Finite Group Databasebeta

← #19141127

Subgroups — #19141127

Order 5504.

504 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13063318C211yesmaximal, characteristic, complemented
2C2×#13063307C211yesmaximal, characteristic
3#14582841C211yesmaximal, characteristic, complemented
4#14582833C211yesmaximal, characteristic, complemented
5#14582832C211yesmaximal, characteristic, complemented
6#14582827C211yesmaximal, characteristic, complemented
7#14582821C211yesmaximal, characteristic, complemented
8#14582814C211yesmaximal, characteristic
9#14582794C211yesmaximal, characteristic, complemented
10#14582788C211yesmaximal, characteristic, complemented
11#14582778C211yesmaximal, characteristic
12#14582772C211yesmaximal, characteristic, complemented
13#14582770C211yesmaximal, characteristic, complemented
14#14582758C211yesmaximal, characteristic, complemented
15C43×#380C211yesmaximal, characteristic, complemented
16C22×C22⋊D43C2211yescharacteristic
17C22×C4×D43C2211yescharacteristic
18#13063318—24no—
19#13063307—24no—
20C2×C4⋊Dic43C2211yescharacteristic
21C2×C4⋊Dic43C2211yescharacteristic
22C2×Dic43⋊C4C2211yescharacteristic
23C2×Dic43⋊C4C2211yescharacteristic
24C2×Dic43⋊C4C2211yescharacteristic
25C2×Dic43⋊C4C2211yescharacteristic
26C2×Dic43⋊C4C2211yescharacteristic
27C2×Dic43⋊C4C2211yescharacteristic
28C2×Dic43⋊C4C2211yescharacteristic
29C2×C22⋊Dic43C2211yescharacteristic
30C2×C22⋊Dic43C2211yescharacteristic
31C2×C22⋊Dic43C2211yescharacteristic
32C2×(C2×D43)⋊C4C2211yescharacteristic
33C2×(C2×D43)⋊C4C2211yescharacteristic
34C2×(C2×D43)⋊C4C2211yescharacteristic
35C2×(C2×D43)⋊C4C2211yescharacteristic
36C2×(C2×D43)⋊C4C2211yescharacteristic
37C2×C4×Dic43C2211yescharacteristic
38C43⋊#95C2211yescharacteristic
39C43⋊#95C2211yescharacteristic
40C43⋊#95C2211yescharacteristic
41C43⋊#95C2211yescharacteristic
42C43⋊#95C2211yescharacteristic
43C43⋊#95C2211yescharacteristic
44C43⋊#95C2211yescharacteristic
45C43⋊#95C2211yescharacteristic
46C23×C4×C43C2211yescharacteristic
47C2×C4⋊C4×C43C2211yescharacteristic
48C2×C4⋊C4×C43C2211yescharacteristic
49C2×C22⋊C4×C43C2211yescharacteristic
50C2×C22⋊C4×C43C2211yescharacteristic
51#95×C43C2211yescharacteristic
52#95×C43C2211yescharacteristic
53C24×C43C2311yescharacteristic
54C23×D43C2311yescharacteristic
55C22×C4×C43—22no—
56C22×C4×C43—41no—
57C22×C4×C43—41no—
58C22×C4×C43C2311yescharacteristic
59C22×C4×C43C2311yescharacteristic
60C22×C4×C43C2311yescharacteristic
61C22×C4×C43C2311yescharacteristic
62C22×C4×C43C2311yescharacteristic
63C22×C4×C43C2311yescharacteristic
64C2×C22⋊D43—22no—
65C2×C22⋊D43—22no—
66C2×C22⋊D43—41no—
67C22×Dic43C2311yescharacteristic
68C22×Dic43C2311yescharacteristic
69C22×Dic43C2311yescharacteristic
70C22×Dic43C2311yescharacteristic
71C22×Dic43C2311yescharacteristic
72C22×Dic43C2311yescharacteristic
73C22×Dic43C2311yescharacteristic
74C2×C4×D43—22no—
75C2×C4×D43—22no—
76C2×C4×D43—41no—
77C4⋊C4×C43—41no—
78C4⋊C4×C43—41no—
79C22⋊C4×C43—22no—
80C22⋊C4×C43—22no—
81C22⋊Dic43—22no—
82C22⋊Dic43—41no—
83C22⋊Dic43D414yes—
84(C2×D43)⋊C4—22no—
85(C2×D43)⋊C4—22no—
86(C2×D43)⋊C4—22no—
87(C2×D43)⋊C4—41no—
88(C2×D43)⋊C4—41no—
89C4⋊Dic43—22no—
90C4⋊Dic43—22no—
91Dic43⋊C4—22no—
92Dic43⋊C4—22no—
93Dic43⋊C4—22no—
94Dic43⋊C4—22no—
95Dic43⋊C4—41no—
96Dic43⋊C4—41no—
97Dic43⋊C4—41no—
98C4×Dic43—22no—
99C23×C43—21no—
100C23×C43—21no—
101C23×C43—21no—
102C23×C43—21no—
103C23×C43—21no—
104C23×C43—21no—
105C23×C43C2×D412yes—
106C23×C43C2411yescharacteristic
107C22×D43—21no—
108C22×D43—21no—
109C22×D43—21no—
110C22×D43—21no—
111C22×D43—21no—
112C22×D43—21no—
113C22×D43#4112yes—
114C2×C4×C43—21no—
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—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—21no—
131C2×C4×C43—44no—
132C2×C4×C43#4112yes—
133C22⋊D43—44no—
134C2×Dic43—21no—
135C2×Dic43—21no—
136C2×Dic43—21no—
137C2×Dic43—21no—
138C2×Dic43—21no—
139C2×Dic43—21no—
140C2×Dic43—21no—
141C2×Dic43—21no—
142C2×Dic43—21no—
143C2×Dic43—21no—
144C2×Dic43—21no—
145C2×Dic43—21no—
146C2×Dic43—21no—
147C2×Dic43—21no—
148C2×Dic43—21no—
149C2×Dic43—21no—
150C2×Dic43—21no—
151C2×Dic43—21no—
152C2×Dic43—21no—
153C2×Dic43C2×D412yes—
154C2×Dic43C2×D412yes—
155C4×D43—44no—
156C22×C43—22no—
157C22×C43—22no—
158C22×C43—22no—
159C22×C43—41no—
160C22×C43—41no—
161C22×C43—41no—
162C22×C43—41no—
163C22×C43C22×D411yescharacteristic
164C22×C43C2×#4111yescharacteristic
165C22×C43C2×#4111yescharacteristic
166C22×C43H(5,𝔽2)11yescharacteristic
167C22×C43H(5,𝔽2)11yescharacteristic
168C22×C432−1+411yescharacteristic
169C22×C432−1+411yescharacteristic
170C2×D43—22no—
171C2×D43—22no—
172C2×D43—22no—
173C2×D43—41no—
174C2×D43—41no—
175C2×D43—41no—
176C2×D43—41no—
177C4×C43—22no—
178C4×C43—41no—
179C4×C43—41no—
180C4×C43—41no—
181C4×C43—41no—
182C4×C43—41no—
183Dic43—22no—
184Dic43—22no—
185Dic43—41no—
186Dic43—41no—
187Dic43—41no—
188Dic43—41no—
189Dic43—41no—
190#2695—431nomaximal, Sylow
191C2×C43—42no—
192C2×C43#53711yescharacteristic
193C2×C43#53811yescharacteristic
194C2×C43#53911yescharacteristic
195C2×C43#54611yescharacteristic
196C2×C43#54711yescharacteristic
197C2×C43#55211yescharacteristic
198C2×C43#56311yescharacteristic
199D43—42no—
200C2×#126—431no—
201C2×#123—431no—
202#400—431no—
203#398—431no—
204#398—431no—
205#397—431no—
206#396—431no—
207#394—431no—
208#389—431no—
209#388—431no—
210#386—431no—
211#385—431no—
212#385—431no—
213#380—431no—
214#380D4311yescharacteristic, complemented
215C43#269511yescharacteristic, complemented, Sylow
216C22×D4—431no—
217C23×C4—431no—
218C23×C4C2×D4311yescharacteristic
219#126—864no—
220#123—864no—
221C2×C4⋊C4—431no—
222C2×C4⋊C4—431no—
223C2×C4⋊C4—431no—
224C2×C4⋊C4—431no—
225C2×C4⋊C4—431no—
226C2×C4⋊C4—431no—
227C2×C4⋊C4—431no—
228C2×C4⋊C4—431no—
229C2×C4⋊C4—431no—
230C2×C4⋊C4C2×D4311yescharacteristic
231C2×C4⋊C4C2×D4311yescharacteristic
232C2×C22⋊C4—431no—
233C2×C22⋊C4—431no—
234C2×C22⋊C4—431no—
235C2×C22⋊C4—431no—
236C2×C22⋊C4—431no—
237C2×C22⋊C4—431no—
238C2×C22⋊C4—431no—
239C2×C22⋊C4—431no—
240C2×C22⋊C4C2×D4311yescharacteristic
241C2×C22⋊C4C2×D4311yescharacteristic
242C2×C42—431no—
243#95—431no—
244#95—431no—
245#95—431no—
246#95—431no—
247#95—431no—
248#95—431no—
249#95—431no—
250#95—431no—
251#95C2×D4311yescharacteristic
252#95C2×D4311yescharacteristic
253C24—431no—
254C24C22×D4311yescharacteristic
255C2×D4—862no—
256C2×D4—862no—
257C2×D4—1721no—
258C22×C4—22no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4—431no—
262C22×C4—431no—
263C22×C4—431no—
264C22×C4—431no—
265C22×C4—431no—
266C22×C4—431no—
267C22×C4—431no—
268C22×C4—862no—
269C22×C4—862no—
270C22×C4—1721no—
271C22×C4C22×D4311yescharacteristic
272C22×C4C22×D4311yescharacteristic
273C22×C4C22×D4311yescharacteristic
274C22×C4C22×D4311yescharacteristic
275C22×C4C22×D4311yescharacteristic
276C22×C4C22×D4311yescharacteristic
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—862no—
280C4⋊C4—862no—
281C4⋊C4—862no—
282C4⋊C4—862no—
283C4⋊C4—862no—
284C4⋊C4—862no—
285C4⋊C4—1721no—
286C4⋊C4—1721no—
287C4⋊C4—1721no—
288C22⋊C4—22no—
289C22⋊C4—22no—
290C22⋊C4—434no—
291C22⋊C4—862no—
292C22⋊C4—862no—
293C22⋊C4—862no—
294C22⋊C4—862no—
295C22⋊C4—1721no—
296C22⋊C4—1721no—
297C22⋊C4—1721no—
298C42—862no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—432no—
306C23—861no—
307C23—861no—
308C23—861no—
309C23—861no—
310C23—861no—
311C23—861no—
312C23D4×D4312yes—
313C23C23×D4311yescharacteristic
314D4—1724no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—44no—
333C2×C4—432no—
334C2×C4—432no—
335C2×C4—861no—
336C2×C4—861no—
337C2×C4—861no—
338C2×C4—861no—
339C2×C4—861no—
340C2×C4—861no—
341C2×C4—861no—
342C2×C4—861no—
343C2×C4—861no—
344C2×C4—861no—
345C2×C4—861no—
346C2×C4—861no—
347C2×C4—861no—
348C2×C4—861no—
349C2×C4—861no—
350C2×C4—861no—
351C2×C4—861no—
352C2×C4—861no—
353C2×C4—861no—
354C2×C4—1724no—
355C2×C4#1062189812yes—
356C22—22no—
357C22—22no—
358C22—22no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—862no—
364C22—862no—
365C22—862no—
366C22—1721no—
367C22—1721no—
368C22—1721no—
369C22—1721no—
370C22C2×D4×D4311yescharacteristic
371C22#41×D4311yescharacteristic
372C22C2×#1062189811yescharacteristic
373C22#1306337011yescharacteristic
374C22#1306337011yescharacteristic
375C22#1306337211yescharacteristic
376C22#1306337311yescharacteristic
377C4—22no—
378C4—41no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—41no—
383C4—862no—
384C4—862no—
385C4—1721no—
386C4—1721no—
387C4—1721no—
388C4—1721no—
389C4—1721no—
390C2—42no—
391C2—1722no—
392C2#1458347611yescharacteristic
393C2#1458348711yescharacteristic
394C2#1458349511yescharacteristic
395C2#1458353811yescharacteristic
396C2#1458355011yescharacteristic
397C2#1458358811yescharacteristic
398C2#1458365011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#380C2
hypercenter#380D43
hypocenterC43#2695
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
1. C2×#13063318C2semidirect
3. #14582841C2semidirect
4. #14582833C2semidirect
5. #14582832C2semidirect
6. #14582827C2semidirect
7. #14582821C2semidirect
9. #14582794C2semidirect
10. #14582788C2semidirect
12. #14582772C2semidirect
13. #14582770C2semidirect
14. #14582758C2semidirect
15. C43×#380C2semidirect
214. #380D43semidirect
215. C43#2695semidirect