Finite Group Databasebeta

← #19139666

Subgroups — #19139666

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×#13063314C211yesmaximal, characteristic, complemented
2C2×#13063298C211yesmaximal, characteristic, complemented
3C2×#13063297C211yesmaximal, characteristic, complemented
4#14582818C211yesmaximal, characteristic, complemented
5#14582814C211yesmaximal, characteristic, complemented
6#14582808C211yesmaximal, characteristic, complemented
7#14582807C211yesmaximal, characteristic, complemented
8#14582799C211yesmaximal, characteristic, complemented
9#14582793C211yesmaximal, characteristic, complemented
10#14582790C211yesmaximal, characteristic, complemented
11#14582776C211yesmaximal, characteristic, complemented
12#14582775C211yesmaximal, characteristic, complemented
13C22⋊C4×Dic43C211yesmaximal, characteristic, complemented
14C4×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
15C2×#124×C43C211yesmaximal, characteristic, complemented
16C22×D172C2211yescharacteristic
17C22×C22⋊D43C2211yescharacteristic
18C22×C22⋊D43C2211yescharacteristic
19C22×C22⋊D43C2211yescharacteristic
20C22×C22⋊D43C2211yescharacteristic
21C23×Dic43C2211yescharacteristic
22C22×C4×D43C2211yescharacteristic
23#13063314—24no—
24#13063298—24no—
25#13063297—24no—
26C2×Dic43⋊C4C2211yescharacteristic
27C2×Dic43⋊C4C2211yescharacteristic
28C2×Dic43⋊C4C2211yescharacteristic
29C2×C22⋊Dic43C2211yescharacteristic
30C2×C22⋊Dic43C2211yescharacteristic
31C2×C22⋊Dic43C2211yescharacteristic
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×C4×Dic43C2211yescharacteristic
40C2×C4×Dic43C2211yescharacteristic
41C43⋊#95C2211yescharacteristic
42C43⋊#95C2211yescharacteristic
43C43⋊#95C2211yescharacteristic
44C43⋊#95C2211yescharacteristic
45C43⋊#95C2211yescharacteristic
46C43⋊#95C2211yescharacteristic
47C22×Q8×C43C2211yescharacteristic
48C22×D4×C43C2211yescharacteristic
49#124×C43—24no—
50C2×C22⋊C4×C43C2211yescharacteristic
51C2×C22⋊C4×C43C2211yescharacteristic
52C2×C22⋊C4×C43C2211yescharacteristic
53C2×C22⋊C4×C43C2211yescharacteristic
54C2×C42×C43C2211yescharacteristic
55C24×C43C2311yescharacteristic
56C24×C43C2311yescharacteristic
57C23×D43C2311yescharacteristic
58C23×D43C2311yescharacteristic
59C2×Q8×C43—22no—
60C2×Q8×C43—22no—
61C2×Q8×C43—41no—
62C2×D4×C43—22no—
63C2×D4×C43—22no—
64C2×D4×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—41no—
78C2×C22⋊D43—41no—
79C2×C22⋊D43—41no—
80C2×C22⋊D43—41no—
81C2×C22⋊D43—41no—
82C22×Dic43—22no—
83C22×Dic43—22no—
84C22×Dic43—41no—
85C22×Dic43C2311yescharacteristic
86C22×Dic43C2311yescharacteristic
87C22×Dic43C2311yescharacteristic
88C22×Dic43C2311yescharacteristic
89C22×Dic43C2311yescharacteristic
90C22×Dic43C2311yescharacteristic
91C2×D172—22no—
92C2×D172—22no—
93C2×D172—41no—
94C2×C4×D43—22no—
95C2×C4×D43—22no—
96C2×C4×D43—41no—
97C22⋊C4×C43—22no—
98C22⋊C4×C43—22no—
99C22⋊C4×C43—22no—
100C22⋊C4×C43D414yescomplemented
101C42×C43—22no—
102C22⋊Dic43—22no—
103C22⋊Dic43—22no—
104C22⋊Dic43—22no—
105(C2×D43)⋊C4—22no—
106(C2×D43)⋊C4—22no—
107(C2×D43)⋊C4—22no—
108(C2×D43)⋊C4—22no—
109(C2×D43)⋊C4—22no—
110(C2×D43)⋊C4—22no—
111(C2×D43)⋊C4D414yescomplemented
112Dic43⋊C4—22no—
113Dic43⋊C4—22no—
114Dic43⋊C4—41no—
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×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—
146Q8×C43—44no—
147D4×C43—44no—
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—21no—
160C2×C4×C43C2×D412yes—
161C2×C4×C43C2×D412yes—
162C2×C4×C43C2×D412yes—
163C22⋊D43—44no—
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×Dic43—44no—
182C2×Dic43C2×D412yes—
183C2×Dic43#4112yes—
184C2×Dic43#4112yes—
185C2×Dic43#4112yes—
186D172—44no—
187C4×D43—44no—
188C22×C43—22no—
189C22×C43—22no—
190C22×C43—22no—
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×C43—41no—
202C22×C43C22×D411yescharacteristic
203C22×C43C22×D411yescharacteristic
204C22×C43C2×#4111yescharacteristic
205C22×C43C2×#4111yescharacteristic
206C22×C43C2×#4111yescharacteristic
207C22×C43H(5,𝔽2)11yescharacteristic
208C22×C43H(5,𝔽2)11yescharacteristic
209C2×D43—22no—
210C2×D43—22no—
211C2×D43—22no—
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—
222C2×D43—41no—
223C4×C43—22no—
224C4×C43—22no—
225C4×C43—22no—
226C4×C43—41no—
227C4×C43—41no—
228Dic43—22no—
229Dic43—22no—
230Dic43—22no—
231Dic43—22no—
232Dic43—41no—
233Dic43—41no—
234#2555—431nomaximal, Sylow
235C2×C43—42no—
236C2×C43—81no—
237C2×C43#53211yescharacteristic
238C2×C43#53211yescharacteristic
239C2×C43#53811yescharacteristic
240C2×C43D4211yescharacteristic
241C2×C43#54611yescharacteristic
242C2×C43#54611yescharacteristic
243C2×C43#55511yescharacteristic
244D43—42no—
245D43—81no—
246C2×#124—431no—
247C2×#124D4311yescharacteristic, complemented
248C2×#121—431no—
249C2×#121—431no—
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×Q8C2×D4311yescharacteristic
263C22×D4—431no—
264C22×D4—431no—
265C22×D4—431no—
266C22×D4—431no—
267C22×D4—431no—
268C22×D4C2×D4311yescharacteristic
269C23×C4—431no—
270C23×C4—431no—
271#124—24no—
272#124—864no—
273#121—864no—
274#121—864no—
275C2×C4⋊C4—431no—
276C2×C4⋊C4—431no—
277C2×C4⋊C4—431no—
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⋊C4C2×D4311yescharacteristic
289C2×C22⋊C4C2×D4311yescharacteristic
290C2×C22⋊C4C2×D4311yescharacteristic
291C2×C22⋊C4C2×D4311yescharacteristic
292C2×C42—431no—
293C2×C42—431no—
294C2×C42C2×D4311yescharacteristic
295#95—431no—
296#95—431no—
297#95—431no—
298#95—431no—
299#95—431no—
300#95—431no—
301C24—431no—
302C24—431no—
303C24C22×D4311yescharacteristic
304C24C22×D4311yescharacteristic
305C2×Q8—22no—
306C2×Q8—22no—
307C2×Q8—41no—
308C2×D4—22no—
309C2×D4—22no—
310C2×D4—41no—
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—862no—
320C2×D4—1721no—
321C2×D4—1721no—
322C2×D4—1721no—
323C2×D4—1721no—
324C2×D4—1721no—
325C2×D4—1721no—
326C22×C4—431no—
327C22×C4—431no—
328C22×C4—431no—
329C22×C4—431no—
330C22×C4—431no—
331C22×C4—431no—
332C22×C4—862no—
333C22×C4—862no—
334C22×C4—862no—
335C22×C4—862no—
336C22×C4—1721no—
337C22×C4—1721no—
338C22×C4C22×D4311yescharacteristic
339C22×C4C22×D4311yescharacteristic
340C22×C4C22×D4311yescharacteristic
341C22×C4C22×D4311yescharacteristic
342C22×C4C22×D4311yescharacteristic
343C4⋊C4—862no—
344C4⋊C4—862no—
345C4⋊C4—1721no—
346C22⋊C4—22no—
347C22⋊C4—22no—
348C22⋊C4—22no—
349C22⋊C4—434no—
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—22no—
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—432no—
377C23—861no—
378C23—861no—
379C23—861no—
380C23—861no—
381C23—861no—
382C23—861no—
383C23—861no—
384C23—861no—
385C23—861no—
386C23—861no—
387C23—861no—
388C23—861no—
389C23—861no—
390C23C2×C22⋊D4312yes—
391C23C23×D4311yescharacteristic
392Q8—44no—
393D4—44no—
394D4—1724no—
395D4—1724no—
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—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—432no—
412C2×C4—432no—
413C2×C4—432no—
414C2×C4—432no—
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—1724no—
430C2×C4—1724no—
431C2×C4D4×D4312yes—
432C2×C4C2×C22⋊D4312yes—
433C2×C4C2×C22⋊D4312yes—
434C22—22no—
435C22—22no—
436C22—22no—
437C22—41no—
438C22—41no—
439C22—41no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22—41no—
444C22—41no—
445C22—41no—
446C22—41no—
447C22—41no—
448C22—862no—
449C22—862no—
450C22—862no—
451C22—1721no—
452C22—1721no—
453C22—1721no—
454C22—1721no—
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
466C22#41×D4311yescharacteristic
467C22#1306337011yescharacteristic
468C22#1306337111yescharacteristic
469C4—22no—
470C4—22no—
471C4—22no—
472C4—41no—
473C4—41no—
474C4—862no—
475C4—862no—
476C4—862no—
477C4—862no—
478C4—1721no—
479C4—1721no—
480C2—42no—
481C2—81no—
482C2—3441no—
483C2—1722no—
484C2#1458344511yescharacteristic
485C2#1458344811yescharacteristic
486C2#1458348311yescharacteristic
487C2D4×C22⋊D4311yescharacteristic
488C2#1458353711yescharacteristic
489C2#1458354211yescharacteristic
490C2#1458361111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC2×#124×C43C2
hypercenterC2×#124D43
hypocenterC43#2555
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C2×#13063314C2semidirect
2. C2×#13063298C2semidirect
3. C2×#13063297C2semidirect
4. #14582818C2semidirect
5. #14582814C2semidirect
6. #14582808C2semidirect
7. #14582807C2semidirect
8. #14582799C2semidirect
9. #14582793C2semidirect
10. #14582790C2semidirect
11. #14582776C2semidirect
12. #14582775C2semidirect
13. C22⋊C4×Dic43C2semidirect
14. C4×(C2×D43)⋊C4C2semidirect
15. C2×#124×C43C2semidirect
100. C22⋊C4×C43D4semidirect
111. (C2×D43)⋊C4D4semidirect
247. C2×#124D43semidirect
261. C43#2555semidirect
359. C22⋊C4C22⋊D43semidirect