Finite Group Databasebeta

← #19140859

Subgroups — #19140859

Order 5504.

734 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13063321C211yesmaximal, characteristic, complemented
2C2×#13063309C211yesmaximal, characteristic, complemented
3C2×#13063299C211yesmaximal, characteristic, complemented
4C2×#13063297C211yesmaximal, characteristic, complemented
5#14582817C211yesmaximal, characteristic, complemented
6#14582815C211yesmaximal, characteristic, complemented
7#14582809C211yesmaximal, characteristic, complemented
8#14582808C211yesmaximal, characteristic, complemented
9#14582808C211yesmaximal, characteristic, complemented
10#14582808C211yesmaximal, characteristic, complemented
11#14582791C211yesmaximal, characteristic, complemented
12#14582784C211yesmaximal, characteristic, complemented
13#14582778C211yesmaximal, characteristic, complemented
14#14582776C211yesmaximal, characteristic, complemented
15C43×#386C211yesmaximal, characteristic, complemented
16C22×D172C2211yescharacteristic
17C22×D172C2211yescharacteristic
18C22×D172C2211yescharacteristic
19C22×C22⋊D43C2211yescharacteristic
20C22×C22⋊D43C2211yescharacteristic
21C22×C22⋊D43C2211yescharacteristic
22C22×C22⋊D43C2211yescharacteristic
23C22×C22⋊D43C2211yescharacteristic
24C22×C22⋊D43C2211yescharacteristic
25C23×Dic43C2211yescharacteristic
26#13063321—24no—
27#13063309—24no—
28#13063299—24no—
29#13063297—24no—
30C2×C4⋊Dic43C2211yescharacteristic
31C2×C4⋊Dic43C2211yescharacteristic
32C2×Dic43⋊C4C2211yescharacteristic
33C2×C22⋊Dic43C2211yescharacteristic
34C2×(C2×D43)⋊C4C2211yescharacteristic
35C2×(C2×D43)⋊C4C2211yescharacteristic
36C2×(C2×D43)⋊C4C2211yescharacteristic
37C2×(C2×D43)⋊C4C2211yescharacteristic
38C2×(C2×D43)⋊C4C2211yescharacteristic
39C2×(C2×D43)⋊C4C2211yescharacteristic
40C2×(C2×D43)⋊C4C2211yescharacteristic
41C2×(C2×D43)⋊C4C2211yescharacteristic
42C2×(C2×D43)⋊C4C2211yescharacteristic
43C2×C4×Dic43C2211yescharacteristic
44C43⋊#95C2211yescharacteristic
45C43⋊#95C2211yescharacteristic
46C43⋊#95C2211yescharacteristic
47C43⋊#95C2211yescharacteristic
48C22×D4×C43C2211yescharacteristic
49C23×C4×C43C2211yescharacteristic
50C2×C22⋊C4×C43C2211yescharacteristic
51C2×C22⋊C4×C43C2211yescharacteristic
52C2×C22⋊C4×C43C2211yescharacteristic
53#95×C43C2211yescharacteristic
54#95×C43C2211yescharacteristic
55C24×C43C2311yescharacteristic
56C24×C43C2311yescharacteristic
57C23×D43C2311yescharacteristic
58C23×D43C2311yescharacteristic
59C23×D43C2311yescharacteristic
60C2×D4×C43—41no—
61C2×D4×C43—41no—
62C2×D4×C43D414yescomplemented
63C22×C4×C43—22no—
64C22×C4×C43—41no—
65C22×C4×C43—41no—
66C22×C4×C43C2311yescharacteristic
67C22×C4×C43C2311yescharacteristic
68C22×C4×C43C2311yescharacteristic
69C22×C4×C43C2311yescharacteristic
70C22×C4×C43C2311yescharacteristic
71C2×C22⋊D43—22no—
72C2×C22⋊D43—22no—
73C2×C22⋊D43—22no—
74C2×C22⋊D43—22no—
75C2×C22⋊D43—22no—
76C2×C22⋊D43—22no—
77C2×C22⋊D43—22no—
78C2×C22⋊D43—22no—
79C2×C22⋊D43—22no—
80C2×C22⋊D43—22no—
81C2×C22⋊D43—22no—
82C2×C22⋊D43—41no—
83C2×C22⋊D43—41no—
84C2×C22⋊D43—41no—
85C2×C22⋊D43—41no—
86C2×C22⋊D43—41no—
87C2×C22⋊D43—41no—
88C2×C22⋊D43—41no—
89C22×Dic43—22no—
90C22×Dic43—22no—
91C22×Dic43—41no—
92C22×Dic43C2311yescharacteristic
93C22×Dic43C2311yescharacteristic
94C22×Dic43C2311yescharacteristic
95C22×Dic43C2311yescharacteristic
96C22×Dic43C2311yescharacteristic
97C2×D172—22no—
98C2×D172—22no—
99C2×D172—41no—
100C2×D172—41no—
101C2×D172—41no—
102C2×D172—41no—
103C2×D172—41no—
104C2×D172—41no—
105C2×D172—41no—
106C22⋊C4×C43—22no—
107C22⋊C4×C43—41no—
108C22⋊C4×C43—41no—
109C22⋊Dic43—22no—
110(C2×D43)⋊C4—22no—
111(C2×D43)⋊C4—22no—
112(C2×D43)⋊C4—22no—
113(C2×D43)⋊C4—22no—
114(C2×D43)⋊C4—22no—
115(C2×D43)⋊C4—22no—
116(C2×D43)⋊C4—41no—
117(C2×D43)⋊C4—41no—
118(C2×D43)⋊C4—41no—
119C4⋊Dic43—22no—
120C4⋊Dic43D414yescomplemented
121Dic43⋊C4—22no—
122C4×Dic43—22no—
123C23×C43—21no—
124C23×C43—21no—
125C23×C43—21no—
126C23×C43—21no—
127C23×C43—21no—
128C23×C43—21no—
129C23×C43—21no—
130C23×C43—21no—
131C23×C43—21no—
132C23×C43—21no—
133C23×C43—21no—
134C23×C43—21no—
135C23×C43C2×D412yes—
136C23×C43C2×D412yes—
137C23×C43C2411yescharacteristic
138C22×D43—21no—
139C22×D43—21no—
140C22×D43—21no—
141C22×D43—21no—
142C22×D43—21no—
143C22×D43—21no—
144C22×D43—21no—
145C22×D43—21no—
146C22×D43—21no—
147C22×D43—21no—
148C22×D43—21no—
149C22×D43—21no—
150C22×D43—21no—
151C22×D43—21no—
152C22×D43—21no—
153C22×D43—21no—
154C22×D43—21no—
155C22×D43—21no—
156C22×D43—21no—
157C22×D43—21no—
158C22×D43—21no—
159D4×C43—44no—
160C2×C4×C43—21no—
161C2×C4×C43—21no—
162C2×C4×C43—21no—
163C2×C4×C43—21no—
164C2×C4×C43—21no—
165C2×C4×C43—21no—
166C2×C4×C43—21no—
167C2×C4×C43—21no—
168C2×C4×C43—21no—
169C2×C4×C43—21no—
170C2×C4×C43—21no—
171C2×C4×C43—21no—
172C2×C4×C43—21no—
173C2×C4×C43—44no—
174C2×C4×C43C2×D412yes—
175C2×C4×C43C2×D412yes—
176C22⋊D43—44no—
177C22⋊D43—44no—
178C22⋊D43—44no—
179C22⋊D43—44no—
180C22⋊D43—44no—
181C22⋊D43—44no—
182C2×Dic43—21no—
183C2×Dic43—21no—
184C2×Dic43—21no—
185C2×Dic43—21no—
186C2×Dic43—21no—
187C2×Dic43—21no—
188C2×Dic43—21no—
189C2×Dic43—21no—
190C2×Dic43—21no—
191C2×Dic43—21no—
192C2×Dic43—21no—
193C2×Dic43—21no—
194C2×Dic43—44no—
195C2×Dic43C2×D412yes—
196C2×Dic43C2×D412yes—
197C2×Dic43#4112yes—
198D172—44no—
199D172—44no—
200D172—44no—
201C22×C43—22no—
202C22×C43—22no—
203C22×C43—22no—
204C22×C43—22no—
205C22×C43—22no—
206C22×C43—22no—
207C22×C43—41no—
208C22×C43—41no—
209C22×C43—41no—
210C22×C43—41no—
211C22×C43—41no—
212C22×C43—41no—
213C22×C43—41no—
214C22×C43—41no—
215C22×C43C22×D411yescharacteristic
216C22×C43C22×D411yescharacteristic
217C22×C43C2×#4111yescharacteristic
218C22×C43H(5,𝔽2)11yescharacteristic
219C22×C43H(5,𝔽2)11yescharacteristic
220C22×C43H(5,𝔽2)11yescharacteristic
221C22×C43H(5,𝔽2)11yescharacteristic
222C2×D43—41no—
223C2×D43—41no—
224C2×D43—41no—
225C2×D43—41no—
226C2×D43—41no—
227C2×D43—41no—
228C2×D43—41no—
229C2×D43—41no—
230C2×D43—41no—
231C2×D43—41no—
232C2×D43—41no—
233C2×D43—41no—
234C2×D43—41no—
235C2×D43—41no—
236C2×D43—41no—
237C2×D43—41no—
238C2×D43—41no—
239C2×D43—41no—
240C2×D43—41no—
241C2×D43—41no—
242C2×D43—41no—
243C4×C43—22no—
244C4×C43—22no—
245C4×C43—41no—
246C4×C43—41no—
247C4×C43—41no—
248Dic43—22no—
249Dic43—22no—
250Dic43—22no—
251Dic43—41no—
252Dic43—41no—
253#2673—431nomaximal, Sylow
254C2×C43—42no—
255C2×C43—42no—
256C2×C43#53411yescharacteristic
257C2×C43#53511yescharacteristic
258C2×C43#54011yescharacteristic
259C2×C43D4211yescharacteristic
260C2×C43#54611yescharacteristic
261C2×C43#55011yescharacteristic
262C2×C43#56011yescharacteristic
263D43—81no—
264D43—81no—
265D43—81no—
266C2×#127—431no—
267C2×#123—431no—
268C2×#121—431no—
269C2×#121—431no—
270#394—431no—
271#394—431no—
272#392—431no—
273#392—431no—
274#392—431no—
275#392—431no—
276#388—431no—
277#387—431no—
278#386—431no—
279#386—431no—
280#386D4311yescharacteristic, complemented
281C43#267311yescharacteristic, complemented, Sylow
282C22×D4—431no—
283C22×D4—431no—
284C22×D4—431no—
285C22×D4—431no—
286C22×D4—431no—
287C22×D4—431no—
288C22×D4—431no—
289C22×D4—431no—
290C22×D4—431no—
291C22×D4C2×D4311yescharacteristic
292C23×C4—431no—
293C23×C4C2×D4311yescharacteristic
294#127—864no—
295#123—864no—
296#121—864no—
297#121—864no—
298C2×C4⋊C4—431no—
299C2×C4⋊C4—431no—
300C2×C4⋊C4—431no—
301C2×C22⋊C4—431no—
302C2×C22⋊C4—431no—
303C2×C22⋊C4—431no—
304C2×C22⋊C4—431no—
305C2×C22⋊C4—431no—
306C2×C22⋊C4—431no—
307C2×C22⋊C4—431no—
308C2×C22⋊C4—431no—
309C2×C22⋊C4—431no—
310C2×C22⋊C4—431no—
311C2×C22⋊C4C2×D4311yescharacteristic
312C2×C22⋊C4C2×D4311yescharacteristic
313C2×C22⋊C4C2×D4311yescharacteristic
314C2×C42—431no—
315#95—431no—
316#95—431no—
317#95—431no—
318#95—431no—
319#95C2×D4311yescharacteristic
320#95C2×D4311yescharacteristic
321C24—431no—
322C24—431no—
323C24—431no—
324C24C22×D4311yescharacteristic
325C24C22×D4311yescharacteristic
326C2×D4—41no—
327C2×D4—41no—
328C2×D4—862no—
329C2×D4—862no—
330C2×D4—862no—
331C2×D4—862no—
332C2×D4—862no—
333C2×D4—862no—
334C2×D4—862no—
335C2×D4—862no—
336C2×D4—862no—
337C2×D4—862no—
338C2×D4—862no—
339C2×D4—862no—
340C2×D4—862no—
341C2×D4—1721no—
342C2×D4—1721no—
343C2×D4—1721no—
344C2×D4—1721no—
345C2×D4—1721no—
346C2×D4—1721no—
347C2×D4—1721no—
348C2×D4—1721no—
349C2×D4—1721no—
350C2×D4—1721no—
351C2×D4—1721no—
352C2×D4—1721no—
353C2×D4—1721no—
354C2×D4—1721no—
355C2×D4D17214yescomplemented
356C22×C4—22no—
357C22×C4—41no—
358C22×C4—41no—
359C22×C4—431no—
360C22×C4—431no—
361C22×C4—431no—
362C22×C4—431no—
363C22×C4—431no—
364C22×C4—862no—
365C22×C4—862no—
366C22×C4—1721no—
367C22×C4C22×D4311yescharacteristic
368C22×C4C22×D4311yescharacteristic
369C22×C4C22×D4311yescharacteristic
370C22×C4C22×D4311yescharacteristic
371C22×C4C22×D4311yescharacteristic
372C4⋊C4—434no—
373C4⋊C4—862no—
374C4⋊C4—862no—
375C22⋊C4—22no—
376C22⋊C4—41no—
377C22⋊C4—41no—
378C22⋊C4—862no—
379C22⋊C4—862no—
380C22⋊C4—862no—
381C22⋊C4—862no—
382C22⋊C4—862no—
383C22⋊C4—862no—
384C22⋊C4—862no—
385C22⋊C4—1721no—
386C22⋊C4—1721no—
387C22⋊C4—1721no—
388C42—862no—
389C23—21no—
390C23—21no—
391C23—21no—
392C23—21no—
393C23—21no—
394C23—21no—
395C23—21no—
396C23—21no—
397C23—21no—
398C23—21no—
399C23—21no—
400C23—21no—
401C23—861no—
402C23—861no—
403C23—861no—
404C23—861no—
405C23—861no—
406C23—861no—
407C23—861no—
408C23—861no—
409C23—861no—
410C23—861no—
411C23—861no—
412C23—861no—
413C23—861no—
414C23—861no—
415C23—861no—
416C23—861no—
417C23—861no—
418C23—861no—
419C23—861no—
420C23—861no—
421C23—861no—
422C23C2×D17212yes—
423C23C2×D17212yes—
424C23C23×D4311yescharacteristic
425D4—44no—
426D4—1724no—
427D4—1724no—
428D4—1724no—
429D4—1724no—
430D4—1724no—
431D4—1724no—
432D4—1724no—
433D4—1724no—
434D4—1724no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—44no—
449C2×C4—432no—
450C2×C4—432no—
451C2×C4—432no—
452C2×C4—861no—
453C2×C4—861no—
454C2×C4—861no—
455C2×C4—861no—
456C2×C4—861no—
457C2×C4—861no—
458C2×C4—861no—
459C2×C4—861no—
460C2×C4—861no—
461C2×C4—861no—
462C2×C4—861no—
463C2×C4—861no—
464C2×C4—1724no—
465C2×C4C2×D17212yes—
466C2×C4D4×D4312yes—
467C22—22no—
468C22—22no—
469C22—22no—
470C22—22no—
471C22—22no—
472C22—22no—
473C22—41no—
474C22—41no—
475C22—41no—
476C22—41no—
477C22—41no—
478C22—41no—
479C22—41no—
480C22—41no—
481C22—1721no—
482C22—1721no—
483C22—1721no—
484C22—1721no—
485C22—1721no—
486C22—1721no—
487C22—1721no—
488C22—1721no—
489C22—1721no—
490C22—1721no—
491C22—1721no—
492C22—1721no—
493C22—1721no—
494C22—1721no—
495C22—1721no—
496C22—1721no—
497C22—1721no—
498C22—1721no—
499C22—1721no—
500C22—1721no—
501C22—1721no—
502C22C2×D4×D4311yescharacteristic
503C22C22×D17211yescharacteristic
504C22#41×D4311yescharacteristic
505C22#1306337011yescharacteristic
506C22#1306337011yescharacteristic
507C22#1306337011yescharacteristic
508C22#1306337111yescharacteristic
509C4—22no—
510C4—22no—
511C4—41no—
512C4—41no—
513C4—41no—
514C4—862no—
515C4—862no—
516C4—862no—
517C4—1721no—
518C4—1721no—
519C2—42no—
520C2—42no—
521C2—3441no—
522C2—3441no—
523C2—3441no—
524C2#1458346111yescharacteristic
525C2#1458346411yescharacteristic
526C2#1458350111yescharacteristic
527C2D4×D17211yescharacteristic
528C2#1458354411yescharacteristic
529C2#1458356711yescharacteristic
530C2#1458363711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#386C2
hypercenter#386D43
hypocenterC43#2673
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
1. C2×#13063321C2semidirect
2. C2×#13063309C2semidirect
3. C2×#13063299C2semidirect
4. C2×#13063297C2semidirect
5. #14582817C2semidirect
6. #14582815C2semidirect
7. #14582809C2semidirect
8. #14582808C2semidirect
9. #14582808C2semidirect
10. #14582808C2semidirect
11. #14582791C2semidirect
12. #14582784C2semidirect
13. #14582778C2semidirect
14. #14582776C2semidirect
15. C43×#386C2semidirect
62. C2×D4×C43D4semidirect
120. C4⋊Dic43D4semidirect
280. #386D43semidirect
281. C43#2673semidirect
355. C2×D4D172semidirect