Finite Group Databasebeta

← #19138604

Subgroups — #19138604

Order 5504.

710 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×#13063310C211yesmaximal, characteristic, complemented
2C2×#13063300C211yesmaximal, characteristic, complemented
3C2×#13063300C211yesmaximal, characteristic, complemented
4C2×#13063287C211yesmaximal, characteristic, complemented
5#14582816C211yesmaximal, characteristic, complemented
6#14582809C211yesmaximal, characteristic, complemented
7#14582809C211yesmaximal, characteristic, complemented
8#14582800C211yesmaximal, characteristic, complemented
9#14582789C211yesmaximal, characteristic, complemented
10#14582788C211yesmaximal, characteristic, complemented
11#14582777C211yesmaximal, characteristic, complemented
12#14582777C211yesmaximal, characteristic, complemented
13#14582770C211yesmaximal, characteristic, complemented
14#14582746C211yesmaximal, characteristic, complemented
15C43×#398C211yesmaximal, characteristic, complemented
16C22×D172C2211yescharacteristic
17C22×D172C2211yescharacteristic
18C22×D172C2211yescharacteristic
19C22×D172C2211yescharacteristic
20C22×D172C2211yescharacteristic
21C22×D172C2211yescharacteristic
22C22×C4×D43C2211yescharacteristic
23C22×C4×D43C2211yescharacteristic
24C22×C4×D43C2211yescharacteristic
25#13063310—24no—
26#13063300—24no—
27#13063300—24no—
28#13063287—24no—
29C2×Dic43⋊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
39C2×(C2×D43)⋊C4C2211yescharacteristic
40C2×(C2×D43)⋊C4C2211yescharacteristic
41C2×(C2×D43)⋊C4C2211yescharacteristic
42C2×(C2×D43)⋊C4C2211yescharacteristic
43C2×C4×Dic43C2211yescharacteristic
44C2×C4×Dic43C2211yescharacteristic
45C43⋊#95C2211yescharacteristic
46C43⋊#95C2211yescharacteristic
47C43⋊#95C2211yescharacteristic
48C2×C4⋊C4×C43C2211yescharacteristic
49C2×C4⋊C4×C43C2211yescharacteristic
50C2×C4⋊C4×C43C2211yescharacteristic
51C2×C4⋊C4×C43C2211yescharacteristic
52#95×C43C2211yescharacteristic
53#95×C43C2211yescharacteristic
54#95×C43C2211yescharacteristic
55C23×D43C2311yescharacteristic
56C23×D43C2311yescharacteristic
57C23×D43C2311yescharacteristic
58C23×D43C2311yescharacteristic
59C22×C4×C43C2311yescharacteristic
60C22×C4×C43C2311yescharacteristic
61C22×C4×C43C2311yescharacteristic
62C22×C4×C43C2311yescharacteristic
63C22×C4×C43C2311yescharacteristic
64C22×C4×C43C2311yescharacteristic
65C22×C4×C43C2311yescharacteristic
66C22×Dic43C2311yescharacteristic
67C22×Dic43C2311yescharacteristic
68C22×Dic43C2311yescharacteristic
69C22×Dic43C2311yescharacteristic
70C2×D172—22no—
71C2×D172—22no—
72C2×D172—22no—
73C2×D172—22no—
74C2×D172—22no—
75C2×D172—22no—
76C2×D172—22no—
77C2×D172—22no—
78C2×D172—22no—
79C2×D172—22no—
80C2×D172—22no—
81C2×D172—22no—
82C2×D172—22no—
83C2×D172—41no—
84C2×D172—41no—
85C2×D172—41no—
86C2×D172—41no—
87C2×D172—41no—
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—41no—
95C2×C4×D43—41no—
96C2×C4×D43—41no—
97C4⋊C4×C43—22no—
98C4⋊C4×C43—22no—
99C4⋊C4×C43—22no—
100C4⋊C4×C43—22no—
101(C2×D43)⋊C4—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—41no—
110(C2×D43)⋊C4—41no—
111(C2×D43)⋊C4—41no—
112(C2×D43)⋊C4D414yescomplemented
113(C2×D43)⋊C4D414yescomplemented
114Dic43⋊C4—22no—
115C4×Dic43—22no—
116C4×Dic43—41no—
117C23×C43C2411yescharacteristic
118C22×D43—21no—
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×D43—21no—
139C22×D43—21no—
140C22×D43—21no—
141C22×D43—21no—
142C22×D43—21no—
143C22×D43C2×D412yes—
144C22×D43C2×D412yes—
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×C43—21no—
162C2×C4×C43—21no—
163C2×C4×C43C2×D412yes—
164C2×C4×C43C2×D412yes—
165C2×C4×C43#4112yes—
166C2×C4×C43#4112yes—
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—28no—
180D172—44no—
181D172—44no—
182D172—44no—
183D172—44no—
184D172—44no—
185C4×D43—44no—
186C4×D43—44no—
187C4×D43—44no—
188C22×C43C22×D411yescharacteristic
189C22×C43C22×D411yescharacteristic
190C22×C43C2×#4111yescharacteristic
191C22×C43C2×#4111yescharacteristic
192C22×C43C2×#4111yescharacteristic
193C22×C43H(5,𝔽2)11yescharacteristic
194C22×C43H(5,𝔽2)11yescharacteristic
195C2×D43—22no—
196C2×D43—22no—
197C2×D43—22no—
198C2×D43—22no—
199C2×D43—22no—
200C2×D43—22no—
201C2×D43—22no—
202C2×D43—22no—
203C2×D43—22no—
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—
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—22no—
227C4×C43—41no—
228C4×C43—41no—
229C4×C43—41no—
230Dic43—22no—
231Dic43—22no—
232Dic43—41no—
233Dic43—41no—
234#2464—431nomaximal, Sylow
235C2×C43#52511yescharacteristic
236C2×C43#53211yescharacteristic
237C2×C43#54011yescharacteristic
238C2×C43D4211yescharacteristic
239C2×C43#54611yescharacteristic
240C2×C43#54611yescharacteristic
241C2×C43#55311yescharacteristic
242D43—42no—
243D43—42no—
244D43—42no—
245D43—81no—
246C2×#123—431no—
247C2×#121—431no—
248C2×#121—431no—
249C2×C4×D4—431no—
250#398D4311yescharacteristic, complemented
251#394—431no—
252#392—431no—
253#392—431no—
254#390—431no—
255#388—431no—
256#388—431no—
257#386—431no—
258#386—431no—
259#385—431no—
260C4×C22⋊C4—431no—
261C43#246411yescharacteristic, 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—
273#121—864no—
274C4×D4—864no—
275C2×C4⋊C4—431no—
276C2×C4⋊C4C2×D4311yescharacteristic
277C2×C4⋊C4C2×D4311yescharacteristic
278C2×C4⋊C4C2×D4311yescharacteristic
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⋊C4—431no—
291C2×C22⋊C4—431no—
292C2×C22⋊C4—431no—
293C2×C42—431no—
294C2×C42—431no—
295#95—431no—
296#95—431no—
297#95—431no—
298#95C2×D4311yescharacteristic
299#95C2×D4311yescharacteristic
300#95C2×D4311yescharacteristic
301C24—431no—
302C24—431no—
303C24—431no—
304C24—431no—
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—862no—
328C22×C4—862no—
329C22×C4—862no—
330C22×C4—862no—
331C22×C4—862no—
332C22×C4—862no—
333C22×C4—1721no—
334C22×C4—1721no—
335C22×C4—1721no—
336C22×C4C22×D4311yescharacteristic
337C22×C4C22×D4311yescharacteristic
338C22×C4C22×D4311yescharacteristic
339C22×C4C22×D4311yescharacteristic
340C22×C4C22×D4311yescharacteristic
341C22×C4C22×D4311yescharacteristic
342C22×C4C22×D4311yescharacteristic
343C4⋊C4—22no—
344C4⋊C4—22no—
345C4⋊C4—22no—
346C4⋊C4—22no—
347C4⋊C4—862no—
348C22⋊C4—434no—
349C22⋊C4—434no—
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⋊C4—1721no—
361C42—862no—
362C42—1721no—
363C23—432no—
364C23—432no—
365C23—432no—
366C23—861no—
367C23—861no—
368C23—861no—
369C23—861no—
370C23—861no—
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—
390C23—861no—
391C23C23×D4311yescharacteristic
392D4—868no—
393D4—1724no—
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—21no—
414C2×C4—21no—
415C2×C4—432no—
416C2×C4—432no—
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—1724no—
428C2×C4—1724no—
429C2×C4—1724no—
430C2×C4D4×D4312yes—
431C2×C4D4×D4312yes—
432C2×C4#1062190212yes—
433C2×C4#1062190212yes—
434C22—862no—
435C22—862no—
436C22—862no—
437C22—862no—
438C22—862no—
439C22—862no—
440C22—862no—
441C22—862no—
442C22—862no—
443C22—1721no—
444C22—1721no—
445C22—1721no—
446C22—1721no—
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
463C22C2×D4×D4311yescharacteristic
464C22#41×D4311yescharacteristic
465C22C2×#1062190211yescharacteristic
466C22C2×#1062190211yescharacteristic
467C22#1306337111yescharacteristic
468C22#1306337111yescharacteristic
469C4—22no—
470C4—22no—
471C4—22no—
472C4—22no—
473C4—41no—
474C4—41no—
475C4—41no—
476C4—862no—
477C4—862no—
478C4—1721no—
479C4—1721no—
480C2—3441no—
481C2—1722no—
482C2—1722no—
483C2—1722no—
484C2#1458341211yescharacteristic
485C2#1458345011yescharacteristic
486C2#1458350511yescharacteristic
487C2#1458353311yescharacteristic
488C2#1458354011yescharacteristic
489C2#1458354111yescharacteristic
490C2#1458360211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#398C2
hypercenter#398D43
hypocenterC43#2464
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. C2×#13063310C2semidirect
2. C2×#13063300C2semidirect
3. C2×#13063300C2semidirect
4. C2×#13063287C2semidirect
5. #14582816C2semidirect
6. #14582809C2semidirect
7. #14582809C2semidirect
8. #14582800C2semidirect
9. #14582789C2semidirect
10. #14582788C2semidirect
11. #14582777C2semidirect
12. #14582777C2semidirect
13. #14582770C2semidirect
14. #14582746C2semidirect
15. C43×#398C2semidirect
112. (C2×D43)⋊C4D4semidirect
113. (C2×D43)⋊C4D4semidirect
250. #398D43semidirect
261. C43#2464semidirect