—21no—
232C2×Q8—431no—
233C2×D4—21no—
234C2×D4—21no—
235C2×D4C22⋊D4311yescharacteristic
236C2×D4C22×D4311yescharacteristic
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—861no—
241C22×C4C22×D4311yescharacteristic
242C22×C4C22×D4311yescharacteristic
243SD16—862no—
244M16—862no—
245C2×C8—431no—
246C2×C8—431no—
247C2×C8—431no—
248C2×C8—431no—
249C2×C8—862no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—431no—
254C4⋊C4—431no—
255C4⋊C4—431no—
256C4⋊C4—861no—
257C4⋊C4—861no—
258C4⋊C4—861no—
259C4⋊C4—861no—
260C4⋊C4—861no—
261C4⋊C4—861no—
262C4⋊C4C22⋊D4311yescharacteristic
263C4⋊C4C22×D4311yescharacteristic
264C4⋊C4C22×D4311yescharacteristic
265C4⋊C4C22×D4311yescharacteristic
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—861no—
270C22⋊C4—861no—
271C22⋊C4—861no—
272C22⋊C4C22⋊D4311yescharacteristic
273C22⋊C4C22⋊D4311yescharacteristic
274C42—861no—
275C42—861no—
276C42C22×D4311yescharacteristic
277C23—21no—
278C23C2×C22⋊D4311yescharacteristic
279C23C2×C22⋊D4311yescharacteristic
280Q8—42no—
281Q8—861no—
282Q8—861no—
283D4—22no—
284D4—21no—
285D4—21no—
286D4—42no—
287D4—42no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—861no—
299C2×C4—861no—
300C2×C4—861no—
301C2×C4—861no—
302C2×C4—1722no—
303C2×C4C2×C22⋊D4311yescharacteristic
304C2×C4C2×C22⋊D4311yescharacteristic
305C2×C4C2×C22⋊D4311yescharacteristic
306C2×C4C2×C22⋊D4311yescharacteristic
307C2×C4C23×D4311yescharacteristic
308C8—432no—
309C8—861no—
310C8—861no—
311C8—861no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—21no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22#1306335112yes—
321C22C22×C22⋊D4311yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—41no—
327C4—41no—
328C4—41no—
329C4—1721no—
330C4—1721no—
331C4—1721no—
332C4—1721no—
333C4#41×D4311yescharacteristic
334C4#1306337211yescharacteristic
335C2—22no—
336C2—41no—
337C2—81no—
338C2#1458354811yescharacteristic
339C2C2×#1306335111yescharacteristic
340C2#1458371411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#547C2
socleC22×C43C22×D4
hypercenter#547D43
hypocenterC43#3343
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. #14583589C2semidirect
2. #14583305C2semidirect
3. #14583234C2semidirect
4. #14583229C2semidirect
5. #14583220C2semidirect
6. #14583210C2semidirect
7. #14583199C2semidirect
8. #14583191C2semidirect
9. #14583143C2semidirect
10. #14583126C2semidirect
11. #14582999C2semidirect
12. #14582971C2semidirect
13. #14582939C2semidirect
14. C2×#13063258C2semidirect
140. C43⋊C8#41semidirect
186. C43#3343semidirect