Finite Group Databasebeta

← #29583303

Subgroups — #29583303

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#21451561C211yesmaximal, characteristic
2#21446134C211yesmaximal, characteristic
3#21446009C211yesmaximal, characteristic, complemented
4C2×#16839497C211yesmaximal, characteristic
5#21444072C211yesmaximal, characteristic, complemented
6#21443699C211yesmaximal, characteristic, complemented
7C2×C61×#324C211yesmaximal, characteristic, complemented
8C2×#14519760—21no—
9C2×#14519751C2211yescharacteristic
10C22×C4⋊Dic61C2211yescharacteristic
11C2×#14519711—21no—
12C2×#14519699—21no—
13#16839692—21no—
14#16839684—21no—
15#16839684—21no—
16#16839679—21no—
17#16839641—21no—
18#16839622C2211yescharacteristic
19C2×#14519684—21no—
20C2×#14519684—21no—
21C2×#14519684C2211yescharacteristic
22#16839525—21no—
23#16839525—21no—
24#16839497—22no—
25C22×C4⋊C4×C61C2211yescharacteristic
26C2×C22⋊C8×C61C2211yescharacteristic
27C2×C22⋊C8×C61C2211yescharacteristic
28C61×#324—22no—
29C22×D244D411yescharacteristic
30C22×C22⋊D61—21no—
31C23×Dic61—21no—
32C23×Dic61—21no—
33#14519760—42no—
34#14519760—42no—
35#14519751—21no—
36#14519751—21no—
37#14519751—21no—
38#14519751—21no—
39C2×C4⋊Dic61—21no—
40C2×C4⋊Dic61—21no—
41C2×C4⋊Dic61—42no—
42C2×C4⋊Dic61D411yescharacteristic
43C2×C4⋊Dic61D411yescharacteristic
44C2×C4⋊Dic61D411yescharacteristic
45C2×#11758196—21no—
46C2×#11758196—21no—
47C2×C22⋊Dic61—21no—
48C2×#11758198—21no—
49C2×#11758198—21no—
50C2×#11758198—21no—
51C2×#11758198—21no—
52C2×#11758198—21no—
53#14519711—42no—
54#14519699—42no—
55#14519684—21no—
56#14519684—21no—
57#14519684—21no—
58#14519684—21no—
59#14519684—21no—
60#14519684—42no—
61#14519684—42no—
62C23×C4×C61D411yescharacteristic
63C23×C4×C61D411yescharacteristic
64C23×C4×C61C2311yescharacteristic
65C22×C8×C61—21no—
66C22×C8×C61—21no—
67C2×C4⋊C4×C61—21no—
68C2×C4⋊C4×C61—21no—
69C2×C4⋊C4×C61—21no—
70C2×C4⋊C4×C61—21no—
71C2×C4⋊C4×C61—21no—
72C2×C4⋊C4×C61—21no—
73C22⋊C8×C61—21no—
74C22⋊C8×C61—21no—
75C22⋊C8×C61—21no—
76C22⋊C8×C61D412yes—
77C24×C61C2×D411yescharacteristic
78C23×D61—21no—
79C22×C4×C61—21no—
80C22×C4×C61—21no—
81C22×C4×C61—21no—
82C22×C4×C61—21no—
83C22×C4×C61—21no—
84C22×C4×C61—21no—
85C22×C4×C61—21no—
86C22×C4×C61—21no—
87C22×C4×C61—21no—
88C22×C4×C61—41no—
89C22×C4×C61—41no—
90C22×C4×C61—41no—
91C22×C4×C61—41no—
92C22×C4×C61D812yes—
93C22×C4×C61C2×D411yescharacteristic
94C22×C4×C61C2×D411yescharacteristic
95C22×C4×C61C2×D411yescharacteristic
96C22×C4×C61#4111yescharacteristic
97C22×C4×C61#4111yescharacteristic
98C22×C4×C61#4111yescharacteristic
99C2×C22⋊D61—41no—
100C2×C22⋊D61—41no—
101C2×C22⋊D61—41no—
102C2×C22⋊D61—41no—
103C2×C22⋊D61—41no—
104C2×C22⋊D61—41no—
105C22×Dic61—22no—
106C22×Dic61—22no—
107C22×Dic61—21no—
108C22×Dic61—21no—
109C22×Dic61—21no—
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×Dic61—41no—
120C22×Dic61—41no—
121C22×Dic61—41no—
122C2×D244—21no—
123C2×D244—21no—
124C2×D244—41no—
125C2×D244—41no—
126C2×C8×C61—22no—
127C2×C8×C61—41no—
128C2×C8×C61—41no—
129C2×C8×C61—41no—
130C2×C8×C61—41no—
131C2×C8×C61—41no—
132C4⋊C4×C61—41no—
133C4⋊C4×C61—41no—
134C4⋊C4×C61—41no—
135C4⋊C4×C61—41no—
136C22⋊Dic61—41no—
137C22⋊Dic61—41no—
138#11758198—42no—
139#11758198—42no—
140#11758198—41no—
141#11758198—41no—
142#11758198—81no—
143#11758198—81no—
144C4⋊Dic61—22no—
145C4⋊Dic61—22no—
146C4⋊Dic61—21no—
147C4⋊Dic61—21no—
148C4⋊Dic61—41no—
149C4⋊Dic61—41no—
150C4⋊Dic61—41no—
151C4⋊Dic61—41no—
152#11758196—42no—
153#11758196—42no—
154C23×C61—21no—
155C23×C61—21no—
156C23×C61—21no—
157C23×C61—21no—
158C23×C61#12011yescharacteristic
159C23×C61#12111yescharacteristic
160C23×C61#12311yescharacteristic
161C23×C61C2×D811yescharacteristic
162C23×C61#13511yescharacteristic
163C23×C61AGL(1,ℤ/8)11yescharacteristic
164C23×C61#13711yescharacteristic
165C22×D61—41no—
166C22×D61—41no—
167C22×D61—41no—
168C22×D61—41no—
169C22×D61—41no—
170C22×D61—41no—
171C22×D61—41no—
172C2×C4×C61—21no—
173C2×C4×C61—21no—
174C2×C4×C61—21no—
175C2×C4×C61—21no—
176C2×C4×C61—22no—
177C2×C4×C61—22no—
178C2×C4×C61—22no—
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—41no—
186C2×C4×C61—41no—
187C2×C4×C61—42no—
188C2×C4×C61—41no—
189C2×C4×C61—41no—
190C2×C4×C61—41no—
191C2×C4×C61—81no—
192C2×C4×C61#12111yescharacteristic
193C2×C4×C61#12111yescharacteristic
194C2×C4×C61#12311yescharacteristic
195C2×C4×C61#12411yescharacteristic
196C22⋊D61—81no—
197C22⋊D61—81no—
198C22⋊D61—81no—
199C22⋊D61—81no—
200C2×Dic61—42no—
201C2×Dic61—42no—
202C2×Dic61—42no—
203C2×Dic61—42no—
204C2×Dic61—42no—
205C2×Dic61—41no—
206C2×Dic61—41no—
207C2×Dic61—41no—
208C2×Dic61—41no—
209C2×Dic61—41no—
210C2×Dic61—41no—
211C2×Dic61—41no—
212C2×Dic61—42no—
213C2×Dic61—41no—
214C2×Dic61—41no—
215C2×Dic61—81no—
216C2×Dic61—81no—
217C2×Dic61—81no—
218C2×Dic61—81no—
219C2×Dic61—81no—
220C2×Dic61—81no—
221C2×Dic61—81no—
222C2×Dic61—81no—
223D244—42no—
224D244—81no—
225C8×C61—42no—
226C8×C61—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#39411yescharacteristic
241C22×C61#44711yescharacteristic
242C22×C61#45211yescharacteristic
243C22×C61#45411yescharacteristic
244C22×C61#45611yescharacteristic
245C22×C61B(4,𝔽2)11yescharacteristic
246C22×C61#45811yescharacteristic
247C22×C61#46611yescharacteristic
248C22×C61#46811yescharacteristic
249C22×C61#48011yescharacteristic
250C22×C61#48211yescharacteristic
251C2×D61—81no—
252C2×D61—81no—
253C2×D61—81no—
254C2×D61—81no—
255C2×D61—81no—
256C2×D61—81no—
257C2×D61—81no—
258C4×C61—21no—
259C4×C61—21no—
260C4×C61—21no—
261C4×C61—21no—
262C4×C61—42no—
263C4×C61—81no—
264Dic61—82no—
265Dic61—81no—
266Dic61—82no—
267Dic61—81no—
268Dic61—81no—
269#2618—611no—
270#1874—611no—
271#1852—611no—
272C2×#327—611no—
273C2×#324D6111yescharacteristic, complemented
274#1441—611no—
275#1294—611no—
276C2×C61—21no—
277C2×C61—21no—
278C2×C61—21no—
279C2×C61—21no—
280C2×C61#159811yescharacteristic
281C2×C61#160311yescharacteristic
282C2×C61#161011yescharacteristic
283C2×C61#161511yescharacteristic
284C2×C61#203311yescharacteristic
285C2×C61#203811yescharacteristic
286C2×C61#204411yescharacteristic
287D61—161no—
288C2×#123—1221no—
289C2×#121—611no—
290C22×C4⋊C4—611no—
291C22×C4⋊C4C2×D6111yescharacteristic
292C2×#107—1221no—
293C2×#102—1221no—
294C2×C22⋊C8C2×D6111yescharacteristic
295C2×C22⋊C8C2×D6111yescharacteristic
296#398—1221no—
297#396—1221no—
298#396—1221no—
299#394—1221no—
300#386—1221no—
301#380—611no—
302C2×#95—611no—
303C2×#95—1221no—
304C2×#95—1221no—
305#340—1221no—
306#340—1221no—
307#327—1222no—
308#324—22no—
309C61#1039711yescharacteristic, complemented, Sylow
310C22×D4—611no—
311C22×D4—1221no—
312C23×C4—1221no—
313C23×C4—1221no—
314C23×C4D24411yescharacteristic
315C23×C4D24411yescharacteristic
316C23×C4C22×D6111yescharacteristic
317C22×C8—21no—
318C22×C8—21no—
319#123—2442no—
320#123—2442no—
321#121—1221no—
322#121—1221no—
323#121—1221no—
324#121—1221no—
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—611no—
332C2×C4⋊C4—611no—
333C2×C4⋊C4—611no—
334C2×C4⋊C4—1221no—
335C2×C4⋊C4—1221no—
336C2×C4⋊C4—1221no—
337C2×C4⋊C4—1221no—
338C2×C4⋊C4—2442no—
339C2×C22⋊C4—1221no—
340C2×C22⋊C4—1221no—
341C2×C22⋊C4—1221no—
342C2×C22⋊C4—1221no—
343C2×C22⋊C4—1221no—
344C2×C22⋊C4—1221no—
345#107—2442no—
346#102—2442no—
347C22⋊C8—21no—
348C22⋊C8—21no—
349C22⋊C8—21no—
350C22⋊C8C22⋊D6112yes—
351#95—1221no—
352#95—1221no—
353#95—1221no—
354#95—1221no—
355#95—1221no—
356#95—2442no—
357#95—2442no—
358C24—1221no—
359C24C2×D24411yescharacteristic
360C2×D4—1221no—
361C2×D4—1221no—
362C2×D4—2441no—
363C2×D4—2441no—
364C2×D4—2441no—
365C2×D4—2441no—
366C2×D4—2441no—
367C2×D4—2441no—
368C2×D4—2441no—
369C2×D4—2441no—
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—41no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4—41no—
383C22×C4—1222no—
384C22×C4—1222no—
385C22×C4—1221no—
386C22×C4—1221no—
387C22×C4—1221no—
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×C4D48812yes—
401C22×C4#1175822211yescharacteristic
402C22×C4D4×D6111yescharacteristic
403C22×C4D4×D6111yescharacteristic
404C22×C4#1175822411yescharacteristic
405C22×C4#1175822411yescharacteristic
406C22×C4C2×C22⋊D6111yescharacteristic
407C2×C8—22no—
408C2×C8—41no—
409C2×C8—41no—
410C2×C8—41no—
411C2×C8—41no—
412C2×C8—41no—
413C4⋊C4—41no—
414C4⋊C4—41no—
415C4⋊C4—41no—
416C4⋊C4—41no—
417C4⋊C4—1222no—
418C4⋊C4—1222no—
419C4⋊C4—1221no—
420C4⋊C4—1221no—
421C4⋊C4—2441no—
422C4⋊C4—2441no—
423C4⋊C4—2441no—
424C4⋊C4—2441no—
425C4⋊C4—2442no—
426C4⋊C4—2442no—
427C22⋊C4—4881no—
428C22⋊C4—4881no—
429C22⋊C4—2442no—
430C22⋊C4—2442no—
431C22⋊C4—2441no—
432C22⋊C4—2441no—
433C22⋊C4—2441no—
434C22⋊C4—2441no—
435C23—21no—
436C23—21no—
437C23—21no—
438C23—21no—
439C23—2441no—
440C23—2441no—
441C23—2441no—
442C23—2441no—
443C23—2441no—
444C23—2441no—
445C23—2441no—
446C23#1451974711yescharacteristic
447C23#1451975111yescharacteristic
448C23#1451976111yescharacteristic
449C23C2×D48811yescharacteristic
450C23#1451979911yescharacteristic
451C23#1451980511yescharacteristic
452C23#1451981011yescharacteristic
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—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—81no—
479C2×C4—4881no—
480C2×C4—4881no—
481C2×C4—4881no—
482C2×C4—4881no—
483C2×C4—4881no—
484C2×C4—4881no—
485C2×C4—4881no—
486C2×C4—4881no—
487C2×C4—2442no—
488C2×C4—2442no—
489C2×C4—2442no—
490C2×C4—2442no—
491C2×C4—2442no—
492C2×C4—2441no—
493C2×C4—2441no—
494C2×C4—2441no—
495C2×C4—2442no—
496C2×C4—2441no—
497C2×C4—2441no—
498C2×C4—2441no—
499C2×C4—2441no—
500C2×C4—2441no—
501C2×C4—2441no—
502C2×C4#1451974811yescharacteristic
503C2×C4#1451974911yescharacteristic
504C2×C4#1451975911yescharacteristic
505C2×C4#1451976311yescharacteristic
506C8—42no—
507C8—81no—
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—4881no—
521C22—4881no—
522C22—4881no—
523C22—4881no—
524C22—4881no—
525C22—4881no—
526C22—4881no—
527C22#1683967811yescharacteristic
528C22#1683989811yescharacteristic
529C22#1683992611yescharacteristic
530C22#1683993711yescharacteristic
531C22#1683994711yescharacteristic
532C22#1683995011yescharacteristic
533C22#1683995311yescharacteristic
534C22#1683999811yescharacteristic
535C22#1684000811yescharacteristic
536C22#1684007611yescharacteristic
537C22#1684008711yescharacteristic
538C4—21no—
539C4—21no—
540C4—21no—
541C4—21no—
542C4—42no—
543C4—81no—
544C4—4882no—
545C4—4881no—
546C4—4882no—
547C4—4881no—
548C4—4881no—
549C2—21no—
550C2—21no—
551C2—21no—
552C2—21no—
553C2—9761no—
554C2#2144475611yescharacteristic
555C2#2144478411yescharacteristic
556C2#2144482411yescharacteristic
557C2#2144485211yescharacteristic
558C2#2144700211yescharacteristic
559C2#2144703711yescharacteristic
560C2#2144706911yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC2×C61×#324C2
socleC23×C61#120
prime radicalC2×#14519751C22
hypercenterC2×#324D61
hypocenterC61#10397
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
3. #21446009C2semidirect
5. #21444072C2semidirect
6. #21443699C2semidirect
7. C2×C61×#324C2semidirect
273. C2×#324D61semidirect
309. C61#10397semidirect

Maximal subgroups

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

subgroupindex
#214515612
#214461342
#214460092
C2×#168394972
#214440722
#214436992
C2×C61×#3242
#1039761