Finite Group Databasebeta

← #29577666

Subgroups — #29577666

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#21450281C211yesmaximal, characteristic
3#21445894C211yesmaximal, characteristic, complemented
4#21444349C211yesmaximal, characteristic
5#21444347C211yesmaximal, characteristic
6#21443672C211yesmaximal, characteristic, complemented
7C61×#1284C211yesmaximal, characteristic, complemented
8C2×#14519751C2211yescharacteristic
9C2×#14519736C2211yescharacteristic
10#16839820—22no—
11#16839820—22no—
12#16839785—21no—
13#16839726C2211yescharacteristic
14M16×Dic61—21no—
15#16839678—21no—
16#16839678—21no—
17#16839664C411yescharacteristic, complemented
18#16839664C411yescharacteristic, complemented
19#16839654—21no—
20#16839654—21no—
21#16839632C411yescharacteristic, complemented
22#16839628C411yescharacteristic, complemented
23#16839625C2211yescharacteristic
24#16839528—21no—
25#16839528—21no—
26#16839497—22no—
27#16839495—22no—
28C61×#407C2211yescharacteristic
29C61×#381C2211yescharacteristic
30C4×C22⋊C4×C61C2211yescharacteristic
31C22×D244C2×C411yescharacteristic
32C22×C22⋊D61—21no—
33C2×#11758194—21no—
34#14519751—21no—
35#14519751—21no—
36#14519751—21no—
37#14519751—21no—
38#14519736—21no—
39#14519736—21no—
40#14519736—21no—
41#14519736—21no—
42C2×C4⋊Dic61—21no—
43C2×C4⋊Dic61—21no—
44C2×C4⋊Dic61C2×C411yescharacteristic
45C2×C4⋊Dic61C2×C411yescharacteristic
46C2×C4⋊Dic61C2×C411yescharacteristic
47C2×C22⋊Dic61—21no—
48C2×C22⋊Dic61D411yescharacteristic
49C2×C22⋊Dic61D411yescharacteristic
50C2×#11758198—21no—
51C2×#11758198—21no—
52C2×#11758198—21no—
53C2×#11758198—21no—
54C2×#11758198—21no—
55C2×C4×Dic61D411yescharacteristic
56C2×C4×Dic61D411yescharacteristic
57#14519706—24no—
58C22⋊#92418—21no—
59C22⋊#92418D412yes—
60#14519687—22no—
61C8×Dic61—22no—
62#14519684—21no—
63#14519684—21no—
64#14519684—21no—
65#14519684—21no—
66C23×C4×C61C2311yescharacteristic
67C2×M16×C61—21no—
68C2×C22⋊C4×C61—21no—
69C2×C22⋊C4×C61—21no—
70C2×C42×C61C2×C411yescharacteristic
71C2×C42×C61C2×C411yescharacteristic
72C22⋊C8×C61—21no—
73C22⋊C8×C61D412yes—
74#95×C61—21no—
75#95×C61—21no—
76#95×C61—21no—
77C24×C61C2×D411yescharacteristic
78C23×D61—21no—
79C22×C4×C61—21no—
80C22×C4×C61—21no—
81C22×C4×C61—41no—
82C22×C4×C61—41no—
83C22×C4×C61—41no—
84C22×C4×C61C22×C411yescharacteristic
85C22×C4×C61C2×D411yescharacteristic
86C22×C4×C61C2×D411yescharacteristic
87C22×C4×C61C2×D411yescharacteristic
88C22×C4×C61#4111yescharacteristic
89C22×C4×C61#4111yescharacteristic
90C2×C22⋊D61—41no—
91C2×C22⋊D61—41no—
92C2×C22⋊D61—81no—
93C2×C22⋊D61—81no—
94C22×Dic61—21no—
95C22×Dic61—41no—
96C22×Dic61C22⋊C411yescharacteristic
97C22×Dic61C22⋊C411yescharacteristic
98C22×Dic61C22⋊C411yescharacteristic
99C22×Dic61C22⋊C411yescharacteristic
100C2×D244—21no—
101C2×D244—21no—
102C2×D244—41no—
103C2×D244—41no—
104M16×C61—41no—
105M16×C61—41no—
106C2×C8×C61—22no—
107C22⋊C4×C61—42no—
108C22⋊C4×C61—41no—
109C22⋊C4×C61—41no—
110C42×C61—41no—
111C42×C61—41no—
112C22⋊Dic61—21no—
113C22⋊Dic61—21no—
114C22⋊Dic61—21no—
115C22⋊Dic61—21no—
116C22⋊Dic61—41no—
117C22⋊Dic61—41no—
118#11758198—42no—
119#11758198—42no—
120#11758198—41no—
121#11758198—41no—
122#11758198—81no—
123#11758198—81no—
124C4⋊Dic61—21no—
125C4⋊Dic61—21no—
126C4⋊Dic61—21no—
127C4⋊Dic61—21no—
128C4⋊Dic61—21no—
129C4⋊Dic61—21no—
130C4⋊Dic61—81no—
131C4⋊Dic61—81no—
132C4×Dic61—21no—
133C4×Dic61—21no—
134C4×Dic61—21no—
135C4×Dic61—21no—
136#11758194—41no—
137#11758194—41no—
138C2×#92418—22no—
139C23×C61—21no—
140C23×C61—21no—
141C23×C61—41no—
142C23×C61—41no—
143C23×C61C2×C22⋊C411yescharacteristic
144C23×C61#12111yescharacteristic
145C23×C61#12111yescharacteristic
146C22×D61—41no—
147C22×D61—41no—
148C22×D61—41no—
149C22×D61—41no—
150C22×D61—41no—
151C22×D61—41no—
152C22×D61—41no—
153C2×C4×C61—21no—
154C2×C4×C61—21no—
155C2×C4×C61—21no—
156C2×C4×C61—21no—
157C2×C4×C61—22no—
158C2×C4×C61—41no—
159C2×C4×C61—41no—
160C2×C4×C61—41no—
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—81no—
168C2×C4×C61—81no—
169C2×C4×C61—81no—
170C2×C4×C61C4×D411yescharacteristic
171C2×C4×C61C4×D411yescharacteristic
172C2×C4×C61#12011yescharacteristic
173C2×C4×C61#12311yescharacteristic
174C22⋊D61—82no—
175C22⋊D61—82no—
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—81no—
188C2×Dic61—81no—
189C2×Dic61—81no—
190D244—81no—
191D244—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#38611yescharacteristic
206C22×C61#41011yescharacteristic
207C22×C61#41011yescharacteristic
208C2×D61—81no—
209C2×D61—81no—
210C2×D61—81no—
211C2×D61—81no—
212C2×D61—81no—
213C2×D61—81no—
214C2×D61—81no—
215C4×C61—21no—
216C4×C61—21no—
217C4×C61—21no—
218C4×C61—21no—
219C4×C61—42no—
220C4×C61—81no—
221C4×C61—161no—
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#1510—611no—
233#1284—611no—
234#1284D6111yescharacteristic, complemented
235C2×C61—21no—
236C2×C61—21no—
237C2×C61—41no—
238C2×C61—41no—
239C2×C61#188411yescharacteristic
240C2×C61#189911yescharacteristic
241C2×C61#191011yescharacteristic
242D61—161no—
243C2×#121—611no—
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⋊C4C2×D6111yescharacteristic
262#342—1221no—
263#342—1221no—
264#327—1222no—
265#327—1222no—
266C61#944611yescharacteristic, complemented, Sylow
267C22×D4—611no—
268C22×D4—1221no—
269C23×C4C22×D6111yescharacteristic
270C2×M16—21no—
271C2×M16—1221no—
272#121—1221no—
273#121—1221no—
274#121—1221no—
275#121—1221no—
276#117—1221no—
277#117—1221no—
278#117—1221no—
279#117—1221no—
280C2×C4⋊C4—611no—
281C2×C4⋊C4—611no—
282C2×C4⋊C4—611no—
283C2×C4⋊C4—1221no—
284C2×C4⋊C4—1221no—
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×C42C4×D6111yescharacteristic
298C2×C42C4×D6111yescharacteristic
299C4⋊C8—1224no—
300C22⋊C8—21no—
301C22⋊C8—612no—
302C22⋊C8—1221no—
303C22⋊C8D24412yes—
304#97—1222no—
305C4×C8—1222no—
306#95—21no—
307#95—21no—
308#95—21no—
309#95—1221no—
310#95—1221no—
311#95—1221no—
312#95—1221no—
313C24—1221no—
314C24D4×D6111yescharacteristic
315C2×D4—1221no—
316C2×D4—1221no—
317C2×D4—4881no—
318C2×D4—4881no—
319C2×D4—2441no—
320C2×D4—2441no—
321C2×D4—2441no—
322C2×D4—2441no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—41no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—611no—
329C22×C4—611no—
330C22×C4—611no—
331C22×C4—611no—
332C22×C4—1221no—
333C22×C4—2441no—
334C22×C4C2×C4×D6111yescharacteristic
335C22×C4C2×D24411yescharacteristic
336C22×C4#1175822211yescharacteristic
337C22×C4D4×D6111yescharacteristic
338C22×C4D4×D6111yescharacteristic
339C22×C4#1175822611yescharacteristic
340M16—41no—
341M16—41no—
342M16—2441no—
343M16—2441no—
344C2×C8—22no—
345C2×C8—1222no—
346C4⋊C4—1221no—
347C4⋊C4—1221no—
348C4⋊C4—1221no—
349C4⋊C4—1221no—
350C4⋊C4—1221no—
351C4⋊C4—1221no—
352C4⋊C4—4881no—
353C4⋊C4—4881no—
354C22⋊C4—42no—
355C22⋊C4—41no—
356C22⋊C4—41no—
357C22⋊C4—1221no—
358C22⋊C4—1221no—
359C22⋊C4—1221no—
360C22⋊C4—1221no—
361C22⋊C4—4881no—
362C22⋊C4—4881no—
363C22⋊C4—2442no—
364C22⋊C4—2442no—
365C22⋊C4—2441no—
366C22⋊C4—2441no—
367C22⋊C4—2441no—
368C22⋊C4—2441no—
369C42—41no—
370C42—41no—
371C42—1221no—
372C42—1221no—
373C42—1221no—
374C42—1221no—
375C23—21no—
376C23—21no—
377C23—41no—
378C23—41no—
379C23—2441no—
380C23—2441no—
381C23—2441no—
382C23—2441no—
383C23—2441no—
384C23—2441no—
385C23—2441no—
386C23C22⋊C4×D6111yescharacteristic
387C23#1451975011yescharacteristic
388C23#1451975211yescharacteristic
389D4—4881no—
390D4—4881no—
391D4—4882no—
392D4—4882no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—22no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—81no—
408C2×C4—81no—
409C2×C4—81no—
410C2×C4—1221no—
411C2×C4—1221no—
412C2×C4—1221no—
413C2×C4—1221no—
414C2×C4—4881no—
415C2×C4—4881no—
416C2×C4—4881no—
417C2×C4—2441no—
418C2×C4—2441no—
419C2×C4—2441no—
420C2×C4—2441no—
421C2×C4—2441no—
422C2×C4—2441no—
423C2×C4—2441no—
424C2×C4#1451973911yescharacteristic
425C2×C4C4×D24411yescharacteristic
426C2×C4#1451974711yescharacteristic
427C2×C4#1451976211yescharacteristic
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—4881no—
441C22—4881no—
442C22—4881no—
443C22—4881no—
444C22—4881no—
445C22—4881no—
446C22—4881no—
447C22#1683964011yescharacteristic
448C22#1683973411yescharacteristic
449C22#1683973411yescharacteristic
450C4—21no—
451C4—21no—
452C4—21no—
453C4—21no—
454C4—42no—
455C4—81no—
456C4—161no—
457C4—9761no—
458C4—4881no—
459C4—2441no—
460C4—2441no—
461C4—2441no—
462C4—2441no—
463C2—21no—
464C2—21no—
465C2—41no—
466C2—41no—
467C2—9761no—
468C2#2144620111yescharacteristic
469C2#2144627611yescharacteristic
470C2#2144634511yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1284C2
socleC22×C61#386
prime radicalC2×#14519751C22
cosocleC23×C4×C61C23
hypercenter#1284D61
hypocenterC61#9446
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1284

Complements

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

NH ≅ G/Ntype
1. #21454454C2semidirect
3. #21445894C2semidirect
6. #21443672C2semidirect
7. C61×#1284C2semidirect
17. #16839664C4semidirect
18. #16839664C4semidirect
21. #16839632C4semidirect
22. #16839628C4semidirect
234. #1284D61semidirect
266. C61#9446semidirect

Maximal subgroups

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

subgroupindex
#214544542
#214502812
#214458942
#214443492
#214443472
#214436722
C61×#12842
#944661