Finite Group Databasebeta

← #29573401

Subgroups — #29573401

Order 15616.

868 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21448202C211yesmaximal, characteristic
2#21444042C211yesmaximal, characteristic
3#21443699C212yesmaximal, complemented
4#21443699C212yesmaximal, complemented
5C61×#1779C211yesmaximal, characteristic
6C2×#14519736C411yescharacteristic, complemented
7C2×#14519736C411yescharacteristic, complemented
8C22×C22⋊Dic61—21no—
9#16839625—21no—
10#16839622C411yescharacteristic, complemented
11#16839622C411yescharacteristic, complemented
12#16839622C2211yescharacteristic
13#16839622C2211yescharacteristic
14#16839618—21no—
15C4×C22⋊Dic61—21no—
16C4×C22⋊Dic61—21no—
17C2×#14519684—21no—
18C2×#14519684C2212yes—
19C24×C4×C61C2211yescharacteristic
20C2×C22⋊C8×C61—21no—
21C2×C22⋊C8×C61—21no—
22C2×C22⋊C8×C61C2212yes—
23C23×Dic61—22no—
24#14519736—42no—
25#14519736—42no—
26C2×C4⋊Dic61C2×C411yescharacteristic
27C2×C4⋊Dic61C2×C411yescharacteristic
28C2×C4⋊Dic61C2×C411yescharacteristic
29C2×C4⋊Dic61C2×C411yescharacteristic
30C2×C22⋊Dic61—24no—
31C2×C22⋊Dic61—21no—
32C2×C22⋊Dic61—21no—
33C2×C22⋊Dic61—21no—
34C2×C22⋊Dic61—21no—
35C2×C22⋊Dic61—21no—
36C2×C22⋊Dic61—21no—
37C2×C22⋊Dic61—42no—
38C2×C22⋊Dic61—42no—
39C2×C4×Dic61—21no—
40C2×C4×Dic61—21no—
41#14519684—21no—
42#14519684—21no—
43#14519684—21no—
44#14519684—21no—
45#14519684—24no—
46#14519684—42no—
47C25×C61D411yescharacteristic
48C23×C4×C61—24no—
49C23×C4×C61—42no—
50C23×C4×C61—42no—
51C23×C4×C61C2×C411yescharacteristic
52C23×C4×C61C2×C411yescharacteristic
53C23×C4×C61D411yescharacteristic
54C23×C4×C61D411yescharacteristic
55C23×C4×C61D411yescharacteristic
56C23×C4×C61C2311yescharacteristic
57C22×C8×C61—22no—
58C22⋊C8×C61—24no—
59C22⋊C8×C61—42no—
60C22⋊C8×C61—42no—
61C24×C61—22no—
62C24×C61—22no—
63C24×C61—21no—
64C24×C61—21no—
65C24×C61—22no—
66C24×C61—22no—
67C24×C61—41no—
68C24×C61—41no—
69C24×C61C22⋊C411yescharacteristic
70C24×C61C22⋊C411yescharacteristic
71C24×C61C2×D411yescharacteristic
72C22×C4×C61—22no—
73C22×C4×C61—22no—
74C22×C4×C61—22no—
75C22×C4×C61—22no—
76C22×C4×C61—22no—
77C22×C4×C61—22no—
78C22×C4×C61—22no—
79C22×C4×C61—22no—
80C22×C4×C61—22no—
81C22×C4×C61—22no—
82C22×C4×C61—41no—
83C22×C4×C61—41no—
84C22×C4×C61—41no—
85C22×C4×C61—41no—
86C22×C4×C61—41no—
87C22×C4×C61—41no—
88C22×C4×C61—41no—
89C22×C4×C61—416no—
90C22×C4×C61C22⋊C411yescharacteristic
91C22×C4×C61C22⋊C411yescharacteristic
92C22×C4×C61C22×C411yescharacteristic
93C22×C4×C61C2×D411yescharacteristic
94C22×C4×C61#4114yes—
95C22×Dic61—24no—
96C22×Dic61—21no—
97C22×Dic61—21no—
98C22×Dic61—21no—
99C22×Dic61—21no—
100C22×Dic61—42no—
101C22×Dic61—42no—
102C22×Dic61—42no—
103C22×Dic61—42no—
104C22×Dic61—42no—
105C22×Dic61—42no—
106C2×C8×C61—42no—
107C2×C8×C61—42no—
108C2×C8×C61—42no—
109C22⋊Dic61—42no—
110C22⋊Dic61—48no—
111C22⋊Dic61—42no—
112C22⋊Dic61—42no—
113C22⋊Dic61—42no—
114C22⋊Dic61—42no—
115C22⋊Dic61—41no—
116C22⋊Dic61—41no—
117C4⋊Dic61—41no—
118C4⋊Dic61—41no—
119C4⋊Dic61—41no—
120C4⋊Dic61—41no—
121C4×Dic61—42no—
122C4×Dic61—42no—
123C23×C61—21no—
124C23×C61—21no—
125C23×C61—21no—
126C23×C61—21no—
127C23×C61—24no—
128C23×C61—24no—
129C23×C61—21no—
130C23×C61—21no—
131C23×C61—21no—
132C23×C61—21no—
133C23×C61—21no—
134C23×C61—21no—
135C23×C61—21no—
136C23×C61—21no—
137C23×C61—21no—
138C23×C61—21no—
139C23×C61—21no—
140C23×C61—21no—
141C23×C61—44no—
142C23×C61—44no—
143C23×C61—44no—
144C23×C61—44no—
145C23×C61—42no—
146C23×C61—42no—
147C23×C61—42no—
148C23×C61—42no—
149C23×C61#9912yes—
150C23×C61#10412yes—
151C23×C61C2×C22⋊C411yescharacteristic
152C23×C61#12312yes—
153C23×C61#13512yes—
154C23×C61AGL(1,ℤ/8)11yescharacteristic
155C23×C61#13711yescharacteristic
156C2×C4×C61—28no—
157C2×C4×C61—21no—
158C2×C4×C61—21no—
159C2×C4×C61—21no—
160C2×C4×C61—21no—
161C2×C4×C61—21no—
162C2×C4×C61—21no—
163C2×C4×C61—21no—
164C2×C4×C61—21no—
165C2×C4×C61—21no—
166C2×C4×C61—44no—
167C2×C4×C61—44no—
168C2×C4×C61—44no—
169C2×C4×C61—44no—
170C2×C4×C61—44no—
171C2×C4×C61#9912yes—
172C2×C4×C61#11712yes—
173C2×C4×C61#12312yes—
174C2×Dic61—44no—
175C2×Dic61—44no—
176C2×Dic61—44no—
177C2×Dic61—41no—
178C2×Dic61—41no—
179C2×Dic61—41no—
180C2×Dic61—41no—
181C2×Dic61—41no—
182C2×Dic61—41no—
183C2×Dic61—41no—
184C2×Dic61—41no—
185C2×Dic61—41no—
186C2×Dic61—41no—
187C2×Dic61—41no—
188C2×Dic61—41no—
189C2×Dic61—82no—
190C2×Dic61—82no—
191C2×Dic61—82no—
192C2×Dic61—82no—
193C8×C61—82no—
194#8715—611nomaximal, Sylow
195C22×C61—22no—
196C22×C61—22no—
197C22×C61—22no—
198C22×C61—21no—
199C22×C61—21no—
200C22×C61—21no—
201C22×C61—21no—
202C22×C61—22no—
203C22×C61—22no—
204C22×C61—22no—
205C22×C61—22no—
206C22×C61—22no—
207C22×C61—22no—
208C22×C61—22no—
209C22×C61—48no—
210C22×C61—48no—
211C22×C61—41no—
212C22×C61—41no—
213C22×C61—41no—
214C22×C61—41no—
215C22×C61—41no—
216C22×C61—41no—
217C22×C61—41no—
218C22×C61—41no—
219C22×C61#38111yescharacteristic
220C22×C61C2×#9911yescharacteristic
221C22×C61C2×#9911yescharacteristic
222C22×C61#41611yescharacteristic
223C22×C61#41711yescharacteristic
224C22×C61C2×#10411yescharacteristic
225C22×C61#42111yescharacteristic
226C22×C61#48212yes—
227C22×C61#48512yes—
228C4×C61—22no—
229C4×C61—22no—
230C4×C61—22no—
231C4×C61—41no—
232Dic61—84no—
233Dic61—81no—
234Dic61—81no—
235Dic61—81no—
236Dic61—81no—
237#2280—611no—
238#1779D6111yescharacteristic
239C22⋊#95—611no—
240#1294—612no—
241#1294—612no—
242C2×C61—22no—
243C2×C61—22no—
244C2×C61—42no—
245C2×C61—42no—
246C2×C61#150111yescharacteristic
247C2×C61#150411yescharacteristic
248C2×C61#151311yescharacteristic
249C2×C61#151611yescharacteristic
250C2×C61#181911yescharacteristic
251C2×C61#182511yescharacteristic
252C2×C61#182611yescharacteristic
253C24×C4C2×D6111yescharacteristic
254C2×#117—611no—
255C2×#117—611no—
256C22×C22⋊C4—1221no—
257C2×C22⋊C8—21no—
258C2×C22⋊C8—21no—
259C2×C22⋊C8C2×D6112yes—
260#381—1221no—
261#380—611no—
262#380—611no—
263#380—611no—
264#380—611no—
265#379—1221no—
266C4×C22⋊C4—1221no—
267C4×C22⋊C4—1221no—
268C2×#95—612no—
269C2×#95—1221no—
270C61#871511yescharacteristic, complemented, Sylow
271C25D24411yescharacteristic
272C23×C4—24no—
273C23×C4—42no—
274C23×C4—42no—
275C23×C4—1222no—
276C23×C4C4×D6111yescharacteristic
277C23×C4C4×D6111yescharacteristic
278C23×C4D24411yescharacteristic
279C23×C4C22⋊D6111yescharacteristic
280C23×C4C22⋊D6111yescharacteristic
281C23×C4C22×D6111yescharacteristic
282C22×C8—22no—
283#117—2442no—
284#117—2442no—
285C2×C4⋊C4—611no—
286C2×C4⋊C4—611no—
287C2×C4⋊C4—611no—
288C2×C4⋊C4—611no—
289C2×C22⋊C4—1224no—
290C2×C22⋊C4—1221no—
291C2×C22⋊C4—1221no—
292C2×C22⋊C4—1221no—
293C2×C22⋊C4—1221no—
294C2×C22⋊C4—1221no—
295C2×C22⋊C4—1221no—
296C2×C22⋊C4—2442no—
297C2×C22⋊C4—2442no—
298C2×C42—1221no—
299C2×C42—1221no—
300C22⋊C8—24no—
301C22⋊C8—42no—
302C22⋊C8—42no—
303#95—1221no—
304#95—1221no—
305#95—1221no—
306#95—1221no—
307#95—1224no—
308#95—2442no—
309C24—21no—
310C24—22no—
311C24—22no—
312C24—21no—
313C24—22no—
314C24—22no—
315C24—41no—
316C24—41no—
317C24#1175819811yescharacteristic
318C24#1175819811yescharacteristic
319C24C2×D24411yescharacteristic
320C22×C4—22no—
321C22×C4—22no—
322C22×C4—22no—
323C22×C4—22no—
324C22×C4—22no—
325C22×C4—22no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4—41no—
333C22×C4—41no—
334C22×C4—41no—
335C22×C4—41no—
336C22×C4—41no—
337C22×C4—416no—
338C22×C4—1224no—
339C22×C4—1221no—
340C22×C4—1221no—
341C22×C4—1221no—
342C22×C4—1221no—
343C22×C4—2442no—
344C22×C4—2442no—
345C22×C4—2442no—
346C22×C4—2442no—
347C22×C4—2442no—
348C22×C4—2442no—
349C22×C4#1175819811yescharacteristic
350C22×C4#1175819811yescharacteristic
351C22×C4C2×C4×D6111yescharacteristic
352C22×C4#1175822414yes—
353C22×C4C2×C22⋊D6111yescharacteristic
354C2×C8—42no—
355C2×C8—42no—
356C2×C8—42no—
357C4⋊C4—2441no—
358C4⋊C4—2441no—
359C4⋊C4—2441no—
360C4⋊C4—2441no—
361C22⋊C4—2448no—
362C22⋊C4—2442no—
363C22⋊C4—2442no—
364C22⋊C4—2441no—
365C22⋊C4—2442no—
366C22⋊C4—2442no—
367C22⋊C4—2442no—
368C22⋊C4—2441no—
369C42—2442no—
370C42—2442no—
371C23—21no—
372C23—21no—
373C23—21no—
374C23—21no—
375C23—24no—
376C23—24no—
377C23—21no—
378C23—21no—
379C23—21no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—21no—
387C23—21no—
388C23—21no—
389C23—44no—
390C23—44no—
391C23—44no—
392C23—44no—
393C23—42no—
394C23—42no—
395C23—42no—
396C23—42no—
397C23#1451969112yes—
398C23#1451970312yes—
399C23C2×#1175819811yescharacteristic
400C23#1451976112yes—
401C23#1451979912yes—
402C23#1451980511yescharacteristic
403C23#1451981011yescharacteristic
404C2×C4—28no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—44no—
415C2×C4—44no—
416C2×C4—44no—
417C2×C4—44no—
418C2×C4—44no—
419C2×C4—4882no—
420C2×C4—4882no—
421C2×C4—4882no—
422C2×C4—4882no—
423C2×C4—2444no—
424C2×C4—2444no—
425C2×C4—2444no—
426C2×C4—2441no—
427C2×C4—2441no—
428C2×C4—2441no—
429C2×C4—2441no—
430C2×C4—2441no—
431C2×C4—2441no—
432C2×C4—2441no—
433C2×C4—2441no—
434C2×C4—2441no—
435C2×C4—2441no—
436C2×C4—2441no—
437C2×C4—2441no—
438C2×C4#1451969112yes—
439C2×C4#1451973312yes—
440C2×C4#1451975812yes—
441C8—82no—
442C22—22no—
443C22—21no—
444C22—21no—
445C22—22no—
446C22—22no—
447C22—22no—
448C22—21no—
449C22—21no—
450C22—22no—
451C22—22no—
452C22—22no—
453C22—22no—
454C22—22no—
455C22—22no—
456C22—48no—
457C22—48no—
458C22—41no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—41no—
465C22—41no—
466C22#1683962311yescharacteristic
467C22C2×#1451969111yescharacteristic
468C22C2×#1451969111yescharacteristic
469C22#1683975911yescharacteristic
470C22#1683976411yescharacteristic
471C22C2×#1451970311yescharacteristic
472C22#1683977811yescharacteristic
473C22#1684008712yes—
474C22#1684010412yes—
475C4—22no—
476C4—22no—
477C4—22no—
478C4—41no—
479C4—4884no—
480C4—4881no—
481C4—4881no—
482C4—4881no—
483C4—4881no—
484C2—22no—
485C2—22no—
486C2—42no—
487C2—42no—
488C2#2144431111yescharacteristic
489C2#2144432411yescharacteristic
490C2#2144436311yescharacteristic
491C2#2144437611yescharacteristic
492C2#2144589111yescharacteristic
493C2#2144591511yescharacteristic
494C2#2144591611yescharacteristic
subgroupG/H
centerC23C2×#11758198
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1779C2
socleC23×C61C2×C22⋊C4
prime radicalC25×C61D4
cosocleC23×C4×C61C23
hypercenter#1779D61
hypocenterC61#8715
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C24×C4 ◁ #1779

Complements

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

NH ≅ G/Ntype
3. #21443699C2semidirect
4. #21443699C2semidirect
6. C2×#14519736C4semidirect
7. C2×#14519736C4semidirect
10. #16839622C4semidirect
11. #16839622C4semidirect
270. C61#8715semidirect

Maximal subgroups

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

subgroupindex
#214482022
#214440422
#214436992
C61×#17792
#871561