Finite Group Databasebeta

← #19141553

Subgroups — #19141553

Order 5504.

476 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
1C2×#13063320C211yesmaximal, characteristic, complemented
2#14582835C211yesmaximal, characteristic, complemented
3#14582834C211yesmaximal, characteristic, complemented
4#14582822C211yesmaximal, characteristic, complemented
5#14582821C211yesmaximal, characteristic, complemented
6#14582815C211yesmaximal, characteristic
7#14582815C211yesmaximal, characteristic
8#14582799C211yesmaximal, characteristic
9#14582798C211yesmaximal, characteristic, complemented
10#14582797C211yesmaximal, characteristic, complemented
11#14582795C211yesmaximal, characteristic, complemented
12#14582794C211yesmaximal, characteristic, complemented
13#14582790C211yesmaximal, characteristic, complemented
14#14582787C211yesmaximal, characteristic, complemented
15C2×#126×C43C211yesmaximal, characteristic, complemented
16C22×C22⋊D43C2211yescharacteristic
17#13063320—24no—
18C2×C4⋊Dic43C2211yescharacteristic
19C2×C4⋊Dic43C2211yescharacteristic
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×C22⋊Dic43C2211yescharacteristic
29C2×C22⋊Dic43C2211yescharacteristic
30C2×C22⋊Dic43C2211yescharacteristic
31C2×(C2×D43)⋊C4C2211yescharacteristic
32C2×(C2×D43)⋊C4C2211yescharacteristic
33C2×(C2×D43)⋊C4C2211yescharacteristic
34C2×(C2×D43)⋊C4C2211yescharacteristic
35C2×(C2×D43)⋊C4C2211yescharacteristic
36C2×(C2×D43)⋊C4C2211yescharacteristic
37C2×C4×Dic43C2211yescharacteristic
38C2×C4×Dic43C2211yescharacteristic
39C43⋊#95C2211yescharacteristic
40C43⋊#95C2211yescharacteristic
41C43⋊#95C2211yescharacteristic
42C43⋊#95C2211yescharacteristic
43C43⋊#95C2211yescharacteristic
44C43⋊#95C2211yescharacteristic
45#126×C43—24no—
46C2×C4⋊C4×C43C2211yescharacteristic
47C2×C4⋊C4×C43C2211yescharacteristic
48C2×C4⋊C4×C43C2211yescharacteristic
49C2×C22⋊C4×C43C2211yescharacteristic
50C2×C22⋊C4×C43C2211yescharacteristic
51C2×C22⋊C4×C43C2211yescharacteristic
52C2×C42×C43C2211yescharacteristic
53C24×C43C2311yescharacteristic
54C23×D43C2311yescharacteristic
55C22×C4×C43C2311yescharacteristic
56C22×C4×C43C2311yescharacteristic
57C22×C4×C43C2311yescharacteristic
58C22×C4×C43C2311yescharacteristic
59C22×C4×C43C2311yescharacteristic
60C22×C4×C43C2311yescharacteristic
61C2×C22⋊D43—22no—
62C2×C22⋊D43—41no—
63C2×C22⋊D43—41no—
64C22×Dic43C2311yescharacteristic
65C22×Dic43C2311yescharacteristic
66C22×Dic43C2311yescharacteristic
67C22×Dic43C2311yescharacteristic
68C22×Dic43C2311yescharacteristic
69C22×Dic43C2311yescharacteristic
70C22×Dic43C2311yescharacteristic
71C4⋊C4×C43—22no—
72C4⋊C4×C43—22no—
73C4⋊C4×C43D414yescomplemented
74C22⋊C4×C43—22no—
75C22⋊C4×C43—22no—
76C22⋊C4×C43—22no—
77C42×C43—22no—
78C22⋊Dic43—22no—
79C22⋊Dic43—41no—
80C22⋊Dic43—41no—
81(C2×D43)⋊C4—22no—
82(C2×D43)⋊C4—22no—
83(C2×D43)⋊C4—22no—
84(C2×D43)⋊C4—22no—
85(C2×D43)⋊C4—41no—
86(C2×D43)⋊C4—41no—
87C4⋊Dic43—22no—
88C4⋊Dic43—22no—
89C4⋊Dic43—22no—
90C4⋊Dic43—41no—
91Dic43⋊C4—22no—
92Dic43⋊C4—22no—
93Dic43⋊C4—41no—
94Dic43⋊C4—41no—
95Dic43⋊C4—41no—
96Dic43⋊C4—41no—
97C4×Dic43—22no—
98C4×Dic43—41no—
99C23×C43—21no—
100C23×C43—21no—
101C23×C43—21no—
102C23×C43—21no—
103C23×C43—21no—
104C23×C43—21no—
105C23×C43—21no—
106C23×C43C2411yescharacteristic
107C22×D43—21no—
108C22×D43—21no—
109C22×D43—21no—
110C22×D43—21no—
111C22×D43—21no—
112C22×D43—21no—
113C22×D43—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×C43C2×D412yes—
130C2×C4×C43C2×D412yes—
131C2×C4×C43C2×D412yes—
132C22⋊D43—44no—
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—21no—
150C2×Dic43—21no—
151C2×Dic43—21no—
152C2×Dic43#4112yes—
153C2×Dic43#4112yes—
154C22×C43—41no—
155C22×C43—41no—
156C22×C43—41no—
157C22×C43—41no—
158C22×C43—41no—
159C22×C43—41no—
160C22×C43—41no—
161C22×C43C22×D411yescharacteristic
162C22×C43C2×#4111yescharacteristic
163C22×C43C2×#4111yescharacteristic
164C22×C43H(5,𝔽2)11yescharacteristic
165C22×C43H(5,𝔽2)11yescharacteristic
166C22×C432−1+411yescharacteristic
167C22×C432−1+411yescharacteristic
168C2×D43—41no—
169C2×D43—41no—
170C2×D43—41no—
171C2×D43—41no—
172C2×D43—41no—
173C2×D43—41no—
174C2×D43—41no—
175C4×C43—22no—
176C4×C43—22no—
177C4×C43—22no—
178C4×C43—41no—
179C4×C43—41no—
180C4×C43—41no—
181Dic43—22no—
182Dic43—22no—
183Dic43—41no—
184Dic43—41no—
185Dic43—41no—
186Dic43—41no—
187Dic43—41no—
188#2727—431nomaximal, Sylow
189C2×C43—81no—
190C2×C43#53711yescharacteristic
191C2×C43#53811yescharacteristic
192C2×C43#53911yescharacteristic
193C2×C43#54711yescharacteristic
194C2×C43#55011yescharacteristic
195C2×C43#55611yescharacteristic
196C2×C43#56311yescharacteristic
197D43—81no—
198C2×#126—431no—
199C2×#126D4311yescharacteristic, complemented
200#399—431no—
201#399—431no—
202#396—431no—
203#396—431no—
204#394—431no—
205#394—431no—
206#390—431no—
207#389—431no—
208#389—431no—
209#389—431no—
210#389—431no—
211#388—431no—
212#388—431no—
213C43#272711yescharacteristic, complemented, Sylow
214C22×D4—431no—
215#126—24no—
216#126—864no—
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⋊C4—431no—
226C2×C4⋊C4—431no—
227C2×C4⋊C4C2×D4311yescharacteristic
228C2×C4⋊C4C2×D4311yescharacteristic
229C2×C4⋊C4C2×D4311yescharacteristic
230C2×C22⋊C4—431no—
231C2×C22⋊C4—431no—
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⋊C4C2×D4311yescharacteristic
240C2×C22⋊C4C2×D4311yescharacteristic
241C2×C22⋊C4C2×D4311yescharacteristic
242C2×C42—431no—
243C2×C42—431no—
244C2×C42C2×D4311yescharacteristic
245#95—431no—
246#95—431no—
247#95—431no—
248#95—431no—
249#95—431no—
250#95—431no—
251C24—431no—
252C24C22×D4311yescharacteristic
253C2×D4—862no—
254C2×D4—1721no—
255C2×D4—1721no—
256C22×C4—431no—
257C22×C4—431no—
258C22×C4—431no—
259C22×C4—431no—
260C22×C4—431no—
261C22×C4—431no—
262C22×C4—431no—
263C22×C4C22×D4311yescharacteristic
264C22×C4C22×D4311yescharacteristic
265C22×C4C22×D4311yescharacteristic
266C22×C4C22×D4311yescharacteristic
267C22×C4C22×D4311yescharacteristic
268C22×C4C22×D4311yescharacteristic
269C4⋊C4—22no—
270C4⋊C4—22no—
271C4⋊C4—862no—
272C4⋊C4—862no—
273C4⋊C4—862no—
274C4⋊C4—862no—
275C4⋊C4—862no—
276C4⋊C4—1721no—
277C4⋊C4—1721no—
278C4⋊C4—1721no—
279C4⋊C4—1721no—
280C4⋊C4—1721no—
281C4⋊C4C22⋊D4314yescomplemented
282C22⋊C4—22no—
283C22⋊C4—22no—
284C22⋊C4—22no—
285C22⋊C4—862no—
286C22⋊C4—862no—
287C22⋊C4—862no—
288C22⋊C4—862no—
289C22⋊C4—862no—
290C22⋊C4—1721no—
291C22⋊C4—1721no—
292C22⋊C4—1721no—
293C22⋊C4—1721no—
294C42—22no—
295C42—862no—
296C42—1721no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—861no—
305C23—861no—
306C23—861no—
307C23—861no—
308C23—861no—
309C23—861no—
310C23—861no—
311C23C23×D4311yescharacteristic
312D4—1724no—
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—432no—
329C2×C4—432no—
330C2×C4—861no—
331C2×C4—861no—
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×C4C2×C22⋊D4312yes—
350C2×C4C2×C22⋊D4312yes—
351C2×C4C2×C22⋊D4312yes—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—1721no—
360C22—1721no—
361C22—1721no—
362C22—1721no—
363C22—1721no—
364C22—1721no—
365C22—1721no—
366C22C22×C22⋊D4311yescharacteristic
367C22#41×D4311yescharacteristic
368C22#41×D4311yescharacteristic
369C22#1306337111yescharacteristic
370C22#1306337111yescharacteristic
371C22#1306337211yescharacteristic
372C22#1306337211yescharacteristic
373C4—22no—
374C4—22no—
375C4—22no—
376C4—41no—
377C4—41no—
378C4—41no—
379C4—862no—
380C4—862no—
381C4—1721no—
382C4—1721no—
383C4—1721no—
384C4—1721no—
385C4—1721no—
386C2—81no—
387C2—3441no—
388C2#1458347711yescharacteristic
389C2#1458348811yescharacteristic
390C2#1458349011yescharacteristic
391C2#1458354811yescharacteristic
392C2#1458356811yescharacteristic
393C2#1458361611yescharacteristic
394C2#1458365111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC2×#126×C43C2
hypercenterC2×#126D43
hypocenterC43#2727
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#126

Complements

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

NH ≅ G/Ntype
1. C2×#13063320C2semidirect
2. #14582835C2semidirect
3. #14582834C2semidirect
4. #14582822C2semidirect
5. #14582821C2semidirect
9. #14582798C2semidirect
10. #14582797C2semidirect
11. #14582795C2semidirect
12. #14582794C2semidirect
13. #14582790C2semidirect
14. #14582787C2semidirect
15. C2×#126×C43C2semidirect
73. C4⋊C4×C43D4semidirect
199. C2×#126D43semidirect
213. C43#2727semidirect
281. C4⋊C4C22⋊D43semidirect