Finite Group Databasebeta

← #19142250

Subgroups — #19142250

Order 5504.

464 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14582837C211yesmaximal, characteristic, complemented
2#14582834C211yesmaximal, characteristic, complemented
3#14582830C211yesmaximal, characteristic, complemented
4#14582822C211yesmaximal, characteristic, complemented
5#14582821C211yesmaximal, characteristic, complemented
6#14582799C211yesmaximal, characteristic
7#14582794C211yesmaximal, characteristic, complemented
8#14582784C211yesmaximal, characteristic, complemented
9#14582776C211yesmaximal, characteristic
10#14582775C211yesmaximal, characteristic
11#14582771C211yesmaximal, characteristic, complemented
12#14582771C211yesmaximal, characteristic, complemented
13#14582770C211yesmaximal, characteristic, complemented
14#14582758C211yesmaximal, characteristic, complemented
15C43×#396C211yesmaximal, characteristic, complemented
16C22×C22⋊D43C2211yescharacteristic
17C23×Dic43C2211yescharacteristic
18C22×C4×D43C2211yescharacteristic
19C2×C4⋊Dic43C2211yescharacteristic
20C2×Dic43⋊C4C2211yescharacteristic
21C2×Dic43⋊C4C2211yescharacteristic
22C2×Dic43⋊C4C2211yescharacteristic
23C2×Dic43⋊C4C2211yescharacteristic
24C2×Dic43⋊C4C2211yescharacteristic
25C2×Dic43⋊C4C2211yescharacteristic
26C2×Dic43⋊C4C2211yescharacteristic
27C2×C22⋊Dic43C2211yescharacteristic
28C2×C22⋊Dic43C2211yescharacteristic
29C2×(C2×D43)⋊C4C2211yescharacteristic
30C2×(C2×D43)⋊C4C2211yescharacteristic
31C2×(C2×D43)⋊C4C2211yescharacteristic
32C2×(C2×D43)⋊C4C2211yescharacteristic
33C2×(C2×D43)⋊C4C2211yescharacteristic
34C2×C4×Dic43C2211yescharacteristic
35C43⋊#95C2211yescharacteristic
36C43⋊#95C2211yescharacteristic
37C43⋊#95C2211yescharacteristic
38C43⋊#95C2211yescharacteristic
39C43⋊#95C2211yescharacteristic
40C43⋊#95C2211yescharacteristic
41C43⋊#95C2211yescharacteristic
42C43⋊#95C2211yescharacteristic
43C43⋊#95C2211yescharacteristic
44C2×C4⋊C4×C43C2211yescharacteristic
45C2×C4⋊C4×C43C2211yescharacteristic
46C2×C4⋊C4×C43C2211yescharacteristic
47C2×C22⋊C4×C43C2211yescharacteristic
48C2×C22⋊C4×C43C2211yescharacteristic
49C2×C22⋊C4×C43C2211yescharacteristic
50#95×C43C2211yescharacteristic
51C24×C43C2311yescharacteristic
52C23×D43C2311yescharacteristic
53C22×C4×C43C2311yescharacteristic
54C22×C4×C43C2311yescharacteristic
55C22×C4×C43C2311yescharacteristic
56C22×C4×C43C2311yescharacteristic
57C22×C4×C43C2311yescharacteristic
58C22×C4×C43C2311yescharacteristic
59C2×C22⋊D43—41no—
60C2×C22⋊D43—41no—
61C2×C22⋊D43Q814yes—
62C22×Dic43—41no—
63C22×Dic43—41no—
64C22×Dic43—41no—
65C22×Dic43C2311yescharacteristic
66C22×Dic43C2311yescharacteristic
67C22×Dic43C2311yescharacteristic
68C22×Dic43C2311yescharacteristic
69C22×Dic43C2311yescharacteristic
70C22×Dic43C2311yescharacteristic
71C22×Dic43C2311yescharacteristic
72C2×C4×D43—22no—
73C2×C4×D43—41no—
74C2×C4×D43—41no—
75C4⋊C4×C43—41no—
76C4⋊C4×C43—41no—
77C4⋊C4×C43—41no—
78C22⋊C4×C43—41no—
79C22⋊C4×C43—41no—
80C22⋊C4×C43—41no—
81C22⋊Dic43—22no—
82C22⋊Dic43—22no—
83(C2×D43)⋊C4—22no—
84(C2×D43)⋊C4—41no—
85(C2×D43)⋊C4—41no—
86(C2×D43)⋊C4—41no—
87(C2×D43)⋊C4—41no—
88C4⋊Dic43—22no—
89Dic43⋊C4—22no—
90Dic43⋊C4—41no—
91Dic43⋊C4—41no—
92Dic43⋊C4—41no—
93Dic43⋊C4—41no—
94Dic43⋊C4—41no—
95Dic43⋊C4—41no—
96C4×Dic43—41no—
97C23×C43—21no—
98C23×C43—21no—
99C23×C43—21no—
100C23×C43—21no—
101C23×C43—21no—
102C23×C43—21no—
103C23×C43C2×Q812yes—
104C23×C43C2411yescharacteristic
105C22×D43—21no—
106C22×D43—21no—
107C22×D43—21no—
108C22×D43—21no—
109C22×D43—21no—
110C22×D43—21no—
111C22×D43C2×Q812yes—
112C2×C4×C43—21no—
113C2×C4×C43—21no—
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—
130C22⋊D43—44no—
131C2×Dic43—21no—
132C2×Dic43—21no—
133C2×Dic43—21no—
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—44no—
150C2×Dic43C2×Q812yes—
151C2×Dic43#4112yes—
152C2×Dic43#4112yes—
153C4×D43—44no—
154C22×C43—22no—
155C22×C43—22no—
156C22×C43—22no—
157C22×C43—41no—
158C22×C43—41no—
159C22×C43—41no—
160C22×C43—41no—
161C22×C43C22×Q811yescharacteristic
162C22×C43C2×#4111yescharacteristic
163C22×C43C2×#4111yescharacteristic
164C22×C43H(5,𝔽2)11yescharacteristic
165C22×C43H(5,𝔽2)11yescharacteristic
166C22×C43H(5,𝔽2)11yescharacteristic
167C22×C43H(5,𝔽2)11yescharacteristic
168C2×D43—22no—
169C2×D43—22no—
170C2×D43—22no—
171C2×D43—41no—
172C2×D43—41no—
173C2×D43—41no—
174C2×D43—41no—
175C4×C43—41no—
176C4×C43—41no—
177C4×C43—41no—
178C4×C43—41no—
179C4×C43—41no—
180C4×C43—41no—
181Dic43—22no—
182Dic43—22no—
183Dic43—22no—
184Dic43—41no—
185Dic43—41no—
186Dic43—41no—
187Dic43—41no—
188#2780—431nomaximal, Sylow
189C2×C43—42no—
190C2×C43#53811yescharacteristic
191C2×C43#54011yescharacteristic
192C2×C43#54311yescharacteristic
193C2×C43#55311yescharacteristic
194C2×C43#55411yescharacteristic
195C2×C43#55411yescharacteristic
196C2×C43#56011yescharacteristic
197D43—42no—
198#400—431no—
199#399—431no—
200#398—431no—
201#396—431no—
202#396—431no—
203#396D4311yescharacteristic, complemented
204#390—431no—
205#389—431no—
206#387—431no—
207#386—431no—
208#386—431no—
209#385—431no—
210#385—431no—
211#385—431no—
212#380—431no—
213C43#278011yescharacteristic, complemented, Sylow
214C22×D4—431no—
215C23×C4—431no—
216C23×C4—431no—
217C2×C4⋊C4—431no—
218C2×C4⋊C4—431no—
219C2×C4⋊C4—431no—
220C2×C4⋊C4—431no—
221C2×C4⋊C4—431no—
222C2×C4⋊C4—431no—
223C2×C4⋊C4—431no—
224C2×C4⋊C4—431no—
225C2×C4⋊C4C2×D4311yescharacteristic
226C2×C4⋊C4C2×D4311yescharacteristic
227C2×C4⋊C4C2×D4311yescharacteristic
228C2×C22⋊C4—431no—
229C2×C22⋊C4—431no—
230C2×C22⋊C4—431no—
231C2×C22⋊C4—431no—
232C2×C22⋊C4—431no—
233C2×C22⋊C4—431no—
234C2×C22⋊C4—431no—
235C2×C22⋊C4C2×D4311yescharacteristic
236C2×C22⋊C4C2×D4311yescharacteristic
237C2×C22⋊C4C2×D4311yescharacteristic
238C2×C42—431no—
239#95—431no—
240#95—431no—
241#95—431no—
242#95—431no—
243#95—431no—
244#95—431no—
245#95—431no—
246#95—431no—
247#95—431no—
248#95C2×D4311yescharacteristic
249C24—431no—
250C24C22×D4311yescharacteristic
251C2×D4—434no—
252C2×D4—1721no—
253C2×D4—1721no—
254C22×C4—431no—
255C22×C4—431no—
256C22×C4—431no—
257C22×C4—431no—
258C22×C4—431no—
259C22×C4—431no—
260C22×C4—431no—
261C22×C4—862no—
262C22×C4—1721no—
263C22×C4—1721no—
264C22×C4—1721no—
265C22×C4—1721no—
266C22×C4—1721no—
267C22×C4C22×D4311yescharacteristic
268C22×C4C22×D4311yescharacteristic
269C22×C4C22×D4311yescharacteristic
270C22×C4C22×D4311yescharacteristic
271C22×C4C22×D4311yescharacteristic
272C22×C4C22×D4311yescharacteristic
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—862no—
277C4⋊C4—862no—
278C4⋊C4—1721no—
279C4⋊C4—1721no—
280C4⋊C4—1721no—
281C4⋊C4—1721no—
282C4⋊C4—1721no—
283C4⋊C4—1721no—
284C22⋊C4—41no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C22⋊C4—862no—
288C22⋊C4—862no—
289C22⋊C4—862no—
290C22⋊C4—1721no—
291C22⋊C4—1721no—
292C22⋊C4—1721no—
293C22⋊C4—1721no—
294C42—1721no—
295C23—21no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—432no—
302C23—861no—
303C23—861no—
304C23—861no—
305C23—861no—
306C23—861no—
307C23—861no—
308C23Q8×D4312yes—
309C23C23×D4311yescharacteristic
310D4—1724no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
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—432no—
330C2×C4—432no—
331C2×C4—432no—
332C2×C4—861no—
333C2×C4—861no—
334C2×C4—861no—
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—1724no—
351C2×C4—1724no—
352C22—22no—
353C22—22no—
354C22—22no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—862no—
360C22—862no—
361C22—862no—
362C22—1721no—
363C22—1721no—
364C22—1721no—
365C22—1721no—
366C22C2×Q8×D4311yescharacteristic
367C22#41×D4311yescharacteristic
368C22#41×D4311yescharacteristic
369C22#1306337011yescharacteristic
370C22#1306337011yescharacteristic
371C22#1306337011yescharacteristic
372C22#1306337111yescharacteristic
373C4—41no—
374C4—41no—
375C4—41no—
376C4—41no—
377C4—41no—
378C4—41no—
379C4—862no—
380C4—862no—
381C4—862no—
382C4—1721no—
383C4—1721no—
384C4—1721no—
385C4—1721no—
386C2—42no—
387C2—1722no—
388C2#1458348111yescharacteristic
389C2#1458349911yescharacteristic
390C2#1458352411yescharacteristic
391C2#1458360011yescharacteristic
392C2#1458360311yescharacteristic
393C2#1458360311yescharacteristic
394C2#1458363711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#396C2
hypercenter#396D43
hypocenterC43#2780
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #396

Complements

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

NH ≅ G/Ntype
1. #14582837C2semidirect
2. #14582834C2semidirect
3. #14582830C2semidirect
4. #14582822C2semidirect
5. #14582821C2semidirect
7. #14582794C2semidirect
8. #14582784C2semidirect
11. #14582771C2semidirect
12. #14582771C2semidirect
13. #14582770C2semidirect
14. #14582758C2semidirect
15. C43×#396C2semidirect
203. #396D43semidirect
213. C43#2780semidirect