Finite Group Databasebeta

← #29575787

Subgroups — #29575787

Order 15616.

1024 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454102C211yesmaximal, characteristic
2C2×#16839621C211yesmaximal, characteristic, complemented
3#21445728C211yesmaximal, characteristic, complemented
4C2×#16839497C211yesmaximal, characteristic, complemented
5C2×#16839495C211yesmaximal, characteristic, complemented
6#21443697C211yesmaximal, characteristic, complemented
7C61×#1294C211yesmaximal, characteristic, complemented
8C23×C4×D61C2211yescharacteristic
9C2×#14519752C412yescomplemented
10C2×#14519751C2211yescharacteristic
11C2×#14519747—21no—
12C22×#11758196—21no—
13C22×#11758198—21no—
14C2×C22⋊#92418C2211yescharacteristic
15C2×#14519689—22no—
16#16839640—22no—
17#16839639—21no—
18#16839621—22no—
19#16839621—22no—
20#16839619C412yescomplemented
21C2×#14519684C2211yescharacteristic
22#16839497—22no—
23#16839495—22no—
24C2×C22⋊C8×C61C2211yescharacteristic
25C61×#380C2211yescharacteristic
26C2×#95×C61C2211yescharacteristic
27C24×D61D411yescharacteristic
28C22×D244—22no—
29C22×D244C2×C411yescharacteristic
30C22×C22⋊D61—21no—
31C23×Dic61—21no—
32C23×Dic61D411yescharacteristic
33C22×C4×D61—21no—
34C22×C4×D61—21no—
35C22×C4×D61—21no—
36C22×C4×D61—21no—
37C22×C4×D61—44no—
38C22×C4×D61C2×C412yes—
39C22×C4×D61D412yes—
40C22×#92418—21no—
41#14519752—44no—
42#14519751—21no—
43#14519751—21no—
44#14519751—21no—
45#14519751—21no—
46#14519747—42no—
47#14519747—42no—
48C2×C4⋊Dic61C2×C411yescharacteristic
49C2×#11758196—24no—
50C2×#11758196—44no—
51C2×#11758198—24no—
52C2×#11758198—22no—
53C2×#11758198—21no—
54C2×#11758198—22no—
55C2×#11758198—42no—
56C2×#11758198—42no—
57C22⋊#92418—21no—
58C22⋊#92418—21no—
59#14519689—44no—
60#14519684—21no—
61#14519684—22no—
62#14519684D412yescomplemented
63C23×C4×C61—21no—
64C23×C4×C61C2311yescharacteristic
65C22×C8×C61—21no—
66C2×C4⋊C4×C61C2×C412yes—
67C2×C22⋊C4×C61—21no—
68C22⋊C8×C61—21no—
69C22⋊C8×C61—21no—
70#95×C61—21no—
71#95×C61—21no—
72#95×C61D412yescomplemented
73C24×C61C2×D411yescharacteristic
74C23×D61—21no—
75C23×D61—21no—
76C23×D61—21no—
77C23×D61—21no—
78C23×D61—21no—
79C23×D61—42no—
80C23×D61—42no—
81C23×D61C22⋊C412yes—
82C23×D61D812yes—
83C23×D61SD1612yes—
84C22×C4×C61—22no—
85C22×C4×C61—22no—
86C22×C4×C61—42no—
87C22×C4×C61—42no—
88C22×C4×C61—42no—
89C22×C4×C61—41no—
90C22×C4×C61—41no—
91C22×C4×C61C22×C411yescharacteristic
92C22×C4×C61C2×D411yescharacteristic
93C22×C4×C61C2×D411yescharacteristic
94C22×C4×C61C2×D411yescharacteristic
95C22×C4×C61#4111yescharacteristic
96C22×C4×C61#4111yescharacteristic
97C2×C22⋊D61—41no—
98C2×C22⋊D61—41no—
99C2×C22⋊D61—41no—
100C2×C22⋊D61—41no—
101C2×C22⋊D61—41no—
102C2×C22⋊D61—41no—
103C22×Dic61—21no—
104C22×Dic61—21no—
105C22×Dic61—24no—
106C22×Dic61—21no—
107C22×Dic61—22no—
108C22×Dic61—42no—
109C22×Dic61—42no—
110C22×Dic61—41no—
111C22×Dic61—41no—
112C22×Dic61C22⋊C412yes—
113C2×D244—21no—
114C2×D244—21no—
115C2×D244—42no—
116C2×D244—44no—
117C2×D244—44no—
118C2×D244—44no—
119C2×C4×D61—22no—
120C2×C4×D61—22no—
121C2×C4×D61—22no—
122C2×C4×D61—22no—
123C2×C4×D61—24no—
124C2×C4×D61—24no—
125C2×C4×D61—42no—
126C2×C4×D61—42no—
127C2×C4×D61—44no—
128C2×C4×D61—44no—
129C2×C4×D61—44no—
130C2×C4×D61—44no—
131C2×C8×C61—42no—
132C2×C8×C61—41no—
133C4⋊C4×C61—42no—
134C22⋊C4×C61—41no—
135C22⋊C4×C61—41no—
136#11758198—48no—
137#11758198—44no—
138#11758198—41no—
139#11758198—41no—
140#11758198—44no—
141C4⋊Dic61—21no—
142C4⋊Dic61—21no—
143#11758196—48no—
144C2×#92418—42no—
145C2×#92418—41no—
146C23×C61—22no—
147C23×C61—22no—
148C23×C61C2×C22⋊C411yescharacteristic
149C23×C61#12011yescharacteristic
150C23×C61#12311yescharacteristic
151C23×C61C2×D811yescharacteristic
152C23×C61C2×SD1611yescharacteristic
153C23×C61AGL(1,ℤ/8)11yescharacteristic
154C23×C61#13711yescharacteristic
155C22×D61—22no—
156C22×D61—22no—
157C22×D61—22no—
158C22×D61—22no—
159C22×D61—22no—
160C22×D61—22no—
161C22×D61—22no—
162C22×D61—22no—
163C22×D61—22no—
164C22×D61—22no—
165C22×D61—44no—
166C22×D61—44no—
167C22×D61—42no—
168C22×D61—42no—
169C22×D61—42no—
170C22×D61—42no—
171C22×D61—44no—
172C22×D61—44no—
173C22×D61—41no—
174C22×D61—42no—
175C22×D61—41no—
176C22×D61—41no—
177C22×D61—42no—
178C22×D61#10214yes—
179C2×C4×C61—22no—
180C2×C4×C61—22no—
181C2×C4×C61—41no—
182C2×C4×C61—41no—
183C2×C4×C61—41no—
184C2×C4×C61—41no—
185C2×C4×C61—42no—
186C2×C4×C61—42no—
187C2×C4×C61—42no—
188C2×C4×C61—42no—
189C2×C4×C61—42no—
190C2×C4×C61—42no—
191C2×C4×C61—82no—
192C2×C4×C61—82no—
193C2×C4×C61C4×D411yescharacteristic
194C2×C4×C61C4×D411yescharacteristic
195C2×C4×C61#12111yescharacteristic
196C2×C4×C61#12111yescharacteristic
197C22⋊D61—81no—
198C22⋊D61—81no—
199C22⋊D61—81no—
200C22⋊D61—81no—
201C2×Dic61—24no—
202C2×Dic61—24no—
203C2×Dic61—22no—
204C2×Dic61—22no—
205C2×Dic61—42no—
206C2×Dic61—42no—
207C2×Dic61—41no—
208C2×Dic61—41no—
209C2×Dic61—41no—
210C2×Dic61—42no—
211C2×Dic61—82no—
212C2×Dic61—82no—
213C2×Dic61#9914yes—
214D244—81no—
215D244—81no—
216D244—88no—
217C4×D61—44no—
218C4×D61—44no—
219C4×D61—44no—
220C4×D61—44no—
221C8×C61—81no—
222#92418—81no—
223#9155—611nomaximal, Sylow
224C22×C61—21no—
225C22×C61—21no—
226C22×C61—21no—
227C22×C61—21no—
228C22×C61—22no—
229C22×C61—22no—
230C22×C61—22no—
231C22×C61—22no—
232C22×C61#38611yescharacteristic
233C22×C61C2×#9912yes—
234C22×C61C2×#10211yescharacteristic
235C22×C61#41711yescharacteristic
236C22×C61#42112yes—
237C22×C61#44711yescharacteristic
238C22×C61#44811yescharacteristic
239C22×C61#48011yescharacteristic
240C22×C61#48111yescharacteristic
241C2×D61—24no—
242C2×D61—24no—
243C2×D61—24no—
244C2×D61—44no—
245C2×D61—44no—
246C2×D61—44no—
247C2×D61—44no—
248C2×D61—42no—
249C2×D61—42no—
250C2×D61—42no—
251C2×D61—42no—
252C2×D61—81no—
253C2×D61—81no—
254C2×D61—81no—
255C2×D61—82no—
256C2×D61—82no—
257C4×C61—21no—
258C4×C61—21no—
259C4×C61—21no—
260C4×C61—21no—
261C4×C61—82no—
262C4×C61—82no—
263Dic61—24no—
264Dic61—82no—
265Dic61—81no—
266#2847—611no—
267C2×#380—611no—
268#1779—611no—
269C2×#327—611no—
270C2×#327—611no—
271#1294—611no—
272#1294D6111yescharacteristic, complemented
273C2×C61—21no—
274C2×C61—21no—
275C2×C61—21no—
276C2×C61—21no—
277C2×C61#151312yes—
278C2×C61#151912yes—
279C2×C61#187411yescharacteristic
280C2×C61#189711yescharacteristic
281C2×C61#189811yescharacteristic
282D61—44no—
283D61—161no—
284C24×C4—611no—
285C2×#121—611no—
286C2×#121—612no—
287C2×#120—1221no—
288C22×C4⋊C4—1221no—
289C22×C22⋊C4—1221no—
290C2×C22⋊C8—611no—
291C2×C22⋊C8—1222no—
292C2×C22⋊C8C2×D6111yescharacteristic
293#386—1222no—
294#386—1221no—
295#380—612no—
296#380—1222no—
297#380—1222no—
298#380C2×D6111yescharacteristic
299C2×#95—611no—
300C2×#95C2×D6111yescharacteristic
301#327—1222no—
302#327—1222no—
303C61#915511yescharacteristic, complemented, Sylow
304C25—611no—
305C22×D4—611no—
306C22×D4—1222no—
307C22×D4—1221no—
308C23×C4—21no—
309C23×C4—611no—
310C23×C4—612no—
311C23×C4—612no—
312C23×C4—1221no—
313C23×C4—1221no—
314C23×C4—1221no—
315C23×C4—1221no—
316C23×C4—1221no—
317C23×C4—2444no—
318C23×C4C22×D6111yescharacteristic
319C22×C8—21no—
320C22×C8—1221no—
321#121—1221no—
322#121—1221no—
323#121—1221no—
324#121—1221no—
325#121—2444no—
326#120—2442no—
327#120—2442no—
328C2×C4⋊C4—611no—
329C2×C4⋊C4—1224no—
330C2×C4⋊C4—2444no—
331C2×C4⋊C4C4×D6112yes—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—1222no—
334C2×C22⋊C4—1222no—
335C2×C22⋊C4—1224no—
336C2×C22⋊C4—1221no—
337C2×C22⋊C4—2442no—
338C2×C22⋊C4—2442no—
339C22⋊C8—21no—
340C22⋊C8—21no—
341C22⋊C8—1221no—
342C22⋊C8—1221no—
343C22⋊C8—2444no—
344#95—21no—
345#95—21no—
346#95—612no—
347#95—1222no—
348#95—1221no—
349#95D24412yescomplemented
350C24—612no—
351C24—612no—
352C24—612no—
353C24—1221no—
354C24—1221no—
355C24—1221no—
356C24—1221no—
357C24—1221no—
358C24—2442no—
359C24—2442no—
360C24D4×D6111yescharacteristic
361C2×D4—1221no—
362C2×D4—1221no—
363C2×D4—2442no—
364C2×D4—2444no—
365C2×D4—2444no—
366C2×D4—2444no—
367C2×D4—2441no—
368C2×D4—2441no—
369C2×D4—2441no—
370C2×D4—2441no—
371C2×D4—2441no—
372C2×D4—2441no—
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—42no—
376C22×C4—42no—
377C22×C4—42no—
378C22×C4—41no—
379C22×C4—41no—
380C22×C4—612no—
381C22×C4—1224no—
382C22×C4—1224no—
383C22×C4—1224no—
384C22×C4—1221no—
385C22×C4—1221no—
386C22×C4—1222no—
387C22×C4—1222no—
388C22×C4—1222no—
389C22×C4—1222no—
390C22×C4—1221no—
391C22×C4—1222no—
392C22×C4—2442no—
393C22×C4—2442no—
394C22×C4—2444no—
395C22×C4—2444no—
396C22×C4—2444no—
397C22×C4—2444no—
398C22×C4—2442no—
399C22×C4—2442no—
400C22×C4—2441no—
401C22×C4—2441no—
402C22×C4C2×C4×D6111yescharacteristic
403C22×C4C2×D24411yescharacteristic
404C22×C4#1175822211yescharacteristic
405C22×C4D4×D6111yescharacteristic
406C22×C4D4×D6111yescharacteristic
407C22×C4#1175822611yescharacteristic
408C2×C8—42no—
409C2×C8—41no—
410C2×C8—2442no—
411C2×C8—2441no—
412C4⋊C4—42no—
413C4⋊C4—1221no—
414C4⋊C4—1221no—
415C4⋊C4—2448no—
416C22⋊C4—41no—
417C22⋊C4—41no—
418C22⋊C4—2444no—
419C22⋊C4—2444no—
420C22⋊C4—2448no—
421C22⋊C4—2441no—
422C22⋊C4—2441no—
423C23—22no—
424C23—22no—
425C23—614no—
426C23—1222no—
427C23—1222no—
428C23—1222no—
429C23—1222no—
430C23—1222no—
431C23—1222no—
432C23—1222no—
433C23—1222no—
434C23—1222no—
435C23—1222no—
436C23—2444no—
437C23—2444no—
438C23—2442no—
439C23—2442no—
440C23—2444no—
441C23—2444no—
442C23—2442no—
443C23—2442no—
444C23—2442no—
445C23—2441no—
446C23—2441no—
447C23—2442no—
448C23—2441no—
449C23C22⋊C4×D6111yescharacteristic
450C23#1451974711yescharacteristic
451C23#1451976211yescharacteristic
452C23D8×D6111yescharacteristic
453C23SD16×D6111yescharacteristic
454C23#1451980411yescharacteristic
455C23#1451980911yescharacteristic
456D4—4881no—
457D4—4881no—
458D4—4888no—
459D4—4881no—
460D4—4881no—
461D4—4881no—
462D4—4881no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—42no—
475C2×C4—82no—
476C2×C4—82no—
477C2×C4—614no—
478C2×C4—1224no—
479C2×C4—1224no—
480C2×C4—1222no—
481C2×C4—1222no—
482C2×C4—4882no—
483C2×C4—4882no—
484C2×C4—2444no—
485C2×C4—2444no—
486C2×C4—2444no—
487C2×C4—2444no—
488C2×C4—2442no—
489C2×C4—2442no—
490C2×C4—2441no—
491C2×C4—2441no—
492C2×C4—2441no—
493C2×C4—2442no—
494C2×C4#1451973911yescharacteristic
495C2×C4C4×D24411yescharacteristic
496C2×C4#1451975011yescharacteristic
497C2×C4#1451975211yescharacteristic
498C8—81no—
499C8—4881no—
500C22—22no—
501C22—22no—
502C22—22no—
503C22—22no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—1224no—
509C22—1224no—
510C22—1224no—
511C22—4882no—
512C22—4882no—
513C22—4881no—
514C22—4881no—
515C22—4881no—
516C22—2444no—
517C22—2444no—
518C22—2444no—
519C22—2444no—
520C22—2442no—
521C22—2442no—
522C22—2442no—
523C22—2442no—
524C22#1683964011yescharacteristic
525C22#99×D6112yes—
526C22#102×D6111yescharacteristic
527C22#1683976211yescharacteristic
528C22#1683977712yes—
529C22#1683989711yescharacteristic
530C22#1683990211yescharacteristic
531C22#1684007711yescharacteristic
532C22#1684008211yescharacteristic
533C4—21no—
534C4—21no—
535C4—21no—
536C4—21no—
537C4—82no—
538C4—82no—
539C4—1224no—
540C4—4882no—
541C4—4881no—
542C2—21no—
543C2—21no—
544C2—21no—
545C2—21no—
546C2—9761no—
547C2—2444no—
548C2#2144436112yes—
549C2#2144438512yes—
550C2#2144613511yescharacteristic
551C2#2144626611yescharacteristic
552C2#2144627111yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1294C2
socleC23×C61C2×C22⋊C4
prime radical#21454102C2
cosocleC23×C4×C61C23
hypercenter#1294D61
hypocenterC61#9155
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1294

Complements

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

NH ≅ G/Ntype
2. C2×#16839621C2semidirect
3. #21445728C2semidirect
4. C2×#16839497C2semidirect
5. C2×#16839495C2semidirect
6. #21443697C2semidirect
7. C61×#1294C2semidirect
9. C2×#14519752C4semidirect
20. #16839619C4semidirect
62. #14519684D4semidirect
72. #95×C61D4semidirect
272. #1294D61semidirect
303. C61#9155semidirect
349. #95D244semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#214541022
C2×#168396212
#214457282
C2×#168394972
C2×#168394952
#214436972
C61×#12942
#915561