Finite Group Databasebeta

← #19142291

Subgroups — #19142291

Order 5504.

472 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14582841C211yesmaximal, characteristic, complemented
2#14582823C211yesmaximal, characteristic, complemented
3#14582821C211yesmaximal, characteristic, complemented
4#14582820C211yesmaximal, characteristic, complemented
5#14582812C211yesmaximal, characteristic, complemented
6#14582812C211yesmaximal, characteristic, complemented
7#14582801C211yesmaximal, characteristic
8#14582783C211yesmaximal, characteristic, complemented
9#14582777C211yesmaximal, characteristic
10#14582777C211yesmaximal, characteristic
11#14582770C211yesmaximal, characteristic, complemented
12#14582770C211yesmaximal, characteristic, complemented
13#14582758C211yesmaximal, characteristic, complemented
14#14582756C211yesmaximal, characteristic, complemented
15C43×#387C211yesmaximal, characteristic, complemented
16C22×Dic86C2211yescharacteristic
17C22×D172C2211yescharacteristic
18C22×C4×D43C2211yescharacteristic
19C22×C4×D43C2211yescharacteristic
20C2×C4⋊Dic43C2211yescharacteristic
21C2×C4⋊Dic43C2211yescharacteristic
22C2×Dic43⋊C4C2211yescharacteristic
23C2×Dic43⋊C4C2211yescharacteristic
24C2×Dic43⋊C4C2211yescharacteristic
25C2×Dic43⋊C4C2211yescharacteristic
26C2×(C2×D43)⋊C4C2211yescharacteristic
27C2×(C2×D43)⋊C4C2211yescharacteristic
28C2×(C2×D43)⋊C4C2211yescharacteristic
29C2×(C2×D43)⋊C4C2211yescharacteristic
30C2×(C2×D43)⋊C4C2211yescharacteristic
31C2×(C2×D43)⋊C4C2211yescharacteristic
32C2×(C2×D43)⋊C4C2211yescharacteristic
33C2×(C2×D43)⋊C4C2211yescharacteristic
34C2×(C2×D43)⋊C4C2211yescharacteristic
35C2×(C2×D43)⋊C4C2211yescharacteristic
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×C42×C43C2211yescharacteristic
47#95×C43C2211yescharacteristic
48#95×C43C2211yescharacteristic
49#95×C43C2211yescharacteristic
50#95×C43C2211yescharacteristic
51C23×D43C2311yescharacteristic
52C23×D43C2311yescharacteristic
53C22×C4×C43C2311yescharacteristic
54C22×C4×C43C2311yescharacteristic
55C22×C4×C43C2311yescharacteristic
56C22×C4×C43C2311yescharacteristic
57C22×C4×C43C2311yescharacteristic
58C22×C4×C43C2311yescharacteristic
59C22×C4×C43C2311yescharacteristic
60C22×Dic43C2311yescharacteristic
61C22×Dic43C2311yescharacteristic
62C22×Dic43C2311yescharacteristic
63C22×Dic43C2311yescharacteristic
64C22×Dic43C2311yescharacteristic
65C22×Dic43C2311yescharacteristic
66C2×D172—41no—
67C2×D172—41no—
68C2×D172Q814yescomplemented
69C2×C4×D43—22no—
70C2×C4×D43—22no—
71C2×C4×D43—41no—
72C2×C4×D43—41no—
73C2×C4×D43—41no—
74C2×C4×D43—41no—
75C2×Dic86—41no—
76C2×Dic86—41no—
77C2×Dic86—41no—
78C4⋊C4×C43—22no—
79C4⋊C4×C43—41no—
80C42×C43—41no—
81(C2×D43)⋊C4—22no—
82(C2×D43)⋊C4—22no—
83(C2×D43)⋊C4—41no—
84(C2×D43)⋊C4—41no—
85(C2×D43)⋊C4—41no—
86(C2×D43)⋊C4—41no—
87(C2×D43)⋊C4—41no—
88(C2×D43)⋊C4—41no—
89(C2×D43)⋊C4—41no—
90(C2×D43)⋊C4—41no—
91C4⋊Dic43—41no—
92C4⋊Dic43—41no—
93Dic43⋊C4—22no—
94Dic43⋊C4—41no—
95Dic43⋊C4—41no—
96Dic43⋊C4—41no—
97C23×C43C2411yescharacteristic
98C22×D43—21no—
99C22×D43—21no—
100C22×D43—21no—
101C22×D43—21no—
102C22×D43—21no—
103C22×D43—21no—
104C22×D43—21no—
105C22×D43—21no—
106C22×D43—21no—
107C22×D43—21no—
108C22×D43—21no—
109C22×D43—21no—
110C22×D43C2×Q812yes—
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—
130C2×C4×C43—21no—
131C2×C4×C43C2×Q812yes—
132C2×C4×C43#4112yes—
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#4112yes—
151D172—44no—
152C4×D43—44no—
153C4×D43—44no—
154Dic86—44no—
155C22×C43C22×Q811yescharacteristic
156C22×C43C2×#4111yescharacteristic
157C22×C43C2×#4111yescharacteristic
158C22×C43H(5,𝔽2)11yescharacteristic
159C22×C43H(5,𝔽2)11yescharacteristic
160C22×C43H(5,𝔽2)11yescharacteristic
161C22×C43H(5,𝔽2)11yescharacteristic
162C2×D43—22no—
163C2×D43—22no—
164C2×D43—22no—
165C2×D43—22no—
166C2×D43—22no—
167C2×D43—22no—
168C2×D43—41no—
169C2×D43—41no—
170C2×D43—41no—
171C2×D43—41no—
172C2×D43—41no—
173C2×D43—41no—
174C2×D43—41no—
175C2×D43—41no—
176C4×C43—22no—
177C4×C43—22no—
178C4×C43—41no—
179C4×C43—41no—
180C4×C43—41no—
181C4×C43—41no—
182C4×C43—41no—
183Dic43—22no—
184Dic43—41no—
185Dic43—41no—
186Dic43—41no—
187Dic43—41no—
188Dic43—41no—
189#2784—431nomaximal, Sylow
190C2×C43#53811yescharacteristic
191C2×C43#53811yescharacteristic
192C2×C43#54311yescharacteristic
193C2×C43#55411yescharacteristic
194C2×C43#55411yescharacteristic
195C2×C43#55511yescharacteristic
196C2×C43#56011yescharacteristic
197D43—42no—
198D43—42no—
199#400—431no—
200#396—431no—
201#396—431no—
202#395—431no—
203#393—431no—
204#393—431no—
205#390—431no—
206#387—431no—
207#387D4311yescharacteristic, complemented
208#386—431no—
209#386—431no—
210#385—431no—
211#385—431no—
212#380—431no—
213#380—431no—
214C43#278411yescharacteristic, complemented, Sylow
215C22×Q8—431no—
216C22×D4—431no—
217C23×C4—431no—
218C23×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×C22⋊C4—431no—
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⋊C4—431no—
236C2×C22⋊C4—431no—
237C2×C42C2×D4311yescharacteristic
238#95—431no—
239#95—431no—
240#95—431no—
241#95—431no—
242#95—431no—
243#95—431no—
244#95—431no—
245#95—431no—
246#95C2×D4311yescharacteristic
247#95C2×D4311yescharacteristic
248#95C2×D4311yescharacteristic
249#95C2×D4311yescharacteristic
250C24—431no—
251C24—431no—
252C2×Q8—1721no—
253C2×Q8—1721no—
254C2×Q8—1721no—
255C2×D4—434no—
256C2×D4—1721no—
257C2×D4—1721no—
258C22×C4—431no—
259C22×C4—431no—
260C22×C4—431no—
261C22×C4—431no—
262C22×C4—431no—
263C22×C4—431no—
264C22×C4—862no—
265C22×C4—862no—
266C22×C4—1721no—
267C22×C4—1721no—
268C22×C4—1721no—
269C22×C4—1721no—
270C22×C4C22×D4311yescharacteristic
271C22×C4C22×D4311yescharacteristic
272C22×C4C22×D4311yescharacteristic
273C22×C4C22×D4311yescharacteristic
274C22×C4C22×D4311yescharacteristic
275C22×C4C22×D4311yescharacteristic
276C22×C4C22×D4311yescharacteristic
277C4⋊C4—22no—
278C4⋊C4—41no—
279C4⋊C4—862no—
280C4⋊C4—1721no—
281C4⋊C4—1721no—
282C4⋊C4—1721no—
283C4⋊C4—1721no—
284C4⋊C4—1721no—
285C22⋊C4—862no—
286C22⋊C4—862no—
287C22⋊C4—1721no—
288C22⋊C4—1721no—
289C22⋊C4—1721no—
290C22⋊C4—1721no—
291C22⋊C4—1721no—
292C22⋊C4—1721no—
293C22⋊C4—1721no—
294C22⋊C4—1721no—
295C42—41no—
296C23—432no—
297C23—432no—
298C23—861no—
299C23—861no—
300C23—861no—
301C23—861no—
302C23—861no—
303C23—861no—
304C23—861no—
305C23—861no—
306C23—861no—
307C23—861no—
308C23—861no—
309C23—861no—
310C23C23×D4311yescharacteristic
311Q8—1724no—
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—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—432no—
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—
352C2×C4#1062189812yes—
353C2×C4Q8×D4312yes—
354C22—862no—
355C22—862no—
356C22—862no—
357C22—862no—
358C22—862no—
359C22—862no—
360C22—1721no—
361C22—1721no—
362C22—1721no—
363C22—1721no—
364C22—1721no—
365C22—1721no—
366C22—1721no—
367C22—1721no—
368C22C2×Q8×D4311yescharacteristic
369C22#41×D4311yescharacteristic
370C22C2×#1062189811yescharacteristic
371C22#1306337011yescharacteristic
372C22#1306337111yescharacteristic
373C22#1306337111yescharacteristic
374C22#1306337111yescharacteristic
375C4—22no—
376C4—22no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—862no—
383C4—1721no—
384C4—1721no—
385C4—1721no—
386C4—1721no—
387C4—1721no—
388C2—1722no—
389C2—1722no—
390C2#1458348211yescharacteristic
391C2#1458348511yescharacteristic
392C2#1458352411yescharacteristic
393C2#1458360511yescharacteristic
394C2#1458360911yescharacteristic
395C2#1458361211yescharacteristic
396C2#1458364011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#387C2
hypercenter#387D43
hypocenterC43#2784
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
1. #14582841C2semidirect
2. #14582823C2semidirect
3. #14582821C2semidirect
4. #14582820C2semidirect
5. #14582812C2semidirect
6. #14582812C2semidirect
8. #14582783C2semidirect
11. #14582770C2semidirect
12. #14582770C2semidirect
13. #14582758C2semidirect
14. #14582756C2semidirect
15. C43×#387C2semidirect
68. C2×D172Q8semidirect
207. #387D43semidirect
214. C43#2784semidirect