Finite Group Databasebeta

← #19137928

Subgroups — #19137928

Order 5504.

864 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#10621898C211yesmaximal, characteristic
2C2×#13063310C211yesmaximal, characteristic, complemented
3C2×#13063307C211yesmaximal, characteristic, complemented
4C2×C4⋊C4×D43C211yesmaximal, characteristic, complemented
5#14582820C211yesmaximal, characteristic, complemented
6#14582819C211yesmaximal, characteristic, complemented
7#14582815C211yesmaximal, characteristic, complemented
8#14582814C211yesmaximal, characteristic, complemented
9#14582777C211yesmaximal, characteristic, complemented
10#14582775C211yesmaximal, characteristic, complemented
11#14582773C211yesmaximal, characteristic, complemented
12#14582772C211yesmaximal, characteristic, complemented
13#14582770C211yesmaximal, characteristic, complemented
14#14582761C211yesmaximal, characteristic, complemented
15C43×#385C211yesmaximal, characteristic, complemented
16C2×#10621898—24no—
17C2×#10621898—24no—
18C2×#10621898—24no—
19C22×Dic86C2211yescharacteristic
20C22×D172C2211yescharacteristic
21C22×C22⋊D43C2211yescharacteristic
22C22×C22⋊D43C2211yescharacteristic
23C22×C4×D43C2211yescharacteristic
24C22×C4×D43C2211yescharacteristic
25C22×C4×D43C2211yescharacteristic
26C22×C4×D43C2211yescharacteristic
27#13063310—24no—
28#13063307—24no—
29C2×C4⋊Dic43C2211yescharacteristic
30C2×C4⋊Dic43C2211yescharacteristic
31C2×Dic43⋊C4C2211yescharacteristic
32C2×Dic43⋊C4C2211yescharacteristic
33C2×Dic43⋊C4C2211yescharacteristic
34C2×Dic43⋊C4C2211yescharacteristic
35C4⋊C4×D43—24no—
36C2×C22⋊Dic43C2211yescharacteristic
37C2×C22⋊Dic43C2211yescharacteristic
38C2×(C2×D43)⋊C4C2211yescharacteristic
39C2×(C2×D43)⋊C4C2211yescharacteristic
40C2×(C2×D43)⋊C4C2211yescharacteristic
41C2×(C2×D43)⋊C4C2211yescharacteristic
42C2×(C2×D43)⋊C4C2211yescharacteristic
43C2×(C2×D43)⋊C4C2211yescharacteristic
44C43⋊#95C2211yescharacteristic
45C43⋊#95C2211yescharacteristic
46C43⋊#95C2211yescharacteristic
47C43⋊#95C2211yescharacteristic
48C43⋊#95C2211yescharacteristic
49C43⋊#95C2211yescharacteristic
50C23×C4×C43C2211yescharacteristic
51C2×C4⋊C4×C43C2211yescharacteristic
52C2×C4⋊C4×C43C2211yescharacteristic
53C2×C22⋊C4×C43C2211yescharacteristic
54C2×C22⋊C4×C43C2211yescharacteristic
55#95×C43C2211yescharacteristic
56#95×C43C2211yescharacteristic
57C24×C43C2311yescharacteristic
58C23×D43C2311yescharacteristic
59C23×D43C2311yescharacteristic
60C22×C4×C43—22no—
61C22×C4×C43—22no—
62C22×C4×C43—22no—
63C22×C4×C43C2311yescharacteristic
64C22×C4×C43C2311yescharacteristic
65C22×C4×C43C2311yescharacteristic
66C22×C4×C43C2311yescharacteristic
67C22×C4×C43C2311yescharacteristic
68C22×C4×C43C2311yescharacteristic
69C2×C22⋊D43—22no—
70C2×C22⋊D43—22no—
71C2×C22⋊D43—22no—
72C2×C22⋊D43—22no—
73C2×C22⋊D43—22no—
74C2×C22⋊D43D414yes—
75C22×Dic43C2311yescharacteristic
76C22×Dic43C2311yescharacteristic
77C22×Dic43C2311yescharacteristic
78C22×Dic43C2311yescharacteristic
79C22×Dic43C2311yescharacteristic
80C22×Dic43C2311yescharacteristic
81#10621898—232no—
82C2×D172—22no—
83C2×D172—22no—
84C2×D172D414yes—
85C2×C4×D43—22no—
86C2×C4×D43—22no—
87C2×C4×D43—22no—
88C2×C4×D43—22no—
89C2×C4×D43—22no—
90C2×C4×D43—22no—
91C2×C4×D43—22no—
92C2×C4×D43—22no—
93C2×C4×D43—22no—
94C2×C4×D43—22no—
95C2×C4×D43—22no—
96C2×C4×D43D414yes—
97C2×Dic86—22no—
98C2×Dic86—22no—
99C2×Dic86—22no—
100C4⋊C4×C43—22no—
101C4⋊C4×C43—22no—
102C22⋊C4×C43—22no—
103C22⋊C4×C43—22no—
104C22⋊Dic43—22no—
105C22⋊Dic43—22no—
106(C2×D43)⋊C4—22no—
107(C2×D43)⋊C4—22no—
108(C2×D43)⋊C4—22no—
109(C2×D43)⋊C4—22no—
110(C2×D43)⋊C4—22no—
111(C2×D43)⋊C4—22no—
112C4⋊Dic43—22no—
113C4⋊Dic43—22no—
114Dic43⋊C4—22no—
115Dic43⋊C4—22no—
116Dic43⋊C4—22no—
117Dic43⋊C4—22no—
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×D43C2×D412yes—
137C22×D43C2×D412yes—
138C22×D43C2×D412yes—
139C22×D43C2×D412yes—
140C2×C4×C43—28no—
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×C43C2×D412yes—
157C2×C4×C43C2×D412yes—
158C2×C4×C43#4112yescomplemented
159C22⋊D43—28no—
160C22⋊D43—28no—
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×Dic43C2×D412yes—
177C2×Dic43C2×D412yes—
178C2×Dic43#4112yescomplemented
179D172—28no—
180C4×D43—28no—
181C4×D43—28no—
182C4×D43—28no—
183C4×D43—44no—
184Dic86—28no—
185C22×C43—22no—
186C22×C43—22no—
187C22×C43—22no—
188C22×C43—41no—
189C22×C43—41no—
190C22×C43—41no—
191C22×C43—41no—
192C22×C43C22×D411yescharacteristic
193C22×C43C22×D411yescharacteristic
194C22×C43C22×D411yescharacteristic
195C22×C43C2×#4111yescharacteristic
196C22×C43C2×#4111yescharacteristic
197C22×C432−1+411yescharacteristic
198C22×C432−1+411yescharacteristic
199C2×D43—22no—
200C2×D43—22no—
201C2×D43—22no—
202C2×D43—22no—
203C2×D43—22no—
204C2×D43—22no—
205C2×D43—22no—
206C2×D43—22no—
207C2×D43—22no—
208C2×D43—41no—
209C2×D43—41no—
210C2×D43—41no—
211C2×D43—41no—
212C2×D43#12014yes—
213C4×C43—22no—
214C4×C43—22no—
215C4×C43—22no—
216C4×C43—41no—
217C4×C43—41no—
218C4×C43—41no—
219Dic43—22no—
220Dic43—22no—
221Dic43—22no—
222Dic43—41no—
223Dic43—41no—
224Dic43—41no—
225#2406—431nomaximal, Sylow
226C2×C43—42no—
227C2×C43C2×#12011yescharacteristic
228C2×C43#52511yescharacteristic
229C2×C43#53611yescharacteristic
230C2×C43#54711yescharacteristic
231C2×C43#54711yescharacteristic
232C2×C43#54711yescharacteristic
233C2×C43#54711yescharacteristic
234D43—24no—
235D43—42no—
236C22×#41—431no—
237C2×#123—431no—
238C2×#123—431no—
239C22×C4⋊C4—431no—
240#395—431no—
241#395—431no—
242#394—431no—
243#394—431no—
244#386—431no—
245#386—431no—
246#385—431no—
247#385—431no—
248#385—431no—
249#385D4311yescharacteristic, complemented
250#381—431no—
251C43#240611yescharacteristic, complemented, Sylow
252C2×#41—864no—
253C2×#41—864no—
254C2×#41—864no—
255C22×Q8—431no—
256C22×D4—431no—
257C22×D4—431no—
258C22×D4—431no—
259C23×C4—431no—
260C23×C4—431no—
261C23×C4—431no—
262C23×C4—431no—
263C23×C4C2×D4311yescharacteristic
264#123—864no—
265#123—864no—
266C2×C4⋊C4—431no—
267C2×C4⋊C4—431no—
268C2×C4⋊C4—431no—
269C2×C4⋊C4—431no—
270C2×C4⋊C4—431no—
271C2×C4⋊C4—431no—
272C2×C4⋊C4—864no—
273C2×C4⋊C4C2×D4311yescharacteristic
274C2×C4⋊C4C2×D4311yescharacteristic
275C2×C22⋊C4—431no—
276C2×C22⋊C4—431no—
277C2×C22⋊C4—431no—
278C2×C22⋊C4—431no—
279C2×C22⋊C4—431no—
280C2×C22⋊C4—431no—
281C2×C22⋊C4—431no—
282C2×C22⋊C4—431no—
283C2×C22⋊C4C2×D4311yescharacteristic
284C2×C22⋊C4C2×D4311yescharacteristic
285#95—431no—
286#95—431no—
287#95—431no—
288#95—431no—
289#95—431no—
290#95—431no—
291#95C2×D4311yescharacteristic
292#95C2×D4311yescharacteristic
293C24—431no—
294C24—431no—
295C24C22×D4311yescharacteristic
296#41—8632no—
297C2×Q8—862no—
298C2×Q8—862no—
299C2×Q8—862no—
300C2×D4—434no—
301C2×D4—434no—
302C2×D4—862no—
303C2×D4—862no—
304C2×D4—862no—
305C2×D4—862no—
306C2×D4—862no—
307C2×D4—862no—
308C2×D4—862no—
309C22×C4—22no—
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—431no—
313C22×C4—431no—
314C22×C4—431no—
315C22×C4—434no—
316C22×C4—431no—
317C22×C4—431no—
318C22×C4—431no—
319C22×C4—862no—
320C22×C4—862no—
321C22×C4—862no—
322C22×C4—862no—
323C22×C4—862no—
324C22×C4—862no—
325C22×C4—862no—
326C22×C4—862no—
327C22×C4—862no—
328C22×C4—862no—
329C22×C4—862no—
330C22×C4C22×D4311yescharacteristic
331C22×C4C22×D4311yescharacteristic
332C22×C4C22×D4311yescharacteristic
333C22×C4C22×D4311yescharacteristic
334C22×C4C22×D4311yescharacteristic
335C22×C4C22×D4311yescharacteristic
336C4⋊C4—22no—
337C4⋊C4—22no—
338C4⋊C4—862no—
339C4⋊C4—862no—
340C4⋊C4—862no—
341C4⋊C4—862no—
342C4⋊C4—862no—
343C4⋊C4—862no—
344C22⋊C4—22no—
345C22⋊C4—22no—
346C22⋊C4—862no—
347C22⋊C4—862no—
348C22⋊C4—862no—
349C22⋊C4—862no—
350C22⋊C4—862no—
351C22⋊C4—862no—
352C22⋊C4—862no—
353C22⋊C4—862no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—432no—
361C23—432no—
362C23—432no—
363C23—432no—
364C23—861no—
365C23—861no—
366C23—861no—
367C23—861no—
368C23—861no—
369C23—861no—
370C23—861no—
371C23—861no—
372C23—861no—
373C23—861no—
374C23D4×D4312yes—
375C23C23×D4311yescharacteristic
376Q8—868no—
377D4—868no—
378D4—868no—
379D4—868no—
380C2×C4—28no—
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—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—432no—
397C2×C4—432no—
398C2×C4—432no—
399C2×C4—868no—
400C2×C4—868no—
401C2×C4—868no—
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—1724no—
418C2×C4#1062189812yescomplemented
419C2×C4D4×D4312yes—
420C2×C4D4×D4312yes—
421C22—22no—
422C22—22no—
423C22—22no—
424C22—41no—
425C22—41no—
426C22—41no—
427C22—41no—
428C22—434no—
429C22—862no—
430C22—862no—
431C22—862no—
432C22—862no—
433C22—862no—
434C22—862no—
435C22—862no—
436C22—862no—
437C22—862no—
438C22—1721no—
439C22—1721no—
440C22—1721no—
441C22—1721no—
442C22C2×D4×D4311yescharacteristic
443C22C2×D4×D4311yescharacteristic
444C22C2×D4×D4311yescharacteristic
445C22#41×D4311yescharacteristic
446C22C2×#1062189811yescharacteristic
447C22#1306337211yescharacteristic
448C22#1306337311yescharacteristic
449C4—22no—
450C4—22no—
451C4—22no—
452C4—41no—
453C4—41no—
454C4—41no—
455C4—862no—
456C4—862no—
457C4—862no—
458C4—1721no—
459C4—1721no—
460C4—1721no—
461C2—42no—
462C2—864no—
463C2—1722no—
464C2#120×D4311yescharacteristic
465C2#1458340811yescharacteristic
466C2#1458347211yescharacteristic
467C2#1458354711yescharacteristic
468C2#1458355011yescharacteristic
469C2#1458355111yescharacteristic
470C2#1458355411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#385C2
hypercenter#385D43
hypocenterC43#2406
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
2. C2×#13063310C2semidirect
3. C2×#13063307C2semidirect
4. C2×C4⋊C4×D43C2semidirect
5. #14582820C2semidirect
6. #14582819C2semidirect
7. #14582815C2semidirect
8. #14582814C2semidirect
9. #14582777C2semidirect
10. #14582775C2semidirect
11. #14582773C2semidirect
12. #14582772C2semidirect
13. #14582770C2semidirect
14. #14582761C2semidirect
15. C43×#385C2semidirect
158. C2×C4×C43#41semidirect
178. C2×Dic43#41semidirect
249. #385D43semidirect
251. C43#2406semidirect
418. C2×C4#10621898semidirect