Finite Group Databasebeta

← #19141024

Subgroups — #19141024

Order 5504.

626 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13063298C211yesmaximal, characteristic, complemented
2C2×#13063298C211yesmaximal, characteristic, complemented
3#14582840C211yesmaximal, characteristic, complemented
4#14582828C211yesmaximal, characteristic, complemented
5#14582816C211yesmaximal, characteristic, complemented
6#14582809C211yesmaximal, characteristic, complemented
7#14582808C211yesmaximal, characteristic, complemented
8#14582777C211yesmaximal, characteristic, complemented
9#14582777C211yesmaximal, characteristic, complemented
10#14582776C211yesmaximal, characteristic, complemented
11#14582776C211yesmaximal, characteristic, complemented
12#14582776C211yesmaximal, characteristic, complemented
13#14582770C211yesmaximal, characteristic, complemented
14#14582761C211yesmaximal, characteristic, complemented
15C43×#397C211yesmaximal, characteristic, complemented
16C22×D172C2211yescharacteristic
17C22×D172C2211yescharacteristic
18C22×D172C2211yescharacteristic
19C22×C22⋊D43C2211yescharacteristic
20C22×C22⋊D43C2211yescharacteristic
21C22×C22⋊D43C2211yescharacteristic
22C23×Dic43C2211yescharacteristic
23C22×C4×D43C2211yescharacteristic
24C22×C4×D43C2211yescharacteristic
25#13063298—24no—
26#13063298—24no—
27C2×Dic43⋊C4C2211yescharacteristic
28C2×Dic43⋊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
37C2×(C2×D43)⋊C4C2211yescharacteristic
38C2×(C2×D43)⋊C4C2211yescharacteristic
39C43⋊#95C2211yescharacteristic
40C43⋊#95C2211yescharacteristic
41C43⋊#95C2211yescharacteristic
42C43⋊#95C2211yescharacteristic
43C43⋊#95C2211yescharacteristic
44C43⋊#95C2211yescharacteristic
45C43⋊#95C2211yescharacteristic
46C2×C4⋊C4×C43C2211yescharacteristic
47C2×C22⋊C4×C43C2211yescharacteristic
48C2×C22⋊C4×C43C2211yescharacteristic
49C2×C22⋊C4×C43C2211yescharacteristic
50#95×C43C2211yescharacteristic
51#95×C43C2211yescharacteristic
52#95×C43C2211yescharacteristic
53C24×C43C2311yescharacteristic
54C23×D43C2311yescharacteristic
55C23×D43C2311yescharacteristic
56C23×D43C2311yescharacteristic
57C22×C4×C43C2311yescharacteristic
58C22×C4×C43C2311yescharacteristic
59C22×C4×C43C2311yescharacteristic
60C22×C4×C43C2311yescharacteristic
61C22×C4×C43C2311yescharacteristic
62C22×C4×C43C2311yescharacteristic
63C2×C22⋊D43—22no—
64C2×C22⋊D43—22no—
65C2×C22⋊D43—22no—
66C2×C22⋊D43—22no—
67C2×C22⋊D43—41no—
68C2×C22⋊D43—41no—
69C2×C22⋊D43—41no—
70C2×C22⋊D43—41no—
71C2×C22⋊D43D414yescomplemented
72C22×Dic43—41no—
73C22×Dic43—41no—
74C22×Dic43—41no—
75C22×Dic43C2311yescharacteristic
76C22×Dic43C2311yescharacteristic
77C22×Dic43C2311yescharacteristic
78C22×Dic43C2311yescharacteristic
79C22×Dic43C2311yescharacteristic
80C2×D172—22no—
81C2×D172—22no—
82C2×D172—22no—
83C2×D172—22no—
84C2×D172—41no—
85C2×D172—41no—
86C2×D172—41no—
87C2×D172—41no—
88C2×D172—41no—
89C2×C4×D43—22no—
90C2×C4×D43—22no—
91C2×C4×D43—22no—
92C2×C4×D43—41no—
93C2×C4×D43—41no—
94C2×C4×D43—41no—
95C4⋊C4×C43—41no—
96C22⋊C4×C43—22no—
97C22⋊C4×C43—22no—
98C22⋊C4×C43—41no—
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—
106(C2×D43)⋊C4—41no—
107(C2×D43)⋊C4—41no—
108(C2×D43)⋊C4—41no—
109Dic43⋊C4—22no—
110Dic43⋊C4—22no—
111C23×C43—21no—
112C23×C43—21no—
113C23×C43—21no—
114C23×C43—21no—
115C23×C43—21no—
116C23×C43—21no—
117C23×C43C2×D412yes—
118C23×C43C2411yescharacteristic
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—21no—
134C22×D43—21no—
135C22×D43—21no—
136C22×D43—21no—
137C22×D43—21no—
138C22×D43C2×D412yes—
139C22×D43#4112yes—
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×C43—21no—
156C2×C4×C43—21no—
157C2×C4×C43—21no—
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—44no—
175C2×Dic43C2×D412yes—
176C2×Dic43#4112yes—
177D172—44no—
178D172—44no—
179D172—44no—
180C4×D43—44no—
181C4×D43—44no—
182C22×C43—22no—
183C22×C43—22no—
184C22×C43—22no—
185C22×C43—41no—
186C22×C43—41no—
187C22×C43—41no—
188C22×C43—41no—
189C22×C43C22×D411yescharacteristic
190C22×C43C2×#4111yescharacteristic
191C22×C43C2×#4111yescharacteristic
192C22×C43H(5,𝔽2)11yescharacteristic
193C22×C43H(5,𝔽2)11yescharacteristic
194C22×C43H(5,𝔽2)11yescharacteristic
195C22×C43H(5,𝔽2)11yescharacteristic
196C2×D43—22no—
197C2×D43—22no—
198C2×D43—22no—
199C2×D43—22no—
200C2×D43—22no—
201C2×D43—22no—
202C2×D43—41no—
203C2×D43—41no—
204C2×D43—41no—
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—
216C2×D43—41no—
217C4×C43—41no—
218C4×C43—41no—
219C4×C43—41no—
220C4×C43—41no—
221C4×C43—41no—
222C4×C43—41no—
223Dic43—22no—
224Dic43—22no—
225Dic43—41no—
226Dic43—41no—
227Dic43—41no—
228#2688—431nomaximal, Sylow
229C2×C43—42no—
230C2×C43#53411yescharacteristic
231C2×C43#53811yescharacteristic
232C2×C43#54011yescharacteristic
233C2×C43#54611yescharacteristic
234C2×C43#54611yescharacteristic
235C2×C43#55311yescharacteristic
236C2×C43#56011yescharacteristic
237D43—42no—
238D43—42no—
239D43—81no—
240C2×#121—431no—
241C2×#121—431no—
242#400—431no—
243#397—431no—
244#397D4311yescharacteristic, complemented
245#394—431no—
246#392—431no—
247#392—431no—
248#386—431no—
249#386—431no—
250#386—431no—
251#386—431no—
252#386—431no—
253#385—431no—
254#381—431no—
255C43#268811yescharacteristic, complemented, Sylow
256C22×D4—431no—
257C22×D4—431no—
258C22×D4—431no—
259C22×D4—431no—
260C22×D4—431no—
261C22×D4—431no—
262C23×C4—431no—
263C23×C4—431no—
264C23×C4—431no—
265#121—864no—
266#121—864no—
267C2×C4⋊C4—431no—
268C2×C4⋊C4—431no—
269C2×C4⋊C4C2×D4311yescharacteristic
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
283#95—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
292#95C2×D4311yescharacteristic
293C24—431no—
294C24—431no—
295C24—431no—
296C24C22×D4311yescharacteristic
297C2×D4—434no—
298C2×D4—862no—
299C2×D4—862no—
300C2×D4—862no—
301C2×D4—862no—
302C2×D4—862no—
303C2×D4—862no—
304C2×D4—862no—
305C2×D4—862no—
306C2×D4—1721no—
307C2×D4—1721no—
308C2×D4—1721no—
309C2×D4—1721no—
310C2×D4—1721no—
311C2×D4—1721no—
312C2×D4—1721no—
313C2×D4—1721no—
314C2×D4—1721no—
315C22×C4—431no—
316C22×C4—431no—
317C22×C4—431no—
318C22×C4—431no—
319C22×C4—431no—
320C22×C4—862no—
321C22×C4—862no—
322C22×C4—862no—
323C22×C4—1721no—
324C22×C4—1721no—
325C22×C4—1721no—
326C22×C4—1721no—
327C22×C4—1721no—
328C22×C4—1721no—
329C22×C4C22×D4311yescharacteristic
330C22×C4C22×D4311yescharacteristic
331C22×C4C22×D4311yescharacteristic
332C22×C4C22×D4311yescharacteristic
333C22×C4C22×D4311yescharacteristic
334C22×C4C22×D4311yescharacteristic
335C4⋊C4—41no—
336C4⋊C4—862no—
337C4⋊C4—862no—
338C22⋊C4—22no—
339C22⋊C4—22no—
340C22⋊C4—41no—
341C22⋊C4—862no—
342C22⋊C4—862no—
343C22⋊C4—862no—
344C22⋊C4—1721no—
345C22⋊C4—1721no—
346C22⋊C4—1721no—
347C22⋊C4—1721no—
348C22⋊C4—1721no—
349C22⋊C4—1721no—
350C22⋊C4—1721no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—432no—
358C23—432no—
359C23—861no—
360C23—861no—
361C23—861no—
362C23—861no—
363C23—861no—
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—
377C23—861no—
378C23D4×D4312yes—
379C23C23×D4311yescharacteristic
380D4—1724no—
381D4—1724no—
382D4—1724no—
383D4—1724no—
384D4—1724no—
385D4—1724no—
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—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—432no—
405C2×C4—432no—
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—861no—
419C2×C4—1724no—
420C2×C4—1724no—
421C2×C4—1724no—
422C22—22no—
423C22—22no—
424C22—22no—
425C22—41no—
426C22—41no—
427C22—41no—
428C22—41no—
429C22—862no—
430C22—862no—
431C22—862no—
432C22—862no—
433C22—862no—
434C22—862no—
435C22—1721no—
436C22—1721no—
437C22—1721no—
438C22—1721no—
439C22—1721no—
440C22—1721no—
441C22—1721no—
442C22—1721no—
443C22—1721no—
444C22—1721no—
445C22—1721no—
446C22—1721no—
447C22—1721no—
448C22—1721no—
449C22—1721no—
450C22C2×D4×D4311yescharacteristic
451C22#41×D4311yescharacteristic
452C22#41×D4311yescharacteristic
453C22#1306337011yescharacteristic
454C22#1306337111yescharacteristic
455C22#1306337111yescharacteristic
456C22#1306337111yescharacteristic
457C4—41no—
458C4—41no—
459C4—41no—
460C4—41no—
461C4—41no—
462C4—41no—
463C4—862no—
464C4—862no—
465C4—1721no—
466C4—1721no—
467C4—1721no—
468C2—42no—
469C2—3441no—
470C2—1722no—
471C2—1722no—
472C2#1458345711yescharacteristic
473C2#1458348311yescharacteristic
474C2#1458350111yescharacteristic
475C2#1458354111yescharacteristic
476C2#1458354111yescharacteristic
477C2#1458360011yescharacteristic
478C2#1458364011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#397C2
hypercenter#397D43
hypocenterC43#2688
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. C2×#13063298C2semidirect
2. C2×#13063298C2semidirect
3. #14582840C2semidirect
4. #14582828C2semidirect
5. #14582816C2semidirect
6. #14582809C2semidirect
7. #14582808C2semidirect
8. #14582777C2semidirect
9. #14582777C2semidirect
10. #14582776C2semidirect
11. #14582776C2semidirect
12. #14582776C2semidirect
13. #14582770C2semidirect
14. #14582761C2semidirect
15. C43×#397C2semidirect
71. C2×C22⋊D43D4semidirect
244. #397D43semidirect
255. C43#2688semidirect