Finite Group Databasebeta

← #29646232

Subgroups — #29646232

Order 15616.

1008 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840458C211yesmaximal, characteristic
2#21454479C212yesmaximal, complemented
3#21444187C214yesmaximal, complemented
4#21444180C212yesmaximal, complemented
5#21444158C212yesmaximal, complemented
6#21444138C212yesmaximal, complemented
7#21444137C211yesmaximal, characteristic, complemented
8C61×#1465C211yesmaximal, characteristic, complemented
9#16840458—22no—
10#16840458—22no—
11#16840458—24no—
12C2×#14519772C2212yes—
13C2×#14519769C411yescharacteristic
14C2×#14519759C412yes—
15C2×#14519751C411yescharacteristic
16C2×#14519751C2211yescharacteristic
17C2×#14519749C412yes—
18C2×C4×D244C411yescharacteristic
19C2×#14519737C2212yes—
20C2×#14519736C2211yescharacteristic
21C22×C4⋊Dic61C411yescharacteristic
22#16839820—24no—
23#16839816C2214yes—
24#16839812C2214yes—
25#16839790—22no—
26C2×C22⋊#92418C2212yes—
27#16839720—22no—
28#16839488C2212yes—
29#16839486C2211yescharacteristic
30#16839486C2211yescharacteristic
31#16839485C2214yes—
32#16839485C2214yes—
33C2×C4×D4×C61C2211yescharacteristic
34C61×#407C2212yes—
35C61×#324C2212yes—
36C61×#323C2212yes—
37C22×D244C2×C411yescharacteristic
38C22×C22⋊D61C2×C412yes—
39C22×C22⋊D61C2×C412yes—
40C23×Dic61C2×C412yes—
41C22×C4×D61C2×C412yes—
42C22×#92418—22no—
43#14519772—24no—
44#14519772—24no—
45#14519769—22no—
46#14519769—22no—
47#14519759—24no—
48#14519759—24no—
49#14519751—22no—
50#14519751—22no—
51#14519751—22no—
52#14519751—22no—
53#14519749—24no—
54#14519749—24no—
55C4×D244—22no—
56C4×D244—21no—
57C4×D244—21no—
58#14519737—24no—
59#14519737—24no—
60#14519736D412yes—
61#14519736D412yes—
62#14519736D414yes—
63C2×C4⋊Dic61—22no—
64C2×C4⋊Dic61—21no—
65C2×C4⋊Dic61—21no—
66C2×C4⋊Dic61C2×C411yescharacteristic
67C2×C4⋊Dic61C2×C412yes—
68C2×C4⋊Dic61C2×C411yescharacteristic
69C2×C4⋊Dic61C2×C411yescharacteristic
70C2×#11758196C2×C412yes—
71C2×#11758196C2×C412yes—
72C2×C22⋊Dic61C2×C412yes—
73C2×#11758198C2×C412yes—
74C2×#11758198C2×C412yes—
75C2×#11758198C2312yes—
76C2×C4×Dic61C2312yes—
77#14519706—24no—
78#14519706—24no—
79C22⋊#92418—22no—
80C22⋊#92418C2312yes—
81C22⋊#92418C2312yes—
82#14519687—24no—
83C8×Dic61—24no—
84C22×D4×C61C2×C411yescharacteristic
85C23×C4×C61C2×C411yescharacteristic
86C23×C4×C61C2311yescharacteristic
87C2×M16×C61—22no—
88C4×D4×C61—22no—
89C4×D4×C61—22no—
90C2×C4⋊C4×C61C2311yescharacteristic
91C2×C22⋊C4×C61C2×C411yescharacteristic
92C2×C22⋊C4×C61C2311yescharacteristic
93C2×C42×C61C2×C411yescharacteristic
94C22⋊C8×C61—22no—
95C22⋊C8×C61C2314yes—
96C24×C61C22×C411yescharacteristic
97C24×C61C22×C411yescharacteristic
98C23×D61C22×C412yes—
99C2×D4×C61—22no—
100C2×D4×C61—22no—
101C2×D4×C61—41no—
102C22×C4×C61—21no—
103C22×C4×C61—21no—
104C22×C4×C61—42no—
105C22×C4×C61—42no—
106C22×C4×C61C22×C411yescharacteristic
107C22×C4×C61C22×C411yescharacteristic
108C22×C4×C61C22×C411yescharacteristic
109C22×C4×C61C22×C411yescharacteristic
110C22×C4×C61C2×D412yes—
111C22×C4×C61C2×D412yes—
112C22×C4×C61C2411yescharacteristic
113C2×C22⋊D61—24no—
114C2×C22⋊D61—24no—
115C2×C22⋊D61—24no—
116C2×C22⋊D61—42no—
117C2×C22⋊D61—82no—
118C22×Dic61—22no—
119C22×Dic61—22no—
120C22×Dic61—82no—
121C22×Dic61C22×C412yes—
122C22×Dic61C22×C412yes—
123C22×Dic61C22×C412yes—
124C2×D244—21no—
125C2×D244—21no—
126C2×D244—42no—
127C2×C4×D61—22no—
128C2×C4×D61—22no—
129C2×C4×D61—82no—
130M16×C61—44no—
131C2×C8×C61—24no—
132C4⋊C4×C61—22no—
133C22⋊C4×C61—22no—
134C22⋊C4×C61—22no—
135C42×C61—21no—
136C42×C61—21no—
137C22⋊Dic61C22⋊C414yes—
138C22⋊Dic61C22⋊C414yes—
139#11758198—24no—
140#11758198—22no—
141#11758198—22no—
142#11758198—24no—
143C4⋊Dic61—21no—
144C4⋊Dic61—21no—
145C4⋊Dic61—22no—
146C4⋊Dic61—22no—
147C4⋊Dic61C22⋊C412yes—
148C4⋊Dic61C22⋊C411yescharacteristic
149C4⋊Dic61C22⋊C411yescharacteristic
150C4⋊Dic61C22⋊C412yes—
151C4⋊Dic61C22⋊C412yes—
152#11758196—24no—
153#11758196—24no—
154C4×Dic61C2×D414yes—
155C4×Dic61C2×D414yes—
156C2×#92418—22no—
157C2×#92418—22no—
158C2×#92418—44no—
159C23×C61—21no—
160C23×C61—21no—
161C23×C61—21no—
162C23×C61—21no—
163C23×C61—41no—
164C23×C61—41no—
165C23×C61—41no—
166C23×C61—41no—
167C23×C61C2×C22⋊C412yes—
168C23×C61#13112yes—
169C23×C61C23×C411yescharacteristic
170C22×D61—22no—
171C22×D61—22no—
172C22×D61—22no—
173C22×D61—42no—
174C22×D61—42no—
175D4×C61—44no—
176C2×C4×C61—24no—
177C2×C4×C61—22no—
178C2×C4×C61—21no—
179C2×C4×C61—21no—
180C2×C4×C61—21no—
181C2×C4×C61—21no—
182C2×C4×C61—21no—
183C2×C4×C61—42no—
184C2×C4×C61—41no—
185C2×C4×C61—42no—
186C2×C4×C61—42no—
187C2×C4×C61—41no—
188C2×C4×C61—41no—
189C2×C4×C61C2×C22⋊C411yescharacteristic
190C2×C4×C61C2×C22⋊C411yescharacteristic
191C2×C4×C61C22×D412yes—
192C22⋊D61—48no—
193C22⋊D61—84no—
194C2×Dic61—22no—
195C2×Dic61—22no—
196C2×Dic61—22no—
197C2×Dic61—42no—
198C2×Dic61—42no—
199C2×Dic61—82no—
200C2×Dic61—82no—
201C2×Dic61C2×C22⋊C414yes—
202C2×Dic61C2×C22⋊C412yes—
203C2×Dic61C2×C22⋊C412yes—
204D244—42no—
205D244—42no—
206C4×D61—82no—
207C4×D61—82no—
208C8×C61—44no—
209#92418—42no—
210#92418—42no—
211#17415—611nomaximal, Sylow
212C22×C61—21no—
213C22×C61—21no—
214C22×C61—22no—
215C22×C61—22no—
216C22×C61—22no—
217C22×C61—22no—
218C22×C61—42no—
219C22×C61—42no—
220C22×C61—41no—
221C22×C61—41no—
222C22×C61—81no—
223C22×C61—81no—
224C22×C61C22×C22⋊C411yescharacteristic
225C22×C61C2×#13111yescharacteristic
226C22×C61#56811yescharacteristic
227C2×D61—42no—
228C2×D61—42no—
229C2×D61—42no—
230C2×D61—82no—
231C2×D61—82no—
232C4×C61—22no—
233C4×C61—21no—
234C4×C61—41no—
235C4×C61—41no—
236C4×C61—41no—
237C4×C61#41012yes—
238Dic61—24no—
239Dic61—22no—
240Dic61—22no—
241Dic61—42no—
242C2×#553—611no—
243#2924—612no—
244#1473—614no—
245#1471—612no—
246#1466—612no—
247#1465D6111yescharacteristic, complemented
248#1460—612no—
249#1459—611no—
250C2×C61—21no—
251C2×C61—21no—
252C2×C61—42no—
253C2×C61—42no—
254C2×C61#288011yescharacteristic
255C2×C61C2×#41011yescharacteristic
256C2×C61#288811yescharacteristic
257D61—82no—
258#553—1222no—
259#553—1222no—
260#553—1224no—
261C2×#126—612no—
262C2×#125—611no—
263C2×#123—612no—
264C2×#121—612no—
265C2×#121—611no—
266C2×#121—611no—
267C2×C4×D4—612no—
268C2×C4×D4—611no—
269C2×C4×D4C2×D6111yescharacteristic
270C2×#117—611no—
271C22×C4⋊C4—611no—
272#433—1224no—
273#432—614no—
274#431—614no—
275#424—1222no—
276#407C2×D6112yes—
277C2×C22⋊C8—612no—
278#405—1222no—
279#324—612no—
280#324C2×D6112yes—
281#323—611no—
282#323—611no—
283#323—614no—
284#323—614no—
285#323C2×D6112yes—
286C61#1741511yescharacteristic, complemented, Sylow
287C22×D4—612no—
288C22×D4—612no—
289C22×D4—611no—
290C22×D4C4×D6111yescharacteristic
291C23×C4—612no—
292C23×C4—612no—
293C23×C4C4×D6111yescharacteristic
294C23×C4C22×D6111yescharacteristic
295C2×M16—22no—
296C22×C8—1222no—
297#126—1224no—
298#126—1224no—
299#125—1222no—
300#125—1222no—
301#123—1224no—
302#123—1224no—
303#121—1224no—
304#121—1224no—
305#121—1222no—
306#121—1222no—
307#121—1222no—
308#121—1222no—
309C4×D4—22no—
310C4×D4—22no—
311C4×D4—1222no—
312C4×D4—1221no—
313C4×D4—1221no—
314C4×D4—1224no—
315C4×D4—1224no—
316#117—612no—
317#117—612no—
318#117—614no—
319C2×C4⋊C4—611no—
320C2×C4⋊C4—611no—
321C2×C4⋊C4—611no—
322C2×C4⋊C4—612no—
323C2×C4⋊C4—612no—
324C2×C4⋊C4—612no—
325C2×C4⋊C4—1222no—
326C2×C4⋊C4—1221no—
327C2×C4⋊C4—1221no—
328C2×C4⋊C4C22×D6111yescharacteristic
329C2×C22⋊C4—612no—
330C2×C22⋊C4—612no—
331C2×C22⋊C4—612no—
332C2×C22⋊C4—612no—
333C2×C22⋊C4C4×D6111yescharacteristic
334C2×C22⋊C4C22×D6111yescharacteristic
335C2×C42—612no—
336C2×C42C4×D6111yescharacteristic
337C4⋊C8—1224no—
338C4⋊C8—1224no—
339C22⋊C8—22no—
340C22⋊C8—612no—
341C22⋊C8—612no—
342C22⋊C8—1222no—
343C22⋊C8C22×D6114yes—
344#97—1224no—
345C4×C8—1224no—
346C24—612no—
347C24C2×C4×D6111yescharacteristic
348C24C2×C4×D6111yescharacteristic
349C2×D4—22no—
350C2×D4—22no—
351C2×D4—41no—
352C2×D4—1224no—
353C2×D4—1224no—
354C2×D4—1224no—
355C2×D4—1221no—
356C2×D4—1221no—
357C2×D4—4882no—
358C2×D4—2442no—
359C2×D4—2442no—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—42no—
363C22×C4—42no—
364C22×C4—612no—
365C22×C4—612no—
366C22×C4—612no—
367C22×C4—1222no—
368C22×C4—1222no—
369C22×C4—1222no—
370C22×C4—1222no—
371C22×C4—4882no—
372C22×C4—4882no—
373C22×C4C2×C4×D6111yescharacteristic
374C22×C4C2×C4×D6111yescharacteristic
375C22×C4C2×C4×D6111yescharacteristic
376C22×C4C2×C4×D6111yescharacteristic
377C22×C4D4×D6112yes—
378C22×C4D4×D6112yes—
379C22×C4C23×D6111yescharacteristic
380M16—44no—
381C2×C8—24no—
382C2×C8—1222no—
383C2×C8—1222no—
384C2×C8—2444no—
385C4⋊C4—22no—
386C4⋊C4—612no—
387C4⋊C4—611no—
388C4⋊C4—611no—
389C4⋊C4—612no—
390C4⋊C4—612no—
391C4⋊C4—1222no—
392C4⋊C4—1222no—
393C4⋊C4—1224no—
394C4⋊C4—1224no—
395C4⋊C4—1221no—
396C4⋊C4—1221no—
397C22⋊C4—22no—
398C22⋊C4—22no—
399C22⋊C4—614no—
400C22⋊C4—614no—
401C22⋊C4—1222no—
402C22⋊C4—1222no—
403C22⋊C4—1224no—
404C22⋊C4—1224no—
405C42—21no—
406C42—21no—
407C42—614no—
408C42—614no—
409C23—21no—
410C23—21no—
411C23—21no—
412C23—21no—
413C23—41no—
414C23—41no—
415C23—41no—
416C23—41no—
417C23—1222no—
418C23—1222no—
419C23—1222no—
420C23—2442no—
421C23—2442no—
422C23C22⋊C4×D6112yes—
423C23#1451978512yes—
424C23C22×C4×D6111yescharacteristic
425D4—44no—
426D4—4884no—
427D4—2442no—
428D4—2448no—
429D4—2442no—
430C2×C4—24no—
431C2×C4—22no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—42no—
438C2×C4—41no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—614no—
444C2×C4—612no—
445C2×C4—612no—
446C2×C4—1222no—
447C2×C4—1222no—
448C2×C4—1222no—
449C2×C4—4882no—
450C2×C4—4882no—
451C2×C4—4882no—
452C2×C4—4882no—
453C2×C4—2442no—
454C2×C4—2442no—
455C2×C4C22⋊C4×D6111yescharacteristic
456C2×C4C22⋊C4×D6111yescharacteristic
457C2×C4C2×D4×D6112yes—
458C8—44no—
459C8—2442no—
460C8—2442no—
461C22—21no—
462C22—21no—
463C22—22no—
464C22—22no—
465C22—22no—
466C22—22no—
467C22—42no—
468C22—42no—
469C22—41no—
470C22—41no—
471C22—81no—
472C22—81no—
473C22—4882no—
474C22—4882no—
475C22—2442no—
476C22—2442no—
477C22—2442no—
478C22C2×C22⋊C4×D6111yescharacteristic
479C22C2×#1451978511yescharacteristic
480C22#1684052811yescharacteristic
481C4—22no—
482C4—21no—
483C4—41no—
484C4—41no—
485C4—41no—
486C4—1224no—
487C4—1222no—
488C4—1222no—
489C4—2442no—
490C4#1683973412yes—
491C2—21no—
492C2—21no—
493C2—42no—
494C2—42no—
495C2—4882no—
496C2#2145426911yescharacteristic
497C2C2×#1683973411yescharacteristic
498C2#2145429611yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1465C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840458C2
cosocleC22×C4×C61C24
hypercenter#1465D61
hypocenterC61#17415
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1465

Complements

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

NH ≅ G/Ntype
2. #21454479C2semidirect
3. #21444187C2semidirect
4. #21444180C2semidirect
5. #21444158C2semidirect
6. #21444138C2semidirect
7. #21444137C2semidirect
8. C61×#1465C2semidirect
247. #1465D61semidirect
286. C61#17415semidirect

Maximal subgroups

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

subgroupindex
C2×#168404582
#214544792
#214441872
#214441802
#214441582
#214441382
#214441372
C61×#14652
#1741561