Finite Group Databasebeta

← #29577482

Subgroups — #29577482

Order 15616.

552 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 93 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#21448419C211yesmaximal, characteristic, complemented
3#21444336C211yesmaximal, characteristic
4#21444334C211yesmaximal, characteristic
5#21444148C211yesmaximal, characteristic, complemented
6#21443705C211yesmaximal, characteristic, complemented
7C61×#1297C211yesmaximal, characteristic, complemented
8C2×#14519751C2211yescharacteristic
9C22×#11758196C2211yescharacteristic
10#16839726C2211yescharacteristic
11#16839702C412yescomplemented
12#16839680C412yescomplemented
13#16839653—22no—
14#16839646—22no—
15#16839644—22no—
16#16839639—21no—
17#16839639—21no—
18#16839623—21no—
19#16839620—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—
36C2×C4⋊Dic61C2×C411yescharacteristic
37C2×#11758196—21no—
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×#11758196—21no—
41C2×#11758196—22no—
42C2×#11758196C2×C412yes—
43C2×#11758196D412yes—
44C2×C22⋊Dic61—21no—
45C2×#11758198—21no—
46C2×#11758198—22no—
47C2×#11758198—22no—
48C2×C4×Dic61—21no—
49C22⋊#92418—21no—
50C22⋊#92418—21no—
51#14519684—22no—
52#14519684—24no—
53#14519684—22no—
54#14519684—22no—
55#14519684D412yes—
56C23×C4×C61C2311yescharacteristic
57C2×M16×C61—21no—
58C2×C22⋊C4×C61—21no—
59C2×C22⋊C4×C61—21no—
60C2×C42×C61—21no—
61C2×C42×C61—21no—
62C22⋊C8×C61—21no—
63C22⋊C8×C61—21no—
64#95×C61C2×C412yes—
65#95×C61D412yes—
66C24×C61C2×D411yescharacteristic
67C23×D61—21no—
68C22×C4×C61—22no—
69C22×C4×C61—22no—
70C22×C4×C61—81no—
71C22×C4×C61C22×C411yescharacteristic
72C22×C4×C61C2×D411yescharacteristic
73C22×C4×C61C2×D411yescharacteristic
74C22×C4×C61C2×D411yescharacteristic
75C22×C4×C61#4111yescharacteristic
76C22×C4×C61#4111yescharacteristic
77C2×C22⋊D61—44no—
78C2×C22⋊D61—41no—
79C2×C22⋊D61—41no—
80C22×Dic61—21no—
81C22×Dic61—21no—
82C22×Dic61—21no—
83C22×Dic61—21no—
84C22×Dic61—21no—
85C22×Dic61—22no—
86C22×Dic61—42no—
87C22×Dic61—81no—
88C22×Dic61C22⋊C412yes—
89C22×Dic61C22⋊C412yes—
90C2×D244—21no—
91C2×D244—21no—
92C2×D244—81no—
93M16×C61—81no—
94C2×C8×C61—41no—
95C22⋊C4×C61—42no—
96C22⋊C4×C61—42no—
97C42×C61—81no—
98C42×C61—81no—
99C22⋊Dic61—42no—
100#11758198—44no—
101#11758198—41no—
102#11758198—41no—
103#11758198—82no—
104C4⋊Dic61—21no—
105C4⋊Dic61—21no—
106#11758196—22no—
107#11758196—22no—
108#11758196—22no—
109#11758196—22no—
110#11758196—82no—
111C4×Dic61—81no—
112#11758194—81no—
113C2×#92418—41no—
114C23×C61—22no—
115C23×C61—22no—
116C23×C61—41no—
117C23×C61C2×C22⋊C411yescharacteristic
118C23×C61#12011yescharacteristic
119C23×C61#12311yescharacteristic
120C22×D61—42no—
121C22×D61—42no—
122C22×D61—41no—
123C22×D61—42no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—42no—
131C2×C4×C61—42no—
132C2×C4×C61—42no—
133C2×C4×C61—42no—
134C2×C4×C61—42no—
135C2×C4×C61—42no—
136C2×C4×C61C4×D411yescharacteristic
137C2×C4×C61C4×D411yescharacteristic
138C2×C4×C61#12111yescharacteristic
139C2×C4×C61#12111yescharacteristic
140C22⋊D61—82no—
141C22⋊D61—82no—
142C2×Dic61—22no—
143C2×Dic61—22no—
144C2×Dic61—22no—
145C2×Dic61—22no—
146C2×Dic61—42no—
147C2×Dic61—42no—
148C2×Dic61—42no—
149C2×Dic61—42no—
150C2×Dic61—42no—
151C2×Dic61—42no—
152C2×Dic61—42no—
153C2×Dic61—41no—
154C2×Dic61—42no—
155C2×Dic61—81no—
156D244—81no—
157D244—81no—
158C8×C61—81no—
159#92418—81no—
160#9414—611nomaximal, Sylow
161C22×C61—21no—
162C22×C61—21no—
163C22×C61—21no—
164C22×C61—21no—
165C22×C61—21no—
166C22×C61—21no—
167C22×C61—21no—
168C22×C61—44no—
169C22×C61#38611yescharacteristic
170C22×C61#42112yes—
171C22×C61#45412yes—
172C2×D61—84no—
173C2×D61—81no—
174C2×D61—81no—
175C2×D61—81no—
176C4×C61—21no—
177C4×C61—21no—
178C4×C61—21no—
179C4×C61—21no—
180C4×C61—82no—
181C4×C61—82no—
182Dic61—42no—
183Dic61—42no—
184Dic61—82no—
185Dic61—81no—
186#2591—611no—
187#2313—611no—
188#1507—611no—
189#1507—611no—
190#1463—611no—
191#1297—611no—
192#1297D6111yescharacteristic, complemented
193C2×C61—22no—
194C2×C61—22no—
195C2×C61—41no—
196C2×C61#188811yescharacteristic
197C2×C61#189711yescharacteristic
198C2×C61#191311yescharacteristic
199D61—161no—
200C2×#121—611no—
201C22×C4⋊C4—611no—
202#407—611no—
203#407C2×D6111yescharacteristic
204#400—612no—
205#394—612no—
206#388—1222no—
207#387—1222no—
208#387—1222no—
209#386—1221no—
210#386—1221no—
211#381—1221no—
212#380—1221no—
213C4×C22⋊C4—611no—
214C4×C22⋊C4C2×D6111yescharacteristic
215C4×C22⋊C4C2×D6111yescharacteristic
216#327—1222no—
217#327—1222no—
218#324—1222no—
219C61#941411yescharacteristic, complemented, Sylow
220C22×D4—611no—
221C22×D4—1221no—
222C23×C4—611no—
223C23×C4—611no—
224C23×C4C22×D6111yescharacteristic
225C2×M16—21no—
226C2×M16—1221no—
227#121—1221no—
228#121—1221no—
229#121—1221no—
230#121—1221no—
231C2×C4⋊C4—612no—
232C2×C4⋊C4—612no—
233C2×C4⋊C4—611no—
234C2×C4⋊C4—1221no—
235C2×C4⋊C4—1221no—
236C2×C4⋊C4—1221no—
237C2×C4⋊C4—1221no—
238C2×C4⋊C4—1222no—
239C2×C22⋊C4—21no—
240C2×C22⋊C4—21no—
241C2×C22⋊C4—1222no—
242C2×C22⋊C4—1222no—
243C2×C22⋊C4—1221no—
244C2×C22⋊C4—1221no—
245C2×C42—21no—
246C2×C42—21no—
247C2×C42—1221no—
248C22⋊C8—21no—
249C22⋊C8—21no—
250C22⋊C8—1221no—
251C22⋊C8—1221no—
252#95—612no—
253#95—1222no—
254#95—1222no—
255#95—1222no—
256#95—1224no—
257#95C4×D6112yes—
258#95D24412yes—
259C24—1221no—
260C24D4×D6111yescharacteristic
261C2×D4—1221no—
262C2×D4—1221no—
263C2×D4—4881no—
264C2×D4—2444no—
265C2×D4—2441no—
266C2×D4—2441no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—81no—
270C22×C4—612no—
271C22×C4—612no—
272C22×C4—1221no—
273C22×C4—1221no—
274C22×C4—1221no—
275C22×C4—1221no—
276C22×C4—1221no—
277C22×C4—1222no—
278C22×C4—4881no—
279C22×C4—2442no—
280C22×C4C2×C4×D6111yescharacteristic
281C22×C4C2×D24411yescharacteristic
282C22×C4#1175822211yescharacteristic
283C22×C4D4×D6111yescharacteristic
284C22×C4D4×D6111yescharacteristic
285C22×C4#1175822611yescharacteristic
286M16—81no—
287M16—4881no—
288C2×C8—41no—
289C2×C8—2441no—
290C4⋊C4—1222no—
291C4⋊C4—1222no—
292C4⋊C4—1222no—
293C4⋊C4—1222no—
294C4⋊C4—1221no—
295C4⋊C4—1221no—
296C4⋊C4—4882no—
297C22⋊C4—42no—
298C22⋊C4—42no—
299C22⋊C4—4882no—
300C22⋊C4—2444no—
301C22⋊C4—2442no—
302C22⋊C4—2441no—
303C22⋊C4—2441no—
304C42—81no—
305C42—81no—
306C42—4881no—
307C23—22no—
308C23—22no—
309C23—41no—
310C23—2442no—
311C23—2442no—
312C23—2442no—
313C23—2441no—
314C23C22⋊C4×D6111yescharacteristic
315C23#1451974711yescharacteristic
316C23#1451976211yescharacteristic
317D4—4881no—
318D4—4881no—
319D4—4882no—
320D4—4882no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—1222no—
334C2×C4—1222no—
335C2×C4—1222no—
336C2×C4—1222no—
337C2×C4—4881no—
338C2×C4—2442no—
339C2×C4—2442no—
340C2×C4—2442no—
341C2×C4—2442no—
342C2×C4—2441no—
343C2×C4—2442no—
344C2×C4—2442no—
345C2×C4—2442no—
346C2×C4—2442no—
347C2×C4#1451973911yescharacteristic
348C2×C4C4×D24411yescharacteristic
349C2×C4#1451975011yescharacteristic
350C2×C4#1451975211yescharacteristic
351C8—81no—
352C8—4881no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—44no—
361C22—4884no—
362C22—4881no—
363C22—4881no—
364C22—4881no—
365C22#1683964011yescharacteristic
366C22#1683977712yes—
367C22#1683993612yes—
368C4—21no—
369C4—21no—
370C4—21no—
371C4—21no—
372C4—82no—
373C4—82no—
374C4—4882no—
375C4—4881no—
376C4—2442no—
377C4—2442no—
378C2—22no—
379C2—22no—
380C2—41no—
381C2—9761no—
382C2#2144622111yescharacteristic
383C2#2144626611yescharacteristic
384C2#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#9414
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. #21448419C2semidirect
5. #21444148C2semidirect
6. #21443705C2semidirect
7. C61×#1297C2semidirect
11. #16839702C4semidirect
12. #16839680C4semidirect
192. #1297D61semidirect
219. C61#9414semidirect

Maximal subgroups

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

subgroupindex
#214512942
#214484192
#214443362
#214443342
#214441482
#214437052
C61×#12972
#941461