Finite Group Databasebeta

← #19139668

Subgroups — #19139668

Order 5504.

696 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×#13063312C211yesmaximal, characteristic, complemented
2C2×#13063311C211yesmaximal, characteristic, complemented
3C2×#13063297C211yesmaximal, characteristic, complemented
4#14582819C211yesmaximal, characteristic, complemented
5#14582813C211yesmaximal, characteristic, complemented
6#14582807C211yesmaximal, characteristic, complemented
7#14582807C211yesmaximal, characteristic, complemented
8#14582799C211yesmaximal, characteristic, complemented
9#14582789C211yesmaximal, characteristic, complemented
10#14582787C211yesmaximal, characteristic, complemented
11#14582779C211yesmaximal, characteristic, complemented
12#14582778C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic43C211yesmaximal, characteristic, complemented
14C4×C22⋊Dic43C211yesmaximal, characteristic, complemented
15C2×#121×C43C211yesmaximal, characteristic, complemented
16C22×Dic86C2211yescharacteristic
17C22×C22⋊D43C2211yescharacteristic
18C22×C22⋊D43C2211yescharacteristic
19C22×C22⋊D43C2211yescharacteristic
20C23×Dic43C2211yescharacteristic
21#13063312—24no—
22#13063311—24no—
23#13063297—24no—
24C2×Dic43⋊C4C2211yescharacteristic
25C2×Dic43⋊C4C2211yescharacteristic
26C2×C22⋊Dic43C2211yescharacteristic
27C2×C22⋊Dic43C2211yescharacteristic
28C2×C22⋊Dic43C2211yescharacteristic
29C2×C22⋊Dic43C2211yescharacteristic
30C2×C22⋊Dic43C2211yescharacteristic
31C2×C22⋊Dic43C2211yescharacteristic
32C2×C22⋊Dic43C2211yescharacteristic
33C2×C22⋊Dic43C2211yescharacteristic
34C2×(C2×D43)⋊C4C2211yescharacteristic
35C2×(C2×D43)⋊C4C2211yescharacteristic
36C2×(C2×D43)⋊C4C2211yescharacteristic
37C2×(C2×D43)⋊C4C2211yescharacteristic
38C2×C4×Dic43C2211yescharacteristic
39C2×C4×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
58C23×D43C2311yescharacteristic
59C2×D4×C43—22no—
60C2×D4×C43—22no—
61C2×D4×C43—22no—
62C2×D4×C43—22no—
63C2×D4×C43—22no—
64C2×D4×C43—22no—
65C2×D4×C43—41no—
66C2×D4×C43—41no—
67C2×D4×C43—41no—
68C22×C4×C43—22no—
69C22×C4×C43—22no—
70C22×C4×C43—41no—
71C22×C4×C43C2311yescharacteristic
72C22×C4×C43C2311yescharacteristic
73C22×C4×C43C2311yescharacteristic
74C22×C4×C43C2311yescharacteristic
75C2×C22⋊D43—22no—
76C2×C22⋊D43—22no—
77C2×C22⋊D43—22no—
78C2×C22⋊D43—22no—
79C2×C22⋊D43—22no—
80C2×C22⋊D43—41no—
81C2×C22⋊D43—41no—
82C2×C22⋊D43—41no—
83C2×C22⋊D43—41no—
84C22×Dic43—22no—
85C22×Dic43—22no—
86C22×Dic43—41no—
87C22×Dic43C2311yescharacteristic
88C22×Dic43C2311yescharacteristic
89C22×Dic43C2311yescharacteristic
90C22×Dic43C2311yescharacteristic
91C22×Dic43C2311yescharacteristic
92C22×Dic43C2311yescharacteristic
93C22×Dic43C2311yescharacteristic
94C2×Dic86—22no—
95C2×Dic86—22no—
96C2×Dic86—41no—
97C4⋊C4×C43—22no—
98C22⋊C4×C43—22no—
99C22⋊C4×C43D414yescomplemented
100C22⋊Dic43—22no—
101C22⋊Dic43—22no—
102C22⋊Dic43—22no—
103C22⋊Dic43—22no—
104C22⋊Dic43—22no—
105C22⋊Dic43—22no—
106C22⋊Dic43—22no—
107C22⋊Dic43D414yescomplemented
108(C2×D43)⋊C4—22no—
109(C2×D43)⋊C4—22no—
110(C2×D43)⋊C4—22no—
111(C2×D43)⋊C4—22no—
112Dic43⋊C4—22no—
113Dic43⋊C4—41no—
114C4×Dic43—22no—
115C4×Dic43—22no—
116C4×Dic43—41no—
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×C43—21no—
131C23×C43—21no—
132C23×C43—21no—
133C23×C43—21no—
134C23×C43—21no—
135C23×C43—21no—
136C23×C43C2×D412yes—
137C23×C43C2×D412yes—
138C23×C43C2411yescharacteristic
139C22×D43—21no—
140C22×D43—21no—
141C22×D43—21no—
142C22×D43—21no—
143C22×D43—21no—
144C22×D43—21no—
145C22×D43—21no—
146D4×C43—44no—
147D4×C43—44no—
148D4×C43—44no—
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—44no—
159C2×C4×C43C2×D412yes—
160C2×C4×C43C2×D412yes—
161C2×C4×C43#4112yes—
162C22⋊D43—44no—
163C22⋊D43—44no—
164C22⋊D43—44no—
165C2×Dic43—21no—
166C2×Dic43—21no—
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×Dic43—21no—
182C2×Dic43—44no—
183C2×Dic43C2×D412yes—
184C2×Dic43C2×D412yes—
185C2×Dic43#4112yes—
186C2×Dic43#4112yes—
187Dic86—44no—
188C22×C43—22no—
189C22×C43—22no—
190C22×C43—22no—
191C22×C43—22no—
192C22×C43—22no—
193C22×C43—22no—
194C22×C43—41no—
195C22×C43—41no—
196C22×C43—41no—
197C22×C43—41no—
198C22×C43—41no—
199C22×C43—41no—
200C22×C43—41no—
201C22×C43—41no—
202C22×C43—41no—
203C22×C43—41no—
204C22×C43—41no—
205C22×C43—41no—
206C22×C43—41no—
207C22×C43—41no—
208C22×C43—41no—
209C22×C43C22×D411yescharacteristic
210C22×C43C22×D411yescharacteristic
211C22×C43C2×#4111yescharacteristic
212C22×C43C2×#4111yescharacteristic
213C22×C43C2×#4111yescharacteristic
214C22×C43H(5,𝔽2)11yescharacteristic
215C22×C43H(5,𝔽2)11yescharacteristic
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—41no—
227Dic43—22no—
228Dic43—22no—
229Dic43—22no—
230Dic43—22no—
231Dic43—41no—
232Dic43—41no—
233Dic43—41no—
234#2555—431nomaximal, Sylow
235C2×C43—42no—
236C2×C43—42no—
237C2×C43—81no—
238C2×C43#53211yescharacteristic
239C2×C43#53211yescharacteristic
240C2×C43#53811yescharacteristic
241C2×C43D4211yescharacteristic
242C2×C43#54611yescharacteristic
243C2×C43#54611yescharacteristic
244C2×C43#55511yescharacteristic
245D43—81no—
246C2×#124—431no—
247C2×#124—431no—
248C2×#121—431no—
249C2×#121D4311yescharacteristic, complemented
250#395—431no—
251#394—431no—
252#392—431no—
253#392—431no—
254#390—431no—
255#388—431no—
256#388—431no—
257#386—431no—
258#386—431no—
259C4×C22⋊C4—431no—
260C4×C22⋊C4—431no—
261C43#255511yescharacteristic, complemented, Sylow
262C22×Q8—431no—
263C22×D4—431no—
264C22×D4—431no—
265C22×D4—431no—
266C22×D4C2×D4311yescharacteristic
267C22×D4C2×D4311yescharacteristic
268C22×D4C2×D4311yescharacteristic
269C23×C4—431no—
270C23×C4C2×D4311yescharacteristic
271#124—864no—
272#124—864no—
273#121—24no—
274#121—864no—
275C2×C4⋊C4—431no—
276C2×C4⋊C4—431no—
277C2×C4⋊C4C2×D4311yescharacteristic
278C2×C22⋊C4—431no—
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×C42—431no—
293C2×C42—431no—
294C2×C42—431no—
295#95—431no—
296#95—431no—
297#95—431no—
298#95—431no—
299#95—431no—
300#95—431no—
301C24—431no—
302C24C22×D4311yescharacteristic
303C24C22×D4311yescharacteristic
304C24C22×D4311yescharacteristic
305C2×Q8—862no—
306C2×Q8—862no—
307C2×Q8—1721no—
308C2×D4—22no—
309C2×D4—22no—
310C2×D4—22no—
311C2×D4—22no—
312C2×D4—22no—
313C2×D4—22no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—862no—
318C2×D4—862no—
319C2×D4—862no—
320C2×D4—862no—
321C2×D4—862no—
322C2×D4—1721no—
323C2×D4—1721no—
324C2×D4—1721no—
325C2×D4—1721no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—41no—
329C22×C4—431no—
330C22×C4—431no—
331C22×C4—431no—
332C22×C4—431no—
333C22×C4—431no—
334C22×C4—431no—
335C22×C4—431no—
336C22×C4—862no—
337C22×C4—862no—
338C22×C4—1721no—
339C22×C4C22×D4311yescharacteristic
340C22×C4C22×D4311yescharacteristic
341C22×C4C22×D4311yescharacteristic
342C22×C4C22×D4311yescharacteristic
343C4⋊C4—22no—
344C4⋊C4—862no—
345C4⋊C4—1721no—
346C22⋊C4—22no—
347C22⋊C4—434no—
348C22⋊C4—862no—
349C22⋊C4—862no—
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—862no—
359C22⋊C4C22⋊D4314yescomplemented
360C42—862no—
361C42—862no—
362C42—1721no—
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—21no—
376C23—21no—
377C23—21no—
378C23—21no—
379C23—21no—
380C23—21no—
381C23—21no—
382C23—861no—
383C23—861no—
384C23—861no—
385C23—861no—
386C23—861no—
387C23—861no—
388C23—861no—
389C23D4×D4312yes—
390C23C2×C22⋊D4312yes—
391C23C23×D4311yescharacteristic
392Q8—1724no—
393D4—44no—
394D4—44no—
395D4—44no—
396D4—1724no—
397D4—1724no—
398D4—1724no—
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—44no—
409C2×C4—432no—
410C2×C4—432no—
411C2×C4—432no—
412C2×C4—432no—
413C2×C4—861no—
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—861no—
429C2×C4—861no—
430C2×C4—1724no—
431C2×C4#1062190012yes—
432C2×C4C2×C22⋊D4312yes—
433C2×C4C2×C22⋊D4312yes—
434C22—22no—
435C22—22no—
436C22—22no—
437C22—22no—
438C22—22no—
439C22—22no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22—41no—
444C22—41no—
445C22—41no—
446C22—41no—
447C22—41no—
448C22—41no—
449C22—41no—
450C22—41no—
451C22—41no—
452C22—41no—
453C22—41no—
454C22—41no—
455C22—1721no—
456C22—1721no—
457C22—1721no—
458C22—1721no—
459C22—1721no—
460C22—1721no—
461C22—1721no—
462C22C2×D4×D4311yescharacteristic
463C22C22×C22⋊D4311yescharacteristic
464C22#41×D4311yescharacteristic
465C22#41×D4311yescharacteristic
466C22C2×#1062190011yescharacteristic
467C22#1306337011yescharacteristic
468C22#1306337011yescharacteristic
469C4—22no—
470C4—22no—
471C4—22no—
472C4—41no—
473C4—862no—
474C4—862no—
475C4—862no—
476C4—862no—
477C4—1721no—
478C4—1721no—
479C4—1721no—
480C2—42no—
481C2—42no—
482C2—81no—
483C2—3441no—
484C2#1458344411yescharacteristic
485C2#1458344511yescharacteristic
486C2#1458348111yescharacteristic
487C2D4×C22⋊D4311yescharacteristic
488C2#1458353811yescharacteristic
489C2#1458354311yescharacteristic
490C2#1458361311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC2×#121×C43C2
hypercenterC2×#121D43
hypocenterC43#2555
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×#13063312C2semidirect
2. C2×#13063311C2semidirect
3. C2×#13063297C2semidirect
4. #14582819C2semidirect
5. #14582813C2semidirect
6. #14582807C2semidirect
7. #14582807C2semidirect
8. #14582799C2semidirect
9. #14582789C2semidirect
10. #14582787C2semidirect
11. #14582779C2semidirect
12. #14582778C2semidirect
13. C22⋊C4×Dic43C2semidirect
14. C4×C22⋊Dic43C2semidirect
15. C2×#121×C43C2semidirect
99. C22⋊C4×C43D4semidirect
107. C22⋊Dic43D4semidirect
249. C2×#121D43semidirect
261. C43#2555semidirect
359. C22⋊C4C22⋊D43semidirect