Finite Group Databasebeta

← #29577342

Subgroups — #29577342

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#21450779C211yesmaximal, characteristic
3#21445804C211yesmaximal, characteristic, complemented
4#21444388C211yesmaximal, characteristic, complemented
5#21444386C211yesmaximal, characteristic, complemented
6#21443698C211yesmaximal, characteristic, complemented
7C61×#1294C211yesmaximal, characteristic, complemented
8C2×#14519751—21no—
9C2×#14519751C2211yescharacteristic
10C2×C4×C22⋊D61C2211yescharacteristic
11#16839833—22no—
12#16839830—22no—
13#16839816—21no—
14C2×#14519691—21no—
15#16839724—21no—
16C2×C22⋊#92418C2211yescharacteristic
17#16839694C411yescharacteristic, complemented
18#16839689C411yescharacteristic, complemented
19#16839680C411yescharacteristic, complemented
20#16839672C411yescharacteristic, complemented
21#16839654—21no—
22#16839641—21no—
23#16839640—21no—
24#16839622C2211yescharacteristic
25#16839528—21no—
26#16839497—22no—
27#16839495—22no—
28C2×C22⋊C8×C61C2211yescharacteristic
29C61×#380C2211yescharacteristic
30C2×#95×C61C2211yescharacteristic
31C22×D244—21no—
32C22×D244C2×C411yescharacteristic
33C22×C22⋊D61—21no—
34C22×C22⋊D61D411yescharacteristic
35C22×C4×D61D411yescharacteristic
36C2×#11758189—22no—
37C22×#92418—21no—
38#14519751—21no—
39#14519751—21no—
40#14519751—21no—
41#14519751—21no—
42#14519751—42no—
43#14519751—42no—
44C4×C22⋊D61—21no—
45C4×C22⋊D61—21no—
46C4×C22⋊D61—21no—
47C4×C22⋊D61—21no—
48C2×C4⋊Dic61—21no—
49C2×C4⋊Dic61—21no—
50C2×C4⋊Dic61C2×C411yescharacteristic
51C2×#11758196C2×C411yescharacteristic
52C2×C22⋊Dic61—21no—
53C2×C22⋊Dic61D411yescharacteristic
54C2×#11758198—21no—
55C2×#11758198—21no—
56C2×#11758198—21no—
57C2×#11758198—21no—
58C2×#11758198—21no—
59C2×#11758198C2×C411yescharacteristic
60C2×C4×Dic61D411yescharacteristic
61#14519706—22no—
62#14519691—42no—
63C22⋊#92418—21no—
64C22⋊#92418D412yescomplemented
65#14519689—22no—
66#14519687—22no—
67#14519684—21no—
68#14519684—21no—
69#14519684—21no—
70C23×C4×C61—21no—
71C23×C4×C61C2311yescharacteristic
72C22×C8×C61—21no—
73C2×C4⋊C4×C61—21no—
74C2×C22⋊C4×C61—21no—
75C22⋊C8×C61—21no—
76C22⋊C8×C61D412yescomplemented
77#95×C61—21no—
78#95×C61—21no—
79#95×C61C2×C411yescharacteristic
80#95×C61C2×C411yescharacteristic
81C24×C61C2×D411yescharacteristic
82C23×D61—21no—
83C23×D61C22⋊C411yescharacteristic
84C22×C4×C61—21no—
85C22×C4×C61—21no—
86C22×C4×C61—42no—
87C22×C4×C61—41no—
88C22×C4×C61—41no—
89C22×C4×C61—41no—
90C22×C4×C61—81no—
91C22×C4×C61—81no—
92C22×C4×C61C22×C411yescharacteristic
93C22×C4×C61C2×D411yescharacteristic
94C22×C4×C61C2×D411yescharacteristic
95C22×C4×C61C2×D411yescharacteristic
96C22×C4×C61#4111yescharacteristic
97C22×C4×C61#4111yescharacteristic
98C2×C22⋊D61—21no—
99C2×C22⋊D61—21no—
100C2×C22⋊D61—21no—
101C2×C22⋊D61—21no—
102C2×C22⋊D61—21no—
103C2×C22⋊D61—21no—
104C2×C22⋊D61—41no—
105C2×C22⋊D61—41no—
106C2×C22⋊D61—41no—
107C2×C22⋊D61—41no—
108C2×C22⋊D61—41no—
109C2×C22⋊D61—41no—
110C22×Dic61—21no—
111C22×Dic61—41no—
112C22×Dic61C22⋊C411yescharacteristic
113C22×Dic61C22⋊C411yescharacteristic
114C22×Dic61C22⋊C411yescharacteristic
115C2×D244—21no—
116C2×D244—21no—
117C2×D244—42no—
118C2×D244—42no—
119C2×D244—81no—
120C2×D244—81no—
121C2×C4×D61—21no—
122C2×C4×D61—21no—
123C2×C4×D61—81no—
124C2×C8×C61—22no—
125C2×C8×C61—81no—
126C4⋊C4×C61—81no—
127C22⋊C4×C61—41no—
128C22⋊C4×C61—41no—
129C22⋊Dic61—21no—
130C22⋊Dic61—21no—
131C22⋊Dic61—41no—
132C22⋊Dic61—41no—
133#11758198—21no—
134#11758198—21no—
135#11758198—42no—
136#11758198—42no—
137#11758198—42no—
138#11758198—41no—
139#11758198—41no—
140#11758198—81no—
141C4⋊Dic61—21no—
142C4⋊Dic61—21no—
143C4⋊Dic61—42no—
144C4⋊Dic61—81no—
145#11758196—21no—
146#11758196—21no—
147C4×Dic61—21no—
148C4×Dic61—21no—
149C2×#92418—22no—
150C2×#92418—81no—
151#11758189—82no—
152C23×C61—41no—
153C23×C61—41no—
154C23×C61C2×C22⋊C411yescharacteristic
155C23×C61#12111yescharacteristic
156C23×C61#12111yescharacteristic
157C23×C61AGL(1,ℤ/8)11yescharacteristic
158C23×C61AGL(1,ℤ/8)11yescharacteristic
159C23×C61AGL(1,ℤ/8)11yescharacteristic
160C23×C61#13711yescharacteristic
161C22×D61—21no—
162C22×D61—21no—
163C22×D61—21no—
164C22×D61—41no—
165C22×D61—41no—
166C22×D61—41no—
167C22×D61—41no—
168C22×D61—41no—
169C22×D61—41no—
170C22×D61—41no—
171C22×D61—41no—
172C22×D61—41no—
173C2×C4×C61—22no—
174C2×C4×C61—41no—
175C2×C4×C61—41no—
176C2×C4×C61—41no—
177C2×C4×C61—41no—
178C2×C4×C61—41no—
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—82no—
186C2×C4×C61—82no—
187C2×C4×C61—81no—
188C2×C4×C61—81no—
189C2×C4×C61—81no—
190C2×C4×C61C4×D411yescharacteristic
191C2×C4×C61C4×D411yescharacteristic
192C2×C4×C61#12011yescharacteristic
193C2×C4×C61#12311yescharacteristic
194C22⋊D61—41no—
195C22⋊D61—41no—
196C22⋊D61—41no—
197C22⋊D61—41no—
198C22⋊D61—81no—
199C22⋊D61—81no—
200C22⋊D61—81no—
201C22⋊D61—81no—
202C2×Dic61—21no—
203C2×Dic61—21no—
204C2×Dic61—21no—
205C2×Dic61—21no—
206C2×Dic61—21no—
207C2×Dic61—41no—
208C2×Dic61—41no—
209C2×Dic61—41no—
210C2×Dic61—41no—
211C2×Dic61—41no—
212C2×Dic61—81no—
213C2×Dic61—81no—
214C2×Dic61—81no—
215D244—81no—
216D244—81no—
217D244—84no—
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#38611yescharacteristic
234C22×C61#41711yescharacteristic
235C22×C61#41811yescharacteristic
236C22×C61#46811yescharacteristic
237C22×C61#46811yescharacteristic
238C22×C61#46911yescharacteristic
239C22×C61#46911yescharacteristic
240C2×D61—42no—
241C2×D61—41no—
242C2×D61—41no—
243C2×D61—41no—
244C2×D61—81no—
245C2×D61—81no—
246C2×D61—81no—
247C2×D61—81no—
248C2×D61—81no—
249C2×D61—81no—
250C2×D61—81no—
251C2×D61—81no—
252C4×C61—21no—
253C4×C61—21no—
254C4×C61—21no—
255C4×C61—21no—
256C4×C61—42no—
257C4×C61—81no—
258C4×C61—161no—
259Dic61—41no—
260Dic61—41no—
261Dic61—41no—
262Dic61—81no—
263Dic61—161no—
264#2973—611no—
265#2543—611no—
266#1799—611no—
267#1519—611no—
268#1519—611no—
269#1294—611no—
270#1294D6111yescharacteristic, complemented
271C2×C61—21no—
272C2×C61—21no—
273C2×C61—21no—
274C2×C61—21no—
275C2×C61—21no—
276C2×C61—21no—
277C2×C61#188411yescharacteristic
278C2×C61#189511yescharacteristic
279C2×C61#191311yescharacteristic
280D61—81no—
281D61—161no—
282C2×#121—611no—
283C2×#121—1221no—
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×#95C2×D6111yescharacteristic
302#342—1221no—
303#327—1222no—
304#327—1222no—
305C61#938611yescharacteristic, complemented, Sylow
306C22×D4—611no—
307C22×D4—611no—
308C22×D4—1221no—
309C22×D4—1221no—
310C23×C4—21no—
311C23×C4—611no—
312C23×C4C22×D6111yescharacteristic
313C2×M16—1222no—
314C22×C8—21no—
315C22×C8—1221no—
316#121—1221no—
317#121—1221no—
318#121—1221no—
319#121—1221no—
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—611no—
329C2×C4⋊C4—1221no—
330C2×C4⋊C4—1221no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—611no—
333C2×C22⋊C4—611no—
334C2×C22⋊C4—1221no—
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⋊C8D24412yescomplemented
348#97—1222no—
349#95—21no—
350#95—21no—
351#95—1221no—
352#95—1221no—
353#95—1221no—
354#95C4×D6111yescharacteristic
355#95C4×D6111yescharacteristic
356C24—611no—
357C24—1221no—
358C24D4×D6111yescharacteristic
359C2×D4—1221no—
360C2×D4—1221no—
361C2×D4—1221no—
362C2×D4—1221no—
363C2×D4—1221no—
364C2×D4—1221no—
365C2×D4—1221no—
366C2×D4—1221no—
367C2×D4—4881no—
368C2×D4—4881no—
369C2×D4—2442no—
370C2×D4—2442no—
371C2×D4—2441no—
372C2×D4—2441no—
373C2×D4—2441no—
374C2×D4—2441no—
375C2×D4—2441no—
376C2×D4—2441no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—42no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4—41no—
383C22×C4—81no—
384C22×C4—81no—
385C22×C4—611no—
386C22×C4—611no—
387C22×C4—611no—
388C22×C4—1221no—
389C22×C4—1221no—
390C22×C4—1221no—
391C22×C4—4881no—
392C22×C4—2441no—
393C22×C4C2×C4×D6111yescharacteristic
394C22×C4C2×D24411yescharacteristic
395C22×C4#1175822211yescharacteristic
396C22×C4D4×D6111yescharacteristic
397C22×C4D4×D6111yescharacteristic
398C22×C4#1175822611yescharacteristic
399M16—4882no—
400C2×C8—22no—
401C2×C8—81no—
402C2×C8—1222no—
403C2×C8—4881no—
404C4⋊C4—81no—
405C4⋊C4—1221no—
406C4⋊C4—1221no—
407C4⋊C4—1221no—
408C4⋊C4—1221no—
409C4⋊C4—4881no—
410C4⋊C4—2442no—
411C22⋊C4—41no—
412C22⋊C4—41no—
413C22⋊C4—1221no—
414C22⋊C4—1221no—
415C22⋊C4—1221no—
416C22⋊C4—1221no—
417C22⋊C4—4881no—
418C22⋊C4—2442no—
419C22⋊C4—2442no—
420C22⋊C4—2442no—
421C22⋊C4—2441no—
422C22⋊C4—2441no—
423C22⋊C4—2441no—
424C22⋊C4—2441no—
425C42—1221no—
426C42—1221no—
427C23—41no—
428C23—41no—
429C23—1221no—
430C23—1221no—
431C23—1221no—
432C23—2441no—
433C23—2441no—
434C23—2441no—
435C23—2441no—
436C23—2441no—
437C23—2441no—
438C23—2441no—
439C23—2441no—
440C23—2441no—
441C23C22⋊C4×D6111yescharacteristic
442C23#1451975011yescharacteristic
443C23#1451975211yescharacteristic
444C23#1451980111yescharacteristic
445C23#1451980411yescharacteristic
446C23#1451980411yescharacteristic
447C23#1451980911yescharacteristic
448D4—4881no—
449D4—4881no—
450D4—4884no—
451D4—4881no—
452D4—4881no—
453D4—4881no—
454D4—4881no—
455D4—2441no—
456D4—2441no—
457D4—2441no—
458D4—2441no—
459C2×C4—22no—
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—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—82no—
472C2×C4—82no—
473C2×C4—81no—
474C2×C4—81no—
475C2×C4—81no—
476C2×C4—1221no—
477C2×C4—1221no—
478C2×C4—1221no—
479C2×C4—1221no—
480C2×C4—1221no—
481C2×C4—4881no—
482C2×C4—4881no—
483C2×C4—4881no—
484C2×C4—4881no—
485C2×C4—2442no—
486C2×C4—2441no—
487C2×C4—2441no—
488C2×C4—2441no—
489C2×C4—2441no—
490C2×C4—2441no—
491C2×C4#1451973911yescharacteristic
492C2×C4C4×D24411yescharacteristic
493C2×C4#1451974711yescharacteristic
494C2×C4#1451976211yescharacteristic
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—4881no—
508C22—4881no—
509C22—4881no—
510C22—4881no—
511C22—4881no—
512C22—4881no—
513C22—4881no—
514C22—4881no—
515C22—2442no—
516C22—2441no—
517C22—2441no—
518C22—2441no—
519C22#1683964011yescharacteristic
520C22#1683976211yescharacteristic
521C22#1683976511yescharacteristic
522C22#1684000911yescharacteristic
523C22#1684001111yescharacteristic
524C22#1684001411yescharacteristic
525C22#1684001611yescharacteristic
526C4—21no—
527C4—21no—
528C4—21no—
529C4—21no—
530C4—42no—
531C4—81no—
532C4—161no—
533C4—9761no—
534C4—4881no—
535C4—2441no—
536C4—2441no—
537C4—2441no—
538C2—21no—
539C2—21no—
540C2—21no—
541C2—21no—
542C2—21no—
543C2—21no—
544C2—9761no—
545C2—4881no—
546C2#2144620111yescharacteristic
547C2#2144625611yescharacteristic
548C2#2144636011yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1294C2
socleC22×C61#386
prime radical#21450779C2
cosocleC23×C4×C61C23
hypercenter#1294D61
hypocenterC61#9386
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1294

Complements

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

NH ≅ G/Ntype
1. #21454845C2semidirect
3. #21445804C2semidirect
4. #21444388C2semidirect
5. #21444386C2semidirect
6. #21443698C2semidirect
7. C61×#1294C2semidirect
17. #16839694C4semidirect
18. #16839689C4semidirect
19. #16839680C4semidirect
20. #16839672C4semidirect
64. C22⋊#92418D4semidirect
76. C22⋊C8×C61D4semidirect
270. #1294D61semidirect
305. C61#9386semidirect
347. C22⋊C8D244semidirect

Maximal subgroups

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

subgroupindex
#214548452
#214507792
#214458042
#214443882
#214443862
#214436982
C61×#12942
#938661