Finite Group Databasebeta

← #19138102

Subgroups — #19138102

Order 5504.

652 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13063307C211yesmaximal, characteristic, complemented
2C2×#13063306C211yesmaximal, characteristic, complemented
3C2×#13063297C211yesmaximal, characteristic
4C2×(C22⋊D43)⋊C4C211yesmaximal, characteristic, complemented
5#14582828C211yesmaximal, characteristic, complemented
6#14582827C211yesmaximal, characteristic, complemented
7#14582815C211yesmaximal, characteristic, complemented
8#14582799C211yesmaximal, characteristic, complemented
9#14582796C211yesmaximal, characteristic, complemented
10#14582774C211yesmaximal, characteristic, complemented
11#14582770C211yesmaximal, characteristic, complemented
12#14582768C211yesmaximal, characteristic, complemented
13#14582757C211yesmaximal, characteristic, complemented
14C22⋊C4×Dic43C211yesmaximal, characteristic, complemented
15C43×#394C211yesmaximal, characteristic, complemented
16C22×C22⋊D43C2211yescharacteristic
17C22×C22⋊D43C2211yescharacteristic
18C23×Dic43C2211yescharacteristic
19C23×Dic43C2211yescharacteristic
20C22×C4×D43C2211yescharacteristic
21#13063307—24no—
22#13063306—24no—
23#13063297—24no—
24(C22⋊D43)⋊C4—24no—
25C2×C4⋊Dic43C2211yescharacteristic
26C2×C4⋊Dic43C2211yescharacteristic
27C2×Dic43⋊C4C2211yescharacteristic
28C2×Dic43⋊C4C2211yescharacteristic
29C2×Dic43⋊C4C2211yescharacteristic
30C2×Dic43⋊C4C2211yescharacteristic
31C2×Dic43⋊C4C2211yescharacteristic
32C2×Dic43⋊C4C2211yescharacteristic
33C2×C22⋊Dic43C2211yescharacteristic
34C2×C22⋊Dic43C2211yescharacteristic
35C2×C22⋊Dic43C2211yescharacteristic
36C2×C22⋊Dic43C2211yescharacteristic
37C2×(C2×D43)⋊C4C2211yescharacteristic
38C2×(C2×D43)⋊C4C2211yescharacteristic
39C2×(C2×D43)⋊C4C2211yescharacteristic
40C2×(C2×D43)⋊C4C2211yescharacteristic
41C2×C4×Dic43C2211yescharacteristic
42C2×C4×Dic43C2211yescharacteristic
43C43⋊#95C2211yescharacteristic
44C43⋊#95C2211yescharacteristic
45C43⋊#95C2211yescharacteristic
46C43⋊#95C2211yescharacteristic
47C43⋊#95C2211yescharacteristic
48C22×D4×C43C2211yescharacteristic
49C2×C4⋊C4×C43C2211yescharacteristic
50C2×C22⋊C4×C43C2211yescharacteristic
51C2×C22⋊C4×C43C2211yescharacteristic
52C2×C22⋊C4×C43C2211yescharacteristic
53C2×C22⋊C4×C43C2211yescharacteristic
54#95×C43C2211yescharacteristic
55C24×C43C2311yescharacteristic
56C24×C43C2311yescharacteristic
57C23×D43C2311yescharacteristic
58C2×D4×C43—22no—
59C2×D4×C43—22no—
60C2×D4×C43—41no—
61C22×C4×C43C2311yescharacteristic
62C22×C4×C43C2311yescharacteristic
63C22×C4×C43C2311yescharacteristic
64C22×C4×C43C2311yescharacteristic
65C22×C4×C43C2311yescharacteristic
66C2×C22⋊D43—22no—
67C2×C22⋊D43—22no—
68C2×C22⋊D43—22no—
69C2×C22⋊D43—22no—
70C2×C22⋊D43—41no—
71C2×C22⋊D43D414yes—
72C22×Dic43—22no—
73C22×Dic43—22no—
74C22×Dic43—22no—
75C22×Dic43—22no—
76C22×Dic43—22no—
77C22×Dic43—41no—
78C22×Dic43C2311yescharacteristic
79C22×Dic43C2311yescharacteristic
80C22×Dic43C2311yescharacteristic
81C22×Dic43C2311yescharacteristic
82C22×Dic43C2311yescharacteristic
83C22×Dic43C2311yescharacteristic
84C22×Dic43C2311yescharacteristic
85C2×C4×D43—22no—
86C2×C4×D43—22no—
87C2×C4×D43—41no—
88C4⋊C4×C43—41no—
89C22⋊C4×C43—22no—
90C22⋊C4×C43—22no—
91C22⋊C4×C43—22no—
92C22⋊C4×C43—22no—
93C22⋊Dic43—22no—
94C22⋊Dic43—22no—
95C22⋊Dic43—22no—
96C22⋊Dic43D414yescomplemented
97(C2×D43)⋊C4—22no—
98(C2×D43)⋊C4—22no—
99(C2×D43)⋊C4—22no—
100(C2×D43)⋊C4—22no—
101C4⋊Dic43—22no—
102C4⋊Dic43—41no—
103Dic43⋊C4—22no—
104Dic43⋊C4—22no—
105Dic43⋊C4—22no—
106Dic43⋊C4—22no—
107Dic43⋊C4—22no—
108Dic43⋊C4—22no—
109C4×Dic43—22no—
110C4×Dic43—22no—
111C23×C43—21no—
112C23×C43—21no—
113C23×C43—21no—
114C23×C43—21no—
115C23×C43—21no—
116C23×C43—21no—
117C23×C43—21no—
118C23×C43—21no—
119C23×C43—21no—
120C23×C43—21no—
121C23×C43—21no—
122C23×C43—21no—
123C23×C43C2×D412yes—
124C23×C43C2×D412yes—
125C23×C43C2411yescharacteristic
126C22×D43—21no—
127C22×D43—21no—
128C22×D43—21no—
129C22×D43—21no—
130C22×D43—21no—
131C22×D43—21no—
132C22×D43C2×D412yes—
133D4×C43—44no—
134C2×C4×C43—21no—
135C2×C4×C43—21no—
136C2×C4×C43—21no—
137C2×C4×C43—21no—
138C2×C4×C43—21no—
139C2×C4×C43—21no—
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#4112yes—
149C22⋊D43—28no—
150C22⋊D43—44no—
151C2×Dic43—21no—
152C2×Dic43—21no—
153C2×Dic43—21no—
154C2×Dic43—21no—
155C2×Dic43—21no—
156C2×Dic43—21no—
157C2×Dic43—21no—
158C2×Dic43—21no—
159C2×Dic43—21no—
160C2×Dic43—21no—
161C2×Dic43—21no—
162C2×Dic43—21no—
163C2×Dic43—21no—
164C2×Dic43—21no—
165C2×Dic43—21no—
166C2×Dic43—21no—
167C2×Dic43—44no—
168C2×Dic43—44no—
169C2×Dic43C2×D412yes—
170C2×Dic43C2×D412yes—
171C2×Dic43C2×D412yes—
172C2×Dic43#4112yes—
173C2×Dic43#4112yes—
174C4×D43—44no—
175C22×C43—22no—
176C22×C43—22no—
177C22×C43—22no—
178C22×C43—22no—
179C22×C43—22no—
180C22×C43—22no—
181C22×C43—41no—
182C22×C43—41no—
183C22×C43—41no—
184C22×C43—41no—
185C22×C43—41no—
186C22×C43—41no—
187C22×C43—41no—
188C22×C43—41no—
189C22×C43C22×D411yescharacteristic
190C22×C43C22×D411yescharacteristic
191C22×C43C2×#4111yescharacteristic
192C22×C43C2×#4111yescharacteristic
193C22×C43C2×#4111yescharacteristic
194C22×C43H(5,𝔽2)11yescharacteristic
195C22×C432−1+411yescharacteristic
196C2×D43—22no—
197C2×D43—22no—
198C2×D43—22no—
199C2×D43—41no—
200C2×D43—41no—
201C2×D43—41no—
202C2×D43—41no—
203C4×C43—22no—
204C4×C43—41no—
205C4×C43—41no—
206C4×C43—41no—
207C4×C43—41no—
208Dic43—22no—
209Dic43—22no—
210Dic43—41no—
211Dic43—41no—
212Dic43—41no—
213Dic43—41no—
214Dic43#12314yescomplemented
215#2422—431nomaximal, Sylow
216C2×C43—42no—
217C2×C43—42no—
218C2×C43C2×#12311yescharacteristic
219C2×C43#53211yescharacteristic
220C2×C43#54211yescharacteristic
221C2×C43D4211yescharacteristic
222C2×C43#54711yescharacteristic
223C2×C43#54711yescharacteristic
224C2×C43#55311yescharacteristic
225D43—42no—
226C2×#123—431no—
227C2×#123—431no—
228C2×#121—431no—
229C2×C4×D4—431no—
230#397—431no—
231#397—431no—
232#394—431no—
233#394D4311yescharacteristic, complemented
234#390—431no—
235#389—431no—
236#385—431no—
237#385—431no—
238#384—431no—
239#380—431no—
240C4×C22⋊C4—431no—
241C43#242211yescharacteristic, complemented, Sylow
242C22×D4—431no—
243C22×D4—431no—
244C22×D4C2×D4311yescharacteristic
245C23×C4—431no—
246C23×C4—431no—
247C23×C4—431no—
248#123—864no—
249#123—864no—
250#121—864no—
251C4×D4—864no—
252C2×C4⋊C4—431no—
253C2×C4⋊C4—431no—
254C2×C4⋊C4—431no—
255C2×C4⋊C4—431no—
256C2×C4⋊C4—431no—
257C2×C4⋊C4—431no—
258C2×C4⋊C4—431no—
259C2×C4⋊C4—431no—
260C2×C4⋊C4C2×D4311yescharacteristic
261C2×C22⋊C4—431no—
262C2×C22⋊C4—431no—
263C2×C22⋊C4—431no—
264C2×C22⋊C4—431no—
265C2×C22⋊C4—431no—
266C2×C22⋊C4—431no—
267C2×C22⋊C4—431no—
268C2×C22⋊C4—431no—
269C2×C22⋊C4C2×D4311yescharacteristic
270C2×C22⋊C4C2×D4311yescharacteristic
271C2×C22⋊C4C2×D4311yescharacteristic
272C2×C22⋊C4C2×D4311yescharacteristic
273C2×C42—431no—
274C2×C42—431no—
275#95—431no—
276#95—431no—
277#95—431no—
278#95—431no—
279#95—431no—
280#95C2×D4311yescharacteristic
281C24—431no—
282C24C22×D4311yescharacteristic
283C24C22×D4311yescharacteristic
284C2×D4—22no—
285C2×D4—22no—
286C2×D4—41no—
287C2×D4—434no—
288C2×D4—862no—
289C2×D4—862no—
290C2×D4—862no—
291C2×D4—862no—
292C2×D4—1721no—
293C22×C4—431no—
294C22×C4—431no—
295C22×C4—431no—
296C22×C4—431no—
297C22×C4—431no—
298C22×C4—431no—
299C22×C4—431no—
300C22×C4—862no—
301C22×C4—862no—
302C22×C4—862no—
303C22×C4—862no—
304C22×C4—862no—
305C22×C4—862no—
306C22×C4—862no—
307C22×C4—1721no—
308C22×C4—1721no—
309C22×C4C22×D4311yescharacteristic
310C22×C4C22×D4311yescharacteristic
311C22×C4C22×D4311yescharacteristic
312C22×C4C22×D4311yescharacteristic
313C22×C4C22×D4311yescharacteristic
314C4⋊C4—41no—
315C4⋊C4—862no—
316C4⋊C4—862no—
317C4⋊C4—862no—
318C4⋊C4—862no—
319C4⋊C4—862no—
320C4⋊C4—862no—
321C4⋊C4—862no—
322C4⋊C4—1721no—
323C22⋊C4—22no—
324C22⋊C4—22no—
325C22⋊C4—22no—
326C22⋊C4—22no—
327C22⋊C4—434no—
328C22⋊C4—862no—
329C22⋊C4—862no—
330C22⋊C4—862no—
331C22⋊C4—862no—
332C22⋊C4—862no—
333C22⋊C4—862no—
334C22⋊C4—862no—
335C42—862no—
336C42—862no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—21no—
347C23—21no—
348C23—21no—
349C23—432no—
350C23—861no—
351C23—861no—
352C23—861no—
353C23—861no—
354C23—861no—
355C23—861no—
356C23D4×D4312yes—
357C23D4×D4312yes—
358C23C23×D4311yescharacteristic
359D4—44no—
360D4—868no—
361D4—1724no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—432no—
377C2×C4—432no—
378C2×C4—432no—
379C2×C4—432no—
380C2×C4—432no—
381C2×C4—861no—
382C2×C4—861no—
383C2×C4—861no—
384C2×C4—861no—
385C2×C4—861no—
386C2×C4—861no—
387C2×C4—861no—
388C2×C4—861no—
389C2×C4—861no—
390C2×C4—861no—
391C2×C4—861no—
392C2×C4—861no—
393C2×C4—861no—
394C2×C4—861no—
395C2×C4—861no—
396C2×C4—861no—
397C2×C4—1724no—
398C2×C4—1724no—
399C2×C4—1724no—
400C2×C4#1062190012yes—
401C22—22no—
402C22—22no—
403C22—22no—
404C22—22no—
405C22—22no—
406C22—22no—
407C22—41no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—862no—
416C22—862no—
417C22—862no—
418C22—1721no—
419C22—1721no—
420C22—1721no—
421C22—1721no—
422C22C2×D4×D4311yescharacteristic
423C22C2×D4×D4311yescharacteristic
424C22#41×D4311yescharacteristic
425C22#41×D4311yescharacteristic
426C22C2×#1062190011yescharacteristic
427C22#1306337011yescharacteristic
428C22#1306337211yescharacteristic
429C4—22no—
430C4—41no—
431C4—41no—
432C4—41no—
433C4—41no—
434C4—434no—
435C4—862no—
436C4—862no—
437C4—1721no—
438C4—1721no—
439C4—1721no—
440C4—1721no—
441C2—42no—
442C2—42no—
443C2—1722no—
444C2#123×D4311yescharacteristic
445C2#1458344411yescharacteristic
446C2#1458351311yescharacteristic
447C2#1458353111yescharacteristic
448C2#1458354711yescharacteristic
449C2#1458354911yescharacteristic
450C2#1458359211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#394C2
hypercenter#394D43
hypocenterC43#2422
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#13063307C2semidirect
2. C2×#13063306C2semidirect
4. C2×(C22⋊D43)⋊C4C2semidirect
5. #14582828C2semidirect
6. #14582827C2semidirect
7. #14582815C2semidirect
8. #14582799C2semidirect
9. #14582796C2semidirect
10. #14582774C2semidirect
11. #14582770C2semidirect
12. #14582768C2semidirect
13. #14582757C2semidirect
14. C22⋊C4×Dic43C2semidirect
15. C43×#394C2semidirect
96. C22⋊Dic43D4semidirect
214. Dic43#123semidirect
233. #394D43semidirect
241. C43#2422semidirect