Finite Group Databasebeta

← #29584050

Subgroups — #29584050

Order 15616.

390 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 99 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#21456965C211yesmaximal, characteristic
2#21446770C211yesmaximal, characteristic
3#21446763C211yesmaximal, characteristic
4#21446663C211yesmaximal, characteristic
5#21444507C211yesmaximal, characteristic
6#21443721C211yesmaximal, characteristic
7C61×#1565C211yesmaximal, characteristic
8#16840319C2211yescharacteristic
9C2×#14519777C2211yescharacteristic
10#16840160—21no—
11#16840113—21no—
12#16840093—22no—
13#16840048—21no—
14#16840048—21no—
15#16839786C2211yescharacteristic
16C2×#14519695—21no—
17C2×#14519695—21no—
18C4×C4⋊Dic61C2211yescharacteristic
19#16839525—22no—
20#16839523—21no—
21#16839523—21no—
22#16839510—21no—
23#16839509—21no—
24C61×#431C2211yescharacteristic
25C2×C4⋊C8×C61C2211yescharacteristic
26C4×M16×C61C2211yescharacteristic
27C61×#335—21no—
28C61×#334—21no—
29C22×Dic122—21no—
30C2×#11758194—21no—
31#14519777—21no—
32#14519777—21no—
33#14519777—21no—
34#14519777—21no—
35#14519777D411yescharacteristic
36#14519777D411yescharacteristic
37#14519769—21no—
38#14519756—21no—
39#14519756—21no—
40C4×Dic122—21no—
41C4×Dic122—21no—
42#14519736—21no—
43C2×C4⋊Dic61—21no—
44C2×C4⋊Dic61—21no—
45C2×C4⋊Dic61D412yes—
46C2×C4×Dic61—21no—
47#14519709—22no—
48#14519709—22no—
49C4⋊#92418—21no—
50C4⋊#92418—21no—
51#14519702—22no—
52#14519702—22no—
53#14519695—42no—
54#14519695—42no—
55#14519684—21no—
56C2×M16×C61D411yescharacteristic
57C2×M16×C61D411yescharacteristic
58C22×C8×C61—21no—
59C2×C42×C61C2311yescharacteristic
60C4⋊C8×C61—21no—
61C4⋊C8×C61—21no—
62C4⋊C8×C61D411yescharacteristic
63C4⋊C8×C61D411yescharacteristic
64C22⋊C8×C61—21no—
65#97×C61—21no—
66C4×C8×C61—21no—
67C4×C8×C61—21no—
68C22×C4×C61C2×D411yescharacteristic
69C22×C4×C61C2×D411yescharacteristic
70C22×C4×C61#4111yescharacteristic
71C22×Dic61—22no—
72C22×Dic61—41no—
73C2×Dic122—21no—
74C2×Dic122—21no—
75C2×Dic122—41no—
76C2×Dic122—41no—
77C2×Dic122—41no—
78C2×Dic122—41no—
79C2×Dic122—41no—
80C2×Dic122—41no—
81M16×C61—21no—
82M16×C61—21no—
83M16×C61—21no—
84M16×C61SD1612yes—
85C2×C8×C61—21no—
86C2×C8×C61—21no—
87C2×C8×C61—21no—
88C2×C8×C61—21no—
89C2×C8×C61—42no—
90C2×C8×C61—41no—
91C42×C61C2×D411yescharacteristic
92C42×C61C2×D411yescharacteristic
93C42×C61#4111yescharacteristic
94C42×C61#4111yescharacteristic
95C22⋊Dic61—41no—
96C4⋊Dic61—22no—
97C4⋊Dic61—22no—
98C4⋊Dic61—21no—
99C4⋊Dic61—21no—
100C4⋊Dic61—21no—
101C4⋊Dic61—22no—
102C4⋊Dic61—21no—
103C4⋊Dic61—41no—
104C4⋊Dic61—41no—
105C4⋊Dic61—41no—
106#11758196—41no—
107#11758196—41no—
108C4×Dic61—41no—
109C4×Dic61—41no—
110C4×Dic61—41no—
111#11758194—41no—
112#11758194—41no—
113C2×#92418—41no—
114C23×C61#12111yescharacteristic
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—41no—
118C2×C4×C61#12011yescharacteristic
119C2×C4×C61#12111yescharacteristic
120C2×C4×C61#12111yescharacteristic
121C2×C4×C61#12311yescharacteristic
122C2×C4×C61#12311yescharacteristic
123C2×C4×C61#12411yescharacteristic
124C2×C4×C61C2×SD1611yescharacteristic
125C2×C4×C61#13511yescharacteristic
126C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
127C2×C4×C61#13711yescharacteristic
128C2×Dic61—42no—
129C2×Dic61—41no—
130C2×Dic61—41no—
131C2×Dic61—42no—
132C2×Dic61—42no—
133C2×Dic61—42no—
134C2×Dic61—81no—
135C2×Dic61—81no—
136Dic122—41no—
137Dic122—41no—
138Dic122—81no—
139Dic122—81no—
140Dic122—81no—
141Dic122—81no—
142Dic122—81no—
143C8×C61—22no—
144C8×C61—41no—
145C8×C61—41no—
146C8×C61—41no—
147C8×C61—81no—
148#92418—81no—
149#10507—611nomaximal, Sylow
150C22×C61—21no—
151C22×C61—21no—
152C22×C61#39411yescharacteristic
153C22×C61#46111yescharacteristic
154C22×C61#46311yescharacteristic
155C4×C61—21no—
156C4×C61—21no—
157C4×C61—21no—
158C4×C61#45411yescharacteristic
159C4×C61#45611yescharacteristic
160C4×C61#46011yescharacteristic
161C4×C61#46411yescharacteristic
162C4×C61#46511yescharacteristic
163C4×C61#46811yescharacteristic
164Dic61—82no—
165Dic61—81no—
166Dic61—82no—
167Dic61—81no—
168#3229—611no—
169#1988—611no—
170#1986—611no—
171#1966—611no—
172#1565D6111yescharacteristic
173#1550—611no—
174#1303—611no—
175C2×C61—21no—
176C2×C61—21no—
177C2×C61#203811yescharacteristic
178C2×C61#204911yescharacteristic
179C2×C61#205511yescharacteristic
180#533—611no—
181C2×C4⋊Q8—611no—
182#498—1221no—
183#487—1221no—
184#483—1222no—
185#475—1221no—
186#475—1221no—
187#431C2×D6111yescharacteristic
188#423—611no—
189C2×C4⋊C8C2×D6111yescharacteristic
190C2×#101—1221no—
191C2×#101—1221no—
192C4×M16C2×D6111yescharacteristic
193C4×C4⋊C4—611no—
194#340—1222no—
195#339—1221no—
196#339—1221no—
197#335—21no—
198#334—21no—
199#333—1221no—
200#332—1221no—
201C61#1050711yescharacteristic, complemented, Sylow
202C22×Q8—1221no—
203C2×M16—1221no—
204C2×M16D24411yescharacteristic
205C2×M16D24411yescharacteristic
206C22×C8—21no—
207C4⋊Q8—611no—
208C4⋊Q8—611no—
209C4⋊Q8—1221no—
210C4⋊Q8—1221no—
211C4⋊Q8—1221no—
212C4⋊Q8—1221no—
213#125—1221no—
214C22⋊Q8—1221no—
215C22⋊Q8—1221no—
216C4×Q8—1221no—
217C4×Q8—1221no—
218#117—1221no—
219C2×C4⋊C4—612no—
220C2×C4⋊C4—1221no—
221C2×C4⋊C4—1221no—
222C2×C42—1221no—
223C2×C42C22×D6111yescharacteristic
224#106—1222no—
225#106—1222no—
226C4⋊C8—21no—
227C4⋊C8—21no—
228C4⋊C8—1221no—
229C4⋊C8—1221no—
230C4⋊C8C22⋊D6111yescharacteristic
231C4⋊C8C22⋊D6111yescharacteristic
232#103—1222no—
233#103—1222no—
234#101—2442no—
235#101—2442no—
236C22⋊C8—21no—
237#97—21no—
238C4×C8—21no—
239C4×C8—21no—
240#95—1221no—
241C2×Q8—1221no—
242C2×Q8—1221no—
243C2×Q8—2441no—
244C2×Q8—2441no—
245C2×Q8—2441no—
246C2×Q8—2441no—
247C2×Q8—2441no—
248C2×Q8—2441no—
249C22×C4—1222no—
250C22×C4—2441no—
251C22×C4C2×D24411yescharacteristic
252C22×C4D4×D6111yescharacteristic
253C22×C4#1175822611yescharacteristic
254M16—21no—
255M16—21no—
256M16—21no—
257M16—2441no—
258M16—2441no—
259M16#1175819012yes—
260C2×C8—21no—
261C2×C8—21no—
262C2×C8—21no—
263C2×C8—21no—
264C2×C8—42no—
265C2×C8—41no—
266C2×C8—2441no—
267C4⋊C4—1222no—
268C4⋊C4—1222no—
269C4⋊C4—1221no—
270C4⋊C4—1221no—
271C4⋊C4—1221no—
272C4⋊C4—1222no—
273C4⋊C4—1221no—
274C4⋊C4—2441no—
275C4⋊C4—2441no—
276C4⋊C4—2441no—
277C4⋊C4—2441no—
278C4⋊C4—2441no—
279C22⋊C4—2441no—
280C42—2441no—
281C42—2441no—
282C42—2441no—
283C42#1175822211yescharacteristic
284C42D4×D6111yescharacteristic
285C42#1175822611yescharacteristic
286C42C2×C22⋊D6111yescharacteristic
287C23#1451975211yescharacteristic
288Q8—4881no—
289Q8—4881no—
290Q8—4881no—
291Q8—4881no—
292Q8—4881no—
293Q8—2441no—
294Q8—2441no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—41no—
298C2×C4—4881no—
299C2×C4—4881no—
300C2×C4—2442no—
301C2×C4—2442no—
302C2×C4—2442no—
303C2×C4—2441no—
304C2×C4—2441no—
305C2×C4—2442no—
306C2×C4#1451974511yescharacteristic
307C2×C4#1451975111yescharacteristic
308C2×C4#1451975211yescharacteristic
309C2×C4#1451976211yescharacteristic
310C2×C4#1451976211yescharacteristic
311C2×C4#1451976611yescharacteristic
312C2×C4C2×#1175819011yescharacteristic
313C2×C4#1451979911yescharacteristic
314C2×C4#1451980511yescharacteristic
315C2×C4#1451981011yescharacteristic
316C8—22no—
317C8—41no—
318C8—41no—
319C8—41no—
320C8—81no—
321C8—4881no—
322C22—21no—
323C22—21no—
324C22#1683967911yescharacteristic
325C22#1683996811yescharacteristic
326C22#1683997811yescharacteristic
327C4—21no—
328C4—21no—
329C4—21no—
330C4—4882no—
331C4—4881no—
332C4—4881no—
333C4—4882no—
334C4#1683993311yescharacteristic
335C4#1683994311yescharacteristic
336C4#1683996311yescharacteristic
337C4#1683998511yescharacteristic
338C4#1683999111yescharacteristic
339C4#1684000811yescharacteristic
340C2—21no—
341C2—21no—
342C2#2144703811yescharacteristic
343C2#2144710111yescharacteristic
344C2#2144713711yescharacteristic
subgroupG/H
centerC22#16839679
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1565C2
socleC22×C61#394
prime radicalC23×C61#121
hypercenter#1565D61
hypocenterC61#10507
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1565

Complements

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

NH ≅ G/Ntype
201. C61#10507semidirect

Maximal subgroups

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

subgroupindex
#214569652
#214467702
#214467632
#214466632
#214445072
#214437212
C61×#15652
#1050761