Finite Group Databasebeta

← #19142685

Subgroups — #19142685

Order 5504.

522 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C43⋊#401C211yesmaximal, characteristic, complemented
2#14582828C211yesmaximal, characteristic, complemented
3#14582826C211yesmaximal, characteristic, complemented
4#14582821C211yesmaximal, characteristic, complemented
5#14582816C211yesmaximal, characteristic, complemented
6#14582815C211yesmaximal, characteristic, complemented
7#14582814C211yesmaximal, characteristic, complemented
8#14582809C211yesmaximal, characteristic, complemented
9#14582808C211yesmaximal, characteristic, complemented
10#14582808C211yesmaximal, characteristic, complemented
11#14582808C211yesmaximal, characteristic, complemented
12#14582777C211yesmaximal, characteristic, complemented
13#14582777C211yesmaximal, characteristic, complemented
14#14582775C211yesmaximal, characteristic, complemented
15C43×#397C211yesmaximal, characteristic, complemented
16C22×D172C2211yescharacteristic
17C22×D172C2211yescharacteristic
18C22×D172C2211yescharacteristic
19C22×C22⋊D43C2211yescharacteristic
20C22×C22⋊D43C2211yescharacteristic
21C22×C22⋊D43C2211yescharacteristic
22C22×C4×D43C2211yescharacteristic
23C2×C4⋊Dic43C2211yescharacteristic
24C2×Dic43⋊C4C2211yescharacteristic
25C2×C22⋊Dic43C2211yescharacteristic
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
36C2×(C2×D43)⋊C4C2211yescharacteristic
37C43⋊#95C2211yescharacteristic
38C43⋊#95C2211yescharacteristic
39C43⋊#95C2211yescharacteristic
40C43⋊#95C2211yescharacteristic
41C43⋊#95C2211yescharacteristic
42C43⋊#95C2211yescharacteristic
43C43⋊#95C2211yescharacteristic
44C2×C4⋊C4×C43C2211yescharacteristic
45C2×C22⋊C4×C43C2211yescharacteristic
46C2×C22⋊C4×C43C2211yescharacteristic
47C2×C22⋊C4×C43C2211yescharacteristic
48#95×C43C2211yescharacteristic
49#95×C43C2211yescharacteristic
50#95×C43C2211yescharacteristic
51C24×C43C2311yescharacteristic
52C23×D43C2311yescharacteristic
53C23×D43C2311yescharacteristic
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—
64C2×C22⋊D43—41no—
65C2×C22⋊D43—41no—
66C2×C22⋊D43—41no—
67C2×C22⋊D43—41no—
68C2×C22⋊D43—41no—
69C2×C22⋊D43—41no—
70C22×Dic43C2311yescharacteristic
71C22×Dic43C2311yescharacteristic
72C22×Dic43C2311yescharacteristic
73C22×Dic43C2311yescharacteristic
74C22×Dic43C2311yescharacteristic
75C2×D172—22no—
76C2×D172—22no—
77C2×D172—41no—
78C2×D172—41no—
79C2×D172—41no—
80C2×D172—41no—
81C2×D172—41no—
82C2×D172—41no—
83C2×D172—41no—
84C2×C4×D43—41no—
85C2×C4×D43—41no—
86C2×C4×D43—41no—
87C4⋊C4×C43—41no—
88C22⋊C4×C43—41no—
89C22⋊C4×C43—41no—
90C22⋊C4×C43—41no—
91C22⋊Dic43—41no—
92(C2×D43)⋊C4—41no—
93(C2×D43)⋊C4—41no—
94(C2×D43)⋊C4—41no—
95(C2×D43)⋊C4—41no—
96(C2×D43)⋊C4—41no—
97(C2×D43)⋊C4—41no—
98(C2×D43)⋊C4—41no—
99(C2×D43)⋊C4—41no—
100(C2×D43)⋊C4—41no—
101(C2×D43)⋊C4—41no—
102(C2×D43)⋊C4—41no—
103C4⋊Dic43—41no—
104Dic43⋊C4—41no—
105C23×C43—21no—
106C23×C43—21no—
107C23×C43—21no—
108C23×C43—21no—
109C23×C43—21no—
110C23×C43—21no—
111C23×C43—21no—
112C23×C43C2411yescharacteristic
113C22×D43—21no—
114C22×D43—21no—
115C22×D43—21no—
116C22×D43—21no—
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—21no—
128C22×D43—21no—
129C22×D43—21no—
130C22×D43—21no—
131C22×D43—21no—
132C22×D43—21no—
133C22×D43#4112yes—
134C2×C4×C43—21no—
135C2×C4×C43—21no—
136C2×C4×C43—21no—
137C2×C4×C43—21no—
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—
152C22⋊D43—44no—
153C22⋊D43—44no—
154C22⋊D43—44no—
155C2×Dic43—21no—
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—
170D172—44no—
171D172—44no—
172D172—44no—
173C4×D43—44no—
174C22×C43—41no—
175C22×C43—41no—
176C22×C43—41no—
177C22×C43—41no—
178C22×C43—41no—
179C22×C43—41no—
180C22×C43—41no—
181C22×C43C2×#4111yescharacteristic
182C22×C43H(5,𝔽2)11yescharacteristic
183C22×C43H(5,𝔽2)11yescharacteristic
184C22×C43H(5,𝔽2)11yescharacteristic
185C22×C43H(5,𝔽2)11yescharacteristic
186C22×C43H(5,𝔽2)11yescharacteristic
187C22×C43H(5,𝔽2)11yescharacteristic
188C2×D43—22no—
189C2×D43—22no—
190C2×D43—22no—
191C2×D43—41no—
192C2×D43—41no—
193C2×D43—41no—
194C2×D43—41no—
195C2×D43—41no—
196C2×D43—41no—
197C2×D43—41no—
198C2×D43—41no—
199C2×D43—41no—
200C2×D43—41no—
201C2×D43—41no—
202C2×D43—41no—
203C2×D43—41no—
204C2×D43—41no—
205C2×D43—41no—
206C2×D43—41no—
207C2×D43—41no—
208C2×D43—41no—
209C4×C43—41no—
210C4×C43—41no—
211C4×C43—41no—
212C4×C43—41no—
213C4×C43—41no—
214C4×C43—41no—
215Dic43—41no—
216Dic43—41no—
217Dic43—41no—
218Dic43—41no—
219Dic43—41no—
220#2825—431nomaximal, Sylow
221C2×C43—81no—
222C2×C43#53811yescharacteristic
223C2×C43#53811yescharacteristic
224C2×C43#53811yescharacteristic
225C2×C43#56011yescharacteristic
226C2×C43#56011yescharacteristic
227C2×C43#56011yescharacteristic
228C2×C43#56011yescharacteristic
229D43—42no—
230D43—81no—
231D43—81no—
232#401—431no—
233#397—431no—
234#397—431no—
235#397D4311yescharacteristic, complemented
236#396—431no—
237#394—431no—
238#394—431no—
239#394—431no—
240#392—431no—
241#392—431no—
242#392—431no—
243#392—431no—
244#386—431no—
245#386—431no—
246#386—431no—
247C43#282511yescharacteristic, complemented, Sylow
248C22×D4—431no—
249C22×D4—431no—
250C22×D4—431no—
251C22×D4—431no—
252C22×D4—431no—
253C22×D4—431no—
254C23×C4—431no—
255C2×C4⋊C4—431no—
256C2×C4⋊C4—431no—
257C2×C4⋊C4C2×D4311yescharacteristic
258C2×C22⋊C4—431no—
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⋊C4C2×D4311yescharacteristic
271C2×C22⋊C4C2×D4311yescharacteristic
272C2×C22⋊C4C2×D4311yescharacteristic
273#95—431no—
274#95—431no—
275#95—431no—
276#95—431no—
277#95—431no—
278#95—431no—
279#95—431no—
280#95C2×D4311yescharacteristic
281#95C2×D4311yescharacteristic
282#95C2×D4311yescharacteristic
283C24—431no—
284C24—431no—
285C24—431no—
286C24C22×D4311yescharacteristic
287C2×D4—862no—
288C2×D4—862no—
289C2×D4—862no—
290C2×D4—1721no—
291C2×D4—1721no—
292C2×D4—1721no—
293C2×D4—1721no—
294C2×D4—1721no—
295C2×D4—1721no—
296C2×D4—1721no—
297C2×D4—1721no—
298C2×D4—1721no—
299C2×D4—1721no—
300C2×D4—1721no—
301C2×D4—1721no—
302C2×D4—1721no—
303C2×D4—1721no—
304C2×D4—1721no—
305C22×C4—431no—
306C22×C4—431no—
307C22×C4—431no—
308C22×C4—431no—
309C22×C4—431no—
310C22×C4—1721no—
311C22×C4—1721no—
312C22×C4—1721no—
313C22×C4C22×D4311yescharacteristic
314C22×C4C22×D4311yescharacteristic
315C22×C4C22×D4311yescharacteristic
316C22×C4C22×D4311yescharacteristic
317C22×C4C22×D4311yescharacteristic
318C22×C4C22×D4311yescharacteristic
319C4⋊C4—41no—
320C4⋊C4—1721no—
321C4⋊C4—1721no—
322C22⋊C4—41no—
323C22⋊C4—41no—
324C22⋊C4—41no—
325C22⋊C4—1721no—
326C22⋊C4—1721no—
327C22⋊C4—1721no—
328C22⋊C4—1721no—
329C22⋊C4—1721no—
330C22⋊C4—1721no—
331C22⋊C4—1721no—
332C22⋊C4—1721no—
333C22⋊C4—1721no—
334C22⋊C4—1721no—
335C22⋊C4—1721no—
336C22⋊C4—1721no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—432no—
345C23—861no—
346C23—861no—
347C23—861no—
348C23—861no—
349C23—861no—
350C23—861no—
351C23—861no—
352C23—861no—
353C23—861no—
354C23—861no—
355C23—861no—
356C23—861no—
357C23—861no—
358C23—861no—
359C23—861no—
360C23—861no—
361C23—861no—
362C23—861no—
363C23—861no—
364C23—861no—
365C23C23×D4311yescharacteristic
366D4—1724no—
367D4—1724no—
368D4—1724no—
369D4—1724no—
370D4—1724no—
371D4—1724no—
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—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
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—861no—
404C2×C4—861no—
405C2×C4—1724no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—862no—
414C22—862no—
415C22—862no—
416C22—1721no—
417C22—1721no—
418C22—1721no—
419C22—1721no—
420C22—1721no—
421C22—1721no—
422C22—1721no—
423C22—1721no—
424C22—1721no—
425C22—1721no—
426C22—1721no—
427C22—1721no—
428C22—1721no—
429C22—1721no—
430C22—1721no—
431C22—1721no—
432C22—1721no—
433C22—1721no—
434C22#41×D4311yescharacteristic
435C22#1306337011yescharacteristic
436C22#1306337011yescharacteristic
437C22#1306337111yescharacteristic
438C22#1306337111yescharacteristic
439C22#1306337111yescharacteristic
440C22#1306337111yescharacteristic
441C4—41no—
442C4—41no—
443C4—41no—
444C4—41no—
445C4—41no—
446C4—41no—
447C4—1721no—
448C4—1721no—
449C4—1721no—
450C4—1721no—
451C4—1721no—
452C2—81no—
453C2—3441no—
454C2—3441no—
455C2—1722no—
456C2#1458348311yescharacteristic
457C2#1458348511yescharacteristic
458C2#1458348811yescharacteristic
459C2#1458363711yescharacteristic
460C2#1458363911yescharacteristic
461C2#1458363911yescharacteristic
462C2#1458364011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#397C2
hypercenter#397D43
hypocenterC43#2825
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. C43⋊#401C2semidirect
2. #14582828C2semidirect
3. #14582826C2semidirect
4. #14582821C2semidirect
5. #14582816C2semidirect
6. #14582815C2semidirect
7. #14582814C2semidirect
8. #14582809C2semidirect
9. #14582808C2semidirect
10. #14582808C2semidirect
11. #14582808C2semidirect
12. #14582777C2semidirect
13. #14582777C2semidirect
14. #14582775C2semidirect
15. C43×#397C2semidirect
235. #397D43semidirect
247. C43#2825semidirect