Finite Group Databasebeta

← #29575161

Subgroups — #29575161

Order 15616.

678 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840075C211yesmaximal, characteristic
2#21448519C211yesmaximal, characteristic
3C2×#16839497C211yesmaximal, characteristic
4#21444087C211yesmaximal, characteristic, complemented
5#21443697C211yesmaximal, characteristic, complemented
6#21443661C211yesmaximal, characteristic, complemented
7C61×#1823C211yesmaximal, characteristic, complemented
8C2×#14519751C2211yescharacteristic
9C2×#14519737—21no—
10#16840075—22no—
11#16840075C414yescomplemented
12C2×#14519710—21no—
13C2×#14519697—21no—
14C2×C22⋊#92418C2211yescharacteristic
15#16839652—21no—
16#16839645—21no—
17#16839640—21no—
18#16839639—21no—
19#16839633—21no—
20C2×#14519684—21no—
21C2×#14519684—21no—
22C2×#14519684C2211yescharacteristic
23C2×#14519684C2211yescharacteristic
24#16839497—22no—
25C22×C4⋊C4×C61C2211yescharacteristic
26C2×C22⋊C8×C61C2211yescharacteristic
27C61×#380C2211yescharacteristic
28C61×#340—21no—
29C61×#340—21no—
30C22×D244D411yescharacteristic
31C22×C22⋊D61—21no—
32C23×Dic61—21no—
33C23×Dic61D411yescharacteristic
34C23×Dic61D411yescharacteristic
35C22×C4×D61—21no—
36C22×#92418—21no—
37#14519751—21no—
38#14519751—21no—
39#14519751C2×C412yes—
40#14519751D412yes—
41#14519737—42no—
42#14519737—42no—
43C2×C4⋊Dic61D411yescharacteristic
44C2×#11758196—21no—
45C2×#11758198—21no—
46C2×#11758198—21no—
47C2×#11758198—21no—
48C2×#11758198—21no—
49C2×C4×Dic61—21no—
50#14519710—24no—
51#14519697—24no—
52C22⋊#92418—21no—
53C22⋊#92418C2×C412yescomplemented
54#14519684—21no—
55#14519684—21no—
56#14519684—21no—
57#14519684—21no—
58#14519684—21no—
59#14519684—21no—
60#14519684—42no—
61#14519684—42no—
62C23×C4×C61—21no—
63C23×C4×C61C2311yescharacteristic
64C22×C8×C61—21no—
65C2×C4⋊C4×C61—21no—
66C2×C4⋊C4×C61—21no—
67C2×C4⋊C4×C61—21no—
68C2×C4⋊C4×C61—21no—
69C2×C4⋊C4×C61—21no—
70C2×C4⋊C4×C61C2×C412yescomplemented
71C2×C4⋊C4×C61D411yescharacteristic
72C2×C4⋊C4×C61D411yescharacteristic
73C2×C22⋊C4×C61—21no—
74C22⋊C8×C61—21no—
75C22⋊C8×C61—21no—
76#95×C61—21no—
77C24×C61C2×D411yescharacteristic
78C23×D61—21no—
79C22×C4×C61—22no—
80C22×C4×C61—21no—
81C22×C4×C61—21no—
82C22×C4×C61—41no—
83C22×C4×C61—41no—
84C22×C4×C61—41no—
85C22×C4×C61—41no—
86C22×C4×C61—41no—
87C22×C4×C61—41no—
88C22×C4×C61—41no—
89C22×C4×C61—41no—
90C22×C4×C61C22×C411yescharacteristic
91C22×C4×C61C2×D411yescharacteristic
92C22×C4×C61C2×D411yescharacteristic
93C22×C4×C61C2×D411yescharacteristic
94C22×C4×C61#4111yescharacteristic
95C22×C4×C61#4111yescharacteristic
96C2×C22⋊D61—22no—
97C2×C22⋊D61—22no—
98C2×C22⋊D61—41no—
99C2×C22⋊D61—41no—
100C2×C22⋊D61—41no—
101C2×C22⋊D61—41no—
102C22×Dic61—21no—
103C22×Dic61—21no—
104C22×Dic61—21no—
105C22×Dic61—22no—
106C22×Dic61—21no—
107C22×Dic61—21no—
108C22×Dic61—21no—
109C22×Dic61—41no—
110C22×Dic61—41no—
111C22×Dic61—41no—
112C22×Dic61—41no—
113C22×Dic61—41no—
114C22×Dic61—41no—
115C22×Dic61—41no—
116C22×Dic61—41no—
117C22×Dic61—41no—
118C22×Dic61—41no—
119C22×Dic61D812yes—
120C2×D244—21no—
121C2×D244—41no—
122C2×D244—41no—
123C2×D244C22⋊C412yes—
124C2×C4×D61—42no—
125C2×C4×D61—81no—
126C2×C4×D61—81no—
127C2×C8×C61—41no—
128C2×C8×C61—41no—
129C2×C8×C61—41no—
130C4⋊C4×C61—22no—
131C4⋊C4×C61—22no—
132C4⋊C4×C61—41no—
133C4⋊C4×C61—41no—
134C4⋊C4×C61—41no—
135C4⋊C4×C61—41no—
136C22⋊C4×C61—41no—
137C22⋊C4×C61—41no—
138#11758198—22no—
139#11758198—22no—
140#11758198—42no—
141#11758198—81no—
142#11758198—81no—
143C4⋊Dic61—21no—
144C4⋊Dic61C22⋊C412yes—
145#11758196—42no—
146C4×Dic61—42no—
147C2×#92418—22no—
148C2×#92418—41no—
149C2×#92418—41no—
150C23×C61—21no—
151C23×C61—21no—
152C23×C61—21no—
153C23×C61—21no—
154C23×C61C4×D411yescharacteristic
155C23×C61#12011yescharacteristic
156C23×C61#12111yescharacteristic
157C23×C61C2×D811yescharacteristic
158C23×C61#13511yescharacteristic
159C23×C61AGL(1,ℤ/8)11yescharacteristic
160C23×C61AGL(1,ℤ/8)11yescharacteristic
161C22×D61—22no—
162C22×D61—41no—
163C22×D61—41no—
164C22×D61—41no—
165C22×D61—41no—
166C22×D61—41no—
167C22×D61—41no—
168C2×C4×C61—21no—
169C2×C4×C61—21no—
170C2×C4×C61—21no—
171C2×C4×C61—21no—
172C2×C4×C61—41no—
173C2×C4×C61—41no—
174C2×C4×C61—41no—
175C2×C4×C61—41no—
176C2×C4×C61—42no—
177C2×C4×C61—42no—
178C2×C4×C61—42no—
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—81no—
186C2×C4×C61—81no—
187C2×C4×C61—81no—
188C2×C4×C61—81no—
189C2×C4×C61C2×C22⋊C411yescharacteristic
190C2×C4×C61C4×D411yescharacteristic
191C2×C4×C61#12111yescharacteristic
192C2×C4×C61#12311yescharacteristic
193C22⋊D61—42no—
194C22⋊D61—42no—
195C22⋊D61—42no—
196C22⋊D61—42no—
197C2×Dic61—22no—
198C2×Dic61—22no—
199C2×Dic61—41no—
200C2×Dic61—41no—
201C2×Dic61—41no—
202C2×Dic61—41no—
203C2×Dic61—42no—
204C2×Dic61—42no—
205C2×Dic61—42no—
206C2×Dic61—42no—
207C2×Dic61—42no—
208C2×Dic61—41no—
209C2×Dic61—41no—
210C2×Dic61—41no—
211C2×Dic61—81no—
212C2×Dic61—81no—
213C2×Dic61—81no—
214C2×Dic61—81no—
215C2×Dic61—81no—
216C2×Dic61—81no—
217D244—42no—
218D244—81no—
219C4×D61—84no—
220C8×C61—81no—
221#92418—42no—
222#9043—611nomaximal, Sylow
223C22×C61—21no—
224C22×C61—21no—
225C22×C61—21no—
226C22×C61—21no—
227C22×C61—21no—
228C22×C61—21no—
229C22×C61—21no—
230C22×C61—21no—
231C22×C61—21no—
232C22×C61—21no—
233C22×C61—21no—
234C22×C61—21no—
235C22×C61#38611yescharacteristic
236C22×C61C4×D811yescharacteristic
237C22×C61#44211yescharacteristic
238C22×C61#44711yescharacteristic
239C22×C61#44911yescharacteristic
240C22×C61#45511yescharacteristic
241C22×C61#45611yescharacteristic
242C22×C61#45811yescharacteristic
243C22×C61#45811yescharacteristic
244C22×C61#45911yescharacteristic
245C22×C61#46311yescharacteristic
246C2×D61—42no—
247C2×D61—42no—
248C2×D61—42no—
249C2×D61—81no—
250C2×D61—81no—
251C2×D61—81no—
252C2×D61—81no—
253C4×C61—21no—
254C4×C61—21no—
255C4×C61—21no—
256C4×C61—21no—
257C4×C61—81no—
258C4×C61—81no—
259C4×C61—82no—
260Dic61—42no—
261Dic61—42no—
262Dic61—82no—
263Dic61—81no—
264C2×#480—611no—
265#2325—611no—
266#1823D6111yescharacteristic, complemented
267C2×#327—611no—
268#1445—611no—
269#1294—611no—
270#1280—611no—
271C2×C61—21no—
272C2×C61—21no—
273C2×C61—21no—
274C2×C61—21no—
275C2×C61#160711yescharacteristic
276C2×C61#160911yescharacteristic
277C2×C61#161011yescharacteristic
278C2×C61#161211yescharacteristic
279C2×C61#187911yescharacteristic
280C2×C61#188211yescharacteristic
281C2×C61#189011yescharacteristic
282D61—82no—
283C2×#121—611no—
284C2×C4×D4—1221no—
285C22×C4⋊C4C2×D6111yescharacteristic
286#480—614no—
287#480—1222no—
288C2×#107—1221no—
289C2×#102—1221no—
290C2×C22⋊C8—611no—
291C2×C22⋊C8C2×D6111yescharacteristic
292#388—1221no—
293#387—1221no—
294#386—1221no—
295#386—1221no—
296#385—1221no—
297#380C2×D6111yescharacteristic
298C2×#95—611no—
299C2×#95—611no—
300C2×#95—1221no—
301C2×#95—1221no—
302#340—21no—
303#340—21no—
304#327—1222no—
305C61#904311yescharacteristic, complemented, Sylow
306C22×D4—611no—
307C22×D4—1221no—
308C23×C4—21no—
309C23×C4—611no—
310C23×C4—611no—
311C23×C4—1221no—
312C23×C4—1221no—
313C23×C4C22×D6111yescharacteristic
314C22×C8—21no—
315C22×C8—1221no—
316#121—612no—
317#121—612no—
318#121—1221no—
319#121—1221no—
320C4×D4—2442no—
321C4×D4—2442no—
322C2×C4⋊C4—21no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—611no—
328C2×C4⋊C4—1221no—
329C2×C4⋊C4C4×D6112yescomplemented
330C2×C4⋊C4C22⋊D6111yescharacteristic
331C2×C4⋊C4C22⋊D6111yescharacteristic
332C2×C22⋊C4—21no—
333C2×C22⋊C4—1221no—
334C2×C22⋊C4—1221no—
335C2×C22⋊C4—1221no—
336C2×C22⋊C4—1221no—
337C2×C42—1221no—
338#107—1224no—
339#102—1224no—
340C22⋊C8—21no—
341C22⋊C8—21no—
342C22⋊C8—612no—
343C22⋊C8—1221no—
344#95—21no—
345#95—1221no—
346#95—1221no—
347#95—1221no—
348#95—1221no—
349#95—1221no—
350#95—1221no—
351#95—2442no—
352#95—2442no—
353C24—1221no—
354C24D4×D6111yescharacteristic
355C2×D4—612no—
356C2×D4—1222no—
357C2×D4—1222no—
358C2×D4—1221no—
359C2×D4—2441no—
360C2×D4—2441no—
361C2×D4—2441no—
362C2×D4—2441no—
363C2×D4—2441no—
364C2×D4—2441no—
365C22×C4—22no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—41no—
369C22×C4—41no—
370C22×C4—41no—
371C22×C4—41no—
372C22×C4—41no—
373C22×C4—41no—
374C22×C4—41no—
375C22×C4—41no—
376C22×C4—612no—
377C22×C4—1221no—
378C22×C4—1221no—
379C22×C4—1221no—
380C22×C4—1221no—
381C22×C4—1222no—
382C22×C4—1221no—
383C22×C4—1221no—
384C22×C4—4881no—
385C22×C4—4881no—
386C22×C4—2442no—
387C22×C4—2441no—
388C22×C4—2441no—
389C22×C4—2441no—
390C22×C4—2441no—
391C22×C4—2441no—
392C22×C4—2441no—
393C22×C4—2441no—
394C22×C4—2441no—
395C22×C4—2441no—
396C22×C4—2441no—
397C22×C4C2×C4×D6111yescharacteristic
398C22×C4#1175822211yescharacteristic
399C22×C4D4×D6111yescharacteristic
400C22×C4D4×D6111yescharacteristic
401C22×C4#1175822411yescharacteristic
402C22×C4C2×C22⋊D6111yescharacteristic
403C2×C8—41no—
404C2×C8—41no—
405C2×C8—41no—
406C2×C8—1222no—
407C2×C8—2441no—
408C2×C8—2441no—
409C4⋊C4—22no—
410C4⋊C4—22no—
411C4⋊C4—41no—
412C4⋊C4—41no—
413C4⋊C4—41no—
414C4⋊C4—41no—
415C4⋊C4—612no—
416C4⋊C4—1221no—
417C4⋊C4—2442no—
418C22⋊C4—41no—
419C22⋊C4—41no—
420C22⋊C4—1222no—
421C22⋊C4—1222no—
422C22⋊C4—4881no—
423C22⋊C4—4881no—
424C22⋊C4—2442no—
425C42—2442no—
426C23—21no—
427C23—21no—
428C23—21no—
429C23—21no—
430C23—1222no—
431C23—2441no—
432C23—2441no—
433C23—2441no—
434C23—2441no—
435C23—2441no—
436C23—2441no—
437C23#1451973711yescharacteristic
438C23#1451974511yescharacteristic
439C23#1451975011yescharacteristic
440C23D8×D6111yescharacteristic
441C23#1451979811yescharacteristic
442C23#1451980111yescharacteristic
443C23#1451980411yescharacteristic
444D4—4881no—
445D4—2442no—
446D4—2442no—
447D4—2442no—
448D4—2442no—
449D4—2442no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—81no—
468C2×C4—81no—
469C2×C4—81no—
470C2×C4—81no—
471C2×C4—1222no—
472C2×C4—1222no—
473C2×C4—4884no—
474C2×C4—4881no—
475C2×C4—4881no—
476C2×C4—4881no—
477C2×C4—4881no—
478C2×C4—4881no—
479C2×C4—4881no—
480C2×C4—2442no—
481C2×C4—2442no—
482C2×C4—2442no—
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—2442no—
492C2×C4C22⋊C4×D6111yescharacteristic
493C2×C4C4×C22⋊D6111yescharacteristic
494C2×C4#1451974811yescharacteristic
495C2×C4#1451975911yescharacteristic
496C8—81no—
497C8—2442no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—21no—
503C22—21no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—4881no—
511C22—4881no—
512C22—4881no—
513C22—4881no—
514C22—2442no—
515C22—2442no—
516C22—2442no—
517C22#1683963811yescharacteristic
518C22#1683984211yescharacteristic
519C22#1683987111yescharacteristic
520C22#1683989411yescharacteristic
521C22#1683990611yescharacteristic
522C22#1683993811yescharacteristic
523C22#1683994311yescharacteristic
524C22#1683995111yescharacteristic
525C22#1683995111yescharacteristic
526C22#1683995611yescharacteristic
527C22#1683997611yescharacteristic
528C4—21no—
529C4—21no—
530C4—21no—
531C4—21no—
532C4—82no—
533C4—81no—
534C4—81no—
535C4—4882no—
536C4—4881no—
537C4—2442no—
538C4—2442no—
539C2—21no—
540C2—21no—
541C2—21no—
542C2—21no—
543C2—4882no—
544C2#2144480311yescharacteristic
545C2#2144481511yescharacteristic
546C2#2144482011yescharacteristic
547C2#2144483211yescharacteristic
548C2#2144616411yescharacteristic
549C2#2144618511yescharacteristic
550C2#2144622911yescharacteristic
subgroupG/H
centerC23#14519745
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1823C2
socleC23×C61#120
prime radicalC2×#14519751C22
cosocleC23×C4×C61C23
hypercenter#1823D61
hypocenterC61#9043
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1823

Complements

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

NH ≅ G/Ntype
4. #21444087C2semidirect
5. #21443697C2semidirect
6. #21443661C2semidirect
7. C61×#1823C2semidirect
11. #16840075C4semidirect
53. C22⋊#92418C2×C4semidirect
70. C2×C4⋊C4×C61C2×C4semidirect
266. #1823D61semidirect
305. C61#9043semidirect
329. C2×C4⋊C4C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168400752
#214485192
C2×#168394972
#214440872
#214436972
#214436612
C61×#18232
#904361