Finite Group Databasebeta

← #29577340

Subgroups — #29577340

Order 15616.

618 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454845C211yesmaximal, characteristic, complemented
2#21450781C211yesmaximal, characteristic
3#21445804C211yesmaximal, characteristic, complemented
4#21444387C211yesmaximal, characteristic, complemented
5#21443699C211yesmaximal, characteristic, complemented
6#21443697C211yesmaximal, characteristic, complemented
7C61×#1519C211yesmaximal, characteristic, complemented
8C2×#14519749—21no—
9C2×C4×C22⋊D61C2211yescharacteristic
10#16839833—22no—
11#16839830—22no—
12#16839816—21no—
13C2×#14519691—21no—
14#16839724—21no—
15C2×C22⋊#92418C2211yescharacteristic
16#16839693C411yescharacteristic, complemented
17#16839688C411yescharacteristic, complemented
18#16839676C411yescharacteristic, complemented
19#16839670C411yescharacteristic, complemented
20#16839650—21no—
21#16839642—21no—
22#16839638—21no—
23#16839622C2211yescharacteristic
24C2×#14519684C2211yescharacteristic
25#16839528—21no—
26#16839496—22no—
27C2×#121×C61C2211yescharacteristic
28C2×C22⋊C8×C61C2211yescharacteristic
29C61×#380C2211yescharacteristic
30C61×#327—22no—
31C22×C22⋊D61—21no—
32C22×C22⋊D61D411yescharacteristic
33C23×Dic61—21no—
34C22×C4×D61D411yescharacteristic
35C2×#11758189—22no—
36C22×#92418—21no—
37#14519749—42no—
38#14519749—42no—
39C4×C22⋊D61—21no—
40C4×C22⋊D61—21no—
41C4×C22⋊D61—21no—
42C4×C22⋊D61—21no—
43C2×C4⋊Dic61—21no—
44C2×#11758196—21no—
45C2×#11758196C2×C411yescharacteristic
46C2×C22⋊Dic61—21no—
47C2×C22⋊Dic61—21no—
48C2×C22⋊Dic61—21no—
49C2×C22⋊Dic61—21no—
50C2×C22⋊Dic61D411yescharacteristic
51C2×#11758198—21no—
52C2×#11758198C2×C411yescharacteristic
53C2×C4×Dic61D411yescharacteristic
54#14519706—22no—
55#14519691—42no—
56C22⋊#92418—21no—
57C22⋊#92418D412yescomplemented
58#14519689—22no—
59#14519687—22no—
60#14519684—21no—
61#14519684—21no—
62#14519684—21no—
63#14519684—21no—
64#14519684C2×C411yescharacteristic
65#14519684C2×C411yescharacteristic
66C22×D4×C61—21no—
67C22×D4×C61C2×C411yescharacteristic
68C23×C4×C61C2311yescharacteristic
69C22×C8×C61—21no—
70#121×C61—21no—
71#121×C61—21no—
72#121×C61—21no—
73#121×C61—21no—
74C2×C4⋊C4×C61—21no—
75C2×C4⋊C4×C61C2×C411yescharacteristic
76C2×C22⋊C4×C61—21no—
77C2×C22⋊C4×C61—21no—
78C22⋊C8×C61—21no—
79C22⋊C8×C61D412yescomplemented
80#95×C61—21no—
81C24×C61—21no—
82C24×C61C2×D411yescharacteristic
83C23×D61C22⋊C411yescharacteristic
84C2×D4×C61—21no—
85C2×D4×C61—21no—
86C2×D4×C61—41no—
87C2×D4×C61—41no—
88C2×D4×C61—41no—
89C2×D4×C61—41no—
90C2×D4×C61—41no—
91C2×D4×C61—41no—
92C2×D4×C61—81no—
93C22×C4×C61—21no—
94C22×C4×C61—41no—
95C22×C4×C61—81no—
96C22×C4×C61C22×C411yescharacteristic
97C22×C4×C61C2×D411yescharacteristic
98C22×C4×C61C2×D411yescharacteristic
99C22×C4×C61C2×D411yescharacteristic
100C22×C4×C61#4111yescharacteristic
101C22×C4×C61#4111yescharacteristic
102C2×C22⋊D61—21no—
103C2×C22⋊D61—21no—
104C2×C22⋊D61—21no—
105C2×C22⋊D61—21no—
106C2×C22⋊D61—21no—
107C2×C22⋊D61—21no—
108C2×C22⋊D61—42no—
109C2×C22⋊D61—42no—
110C2×C22⋊D61—81no—
111C22×Dic61—21no—
112C22×Dic61—21no—
113C22×Dic61—42no—
114C22×Dic61—41no—
115C22×Dic61—41no—
116C22×Dic61—41no—
117C22×Dic61—81no—
118C22×Dic61C22⋊C411yescharacteristic
119C22×Dic61C22⋊C411yescharacteristic
120C22×Dic61C22⋊C411yescharacteristic
121C2×C4×D61—21no—
122C2×C4×D61—21no—
123C2×C4×D61—81no—
124C2×C8×C61—22no—
125C2×C8×C61—81no—
126C4⋊C4×C61—21no—
127C4⋊C4×C61—21no—
128C4⋊C4×C61—81no—
129C22⋊C4×C61—41no—
130C22⋊C4×C61—41no—
131C22⋊C4×C61—41no—
132C22⋊C4×C61—41no—
133C22⋊Dic61—21no—
134C22⋊Dic61—21no—
135C22⋊Dic61—42no—
136C22⋊Dic61—42no—
137C22⋊Dic61—41no—
138C22⋊Dic61—41no—
139C22⋊Dic61—81no—
140#11758198—21no—
141#11758198—21no—
142#11758198—42no—
143C4⋊Dic61—81no—
144#11758196—21no—
145#11758196—21no—
146#11758196—42no—
147C4×Dic61—21no—
148C4×Dic61—21no—
149C2×#92418—22no—
150C2×#92418—81no—
151#11758189—82no—
152C23×C61—41no—
153C23×C61—41no—
154C23×C61—41no—
155C23×C61—41no—
156C23×C61—41no—
157C23×C61—41no—
158C23×C61—41no—
159C23×C61—41no—
160C23×C61—41no—
161C23×C61C2×C22⋊C411yescharacteristic
162C23×C61#12111yescharacteristic
163C23×C61#12111yescharacteristic
164C23×C61AGL(1,ℤ/8)11yescharacteristic
165C23×C61AGL(1,ℤ/8)11yescharacteristic
166C23×C61AGL(1,ℤ/8)11yescharacteristic
167C23×C61#13711yescharacteristic
168C22×D61—21no—
169C22×D61—21no—
170C22×D61—21no—
171C22×D61—41no—
172C22×D61—41no—
173D4×C61—81no—
174D4×C61—81no—
175D4×C61—81no—
176D4×C61—81no—
177D4×C61—81no—
178D4×C61—81no—
179C2×C4×C61—41no—
180C2×C4×C61—41no—
181C2×C4×C61—41no—
182C2×C4×C61—41no—
183C2×C4×C61—41no—
184C2×C4×C61—41no—
185C2×C4×C61—41no—
186C2×C4×C61—41no—
187C2×C4×C61—41no—
188C2×C4×C61—81no—
189C2×C4×C61—81no—
190C2×C4×C61—81no—
191C2×C4×C61C4×D411yescharacteristic
192C2×C4×C61C4×D411yescharacteristic
193C2×C4×C61#12011yescharacteristic
194C2×C4×C61#12311yescharacteristic
195C22⋊D61—41no—
196C22⋊D61—41no—
197C22⋊D61—41no—
198C22⋊D61—41no—
199C22⋊D61—84no—
200C2×Dic61—22no—
201C2×Dic61—21no—
202C2×Dic61—21no—
203C2×Dic61—21no—
204C2×Dic61—21no—
205C2×Dic61—21no—
206C2×Dic61—41no—
207C2×Dic61—41no—
208C2×Dic61—41no—
209C2×Dic61—41no—
210C2×Dic61—41no—
211C2×Dic61—41no—
212C2×Dic61—41no—
213C2×Dic61—82no—
214C2×Dic61—82no—
215C2×Dic61—81no—
216C2×Dic61—81no—
217C2×Dic61—81no—
218C4×D61—42no—
219C4×D61—81no—
220C8×C61—42no—
221#92418—42no—
222#9386—611nomaximal, Sylow
223C22×C61—21no—
224C22×C61—21no—
225C22×C61—21no—
226C22×C61—21no—
227C22×C61—21no—
228C22×C61—21no—
229C22×C61—41no—
230C22×C61—41no—
231C22×C61—41no—
232C22×C61—41no—
233C22×C61—81no—
234C22×C61—81no—
235C22×C61—81no—
236C22×C61—81no—
237C22×C61—81no—
238C22×C61—81no—
239C22×C61—81no—
240C22×C61#38611yescharacteristic
241C22×C61#41711yescharacteristic
242C22×C61#41811yescharacteristic
243C22×C61#46811yescharacteristic
244C22×C61#46811yescharacteristic
245C22×C61#46911yescharacteristic
246C22×C61#46911yescharacteristic
247C2×D61—42no—
248C2×D61—41no—
249C2×D61—41no—
250C2×D61—41no—
251C2×D61—81no—
252C4×C61—21no—
253C4×C61—21no—
254C4×C61—21no—
255C4×C61—21no—
256C4×C61—81no—
257C4×C61—161no—
258Dic61—42no—
259Dic61—41no—
260Dic61—41no—
261Dic61—41no—
262Dic61—81no—
263Dic61—161no—
264#2973—611no—
265#2543—611no—
266#1799—611no—
267#1519—611no—
268#1519D6111yescharacteristic, complemented
269#1294—611no—
270#1294—611no—
271C2×C61—21no—
272C2×C61—21no—
273C2×C61—21no—
274C2×C61—21no—
275C2×C61—21no—
276C2×C61—21no—
277C2×C61—161no—
278C2×C61#188411yescharacteristic
279C2×C61#189511yescharacteristic
280C2×C61#191311yescharacteristic
281D61—81no—
282C2×#121—1221no—
283C2×#121C2×D6111yescharacteristic
284C2×C4×D4—611no—
285#435—1222no—
286#435—1222no—
287#432—1221no—
288C2×#99—1221no—
289#407—1221no—
290C2×C22⋊C8—611no—
291C2×C22⋊C8C2×D6111yescharacteristic
292#398—611no—
293#397—611no—
294#394—611no—
295#392—611no—
296#388—1221no—
297#386—1221no—
298#386—1221no—
299#380—611no—
300#380C2×D6111yescharacteristic
301C2×#95—611no—
302#342—1221no—
303#327—22no—
304#327—1222no—
305C61#938611yescharacteristic, complemented, Sylow
306C22×D4—21no—
307C22×D4—611no—
308C22×D4—1221no—
309C22×D4C4×D6111yescharacteristic
310C23×C4—611no—
311C23×C4—1221no—
312C23×C4C22×D6111yescharacteristic
313C2×M16—1222no—
314C22×C8—21no—
315C22×C8—1221no—
316#121—21no—
317#121—21no—
318#121—21no—
319#121—21no—
320#121—2442no—
321#121—2442no—
322C4×D4—1221no—
323C4×D4—1221no—
324C4×D4—1221no—
325C4×D4—1221no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—611no—
328C2×C4⋊C4—1221no—
329C2×C4⋊C4—1221no—
330C2×C4⋊C4C4×D6111yescharacteristic
331C2×C22⋊C4—21no—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—611no—
334C2×C22⋊C4—611no—
335C2×C22⋊C4—1221no—
336C2×C22⋊C4—1221no—
337C2×C22⋊C4—1221no—
338C2×C22⋊C4—1221no—
339C2×C22⋊C4—1221no—
340C2×C42—611no—
341C4⋊C8—1222no—
342#99—2442no—
343C22⋊C8—21no—
344C22⋊C8—612no—
345C22⋊C8—1222no—
346C22⋊C8—1221no—
347C22⋊C8C22⋊D6112yescomplemented
348#97—1222no—
349#95—21no—
350#95—611no—
351#95—611no—
352#95—1221no—
353#95—1221no—
354#95—1221no—
355#95—1221no—
356C24—21no—
357C24—611no—
358C24D4×D6111yescharacteristic
359C2×D4—21no—
360C2×D4—21no—
361C2×D4—41no—
362C2×D4—41no—
363C2×D4—41no—
364C2×D4—41no—
365C2×D4—41no—
366C2×D4—41no—
367C2×D4—81no—
368C2×D4—1221no—
369C2×D4—1221no—
370C2×D4—1221no—
371C2×D4—1221no—
372C2×D4—1221no—
373C2×D4—1221no—
374C2×D4—4881no—
375C2×D4—2442no—
376C2×D4—2442no—
377C22×C4—21no—
378C22×C4—41no—
379C22×C4—81no—
380C22×C4—611no—
381C22×C4—611no—
382C22×C4—611no—
383C22×C4—1221no—
384C22×C4—1221no—
385C22×C4—1221no—
386C22×C4—1221no—
387C22×C4—4881no—
388C22×C4—4881no—
389C22×C4—2442no—
390C22×C4—2441no—
391C22×C4—2441no—
392C22×C4—2441no—
393C22×C4C2×C4×D6111yescharacteristic
394C22×C4#1175822211yescharacteristic
395C22×C4D4×D6111yescharacteristic
396C22×C4D4×D6111yescharacteristic
397C22×C4#1175822411yescharacteristic
398C22×C4C2×C22⋊D6111yescharacteristic
399M16—4882no—
400C2×C8—22no—
401C2×C8—81no—
402C2×C8—1222no—
403C2×C8—4881no—
404C4⋊C4—21no—
405C4⋊C4—21no—
406C4⋊C4—81no—
407C4⋊C4—1221no—
408C4⋊C4—1221no—
409C4⋊C4—4881no—
410C4⋊C4—2442no—
411C22⋊C4—41no—
412C22⋊C4—41no—
413C22⋊C4—41no—
414C22⋊C4—41no—
415C22⋊C4—1221no—
416C22⋊C4—1221no—
417C22⋊C4—1221no—
418C22⋊C4—1221no—
419C22⋊C4—4881no—
420C22⋊C4—2442no—
421C22⋊C4—2442no—
422C22⋊C4—2442no—
423C22⋊C4—2441no—
424C22⋊C4—2441no—
425C42—1221no—
426C42—1221no—
427C23—41no—
428C23—41no—
429C23—41no—
430C23—41no—
431C23—41no—
432C23—41no—
433C23—41no—
434C23—41no—
435C23—41no—
436C23—1221no—
437C23—1221no—
438C23—1221no—
439C23—2441no—
440C23—2441no—
441C23C22⋊C4×D6111yescharacteristic
442C23#1451974811yescharacteristic
443C23#1451975011yescharacteristic
444C23#1451980111yescharacteristic
445C23#1451980111yescharacteristic
446C23#1451980411yescharacteristic
447C23#1451980611yescharacteristic
448D4—81no—
449D4—81no—
450D4—81no—
451D4—81no—
452D4—81no—
453D4—81no—
454D4—4884no—
455D4—2441no—
456D4—2441no—
457D4—2441no—
458D4—2441no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—81no—
469C2×C4—81no—
470C2×C4—81no—
471C2×C4—1222no—
472C2×C4—1221no—
473C2×C4—1221no—
474C2×C4—1221no—
475C2×C4—1221no—
476C2×C4—1221no—
477C2×C4—4881no—
478C2×C4—4881no—
479C2×C4—4881no—
480C2×C4—4881no—
481C2×C4—4882no—
482C2×C4—4882no—
483C2×C4—2442no—
484C2×C4—2441no—
485C2×C4—2441no—
486C2×C4—2441no—
487C2×C4—2441no—
488C2×C4—2441no—
489C2×C4—2441no—
490C2×C4—2441no—
491C2×C4#1451973711yescharacteristic
492C2×C4C4×C22⋊D6111yescharacteristic
493C2×C4#1451974511yescharacteristic
494C2×C4#1451975911yescharacteristic
495C8—42no—
496C8—2442no—
497C22—21no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—21no—
503C22—41no—
504C22—41no—
505C22—41no—
506C22—41no—
507C22—81no—
508C22—81no—
509C22—81no—
510C22—81no—
511C22—81no—
512C22—81no—
513C22—81no—
514C22—4881no—
515C22—2442no—
516C22—2441no—
517C22—2441no—
518C22—2441no—
519C22#1683963811yescharacteristic
520C22#1683976011yescharacteristic
521C22#1683976511yescharacteristic
522C22#1684000511yescharacteristic
523C22#1684000711yescharacteristic
524C22#1684001211yescharacteristic
525C22#1684001411yescharacteristic
526C4—21no—
527C4—21no—
528C4—21no—
529C4—21no—
530C4—81no—
531C4—161no—
532C4—9761no—
533C4—4881no—
534C4—2442no—
535C4—2441no—
536C4—2441no—
537C4—2441no—
538C2—21no—
539C2—21no—
540C2—21no—
541C2—21no—
542C2—21no—
543C2—21no—
544C2—161no—
545C2—4881no—
546C2#2144619911yescharacteristic
547C2#2144625411yescharacteristic
548C2#2144635811yescharacteristic
subgroupG/H
centerC22#16839638
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1519C2
socleC22×C61#386
prime radical#21450781C2
cosocleC23×C4×C61C23
hypercenter#1519D61
hypocenterC61#9386
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1519

Complements

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

NH ≅ G/Ntype
1. #21454845C2semidirect
3. #21445804C2semidirect
4. #21444387C2semidirect
5. #21443699C2semidirect
6. #21443697C2semidirect
7. C61×#1519C2semidirect
16. #16839693C4semidirect
17. #16839688C4semidirect
18. #16839676C4semidirect
19. #16839670C4semidirect
57. C22⋊#92418D4semidirect
79. C22⋊C8×C61D4semidirect
268. #1519D61semidirect
305. C61#9386semidirect
347. C22⋊C8C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
#214548452
#214507812
#214458042
#214443872
#214436992
#214436972
C61×#15192
#938661