Finite Group Databasebeta

← #19140941

Subgroups — #19140941

Order 5504.

618 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×#13063306C211yesmaximal, characteristic, complemented
2C2×#13063304C211yesmaximal, characteristic, complemented
3C2×#13063302C211yesmaximal, characteristic, complemented
4#14582829C211yesmaximal, characteristic, complemented
5#14582822C211yesmaximal, characteristic, complemented
6#14582813C211yesmaximal, characteristic, complemented
7#14582813C211yesmaximal, characteristic, complemented
8#14582813C211yesmaximal, characteristic, complemented
9#14582811C211yesmaximal, characteristic, complemented
10#14582802C211yesmaximal, characteristic, complemented
11#14582794C211yesmaximal, characteristic, complemented
12#14582792C211yesmaximal, characteristic, complemented
13#14582779C211yesmaximal, characteristic, complemented
14#14582772C211yesmaximal, characteristic, complemented
15C2×#121×C43C211yesmaximal, characteristic
16C22×Dic86C2211yescharacteristic
17C23×Dic43C2211yescharacteristic
18#13063306—24no—
19#13063304—24no—
20#13063302—24no—
21C2×C4⋊Dic43C2211yescharacteristic
22C2×C4⋊Dic43C2211yescharacteristic
23C2×Dic43⋊C4C2211yescharacteristic
24C2×Dic43⋊C4C2211yescharacteristic
25C2×Dic43⋊C4C2211yescharacteristic
26C2×Dic43⋊C4C2211yescharacteristic
27C2×Dic43⋊C4C2211yescharacteristic
28C2×Dic43⋊C4C2211yescharacteristic
29C2×C22⋊Dic43C2211yescharacteristic
30C2×C22⋊Dic43C2211yescharacteristic
31C2×C22⋊Dic43C2211yescharacteristic
32C2×C22⋊Dic43C2211yescharacteristic
33C2×C22⋊Dic43C2211yescharacteristic
34C2×C22⋊Dic43C2211yescharacteristic
35C2×C22⋊Dic43C2211yescharacteristic
36C2×C22⋊Dic43C2211yescharacteristic
37C2×C22⋊Dic43C2211yescharacteristic
38C2×C22⋊Dic43C2211yescharacteristic
39C2×C22⋊Dic43C2211yescharacteristic
40C2×C4×Dic43C2211yescharacteristic
41C43⋊#95C2211yescharacteristic
42C43⋊#95C2211yescharacteristic
43C43⋊#95C2211yescharacteristic
44C43⋊#95C2211yescharacteristic
45C43⋊#95C2211yescharacteristic
46C43⋊#95C2211yescharacteristic
47C22×D4×C43C2211yescharacteristic
48C22×D4×C43C2211yescharacteristic
49C22×D4×C43C2211yescharacteristic
50C23×C4×C43C2211yescharacteristic
51#121×C43—24no—
52C2×C4⋊C4×C43C2211yescharacteristic
53C2×C22⋊C4×C43C2211yescharacteristic
54C2×C22⋊C4×C43C2211yescharacteristic
55C24×C43C2311yescharacteristic
56C24×C43C2311yescharacteristic
57C24×C43C2311yescharacteristic
58C2×D4×C43—22no—
59C2×D4×C43—22no—
60C2×D4×C43—22no—
61C2×D4×C43—22no—
62C2×D4×C43—22no—
63C2×D4×C43—22no—
64C2×D4×C43—41no—
65C2×D4×C43—41no—
66C2×D4×C43—41no—
67C22×C4×C43—22no—
68C22×C4×C43—22no—
69C22×C4×C43—41no—
70C22×C4×C43C2311yescharacteristic
71C22×C4×C43C2311yescharacteristic
72C22×C4×C43C2311yescharacteristic
73C22×C4×C43C2311yescharacteristic
74C22×Dic43—22no—
75C22×Dic43—22no—
76C22×Dic43—41no—
77C22×Dic43C2311yescharacteristic
78C22×Dic43C2311yescharacteristic
79C22×Dic43C2311yescharacteristic
80C22×Dic43C2311yescharacteristic
81C22×Dic43C2311yescharacteristic
82C22×Dic43C2311yescharacteristic
83C22×Dic43C2311yescharacteristic
84C22×Dic43C2311yescharacteristic
85C2×Dic86—22no—
86C2×Dic86—22no—
87C2×Dic86—41no—
88C4⋊C4×C43—22no—
89C22⋊C4×C43—22no—
90C22⋊C4×C43D414yes—
91C22⋊Dic43—22no—
92C22⋊Dic43—22no—
93C22⋊Dic43—22no—
94C22⋊Dic43—22no—
95C22⋊Dic43—22no—
96C22⋊Dic43—22no—
97C22⋊Dic43—22no—
98C22⋊Dic43—41no—
99C22⋊Dic43—41no—
100C22⋊Dic43—41no—
101C22⋊Dic43—41no—
102C4⋊Dic43—22no—
103C4⋊Dic43—22no—
104Dic43⋊C4—22no—
105Dic43⋊C4—22no—
106Dic43⋊C4—22no—
107Dic43⋊C4—22no—
108Dic43⋊C4—41no—
109Dic43⋊C4D414yescomplemented
110C4×Dic43—41no—
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×C43—21no—
124C23×C43—21no—
125C23×C43—21no—
126C23×C43—21no—
127C23×C43—21no—
128C23×C43—21no—
129C23×C43—21no—
130C23×C43C2×D412yes—
131C23×C43#4112yes—
132C23×C43C2411yescharacteristic
133D4×C43—44no—
134D4×C43—44no—
135D4×C43—44no—
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—44no—
146C2×C4×C43C2×D412yes—
147C2×C4×C43C2×D412yes—
148C2×C4×C43C2×D412yes—
149C2×Dic43—21no—
150C2×Dic43—21no—
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—21no—
168C2×Dic43—21no—
169C2×Dic43—21no—
170C2×Dic43—21no—
171C2×Dic43—44no—
172C2×Dic43C2×D412yes—
173C2×Dic43C2×D412yes—
174Dic86—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×C43—41no—
190C22×C43—41no—
191C22×C43—41no—
192C22×C43—41no—
193C22×C43—41no—
194C22×C43—41no—
195C22×C43—41no—
196C22×C43C22×D411yescharacteristic
197C22×C43C22×D411yescharacteristic
198C22×C43C2×#4111yescharacteristic
199C22×C43H(5,𝔽2)11yescharacteristic
200C22×C43H(5,𝔽2)11yescharacteristic
201C22×C432−1+411yescharacteristic
202C22×C432−1+411yescharacteristic
203C4×C43—22no—
204C4×C43—22no—
205C4×C43—22no—
206C4×C43—41no—
207Dic43—22no—
208Dic43—22no—
209Dic43—41no—
210Dic43—41no—
211Dic43—41no—
212Dic43—41no—
213Dic43—41no—
214Dic43—41no—
215#2681—431nomaximal, Sylow
216C2×C43—42no—
217C2×C43—42no—
218C2×C43—81no—
219C2×C43#53611yescharacteristic
220C2×C43#53711yescharacteristic
221C2×C43#53911yescharacteristic
222C2×C43D4211yescharacteristic
223C2×C43#54611yescharacteristic
224C2×C43#54811yescharacteristic
225C2×C43#56211yescharacteristic
226C2×#123—431no—
227C2×C22⋊Q8—431no—
228C2×C22⋊Q8—431no—
229C2×#121D4311yescharacteristic
230#398—431no—
231#396—431no—
232#394—431no—
233#394—431no—
234#394—431no—
235#393—431no—
236#390—431no—
237#389—431no—
238#388—431no—
239#386—431no—
240#385—431no—
241C43#268111yescharacteristic, complemented, Sylow
242C22×Q8—431no—
243C22×D4C2×D4311yescharacteristic
244C22×D4C2×D4311yescharacteristic
245C22×D4C2×D4311yescharacteristic
246C23×C4—431no—
247C23×C4C2×D4311yescharacteristic
248#123—864no—
249C22⋊Q8—864no—
250C22⋊Q8—864no—
251#121—24no—
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⋊C4—431no—
270C2×C22⋊C4—431no—
271C2×C22⋊C4—431no—
272C2×C22⋊C4C2×D4311yescharacteristic
273C2×C22⋊C4C2×D4311yescharacteristic
274C2×C42—431no—
275#95—431no—
276#95—431no—
277#95—431no—
278#95—431no—
279#95—431no—
280#95—431no—
281C24C22×D4311yescharacteristic
282C24C22×D4311yescharacteristic
283C24C22×D4311yescharacteristic
284C2×Q8—862no—
285C2×Q8—862no—
286C2×Q8—1721no—
287C2×D4—22no—
288C2×D4—22no—
289C2×D4—22no—
290C2×D4—22no—
291C2×D4—22no—
292C2×D4—22no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—41no—
296C22×C4—22no—
297C22×C4—22no—
298C22×C4—41no—
299C22×C4—431no—
300C22×C4—431no—
301C22×C4—431no—
302C22×C4—431no—
303C22×C4—431no—
304C22×C4—431no—
305C22×C4—431no—
306C22×C4—431no—
307C22×C4—862no—
308C22×C4—862no—
309C22×C4—1721no—
310C22×C4C22×D4311yescharacteristic
311C22×C4C22×D4311yescharacteristic
312C22×C4C22×D4311yescharacteristic
313C22×C4C22×D4311yescharacteristic
314C4⋊C4—22no—
315C4⋊C4—434no—
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—862no—
325C22⋊C4—862no—
326C22⋊C4—862no—
327C22⋊C4—862no—
328C22⋊C4—862no—
329C22⋊C4—862no—
330C22⋊C4—862no—
331C22⋊C4—1721no—
332C22⋊C4—1721no—
333C22⋊C4—1721no—
334C22⋊C4—1721no—
335C22⋊C4C22⋊D4314yes—
336C42—1721no—
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—21no—
350C23—21no—
351C23—21no—
352C23—21no—
353C23—21no—
354C23—21no—
355C23—21no—
356C23#1062190012yes—
357C23C2×C22⋊D4312yes—
358C23C23×D4311yescharacteristic
359Q8—1724no—
360D4—44no—
361D4—44no—
362D4—44no—
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—44no—
373C2×C4—432no—
374C2×C4—432no—
375C2×C4—861no—
376C2×C4—861no—
377C2×C4—861no—
378C2×C4—861no—
379C2×C4—861no—
380C2×C4—861no—
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×C4D4×D4312yes—
399C2×C4C2×C22⋊D4312yes—
400C2×C4C2×C22⋊D4312yes—
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—41no—
416C22—41no—
417C22—41no—
418C22—41no—
419C22—41no—
420C22—41no—
421C22—41no—
422C22C2×D4×D4311yescharacteristic
423C22C22×C22⋊D4311yescharacteristic
424C22C2×#1062190011yescharacteristic
425C22#1306337011yescharacteristic
426C22#1306337011yescharacteristic
427C22#1306337211yescharacteristic
428C22#1306337211yescharacteristic
429C4—22no—
430C4—22no—
431C4—22no—
432C4—41no—
433C4—862no—
434C4—862no—
435C4—1721no—
436C4—1721no—
437C4—1721no—
438C4—1721no—
439C4—1721no—
440C4—1721no—
441C2—42no—
442C2—42no—
443C2—81no—
444C2#1458347011yescharacteristic
445C2#1458347811yescharacteristic
446C2#1458349411yescharacteristic
447C2D4×C22⋊D4311yescharacteristic
448C2#1458354311yescharacteristic
449C2#1458355511yescharacteristic
450C2#1458364411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC2×#121×C43C2
hypercenterC2×#121D43
hypocenterC43#2681
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×#13063306C2semidirect
2. C2×#13063304C2semidirect
3. C2×#13063302C2semidirect
4. #14582829C2semidirect
5. #14582822C2semidirect
6. #14582813C2semidirect
7. #14582813C2semidirect
8. #14582813C2semidirect
9. #14582811C2semidirect
10. #14582802C2semidirect
11. #14582794C2semidirect
12. #14582792C2semidirect
13. #14582779C2semidirect
14. #14582772C2semidirect
109. Dic43⋊C4D4semidirect
241. C43#2681semidirect