Finite Group Databasebeta

← #29583352

Subgroups — #29583352

Order 15616.

646 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21451753C211yesmaximal, characteristic
2#21446136C211yesmaximal, characteristic
3C2×#16839499C211yesmaximal, characteristic, complemented
4C2×#16839497C211yesmaximal, characteristic
5#21444082C211yesmaximal, characteristic, complemented
6#21443661C211yesmaximal, characteristic, complemented
7C61×#1872C211yesmaximal, characteristic, complemented
8C2×#14519751C2211yescharacteristic
9C22×#11758196—21no—
10C2×#14519697—21no—
11C2×C22⋊#92418C2211yescharacteristic
12#16839701—21no—
13#16839688—21no—
14#16839679—21no—
15#16839673—21no—
16#16839639—21no—
17#16839639—21no—
18C2×#14519684—21no—
19C2×#14519684C2211yescharacteristic
20C2×#14519684C2211yescharacteristic
21#16839524—21no—
22#16839499—22no—
23#16839497—22no—
24C2×C22⋊Q8×C61C2211yescharacteristic
25C22×C4⋊C4×C61C2211yescharacteristic
26C2×#103×C61—21no—
27C2×C22⋊C8×C61C2211yescharacteristic
28C61×#340—21no—
29C22×D244D411yescharacteristic
30C22×C22⋊D61—21no—
31C23×Dic61—21no—
32C23×Dic61D411yescharacteristic
33C23×Dic61D411yescharacteristic
34C22×#92418—21no—
35#14519751—21no—
36#14519751—21no—
37#14519751—21no—
38#14519751—21no—
39C2×C4⋊Dic61D411yescharacteristic
40C2×#11758196—42no—
41C2×#11758196—42no—
42C2×#11758196—42no—
43C2×#11758198—21no—
44C2×#11758198—21no—
45C2×#11758198—21no—
46C2×#11758198—21no—
47C2×#11758198—21no—
48#14519697—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
78C23×D61—21no—
79C2×Q8×C61—21no—
80C2×Q8×C61—21no—
81C2×Q8×C61—41no—
82C2×Q8×C61—41no—
83C22×C4×C61—22no—
84C22×C4×C61—21no—
85C22×C4×C61—21no—
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×C61—41no—
94C22×C4×C61C2×D411yescharacteristic
95C22×C4×C61C2×D411yescharacteristic
96C22×C4×C61C2×D411yescharacteristic
97C22×C4×C61#4111yescharacteristic
98C22×C4×C61#4111yescharacteristic
99C22×C4×C61#4111yescharacteristic
100C2×C22⋊D61—41no—
101C2×C22⋊D61—41no—
102C2×C22⋊D61—41no—
103C2×C22⋊D61—41no—
104C2×C22⋊D61—41no—
105C2×C22⋊D61—41no—
106C22×Dic61—22no—
107C22×Dic61—22no—
108C22×Dic61—22no—
109C22×Dic61—21no—
110C22×Dic61—21no—
111C22×Dic61—21no—
112C22×Dic61—21no—
113C22×Dic61—21no—
114C22×Dic61—21no—
115C22×Dic61—21no—
116C22×Dic61—41no—
117C22×Dic61—41no—
118C22×Dic61—41no—
119C22×Dic61—41no—
120C22×Dic61—41no—
121C22×Dic61—41no—
122C22×Dic61—41no—
123C22×Dic61—41no—
124C2×D244—21no—
125C2×D244—21no—
126C2×D244—41no—
127C2×D244—41no—
128C2×C8×C61—41no—
129C2×C8×C61—41no—
130C2×C8×C61—41no—
131C4⋊C4×C61—22no—
132C4⋊C4×C61—22no—
133C4⋊C4×C61—21no—
134C4⋊C4×C61—21no—
135C4⋊C4×C61—41no—
136C4⋊C4×C61—41no—
137C4⋊C4×C61—41no—
138C4⋊C4×C61—41no—
139C22⋊C4×C61—41no—
140C22⋊C4×C61—41no—
141#11758198—41no—
142#11758198—41no—
143#11758198—81no—
144#11758198—81no—
145#11758198—81no—
146#11758198—81no—
147C4⋊Dic61—21no—
148C4⋊Dic61—21no—
149#11758196—48no—
150C2×#92418—41no—
151C2×#92418—41no—
152C2×#92418—41no—
153C23×C61—21no—
154C23×C61—21no—
155C23×C61—21no—
156C23×C61—21no—
157C23×C61#12011yescharacteristic
158C23×C61#12111yescharacteristic
159C23×C61#12411yescharacteristic
160C23×C61#13511yescharacteristic
161C23×C61#13511yescharacteristic
162C23×C61AGL(1,ℤ/8)11yescharacteristic
163C23×C61#13711yescharacteristic
164C22×D61—41no—
165C22×D61—41no—
166C22×D61—41no—
167C22×D61—41no—
168C22×D61—41no—
169C22×D61—41no—
170C22×D61—41no—
171Q8×C61—42no—
172Q8×C61—81no—
173C2×C4×C61—21no—
174C2×C4×C61—21no—
175C2×C4×C61—21no—
176C2×C4×C61—21no—
177C2×C4×C61—41no—
178C2×C4×C61—41no—
179C2×C4×C61—41no—
180C2×C4×C61—41no—
181C2×C4×C61—42no—
182C2×C4×C61—42no—
183C2×C4×C61—41no—
184C2×C4×C61—41no—
185C2×C4×C61—41no—
186C2×C4×C61—41no—
187C2×C4×C61—41no—
188C2×C4×C61—42no—
189C2×C4×C61—41no—
190C2×C4×C61—81no—
191C2×C4×C61—81no—
192C2×C4×C61—81no—
193C2×C4×C61—81no—
194C2×C4×C61#12111yescharacteristic
195C2×C4×C61#12111yescharacteristic
196C2×C4×C61#12311yescharacteristic
197C2×C4×C61#12311yescharacteristic
198C22⋊D61—81no—
199C22⋊D61—81no—
200C22⋊D61—81no—
201C22⋊D61—81no—
202C2×Dic61—24no—
203C2×Dic61—42no—
204C2×Dic61—42no—
205C2×Dic61—42no—
206C2×Dic61—42no—
207C2×Dic61—42no—
208C2×Dic61—42no—
209C2×Dic61—42no—
210C2×Dic61—42no—
211C2×Dic61—41no—
212C2×Dic61—41no—
213C2×Dic61—41no—
214C2×Dic61—41no—
215C2×Dic61—41no—
216C2×Dic61—41no—
217C2×Dic61—41no—
218C2×Dic61—41no—
219C2×Dic61—41no—
220C2×Dic61—81no—
221C2×Dic61—81no—
222D244—42no—
223D244—81no—
224C8×C61—81no—
225#92418—81no—
226#10405—611nomaximal, Sylow
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—21no—
236C22×C61—21no—
237C22×C61—21no—
238C22×C61—21no—
239C22×C61#39411yescharacteristic
240C22×C61#44911yescharacteristic
241C22×C61#45211yescharacteristic
242C22×C61#45311yescharacteristic
243C22×C61#45611yescharacteristic
244C22×C61B(4,𝔽2)11yescharacteristic
245C22×C61#45811yescharacteristic
246C22×C61#46311yescharacteristic
247C22×C61#46411yescharacteristic
248C22×C61#48811yescharacteristic
249C22×C61#48911yescharacteristic
250C2×D61—81no—
251C2×D61—81no—
252C2×D61—81no—
253C2×D61—81no—
254C2×D61—81no—
255C2×D61—81no—
256C2×D61—81no—
257C4×C61—21no—
258C4×C61—21no—
259C4×C61—21no—
260C4×C61—21no—
261C4×C61—82no—
262C4×C61—81no—
263C4×C61—81no—
264Dic61—44no—
265Dic61—81no—
266Dic61—81no—
267Dic61—81no—
268#2639—611no—
269#1874—611no—
270#1872D6111yescharacteristic, complemented
271C2×#328—611no—
272C2×#327—611no—
273#1444—611no—
274#1280—611no—
275C2×C61—21no—
276C2×C61—21no—
277C2×C61—21no—
278C2×C61—21no—
279C2×C61#160011yescharacteristic
280C2×C61#160311yescharacteristic
281C2×C61#160911yescharacteristic
282C2×C61#161811yescharacteristic
283C2×C61#203911yescharacteristic
284C2×C61#204211yescharacteristic
285C2×C61#204411yescharacteristic
286D61—161no—
287C2×C22⋊Q8C2×D6111yescharacteristic
288C2×#121—611no—
289C22×C4⋊C4—1221no—
290C22×C4⋊C4C2×D6111yescharacteristic
291C2×#103—21no—
292C2×#102—1221no—
293C2×C22⋊C8—611no—
294C2×C22⋊C8C2×D6111yescharacteristic
295#400—1221no—
296#397—1221no—
297#394—1221no—
298#393—1221no—
299#386—1221no—
300#386—1221no—
301C2×#95—611no—
302C2×#95—611no—
303C2×#95—1221no—
304#340—21no—
305#340—1221no—
306#328—1222no—
307#327—1222no—
308C61#1040511yescharacteristic, complemented, Sylow
309C22×Q8C22⋊D6111yescharacteristic
310C22×D4—611no—
311C22×D4—1221no—
312C23×C4—21no—
313C23×C4—611no—
314C23×C4—611no—
315C23×C4—1221no—
316C23×C4C22×D6111yescharacteristic
317C22×C8—21no—
318C22×C8—1221no—
319C22⋊Q8—21no—
320C22⋊Q8—21no—
321C22⋊Q8—21no—
322C22⋊Q8—21no—
323#121—1221no—
324#121—1221no—
325#121—1221no—
326#121—1221no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—42no—
331C2×C4⋊C4—611no—
332C2×C4⋊C4—2442no—
333C2×C4⋊C4—2442no—
334C2×C4⋊C4—2442no—
335C2×C4⋊C4C22⋊D6111yescharacteristic
336C2×C22⋊C4—21no—
337C2×C22⋊C4—1221no—
338C2×C22⋊C4—1221no—
339C2×C22⋊C4—1221no—
340C2×C22⋊C4—1221no—
341C2×C22⋊C4—1221no—
342#103—42no—
343#102—2442no—
344C22⋊C8—21no—
345C22⋊C8—21no—
346C22⋊C8—1221no—
347C22⋊C8—1221no—
348#95—612no—
349#95—1221no—
350#95—1221no—
351#95—1221no—
352#95—1221no—
353#95—1221no—
354#95—1221no—
355#95—1221no—
356#95—2442no—
357C24—1221no—
358C24D4×D6111yescharacteristic
359C2×Q8—21no—
360C2×Q8—21no—
361C2×Q8—41no—
362C2×Q8—41no—
363C2×D4—1221no—
364C2×D4—1221no—
365C2×D4—2441no—
366C2×D4—2441no—
367C2×D4—2441no—
368C2×D4—2441no—
369C2×D4—2441no—
370C2×D4—2441no—
371C2×D4—2441no—
372C2×D4—2441no—
373C22×C4—22no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—41no—
377C22×C4—41no—
378C22×C4—41no—
379C22×C4—41no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4—41no—
383C22×C4—41no—
384C22×C4—1222no—
385C22×C4—1222no—
386C22×C4—1222no—
387C22×C4—1221no—
388C22×C4—1221no—
389C22×C4—1221no—
390C22×C4—1221no—
391C22×C4—1221no—
392C22×C4—1221no—
393C22×C4—1221no—
394C22×C4—2441no—
395C22×C4—2441no—
396C22×C4—2441no—
397C22×C4—2441no—
398C22×C4—2441no—
399C22×C4—2441no—
400C22×C4—2441no—
401C22×C4—2441no—
402C22×C4#1175822211yescharacteristic
403C22×C4#1175822211yescharacteristic
404C22×C4D4×D6111yescharacteristic
405C22×C4D4×D6111yescharacteristic
406C22×C4#1175822411yescharacteristic
407C22×C4C2×C22⋊D6111yescharacteristic
408C2×C8—41no—
409C2×C8—41no—
410C2×C8—41no—
411C2×C8—2441no—
412C2×C8—2441no—
413C2×C8—2441no—
414C4⋊C4—22no—
415C4⋊C4—22no—
416C4⋊C4—21no—
417C4⋊C4—21no—
418C4⋊C4—41no—
419C4⋊C4—41no—
420C4⋊C4—41no—
421C4⋊C4—41no—
422C4⋊C4—1221no—
423C4⋊C4—1221no—
424C4⋊C4—2448no—
425C22⋊C4—41no—
426C22⋊C4—41no—
427C22⋊C4—4881no—
428C22⋊C4—4881no—
429C22⋊C4—4881no—
430C22⋊C4—4881no—
431C22⋊C4—2441no—
432C22⋊C4—2441no—
433C23—21no—
434C23—21no—
435C23—21no—
436C23—21no—
437C23—2441no—
438C23—2441no—
439C23—2441no—
440C23—2441no—
441C23—2441no—
442C23—2441no—
443C23—2441no—
444C23#1451974511yescharacteristic
445C23#1451975011yescharacteristic
446C23#1451976311yescharacteristic
447C23#1451979811yescharacteristic
448C23#1451980011yescharacteristic
449C23#1451980411yescharacteristic
450C23#1451980911yescharacteristic
451Q8—42no—
452Q8—81no—
453D4—4881no—
454D4—4881no—
455D4—4881no—
456D4—4881no—
457D4—4881no—
458D4—2442no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—42no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—81no—
477C2×C4—81no—
478C2×C4—81no—
479C2×C4—81no—
480C2×C4—1224no—
481C2×C4—4881no—
482C2×C4—4881no—
483C2×C4—2442no—
484C2×C4—2442no—
485C2×C4—2441no—
486C2×C4—2441no—
487C2×C4—2441no—
488C2×C4—2441no—
489C2×C4—2441no—
490C2×C4—2441no—
491C2×C4—2441no—
492C2×C4—2441no—
493C2×C4—2441no—
494C2×C4—2442no—
495C2×C4—2442no—
496C2×C4—2442no—
497C2×C4—2442no—
498C2×C4—2442no—
499C2×C4—2442no—
500C2×C4#1451974911yescharacteristic
501C2×C4#1451975011yescharacteristic
502C2×C4#1451975911yescharacteristic
503C2×C4#1451976011yescharacteristic
504C8—81no—
505C8—4881no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—21no—
513C22—21no—
514C22—21no—
515C22—21no—
516C22—21no—
517C22—21no—
518C22—4881no—
519C22—4881no—
520C22—4881no—
521C22—4881no—
522C22—4881no—
523C22—4881no—
524C22—4881no—
525C22#1683967711yescharacteristic
526C22#1683990611yescharacteristic
527C22#1683992311yescharacteristic
528C22#1683992811yescharacteristic
529C22#1683994311yescharacteristic
530C22#1683994811yescharacteristic
531C22#1683995111yescharacteristic
532C22#1683998011yescharacteristic
533C22#1683998711yescharacteristic
534C22#1684011811yescharacteristic
535C22#1684012311yescharacteristic
536C4—21no—
537C4—21no—
538C4—21no—
539C4—21no—
540C4—81no—
541C4—82no—
542C4—81no—
543C4—4881no—
544C4—4881no—
545C4—4881no—
546C4—2444no—
547C2—21no—
548C2—21no—
549C2—21no—
550C2—21no—
551C2—9761no—
552C2#2144476411yescharacteristic
553C2#2144478111yescharacteristic
554C2#2144481511yescharacteristic
555C2#2144486611yescharacteristic
556C2#2144704111yescharacteristic
557C2#2144705611yescharacteristic
558C2#2144706811yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC61×#1872C2
socleC23×C61#120
prime radicalC2×#14519751C22
hypercenter#1872D61
hypocenterC61#10405
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
3. C2×#16839499C2semidirect
5. #21444082C2semidirect
6. #21443661C2semidirect
7. C61×#1872C2semidirect
270. #1872D61semidirect
308. C61#10405semidirect

Maximal subgroups

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

subgroupindex
#214517532
#214461362
C2×#168394992
C2×#168394972
#214440822
#214436612
C61×#18722
#1040561