Finite Group Databasebeta

← #19141237

Subgroups — #19141237

Order 5504.

612 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13063310C211yesmaximal, characteristic, complemented
2C2×#13063300C211yesmaximal, characteristic, complemented
3#14582828C211yesmaximal, characteristic, complemented
4#14582817C211yesmaximal, characteristic, complemented
5#14582809C211yesmaximal, 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#14582777C211yesmaximal, characteristic, complemented
14#14582758C211yesmaximal, characteristic, complemented
15C43×#400C211yesmaximal, characteristic, complemented
16C22×D172C2211yescharacteristic
17C22×D172C2211yescharacteristic
18C22×D172C2211yescharacteristic
19C22×D172C2211yescharacteristic
20C22×D172C2211yescharacteristic
21C22×D172C2211yescharacteristic
22C22×C4×D43C2211yescharacteristic
23C22×C4×D43C2211yescharacteristic
24#13063310—24no—
25#13063300—24no—
26C2×Dic43⋊C4C2211yescharacteristic
27C2×Dic43⋊C4C2211yescharacteristic
28C2×(C2×D43)⋊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
39C2×(C2×D43)⋊C4C2211yescharacteristic
40C2×(C2×D43)⋊C4C2211yescharacteristic
41C2×(C2×D43)⋊C4C2211yescharacteristic
42C2×C4×Dic43C2211yescharacteristic
43C43⋊#95C2211yescharacteristic
44C43⋊#95C2211yescharacteristic
45C43⋊#95C2211yescharacteristic
46C2×C4⋊C4×C43C2211yescharacteristic
47C2×C4⋊C4×C43C2211yescharacteristic
48#95×C43C2211yescharacteristic
49#95×C43C2211yescharacteristic
50#95×C43C2211yescharacteristic
51#95×C43C2211yescharacteristic
52#95×C43C2211yescharacteristic
53C23×D43C2311yescharacteristic
54C23×D43C2311yescharacteristic
55C23×D43C2311yescharacteristic
56C23×D43C2311yescharacteristic
57C22×C4×C43C2311yescharacteristic
58C22×C4×C43C2311yescharacteristic
59C22×C4×C43C2311yescharacteristic
60C22×C4×C43C2311yescharacteristic
61C22×C4×C43C2311yescharacteristic
62C22×C4×C43C2311yescharacteristic
63C22×C4×C43C2311yescharacteristic
64C22×Dic43C2311yescharacteristic
65C22×Dic43C2311yescharacteristic
66C22×Dic43C2311yescharacteristic
67C22×Dic43C2311yescharacteristic
68C2×D172—22no—
69C2×D172—22no—
70C2×D172—22no—
71C2×D172—22no—
72C2×D172—22no—
73C2×D172—22no—
74C2×D172—22no—
75C2×D172—22no—
76C2×D172—41no—
77C2×D172—41no—
78C2×D172—41no—
79C2×D172—41no—
80C2×D172—41no—
81C2×D172—41no—
82C2×D172—41no—
83C2×D172—41no—
84C2×D172—41no—
85C2×D172—41no—
86C2×C4×D43—22no—
87C2×C4×D43—22no—
88C2×C4×D43—22no—
89C2×C4×D43—41no—
90C2×C4×D43—41no—
91C2×C4×D43—41no—
92C4⋊C4×C43—22no—
93C4⋊C4×C43—22no—
94(C2×D43)⋊C4—22no—
95(C2×D43)⋊C4—22no—
96(C2×D43)⋊C4—22no—
97(C2×D43)⋊C4—22no—
98(C2×D43)⋊C4—41no—
99(C2×D43)⋊C4—41no—
100(C2×D43)⋊C4—41no—
101(C2×D43)⋊C4—41no—
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)⋊C4D414yescomplemented
108Dic43⋊C4—22no—
109Dic43⋊C4—41no—
110C4×Dic43—41no—
111C23×C43C2411yescharacteristic
112C22×D43—21no—
113C22×D43—21no—
114C22×D43—21no—
115C22×D43—21no—
116C22×D43—21no—
117C22×D43—21no—
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×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—
158C2×C4×C43—21no—
159C2×C4×C43C2×D412yes—
160C2×C4×C43#4112yes—
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×Dic43C2×D412yes—
173D172—44no—
174D172—44no—
175D172—44no—
176D172—44no—
177D172—44no—
178D172—44no—
179C4×D43—44no—
180C4×D43—44no—
181C22×C43C22×D411yescharacteristic
182C22×C43C2×#4111yescharacteristic
183C22×C43C2×#4111yescharacteristic
184C22×C43H(5,𝔽2)11yescharacteristic
185C22×C43H(5,𝔽2)11yescharacteristic
186C22×C43H(5,𝔽2)11yescharacteristic
187C22×C43H(5,𝔽2)11yescharacteristic
188C2×D43—22no—
189C2×D43—22no—
190C2×D43—22no—
191C2×D43—22no—
192C2×D43—22no—
193C2×D43—22no—
194C2×D43—41no—
195C2×D43—41no—
196C2×D43—41no—
197C2×D43—41no—
198C2×D43—41no—
199C2×D43—41no—
200C2×D43—41no—
201C2×D43—41no—
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—
216C4×C43—22no—
217C4×C43—22no—
218C4×C43—41no—
219C4×C43—41no—
220C4×C43—41no—
221C4×C43—41no—
222C4×C43—41no—
223Dic43—22no—
224Dic43—41no—
225Dic43—41no—
226Dic43—41no—
227#2703—431nomaximal, Sylow
228C2×C43#53511yescharacteristic
229C2×C43#53811yescharacteristic
230C2×C43#54011yescharacteristic
231C2×C43#54611yescharacteristic
232C2×C43#54611yescharacteristic
233C2×C43#55311yescharacteristic
234C2×C43#56011yescharacteristic
235D43—42no—
236D43—42no—
237D43—81no—
238D43—81no—
239C2×#123—431no—
240C2×#121—431no—
241#400D4311yescharacteristic, complemented
242#397—431no—
243#394—431no—
244#392—431no—
245#392—431no—
246#392—431no—
247#390—431no—
248#388—431no—
249#388—431no—
250#386—431no—
251#386—431no—
252#386—431no—
253#380—431no—
254C43#270311yescharacteristic, complemented, Sylow
255C22×D4—431no—
256C22×D4—431no—
257C22×D4—431no—
258C22×D4—431no—
259C22×D4—431no—
260C22×D4—431no—
261C23×C4—431no—
262C23×C4—431no—
263#123—864no—
264#121—864no—
265C2×C4⋊C4—431no—
266C2×C4⋊C4—431no—
267C2×C4⋊C4C2×D4311yescharacteristic
268C2×C4⋊C4C2×D4311yescharacteristic
269C2×C22⋊C4—431no—
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⋊C4—431no—
281C2×C22⋊C4—431no—
282C2×C22⋊C4—431no—
283C2×C42—431no—
284#95—431no—
285#95—431no—
286#95—431no—
287#95C2×D4311yescharacteristic
288#95C2×D4311yescharacteristic
289#95C2×D4311yescharacteristic
290#95C2×D4311yescharacteristic
291#95C2×D4311yescharacteristic
292C24—431no—
293C24—431no—
294C24—431no—
295C24—431no—
296C2×D4—862no—
297C2×D4—862no—
298C2×D4—862no—
299C2×D4—862no—
300C2×D4—862no—
301C2×D4—862no—
302C2×D4—862no—
303C2×D4—862no—
304C2×D4—1721no—
305C2×D4—1721no—
306C2×D4—1721no—
307C2×D4—1721no—
308C2×D4—1721no—
309C2×D4—1721no—
310C2×D4—1721no—
311C2×D4—1721no—
312C2×D4—1721no—
313C2×D4—1721no—
314C22×C4—431no—
315C22×C4—431no—
316C22×C4—431no—
317C22×C4—431no—
318C22×C4—862no—
319C22×C4—862no—
320C22×C4—862no—
321C22×C4—1721no—
322C22×C4—1721no—
323C22×C4—1721no—
324C22×C4C22×D4311yescharacteristic
325C22×C4C22×D4311yescharacteristic
326C22×C4C22×D4311yescharacteristic
327C22×C4C22×D4311yescharacteristic
328C22×C4C22×D4311yescharacteristic
329C22×C4C22×D4311yescharacteristic
330C22×C4C22×D4311yescharacteristic
331C4⋊C4—22no—
332C4⋊C4—22no—
333C4⋊C4—862no—
334C4⋊C4—1721no—
335C22⋊C4—434no—
336C22⋊C4—862no—
337C22⋊C4—862no—
338C22⋊C4—862no—
339C22⋊C4—862no—
340C22⋊C4—1721no—
341C22⋊C4—1721no—
342C22⋊C4—1721no—
343C22⋊C4—1721no—
344C22⋊C4—1721no—
345C22⋊C4—1721no—
346C22⋊C4—1721no—
347C22⋊C4—1721no—
348C22⋊C4—1721no—
349C42—1721no—
350C23—432no—
351C23—432no—
352C23—861no—
353C23—861no—
354C23—861no—
355C23—861no—
356C23—861no—
357C23—861no—
358C23—861no—
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—
378C23C23×D4311yescharacteristic
379D4—1724no—
380D4—1724no—
381D4—1724no—
382D4—1724no—
383D4—1724no—
384D4—1724no—
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—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—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—1724no—
417C2×C4—1724no—
418C2×C4D4×D4312yes—
419C2×C4#1062190212yes—
420C22—862no—
421C22—862no—
422C22—862no—
423C22—862no—
424C22—862no—
425C22—862no—
426C22—1721no—
427C22—1721no—
428C22—1721no—
429C22—1721no—
430C22—1721no—
431C22—1721no—
432C22—1721no—
433C22—1721no—
434C22—1721no—
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—
448C22C2×D4×D4311yescharacteristic
449C22#41×D4311yescharacteristic
450C22C2×#1062190211yescharacteristic
451C22#1306337111yescharacteristic
452C22#1306337111yescharacteristic
453C22#1306337111yescharacteristic
454C22#1306337111yescharacteristic
455C4—22no—
456C4—22no—
457C4—41no—
458C4—41no—
459C4—41no—
460C4—41no—
461C4—41no—
462C4—862no—
463C4—1721no—
464C4—1721no—
465C4—1721no—
466C2—3441no—
467C2—3441no—
468C2—1722no—
469C2—1722no—
470C2#1458346711yescharacteristic
471C2#1458348811yescharacteristic
472C2#1458350511yescharacteristic
473C2#1458354011yescharacteristic
474C2#1458354111yescharacteristic
475C2#1458360211yescharacteristic
476C2#1458364011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#400C2
hypercenter#400D43
hypocenterC43#2703
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
1. C2×#13063310C2semidirect
2. C2×#13063300C2semidirect
3. #14582828C2semidirect
4. #14582817C2semidirect
5. #14582809C2semidirect
6. #14582809C2semidirect
7. #14582809C2semidirect
8. #14582800C2semidirect
9. #14582789C2semidirect
10. #14582788C2semidirect
11. #14582777C2semidirect
12. #14582777C2semidirect
13. #14582777C2semidirect
14. #14582758C2semidirect
15. C43×#400C2semidirect
107. (C2×D43)⋊C4D4semidirect
241. #400D43semidirect
254. C43#2703semidirect