Finite Group Databasebeta

← #29583345

Subgroups — #29583345

Order 15616.

602 conjugacy classes of subgroups.

The subgroup lattice has 554 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#21444078C211yesmaximal, characteristic, complemented
6#21443661C211yesmaximal, characteristic, complemented
7C61×#1872C211yesmaximal, characteristic, complemented
8C2×#14519751C2211yescharacteristic
9C2×#14519697—21no—
10C2×C22⋊#92418C2211yescharacteristic
11#16839701—21no—
12#16839688—21no—
13#16839679—21no—
14#16839673—21no—
15#16839639—21no—
16#16839639—21no—
17C2×#14519684—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×#11758198—21no—
41C2×#11758198—21no—
42C2×#11758198—21no—
43C2×#11758198—21no—
44C2×#11758198—21no—
45#14519697—42no—
46C22⋊#92418—21no—
47C22⋊#92418—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54#14519684—21no—
55#14519684—42no—
56#14519684—42no—
57#14519684D412yes—
58C22×Q8×C61D411yescharacteristic
59C23×C4×C61—21no—
60C23×C4×C61C2311yescharacteristic
61C22×C8×C61—21no—
62C22⋊Q8×C61—21no—
63C22⋊Q8×C61—21no—
64C22⋊Q8×C61—21no—
65C22⋊Q8×C61—21no—
66C2×C4⋊C4×C61—21no—
67C2×C4⋊C4×C61—21no—
68C2×C4⋊C4×C61—21no—
69C2×C4⋊C4×C61—42no—
70C2×C4⋊C4×C61D411yescharacteristic
71C2×C22⋊C4×C61—21no—
72#103×C61—42no—
73C22⋊C8×C61—21no—
74C22⋊C8×C61—21no—
75C24×C61C2×D411yescharacteristic
76C23×D61—21no—
77C2×Q8×C61—21no—
78C2×Q8×C61—21no—
79C2×Q8×C61—41no—
80C2×Q8×C61—41no—
81C22×C4×C61—22no—
82C22×C4×C61—21no—
83C22×C4×C61—21no—
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×C61—41no—
91C22×C4×C61—41no—
92C22×C4×C61C2×D411yescharacteristic
93C22×C4×C61C2×D411yescharacteristic
94C22×C4×C61C2×D411yescharacteristic
95C22×C4×C61#4111yescharacteristic
96C22×C4×C61#4111yescharacteristic
97C22×C4×C61#4111yescharacteristic
98C2×C22⋊D61—41no—
99C2×C22⋊D61—41no—
100C2×C22⋊D61—41no—
101C2×C22⋊D61—41no—
102C2×C22⋊D61—41no—
103C2×C22⋊D61—41no—
104C22×Dic61—21no—
105C22×Dic61—21no—
106C22×Dic61—21no—
107C22×Dic61—22no—
108C22×Dic61—21no—
109C22×Dic61—21no—
110C22×Dic61—21no—
111C22×Dic61—21no—
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—41no—
127C2×C8×C61—41no—
128C2×C8×C61—41no—
129C4⋊C4×C61—22no—
130C4⋊C4×C61—22no—
131C4⋊C4×C61—21no—
132C4⋊C4×C61—21no—
133C4⋊C4×C61—41no—
134C4⋊C4×C61—41no—
135C4⋊C4×C61—41no—
136C4⋊C4×C61—41no—
137C22⋊C4×C61—41no—
138C22⋊C4×C61—41no—
139#11758198—41no—
140#11758198—41no—
141#11758198—81no—
142#11758198—81no—
143#11758198—81no—
144#11758198—81no—
145C4⋊Dic61—21no—
146C4⋊Dic61—21no—
147C2×#92418—41no—
148C2×#92418—41no—
149C2×#92418—41no—
150C23×C61—21no—
151C23×C61—21no—
152C23×C61—21no—
153C23×C61—21no—
154C23×C61#12011yescharacteristic
155C23×C61#12111yescharacteristic
156C23×C61#12411yescharacteristic
157C23×C61#13511yescharacteristic
158C23×C61#13511yescharacteristic
159C23×C61AGL(1,ℤ/8)11yescharacteristic
160C23×C61#13711yescharacteristic
161C22×D61—41no—
162C22×D61—41no—
163C22×D61—41no—
164C22×D61—41no—
165C22×D61—41no—
166C22×D61—41no—
167C22×D61—41no—
168Q8×C61—42no—
169Q8×C61—81no—
170C2×C4×C61—21no—
171C2×C4×C61—21no—
172C2×C4×C61—21no—
173C2×C4×C61—21no—
174C2×C4×C61—41no—
175C2×C4×C61—41no—
176C2×C4×C61—41no—
177C2×C4×C61—41no—
178C2×C4×C61—42no—
179C2×C4×C61—42no—
180C2×C4×C61—41no—
181C2×C4×C61—41no—
182C2×C4×C61—41no—
183C2×C4×C61—41no—
184C2×C4×C61—41no—
185C2×C4×C61—42no—
186C2×C4×C61—41no—
187C2×C4×C61—81no—
188C2×C4×C61—81no—
189C2×C4×C61—81no—
190C2×C4×C61—81no—
191C2×C4×C61#12111yescharacteristic
192C2×C4×C61#12111yescharacteristic
193C2×C4×C61#12311yescharacteristic
194C2×C4×C61#12311yescharacteristic
195C22⋊D61—81no—
196C22⋊D61—81no—
197C22⋊D61—81no—
198C22⋊D61—81no—
199C2×Dic61—42no—
200C2×Dic61—42no—
201C2×Dic61—42no—
202C2×Dic61—42no—
203C2×Dic61—41no—
204C2×Dic61—41no—
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—81no—
214C2×Dic61—81no—
215C2×Dic61—81no—
216C2×Dic61—81no—
217C2×Dic61—81no—
218C2×Dic61—81no—
219D244—42no—
220D244—81no—
221C8×C61—81no—
222#92418—81no—
223#10404—611nomaximal, Sylow
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—21no—
236C22×C61#39411yescharacteristic
237C22×C61#44911yescharacteristic
238C22×C61#45211yescharacteristic
239C22×C61#45411yescharacteristic
240C22×C61#45511yescharacteristic
241C22×C61B(4,𝔽2)11yescharacteristic
242C22×C61#45811yescharacteristic
243C22×C61#46311yescharacteristic
244C22×C61#46411yescharacteristic
245C22×C61#48811yescharacteristic
246C22×C61#48911yescharacteristic
247C2×D61—81no—
248C2×D61—81no—
249C2×D61—81no—
250C2×D61—81no—
251C2×D61—81no—
252C2×D61—81no—
253C2×D61—81no—
254C4×C61—21no—
255C4×C61—21no—
256C4×C61—21no—
257C4×C61—21no—
258C4×C61—82no—
259C4×C61—81no—
260C4×C61—81no—
261Dic61—82no—
262Dic61—81no—
263Dic61—81no—
264Dic61—81no—
265#2639—611no—
266#1874—611no—
267#1872D6111yescharacteristic, complemented
268C2×#328—611no—
269C2×#327—611no—
270#1442—611no—
271#1280—611no—
272C2×C61—21no—
273C2×C61—21no—
274C2×C61—21no—
275C2×C61—21no—
276C2×C61#159711yescharacteristic
277C2×C61#160611yescharacteristic
278C2×C61#161211yescharacteristic
279C2×C61#161511yescharacteristic
280C2×C61#204011yescharacteristic
281C2×C61#204211yescharacteristic
282C2×C61#204411yescharacteristic
283D61—161no—
284C2×C22⋊Q8C2×D6111yescharacteristic
285C2×#121—611no—
286C22×C4⋊C4C2×D6111yescharacteristic
287C2×#103—21no—
288C2×#102—1221no—
289C2×C22⋊C8—611no—
290C2×C22⋊C8C2×D6111yescharacteristic
291#400—1221no—
292#397—1221no—
293#394—1221no—
294#393—1221no—
295#386—1221no—
296#386—1221no—
297C2×#95—611no—
298C2×#95—611no—
299C2×#95—1221no—
300C2×#95—1221no—
301#340—21no—
302#340—1221no—
303#328—1222no—
304#327—1222no—
305C61#1040411yescharacteristic, complemented, Sylow
306C22×Q8C22⋊D6111yescharacteristic
307C22×D4—611no—
308C22×D4—1221no—
309C23×C4—21no—
310C23×C4—611no—
311C23×C4—611no—
312C23×C4—1221no—
313C23×C4C22×D6111yescharacteristic
314C22×C8—21no—
315C22×C8—1221no—
316C22⋊Q8—21no—
317C22⋊Q8—21no—
318C22⋊Q8—21no—
319C22⋊Q8—21no—
320#121—1221no—
321#121—1221no—
322#121—1221no—
323#121—1221no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—42no—
328C2×C4⋊C4—611no—
329C2×C4⋊C4C22⋊D6111yescharacteristic
330C2×C22⋊C4—21no—
331C2×C22⋊C4—1221no—
332C2×C22⋊C4—1221no—
333C2×C22⋊C4—1221no—
334C2×C22⋊C4—1221no—
335C2×C22⋊C4—1221no—
336#103—42no—
337#102—2442no—
338C22⋊C8—21no—
339C22⋊C8—21no—
340C22⋊C8—1221no—
341C22⋊C8—1221no—
342#95—612no—
343#95—1221no—
344#95—1221no—
345#95—1221no—
346#95—1221no—
347#95—1221no—
348#95—1221no—
349#95—1221no—
350#95—2442no—
351#95—2442no—
352C24—1221no—
353C24D4×D6111yescharacteristic
354C2×Q8—21no—
355C2×Q8—21no—
356C2×Q8—41no—
357C2×Q8—41no—
358C2×D4—1221no—
359C2×D4—1221no—
360C2×D4—2441no—
361C2×D4—2441no—
362C2×D4—2441no—
363C2×D4—2441no—
364C2×D4—2441no—
365C2×D4—2441no—
366C2×D4—2441no—
367C2×D4—2441no—
368C22×C4—22no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—41no—
372C22×C4—41no—
373C22×C4—41no—
374C22×C4—41no—
375C22×C4—41no—
376C22×C4—41no—
377C22×C4—41no—
378C22×C4—41no—
379C22×C4—1221no—
380C22×C4—1221no—
381C22×C4—1221no—
382C22×C4—1221no—
383C22×C4—1221no—
384C22×C4—1221no—
385C22×C4—1222no—
386C22×C4—1221no—
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×C4#1175822211yescharacteristic
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—2441no—
407C2×C8—2441no—
408C2×C8—2441no—
409C4⋊C4—22no—
410C4⋊C4—22no—
411C4⋊C4—21no—
412C4⋊C4—21no—
413C4⋊C4—41no—
414C4⋊C4—41no—
415C4⋊C4—41no—
416C4⋊C4—41no—
417C4⋊C4—1221no—
418C4⋊C4—1221no—
419C22⋊C4—41no—
420C22⋊C4—41no—
421C22⋊C4—4881no—
422C22⋊C4—4881no—
423C22⋊C4—4881no—
424C22⋊C4—4881no—
425C22⋊C4—2441no—
426C22⋊C4—2441no—
427C23—21no—
428C23—21no—
429C23—21no—
430C23—21no—
431C23—2441no—
432C23—2441no—
433C23—2441no—
434C23—2441no—
435C23—2441no—
436C23—2441no—
437C23—2441no—
438C23#1451974511yescharacteristic
439C23#1451975011yescharacteristic
440C23#1451976311yescharacteristic
441C23#1451979811yescharacteristic
442C23#1451980011yescharacteristic
443C23#1451980411yescharacteristic
444C23#1451980911yescharacteristic
445Q8—42no—
446Q8—81no—
447D4—4881no—
448D4—4881no—
449D4—4881no—
450D4—4881no—
451D4—4881no—
452D4—2442no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—42no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—81no—
471C2×C4—81no—
472C2×C4—81no—
473C2×C4—81no—
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—2442no—
489C2×C4—2441no—
490C2×C4—2441no—
491C2×C4—2441no—
492C2×C4—2441no—
493C2×C4—2441no—
494C2×C4#1451974911yescharacteristic
495C2×C4#1451975011yescharacteristic
496C2×C4#1451975911yescharacteristic
497C2×C4#1451976011yescharacteristic
498C8—81no—
499C8—4881no—
500C22—21no—
501C22—21no—
502C22—21no—
503C22—21no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—4881no—
513C22—4881no—
514C22—4881no—
515C22—4881no—
516C22—4881no—
517C22—4881no—
518C22—4881no—
519C22#1683967711yescharacteristic
520C22#1683990611yescharacteristic
521C22#1683992311yescharacteristic
522C22#1683993311yescharacteristic
523C22#1683993811yescharacteristic
524C22#1683994811yescharacteristic
525C22#1683995111yescharacteristic
526C22#1683998011yescharacteristic
527C22#1683998711yescharacteristic
528C22#1684011811yescharacteristic
529C22#1684012311yescharacteristic
530C4—21no—
531C4—21no—
532C4—21no—
533C4—21no—
534C4—81no—
535C4—82no—
536C4—81no—
537C4—4882no—
538C4—4881no—
539C4—4881no—
540C4—4881no—
541C2—21no—
542C2—21no—
543C2—21no—
544C2—21no—
545C2—9761no—
546C2#2144474711yescharacteristic
547C2#2144479811yescharacteristic
548C2#2144483211yescharacteristic
549C2#2144484911yescharacteristic
550C2#2144704611yescharacteristic
551C2#2144705611yescharacteristic
552C2#2144706811yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC61×#1872C2
socleC23×C61#120
prime radicalC2×#14519751C22
hypercenter#1872D61
hypocenterC61#10404
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. #21444078C2semidirect
6. #21443661C2semidirect
7. C61×#1872C2semidirect
267. #1872D61semidirect
305. C61#10404semidirect

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
#214440782
#214436612
C61×#18722
#1040461