Finite Group Databasebeta

← #19141241

Subgroups — #19141241

Order 5504.

612 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13063308C211yesmaximal, characteristic, complemented
2C2×#13063296C211yesmaximal, characteristic, complemented
3#14582841C211yesmaximal, characteristic, complemented
4#14582827C211yesmaximal, characteristic, complemented
5#14582814C211yesmaximal, characteristic, complemented
6#14582808C211yesmaximal, characteristic, complemented
7#14582808C211yesmaximal, characteristic, complemented
8#14582807C211yesmaximal, characteristic, complemented
9#14582799C211yesmaximal, characteristic, complemented
10#14582793C211yesmaximal, characteristic, complemented
11#14582791C211yesmaximal, characteristic, complemented
12#14582778C211yesmaximal, characteristic, complemented
13#14582777C211yesmaximal, characteristic, complemented
14#14582758C211yesmaximal, characteristic, complemented
15C43×#386C211yesmaximal, characteristic, complemented
16C22×D172C2211yescharacteristic
17C22×C22⋊D43C2211yescharacteristic
18C22×C22⋊D43C2211yescharacteristic
19C22×C22⋊D43C2211yescharacteristic
20C22×C22⋊D43C2211yescharacteristic
21C22×C4×D43C2211yescharacteristic
22#13063308—24no—
23#13063296—24no—
24C2×C4⋊Dic43C2211yescharacteristic
25C2×Dic43⋊C4C2211yescharacteristic
26C2×Dic43⋊C4C2211yescharacteristic
27C2×Dic43⋊C4C2211yescharacteristic
28C2×C22⋊Dic43C2211yescharacteristic
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×(C2×D43)⋊C4C2211yescharacteristic
38C2×(C2×D43)⋊C4C2211yescharacteristic
39C2×C4×Dic43C2211yescharacteristic
40C43⋊#95C2211yescharacteristic
41C43⋊#95C2211yescharacteristic
42C43⋊#95C2211yescharacteristic
43C43⋊#95C2211yescharacteristic
44C43⋊#95C2211yescharacteristic
45C43⋊#95C2211yescharacteristic
46C22×D4×C43C2211yescharacteristic
47C23×C4×C43C2211yescharacteristic
48C2×C22⋊C4×C43C2211yescharacteristic
49C2×C22⋊C4×C43C2211yescharacteristic
50C2×C22⋊C4×C43C2211yescharacteristic
51#95×C43C2211yescharacteristic
52#95×C43C2211yescharacteristic
53C24×C43C2311yescharacteristic
54C24×C43C2311yescharacteristic
55C23×D43C2311yescharacteristic
56C23×D43C2311yescharacteristic
57C2×D4×C43—22no—
58C2×D4×C43—22no—
59C2×D4×C43—41no—
60C22×C4×C43—22no—
61C22×C4×C43—41no—
62C22×C4×C43—41no—
63C22×C4×C43C2311yescharacteristic
64C22×C4×C43C2311yescharacteristic
65C22×C4×C43C2311yescharacteristic
66C22×C4×C43C2311yescharacteristic
67C22×C4×C43C2311yescharacteristic
68C2×C22⋊D43—22no—
69C2×C22⋊D43—22no—
70C2×C22⋊D43—22no—
71C2×C22⋊D43—22no—
72C2×C22⋊D43—22no—
73C2×C22⋊D43—41no—
74C2×C22⋊D43—41no—
75C2×C22⋊D43—41no—
76C2×C22⋊D43—41no—
77C2×C22⋊D43—41no—
78C2×C22⋊D43—41no—
79C2×C22⋊D43—41no—
80C22×Dic43C2311yescharacteristic
81C22×Dic43C2311yescharacteristic
82C22×Dic43C2311yescharacteristic
83C22×Dic43C2311yescharacteristic
84C22×Dic43C2311yescharacteristic
85C22×Dic43C2311yescharacteristic
86C2×D172—22no—
87C2×D172—41no—
88C2×D172—41no—
89C2×C4×D43—22no—
90C2×C4×D43—22no—
91C2×C4×D43—41no—
92C22⋊C4×C43—41no—
93C22⋊C4×C43—41no—
94C22⋊C4×C43—41no—
95C22⋊Dic43—22no—
96C22⋊Dic43—41no—
97C22⋊Dic43—41no—
98C22⋊Dic43D414yescomplemented
99(C2×D43)⋊C4—22no—
100(C2×D43)⋊C4—22no—
101(C2×D43)⋊C4—22no—
102(C2×D43)⋊C4—41no—
103(C2×D43)⋊C4—41no—
104(C2×D43)⋊C4—41no—
105(C2×D43)⋊C4—41no—
106C4⋊Dic43—22no—
107Dic43⋊C4—22no—
108Dic43⋊C4—22no—
109Dic43⋊C4—41no—
110C4×Dic43—41no—
111C23×C43—21no—
112C23×C43—21no—
113C23×C43—21no—
114C23×C43—21no—
115C23×C43—21no—
116C23×C43—21no—
117C23×C43—21no—
118C23×C43—21no—
119C23×C43—21no—
120C23×C43—21no—
121C23×C43—21no—
122C23×C43—21no—
123C23×C43—21no—
124C23×C43C2×D412yes—
125C23×C43C2411yescharacteristic
126C22×D43—21no—
127C22×D43—21no—
128C22×D43—21no—
129C22×D43—21no—
130C22×D43—21no—
131C22×D43—21no—
132C22×D43—21no—
133C22×D43—21no—
134C22×D43—21no—
135C22×D43—21no—
136C22×D43—21no—
137C22×D43—21no—
138C22×D43—21no—
139C22×D43#4112yes—
140D4×C43—44no—
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×C43—44no—
156C2×C4×C43#4112yes—
157C22⋊D43—44no—
158C22⋊D43—44no—
159C22⋊D43—44no—
160C22⋊D43—44no—
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×Dic43—21no—
174C2×Dic43—21no—
175C2×Dic43—21no—
176C2×Dic43—21no—
177C2×Dic43C2×D412yes—
178C2×Dic43C2×D412yes—
179D172—44no—
180C4×D43—44no—
181C22×C43—22no—
182C22×C43—22no—
183C22×C43—22no—
184C22×C43—41no—
185C22×C43—41no—
186C22×C43—41no—
187C22×C43—41no—
188C22×C43—41no—
189C22×C43—41no—
190C22×C43—41no—
191C22×C43—41no—
192C22×C43—41no—
193C22×C43—41no—
194C22×C43—41no—
195C22×C43C22×D411yescharacteristic
196C22×C43C2×#4111yescharacteristic
197C22×C43C2×#4111yescharacteristic
198C22×C43H(5,𝔽2)11yescharacteristic
199C22×C43H(5,𝔽2)11yescharacteristic
200C22×C43H(5,𝔽2)11yescharacteristic
201C22×C43H(5,𝔽2)11yescharacteristic
202C2×D43—22no—
203C2×D43—22no—
204C2×D43—22no—
205C2×D43—41no—
206C2×D43—41no—
207C2×D43—41no—
208C2×D43—41no—
209C2×D43—41no—
210C2×D43—41no—
211C2×D43—41no—
212C2×D43—41no—
213C2×D43—41no—
214C2×D43—41no—
215C2×D43—41no—
216C4×C43—22no—
217C4×C43—41no—
218C4×C43—41no—
219C4×C43—41no—
220C4×C43—41no—
221Dic43—22no—
222Dic43—22no—
223Dic43—41no—
224Dic43—41no—
225Dic43—41no—
226Dic43—41no—
227#2703—431nomaximal, Sylow
228C2×C43—42no—
229C2×C43—81no—
230C2×C43#53511yescharacteristic
231C2×C43#53811yescharacteristic
232C2×C43#54011yescharacteristic
233C2×C43#54611yescharacteristic
234C2×C43#54611yescharacteristic
235C2×C43#55311yescharacteristic
236C2×C43#56011yescharacteristic
237D43—42no—
238D43—81no—
239C2×#123—431no—
240C2×#121—431no—
241#400—431no—
242#397—431no—
243#394—431no—
244#392—431no—
245#392—431no—
246#392—431no—
247#390—431no—
248#388—431no—
249#388—431no—
250#386—431no—
251#386—431no—
252#386D4311yescharacteristic, complemented
253#380—431no—
254C43#270311yescharacteristic, complemented, Sylow
255C22×D4—431no—
256C22×D4—431no—
257C22×D4—431no—
258C22×D4—431no—
259C22×D4—431no—
260C22×D4C2×D4311yescharacteristic
261C23×C4—431no—
262C23×C4C2×D4311yescharacteristic
263#123—864no—
264#121—864no—
265C2×C4⋊C4—431no—
266C2×C4⋊C4—431no—
267C2×C4⋊C4—431no—
268C2×C4⋊C4—431no—
269C2×C22⋊C4—431no—
270C2×C22⋊C4—431no—
271C2×C22⋊C4—431no—
272C2×C22⋊C4—431no—
273C2×C22⋊C4—431no—
274C2×C22⋊C4—431no—
275C2×C22⋊C4—431no—
276C2×C22⋊C4—431no—
277C2×C22⋊C4—431no—
278C2×C22⋊C4—431no—
279C2×C22⋊C4—431no—
280C2×C22⋊C4C2×D4311yescharacteristic
281C2×C22⋊C4C2×D4311yescharacteristic
282C2×C22⋊C4C2×D4311yescharacteristic
283C2×C42—431no—
284#95—431no—
285#95—431no—
286#95—431no—
287#95—431no—
288#95—431no—
289#95—431no—
290#95C2×D4311yescharacteristic
291#95C2×D4311yescharacteristic
292C24—431no—
293C24—431no—
294C24C22×D4311yescharacteristic
295C24C22×D4311yescharacteristic
296C2×D4—22no—
297C2×D4—22no—
298C2×D4—41no—
299C2×D4—862no—
300C2×D4—862no—
301C2×D4—862no—
302C2×D4—862no—
303C2×D4—862no—
304C2×D4—862no—
305C2×D4—1721no—
306C2×D4—1721no—
307C2×D4—1721no—
308C2×D4—1721no—
309C2×D4—1721no—
310C2×D4—1721no—
311C2×D4—1721no—
312C2×D4—1721no—
313C2×D4—1721no—
314C22×C4—22no—
315C22×C4—41no—
316C22×C4—41no—
317C22×C4—431no—
318C22×C4—431no—
319C22×C4—431no—
320C22×C4—431no—
321C22×C4—431no—
322C22×C4—431no—
323C22×C4—862no—
324C22×C4—862no—
325C22×C4—1721no—
326C22×C4C22×D4311yescharacteristic
327C22×C4C22×D4311yescharacteristic
328C22×C4C22×D4311yescharacteristic
329C22×C4C22×D4311yescharacteristic
330C22×C4C22×D4311yescharacteristic
331C4⋊C4—862no—
332C4⋊C4—862no—
333C4⋊C4—862no—
334C4⋊C4—1721no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C22⋊C4—434no—
339C22⋊C4—862no—
340C22⋊C4—862no—
341C22⋊C4—862no—
342C22⋊C4—862no—
343C22⋊C4—1721no—
344C22⋊C4—1721no—
345C22⋊C4—1721no—
346C22⋊C4—1721no—
347C22⋊C4—1721no—
348C22⋊C4—1721no—
349C42—1721no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—21no—
362C23—21no—
363C23—432no—
364C23—861no—
365C23—861no—
366C23—861no—
367C23—861no—
368C23—861no—
369C23—861no—
370C23—861no—
371C23—861no—
372C23—861no—
373C23—861no—
374C23—861no—
375C23—861no—
376C23—861no—
377C23D4×D4312yes—
378C23C23×D4311yescharacteristic
379D4—44no—
380D4—1724no—
381D4—1724no—
382D4—1724no—
383D4—1724no—
384D4—1724no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—44no—
400C2×C4—432no—
401C2×C4—432no—
402C2×C4—861no—
403C2×C4—861no—
404C2×C4—861no—
405C2×C4—861no—
406C2×C4—861no—
407C2×C4—861no—
408C2×C4—861no—
409C2×C4—861no—
410C2×C4—861no—
411C2×C4—861no—
412C2×C4—861no—
413C2×C4—861no—
414C2×C4—861no—
415C2×C4—861no—
416C2×C4—861no—
417C2×C4—861no—
418C2×C4—1724no—
419C2×C4#1062189812yes—
420C22—22no—
421C22—22no—
422C22—22no—
423C22—41no—
424C22—41no—
425C22—41no—
426C22—41no—
427C22—41no—
428C22—41no—
429C22—41no—
430C22—41no—
431C22—41no—
432C22—41no—
433C22—41no—
434C22—862no—
435C22—862no—
436C22—862no—
437C22—1721no—
438C22—1721no—
439C22—1721no—
440C22—1721no—
441C22—1721no—
442C22—1721no—
443C22—1721no—
444C22—1721no—
445C22—1721no—
446C22—1721no—
447C22—1721no—
448C22C2×D4×D4311yescharacteristic
449C22#41×D4311yescharacteristic
450C22C2×#1062189811yescharacteristic
451C22#1306337011yescharacteristic
452C22#1306337011yescharacteristic
453C22#1306337011yescharacteristic
454C22#1306337111yescharacteristic
455C4—22no—
456C4—41no—
457C4—41no—
458C4—41no—
459C4—41no—
460C4—862no—
461C4—862no—
462C4—1721no—
463C4—1721no—
464C4—1721no—
465C4—1721no—
466C2—42no—
467C2—81no—
468C2—3441no—
469C2—1722no—
470C2#1458346411yescharacteristic
471C2#1458348111yescharacteristic
472C2#1458350011yescharacteristic
473C2#1458353911yescharacteristic
474C2#1458354111yescharacteristic
475C2#1458359911yescharacteristic
476C2#1458363711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#386C2
hypercenter#386D43
hypocenterC43#2703
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C2×#13063308C2semidirect
2. C2×#13063296C2semidirect
3. #14582841C2semidirect
4. #14582827C2semidirect
5. #14582814C2semidirect
6. #14582808C2semidirect
7. #14582808C2semidirect
8. #14582807C2semidirect
9. #14582799C2semidirect
10. #14582793C2semidirect
11. #14582791C2semidirect
12. #14582778C2semidirect
13. #14582777C2semidirect
14. #14582758C2semidirect
15. C43×#386C2semidirect
98. C22⋊Dic43D4semidirect
252. #386D43semidirect
254. C43#2703semidirect