Finite Group Databasebeta

← #29583359

Subgroups — #29583359

Order 15616.

620 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21451935C211yesmaximal, characteristic
2#21446126C211yesmaximal, characteristic
3C2×#16839500C211yesmaximal, characteristic
4C2×#16839499C211yesmaximal, characteristic
5#21444082C211yesmaximal, characteristic
6#21443661C211yesmaximal, characteristic
7C61×#1872C211yesmaximal, characteristic
8C2×#14519756C2211yescharacteristic
9C22×#11758196—21no—
10C2×#14519700—21no—
11C2×C22⋊#92418C2211yescharacteristic
12#16839693—21no—
13#16839692—21no—
14#16839682—21no—
15#16839681—21no—
16#16839620—21no—
17#16839620—21no—
18C2×#14519684—21no—
19C2×#14519684C2211yescharacteristic
20C2×#14519684C2211yescharacteristic
21#16839524—21no—
22#16839500—22no—
23#16839499—22no—
24C2×C22⋊Q8×C61C2211yescharacteristic
25C22×C4⋊C4×C61C2211yescharacteristic
26C2×#103×C61—21no—
27C2×C22⋊C8×C61C2211yescharacteristic
28C61×#340—21no—
29C22×Dic122D411yescharacteristic
30C23×Dic61—21no—
31C23×Dic61D411yescharacteristic
32C23×Dic61D411yescharacteristic
33C22×#92418—21no—
34#14519756—21no—
35#14519756—21no—
36#14519756—21no—
37#14519756—21no—
38C2×C4⋊Dic61D411yescharacteristic
39C2×#11758196—21no—
40C2×#11758196—21no—
41C2×#11758196—21no—
42C2×#11758196—21no—
43C2×#11758196—21no—
44C2×#11758196—42no—
45C2×#11758196—42no—
46C2×#11758196—42no—
47C2×C22⋊Dic61—21no—
48#14519700—42no—
49C22⋊#92418—21no—
50C22⋊#92418—21no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54#14519684—21no—
55#14519684—21no—
56#14519684—21no—
57#14519684—21no—
58#14519684—42no—
59#14519684D412yes—
60C22×Q8×C61D411yescharacteristic
61C23×C4×C61—21no—
62C23×C4×C61C2311yescharacteristic
63C22×C8×C61—21no—
64C22⋊Q8×C61—21no—
65C22⋊Q8×C61—21no—
66C22⋊Q8×C61—21no—
67C22⋊Q8×C61—21no—
68C2×C4⋊C4×C61—21no—
69C2×C4⋊C4×C61—21no—
70C2×C4⋊C4×C61—21no—
71C2×C4⋊C4×C61—42no—
72C2×C4⋊C4×C61D411yescharacteristic
73C2×C22⋊C4×C61—21no—
74#103×C61—42no—
75C22⋊C8×C61—21no—
76C22⋊C8×C61—21no—
77C24×C61C2×D411yescharacteristic
78C2×Q8×C61—21no—
79C2×Q8×C61—21no—
80C2×Q8×C61—41no—
81C2×Q8×C61—41no—
82C22×C4×C61—22no—
83C22×C4×C61—21no—
84C22×C4×C61—21no—
85C22×C4×C61—41no—
86C22×C4×C61—41no—
87C22×C4×C61—41no—
88C22×C4×C61—41no—
89C22×C4×C61—41no—
90C22×C4×C61—41no—
91C22×C4×C61—41no—
92C22×C4×C61—41no—
93C22×C4×C61C2×D411yescharacteristic
94C22×C4×C61C2×D411yescharacteristic
95C22×C4×C61C2×D411yescharacteristic
96C22×C4×C61#4111yescharacteristic
97C22×C4×C61#4111yescharacteristic
98C22×C4×C61#4111yescharacteristic
99C22×Dic61—22no—
100C22×Dic61—22no—
101C22×Dic61—21no—
102C22×Dic61—21no—
103C22×Dic61—22no—
104C22×Dic61—21no—
105C22×Dic61—21no—
106C22×Dic61—21no—
107C22×Dic61—21no—
108C22×Dic61—41no—
109C22×Dic61—41no—
110C22×Dic61—41no—
111C22×Dic61—41no—
112C22×Dic61—41no—
113C22×Dic61—41no—
114C22×Dic61—41no—
115C22×Dic61—41no—
116C22×Dic61SD1612yes—
117C22×Dic61Q1612yes—
118C2×Dic122—21no—
119C2×Dic122—21no—
120C2×Dic122—41no—
121C2×Dic122—41no—
122C2×C8×C61—41no—
123C2×C8×C61—41no—
124C2×C8×C61—41no—
125C4⋊C4×C61—22no—
126C4⋊C4×C61—22no—
127C4⋊C4×C61—21no—
128C4⋊C4×C61—21no—
129C4⋊C4×C61—41no—
130C4⋊C4×C61—41no—
131C4⋊C4×C61—41no—
132C4⋊C4×C61—41no—
133C22⋊C4×C61—41no—
134C22⋊C4×C61—41no—
135C22⋊Dic61—41no—
136C22⋊Dic61—41no—
137C4⋊Dic61—21no—
138C4⋊Dic61—21no—
139#11758196—48no—
140#11758196—41no—
141#11758196—41no—
142#11758196—81no—
143#11758196—81no—
144#11758196—81no—
145#11758196—81no—
146C2×#92418—41no—
147C2×#92418—41no—
148C2×#92418—41no—
149C23×C61—21no—
150C23×C61—21no—
151C23×C61—21no—
152C23×C61—21no—
153C23×C61#12011yescharacteristic
154C23×C61#12111yescharacteristic
155C23×C61#12411yescharacteristic
156C23×C61C2×SD1611yescharacteristic
157C23×C61C2×Q1611yescharacteristic
158C23×C61#13711yescharacteristic
159C23×C61#13711yescharacteristic
160Q8×C61—42no—
161Q8×C61—81no—
162C2×C4×C61—21no—
163C2×C4×C61—21no—
164C2×C4×C61—21no—
165C2×C4×C61—21no—
166C2×C4×C61—41no—
167C2×C4×C61—41no—
168C2×C4×C61—41no—
169C2×C4×C61—41no—
170C2×C4×C61—42no—
171C2×C4×C61—42no—
172C2×C4×C61—41no—
173C2×C4×C61—41no—
174C2×C4×C61—41no—
175C2×C4×C61—41no—
176C2×C4×C61—41no—
177C2×C4×C61—42no—
178C2×C4×C61—41no—
179C2×C4×C61—81no—
180C2×C4×C61—81no—
181C2×C4×C61—81no—
182C2×C4×C61—81no—
183C2×C4×C61#12111yescharacteristic
184C2×C4×C61#12111yescharacteristic
185C2×C4×C61#12311yescharacteristic
186C2×C4×C61#12311yescharacteristic
187C2×Dic61—24no—
188C2×Dic61—22no—
189C2×Dic61—22no—
190C2×Dic61—42no—
191C2×Dic61—42no—
192C2×Dic61—42no—
193C2×Dic61—42no—
194C2×Dic61—42no—
195C2×Dic61—41no—
196C2×Dic61—41no—
197C2×Dic61—41no—
198C2×Dic61—41no—
199C2×Dic61—42no—
200C2×Dic61—42no—
201C2×Dic61—42no—
202C2×Dic61—41no—
203C2×Dic61—41no—
204C2×Dic61—41no—
205C2×Dic61—41no—
206C2×Dic61—41no—
207C2×Dic61—41no—
208C2×Dic61—81no—
209C2×Dic61—81no—
210Dic122—42no—
211Dic122—81no—
212C8×C61—81no—
213#92418—81no—
214#10406—611nomaximal, Sylow
215C22×C61—21no—
216C22×C61—21no—
217C22×C61—21no—
218C22×C61—21no—
219C22×C61—21no—
220C22×C61—21no—
221C22×C61—21no—
222C22×C61—21no—
223C22×C61—21no—
224C22×C61—21no—
225C22×C61—21no—
226C22×C61—21no—
227C22×C61#39411yescharacteristic
228C22×C61#44811yescharacteristic
229C22×C61#45111yescharacteristic
230C22×C61#45311yescharacteristic
231C22×C61#45611yescharacteristic
232C22×C61B(4,𝔽2)11yescharacteristic
233C22×C61#45811yescharacteristic
234C22×C61#46111yescharacteristic
235C22×C61#46211yescharacteristic
236C22×C61#48711yescharacteristic
237C22×C61#49111yescharacteristic
238C4×C61—21no—
239C4×C61—21no—
240C4×C61—21no—
241C4×C61—21no—
242C4×C61—82no—
243C4×C61—81no—
244C4×C61—81no—
245Dic61—44no—
246Dic61—42no—
247Dic61—42no—
248Dic61—81no—
249Dic61—81no—
250#2659—611no—
251#1872—611no—
252#1872D6111yescharacteristic
253C2×#328—611no—
254C2×#328—611no—
255#1444—611no—
256#1280—611no—
257C2×C61—21no—
258C2×C61—21no—
259C2×C61—21no—
260C2×C61—21no—
261C2×C61#159611yescharacteristic
262C2×C61#160511yescharacteristic
263C2×C61#161111yescharacteristic
264C2×C61#161411yescharacteristic
265C2×C61#203911yescharacteristic
266C2×C61#204311yescharacteristic
267C2×C61#204411yescharacteristic
268C2×C22⋊Q8—611no—
269C2×C22⋊Q8C2×D6111yescharacteristic
270C22×C4⋊C4—1221no—
271C22×C4⋊C4C2×D6111yescharacteristic
272C2×#103—21no—
273C2×#103—1221no—
274C2×C22⋊C8—611no—
275C2×C22⋊C8C2×D6111yescharacteristic
276#398—1221no—
277#398—1221no—
278#395—1221no—
279#395—1221no—
280#380—1221no—
281#380—1221no—
282C2×#95—611no—
283C2×#95—611no—
284C2×#95—1221no—
285#340—21no—
286#340—1221no—
287#328—1222no—
288#328—1222no—
289C61#1040611yescharacteristic, complemented, Sylow
290C22×Q8—611no—
291C22×Q8C22⋊D6111yescharacteristic
292C23×C4—21no—
293C23×C4—611no—
294C23×C4—611no—
295C23×C4—1221no—
296C23×C4C22×D6111yescharacteristic
297C22×C8—21no—
298C22×C8—1221no—
299C22⋊Q8—21no—
300C22⋊Q8—21no—
301C22⋊Q8—21no—
302C22⋊Q8—21no—
303C22⋊Q8—1221no—
304C22⋊Q8—1221no—
305C22⋊Q8—1221no—
306C22⋊Q8—1221no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—42no—
311C2×C4⋊C4—611no—
312C2×C4⋊C4—1221no—
313C2×C4⋊C4—1221no—
314C2×C4⋊C4—1221no—
315C2×C4⋊C4—1221no—
316C2×C4⋊C4—1221no—
317C2×C4⋊C4—2442no—
318C2×C4⋊C4—2442no—
319C2×C4⋊C4—2442no—
320C2×C4⋊C4C22⋊D6111yescharacteristic
321C2×C22⋊C4—21no—
322C2×C22⋊C4—1221no—
323#103—42no—
324#103—2442no—
325C22⋊C8—21no—
326C22⋊C8—21no—
327C22⋊C8—1221no—
328C22⋊C8—1221no—
329#95—612no—
330#95—1221no—
331#95—1221no—
332#95—1221no—
333#95—1221no—
334#95—1221no—
335#95—1221no—
336#95—1221no—
337#95—2442no—
338C24D4×D6111yescharacteristic
339C2×Q8—21no—
340C2×Q8—21no—
341C2×Q8—41no—
342C2×Q8—41no—
343C2×Q8—1221no—
344C2×Q8—1221no—
345C2×Q8—2441no—
346C2×Q8—2441no—
347C22×C4—22no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—41no—
351C22×C4—41no—
352C22×C4—41no—
353C22×C4—41no—
354C22×C4—41no—
355C22×C4—41no—
356C22×C4—41no—
357C22×C4—41no—
358C22×C4—612no—
359C22×C4—612no—
360C22×C4—1221no—
361C22×C4—1221no—
362C22×C4—1222no—
363C22×C4—1222no—
364C22×C4—1221no—
365C22×C4—1221no—
366C22×C4—1222no—
367C22×C4—1221no—
368C22×C4—1221no—
369C22×C4—2441no—
370C22×C4—2441no—
371C22×C4—2441no—
372C22×C4—2441no—
373C22×C4—2441no—
374C22×C4—2441no—
375C22×C4—2441no—
376C22×C4—2441no—
377C22×C4#1175822211yescharacteristic
378C22×C4#1175822211yescharacteristic
379C22×C4D4×D6111yescharacteristic
380C22×C4D4×D6111yescharacteristic
381C22×C4#1175822411yescharacteristic
382C22×C4C2×C22⋊D6111yescharacteristic
383C2×C8—41no—
384C2×C8—41no—
385C2×C8—41no—
386C2×C8—2441no—
387C2×C8—2441no—
388C2×C8—2441no—
389C4⋊C4—22no—
390C4⋊C4—22no—
391C4⋊C4—21no—
392C4⋊C4—21no—
393C4⋊C4—41no—
394C4⋊C4—41no—
395C4⋊C4—41no—
396C4⋊C4—41no—
397C4⋊C4—1221no—
398C4⋊C4—1221no—
399C4⋊C4—4881no—
400C4⋊C4—4881no—
401C4⋊C4—4881no—
402C4⋊C4—4881no—
403C4⋊C4—2448no—
404C4⋊C4—2441no—
405C4⋊C4—2441no—
406C22⋊C4—41no—
407C22⋊C4—41no—
408C22⋊C4—2441no—
409C22⋊C4—2441no—
410C23—21no—
411C23—21no—
412C23—21no—
413C23—21no—
414C23#1451974511yescharacteristic
415C23#1451975011yescharacteristic
416C23#1451976311yescharacteristic
417C23SD16×D6111yescharacteristic
418C23Q16×D6111yescharacteristic
419C23#1451980611yescharacteristic
420C23#1451980911yescharacteristic
421Q8—42no—
422Q8—81no—
423Q8—4881no—
424Q8—2442no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—41no—
436C2×C4—42no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—81no—
443C2×C4—81no—
444C2×C4—81no—
445C2×C4—81no—
446C2×C4—1224no—
447C2×C4—1222no—
448C2×C4—1222no—
449C2×C4—4881no—
450C2×C4—4881no—
451C2×C4—2441no—
452C2×C4—2441no—
453C2×C4—2441no—
454C2×C4—2441no—
455C2×C4—2441no—
456C2×C4—2441no—
457C2×C4—2442no—
458C2×C4—2442no—
459C2×C4—2442no—
460C2×C4—2442no—
461C2×C4—2442no—
462C2×C4—2441no—
463C2×C4—2441no—
464C2×C4—2442no—
465C2×C4—2441no—
466C2×C4—2441no—
467C2×C4—2442no—
468C2×C4—2442no—
469C2×C4#1451974911yescharacteristic
470C2×C4#1451975011yescharacteristic
471C2×C4#1451975911yescharacteristic
472C2×C4#1451976011yescharacteristic
473C8—81no—
474C8—4881no—
475C22—21no—
476C22—21no—
477C22—21no—
478C22—21no—
479C22—21no—
480C22—21no—
481C22—21no—
482C22—21no—
483C22—21no—
484C22—21no—
485C22—21no—
486C22—21no—
487C22#1683967711yescharacteristic
488C22#1683989911yescharacteristic
489C22#1683991611yescharacteristic
490C22#1683992811yescharacteristic
491C22#1683994311yescharacteristic
492C22#1683994811yescharacteristic
493C22#1683995111yescharacteristic
494C22#1683996611yescharacteristic
495C22#1683997111yescharacteristic
496C22#1684011111yescharacteristic
497C22#1684012911yescharacteristic
498C4—21no—
499C4—21no—
500C4—21no—
501C4—21no—
502C4—81no—
503C4—82no—
504C4—81no—
505C4—4881no—
506C4—4881no—
507C4—2444no—
508C4—2442no—
509C4—2442no—
510C2—21no—
511C2—21no—
512C2—21no—
513C2—21no—
514C2#2144474011yescharacteristic
515C2#2144479111yescharacteristic
516C2#2144482511yescharacteristic
517C2#2144484211yescharacteristic
518C2#2144704111yescharacteristic
519C2#2144706311yescharacteristic
520C2#2144706811yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC61×#1872C2
socleC23×C61#120
prime radicalC24×C61C2×D4
hypercenter#1872D61
hypocenterC61#10406
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1872

Complements

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

NH ≅ G/Ntype
289. C61#10406semidirect

Maximal subgroups

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

subgroupindex
#214519352
#214461262
C2×#168395002
C2×#168394992
#214440822
#214436612
C61×#18722
#1040661