Finite Group Databasebeta

← #19139952

Subgroups — #19139952

Order 5504.

564 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13063290C211yesmaximal, characteristic, complemented
2C2×C4×C22⋊D43C211yesmaximal, characteristic
3#14582835C211yesmaximal, characteristic, complemented
4#14582834C211yesmaximal, characteristic, complemented
5#14582812C211yesmaximal, characteristic, complemented
6#14582811C211yesmaximal, characteristic, complemented
7#14582799C211yesmaximal, characteristic
8#14582799C211yesmaximal, characteristic
9#14582796C211yesmaximal, characteristic, complemented
10#14582794C211yesmaximal, characteristic, complemented
11#14582773C211yesmaximal, characteristic, complemented
12#14582772C211yesmaximal, characteristic, complemented
13#14582770C211yesmaximal, characteristic, complemented
14#14582763C211yesmaximal, characteristic, complemented
15C43×#385C211yesmaximal, characteristic, complemented
16C22×Dic86C2211yescharacteristic
17C22×C22⋊D43C2211yescharacteristic
18C22×C4×D43C2211yescharacteristic
19#13063290—24no—
20C4×C22⋊D43—24no—
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
38C2×C4×Dic43C2211yescharacteristic
39C2×C4×Dic43C2211yescharacteristic
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⋊D43Q814yescomplemented
67C22×Dic43C2311yescharacteristic
68C22×Dic43C2311yescharacteristic
69C22×Dic43C2311yescharacteristic
70C22×Dic43C2311yescharacteristic
71C22×Dic43C2311yescharacteristic
72C22×Dic43C2311yescharacteristic
73C22×Dic43C2311yescharacteristic
74C2×C4×D43—22no—
75C2×C4×D43—41no—
76C2×C4×D43—41no—
77C2×Dic86—22no—
78C2×Dic86—22no—
79C2×Dic86—22no—
80C4⋊C4×C43—22no—
81C4⋊C4×C43—41no—
82C22⋊C4×C43—22no—
83C22⋊C4×C43—41no—
84C22⋊Dic43—22no—
85C22⋊Dic43—22no—
86C22⋊Dic43—41no—
87(C2×D43)⋊C4—22no—
88(C2×D43)⋊C4—22no—
89(C2×D43)⋊C4—22no—
90(C2×D43)⋊C4—41no—
91(C2×D43)⋊C4—41no—
92C4⋊Dic43—41no—
93Dic43⋊C4—22no—
94Dic43⋊C4—22no—
95Dic43⋊C4—22no—
96Dic43⋊C4—22no—
97Dic43⋊C4—22no—
98Dic43⋊C4—41no—
99Dic43⋊C4—41no—
100C4×Dic43—22no—
101C4×Dic43—22no—
102C4×Dic43D414yes—
103C23×C43—21no—
104C23×C43—21no—
105C23×C43—21no—
106C23×C43—21no—
107C23×C43—21no—
108C23×C43—21no—
109C23×C43C2×Q812yes—
110C23×C43C2411yescharacteristic
111C22×D43—21no—
112C22×D43—21no—
113C22×D43—21no—
114C22×D43—21no—
115C22×D43—21no—
116C22×D43—21no—
117C22×D43C2×Q812yes—
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—21no—
132C2×C4×C43—21no—
133C2×C4×C43—21no—
134C2×C4×C43—44no—
135C2×C4×C43C2×D412yes—
136C2×C4×C43#4112yes—
137C22⋊D43—28no—
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×Dic43—21no—
154C2×Dic43C2×D412yes—
155C2×Dic43C2×D412yes—
156C2×Dic43C2×Q812yes—
157C2×Dic43#4112yes—
158C2×Dic43#4112yes—
159C4×D43—44no—
160Dic86—28no—
161C22×C43—22no—
162C22×C43—22no—
163C22×C43—22no—
164C22×C43—41no—
165C22×C43—41no—
166C22×C43—41no—
167C22×C43—41no—
168C22×C43C22×D411yescharacteristic
169C22×C43C22×Q811yescharacteristic
170C22×C43C2×#4111yescharacteristic
171C22×C43C2×#4111yescharacteristic
172C22×C43C2×#4111yescharacteristic
173C22×C43H(5,𝔽2)11yescharacteristic
174C22×C43H(5,𝔽2)11yescharacteristic
175C2×D43—22no—
176C2×D43—22no—
177C2×D43—22no—
178C2×D43—41no—
179C2×D43—41no—
180C2×D43—41no—
181C2×D43—41no—
182C4×C43—22no—
183C4×C43—22no—
184C4×C43—41no—
185C4×C43—41no—
186C4×C43—41no—
187C4×C43—41no—
188Dic43—22no—
189Dic43—22no—
190Dic43—41no—
191Dic43—41no—
192Dic43—41no—
193Dic43—41no—
194Dic43C22⋊Q814yes—
195#2580—431nomaximal, Sylow
196C2×C43—42no—
197C2×C43C2×C22⋊Q811yescharacteristic
198C2×C43#52511yescharacteristic
199C2×C43#53511yescharacteristic
200C2×C43#55411yescharacteristic
201C2×C43#55411yescharacteristic
202C2×C43#55911yescharacteristic
203C2×C43#55911yescharacteristic
204D43—42no—
205C2×C4×Q8—431no—
206C2×C4×D4—431no—
207#399—431no—
208#399—431no—
209#393—431no—
210#393—431no—
211#390—431no—
212#390—431no—
213#389—431no—
214#389—431no—
215#385—431no—
216#385—431no—
217#385—431no—
218#385D4311yescharacteristic, complemented
219#382—431no—
220C43#258011yescharacteristic, complemented, Sylow
221C22×Q8—431no—
222C22×D4—431no—
223C23×C4—431no—
224C23×C4C2×D4311yescharacteristic
225C4×Q8—864no—
226C4×D4—864no—
227C2×C4⋊C4—431no—
228C2×C4⋊C4—431no—
229C2×C4⋊C4—431no—
230C2×C4⋊C4—431no—
231C2×C4⋊C4—431no—
232C2×C4⋊C4—431no—
233C2×C4⋊C4—431no—
234C2×C4⋊C4—431no—
235C2×C4⋊C4C2×D4311yescharacteristic
236C2×C4⋊C4C2×D4311yescharacteristic
237C2×C22⋊C4—431no—
238C2×C22⋊C4—431no—
239C2×C22⋊C4—431no—
240C2×C22⋊C4—431no—
241C2×C22⋊C4—431no—
242C2×C22⋊C4—431no—
243C2×C22⋊C4—431no—
244C2×C22⋊C4—431no—
245C2×C22⋊C4C2×D4311yescharacteristic
246C2×C22⋊C4C2×D4311yescharacteristic
247C2×C42—431no—
248C2×C42—431no—
249C2×C42—431no—
250#95—431no—
251#95—431no—
252#95—431no—
253#95—431no—
254#95—431no—
255#95—431no—
256#95C2×D4311yescharacteristic
257#95C2×D4311yescharacteristic
258C24—431no—
259C24C22×D4311yescharacteristic
260C2×Q8—862no—
261C2×Q8—862no—
262C2×Q8—862no—
263C2×D4—434no—
264C2×D4—862no—
265C2×D4—862no—
266C22×C4—22no—
267C22×C4—41no—
268C22×C4—41no—
269C22×C4—431no—
270C22×C4—431no—
271C22×C4—431no—
272C22×C4—431no—
273C22×C4—431no—
274C22×C4—431no—
275C22×C4—431no—
276C22×C4—862no—
277C22×C4—1721no—
278C22×C4—1721no—
279C22×C4C22×D4311yescharacteristic
280C22×C4C22×D4311yescharacteristic
281C22×C4C22×D4311yescharacteristic
282C22×C4C22×D4311yescharacteristic
283C22×C4C22×D4311yescharacteristic
284C22×C4C22×D4311yescharacteristic
285C4⋊C4—22no—
286C4⋊C4—41no—
287C4⋊C4—862no—
288C4⋊C4—862no—
289C4⋊C4—862no—
290C4⋊C4—862no—
291C4⋊C4—862no—
292C4⋊C4—1721no—
293C4⋊C4—1721no—
294C4⋊C4—1721no—
295C22⋊C4—22no—
296C22⋊C4—41no—
297C22⋊C4—862no—
298C22⋊C4—862no—
299C22⋊C4—862no—
300C22⋊C4—862no—
301C22⋊C4—862no—
302C22⋊C4—1721no—
303C22⋊C4—1721no—
304C22⋊C4—1721no—
305C42—434no—
306C42—862no—
307C42—862no—
308C23—21no—
309C23—21no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—432no—
315C23—861no—
316C23—861no—
317C23—861no—
318C23—861no—
319C23—861no—
320C23—861no—
321C23Q8×D4312yes—
322C23C23×D4311yescharacteristic
323Q8—868no—
324D4—868no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—44no—
342C2×C4—432no—
343C2×C4—432no—
344C2×C4—432no—
345C2×C4—432no—
346C2×C4—432no—
347C2×C4—861no—
348C2×C4—861no—
349C2×C4—861no—
350C2×C4—861no—
351C2×C4—861no—
352C2×C4—861no—
353C2×C4—861no—
354C2×C4—861no—
355C2×C4—861no—
356C2×C4—861no—
357C2×C4—861no—
358C2×C4—861no—
359C2×C4—861no—
360C2×C4—861no—
361C2×C4—861no—
362C2×C4—861no—
363C2×C4—1724no—
364C2×C4#1062189812yes—
365C2×C4D4×D4312yes—
366C22—22no—
367C22—22no—
368C22—22no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—41no—
373C22—862no—
374C22—862no—
375C22—862no—
376C22—1721no—
377C22—1721no—
378C22—1721no—
379C22—1721no—
380C22C2×D4×D4311yescharacteristic
381C22C2×Q8×D4311yescharacteristic
382C22#41×D4311yescharacteristic
383C22#41×D4311yescharacteristic
384C22C2×#1062189811yescharacteristic
385C22#1306337011yescharacteristic
386C22#1306337011yescharacteristic
387C4—22no—
388C4—22no—
389C4—41no—
390C4—41no—
391C4—41no—
392C4—41no—
393C4—434no—
394C4—862no—
395C4—862no—
396C4—1721no—
397C4—1721no—
398C4—1721no—
399C4—1721no—
400C2—42no—
401C2—1722no—
402C2C22⋊Q8×D4311yescharacteristic
403C2#1458340811yescharacteristic
404C2#1458346411yescharacteristic
405C2#1458360311yescharacteristic
406C2#1458360411yescharacteristic
407C2#1458363211yescharacteristic
408C2#1458363311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#385C2
hypercenter#385D43
hypocenterC43#2580
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. C2×#13063290C2semidirect
3. #14582835C2semidirect
4. #14582834C2semidirect
5. #14582812C2semidirect
6. #14582811C2semidirect
9. #14582796C2semidirect
10. #14582794C2semidirect
11. #14582773C2semidirect
12. #14582772C2semidirect
13. #14582770C2semidirect
14. #14582763C2semidirect
15. C43×#385C2semidirect
66. C2×C22⋊D43Q8semidirect
218. #385D43semidirect
220. C43#2580semidirect