Finite Group Databasebeta

← #19138030

Subgroups — #19138030

Order 5504.

788 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13063300C211yesmaximal, characteristic, complemented
2C2×#13063298C211yesmaximal, characteristic, complemented
3C2×#13063298C211yesmaximal, characteristic, complemented
4C2×#13063298C211yesmaximal, characteristic, complemented
5C2×#13063287C211yesmaximal, characteristic, complemented
6C2×C4⋊C4×D43C211yesmaximal, characteristic, complemented
7#14582821C211yesmaximal, characteristic, complemented
8#14582816C211yesmaximal, characteristic, complemented
9#14582815C211yesmaximal, characteristic, complemented
10#14582799C211yesmaximal, characteristic, complemented
11#14582794C211yesmaximal, characteristic, complemented
12#14582777C211yesmaximal, characteristic, complemented
13#14582775C211yesmaximal, characteristic, complemented
14#14582758C211yesmaximal, characteristic, complemented
15C43×#396C211yesmaximal, characteristic, complemented
16C22×D172C2211yescharacteristic
17C22×D172C2211yescharacteristic
18C22×D172C2211yescharacteristic
19C22×C22⋊D43C2211yescharacteristic
20C22×C22⋊D43C2211yescharacteristic
21C22×C22⋊D43C2211yescharacteristic
22C22×C4×D43C2211yescharacteristic
23C22×C4×D43C2211yescharacteristic
24C22×C4×D43C2211yescharacteristic
25C22×C4×D43C2211yescharacteristic
26#13063300—24no—
27#13063298—24no—
28#13063298—24no—
29#13063298—24no—
30#13063287—24no—
31C2×C4⋊Dic43C2211yescharacteristic
32C2×Dic43⋊C4C2211yescharacteristic
33C2×Dic43⋊C4C2211yescharacteristic
34C2×Dic43⋊C4C2211yescharacteristic
35C2×Dic43⋊C4C2211yescharacteristic
36C4⋊C4×D43—24no—
37C2×C22⋊Dic43C2211yescharacteristic
38C2×(C2×D43)⋊C4C2211yescharacteristic
39C2×(C2×D43)⋊C4C2211yescharacteristic
40C2×(C2×D43)⋊C4C2211yescharacteristic
41C2×(C2×D43)⋊C4C2211yescharacteristic
42C2×(C2×D43)⋊C4C2211yescharacteristic
43C2×(C2×D43)⋊C4C2211yescharacteristic
44C2×(C2×D43)⋊C4C2211yescharacteristic
45C2×(C2×D43)⋊C4C2211yescharacteristic
46C2×C4×Dic43C2211yescharacteristic
47C43⋊#95C2211yescharacteristic
48C43⋊#95C2211yescharacteristic
49C43⋊#95C2211yescharacteristic
50C2×C4⋊C4×C43C2211yescharacteristic
51C2×C4⋊C4×C43C2211yescharacteristic
52C2×C4⋊C4×C43C2211yescharacteristic
53C2×C22⋊C4×C43C2211yescharacteristic
54C2×C22⋊C4×C43C2211yescharacteristic
55C2×C22⋊C4×C43C2211yescharacteristic
56#95×C43C2211yescharacteristic
57C24×C43C2311yescharacteristic
58C23×D43C2311yescharacteristic
59C23×D43C2311yescharacteristic
60C23×D43C2311yescharacteristic
61C22×C4×C43C2311yescharacteristic
62C22×C4×C43C2311yescharacteristic
63C22×C4×C43C2311yescharacteristic
64C22×C4×C43C2311yescharacteristic
65C22×C4×C43C2311yescharacteristic
66C22×C4×C43C2311yescharacteristic
67C2×C22⋊D43—22no—
68C2×C22⋊D43—22no—
69C2×C22⋊D43—22no—
70C2×C22⋊D43—22no—
71C2×C22⋊D43—22no—
72C2×C22⋊D43—22no—
73C2×C22⋊D43—22no—
74C2×C22⋊D43—22no—
75C2×C22⋊D43—41no—
76C22×Dic43C2311yescharacteristic
77C22×Dic43C2311yescharacteristic
78C22×Dic43C2311yescharacteristic
79C22×Dic43C2311yescharacteristic
80C22×Dic43C2311yescharacteristic
81C2×D172—22no—
82C2×D172—22no—
83C2×D172—22no—
84C2×D172—22no—
85C2×D172—22no—
86C2×D172—22no—
87C2×D172—22no—
88C2×D172—41no—
89C2×D172D414yescomplemented
90C2×C4×D43—22no—
91C2×C4×D43—22no—
92C2×C4×D43—22no—
93C2×C4×D43—22no—
94C2×C4×D43—22no—
95C2×C4×D43—22no—
96C2×C4×D43—22no—
97C2×C4×D43—22no—
98C2×C4×D43—22no—
99C2×C4×D43—41no—
100C2×C4×D43—41no—
101C2×C4×D43D414yescomplemented
102C4⋊C4×C43—22no—
103C4⋊C4×C43—22no—
104C4⋊C4×C43—22no—
105C22⋊C4×C43—22no—
106C22⋊C4×C43—22no—
107C22⋊C4×C43—22no—
108C22⋊Dic43—41no—
109(C2×D43)⋊C4—22no—
110(C2×D43)⋊C4—22no—
111(C2×D43)⋊C4—22no—
112(C2×D43)⋊C4—22no—
113(C2×D43)⋊C4—22no—
114(C2×D43)⋊C4—22no—
115(C2×D43)⋊C4—22no—
116(C2×D43)⋊C4—41no—
117C4⋊Dic43—22no—
118Dic43⋊C4—22no—
119Dic43⋊C4—22no—
120Dic43⋊C4—22no—
121Dic43⋊C4D414yescomplemented
122C4×Dic43—22no—
123C23×C43—21no—
124C23×C43—21no—
125C23×C43—21no—
126C23×C43—21no—
127C23×C43—21no—
128C23×C43—21no—
129C23×C43—21no—
130C23×C43C2411yescharacteristic
131C22×D43—21no—
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×D43—21no—
146C22×D43—21no—
147C22×D43—21no—
148C22×D43C2×D412yes—
149C22×D43C2×D412yes—
150C22×D43C2×D412yes—
151C22×D43#4112yes—
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×C43—21no—
161C2×C4×C43—21no—
162C2×C4×C43—21no—
163C2×C4×C43—21no—
164C2×C4×C43—21no—
165C2×C4×C43—21no—
166C2×C4×C43—21no—
167C2×C4×C43C2×D412yes—
168C2×C4×C43C2×D412yes—
169C2×C4×C43C2×D412yes—
170C22⋊D43—44no—
171C22⋊D43—44no—
172C22⋊D43—44no—
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—21no—
183C2×Dic43—21no—
184C2×Dic43C2×D412yes—
185C2×Dic43C2×D412yes—
186C2×Dic43C2×D412yes—
187C2×Dic43#4112yes—
188D172—28no—
189D172—44no—
190D172—44no—
191C4×D43—28no—
192C4×D43—44no—
193C4×D43—44no—
194C4×D43—44no—
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×C43C22×D411yescharacteristic
205C22×C43C2×#4111yescharacteristic
206C22×C43C2×#4111yescharacteristic
207C22×C43H(5,𝔽2)11yescharacteristic
208C22×C432−1+411yescharacteristic
209C2×D43—22no—
210C2×D43—22no—
211C2×D43—22no—
212C2×D43—22no—
213C2×D43—22no—
214C2×D43—22no—
215C2×D43—22no—
216C2×D43—22no—
217C2×D43—22no—
218C2×D43—41no—
219C2×D43—41no—
220C2×D43—41no—
221C2×D43—41no—
222C2×D43—41no—
223C2×D43—41no—
224C2×D43—41no—
225C2×D43—41no—
226C2×D43—41no—
227C2×D43—41no—
228C2×D43—41no—
229C2×D43#12114yescomplemented
230C4×C43—22no—
231C4×C43—22no—
232C4×C43—22no—
233C4×C43—41no—
234C4×C43—41no—
235C4×C43—41no—
236Dic43—22no—
237Dic43—41no—
238Dic43—41no—
239Dic43—41no—
240Dic43#12114yescomplemented
241#2416—431nomaximal, Sylow
242C2×C43—81no—
243C2×C43C2×#12111yescharacteristic
244C2×C43C2×#12111yescharacteristic
245C2×C43#53711yescharacteristic
246C2×C43D4211yescharacteristic
247C2×C43#54711yescharacteristic
248C2×C43#54811yescharacteristic
249C2×C43#55311yescharacteristic
250D43—24no—
251D43—42no—
252D43—81no—
253C2×#121—431no—
254C2×#121—431no—
255C2×#121—431no—
256C2×#121—431no—
257C2×C4×D4—431no—
258C22×C4⋊C4—431no—
259#396—431no—
260#396D4311yescharacteristic, complemented
261#394—431no—
262#394—431no—
263#390—431no—
264#389—431no—
265#386—431no—
266#386—431no—
267#380—431no—
268C43#241611yescharacteristic, complemented, Sylow
269C22×D4—431no—
270C22×D4—431no—
271C22×D4—431no—
272C22×D4—431no—
273C22×D4—431no—
274C22×D4—431no—
275C23×C4—431no—
276C23×C4—431no—
277C23×C4—431no—
278C23×C4—431no—
279#121—864no—
280#121—864no—
281#121—864no—
282#121—864no—
283C4×D4—864no—
284C2×C4⋊C4—431no—
285C2×C4⋊C4—431no—
286C2×C4⋊C4—431no—
287C2×C4⋊C4—431no—
288C2×C4⋊C4—431no—
289C2×C4⋊C4—864no—
290C2×C4⋊C4C2×D4311yescharacteristic
291C2×C4⋊C4C2×D4311yescharacteristic
292C2×C4⋊C4C2×D4311yescharacteristic
293C2×C22⋊C4—431no—
294C2×C22⋊C4—431no—
295C2×C22⋊C4—431no—
296C2×C22⋊C4—431no—
297C2×C22⋊C4—431no—
298C2×C22⋊C4—431no—
299C2×C22⋊C4—431no—
300C2×C22⋊C4—431no—
301C2×C22⋊C4—431no—
302C2×C22⋊C4C2×D4311yescharacteristic
303C2×C22⋊C4C2×D4311yescharacteristic
304C2×C22⋊C4C2×D4311yescharacteristic
305C2×C42—431no—
306#95—431no—
307#95—431no—
308#95—431no—
309#95C2×D4311yescharacteristic
310C24—431no—
311C24—431no—
312C24—431no—
313C24C22×D4311yescharacteristic
314C2×D4—434no—
315C2×D4—862no—
316C2×D4—862no—
317C2×D4—862no—
318C2×D4—862no—
319C2×D4—862no—
320C2×D4—862no—
321C2×D4—862no—
322C2×D4—862no—
323C2×D4—862no—
324C2×D4—862no—
325C2×D4—862no—
326C2×D4—862no—
327C2×D4—862no—
328C2×D4—862no—
329C2×D4—862no—
330C2×D4—1721no—
331C2×D4—1721no—
332C22×C4—431no—
333C22×C4—431no—
334C22×C4—434no—
335C22×C4—431no—
336C22×C4—431no—
337C22×C4—431no—
338C22×C4—862no—
339C22×C4—862no—
340C22×C4—862no—
341C22×C4—862no—
342C22×C4—862no—
343C22×C4—862no—
344C22×C4—862no—
345C22×C4—862no—
346C22×C4—862no—
347C22×C4—1721no—
348C22×C4—1721no—
349C22×C4C22×D4311yescharacteristic
350C22×C4C22×D4311yescharacteristic
351C22×C4C22×D4311yescharacteristic
352C22×C4C22×D4311yescharacteristic
353C22×C4C22×D4311yescharacteristic
354C22×C4C22×D4311yescharacteristic
355C4⋊C4—22no—
356C4⋊C4—22no—
357C4⋊C4—22no—
358C4⋊C4—434no—
359C4⋊C4—862no—
360C4⋊C4—862no—
361C4⋊C4—862no—
362C4⋊C4—862no—
363C22⋊C4—22no—
364C22⋊C4—22no—
365C22⋊C4—22no—
366C22⋊C4—862no—
367C22⋊C4—862no—
368C22⋊C4—862no—
369C22⋊C4—862no—
370C22⋊C4—862no—
371C22⋊C4—862no—
372C22⋊C4—862no—
373C22⋊C4—1721no—
374C22⋊C4—1721no—
375C42—862no—
376C23—21no—
377C23—21no—
378C23—21no—
379C23—21no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—432no—
384C23—432no—
385C23—432no—
386C23—432no—
387C23—861no—
388C23—861no—
389C23—861no—
390C23—861no—
391C23—861no—
392C23—861no—
393C23—861no—
394C23—861no—
395C23—861no—
396C23—861no—
397C23—861no—
398C23—861no—
399C23—861no—
400C23—861no—
401C23—861no—
402C23—861no—
403C23—861no—
404C23C23×D4311yescharacteristic
405D4—868no—
406D4—1724no—
407D4—1724no—
408D4—1724no—
409D4—1724no—
410D4—1724no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—432no—
427C2×C4—432no—
428C2×C4—432no—
429C2×C4—432no—
430C2×C4—868no—
431C2×C4—861no—
432C2×C4—861no—
433C2×C4—861no—
434C2×C4—861no—
435C2×C4—861no—
436C2×C4—861no—
437C2×C4—861no—
438C2×C4—861no—
439C2×C4—861no—
440C2×C4—861no—
441C2×C4—861no—
442C2×C4—1724no—
443C2×C4—1724no—
444C2×C4—1724no—
445C2×C4D4×D4312yes—
446C2×C4D4×D4312yes—
447C2×C4D4×D4312yes—
448C22—41no—
449C22—41no—
450C22—41no—
451C22—41no—
452C22—41no—
453C22—41no—
454C22—41no—
455C22—434no—
456C22—862no—
457C22—862no—
458C22—862no—
459C22—862no—
460C22—862no—
461C22—862no—
462C22—862no—
463C22—862no—
464C22—862no—
465C22—1721no—
466C22—1721no—
467C22—1721no—
468C22—1721no—
469C22—1721no—
470C22—1721no—
471C22—1721no—
472C22—1721no—
473C22—1721no—
474C22—1721no—
475C22—1721no—
476C22C2×D4×D4311yescharacteristic
477C22C2×D4×D4311yescharacteristic
478C22C2×D4×D4311yescharacteristic
479C22#41×D4311yescharacteristic
480C22#41×D4311yescharacteristic
481C22#1306337111yescharacteristic
482C22#1306337311yescharacteristic
483C4—22no—
484C4—22no—
485C4—22no—
486C4—41no—
487C4—41no—
488C4—41no—
489C4—434no—
490C4—862no—
491C4—1721no—
492C4—1721no—
493C4—1721no—
494C2—81no—
495C2—864no—
496C2—3441no—
497C2—1722no—
498C2#121×D4311yescharacteristic
499C2#121×D4311yescharacteristic
500C2#1458347911yescharacteristic
501C2#1458353311yescharacteristic
502C2#1458355111yescharacteristic
503C2#1458355911yescharacteristic
504C2#1458360011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#396C2
hypercenter#396D43
hypocenterC43#2416
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #396

Complements

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

NH ≅ G/Ntype
1. C2×#13063300C2semidirect
2. C2×#13063298C2semidirect
3. C2×#13063298C2semidirect
4. C2×#13063298C2semidirect
5. C2×#13063287C2semidirect
6. C2×C4⋊C4×D43C2semidirect
7. #14582821C2semidirect
8. #14582816C2semidirect
9. #14582815C2semidirect
10. #14582799C2semidirect
11. #14582794C2semidirect
12. #14582777C2semidirect
13. #14582775C2semidirect
14. #14582758C2semidirect
15. C43×#396C2semidirect
89. C2×D172D4semidirect
101. C2×C4×D43D4semidirect
121. Dic43⋊C4D4semidirect
229. C2×D43#121semidirect
240. Dic43#121semidirect
260. #396D43semidirect
268. C43#2416semidirect