Finite Group Databasebeta

← #29577462

Subgroups — #29577462

Order 15616.

644 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 644 conjugacy classes of subgroups — too many to draw. Only its 97 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#21451294C211yesmaximal, characteristic
2#21448174C211yesmaximal, characteristic, complemented
3#21444336C211yesmaximal, characteristic
4#21444334C211yesmaximal, characteristic
5#21444148C211yesmaximal, characteristic, complemented
6#21443705C211yesmaximal, characteristic, complemented
7C61×#1297C211yesmaximal, characteristic, complemented
8C2×#14519751C2211yescharacteristic
9C2×#14519733—21no—
10C22×#11758196C2211yescharacteristic
11#16839726C2211yescharacteristic
12#16839702C412yescomplemented
13#16839680C412yescomplemented
14#16839653—22no—
15#16839639—21no—
16#16839639—21no—
17C4×#11758196—22no—
18#16839613—22no—
19C22⋊C4×Dic61—21no—
20C4×C22⋊Dic61C2211yescharacteristic
21#16839497—22no—
22#16839495—22no—
23#16839487—22no—
24C61×#407C2211yescharacteristic
25C4×C22⋊C4×C61C2211yescharacteristic
26C4×C22⋊C4×C61C2211yescharacteristic
27C22×D244C2×C411yescharacteristic
28C22×C22⋊D61—21no—
29C23×Dic61D411yescharacteristic
30C23×Dic61D411yescharacteristic
31C2×#11758194—21no—
32#14519751—21no—
33#14519751—21no—
34#14519751—21no—
35#14519751—21no—
36#14519733—28no—
37C2×C4⋊Dic61C2×C411yescharacteristic
38C2×#11758196—22no—
39C2×#11758196—21no—
40C2×#11758196—21no—
41C2×#11758196—21no—
42C2×#11758196—21no—
43C2×#11758196C2×C412yes—
44C2×#11758196D412yes—
45C2×C22⋊Dic61—21no—
46C2×#11758198—21no—
47C2×#11758198—22no—
48C2×#11758198—22no—
49C2×C4×Dic61—22no—
50C2×C4×Dic61—22no—
51C2×C4×Dic61—21no—
52C22⋊#92418—21no—
53C22⋊#92418—21no—
54#14519684—22no—
55#14519684—22no—
56#14519684—22no—
57#14519684D412yes—
58C23×C4×C61C2311yescharacteristic
59C2×M16×C61—21no—
60C2×C22⋊C4×C61—21no—
61C2×C22⋊C4×C61—21no—
62C2×C42×C61—21no—
63C2×C42×C61—21no—
64C22⋊C8×C61—21no—
65C22⋊C8×C61—21no—
66#95×C61C2×C412yes—
67#95×C61D412yes—
68C24×C61C2×D411yescharacteristic
69C23×D61—21no—
70C22×C4×C61—22no—
71C22×C4×C61—22no—
72C22×C4×C61—81no—
73C22×C4×C61C22×C411yescharacteristic
74C22×C4×C61C2×D411yescharacteristic
75C22×C4×C61C2×D411yescharacteristic
76C22×C4×C61C2×D411yescharacteristic
77C22×C4×C61#4111yescharacteristic
78C22×C4×C61#4111yescharacteristic
79C2×C22⋊D61—44no—
80C2×C22⋊D61—41no—
81C2×C22⋊D61—41no—
82C22×Dic61—21no—
83C22×Dic61—21no—
84C22×Dic61—24no—
85C22×Dic61—21no—
86C22×Dic61—22no—
87C22×Dic61—21no—
88C22×Dic61—21no—
89C22×Dic61—81no—
90C22×Dic61C22⋊C412yes—
91C22×Dic61C22⋊C412yes—
92C2×D244—21no—
93C2×D244—21no—
94C2×D244—81no—
95M16×C61—81no—
96C2×C8×C61—41no—
97C22⋊C4×C61—24no—
98C22⋊C4×C61—42no—
99C42×C61—81no—
100C42×C61—81no—
101C22⋊Dic61—24no—
102#11758198—41no—
103#11758198—41no—
104#11758198—44no—
105#11758198—82no—
106C4⋊Dic61—21no—
107C4⋊Dic61—21no—
108#11758196—28no—
109#11758196—22no—
110#11758196—22no—
111#11758196—22no—
112#11758196—22no—
113C4×Dic61—28no—
114C4×Dic61—81no—
115C4×Dic61—82no—
116#11758194—81no—
117C2×#92418—41no—
118C23×C61—22no—
119C23×C61—22no—
120C23×C61—41no—
121C23×C61C2×C22⋊C411yescharacteristic
122C23×C61#12011yescharacteristic
123C23×C61#12311yescharacteristic
124C22×D61—42no—
125C22×D61—42no—
126C22×D61—41no—
127C22×D61—42no—
128C2×C4×C61—24no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—42no—
136C2×C4×C61—42no—
137C2×C4×C61—42no—
138C2×C4×C61—42no—
139C2×C4×C61—42no—
140C2×C4×C61C4×D411yescharacteristic
141C2×C4×C61C4×D411yescharacteristic
142C2×C4×C61#12111yescharacteristic
143C2×C4×C61#12111yescharacteristic
144C22⋊D61—82no—
145C22⋊D61—82no—
146C2×Dic61—22no—
147C2×Dic61—22no—
148C2×Dic61—24no—
149C2×Dic61—22no—
150C2×Dic61—22no—
151C2×Dic61—24no—
152C2×Dic61—22no—
153C2×Dic61—42no—
154C2×Dic61—42no—
155C2×Dic61—42no—
156C2×Dic61—42no—
157C2×Dic61—42no—
158C2×Dic61—41no—
159C2×Dic61—81no—
160C2×Dic61#10414yes—
161D244—81no—
162D244—81no—
163C8×C61—81no—
164#92418—81no—
165#9410—611nomaximal, Sylow
166C22×C61—21no—
167C22×C61—21no—
168C22×C61—21no—
169C22×C61—21no—
170C22×C61—21no—
171C22×C61—21no—
172C22×C61—21no—
173C22×C61—44no—
174C22×C61#38611yescharacteristic
175C22×C61C2×#10412yes—
176C22×C61#45412yes—
177C2×D61—84no—
178C2×D61—81no—
179C2×D61—81no—
180C2×D61—81no—
181C4×C61—21no—
182C4×C61—21no—
183C4×C61—21no—
184C4×C61—21no—
185C4×C61—44no—
186C4×C61—82no—
187Dic61—24no—
188Dic61—44no—
189Dic61—42no—
190Dic61—81no—
191#2591—611no—
192#2274—611no—
193#1507—611no—
194#1507—611no—
195#1463—611no—
196#1297—611no—
197#1297D6111yescharacteristic, complemented
198C2×C61—22no—
199C2×C61—22no—
200C2×C61—41no—
201C2×C61#188811yescharacteristic
202C2×C61#189611yescharacteristic
203C2×C61#191311yescharacteristic
204D61—161no—
205C2×#121—611no—
206C2×#117—1221no—
207C22×C4⋊C4—611no—
208#407—611no—
209#407C2×D6111yescharacteristic
210#400—612no—
211#394—612no—
212#388—1222no—
213#386—1221no—
214#386—1221no—
215C4×C4⋊C4—1222no—
216C4×C4⋊C4—1222no—
217C4×C22⋊C4—611no—
218C4×C22⋊C4—1221no—
219C4×C22⋊C4C2×D6111yescharacteristic
220C4×C22⋊C4C2×D6111yescharacteristic
221#327—1222no—
222#327—1222no—
223#324—1222no—
224C61#941011yescharacteristic, complemented, Sylow
225C22×D4—611no—
226C22×D4—1221no—
227C23×C4—611no—
228C23×C4—611no—
229C23×C4C22×D6111yescharacteristic
230C2×M16—21no—
231C2×M16—1221no—
232#121—1221no—
233#121—1221no—
234#121—1221no—
235#121—1221no—
236#117—1228no—
237C2×C4⋊C4—612no—
238C2×C4⋊C4—612no—
239C2×C4⋊C4—611no—
240C2×C4⋊C4—1222no—
241C2×C4⋊C4—1221no—
242C2×C4⋊C4—1221no—
243C2×C4⋊C4—1221no—
244C2×C4⋊C4—1221no—
245C2×C22⋊C4—21no—
246C2×C22⋊C4—21no—
247C2×C22⋊C4—1221no—
248C2×C22⋊C4—1222no—
249C2×C22⋊C4—1222no—
250C2×C22⋊C4—1221no—
251C2×C42—21no—
252C2×C42—21no—
253C2×C42—1222no—
254C2×C42—1222no—
255C2×C42—1221no—
256C22⋊C8—21no—
257C22⋊C8—21no—
258C22⋊C8—1221no—
259C22⋊C8—1221no—
260#95—612no—
261#95—1222no—
262#95—1222no—
263#95—1222no—
264#95C4×D6112yes—
265#95D24412yes—
266C24—1221no—
267C24D4×D6111yescharacteristic
268C2×D4—1221no—
269C2×D4—1221no—
270C2×D4—4881no—
271C2×D4—2444no—
272C2×D4—2441no—
273C2×D4—2441no—
274C22×C4—22no—
275C22×C4—22no—
276C22×C4—81no—
277C22×C4—612no—
278C22×C4—612no—
279C22×C4—1224no—
280C22×C4—1221no—
281C22×C4—1221no—
282C22×C4—1221no—
283C22×C4—1222no—
284C22×C4—1221no—
285C22×C4—1221no—
286C22×C4—4881no—
287C22×C4C2×C4×D6111yescharacteristic
288C22×C4C2×D24411yescharacteristic
289C22×C4#1175822211yescharacteristic
290C22×C4D4×D6111yescharacteristic
291C22×C4D4×D6111yescharacteristic
292C22×C4#1175822611yescharacteristic
293M16—81no—
294M16—4881no—
295C2×C8—41no—
296C2×C8—2441no—
297C4⋊C4—1228no—
298C4⋊C4—1222no—
299C4⋊C4—1222no—
300C4⋊C4—1222no—
301C4⋊C4—1222no—
302C4⋊C4—1221no—
303C4⋊C4—1221no—
304C22⋊C4—24no—
305C22⋊C4—42no—
306C22⋊C4—1224no—
307C22⋊C4—4882no—
308C22⋊C4—2444no—
309C22⋊C4—2441no—
310C22⋊C4—2441no—
311C42—81no—
312C42—81no—
313C42—1228no—
314C42—4881no—
315C42—4882no—
316C23—22no—
317C23—22no—
318C23—41no—
319C23—2442no—
320C23—2442no—
321C23—2442no—
322C23—2441no—
323C23C22⋊C4×D6111yescharacteristic
324C23#1451974711yescharacteristic
325C23#1451976211yescharacteristic
326D4—4881no—
327D4—4881no—
328D4—4882no—
329D4—4882no—
330C2×C4—24no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—614no—
343C2×C4—1222no—
344C2×C4—1222no—
345C2×C4—1224no—
346C2×C4—1222no—
347C2×C4—1222no—
348C2×C4—1224no—
349C2×C4—1222no—
350C2×C4—4881no—
351C2×C4—2442no—
352C2×C4—2441no—
353C2×C4—2442no—
354C2×C4—2442no—
355C2×C4—2442no—
356C2×C4—2442no—
357C2×C4#1451973911yescharacteristic
358C2×C4C4×D24411yescharacteristic
359C2×C4#1451975011yescharacteristic
360C2×C4#1451975211yescharacteristic
361C8—81no—
362C8—4881no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—21no—
369C22—21no—
370C22—44no—
371C22—4884no—
372C22—4881no—
373C22—4881no—
374C22—4881no—
375C22#1683964011yescharacteristic
376C22#104×D6112yes—
377C22#1683993612yes—
378C4—21no—
379C4—21no—
380C4—21no—
381C4—21no—
382C4—44no—
383C4—82no—
384C4—1224no—
385C4—4881no—
386C4—2444no—
387C4—2442no—
388C2—22no—
389C2—22no—
390C2—41no—
391C2—9761no—
392C2#2144622111yescharacteristic
393C2#2144626111yescharacteristic
394C2#2144636011yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1297C2
socleC22×C61#386
prime radicalC2×#14519751C22
cosocleC23×C4×C61C23
hypercenter#1297D61
hypocenterC61#9410
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1297

Complements

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

NH ≅ G/Ntype
2. #21448174C2semidirect
5. #21444148C2semidirect
6. #21443705C2semidirect
7. C61×#1297C2semidirect
12. #16839702C4semidirect
13. #16839680C4semidirect
197. #1297D61semidirect
224. C61#9410semidirect

Maximal subgroups

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

subgroupindex
#214512942
#214481742
#214443362
#214443342
#214441482
#214437052
C61×#12972
#941061