Finite Group Databasebeta

← #19138484

Subgroups — #19138484

Order 5504.

718 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13063309C211yesmaximal, characteristic, complemented
2C2×#13063298C211yesmaximal, characteristic, complemented
3C2×C4×D172C211yesmaximal, characteristic, complemented
4C2×(C22⋊D43)⋊C4C211yesmaximal, characteristic, complemented
5#14582821C211yesmaximal, characteristic, complemented
6#14582809C211yesmaximal, characteristic, complemented
7#14582808C211yesmaximal, characteristic, complemented
8#14582808C211yesmaximal, characteristic, complemented
9#14582800C211yesmaximal, characteristic, complemented
10#14582790C211yesmaximal, characteristic, complemented
11#14582784C211yesmaximal, characteristic, complemented
12#14582777C211yesmaximal, characteristic, complemented
13#14582776C211yesmaximal, characteristic, complemented
14#14582773C211yesmaximal, characteristic, complemented
15C43×#388C211yesmaximal, 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#13063309—24no—
26#13063298—24no—
27C4×D172—24no—
28(C22⋊D43)⋊C4—24no—
29C2×C4⋊Dic43C2211yescharacteristic
30C2×C4⋊Dic43C2211yescharacteristic
31C2×Dic43⋊C4C2211yescharacteristic
32C2×Dic43⋊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×(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
48C2×C4⋊C4×C43C2211yescharacteristic
49C2×C22⋊C4×C43C2211yescharacteristic
50C2×C22⋊C4×C43C2211yescharacteristic
51C2×C22⋊C4×C43C2211yescharacteristic
52C2×C42×C43C2211yescharacteristic
53#95×C43C2211yescharacteristic
54#95×C43C2211yescharacteristic
55C24×C43C2311yescharacteristic
56C23×D43C2311yescharacteristic
57C23×D43C2311yescharacteristic
58C23×D43C2311yescharacteristic
59C22×C4×C43C2311yescharacteristic
60C22×C4×C43C2311yescharacteristic
61C22×C4×C43C2311yescharacteristic
62C22×C4×C43C2311yescharacteristic
63C22×C4×C43C2311yescharacteristic
64C22×C4×C43C2311yescharacteristic
65C2×C22⋊D43—22no—
66C2×C22⋊D43—22no—
67C2×C22⋊D43—22no—
68C2×C22⋊D43—22no—
69C2×C22⋊D43—22no—
70C2×C22⋊D43—22no—
71C2×C22⋊D43—22no—
72C2×C22⋊D43—41no—
73C2×C22⋊D43—41no—
74C22×Dic43—22no—
75C22×Dic43—22no—
76C22×Dic43—41no—
77C22×Dic43C2311yescharacteristic
78C22×Dic43C2311yescharacteristic
79C22×Dic43C2311yescharacteristic
80C22×Dic43C2311yescharacteristic
81C22×Dic43C2311yescharacteristic
82C2×D172—22no—
83C2×D172—22no—
84C2×D172—22no—
85C2×D172—22no—
86C2×D172—22no—
87C2×D172—22no—
88C2×D172—41no—
89C2×D172—41no—
90C2×D172—41no—
91C2×C4×D43—22no—
92C2×C4×D43—22no—
93C2×C4×D43—22no—
94C2×C4×D43—22no—
95C2×C4×D43—41no—
96C2×C4×D43—41no—
97C4⋊C4×C43—41no—
98C22⋊C4×C43—22no—
99C22⋊C4×C43—41no—
100C22⋊C4×C43D414yescomplemented
101C42×C43—22no—
102(C2×D43)⋊C4—22no—
103(C2×D43)⋊C4—22no—
104(C2×D43)⋊C4—22no—
105(C2×D43)⋊C4—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—41no—
111(C2×D43)⋊C4—41no—
112C4⋊Dic43—22no—
113C4⋊Dic43D414yescomplemented
114Dic43⋊C4—22no—
115Dic43⋊C4—22no—
116C4×Dic43—22no—
117C23×C43—21no—
118C23×C43—21no—
119C23×C43—21no—
120C23×C43—21no—
121C23×C43—21no—
122C23×C43—21no—
123C23×C43C2×D412yes—
124C23×C43C2411yescharacteristic
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×D43—21no—
139C22×D43—21no—
140C22×D43—21no—
141C22×D43—21no—
142C22×D43—21no—
143C22×D43—21no—
144C22×D43#4112yes—
145C22×D43#4112yes—
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—
158C2×C4×C43—21no—
159C2×C4×C43—21no—
160C2×C4×C43—21no—
161C2×C4×C43C2×D412yes—
162C2×C4×C43C2×D412yes—
163C2×C4×C43C2×D412yes—
164C22⋊D43—28no—
165C22⋊D43—44no—
166C22⋊D43—44no—
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×Dic43—21no—
178C2×Dic43—21no—
179C2×Dic43—44no—
180C2×Dic43C2×D412yes—
181C2×Dic43C2×D412yes—
182C2×Dic43#4112yes—
183D172—28no—
184D172—44no—
185D172—44no—
186C4×D43—44no—
187C4×D43—44no—
188C22×C43—22no—
189C22×C43—22no—
190C22×C43—22no—
191C22×C43—41no—
192C22×C43—41no—
193C22×C43—41no—
194C22×C43—41no—
195C22×C43C22×D411yescharacteristic
196C22×C43C22×D411yescharacteristic
197C22×C43C2×#4111yescharacteristic
198C22×C43C2×#4111yescharacteristic
199C22×C43C2×#4111yescharacteristic
200C22×C43H(5,𝔽2)11yescharacteristic
201C22×C43H(5,𝔽2)11yescharacteristic
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—41no—
213C2×D43—41no—
214C2×D43—41no—
215C2×D43—41no—
216C2×D43—41no—
217C2×D43—41no—
218C2×D43—41no—
219C2×D43—41no—
220C2×D43—41no—
221C2×D43—41no—
222C2×D43—41no—
223C4×C43—22no—
224C4×C43—22no—
225C4×C43—22no—
226C4×C43—41no—
227C4×C43—41no—
228C4×C43—41no—
229Dic43—22no—
230Dic43—22no—
231Dic43—22no—
232Dic43—41no—
233Dic43—41no—
234#2456—431nomaximal, Sylow
235C2×C43—42no—
236C2×C43#52511yescharacteristic
237C2×C43#52511yescharacteristic
238C2×C43#53811yescharacteristic
239C2×C43D4211yescharacteristic
240C2×C43#54611yescharacteristic
241C2×C43#55011yescharacteristic
242C2×C43#55311yescharacteristic
243D43—42no—
244D43—42no—
245D43—81no—
246C2×#123—431no—
247C2×#121—431no—
248C2×C4×D4—431no—
249C2×C4×D4—431no—
250#396—431no—
251#392—431no—
252#392—431no—
253#392—431no—
254#390—431no—
255#388—431no—
256#388D4311yescharacteristic, complemented
257#387—431no—
258#386—431no—
259#386—431no—
260#385—431no—
261C43#245611yescharacteristic, complemented, Sylow
262C22×D4—431no—
263C22×D4—431no—
264C22×D4—431no—
265C22×D4—431no—
266C22×D4—431no—
267C22×D4—431no—
268C23×C4—431no—
269C23×C4—431no—
270C23×C4—431no—
271#123—864no—
272#121—864no—
273C4×D4—864no—
274C4×D4—864no—
275C2×C4⋊C4—431no—
276C2×C4⋊C4—431no—
277C2×C4⋊C4—431no—
278C2×C4⋊C4—431no—
279C2×C4⋊C4C2×D4311yescharacteristic
280C2×C22⋊C4—431no—
281C2×C22⋊C4—431no—
282C2×C22⋊C4—431no—
283C2×C22⋊C4—431no—
284C2×C22⋊C4—431no—
285C2×C22⋊C4—431no—
286C2×C22⋊C4—431no—
287C2×C22⋊C4—431no—
288C2×C22⋊C4—431no—
289C2×C22⋊C4—431no—
290C2×C22⋊C4C2×D4311yescharacteristic
291C2×C22⋊C4C2×D4311yescharacteristic
292C2×C22⋊C4C2×D4311yescharacteristic
293C2×C42—431no—
294C2×C42C2×D4311yescharacteristic
295#95—431no—
296#95—431no—
297#95—431no—
298#95—431no—
299#95C2×D4311yescharacteristic
300#95C2×D4311yescharacteristic
301C24—431no—
302C24—431no—
303C24—431no—
304C24C22×D4311yescharacteristic
305C2×D4—862no—
306C2×D4—862no—
307C2×D4—862no—
308C2×D4—862no—
309C2×D4—862no—
310C2×D4—862no—
311C2×D4—862no—
312C2×D4—862no—
313C2×D4—862no—
314C2×D4—862no—
315C2×D4—862no—
316C2×D4—862no—
317C2×D4—862no—
318C2×D4—1721no—
319C2×D4—1721no—
320C2×D4—1721no—
321C2×D4—1721no—
322C2×D4—1721no—
323C22×C4—431no—
324C22×C4—431no—
325C22×C4—431no—
326C22×C4—431no—
327C22×C4—431no—
328C22×C4—862no—
329C22×C4—862no—
330C22×C4—862no—
331C22×C4—862no—
332C22×C4—862no—
333C22×C4—862no—
334C22×C4—1721no—
335C22×C4—1721no—
336C22×C4—1721no—
337C22×C4C22×D4311yescharacteristic
338C22×C4C22×D4311yescharacteristic
339C22×C4C22×D4311yescharacteristic
340C22×C4C22×D4311yescharacteristic
341C22×C4C22×D4311yescharacteristic
342C22×C4C22×D4311yescharacteristic
343C4⋊C4—41no—
344C4⋊C4—434no—
345C4⋊C4—862no—
346C4⋊C4—862no—
347C4⋊C4—862no—
348C22⋊C4—22no—
349C22⋊C4—41no—
350C22⋊C4—862no—
351C22⋊C4—862no—
352C22⋊C4—862no—
353C22⋊C4—862no—
354C22⋊C4—862no—
355C22⋊C4—862no—
356C22⋊C4—862no—
357C22⋊C4—862no—
358C22⋊C4—1721no—
359C22⋊C4—1721no—
360C22⋊C4D17214yescomplemented
361C42—22no—
362C42—862no—
363C23—21no—
364C23—21no—
365C23—21no—
366C23—21no—
367C23—21no—
368C23—21no—
369C23—432no—
370C23—432no—
371C23—861no—
372C23—861no—
373C23—861no—
374C23—861no—
375C23—861no—
376C23—861no—
377C23—861no—
378C23—861no—
379C23—861no—
380C23—861no—
381C23—861no—
382C23—861no—
383C23—861no—
384C23—861no—
385C23—861no—
386C23—861no—
387C23—861no—
388C23—861no—
389C23—861no—
390C23C2×D17212yes—
391C23C23×D4311yescharacteristic
392D4—868no—
393D4—868no—
394D4—1724no—
395D4—1724no—
396D4—1724no—
397D4—1724no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—432no—
414C2×C4—432no—
415C2×C4—432no—
416C2×C4—861no—
417C2×C4—861no—
418C2×C4—861no—
419C2×C4—861no—
420C2×C4—861no—
421C2×C4—861no—
422C2×C4—861no—
423C2×C4—861no—
424C2×C4—861no—
425C2×C4—861no—
426C2×C4—861no—
427C2×C4—861no—
428C2×C4—1724no—
429C2×C4—1724no—
430C2×C4—1724no—
431C2×C4C2×D17212yes—
432C2×C4C2×D17212yes—
433C2×C4D4×D4312yes—
434C22—22no—
435C22—22no—
436C22—22no—
437C22—41no—
438C22—41no—
439C22—41no—
440C22—41no—
441C22—862no—
442C22—862no—
443C22—862no—
444C22—862no—
445C22—862no—
446C22—862no—
447C22—1721no—
448C22—1721no—
449C22—1721no—
450C22—1721no—
451C22—1721no—
452C22—1721no—
453C22—1721no—
454C22—1721no—
455C22—1721no—
456C22—1721no—
457C22—1721no—
458C22—1721no—
459C22—1721no—
460C22—1721no—
461C22—1721no—
462C22C2×D4×D4311yescharacteristic
463C22C22×D17211yescharacteristic
464C22#41×D4311yescharacteristic
465C22#41×D4311yescharacteristic
466C22#41×D4311yescharacteristic
467C22#1306337011yescharacteristic
468C22#1306337111yescharacteristic
469C4—22no—
470C4—22no—
471C4—22no—
472C4—41no—
473C4—41no—
474C4—41no—
475C4—862no—
476C4—862no—
477C4—862no—
478C4—1721no—
479C4—1721no—
480C2—42no—
481C2—3441no—
482C2—1722no—
483C2—1722no—
484C2#1458340711yescharacteristic
485C2#1458341111yescharacteristic
486C2#1458348311yescharacteristic
487C2D4×D17211yescharacteristic
488C2#1458354411yescharacteristic
489C2#1458356711yescharacteristic
490C2#1458360011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#388C2
hypercenter#388D43
hypocenterC43#2456
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#13063309C2semidirect
2. C2×#13063298C2semidirect
3. C2×C4×D172C2semidirect
4. C2×(C22⋊D43)⋊C4C2semidirect
5. #14582821C2semidirect
6. #14582809C2semidirect
7. #14582808C2semidirect
8. #14582808C2semidirect
9. #14582800C2semidirect
10. #14582790C2semidirect
11. #14582784C2semidirect
12. #14582777C2semidirect
13. #14582776C2semidirect
14. #14582773C2semidirect
15. C43×#388C2semidirect
100. C22⋊C4×C43D4semidirect
113. C4⋊Dic43D4semidirect
256. #388D43semidirect
261. C43#2456semidirect
360. C22⋊C4D172semidirect