Finite Group Databasebeta

← #29583299

Subgroups — #29583299

Order 15616.

632 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21446137C211yesmaximal, characteristic
2#21446006C211yesmaximal, characteristic, complemented
3C2×#16839496C211yesmaximal, characteristic
4C2×#16839488C211yesmaximal, characteristic, complemented
5#21444072C211yesmaximal, characteristic, complemented
6#21443697C211yesmaximal, characteristic, complemented
7C61×#2618C211yesmaximal, characteristic
8C22×C4⋊Dic61C2211yescharacteristic
9C2×#14519710—21no—
10C2×#14519698—21no—
11C2×C22⋊#92418C2211yescharacteristic
12C2×C22⋊#92418C2211yescharacteristic
13C2×#14519684—21no—
14C2×#14519684—21no—
15C2×#14519684C2211yescharacteristic
16#16839524—21no—
17#16839524—21no—
18#16839496—22no—
19#16839488—22no—
20C2×#123×C61—21no—
21C2×#121×C61C2211yescharacteristic
22C22×C4⋊C4×C61C2211yescharacteristic
23C61×#398—21no—
24C61×#396—21no—
25C61×#396—21no—
26C61×#394—21no—
27C61×#386—21no—
28C61×#380C2211yescharacteristic
29C23×Dic61—21no—
30C23×Dic61—21no—
31C22×#92418—21no—
32C22×#92418—21no—
33C2×C4⋊Dic61—21no—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61—42no—
36#14519710—42no—
37#14519698—42no—
38C22⋊#92418—21no—
39C22⋊#92418—21no—
40C22⋊#92418—21no—
41C22⋊#92418D412yes—
42#14519684—21no—
43#14519684—21no—
44#14519684—42no—
45#14519684—42no—
46C22×D4×C61—21no—
47C22×D4×C61D411yescharacteristic
48C23×C4×C61D411yescharacteristic
49C23×C4×C61D411yescharacteristic
50C23×C4×C61C2311yescharacteristic
51#123×C61—42no—
52#123×C61—42no—
53#121×C61—21no—
54#121×C61—21no—
55#121×C61—21no—
56#121×C61—21no—
57C2×C4⋊C4×C61—21no—
58C2×C4⋊C4×C61—21no—
59C2×C4⋊C4×C61—21no—
60C2×C4⋊C4×C61—21no—
61C2×C4⋊C4×C61—21no—
62C2×C4⋊C4×C61—21no—
63C2×C4⋊C4×C61—21no—
64C2×C4⋊C4×C61—21no—
65C2×C4⋊C4×C61D411yescharacteristic
66C2×C4⋊C4×C61D411yescharacteristic
67C2×C4⋊C4×C61D411yescharacteristic
68C2×C22⋊C4×C61—21no—
69C2×C22⋊C4×C61—21no—
70C2×C22⋊C4×C61—21no—
71C2×C22⋊C4×C61—21no—
72C2×C22⋊C4×C61—21no—
73C2×C22⋊C4×C61—21no—
74#95×C61—21no—
75#95×C61—21no—
76#95×C61—21no—
77C24×C61—21no—
78C24×C61C2×D411yescharacteristic
79C2×D4×C61—21no—
80C2×D4×C61—21no—
81C2×D4×C61—41no—
82C2×D4×C61—41no—
83C2×D4×C61—41no—
84C2×D4×C61—41no—
85C2×D4×C61—41no—
86C2×D4×C61—41no—
87C2×D4×C61—41no—
88C2×D4×C61—41no—
89C22×C4×C61—21no—
90C22×C4×C61—21no—
91C22×C4×C61—21no—
92C22×C4×C61—21no—
93C22×C4×C61—21no—
94C22×C4×C61—21no—
95C22×C4×C61—21no—
96C22×C4×C61—21no—
97C22×C4×C61—21no—
98C22×C4×C61—21no—
99C22×C4×C61—21no—
100C22×C4×C61—21no—
101C22×C4×C61—41no—
102C22×C4×C61—41no—
103C22×C4×C61—41no—
104C22×C4×C61—41no—
105C22×C4×C61D812yes—
106C22×C4×C61C2×D411yescharacteristic
107C22×C4×C61C2×D411yescharacteristic
108C22×C4×C61C2×D411yescharacteristic
109C22×C4×C61#4111yescharacteristic
110C22×C4×C61#4111yescharacteristic
111C22×C4×C61#4111yescharacteristic
112C22×Dic61—22no—
113C22×Dic61—22no—
114C22×Dic61—41no—
115C22×Dic61—41no—
116C22×Dic61—41no—
117C22×Dic61—41no—
118C22×Dic61—41no—
119C22×Dic61—41no—
120C22×Dic61—41no—
121C22×Dic61—41no—
122C22×Dic61—41no—
123C22×Dic61—41no—
124C22×Dic61—41no—
125C22×Dic61—41no—
126C4⋊C4×C61—21no—
127C4⋊C4×C61—21no—
128C4⋊C4×C61—42no—
129C4⋊C4×C61—42no—
130C4⋊C4×C61—41no—
131C4⋊C4×C61—41no—
132C4⋊C4×C61—41no—
133C4⋊C4×C61—41no—
134C4⋊C4×C61—41no—
135C4⋊C4×C61—41no—
136C22⋊C4×C61—42no—
137C22⋊C4×C61—42no—
138C22⋊C4×C61—41no—
139C22⋊C4×C61—41no—
140C22⋊C4×C61—41no—
141C22⋊C4×C61—41no—
142C22⋊C4×C61—81no—
143C22⋊C4×C61—81no—
144C4⋊Dic61—22no—
145C4⋊Dic61—22no—
146C4⋊Dic61—41no—
147C4⋊Dic61—41no—
148C2×#92418—22no—
149C2×#92418—41no—
150C2×#92418—41no—
151C2×#92418—41no—
152C2×#92418—41no—
153C2×#92418—41no—
154C23×C61—21no—
155C23×C61—21no—
156C23×C61—21no—
157C23×C61—21no—
158C23×C61—41no—
159C23×C61—41no—
160C23×C61—41no—
161C23×C61—41no—
162C23×C61—41no—
163C23×C61—41no—
164C23×C61—41no—
165C23×C61#12011yescharacteristic
166C23×C61#12111yescharacteristic
167C23×C61#12311yescharacteristic
168C23×C61C2×D811yescharacteristic
169C23×C61#13511yescharacteristic
170C23×C61AGL(1,ℤ/8)11yescharacteristic
171C23×C61#13711yescharacteristic
172D4×C61—42no—
173D4×C61—81no—
174D4×C61—81no—
175D4×C61—81no—
176D4×C61—81no—
177D4×C61—81no—
178C2×C4×C61—21no—
179C2×C4×C61—21no—
180C2×C4×C61—21no—
181C2×C4×C61—21no—
182C2×C4×C61—22no—
183C2×C4×C61—22no—
184C2×C4×C61—22no—
185C2×C4×C61—41no—
186C2×C4×C61—41no—
187C2×C4×C61—41no—
188C2×C4×C61—41no—
189C2×C4×C61—41no—
190C2×C4×C61—41no—
191C2×C4×C61—41no—
192C2×C4×C61—41no—
193C2×C4×C61—42no—
194C2×C4×C61—41no—
195C2×C4×C61—41no—
196C2×C4×C61—41no—
197C2×C4×C61—41no—
198C2×C4×C61—41no—
199C2×C4×C61—41no—
200C2×C4×C61—41no—
201C2×C4×C61—41no—
202C2×C4×C61—41no—
203C2×C4×C61—41no—
204C2×C4×C61—41no—
205C2×C4×C61—41no—
206C2×C4×C61—81no—
207C2×C4×C61#12111yescharacteristic
208C2×C4×C61#12111yescharacteristic
209C2×C4×C61#12311yescharacteristic
210C2×C4×C61#12411yescharacteristic
211C2×Dic61—42no—
212C2×Dic61—42no—
213C2×Dic61—42no—
214C2×Dic61—42no—
215C2×Dic61—42no—
216C2×Dic61—42no—
217C2×Dic61—81no—
218C2×Dic61—81no—
219C2×Dic61—81no—
220C2×Dic61—81no—
221C2×Dic61—81no—
222C2×Dic61—81no—
223C2×Dic61—81no—
224C2×Dic61—81no—
225#92418—42no—
226#92418—81no—
227#10397—611nomaximal, Sylow
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—21no—
240C22×C61—81no—
241C22×C61—81no—
242C22×C61—81no—
243C22×C61—81no—
244C22×C61—81no—
245C22×C61—81no—
246C22×C61—81no—
247C22×C61#39411yescharacteristic
248C22×C61#44711yescharacteristic
249C22×C61#45211yescharacteristic
250C22×C61#45411yescharacteristic
251C22×C61#45611yescharacteristic
252C22×C61B(4,𝔽2)11yescharacteristic
253C22×C61#45811yescharacteristic
254C22×C61#46611yescharacteristic
255C22×C61#46811yescharacteristic
256C22×C61#48011yescharacteristic
257C22×C61#48211yescharacteristic
258C4×C61—21no—
259C4×C61—21no—
260C4×C61—21no—
261C4×C61—21no—
262C4×C61—42no—
263C4×C61—81no—
264C4×C61—81no—
265C4×C61—81no—
266C4×C61—81no—
267Dic61—82no—
268Dic61—82no—
269#2618D6111yescharacteristic
270#1874—611no—
271#1852—611no—
272C2×#327—611no—
273C2×#324—611no—
274#1441—611no—
275#1294—611no—
276C2×C61—21no—
277C2×C61—21no—
278C2×C61—21no—
279C2×C61—21no—
280C2×C61—161no—
281C2×C61#159811yescharacteristic
282C2×C61#160311yescharacteristic
283C2×C61#161011yescharacteristic
284C2×C61#161511yescharacteristic
285C2×C61#203311yescharacteristic
286C2×C61#203811yescharacteristic
287C2×C61#204411yescharacteristic
288C2×#123—21no—
289C2×#121C2×D6111yescharacteristic
290C22×C4⋊C4—611no—
291C22×C4⋊C4C2×D6111yescharacteristic
292C2×#107—1221no—
293C2×#102—1221no—
294C2×C22⋊C8—611no—
295C2×C22⋊C8—611no—
296#398—21no—
297#396—21no—
298#396—21no—
299#394—21no—
300#386—21no—
301#380C2×D6111yescharacteristic
302C2×#95—611no—
303C2×#95—1221no—
304C2×#95—1221no—
305#340—1221no—
306#340—1221no—
307#327—1222no—
308#324—1222no—
309C61#1039711yescharacteristic, complemented, Sylow
310C22×D4—21no—
311C22×D4C22⋊D6111yescharacteristic
312C23×C4—1221no—
313C23×C4—1221no—
314C23×C4C22⋊D6111yescharacteristic
315C23×C4C22⋊D6111yescharacteristic
316C23×C4C22×D6111yescharacteristic
317C22×C8—1221no—
318C22×C8—1221no—
319#123—42no—
320#123—42no—
321#121—21no—
322#121—21no—
323#121—21no—
324#121—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—1221no—
334C2×C4⋊C4—1221no—
335C2×C4⋊C4—2442no—
336C2×C4⋊C4C22⋊D6111yescharacteristic
337C2×C4⋊C4C22⋊D6111yescharacteristic
338C2×C4⋊C4C22⋊D6111yescharacteristic
339C2×C22⋊C4—21no—
340C2×C22⋊C4—21no—
341C2×C22⋊C4—21no—
342C2×C22⋊C4—21no—
343C2×C22⋊C4—21no—
344C2×C22⋊C4—21no—
345#107—2442no—
346#102—2442no—
347C22⋊C8—612no—
348C22⋊C8—1221no—
349C22⋊C8—1221no—
350C22⋊C8—1221no—
351#95—21no—
352#95—21no—
353#95—21no—
354#95—1221no—
355#95—1221no—
356#95—2442no—
357#95—2442no—
358C24—21no—
359C24C2×C22⋊D6111yescharacteristic
360C2×D4—21no—
361C2×D4—21no—
362C2×D4—41no—
363C2×D4—41no—
364C2×D4—41no—
365C2×D4—41no—
366C2×D4—41no—
367C2×D4—41no—
368C2×D4—41no—
369C2×D4—41no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—41no—
383C22×C4—41no—
384C22×C4—41no—
385C22×C4—41no—
386C22×C4—1222no—
387C22×C4—1222no—
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×C4—2441no—
398C22×C4—2441no—
399C22×C4—2441no—
400C22×C4#1175819912yes—
401C22×C4D4×D6111yescharacteristic
402C22×C4#1175822411yescharacteristic
403C22×C4#1175822411yescharacteristic
404C22×C4#1175822411yescharacteristic
405C22×C4C2×C22⋊D6111yescharacteristic
406C22×C4C2×C22⋊D6111yescharacteristic
407C2×C8—1222no—
408C2×C8—2441no—
409C2×C8—2441no—
410C2×C8—2441no—
411C2×C8—2441no—
412C2×C8—2441no—
413C4⋊C4—21no—
414C4⋊C4—21no—
415C4⋊C4—41no—
416C4⋊C4—41no—
417C4⋊C4—42no—
418C4⋊C4—42no—
419C4⋊C4—41no—
420C4⋊C4—41no—
421C4⋊C4—41no—
422C4⋊C4—41no—
423C4⋊C4—1222no—
424C4⋊C4—1222no—
425C4⋊C4—2441no—
426C4⋊C4—2441no—
427C22⋊C4—42no—
428C22⋊C4—42no—
429C22⋊C4—41no—
430C22⋊C4—41no—
431C22⋊C4—41no—
432C22⋊C4—41no—
433C22⋊C4—81no—
434C22⋊C4—81no—
435C23—21no—
436C23—21no—
437C23—21no—
438C23—21no—
439C23—41no—
440C23—41no—
441C23—41no—
442C23—41no—
443C23—41no—
444C23—41no—
445C23—41no—
446C23#1451974611yescharacteristic
447C23#1451974911yescharacteristic
448C23#1451975811yescharacteristic
449C23C2×#1175819911yescharacteristic
450C23#1451979711yescharacteristic
451C23#1451980311yescharacteristic
452C23#1451980711yescharacteristic
453D4—42no—
454D4—81no—
455D4—81no—
456D4—81no—
457D4—81no—
458D4—81no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—42no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—41no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—81no—
488C2×C4—4881no—
489C2×C4—4881no—
490C2×C4—4881no—
491C2×C4—4881no—
492C2×C4—4881no—
493C2×C4—4881no—
494C2×C4—4881no—
495C2×C4—4881no—
496C2×C4—2442no—
497C2×C4—2442no—
498C2×C4—2442no—
499C2×C4—2442no—
500C2×C4—2442no—
501C2×C4—2442no—
502C2×C4#1451974811yescharacteristic
503C2×C4#1451974911yescharacteristic
504C2×C4#1451975811yescharacteristic
505C2×C4#1451976411yescharacteristic
506C8—4881no—
507C8—2442no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—21no—
513C22—21no—
514C22—21no—
515C22—21no—
516C22—21no—
517C22—21no—
518C22—21no—
519C22—21no—
520C22—81no—
521C22—81no—
522C22—81no—
523C22—81no—
524C22—81no—
525C22—81no—
526C22—81no—
527C22#1683967611yescharacteristic
528C22#1683989611yescharacteristic
529C22#1683992411yescharacteristic
530C22#1683993511yescharacteristic
531C22#1683994511yescharacteristic
532C22#1683994911yescharacteristic
533C22#1683995211yescharacteristic
534C22#1683999611yescharacteristic
535C22#1684000611yescharacteristic
536C22#1684007311yescharacteristic
537C22#1684008311yescharacteristic
538C4—21no—
539C4—21no—
540C4—21no—
541C4—21no—
542C4—42no—
543C4—81no—
544C4—81no—
545C4—81no—
546C4—81no—
547C4—4882no—
548C4—4882no—
549C2—21no—
550C2—21no—
551C2—21no—
552C2—21no—
553C2—161no—
554C2#2144475411yescharacteristic
555C2#2144478211yescharacteristic
556C2#2144482211yescharacteristic
557C2#2144485011yescharacteristic
558C2#2144699811yescharacteristic
559C2#2144703311yescharacteristic
560C2#2144706711yescharacteristic
subgroupG/H
centerC23#14519746
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC61×#2618C2
socleC23×C61#120
prime radicalC2×#121×C61C22
hypercenter#2618D61
hypocenterC61#10397
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2618

Complements

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

NH ≅ G/Ntype
2. #21446006C2semidirect
4. C2×#16839488C2semidirect
5. #21444072C2semidirect
6. #21443697C2semidirect
309. C61#10397semidirect

Maximal subgroups

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

subgroupindex
#214461372
#214460062
C2×#168394962
C2×#168394882
#214440722
#214436972
C61×#26182
#1039761