Finite Group Databasebeta

← #29646058

Subgroups — #29646058

Order 15616.

1040 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840367C211yesmaximal, characteristic
2#21454859C211yesmaximal, characteristic, complemented
3#21454842C211yesmaximal, characteristic, complemented
4#21444177C214yesmaximal, complemented
5#21444166C214yesmaximal, complemented
6#21444139C211yesmaximal, characteristic, complemented
7#21444139C211yesmaximal, characteristic, complemented
8#21444133C211yesmaximal, characteristic, complemented
9C61×#1458C211yesmaximal, characteristic, complemented
10#16840367—22no—
11#16840367—22no—
12#16840367—22no—
13#16840367—22no—
14C2×#14519774C411yescharacteristic
15C2×#14519769C411yescharacteristic
16C2×#14519762C412yes—
17C2×#14519762C2212yes—
18C2×#14519751C411yescharacteristic
19C2×#14519751C411yescharacteristic
20C2×#14519750C412yes—
21C2×#14519750C2212yes—
22C2×C4×D244C2211yescharacteristic
23C2×C4×D244C2211yescharacteristic
24#16839841—22no—
25#16839839—22no—
26C8×D244—22no—
27#16839827—22no—
28#16839815C2211yescharacteristic
29#16839815C2211yescharacteristic
30#16839724C2214yes—
31C22⋊C8×D61C2214yes—
32#16839488C2212yes—
33#16839486C2212yes—
34#16839485C2214yes—
35#16839485C2214yes—
36C2×#117×C61C2211yescharacteristic
37C61×#431C2211yescharacteristic
38C61×#431C2211yescharacteristic
39C61×#324C2212yes—
40C61×#323C2212yes—
41C22×D244C2×C411yescharacteristic
42C22×D244C2×C411yescharacteristic
43C22×D244C2×C412yes—
44C22×D244C2×C412yes—
45C22×C22⋊D61C2×C412yes—
46C22×C22⋊D61C2×C412yes—
47C22×C4×D61C2×C412yes—
48C22×C4×D61C2312yes—
49C2×#11758189—24no—
50C2×C8×D61—24no—
51#14519774—22no—
52#14519774—22no—
53#14519769—22no—
54#14519769—22no—
55#14519762—24no—
56#14519762—24no—
57#14519762—24no—
58#14519762—24no—
59#14519751—22no—
60#14519751—22no—
61#14519751—22no—
62#14519751—22no—
63#14519750—24no—
64#14519750—24no—
65#14519750—24no—
66#14519750—24no—
67C4×D244—21no—
68C4×D244—21no—
69C4×D244—21no—
70C4×D244—21no—
71C4×D244D412yes—
72C4×D244D412yes—
73C4×D244D412yes—
74C4×D244D412yes—
75C2×C4⋊Dic61C2×C411yescharacteristic
76C2×C4⋊Dic61C2×C411yescharacteristic
77C2×#11758196C2×C412yes—
78C2×#11758196C2×C412yes—
79C2×#11758198C2×C412yes—
80C2×#11758198C2×C412yes—
81C2×#11758198C2×C412yes—
82C2×#11758198C2312yes—
83C4⋊#92418—21no—
84C4⋊#92418—21no—
85C22⋊#92418C2312yes—
86C22⋊#92418C2312yes—
87#14519689—24no—
88#14519689—24no—
89C4×#92418—21no—
90C4×#92418—21no—
91C23×C4×C61C2×C411yescharacteristic
92#117×C61—21no—
93#117×C61—21no—
94#117×C61—21no—
95#117×C61—21no—
96C2×C4⋊C4×C61C2×C411yescharacteristic
97C2×C4⋊C4×C61C2311yescharacteristic
98C2×C22⋊C4×C61C2×C411yescharacteristic
99C2×C22⋊C4×C61C2311yescharacteristic
100C2×C42×C61C2×C411yescharacteristic
101C2×C42×C61C2311yescharacteristic
102C4⋊C8×C61—21no—
103C4⋊C8×C61—21no—
104C22⋊C8×C61C2312yes—
105C22⋊C8×C61C2312yes—
106C4×C8×C61—21no—
107C4×C8×C61—21no—
108C24×C61C22×C411yescharacteristic
109C23×D61C22×C412yes—
110C23×D61C22×C412yes—
111C22×C4×C61—21no—
112C22×C4×C61—21no—
113C22×C4×C61—22no—
114C22×C4×C61—22no—
115C22×C4×C61C22×C411yescharacteristic
116C22×C4×C61C22×C411yescharacteristic
117C22×C4×C61C22×C411yescharacteristic
118C22×C4×C61C22×C411yescharacteristic
119C22×C4×C61C22×C411yescharacteristic
120C22×C4×C61C2411yescharacteristic
121C2×C22⋊D61—24no—
122C2×C22⋊D61—24no—
123C2×C22⋊D61—82no—
124C2×C22⋊D61—82no—
125C22×Dic61C22×C412yes—
126C22×Dic61C22×C412yes—
127C2×D244—22no—
128C2×D244—22no—
129C2×D244—21no—
130C2×D244—21no—
131C2×D244—22no—
132C2×D244—22no—
133C2×D244—24no—
134C2×D244—24no—
135C2×D244—82no—
136C2×D244—82no—
137C2×D244C22⋊C412yes—
138C2×D244C22⋊C412yes—
139C2×C4×D61—22no—
140C2×C4×D61—22no—
141C2×C4×D61—82no—
142C2×C4×D61—82no—
143C2×C4×D61C2×D414yes—
144C2×C4×D61C2×D414yes—
145C2×C8×C61—22no—
146C2×C8×C61—22no—
147C4⋊C4×C61—21no—
148C4⋊C4×C61—21no—
149C4⋊C4×C61—21no—
150C4⋊C4×C61—21no—
151C22⋊C4×C61—21no—
152C22⋊C4×C61—21no—
153C22⋊C4×C61—21no—
154C22⋊C4×C61—21no—
155C42×C61—21no—
156C42×C61—21no—
157C42×C61C2×D411yescharacteristic
158C42×C61C2×D411yescharacteristic
159C42×C61C2×D411yescharacteristic
160C42×C61C2×D411yescharacteristic
161#11758198—24no—
162#11758198—22no—
163#11758198—22no—
164#11758198—24no—
165#11758198C22⋊C414yes—
166#11758198C22⋊C414yes—
167C4⋊Dic61—21no—
168C4⋊Dic61—21no—
169C4⋊Dic61C22⋊C412yes—
170C4⋊Dic61C22⋊C412yes—
171#11758196—24no—
172#11758196—24no—
173C2×#92418—22no—
174C2×#92418—22no—
175#11758189—84no—
176C8×D61—84no—
177C23×C61—21no—
178C23×C61—21no—
179C23×C61—21no—
180C23×C61—41no—
181C23×C61—41no—
182C23×C61C23×C411yescharacteristic
183C22×D61—22no—
184C22×D61—22no—
185C22×D61—22no—
186C22×D61—22no—
187C22×D61—22no—
188C22×D61—42no—
189C22×D61—42no—
190C22×D61—42no—
191C22×D61—42no—
192C22×D61C2×C22⋊C414yes—
193C2×C4×C61—21no—
194C2×C4×C61—21no—
195C2×C4×C61—21no—
196C2×C4×C61—21no—
197C2×C4×C61—21no—
198C2×C4×C61—41no—
199C2×C4×C61—41no—
200C2×C4×C61—42no—
201C2×C4×C61—42no—
202C2×C4×C61—41no—
203C2×C4×C61—41no—
204C2×C4×C61C2×C22⋊C411yescharacteristic
205C2×C4×C61C2×C22⋊C411yescharacteristic
206C2×C4×C61C2×C22⋊C411yescharacteristic
207C2×C4×C61C2×C22⋊C411yescharacteristic
208C2×C4×C61#13112yes—
209C2×C4×C61#13112yes—
210C2×C4×C61C22×D411yescharacteristic
211C2×C4×C61C22×D411yescharacteristic
212C22⋊D61—84no—
213C22⋊D61—84no—
214C2×Dic61—22no—
215C2×Dic61—42no—
216C2×Dic61—42no—
217C2×Dic61C2×C22⋊C414yes—
218D244—24no—
219D244—24no—
220D244—42no—
221D244—42no—
222D244—84no—
223D244—84no—
224C4×D61—44no—
225C4×D61—44no—
226C4×D61—82no—
227C4×D61—82no—
228C8×C61—42no—
229C8×C61—42no—
230#92418—42no—
231#92418—42no—
232#17389—611nomaximal, Sylow
233C22×C61—21no—
234C22×C61—21no—
235C22×C61—41no—
236C22×C61—41no—
237C22×C61—41no—
238C22×C61—81no—
239C22×C61—81no—
240C22×C61C22×C22⋊C411yescharacteristic
241C22×C61C2×#13111yescharacteristic
242C22×C61C2×#13111yescharacteristic
243C2×D61—24no—
244C2×D61—24no—
245C2×D61—24no—
246C2×D61—42no—
247C2×D61—42no—
248C2×D61—42no—
249C2×D61—82no—
250C2×D61—82no—
251C2×D61—82no—
252C2×D61—82no—
253C4×C61—21no—
254C4×C61—21no—
255C4×C61—21no—
256C4×C61—21no—
257C4×C61—41no—
258C4×C61—41no—
259C4×C61—41no—
260C4×C61#40812yes—
261C4×C61#40812yes—
262Dic61—24no—
263Dic61—42no—
264C2×#540—611no—
265#2975—611no—
266#2972—611no—
267#1471—614no—
268#1468—614no—
269#1460—611no—
270#1460—611no—
271#1458—611no—
272#1458D6111yescharacteristic, complemented
273C2×C61—21no—
274C2×C61—21no—
275C2×C61—81no—
276C2×C61C2×#40811yescharacteristic
277C2×C61#288311yescharacteristic
278C2×C61#288811yescharacteristic
279D61—44no—
280D61—82no—
281#540—1222no—
282#540—1222no—
283#540—1222no—
284#540—1222no—
285C2×#127—611no—
286C2×#125—611no—
287C2×#123—612no—
288C2×#123—612no—
289C2×#121—611no—
290C2×#121—611no—
291C2×#121—612no—
292C2×#121—612no—
293C2×C4×D4—611no—
294C2×C4×D4—611no—
295C2×#117C2×D6111yescharacteristic
296#436—1222no—
297#436—1222no—
298C8×D4—1222no—
299C8×D4—1222no—
300#431—611no—
301#431—611no—
302#431C2×D6111yescharacteristic
303#431C2×D6111yescharacteristic
304#407—614no—
305C2×C22⋊C8—614no—
306#324—612no—
307#324C2×D6112yes—
308#323—612no—
309#323—614no—
310#323—614no—
311#323C2×D6112yes—
312C61#1738911yescharacteristic, complemented, Sylow
313C22×D4—612no—
314C22×D4—612no—
315C22×D4—611no—
316C22×D4—611no—
317C22×D4—612no—
318C22×D4—612no—
319C23×C4—612no—
320C23×C4—612no—
321C23×C4C4×D6111yescharacteristic
322C2×M16—1224no—
323C22×C8—1224no—
324#127—1222no—
325#127—1222no—
326#125—1222no—
327#125—1222no—
328#123—1224no—
329#123—1224no—
330#123—1224no—
331#123—1224no—
332#121—1224no—
333#121—1224no—
334#121—1224no—
335#121—1224no—
336#121—1222no—
337#121—1222no—
338#121—1222no—
339#121—1222no—
340C4×D4—612no—
341C4×D4—612no—
342C4×D4—612no—
343C4×D4—612no—
344C4×D4—1221no—
345C4×D4—1221no—
346C4×D4—1221no—
347C4×D4—1221no—
348#117—21no—
349#117—21no—
350#117—21no—
351#117—21no—
352C2×C4⋊C4—611no—
353C2×C4⋊C4—611no—
354C2×C4⋊C4—612no—
355C2×C4⋊C4—612no—
356C2×C4⋊C4C4×D6111yescharacteristic
357C2×C4⋊C4C22×D6111yescharacteristic
358C2×C22⋊C4—612no—
359C2×C22⋊C4—612no—
360C2×C22⋊C4—612no—
361C2×C22⋊C4—612no—
362C2×C22⋊C4C4×D6111yescharacteristic
363C2×C22⋊C4C22×D6111yescharacteristic
364C2×C42C4×D6111yescharacteristic
365C2×C42C22×D6111yescharacteristic
366C4⋊C8—21no—
367C4⋊C8—21no—
368C4⋊C8—1221no—
369C4⋊C8—1221no—
370C22⋊C8—612no—
371C22⋊C8—612no—
372C22⋊C8—1224no—
373C22⋊C8—1224no—
374C22⋊C8C22×D6112yes—
375C22⋊C8C22×D6112yes—
376C4×C8—21no—
377C4×C8—21no—
378C4×C8—1221no—
379C4×C8—1221no—
380C24—612no—
381C24—612no—
382C24C2×C4×D6111yescharacteristic
383C2×D4—612no—
384C2×D4—612no—
385C2×D4—1224no—
386C2×D4—1224no—
387C2×D4—1224no—
388C2×D4—1224no—
389C2×D4—1221no—
390C2×D4—1221no—
391C2×D4—1222no—
392C2×D4—1222no—
393C2×D4—1222no—
394C2×D4—1222no—
395C2×D4—4882no—
396C2×D4—4882no—
397C2×D4—4882no—
398C2×D4—4882no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—612no—
404C22×C4—614no—
405C22×C4—614no—
406C22×C4—612no—
407C22×C4—1222no—
408C22×C4—1222no—
409C22×C4—4882no—
410C22×C4—4882no—
411C22×C4C2×C4×D6111yescharacteristic
412C22×C4C2×C4×D6111yescharacteristic
413C22×C4C2×C4×D6111yescharacteristic
414C22×C4C2×C4×D6111yescharacteristic
415C22×C4C2×C4×D6111yescharacteristic
416C22×C4C23×D6111yescharacteristic
417M16—4884no—
418C2×C8—22no—
419C2×C8—22no—
420C2×C8—1222no—
421C2×C8—1222no—
422C2×C8—4884no—
423C4⋊C4—21no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—612no—
428C4⋊C4—612no—
429C4⋊C4—1224no—
430C4⋊C4—1224no—
431C4⋊C4—1221no—
432C4⋊C4—1221no—
433C22⋊C4—21no—
434C22⋊C4—21no—
435C22⋊C4—21no—
436C22⋊C4—21no—
437C22⋊C4—614no—
438C22⋊C4—614no—
439C22⋊C4—1224no—
440C22⋊C4—1224no—
441C22⋊C4—1222no—
442C22⋊C4—1222no—
443C42—21no—
444C42—21no—
445C42D4×D6111yescharacteristic
446C42D4×D6111yescharacteristic
447C42D4×D6111yescharacteristic
448C42D4×D6111yescharacteristic
449C23—21no—
450C23—21no—
451C23—21no—
452C23—41no—
453C23—41no—
454C23—614no—
455C23—1222no—
456C23—1222no—
457C23—1222no—
458C23—1222no—
459C23—1222no—
460C23—2442no—
461C23—2442no—
462C23—2442no—
463C23—2442no—
464C23C22×C4×D6111yescharacteristic
465D4—1224no—
466D4—1224no—
467D4—4884no—
468D4—4884no—
469D4—4884no—
470D4—4884no—
471D4—2442no—
472D4—2442no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—42no—
481C2×C4—42no—
482C2×C4—41no—
483C2×C4—41no—
484C2×C4—614no—
485C2×C4—1222no—
486C2×C4—4882no—
487C2×C4—4882no—
488C2×C4—2444no—
489C2×C4—2444no—
490C2×C4—2442no—
491C2×C4—2442no—
492C2×C4C22⋊C4×D6111yescharacteristic
493C2×C4C22⋊C4×D6111yescharacteristic
494C2×C4C22⋊C4×D6111yescharacteristic
495C2×C4C22⋊C4×D6111yescharacteristic
496C2×C4#1451978312yes—
497C2×C4#1451978512yes—
498C2×C4C2×D4×D6111yescharacteristic
499C2×C4C2×D4×D6111yescharacteristic
500C8—42no—
501C8—42no—
502C8—2442no—
503C8—2442no—
504C22—21no—
505C22—21no—
506C22—41no—
507C22—41no—
508C22—41no—
509C22—81no—
510C22—81no—
511C22—1224no—
512C22—1224no—
513C22—1224no—
514C22—4882no—
515C22—4882no—
516C22—4882no—
517C22—4882no—
518C22—2442no—
519C22—2442no—
520C22—2442no—
521C22C2×C22⋊C4×D6111yescharacteristic
522C22C2×#1451978311yescharacteristic
523C22C2×#1451978511yescharacteristic
524C4—21no—
525C4—21no—
526C4—21no—
527C4—21no—
528C4—41no—
529C4—41no—
530C4—41no—
531C4—1224no—
532C4—2442no—
533C4#1683972712yes—
534C4#1683972712yes—
535C2—21no—
536C2—21no—
537C2—81no—
538C2—4882no—
539C2—2444no—
540C2C2×#1683972711yescharacteristic
541C2#2145427811yescharacteristic
542C2#2145429611yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1458C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840367C2
cosocleC22×C4×C61C24
hypercenter#1458D61
hypocenterC61#17389
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1458

Complements

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

NH ≅ G/Ntype
2. #21454859C2semidirect
3. #21454842C2semidirect
4. #21444177C2semidirect
5. #21444166C2semidirect
6. #21444139C2semidirect
7. #21444139C2semidirect
8. #21444133C2semidirect
9. C61×#1458C2semidirect
272. #1458D61semidirect
312. C61#17389semidirect

Maximal subgroups

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

subgroupindex
C2×#168403672
#214548592
#214548422
#214441772
#214441662
#214441392
#214441332
C61×#14582
#1738961