Finite Group Databasebeta

← #29577480

Subgroups — #29577480

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#21451300C211yesmaximal, characteristic
2#21448419C211yesmaximal, characteristic, complemented
3#21444335C211yesmaximal, characteristic
4#21444148C211yesmaximal, characteristic, complemented
5#21443705C211yesmaximal, characteristic, complemented
6#21443704C211yesmaximal, characteristic, complemented
7C61×#1507C211yesmaximal, characteristic
8C22×#11758196C2211yescharacteristic
9#16839726C2211yescharacteristic
10#16839700C412yescomplemented
11#16839676C412yescomplemented
12#16839656—22no—
13#16839646—22no—
14#16839644—22no—
15#16839642—21no—
16#16839642—21no—
17#16839623—21no—
18#16839620—21no—
19C4×C22⋊Dic61C2211yescharacteristic
20C4×C22⋊Dic61C2211yescharacteristic
21#16839496—22no—
22#16839487—22no—
23C2×#121×C61C2211yescharacteristic
24C61×#407C2211yescharacteristic
25C4×C22⋊C4×C61C2211yescharacteristic
26C61×#327—22no—
27C23×Dic61D411yescharacteristic
28C23×Dic61D411yescharacteristic
29C2×#11758194—21no—
30C2×#11758196—21no—
31C2×#11758196—21no—
32C2×#11758196—21no—
33C2×#11758196—21no—
34C2×#11758196—22no—
35C2×#11758196C2×C412yes—
36C2×#11758196D412yes—
37C2×C22⋊Dic61—21no—
38C2×C22⋊Dic61—21no—
39C2×C22⋊Dic61—22no—
40C2×C22⋊Dic61—22no—
41C2×C4×Dic61—21no—
42C2×C4×Dic61—21no—
43C22⋊#92418—21no—
44C22⋊#92418—21no—
45#14519684—22no—
46#14519684—24no—
47#14519684—22no—
48#14519684—22no—
49#14519684C2×C412yes—
50#14519684D412yes—
51C22×D4×C61—21no—
52C22×D4×C61C2×C411yescharacteristic
53C23×C4×C61C2311yescharacteristic
54C2×M16×C61—21no—
55#121×C61—21no—
56#121×C61—21no—
57#121×C61—21no—
58#121×C61—21no—
59C2×C4⋊C4×C61C2×C411yescharacteristic
60C2×C22⋊C4×C61—21no—
61C2×C22⋊C4×C61—21no—
62C2×C42×C61—21no—
63C22⋊C8×C61—21no—
64C22⋊C8×C61—21no—
65#95×C61D412yes—
66C24×C61—21no—
67C24×C61C2×D411yescharacteristic
68C2×D4×C61—21no—
69C2×D4×C61—21no—
70C2×D4×C61—44no—
71C2×D4×C61—41no—
72C2×D4×C61—41no—
73C2×D4×C61—81no—
74C22×C4×C61—21no—
75C22×C4×C61—22no—
76C22×C4×C61—81no—
77C22×C4×C61C22×C411yescharacteristic
78C22×C4×C61C2×D411yescharacteristic
79C22×C4×C61C2×D411yescharacteristic
80C22×C4×C61C2×D411yescharacteristic
81C22×C4×C61#4111yescharacteristic
82C22×C4×C61#4111yescharacteristic
83C22×Dic61—21no—
84C22×Dic61—21no—
85C22×Dic61—21no—
86C22×Dic61—21no—
87C22×Dic61—22no—
88C22×Dic61—22no—
89C22×Dic61—42no—
90C22×Dic61—81no—
91C22×Dic61C22⋊C412yes—
92C22×Dic61C22⋊C412yes—
93M16×C61—81no—
94C2×C8×C61—41no—
95C4⋊C4×C61—21no—
96C4⋊C4×C61—21no—
97C22⋊C4×C61—42no—
98C22⋊C4×C61—41no—
99C22⋊C4×C61—41no—
100C42×C61—81no—
101C22⋊Dic61—44no—
102C22⋊Dic61—42no—
103C22⋊Dic61—42no—
104C22⋊Dic61—82no—
105#11758196—22no—
106#11758196—22no—
107#11758196—22no—
108#11758196—22no—
109#11758196—82no—
110C4×Dic61—81no—
111C4×Dic61—81no—
112#11758194—81no—
113C2×#92418—41no—
114C23×C61—22no—
115C23×C61—22no—
116C23×C61—41no—
117C23×C61—42no—
118C23×C61—42no—
119C23×C61—41no—
120C23×C61—42no—
121C23×C61C2×C22⋊C411yescharacteristic
122C23×C61#12011yescharacteristic
123C23×C61#12311yescharacteristic
124D4×C61—81no—
125D4×C61—81no—
126D4×C61—82no—
127D4×C61—82no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—42no—
135C2×C4×C61—42no—
136C2×C4×C61—42no—
137C2×C4×C61—41no—
138C2×C4×C61—42no—
139C2×C4×C61C4×D411yescharacteristic
140C2×C4×C61C4×D411yescharacteristic
141C2×C4×C61#12111yescharacteristic
142C2×C4×C61#12111yescharacteristic
143C2×Dic61—22no—
144C2×Dic61—22no—
145C2×Dic61—22no—
146C2×Dic61—22no—
147C2×Dic61—42no—
148C2×Dic61—42no—
149C2×Dic61—42no—
150C2×Dic61—42no—
151C2×Dic61—42no—
152C2×Dic61—42no—
153C2×Dic61—42no—
154C2×Dic61—42no—
155C2×Dic61—42no—
156C2×Dic61—42no—
157C2×Dic61—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—84no—
170C22×C61—81no—
171C22×C61—81no—
172C22×C61—81no—
173C22×C61#38611yescharacteristic
174C22×C61#42112yes—
175C22×C61#45412yes—
176C4×C61—21no—
177C4×C61—21no—
178C4×C61—21no—
179C4×C61—21no—
180C4×C61—82no—
181C4×C61—81no—
182Dic61—42no—
183Dic61—42no—
184Dic61—82no—
185Dic61—82no—
186#2591—611no—
187#2313—611no—
188#1507—611no—
189#1507D6111yescharacteristic
190#1463—611no—
191#1297—611no—
192#1297—611no—
193C2×C61—22no—
194C2×C61—22no—
195C2×C61—41no—
196C2×C61—161no—
197C2×C61#188811yescharacteristic
198C2×C61#189711yescharacteristic
199C2×C61#191311yescharacteristic
200C2×#121C2×D6111yescharacteristic
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⋊C4—611no—
215C4×C22⋊C4C2×D6111yescharacteristic
216#327—22no—
217#327—1222no—
218#324—1222no—
219C61#941411yescharacteristic, complemented, Sylow
220C22×D4—21no—
221C22×D4C4×D6111yescharacteristic
222C23×C4—611no—
223C23×C4—611no—
224C23×C4C22×D6111yescharacteristic
225C2×M16—21no—
226C2×M16—1221no—
227#121—21no—
228#121—21no—
229#121—21no—
230#121—21no—
231C2×C4⋊C4—612no—
232C2×C4⋊C4—612no—
233C2×C4⋊C4—1221no—
234C2×C4⋊C4—1221no—
235C2×C4⋊C4—1221no—
236C2×C4⋊C4—1221no—
237C2×C4⋊C4—1222no—
238C2×C4⋊C4C4×D6111yescharacteristic
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—1221no—
247C2×C42—1221no—
248C22⋊C8—21no—
249C22⋊C8—21no—
250C22⋊C8—1221no—
251C22⋊C8—1221no—
252#95—612no—
253#95—612no—
254#95—1222no—
255#95—1222no—
256#95—1222no—
257#95—1224no—
258#95C22⋊D6112yes—
259C24—21no—
260C24D4×D6111yescharacteristic
261C2×D4—21no—
262C2×D4—21no—
263C2×D4—44no—
264C2×D4—41no—
265C2×D4—41no—
266C2×D4—81no—
267C22×C4—21no—
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—1222no—
277C22×C4—1222no—
278C22×C4—4881no—
279C22×C4—2442no—
280C22×C4C2×C4×D6111yescharacteristic
281C22×C4#1175822211yescharacteristic
282C22×C4D4×D6111yescharacteristic
283C22×C4D4×D6111yescharacteristic
284C22×C4#1175822411yescharacteristic
285C22×C4C2×C22⋊D6111yescharacteristic
286M16—81no—
287M16—4881no—
288C2×C8—41no—
289C2×C8—2441no—
290C4⋊C4—21no—
291C4⋊C4—21no—
292C4⋊C4—1222no—
293C4⋊C4—1222no—
294C4⋊C4—1222no—
295C4⋊C4—1222no—
296C4⋊C4—4882no—
297C22⋊C4—42no—
298C22⋊C4—41no—
299C22⋊C4—41no—
300C22⋊C4—4882no—
301C22⋊C4—2444no—
302C22⋊C4—2442no—
303C22⋊C4—2442no—
304C42—81no—
305C42—4881no—
306C42—4881no—
307C23—22no—
308C23—22no—
309C23—41no—
310C23—42no—
311C23—42no—
312C23—42no—
313C23—41no—
314C23C22⋊C4×D6111yescharacteristic
315C23#1451974511yescharacteristic
316C23#1451975911yescharacteristic
317D4—81no—
318D4—81no—
319D4—82no—
320D4—82no—
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—41no—
331C2×C4—42no—
332C2×C4—1222no—
333C2×C4—1222no—
334C2×C4—1222no—
335C2×C4—1222no—
336C2×C4—4881no—
337C2×C4—2442no—
338C2×C4—2442no—
339C2×C4—2442no—
340C2×C4—2442no—
341C2×C4—2442no—
342C2×C4—2442no—
343C2×C4—2442no—
344C2×C4—2442no—
345C2×C4—2442no—
346C2×C4—2442no—
347C2×C4#1451973711yescharacteristic
348C2×C4C4×C22⋊D6111yescharacteristic
349C2×C4#1451974811yescharacteristic
350C2×C4#1451975011yescharacteristic
351C8—81no—
352C8—4881no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—44no—
361C22—84no—
362C22—81no—
363C22—81no—
364C22—81no—
365C22#1683963811yescharacteristic
366C22#1683977712yes—
367C22#1683993312yes—
368C4—21no—
369C4—21no—
370C4—21no—
371C4—21no—
372C4—82no—
373C4—81no—
374C4—4882no—
375C4—4882no—
376C4—2442no—
377C4—2442no—
378C2—22no—
379C2—22no—
380C2—41no—
381C2—161no—
382C2#2144621911yescharacteristic
383C2#2144626411yescharacteristic
384C2#2144635811yescharacteristic
subgroupG/H
centerC22#16839638
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1507C2
socleC22×C61#386
prime radicalC2×#121×C61C22
cosocleC23×C4×C61C23
hypercenter#1507D61
hypocenterC61#9414
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1507

Complements

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

NH ≅ G/Ntype
2. #21448419C2semidirect
4. #21444148C2semidirect
5. #21443705C2semidirect
6. #21443704C2semidirect
10. #16839700C4semidirect
11. #16839676C4semidirect
219. C61#9414semidirect

Maximal subgroups

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

subgroupindex
#214513002
#214484192
#214443352
#214441482
#214437052
#214437042
C61×#15072
#941461