Finite Group Databasebeta

← #29577664

Subgroups — #29577664

Order 15616.

516 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 89 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454454C211yesmaximal, characteristic, complemented
2#21450282C211yesmaximal, characteristic
3#21445894C211yesmaximal, characteristic, complemented
4#21444348C211yesmaximal, characteristic
5#21443673C211yesmaximal, characteristic, complemented
6#21443671C211yesmaximal, characteristic, complemented
7C61×#1510C211yesmaximal, characteristic
8C2×#14519736C2211yescharacteristic
9#16839820—22no—
10#16839820—22no—
11#16839785—21no—
12#16839726C2211yescharacteristic
13M16×Dic61—21no—
14#16839676—21no—
15#16839676—21no—
16#16839665C411yescharacteristic, complemented
17#16839665C411yescharacteristic, complemented
18#16839650—21no—
19#16839650—21no—
20#16839631C411yescharacteristic, complemented
21#16839627C411yescharacteristic, complemented
22#16839625C2211yescharacteristic
23C4×C22⋊Dic61C2211yescharacteristic
24#16839528—21no—
25#16839528—21no—
26#16839496—22no—
27C2×#121×C61C2211yescharacteristic
28C61×#407C2211yescharacteristic
29C61×#381C2211yescharacteristic
30C61×#327—22no—
31C2×#11758194—21no—
32#14519736—21no—
33#14519736—21no—
34#14519736—21no—
35#14519736—21no—
36C2×C4⋊Dic61C2×C411yescharacteristic
37C2×C4⋊Dic61C2×C411yescharacteristic
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×C22⋊Dic61—21no—
41C2×C22⋊Dic61—21no—
42C2×C22⋊Dic61—21no—
43C2×C22⋊Dic61—21no—
44C2×C22⋊Dic61—21no—
45C2×C22⋊Dic61—21no—
46C2×C22⋊Dic61D411yescharacteristic
47C2×C22⋊Dic61D411yescharacteristic
48C2×C4×Dic61C2×C411yescharacteristic
49C2×C4×Dic61C2×C411yescharacteristic
50C2×C4×Dic61D411yescharacteristic
51C2×C4×Dic61D411yescharacteristic
52#14519706—24no—
53C22⋊#92418—21no—
54C22⋊#92418D412yes—
55#14519687—22no—
56C8×Dic61—22no—
57#14519684—21no—
58#14519684—21no—
59#14519684—21no—
60#14519684—21no—
61#14519684—21no—
62C22×D4×C61—21no—
63C22×D4×C61C2×C411yescharacteristic
64C23×C4×C61C2311yescharacteristic
65C2×M16×C61—21no—
66#121×C61—21no—
67#121×C61—21no—
68#121×C61—21no—
69#121×C61—21no—
70C2×C4⋊C4×C61C2×C411yescharacteristic
71C2×C22⋊C4×C61—21no—
72C2×C22⋊C4×C61—21no—
73C22⋊C8×C61—21no—
74C22⋊C8×C61D412yes—
75#95×C61—21no—
76#95×C61—21no—
77C24×C61—21no—
78C24×C61C2×D411yescharacteristic
79C2×D4×C61—21no—
80C2×D4×C61—21no—
81C2×D4×C61—41no—
82C2×D4×C61—41no—
83C2×D4×C61—41no—
84C2×D4×C61—41no—
85C2×D4×C61—81no—
86C2×D4×C61—81no—
87C22×C4×C61—21no—
88C22×C4×C61—41no—
89C22×C4×C61—41no—
90C22×C4×C61—41no—
91C22×C4×C61C22×C411yescharacteristic
92C22×C4×C61C2×D411yescharacteristic
93C22×C4×C61C2×D411yescharacteristic
94C22×C4×C61C2×D411yescharacteristic
95C22×C4×C61#4111yescharacteristic
96C22×C4×C61#4111yescharacteristic
97C22×Dic61—21no—
98C22×Dic61—21no—
99C22×Dic61—41no—
100C22×Dic61C22⋊C411yescharacteristic
101C22×Dic61C22⋊C411yescharacteristic
102C22×Dic61C22⋊C411yescharacteristic
103C22×Dic61C22⋊C411yescharacteristic
104M16×C61—41no—
105M16×C61—41no—
106C2×C8×C61—22no—
107C4⋊C4×C61—21no—
108C4⋊C4×C61—21no—
109C22⋊C4×C61—41no—
110C22⋊C4×C61—41no—
111C22⋊C4×C61—41no—
112C22⋊C4×C61—41no—
113C22⋊Dic61—21no—
114C22⋊Dic61—21no—
115C22⋊Dic61—21no—
116C22⋊Dic61—21no—
117C22⋊Dic61—42no—
118C22⋊Dic61—42no—
119C22⋊Dic61—42no—
120C22⋊Dic61—41no—
121C22⋊Dic61—41no—
122C22⋊Dic61—81no—
123C22⋊Dic61—81no—
124C4⋊Dic61—21no—
125C4⋊Dic61—21no—
126C4⋊Dic61—21no—
127C4⋊Dic61—21no—
128#11758196—81no—
129#11758196—81no—
130C4×Dic61—21no—
131C4×Dic61—21no—
132C4×Dic61—21no—
133C4×Dic61—21no—
134C4×Dic61—41no—
135C4×Dic61—41no—
136#11758194—41no—
137#11758194—41no—
138C2×#92418—22no—
139C23×C61—21no—
140C23×C61—21no—
141C23×C61—41no—
142C23×C61—41no—
143C23×C61—41no—
144C23×C61—41no—
145C23×C61—41no—
146C23×C61—41no—
147C23×C61—41no—
148C23×C61—41no—
149C23×C61—41no—
150C23×C61C2×C22⋊C411yescharacteristic
151C23×C61#12111yescharacteristic
152C23×C61#12111yescharacteristic
153D4×C61—81no—
154D4×C61—81no—
155D4×C61—82no—
156D4×C61—82no—
157C2×C4×C61—21no—
158C2×C4×C61—21no—
159C2×C4×C61—21no—
160C2×C4×C61—21no—
161C2×C4×C61—41no—
162C2×C4×C61—41no—
163C2×C4×C61—41no—
164C2×C4×C61—41no—
165C2×C4×C61—41no—
166C2×C4×C61—41no—
167C2×C4×C61—41no—
168C2×C4×C61—81no—
169C2×C4×C61—81no—
170C2×C4×C61—81no—
171C2×C4×C61C4×D411yescharacteristic
172C2×C4×C61C4×D411yescharacteristic
173C2×C4×C61#12011yescharacteristic
174C2×C4×C61#12311yescharacteristic
175C2×Dic61—22no—
176C2×Dic61—21no—
177C2×Dic61—21no—
178C2×Dic61—21no—
179C2×Dic61—21no—
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—81no—
190C2×Dic61—81no—
191C2×Dic61—81no—
192C8×C61—42no—
193#92418—42no—
194#9446—611nomaximal, Sylow
195C22×C61—21no—
196C22×C61—21no—
197C22×C61—21no—
198C22×C61—21no—
199C22×C61—21no—
200C22×C61—21no—
201C22×C61—21no—
202C22×C61—21no—
203C22×C61—81no—
204C22×C61—81no—
205C22×C61—81no—
206C22×C61—81no—
207C22×C61—81no—
208C22×C61—81no—
209C22×C61—81no—
210C22×C61—81no—
211C22×C61—81no—
212C22×C61#38611yescharacteristic
213C22×C61#41011yescharacteristic
214C22×C61#41011yescharacteristic
215C4×C61—21no—
216C4×C61—21no—
217C4×C61—21no—
218C4×C61—21no—
219C4×C61—81no—
220C4×C61—161no—
221Dic61—42no—
222Dic61—41no—
223Dic61—41no—
224Dic61—41no—
225Dic61—41no—
226Dic61—81no—
227Dic61—161no—
228#2921—611no—
229#2500—611no—
230#1820—611no—
231#1510—611no—
232#1510D6111yescharacteristic
233#1284—611no—
234#1284—611no—
235C2×C61—21no—
236C2×C61—21no—
237C2×C61—41no—
238C2×C61—41no—
239C2×C61—161no—
240C2×C61#188411yescharacteristic
241C2×C61#189911yescharacteristic
242C2×C61#191011yescharacteristic
243C2×#121C2×D6111yescharacteristic
244C2×#117—611no—
245#433—1222no—
246#433—1222no—
247#423—1221no—
248#407—611no—
249#407C2×D6111yescharacteristic
250C4×M16—1221no—
251#394—1221no—
252#394—1221no—
253#390—611no—
254#390—611no—
255#388—1221no—
256#388—1221no—
257#384—611no—
258#382—611no—
259#381—611no—
260#381C2×D6111yescharacteristic
261C4×C22⋊C4—611no—
262#342—1221no—
263#342—1221no—
264#327—22no—
265#327—1222no—
266C61#944611yescharacteristic, complemented, Sylow
267C22×D4—21no—
268C22×D4C4×D6111yescharacteristic
269C23×C4C22×D6111yescharacteristic
270C2×M16—21no—
271C2×M16—1221no—
272#121—21no—
273#121—21no—
274#121—21no—
275#121—21no—
276#117—1221no—
277#117—1221no—
278#117—1221no—
279#117—1221no—
280C2×C4⋊C4—611no—
281C2×C4⋊C4—611no—
282C2×C4⋊C4—1221no—
283C2×C4⋊C4—1221no—
284C2×C4⋊C4C4×D6111yescharacteristic
285C2×C22⋊C4—21no—
286C2×C22⋊C4—21no—
287C2×C22⋊C4—611no—
288C2×C22⋊C4—611no—
289C2×C22⋊C4—1221no—
290C2×C22⋊C4—1221no—
291C2×C22⋊C4—1221no—
292C2×C22⋊C4—1221no—
293C2×C22⋊C4—1221no—
294C2×C22⋊C4—1221no—
295C2×C42—611no—
296C2×C42—611no—
297C2×C42—611no—
298C2×C42—611no—
299C4⋊C8—1224no—
300C22⋊C8—21no—
301C22⋊C8—612no—
302C22⋊C8—1221no—
303C22⋊C8C22⋊D6112yes—
304#97—1222no—
305C4×C8—1222no—
306#95—21no—
307#95—21no—
308#95—1221no—
309#95—1221no—
310#95—1221no—
311#95—1221no—
312#95—1221no—
313C24—21no—
314C24D4×D6111yescharacteristic
315C2×D4—21no—
316C2×D4—21no—
317C2×D4—41no—
318C2×D4—41no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4—81no—
322C2×D4—81no—
323C22×C4—21no—
324C22×C4—41no—
325C22×C4—41no—
326C22×C4—41no—
327C22×C4—611no—
328C22×C4—611no—
329C22×C4—611no—
330C22×C4—611no—
331C22×C4—1221no—
332C22×C4—1221no—
333C22×C4—2441no—
334C22×C4C2×C4×D6111yescharacteristic
335C22×C4#1175822211yescharacteristic
336C22×C4D4×D6111yescharacteristic
337C22×C4D4×D6111yescharacteristic
338C22×C4#1175822411yescharacteristic
339C22×C4C2×C22⋊D6111yescharacteristic
340M16—41no—
341M16—41no—
342M16—2441no—
343M16—2441no—
344C2×C8—22no—
345C2×C8—1222no—
346C4⋊C4—21no—
347C4⋊C4—21no—
348C4⋊C4—1221no—
349C4⋊C4—1221no—
350C4⋊C4—1221no—
351C4⋊C4—1221no—
352C4⋊C4—4881no—
353C4⋊C4—4881no—
354C22⋊C4—41no—
355C22⋊C4—41no—
356C22⋊C4—41no—
357C22⋊C4—41no—
358C22⋊C4—1221no—
359C22⋊C4—1221no—
360C22⋊C4—1221no—
361C22⋊C4—1221no—
362C22⋊C4—4881no—
363C22⋊C4—4881no—
364C22⋊C4—2442no—
365C22⋊C4—2442no—
366C22⋊C4—2442no—
367C22⋊C4—2441no—
368C22⋊C4—2441no—
369C42—1221no—
370C42—1221no—
371C42—1221no—
372C42—1221no—
373C42—2441no—
374C42—2441no—
375C23—21no—
376C23—21no—
377C23—41no—
378C23—41no—
379C23—41no—
380C23—41no—
381C23—41no—
382C23—41no—
383C23—41no—
384C23—41no—
385C23—41no—
386C23C22⋊C4×D6111yescharacteristic
387C23#1451974811yescharacteristic
388C23#1451975011yescharacteristic
389D4—81no—
390D4—81no—
391D4—82no—
392D4—82no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—81no—
405C2×C4—81no—
406C2×C4—81no—
407C2×C4—1222no—
408C2×C4—1221no—
409C2×C4—1221no—
410C2×C4—1221no—
411C2×C4—1221no—
412C2×C4—4881no—
413C2×C4—4881no—
414C2×C4—4881no—
415C2×C4—2441no—
416C2×C4—2441no—
417C2×C4—2441no—
418C2×C4—2441no—
419C2×C4—2441no—
420C2×C4—2441no—
421C2×C4—2441no—
422C2×C4—2441no—
423C2×C4—2441no—
424C2×C4#1451973711yescharacteristic
425C2×C4C4×C22⋊D6111yescharacteristic
426C2×C4#1451974511yescharacteristic
427C2×C4#1451975911yescharacteristic
428C8—42no—
429C8—2442no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—21no—
437C22—21no—
438C22—81no—
439C22—81no—
440C22—81no—
441C22—81no—
442C22—81no—
443C22—81no—
444C22—81no—
445C22—81no—
446C22—81no—
447C22#1683963811yescharacteristic
448C22#1683973411yescharacteristic
449C22#1683973411yescharacteristic
450C4—21no—
451C4—21no—
452C4—21no—
453C4—21no—
454C4—81no—
455C4—161no—
456C4—9761no—
457C4—4881no—
458C4—2442no—
459C4—2441no—
460C4—2441no—
461C4—2441no—
462C4—2441no—
463C2—21no—
464C2—21no—
465C2—41no—
466C2—41no—
467C2—161no—
468C2#2144619911yescharacteristic
469C2#2144627411yescharacteristic
470C2#2144634311yescharacteristic
subgroupG/H
centerC22#16839638
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1510C2
socleC22×C61#386
prime radicalC2×#121×C61C22
cosocleC23×C4×C61C23
hypercenter#1510D61
hypocenterC61#9446
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1510

Complements

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

NH ≅ G/Ntype
1. #21454454C2semidirect
3. #21445894C2semidirect
5. #21443673C2semidirect
6. #21443671C2semidirect
16. #16839665C4semidirect
17. #16839665C4semidirect
20. #16839631C4semidirect
21. #16839627C4semidirect
266. C61#9446semidirect

Maximal subgroups

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

subgroupindex
#214544542
#214502822
#214458942
#214443482
#214436732
#214436712
C61×#15102
#944661