Finite Group Databasebeta

← #19145676

Subgroups — #19145676

Order 5504.

364 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583509C211yesmaximal, characteristic, complemented
2#14583470C211yesmaximal, characteristic
3#14583290C211yesmaximal, characteristic, complemented
4#14583277C211yesmaximal, characteristic, complemented
5#14583266C211yesmaximal, characteristic, complemented
6#14583252C211yesmaximal, characteristic, complemented
7#14583120C211yesmaximal, characteristic, complemented
8#14583119C211yesmaximal, characteristic, complemented
9#14583108C211yesmaximal, characteristic, complemented
10#14583107C211yesmaximal, characteristic, complemented
11#14583061C211yesmaximal, characteristic
12#14583057C211yesmaximal, characteristic, complemented
13#14583054C211yesmaximal, characteristic, complemented
14#14582957C211yesmaximal, characteristic, complemented
15C43×#452C211yesmaximal, characteristic
16C22×Dic86C2211yescharacteristic
17C2×Dic172C2211yescharacteristic
18C2×Dic172C2211yescharacteristic
19C2×#10621885C2211yescharacteristic
20C2×#10621885C2211yescharacteristic
21C2×#10621885C2211yescharacteristic
22C2×#10621883C2211yescharacteristic
23#13063323C2211yescharacteristic
24#13063323C2211yescharacteristic
25#13063323C2211yescharacteristic
26#13063318—21no—
27#13063318—21no—
28#13063316—21no—
29#13063316C2211yescharacteristic
30#13063315—21no—
31#13063312C2211yescharacteristic
32#13063312C2211yescharacteristic
33#13063306—21no—
34#13063306—21no—
35#13063304—21no—
36#13063304—21no—
37#13063304C2211yescharacteristic
38Q8×Dic43C2211yescharacteristic
39#13063290C2211yescharacteristic
40#13063284C2211yescharacteristic
41Dic43⋊C8C2211yescharacteristic
42Dic43⋊C8C2211yescharacteristic
43#13063250C2211yescharacteristic
44#13063250C2211yescharacteristic
45#13063249C2211yescharacteristic
46#13063248C2211yescharacteristic
47#13063248C2211yescharacteristic
48#13063246C2211yescharacteristic
49C22⋊(C43⋊C8)C2211yescharacteristic
50#13063235C2211yescharacteristic
51C8×Dic43C2211yescharacteristic
52C2×#41×C43C2211yescharacteristic
53C2×Q16×C43C2211yescharacteristic
54C2×SD16×C43C2211yescharacteristic
55C22⋊Q8×C43C2211yescharacteristic
56#103×C43C2211yescharacteristic
57#102×C43C2211yescharacteristic
58C22⋊C8×C43C2211yescharacteristic
59#41×C43—41no—
60#41×C43—41no—
61C2×Q8×C43C2311yescharacteristic
62C2×Q8×C43C2311yescharacteristic
63C2×D4×C43—21no—
64C2×D4×C43C2311yescharacteristic
65C22×C4×C43—21no—
66C22×C4×C43C2311yescharacteristic
67C22×Dic43—21no—
68C2×Dic86—21no—
69C2×Dic86—41no—
70C2×Dic86—41no—
71C2×Dic86C2311yescharacteristic
72C2×Dic86C2311yescharacteristic
73C2×Dic86C2311yescharacteristic
74Q16×C43—41no—
75SD16×C43—41no—
76C2×C8×C43C2311yescharacteristic
77C2×C8×C43C2311yescharacteristic
78C4⋊C4×C43—21no—
79C4⋊C4×C43C2311yescharacteristic
80C22⋊C4×C43—21no—
81C22⋊Dic43—21no—
82C22⋊Dic43—21no—
83C22⋊Dic43—21no—
84C22⋊Dic43—21no—
85C22⋊Dic43—21no—
86C22⋊Dic43D411yescharacteristic
87C22⋊Dic43D411yescharacteristic
88#10621885—41no—
89#10621885—41no—
90#10621885—41no—
91#10621883—41no—
92C4⋊Dic43—21no—
93C4⋊Dic43—21no—
94C4⋊Dic43D411yescharacteristic
95C4⋊Dic43D411yescharacteristic
96C4⋊Dic43C2311yescharacteristic
97Dic43⋊C4—21no—
98Dic43⋊C4—21no—
99Dic43⋊C4—21no—
100Dic43⋊C4—21no—
101Dic43⋊C4—21no—
102Dic43⋊C4—21no—
103Dic43⋊C4—21no—
104Dic43⋊C4—21no—
105Dic43⋊C4—21no—
106C4×Dic43—21no—
107C4×Dic43—21no—
108C4×Dic43C2311yescharacteristic
109C4×Dic43C2311yescharacteristic
110C2×C43⋊C8C2311yescharacteristic
111C2×C43⋊C8C2311yescharacteristic
112Dic172—41no—
113Dic172—41no—
114C23×C43—21no—
115C23×C43C2×D411yescharacteristic
116Q8×C43—21no—
117Q8×C43—21no—
118Q8×C43—21no—
119Q8×C43—21no—
120D4×C43—21no—
121D4×C43—21no—
122D4×C43—42no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43—42no—
129C2×C4×C43C2×D411yescharacteristic
130C2×C4×C43C2411yescharacteristic
131C2×Dic43—21no—
132C2×Dic43—21no—
133C2×Dic43—21no—
134C2×Dic43—21no—
135C2×Dic43—42no—
136C2×Dic43C2×D411yescharacteristic
137C2×Dic43C2×D411yescharacteristic
138C2×Dic43C2×D411yescharacteristic
139C2×Dic43C2×D411yescharacteristic
140Dic86—21no—
141Dic86—21no—
142Dic86—21no—
143Dic86—21no—
144Dic86—21no—
145Dic86—21no—
146Dic86—42no—
147C8×C43—21no—
148C8×C43—21no—
149C43⋊C8—21no—
150C43⋊C8—21no—
151C22×C43—21no—
152C22×C43—21no—
153C22×C43—21no—
154C22×C43—41no—
155C22×C43—41no—
156C22×C43—41no—
157C22×C43C22×D411yescharacteristic
158C4×C43—21no—
159C4×C43—41no—
160C4×C43—41no—
161C4×C43—41no—
162C4×C43H(5,𝔽2)11yescharacteristic
163C4×C43H(5,𝔽2)11yescharacteristic
164Dic43—21no—
165Dic43—21no—
166Dic43—21no—
167Dic43—21no—
168Dic43—41no—
169Dic43—41no—
170Dic43—41no—
171Dic43—41no—
172#3223—431nomaximal, Sylow
173C2×C43—41no—
174C2×C43—81no—
175C2×C43#53511yescharacteristic
176C2×C43#57811yescharacteristic
177C2×C43#57811yescharacteristic
178#541—431no—
179#536—431no—
180#497—431no—
181#494—431no—
182#491—431no—
183#488—431no—
184#464—431no—
185#464—431no—
186#462—431no—
187#462—431no—
188#452—431no—
189#452D4311yescharacteristic
190#451—431no—
191#451—431no—
192#433—431no—
193C43#322311yescharacteristic, complemented, Sylow
194C2×#41C2×D4311yescharacteristic
195C22×Q8—431no—
196C2×Q16—431no—
197C2×Q16—431no—
198C2×Q16—431no—
199C2×Q16—431no—
200C2×Q16—431no—
201C2×Q16C2×D4311yescharacteristic
202C2×SD16—431no—
203C2×SD16C2×D4311yescharacteristic
204C4⋊Q8—431no—
205C4⋊Q8—431no—
206C4⋊Q8—431no—
207#126—861no—
208#126—861no—
209#125—431no—
210#125—861no—
211#125—861no—
212#124—431no—
213#124—431no—
214#123—861no—
215#123—861no—
216C22⋊Q8—431no—
217C22⋊Q8—861no—
218C22⋊Q8—861no—
219C22⋊Q8C2×D4311yescharacteristic
220C4×Q8—431no—
221C4×Q8—431no—
222#117—431no—
223C4⋊C8—431no—
224C4⋊C8—431no—
225#103—431no—
226#103—431no—
227#103—431no—
228#103—431no—
229#103—431no—
230#103C2×D4311yescharacteristic
231#102—431no—
232#102C2×D4311yescharacteristic
233C22⋊C8—431no—
234C22⋊C8C2×D4311yescharacteristic
235#97—431no—
236C4×C8—431no—
237#41—41no—
238#41—41no—
239C2×Q8—431no—
240C2×Q8—431no—
241C2×Q8—431no—
242C2×Q8—861no—
243C2×Q8—1721no—
244C2×Q8—1721no—
245C2×Q8C22×D4311yescharacteristic
246C2×Q8C22×D4311yescharacteristic
247C2×D4—21no—
248C2×D4C22×D4311yescharacteristic
249C22×C4—21no—
250C22×C4—861no—
251C22×C4C22×D4311yescharacteristic
252Q16—41no—
253Q16—1721no—
254Q16—1721no—
255Q16—1721no—
256Q16—1721no—
257Q16—1721no—
258SD16—41no—
259SD16—1721no—
260C2×C8—431no—
261C2×C8—431no—
262C2×C8C22×D4311yescharacteristic
263C2×C8C22×D4311yescharacteristic
264C4⋊C4—21no—
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⋊C4—861no—
279C4⋊C4C22×D4311yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—431no—
282C22⋊C4—431no—
283C22⋊C4—861no—
284C22⋊C4—861no—
285C22⋊C4—861no—
286C22⋊C4—861no—
287C22⋊C4—861no—
288C42—431no—
289C42—431no—
290C42—861no—
291C42—861no—
292C23—21no—
293C23D4×D4311yescharacteristic
294Q8—21no—
295Q8—21no—
296Q8—21no—
297Q8—21no—
298Q8—861no—
299Q8—861no—
300Q8—861no—
301Q8—861no—
302Q8—861no—
303Q8—861no—
304Q8—1722no—
305D4—21no—
306D4—21no—
307D4—42no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—42no—
314C2×C4—431no—
315C2×C4—431no—
316C2×C4—431no—
317C2×C4—431no—
318C2×C4—861no—
319C2×C4—861no—
320C2×C4—861no—
321C2×C4—861no—
322C2×C4—1722no—
323C2×C4D4×D4311yescharacteristic
324C2×C4C23×D4311yescharacteristic
325C8—21no—
326C8—21no—
327C8—861no—
328C8—861no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22C2×D4×D4311yescharacteristic
336C4—21no—
337C4—41no—
338C4—41no—
339C4—41no—
340C4—861no—
341C4—861no—
342C4—861no—
343C4—861no—
344C4—1721no—
345C4—1721no—
346C4—1721no—
347C4—1721no—
348C4#1306337011yescharacteristic
349C4#1306337011yescharacteristic
350C2—41no—
351C2—81no—
352C2#1458346411yescharacteristic
353C2#1458371311yescharacteristic
354C2#1458371511yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#452C2
socleC22×C43C22×D4
hypercenter#452D43
hypocenterC43#3223
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. #14583509C2semidirect
3. #14583290C2semidirect
4. #14583277C2semidirect
5. #14583266C2semidirect
6. #14583252C2semidirect
7. #14583120C2semidirect
8. #14583119C2semidirect
9. #14583108C2semidirect
10. #14583107C2semidirect
12. #14583057C2semidirect
13. #14583054C2semidirect
14. #14582957C2semidirect
193. C43#3223semidirect