Finite Group Databasebeta

← #19138359

Subgroups — #19138359

Order 5504.

696 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13063321C211yesmaximal, characteristic
2C2×#13063310C211yesmaximal, characteristic, complemented
3C2×C4×C22⋊D43C211yesmaximal, characteristic, complemented
4#14582816C211yesmaximal, characteristic, complemented
5#14582815C211yesmaximal, characteristic, complemented
6#14582815C211yesmaximal, characteristic, complemented
7#14582813C211yesmaximal, characteristic, complemented
8#14582799C211yesmaximal, characteristic, complemented
9#14582799C211yesmaximal, characteristic, complemented
10#14582799C211yesmaximal, characteristic, complemented
11#14582794C211yesmaximal, characteristic, complemented
12#14582778C211yesmaximal, characteristic, complemented
13#14582775C211yesmaximal, characteristic, complemented
14C4⋊C4×Dic43C211yesmaximal, characteristic, complemented
15C2×#123×C43C211yesmaximal, characteristic, complemented
16C22×D172C2211yescharacteristic
17C22×C22⋊D43C2211yescharacteristic
18C22×C22⋊D43C2211yescharacteristic
19C22×C22⋊D43C2211yescharacteristic
20C22×C22⋊D43C2211yescharacteristic
21C22×C4×D43C2211yescharacteristic
22#13063321—24no—
23#13063310—24no—
24C4×C22⋊D43—24no—
25C2×C4⋊Dic43C2211yescharacteristic
26C2×Dic43⋊C4C2211yescharacteristic
27C2×Dic43⋊C4C2211yescharacteristic
28C2×Dic43⋊C4C2211yescharacteristic
29C2×C22⋊Dic43C2211yescharacteristic
30C2×C22⋊Dic43C2211yescharacteristic
31C2×C22⋊Dic43C2211yescharacteristic
32C2×C22⋊Dic43C2211yescharacteristic
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×C4×Dic43C2211yescharacteristic
41C2×C4×Dic43C2211yescharacteristic
42C2×C4×Dic43C2211yescharacteristic
43C43⋊#95C2211yescharacteristic
44C43⋊#95C2211yescharacteristic
45C43⋊#95C2211yescharacteristic
46C43⋊#95C2211yescharacteristic
47C22×D4×C43C2211yescharacteristic
48C23×C4×C43C2211yescharacteristic
49#123×C43—24no—
50C2×C4⋊C4×C43C2211yescharacteristic
51C2×C4⋊C4×C43C2211yescharacteristic
52C2×C22⋊C4×C43C2211yescharacteristic
53C2×C22⋊C4×C43C2211yescharacteristic
54C2×C22⋊C4×C43C2211yescharacteristic
55C24×C43C2311yescharacteristic
56C24×C43C2311yescharacteristic
57C23×D43C2311yescharacteristic
58C23×D43C2311yescharacteristic
59C2×D4×C43—22no—
60C2×D4×C43—22no—
61C2×D4×C43—41no—
62C22×C4×C43—22no—
63C22×C4×C43—22no—
64C22×C4×C43—41no—
65C22×C4×C43C2311yescharacteristic
66C22×C4×C43C2311yescharacteristic
67C22×C4×C43C2311yescharacteristic
68C22×C4×C43C2311yescharacteristic
69C22×C4×C43C2311yescharacteristic
70C2×C22⋊D43—22no—
71C2×C22⋊D43—22no—
72C2×C22⋊D43—22no—
73C2×C22⋊D43—22no—
74C2×C22⋊D43—22no—
75C2×C22⋊D43—22no—
76C2×C22⋊D43—22no—
77C2×C22⋊D43—22no—
78C2×C22⋊D43—22no—
79C2×C22⋊D43—41no—
80C2×C22⋊D43—41no—
81C2×C22⋊D43D414yes—
82C22×Dic43C2311yescharacteristic
83C22×Dic43C2311yescharacteristic
84C22×Dic43C2311yescharacteristic
85C22×Dic43C2311yescharacteristic
86C22×Dic43C2311yescharacteristic
87C22×Dic43C2311yescharacteristic
88C2×D172—22no—
89C2×D172—22no—
90C2×D172—41no—
91C2×C4×D43—22no—
92C2×C4×D43—22no—
93C2×C4×D43—41no—
94C4⋊C4×C43—22no—
95C4⋊C4×C43D414yescomplemented
96C22⋊C4×C43—22no—
97C22⋊C4×C43—22no—
98C22⋊C4×C43—22no—
99C22⋊Dic43—22no—
100C22⋊Dic43—41no—
101C22⋊Dic43—41no—
102C22⋊Dic43—41no—
103(C2×D43)⋊C4—22no—
104(C2×D43)⋊C4—22no—
105(C2×D43)⋊C4—22no—
106(C2×D43)⋊C4—22no—
107(C2×D43)⋊C4—41no—
108(C2×D43)⋊C4—41no—
109(C2×D43)⋊C4—41no—
110C4⋊Dic43—22no—
111Dic43⋊C4—22no—
112Dic43⋊C4—22no—
113Dic43⋊C4—22no—
114C4×Dic43—22no—
115C4×Dic43—22no—
116C4×Dic43—22no—
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×C43C2411yescharacteristic
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—21no—
145C22×D43C2×D412yes—
146D4×C43—44no—
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—44no—
160C2×C4×C43C2×D412yes—
161C2×C4×C43C2×D412yes—
162C2×C4×C43C2×D412yes—
163C22⋊D43—28no—
164C22⋊D43—44no—
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—21no—
180C2×Dic43—21no—
181C2×Dic43C2×D412yes—
182C2×Dic43#4112yes—
183C2×Dic43#4112yes—
184C2×Dic43#4112yes—
185D172—44no—
186C4×D43—44no—
187C22×C43—22no—
188C22×C43—22no—
189C22×C43—22no—
190C22×C43—41no—
191C22×C43—41no—
192C22×C43—41no—
193C22×C43—41no—
194C22×C43—41no—
195C22×C43—41no—
196C22×C43—41no—
197C22×C43—41no—
198C22×C43—41no—
199C22×C43—41no—
200C22×C43—41no—
201C22×C43C22×D411yescharacteristic
202C22×C43C22×D411yescharacteristic
203C22×C43C2×#4111yescharacteristic
204C22×C43C2×#4111yescharacteristic
205C22×C43C2×#4111yescharacteristic
206C22×C43H(5,𝔽2)11yescharacteristic
207C22×C43H(5,𝔽2)11yescharacteristic
208C2×D43—22no—
209C2×D43—22no—
210C2×D43—22no—
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—
222C4×C43—22no—
223C4×C43—22no—
224C4×C43—22no—
225C4×C43—41no—
226C4×C43—41no—
227Dic43—22no—
228Dic43—41no—
229Dic43—41no—
230Dic43—41no—
231Dic43—41no—
232Dic43#12314yescomplemented
233#2445—431nomaximal, Sylow
234C2×C43—42no—
235C2×C43—81no—
236C2×C43C2×#12311yescharacteristic
237C2×C43#53211yescharacteristic
238C2×C43#54011yescharacteristic
239C2×C43D4211yescharacteristic
240C2×C43#54611yescharacteristic
241C2×C43#55011yescharacteristic
242C2×C43#55911yescharacteristic
243D43—42no—
244D43—81no—
245C2×#127—431no—
246C2×#123—431no—
247C2×#123D4311yescharacteristic, complemented
248C2×C4×D4—431no—
249#394—431no—
250#394—431no—
251#394—431no—
252#394—431no—
253#390—431no—
254#390—431no—
255#390—431no—
256#389—431no—
257#386—431no—
258#386—431no—
259C4×C4⋊C4—431no—
260C43#244511yescharacteristic, complemented, Sylow
261C22×D4—431no—
262C22×D4—431no—
263C22×D4—431no—
264C22×D4—431no—
265C22×D4—431no—
266C22×D4C2×D4311yescharacteristic
267C23×C4—431no—
268C23×C4C2×D4311yescharacteristic
269#127—864no—
270#123—24no—
271#123—864no—
272C4×D4—864no—
273C2×C4⋊C4—431no—
274C2×C4⋊C4—431no—
275C2×C4⋊C4—431no—
276C2×C4⋊C4—431no—
277C2×C4⋊C4C2×D4311yescharacteristic
278C2×C4⋊C4C2×D4311yescharacteristic
279C2×C22⋊C4—431no—
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×C42—431no—
295C2×C42—431no—
296#95—431no—
297#95—431no—
298#95—431no—
299#95—431no—
300C24—431no—
301C24—431no—
302C24C22×D4311yescharacteristic
303C24C22×D4311yescharacteristic
304C2×D4—22no—
305C2×D4—22no—
306C2×D4—41no—
307C2×D4—434no—
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—862no—
319C2×D4—1721no—
320C2×D4—1721no—
321C2×D4—1721no—
322C22×C4—22no—
323C22×C4—22no—
324C22×C4—41no—
325C22×C4—431no—
326C22×C4—431no—
327C22×C4—431no—
328C22×C4—431no—
329C22×C4—431no—
330C22×C4—431no—
331C22×C4—862no—
332C22×C4—862no—
333C22×C4—1721no—
334C22×C4C22×D4311yescharacteristic
335C22×C4C22×D4311yescharacteristic
336C22×C4C22×D4311yescharacteristic
337C22×C4C22×D4311yescharacteristic
338C22×C4C22×D4311yescharacteristic
339C4⋊C4—22no—
340C4⋊C4—862no—
341C4⋊C4—862no—
342C4⋊C4—862no—
343C4⋊C4—862no—
344C4⋊C4C22⋊D4314yescomplemented
345C22⋊C4—22no—
346C22⋊C4—22no—
347C22⋊C4—22no—
348C22⋊C4—862no—
349C22⋊C4—862no—
350C22⋊C4—862no—
351C22⋊C4—862no—
352C22⋊C4—862no—
353C22⋊C4—1721no—
354C22⋊C4—1721no—
355C22⋊C4—1721no—
356C22⋊C4—1721no—
357C22⋊C4—1721no—
358C22⋊C4—1721no—
359C42—862no—
360C42—862no—
361C42—862no—
362C23—21no—
363C23—21no—
364C23—21no—
365C23—21no—
366C23—21no—
367C23—21no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—21no—
373C23—21no—
374C23—21no—
375C23—432no—
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—
389C23D4×D4312yes—
390C23C23×D4311yescharacteristic
391D4—44no—
392D4—868no—
393D4—1724no—
394D4—1724no—
395D4—1724no—
396D4—1724no—
397C2×C4—21no—
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—44no—
410C2×C4—432no—
411C2×C4—432no—
412C2×C4—432no—
413C2×C4—432no—
414C2×C4—861no—
415C2×C4—861no—
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×C4C2×C22⋊D4312yes—
430C2×C4C2×C22⋊D4312yes—
431C2×C4C2×C22⋊D4312yes—
432C22—22no—
433C22—22no—
434C22—22no—
435C22—41no—
436C22—41no—
437C22—41no—
438C22—41no—
439C22—41no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22—41no—
444C22—41no—
445C22—41no—
446C22—862no—
447C22—862no—
448C22—862no—
449C22—1721no—
450C22—1721no—
451C22—1721no—
452C22—1721no—
453C22—1721no—
454C22—1721no—
455C22—1721no—
456C22—1721no—
457C22—1721no—
458C22—1721no—
459C22—1721no—
460C22C2×D4×D4311yescharacteristic
461C22C22×C22⋊D4311yescharacteristic
462C22#41×D4311yescharacteristic
463C22#41×D4311yescharacteristic
464C22#41×D4311yescharacteristic
465C22#1306337011yescharacteristic
466C22#1306337111yescharacteristic
467C4—22no—
468C4—22no—
469C4—22no—
470C4—41no—
471C4—41no—
472C4—434no—
473C4—862no—
474C4—1721no—
475C4—1721no—
476C4—1721no—
477C4—1721no—
478C2—42no—
479C2—81no—
480C2—3441no—
481C2—1722no—
482C2#123×D4311yescharacteristic
483C2#1458344511yescharacteristic
484C2#1458350111yescharacteristic
485C2D4×C22⋊D4311yescharacteristic
486C2#1458354111yescharacteristic
487C2#1458356811yescharacteristic
488C2#1458363311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC2×#123×C43C2
hypercenterC2×#123D43
hypocenterC43#2445
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
2. C2×#13063310C2semidirect
3. C2×C4×C22⋊D43C2semidirect
4. #14582816C2semidirect
5. #14582815C2semidirect
6. #14582815C2semidirect
7. #14582813C2semidirect
8. #14582799C2semidirect
9. #14582799C2semidirect
10. #14582799C2semidirect
11. #14582794C2semidirect
12. #14582778C2semidirect
13. #14582775C2semidirect
14. C4⋊C4×Dic43C2semidirect
15. C2×#123×C43C2semidirect
95. C4⋊C4×C43D4semidirect
232. Dic43#123semidirect
247. C2×#123D43semidirect
260. C43#2445semidirect
344. C4⋊C4C22⋊D43semidirect