Finite Group Databasebeta

← #29582356

Subgroups — #29582356

Order 15616.

712 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840053C211yesmaximal, characteristic, complemented
2C2×#16840052C211yesmaximal, characteristic, complemented
3#21450732C211yesmaximal, characteristic
4#21446621C211yesmaximal, characteristic, complemented
5C2×#16839491C211yesmaximal, characteristic, complemented
6#21443703C211yesmaximal, characteristic, complemented
7C2×C61×D4⋊C8C211yesmaximal, characteristic, complemented
8C2×#14519777C2211yescharacteristic
9C2×#14519751—21no—
10C2×#14519748—21no—
11C2×C4×D244C2211yescharacteristic
12#16840053—22no—
13#16840053—22no—
14#16840052—22no—
15#16840052—22no—
16C2×#14519709—21no—
17C2×#14519708—21no—
18C2×C4⋊#92418C2211yescharacteristic
19C2×#14519702—22no—
20C2×#14519699—21no—
21C2×#14519698—21no—
22#16839678—22no—
23#16839632C2211yescharacteristic
24#16839622—21no—
25#16839619—21no—
26#16839491—22no—
27C2×C4×D4×C61C2211yescharacteristic
28C2×C4⋊C8×C61C2211yescharacteristic
29C2×C4×C8×C61C2211yescharacteristic
30C61×D4⋊C8—22no—
31C22×Dic122—21no—
32C22×D244D411yescharacteristic
33C22×C22⋊D61—22no—
34C22×C4×D61—21no—
35C22×#92418—21no—
36#14519777—21no—
37#14519777—21no—
38#14519777—21no—
39#14519777D412yescomplemented
40#14519751—42no—
41#14519751—42no—
42#14519748—42no—
43#14519748—42no—
44C4×D244—21no—
45C4×D244—21no—
46C4×D244—21no—
47C4×D244—21no—
48C2×C4⋊Dic61—21no—
49C2×C4⋊Dic61—21no—
50C2×C4⋊Dic61—21no—
51C2×C4⋊Dic61—21no—
52C2×C4⋊Dic61D411yescharacteristic
53C2×C4⋊Dic61D412yes—
54C2×C22⋊Dic61—22no—
55C2×#11758198—22no—
56C2×#11758198—21no—
57#14519709—24no—
58#14519708—24no—
59C4⋊#92418—21no—
60C4⋊#92418D412yescomplemented
61#14519702—44no—
62#14519699—24no—
63#14519698—24no—
64#14519684—22no—
65C22×D4×C61D411yescharacteristic
66C23×C4×C61—21no—
67C22×C8×C61—21no—
68C22×C8×C61—21no—
69C4×D4×C61—21no—
70C4×D4×C61—21no—
71C4×D4×C61—21no—
72C4×D4×C61—21no—
73C2×C4⋊C4×C61D411yescharacteristic
74C2×C22⋊C4×C61—21no—
75C2×C42×C61C2311yescharacteristic
76C4⋊C8×C61—21no—
77C4⋊C8×C61D412yescomplemented
78C4×C8×C61—21no—
79C4×C8×C61—21no—
80C24×C61—21no—
81C23×D61—21no—
82C2×D4×C61—21no—
83C2×D4×C61—21no—
84C2×D4×C61—21no—
85C2×D4×C61—21no—
86C2×D4×C61—21no—
87C2×D4×C61SD1612yes—
88C22×C4×C61—21no—
89C22×C4×C61—41no—
90C22×C4×C61—41no—
91C22×C4×C61—41no—
92C22×C4×C61—41no—
93C22×C4×C61—41no—
94C22×C4×C61—41no—
95C22×C4×C61C2×D411yescharacteristic
96C22×C4×C61C2×D411yescharacteristic
97C22×C4×C61C2×D411yescharacteristic
98C2×C22⋊D61—44no—
99C2×C22⋊D61—44no—
100C2×C22⋊D61—82no—
101C22×Dic61—21no—
102C22×Dic61—22no—
103C22×Dic61—41no—
104C2×D244—21no—
105C2×D244—21no—
106C2×D244—21no—
107C2×D244—21no—
108C2×D244—21no—
109C2×D244SD1612yes—
110C2×C4×D61—41no—
111C2×C4×D61—41no—
112C2×C4×D61—41no—
113C2×C4×D61—41no—
114C2×C4×D61—41no—
115C2×C4×D61—41no—
116C2×Dic122—22no—
117C2×Dic122—42no—
118C2×Dic122—42no—
119C2×Dic122—41no—
120C2×C8×C61—22no—
121C2×C8×C61—22no—
122C2×C8×C61—41no—
123C2×C8×C61—41no—
124C2×C8×C61—41no—
125C2×C8×C61—41no—
126C4⋊C4×C61—21no—
127C4⋊C4×C61—21no—
128C22⋊C4×C61—41no—
129C22⋊C4×C61—41no—
130C42×C61C2×D411yescharacteristic
131C42×C61C2×D411yescharacteristic
132C42×C61C2×D411yescharacteristic
133C42×C61#4111yescharacteristic
134C22⋊Dic61—44no—
135#11758198—44no—
136#11758198—41no—
137#11758198—41no—
138C4⋊Dic61—22no—
139C4⋊Dic61—22no—
140C4⋊Dic61—21no—
141C4⋊Dic61—21no—
142C4⋊Dic61—41no—
143C4⋊Dic61—41no—
144C4⋊Dic61—41no—
145C4⋊Dic61—41no—
146C4⋊Dic61—41no—
147C4⋊Dic61—41no—
148C4⋊Dic61—42no—
149C2×#92418—22no—
150C2×#92418—41no—
151C2×#92418—41no—
152C23×C61—22no—
153C23×C61—41no—
154C23×C61—41no—
155C23×C61—41no—
156C23×C61—41no—
157C23×C61—41no—
158C23×C61—41no—
159C23×C61#12011yescharacteristic
160C22×D61—22no—
161C22×D61—41no—
162C22×D61—41no—
163C22×D61—41no—
164C22×D61—41no—
165C22×D61—41no—
166C22×D61—41no—
167D4×C61—22no—
168D4×C61—22no—
169D4×C61—41no—
170D4×C61—41no—
171C2×C4×C61—21no—
172C2×C4×C61—21no—
173C2×C4×C61—41no—
174C2×C4×C61—41no—
175C2×C4×C61—41no—
176C2×C4×C61—81no—
177C2×C4×C61—81no—
178C2×C4×C61—81no—
179C2×C4×C61—81no—
180C2×C4×C61#12011yescharacteristic
181C2×C4×C61#12011yescharacteristic
182C2×C4×C61#12111yescharacteristic
183C2×C4×C61#12111yescharacteristic
184C2×C4×C61#12111yescharacteristic
185C2×C4×C61#12711yescharacteristic
186C2×C4×C61C2×SD1611yescharacteristic
187C2×C4×C61C2×SD1611yescharacteristic
188C2×C4×C61#13511yescharacteristic
189C2×C4×C61#13511yescharacteristic
190C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
191C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
192C2×C4×C61#13711yescharacteristic
193C2×C4×C61#13711yescharacteristic
194C22⋊D61—88no—
195C2×Dic61—42no—
196C2×Dic61—41no—
197C2×Dic61—42no—
198C2×Dic61—42no—
199C2×Dic61—41no—
200C2×Dic61—41no—
201C2×Dic61—42no—
202C2×Dic61—81no—
203C2×Dic61—81no—
204D244—22no—
205D244—22no—
206D244—41no—
207D244—41no—
208C4×D61—81no—
209C4×D61—81no—
210C4×D61—81no—
211C4×D61—81no—
212Dic122—44no—
213Dic122—82no—
214C8×C61—42no—
215C8×C61—42no—
216#92418—42no—
217#10235—611nomaximal, Sylow
218C22×C61—42no—
219C22×C61—42no—
220C22×C61—42no—
221C22×C61—81no—
222C22×C61—81no—
223C22×C61—81no—
224C22×C61—81no—
225C22×C61#39211yescharacteristic
226C22×C61#45011yescharacteristic
227C22×C61#45011yescharacteristic
228C22×C61#45211yescharacteristic
229C22×C61#45211yescharacteristic
230C22×C61#45311yescharacteristic
231C22×C61#45411yescharacteristic
232C2×D61—42no—
233C2×D61—42no—
234C2×D61—42no—
235C2×D61—81no—
236C2×D61—81no—
237C2×D61—81no—
238C2×D61—81no—
239C4×C61—21no—
240C4×C61—21no—
241C4×C61—81no—
242C4×C61#44811yescharacteristic
243C4×C61#44811yescharacteristic
244C4×C61#44911yescharacteristic
245C4×C61#44911yescharacteristic
246C4×C61#46511yescharacteristic
247C4×C61#46511yescharacteristic
248C4×C61#46811yescharacteristic
249C4×C61#46811yescharacteristic
250Dic61—82no—
251Dic61—81no—
252Dic61—82no—
253C2×#476—611no—
254C2×#476—611no—
255#2537—611no—
256#1956—611no—
257C2×D4⋊C8—611no—
258C2×D4⋊C8D6111yescharacteristic, complemented
259#1296—611no—
260C2×C61—82no—
261C2×C61#162911yescharacteristic
262C2×C61#163411yescharacteristic
263C2×C61#163511yescharacteristic
264C2×C61#163511yescharacteristic
265C2×C61#200011yescharacteristic
266C2×C61#200011yescharacteristic
267C2×C61#200611yescharacteristic
268D61—82no—
269C2×C4⋊Q8—611no—
270C2×#121—1221no—
271C2×#121—1221no—
272C2×C4×D4—611no—
273C2×C4×D4C2×D6111yescharacteristic
274#476—1222no—
275#476—1222no—
276#476—1222no—
277#476—1222no—
278C2×#106—1221no—
279C2×#106—1221no—
280C2×C4⋊C8—611no—
281C2×C4⋊C8C2×D6111yescharacteristic
282C2×#103—1222no—
283C2×#102—1221no—
284C2×#102—1221no—
285C2×C4×C8C2×D6111yescharacteristic
286#394—1222no—
287#384—611no—
288#380—1221no—
289#380—1221no—
290D4⋊C8—22no—
291D4⋊C8—1222no—
292C61#1023511yescharacteristic, complemented, Sylow
293C22×Q8—1221no—
294C22×D4—611no—
295C22×D4—1222no—
296C22×D4D24411yescharacteristic
297C23×C4—21no—
298C23×C4—1221no—
299C22×C8—21no—
300C22×C8—21no—
301C22×C8—1221no—
302C4⋊Q8—612no—
303C4⋊Q8—1221no—
304C4⋊Q8—1221no—
305C4⋊Q8—1221no—
306#121—2442no—
307#121—2442no—
308#121—2442no—
309#121—2442no—
310C4×D4—21no—
311C4×D4—21no—
312C4×D4—21no—
313C4×D4—21no—
314C4×D4—1221no—
315C4×D4—1221no—
316C4×D4—1221no—
317C4×D4—1221no—
318C2×C4⋊C4—611no—
319C2×C4⋊C4—612no—
320C2×C4⋊C4—1221no—
321C2×C4⋊C4—1221no—
322C2×C4⋊C4—1221no—
323C2×C4⋊C4—1221no—
324C2×C4⋊C4D24411yescharacteristic
325C2×C22⋊C4—21no—
326C2×C22⋊C4—1222no—
327C2×C22⋊C4—1222no—
328C2×C22⋊C4—1221no—
329C2×C42C22×D6111yescharacteristic
330#106—1224no—
331#106—1224no—
332C4⋊C8—21no—
333C4⋊C8—612no—
334C4⋊C8—1221no—
335C4⋊C8C22⋊D6112yescomplemented
336#103—2444no—
337#102—1224no—
338#102—1224no—
339C4×C8—21no—
340C4×C8—21no—
341#95—1222no—
342C24—21no—
343C24—1221no—
344C2×Q8—1222no—
345C2×Q8—2442no—
346C2×Q8—2442no—
347C2×Q8—2441no—
348C2×D4—21no—
349C2×D4—21no—
350C2×D4—21no—
351C2×D4—21no—
352C2×D4—21no—
353C2×D4—612no—
354C2×D4—1221no—
355C2×D4—1221no—
356C2×D4—1221no—
357C2×D4—1221no—
358C2×D4—1221no—
359C2×D4—4882no—
360C2×D4—2444no—
361C2×D4—2444no—
362C2×D4#1175819012yes—
363C22×C4—21no—
364C22×C4—41no—
365C22×C4—41no—
366C22×C4—41no—
367C22×C4—41no—
368C22×C4—41no—
369C22×C4—41no—
370C22×C4—1221no—
371C22×C4—1222no—
372C22×C4—2441no—
373C22×C4—2441no—
374C22×C4—2441no—
375C22×C4—2441no—
376C22×C4—2441no—
377C22×C4—2441no—
378C22×C4—2441no—
379C22×C4C2×D24411yescharacteristic
380C22×C4D4×D6111yescharacteristic
381C22×C4D4×D6111yescharacteristic
382C2×C8—22no—
383C2×C8—22no—
384C2×C8—41no—
385C2×C8—41no—
386C2×C8—41no—
387C2×C8—41no—
388C2×C8—1222no—
389C2×C8—2441no—
390C2×C8—2441no—
391C4⋊C4—21no—
392C4⋊C4—21no—
393C4⋊C4—1222no—
394C4⋊C4—1221no—
395C4⋊C4—1222no—
396C4⋊C4—1221no—
397C4⋊C4—2442no—
398C4⋊C4—2441no—
399C4⋊C4—2441no—
400C4⋊C4—2441no—
401C4⋊C4—2441no—
402C4⋊C4—2441no—
403C4⋊C4—2441no—
404C22⋊C4—41no—
405C22⋊C4—41no—
406C22⋊C4—2444no—
407C22⋊C4—2444no—
408C22⋊C4—2441no—
409C22⋊C4—2441no—
410C42#1175822211yescharacteristic
411C42D4×D6111yescharacteristic
412C42D4×D6111yescharacteristic
413C42C2×C22⋊D6111yescharacteristic
414C23—22no—
415C23—41no—
416C23—41no—
417C23—41no—
418C23—41no—
419C23—41no—
420C23—41no—
421C23—1222no—
422C23—2441no—
423C23—2441no—
424C23—2441no—
425C23—2441no—
426C23—2441no—
427C23—2441no—
428C23#1451974711yescharacteristic
429Q8—4882no—
430Q8—2444no—
431D4—22no—
432D4—22no—
433D4—41no—
434D4—41no—
435D4—1222no—
436D4—1222no—
437D4—4888no—
438D4—2441no—
439D4—2441no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—81no—
446C2×C4—81no—
447C2×C4—81no—
448C2×C4—81no—
449C2×C4—4881no—
450C2×C4—4881no—
451C2×C4—4881no—
452C2×C4—4881no—
453C2×C4—4881no—
454C2×C4—4881no—
455C2×C4—2442no—
456C2×C4—2441no—
457C2×C4—2442no—
458C2×C4—2441no—
459C2×C4—2441no—
460C2×C4—2442no—
461C2×C4—2442no—
462C2×C4#1451974511yescharacteristic
463C2×C4#1451974711yescharacteristic
464C2×C4#1451975011yescharacteristic
465C2×C4#1451975011yescharacteristic
466C2×C4#1451975111yescharacteristic
467C2×C4#1451977311yescharacteristic
468C2×C4SD16×D6111yescharacteristic
469C2×C4C2×#1175819011yescharacteristic
470C2×C4#1451979611yescharacteristic
471C2×C4#1451979911yescharacteristic
472C2×C4#1451980111yescharacteristic
473C2×C4#1451980511yescharacteristic
474C2×C4#1451980611yescharacteristic
475C2×C4#1451981011yescharacteristic
476C8—42no—
477C8—42no—
478C8—2442no—
479C22—42no—
480C22—42no—
481C22—42no—
482C22—81no—
483C22—81no—
484C22—81no—
485C22—81no—
486C22—4881no—
487C22—4881no—
488C22—4881no—
489C22—4881no—
490C22—2442no—
491C22—2442no—
492C22—2442no—
493C22#1683967111yescharacteristic
494C22#1683991411yescharacteristic
495C22#1683991511yescharacteristic
496C22#1683992511yescharacteristic
497C22#1683992611yescharacteristic
498C22#1683993111yescharacteristic
499C22#1683993611yescharacteristic
500C4—21no—
501C4—21no—
502C4—81no—
503C4—4882no—
504C4—4881no—
505C4—4882no—
506C4#1683989911yescharacteristic
507C4#1683990311yescharacteristic
508C4#1683990411yescharacteristic
509C4#1683990911yescharacteristic
510C4#1683999011yescharacteristic
511C4#1683999111yescharacteristic
512C4#1684000711yescharacteristic
513C4#1684000811yescharacteristic
514C2—82no—
515C2—4882no—
516C2#2144493711yescharacteristic
517C2#2144496611yescharacteristic
518C2#2144497211yescharacteristic
519C2#2144497311yescharacteristic
520C2#2144682311yescharacteristic
521C2#2144682411yescharacteristic
522C2#2144686211yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC2×C61×D4⋊C8C2
socleC23×C61#120
prime radical#21450732C2
hypercenterC2×D4⋊C8D61
hypocenterC61#10235
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×D4⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×#16840053C2semidirect
2. C2×#16840052C2semidirect
4. #21446621C2semidirect
5. C2×#16839491C2semidirect
6. #21443703C2semidirect
7. C2×C61×D4⋊C8C2semidirect
39. #14519777D4semidirect
60. C4⋊#92418D4semidirect
77. C4⋊C8×C61D4semidirect
258. C2×D4⋊C8D61semidirect
292. C61#10235semidirect
335. C4⋊C8C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168400532
C2×#168400522
#214507322
#214466212
C2×#168394912
#214437032
C2×C61×D4⋊C82
#1023561