Finite Group Databasebeta

← #19140405

Subgroups — #19140405

Order 5504.

668 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13063303C211yesmaximal, characteristic, complemented
2C2×C22⋊C4×D43C211yesmaximal, characteristic
3#14582835C211yesmaximal, characteristic, complemented
4#14582834C211yesmaximal, characteristic, complemented
5#14582822C211yesmaximal, characteristic, complemented
6#14582821C211yesmaximal, characteristic, complemented
7#14582821C211yesmaximal, characteristic, complemented
8#14582812C211yesmaximal, characteristic, complemented
9#14582811C211yesmaximal, characteristic, complemented
10#14582773C211yesmaximal, characteristic, complemented
11#14582770C211yesmaximal, characteristic, complemented
12#14582756C211yesmaximal, characteristic, complemented
13#14582754C211yesmaximal, characteristic
14#14582754C211yesmaximal, characteristic
15C43×#396C211yesmaximal, characteristic, complemented
16C24×D43C2211yescharacteristic
17C22×Dic86C2211yescharacteristic, complemented
18C22×C4×D43C2211yescharacteristic
19C22×C4×D43C2211yescharacteristic
20#13063303—24no—
21C2×C4⋊Dic43C2211yescharacteristic, complemented
22C2×C4⋊Dic43C2211yescharacteristic, complemented
23C2×Dic43⋊C4C2211yescharacteristic, complemented
24C2×Dic43⋊C4C2211yescharacteristic, complemented
25C2×Dic43⋊C4C2211yescharacteristic, complemented
26C2×Dic43⋊C4C2211yescharacteristic, complemented
27C2×C22⋊Dic43C2211yescharacteristic
28C2×C22⋊Dic43C2211yescharacteristic
29C2×C22⋊Dic43C2211yescharacteristic
30C2×(C2×D43)⋊C4C2211yescharacteristic
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×(C2×D43)⋊C4C2211yescharacteristic
38C2×(C2×D43)⋊C4C2211yescharacteristic
39C2×(C2×D43)⋊C4C2211yescharacteristic
40C22⋊C4×D43—24no—
41C43⋊#95C2211yescharacteristic, complemented
42C43⋊#95C2211yescharacteristic, complemented
43C43⋊#95C2211yescharacteristic, complemented
44C43⋊#95C2211yescharacteristic, complemented
45C43⋊#95C2211yescharacteristic, complemented
46C2×C4⋊C4×C43C2211yescharacteristic, complemented
47C2×C4⋊C4×C43C2211yescharacteristic, complemented
48C2×C4⋊C4×C43C2211yescharacteristic, complemented
49C2×C22⋊C4×C43C2211yescharacteristic
50C2×C22⋊C4×C43C2211yescharacteristic
51C2×C22⋊C4×C43C2211yescharacteristic
52#95×C43C2211yescharacteristic, complemented
53C24×C43C2311yescharacteristic
54C23×D43—22no—
55C23×D43—22no—
56C23×D43—41no—
57C23×D43—41no—
58C23×D43—41no—
59C23×D43—41no—
60C23×D43Q814yescomplemented
61C23×D43C2311yescharacteristic
62C23×D43C2311yescharacteristic
63C22×C4×C43C2311yescharacteristic
64C22×C4×C43C2311yescharacteristic
65C22×C4×C43C2311yescharacteristic
66C22×C4×C43C2311yescharacteristic
67C22×C4×C43C2311yescharacteristic
68C22×C4×C43C2311yescharacteristic
69C22×Dic43C2311yescharacteristic
70C22×Dic43C2311yescharacteristic
71C22×Dic43C2311yescharacteristic
72C22×Dic43C2311yescharacteristic
73C22×Dic43C2311yescharacteristic
74C22×Dic43C2311yescharacteristic
75C2×C4×D43—22no—
76C2×C4×D43—41no—
77C2×C4×D43—41no—
78C2×C4×D43—41no—
79C2×C4×D43—41no—
80C2×C4×D43D414yes—
81C2×Dic86—22no—
82C2×Dic86—41no—
83C2×Dic86—41no—
84C4⋊C4×C43—22no—
85C4⋊C4×C43—41no—
86C4⋊C4×C43—41no—
87C22⋊C4×C43—22no—
88C22⋊C4×C43—41no—
89C22⋊C4×C43—41no—
90C22⋊Dic43—22no—
91C22⋊Dic43—41no—
92C22⋊Dic43—41no—
93(C2×D43)⋊C4—22no—
94(C2×D43)⋊C4—22no—
95(C2×D43)⋊C4—22no—
96(C2×D43)⋊C4—22no—
97(C2×D43)⋊C4—22no—
98(C2×D43)⋊C4—22no—
99(C2×D43)⋊C4—41no—
100(C2×D43)⋊C4—41no—
101(C2×D43)⋊C4—41no—
102(C2×D43)⋊C4—41no—
103C4⋊Dic43—41no—
104C4⋊Dic43—41no—
105Dic43⋊C4—22no—
106Dic43⋊C4—22no—
107Dic43⋊C4—41no—
108Dic43⋊C4—41no—
109C23×C43—21no—
110C23×C43—21no—
111C23×C43—21no—
112C23×C43—21no—
113C23×C43—21no—
114C23×C43—21no—
115C23×C43C2×Q812yes—
116C23×C43C2411yescharacteristic
117C22×D43—21no—
118C22×D43—21no—
119C22×D43—21no—
120C22×D43—21no—
121C22×D43—21no—
122C22×D43—21no—
123C22×D43—21no—
124C22×D43—21no—
125C22×D43—21no—
126C22×D43—21no—
127C22×D43—28no—
128C22×D43—44no—
129C22×D43—44no—
130C22×D43—44no—
131C22×D43—44no—
132C22×D43—44no—
133C22×D43—44no—
134C22×D43C2×D412yes—
135C22×D43C2×Q812yes—
136C22×D43C2×Q812yes—
137C22×D43#4112yes—
138C2×C4×C43—21no—
139C2×C4×C43—21no—
140C2×C4×C43—21no—
141C2×C4×C43—21no—
142C2×C4×C43—21no—
143C2×C4×C43—21no—
144C2×C4×C43—21no—
145C2×C4×C43—21no—
146C2×C4×C43—21no—
147C2×C4×C43—21no—
148C2×C4×C43—21no—
149C2×C4×C43—21no—
150C2×C4×C43—21no—
151C2×C4×C43—21no—
152C2×C4×C43—21no—
153C2×C4×C43—21no—
154C2×C4×C43—21no—
155C2×C4×C43C2×D412yes—
156C2×Dic43—21no—
157C2×Dic43—21no—
158C2×Dic43—21no—
159C2×Dic43—21no—
160C2×Dic43—21no—
161C2×Dic43—21no—
162C2×Dic43—21no—
163C2×Dic43—21no—
164C2×Dic43—21no—
165C2×Dic43—21no—
166C2×Dic43—21no—
167C2×Dic43—21no—
168C2×Dic43—21no—
169C2×Dic43—21no—
170C2×Dic43—21no—
171C2×Dic43—21no—
172C2×Dic43—21no—
173C2×Dic43C2×D412yes—
174C4×D43—44no—
175C4×D43—44no—
176Dic86—44no—
177C22×C43—22no—
178C22×C43—22no—
179C22×C43—22no—
180C22×C43—41no—
181C22×C43—41no—
182C22×C43—41no—
183C22×C43—41no—
184C22×C43C22×D411yescharacteristic
185C22×C43C22×Q811yescharacteristic
186C22×C43C2×#4111yescharacteristic
187C22×C43H(5,𝔽2)11yescharacteristic
188C22×C43H(5,𝔽2)11yescharacteristic
189C22×C43H(5,𝔽2)11yescharacteristic
190C22×C43H(5,𝔽2)11yescharacteristic
191C2×D43—22no—
192C2×D43—22no—
193C2×D43—22no—
194C2×D43—22no—
195C2×D43—22no—
196C2×D43—22no—
197C2×D43—22no—
198C2×D43—22no—
199C2×D43—22no—
200C2×D43—416no—
201C2×D43—41no—
202C2×D43—41no—
203C2×D43—41no—
204C2×D43—41no—
205C2×D43C22⋊Q814yes—
206C4×C43—22no—
207C4×C43—41no—
208C4×C43—41no—
209C4×C43—41no—
210C4×C43—41no—
211C4×C43—41no—
212Dic43—22no—
213Dic43—41no—
214Dic43—41no—
215Dic43—41no—
216Dic43—41no—
217Dic43—41no—
218#2626—431nomaximal, Sylow
219C2×C43—42no—
220C2×C43C2×C22⋊Q811yescharacteristic
221C2×C43#53411yescharacteristic
222C2×C43#53511yescharacteristic
223C2×C43#53811yescharacteristic
224C2×C43#53811yescharacteristic
225C2×C43#54311yescharacteristic
226C2×C43#54311yescharacteristic
227D43—24no—
228D43—42no—
229C2×C22⋊Q8—431no—
230C22×C22⋊C4—431no—
231#399—431no—
232#399—431no—
233#396—431no—
234#396—431no—
235#396—431no—
236#396D4311yescharacteristic, complemented
237#393—431no—
238#393—431no—
239#385—431no—
240#385—431no—
241#380—431no—
242#379—431no—
243#379—431no—
244C43#262611yescharacteristic, complemented, Sylow
245C25—431no—
246C22×Q8—431no—
247C23×C4—431no—
248C23×C4—431no—
249C22⋊Q8—864no—
250C2×C4⋊C4—431no—
251C2×C4⋊C4—431no—
252C2×C4⋊C4—431no—
253C2×C4⋊C4—431no—
254C2×C4⋊C4—431no—
255C2×C4⋊C4—431no—
256C2×C4⋊C4C2×D4311yescharacteristic, complemented
257C2×C4⋊C4C2×D4311yescharacteristic, complemented
258C2×C4⋊C4C2×D4311yescharacteristic, complemented
259C2×C22⋊C4—431no—
260C2×C22⋊C4—431no—
261C2×C22⋊C4—431no—
262C2×C22⋊C4—431no—
263C2×C22⋊C4—431no—
264C2×C22⋊C4—431no—
265C2×C22⋊C4—431no—
266C2×C22⋊C4—431no—
267C2×C22⋊C4—431no—
268C2×C22⋊C4—431no—
269C2×C22⋊C4—431no—
270C2×C22⋊C4—431no—
271C2×C22⋊C4—431no—
272C2×C22⋊C4—864no—
273C2×C22⋊C4C2×D4311yescharacteristic
274C2×C22⋊C4C2×D4311yescharacteristic
275C2×C22⋊C4C2×D4311yescharacteristic
276#95—431no—
277#95—431no—
278#95—431no—
279#95—431no—
280#95—431no—
281#95C2×D4311yescharacteristic, complemented
282C24—431no—
283C24—431no—
284C24—434no—
285C24—862no—
286C24—862no—
287C24—1721no—
288C24—1721no—
289C24—1721no—
290C24—1721no—
291C24C22×D4311yescharacteristic
292C2×Q8—862no—
293C2×Q8—1721no—
294C2×Q8—1721no—
295C22×C4—431no—
296C22×C4—434no—
297C22×C4—431no—
298C22×C4—431no—
299C22×C4—431no—
300C22×C4—431no—
301C22×C4—431no—
302C22×C4—862no—
303C22×C4—1721no—
304C22×C4—1721no—
305C22×C4—1721no—
306C22×C4—1721no—
307C22×C4C22×D4311yescharacteristic
308C22×C4C22×D4311yescharacteristic
309C22×C4C22×D4311yescharacteristic
310C22×C4C22×D4311yescharacteristic
311C22×C4C22×D4311yescharacteristic
312C22×C4C22×D4311yescharacteristic
313C4⋊C4—22no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—862no—
317C4⋊C4—862no—
318C4⋊C4—1721no—
319C4⋊C4—1721no—
320C4⋊C4—1721no—
321C4⋊C4—1721no—
322C22⋊C4—22no—
323C22⋊C4—41no—
324C22⋊C4—41no—
325C22⋊C4—862no—
326C22⋊C4—862no—
327C22⋊C4—862no—
328C22⋊C4—862no—
329C22⋊C4—862no—
330C22⋊C4—862no—
331C22⋊C4—862no—
332C22⋊C4—1721no—
333C22⋊C4—1721no—
334C22⋊C4—1721no—
335C22⋊C4—1721no—
336C22⋊C4—1721no—
337C22⋊C4—1721no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—432no—
345C23—432no—
346C23—432no—
347C23—432no—
348C23—868no—
349C23—861no—
350C23—861no—
351C23—861no—
352C23—861no—
353C23—861no—
354C23—861no—
355C23—861no—
356C23—861no—
357C23—861no—
358C23—861no—
359C23—1724no—
360C23—1724no—
361C23—1724no—
362C23—1724no—
363C23—1724no—
364C23—1724no—
365C23Q8×D4312yes—
366C23C23×D4311yescharacteristic
367Q8—1724no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—432no—
386C2×C4—861no—
387C2×C4—861no—
388C2×C4—861no—
389C2×C4—861no—
390C2×C4—861no—
391C2×C4—861no—
392C2×C4—861no—
393C2×C4—861no—
394C2×C4—861no—
395C2×C4—861no—
396C2×C4—861no—
397C2×C4—861no—
398C2×C4—861no—
399C2×C4—861no—
400C2×C4—861no—
401C2×C4—861no—
402C2×C4—861no—
403C2×C4—1724no—
404C2×C4—1724no—
405C2×C4D4×D4312yes—
406C22—22no—
407C22—22no—
408C22—22no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—434no—
414C22—862no—
415C22—862no—
416C22—862no—
417C22—862no—
418C22—862no—
419C22—862no—
420C22—862no—
421C22—862no—
422C22—862no—
423C22—17216no—
424C22—1721no—
425C22—1721no—
426C22—1721no—
427C22—1721no—
428C22C2×D4×D4311yescharacteristic
429C22C2×Q8×D4311yescharacteristic
430C22#41×D4311yescharacteristic
431C22#1306337011yescharacteristic
432C22#1306337011yescharacteristic
433C22#1306337111yescharacteristic
434C22#1306337111yescharacteristic
435C4—22no—
436C4—41no—
437C4—41no—
438C4—41no—
439C4—41no—
440C4—41no—
441C4—862no—
442C4—1721no—
443C4—1721no—
444C4—1721no—
445C4—1721no—
446C4—1721no—
447C2—42no—
448C2—864no—
449C2—1722no—
450C2C22⋊Q8×D4311yescharacteristic
451C2#1458345711yescharacteristic
452C2#1458346511yescharacteristic
453C2#1458348111yescharacteristic
454C2#1458348811yescharacteristic
455C2#1458352411yescharacteristic
456C2#1458352411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#396C2
hypercenter#396D43
hypocenterC43#2626
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #396

Complements

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

NH ≅ G/Ntype
1. C2×#13063303C2semidirect
3. #14582835C2semidirect
4. #14582834C2semidirect
5. #14582822C2semidirect
6. #14582821C2semidirect
7. #14582821C2semidirect
8. #14582812C2semidirect
9. #14582811C2semidirect
10. #14582773C2semidirect
11. #14582770C2semidirect
12. #14582756C2semidirect
15. C43×#396C2semidirect
17. C22×Dic86C22semidirect
21. C2×C4⋊Dic43C22semidirect
22. C2×C4⋊Dic43C22semidirect
23. C2×Dic43⋊C4C22semidirect
24. C2×Dic43⋊C4C22semidirect
25. C2×Dic43⋊C4C22semidirect
26. C2×Dic43⋊C4C22semidirect
41. C43⋊#95C22semidirect
42. C43⋊#95C22semidirect
43. C43⋊#95C22semidirect
44. C43⋊#95C22semidirect
45. C43⋊#95C22semidirect
46. C2×C4⋊C4×C43C22semidirect
47. C2×C4⋊C4×C43C22semidirect
48. C2×C4⋊C4×C43C22semidirect
52. #95×C43C22semidirect
60. C23×D43Q8semidirect
236. #396D43semidirect
244. C43#2626semidirect
256. C2×C4⋊C4C2×D43semidirect
257. C2×C4⋊C4C2×D43semidirect
258. C2×C4⋊C4C2×D43semidirect
281. #95C2×D43semidirect