Finite Group Databasebeta

← #29584078

Subgroups — #29584078

Order 15616.

338 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 79 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#21457027C211yesmaximal, characteristic
2#21446774C211yesmaximal, characteristic
3#21444517C211yesmaximal, characteristic
4#21444319C211yesmaximal, characteristic
5#21444174C211yesmaximal, characteristic
6#21443676C211yesmaximal, characteristic
7C61×#1573C211yesmaximal, characteristic
8#16840319C2211yescharacteristic
9C2×#14519769C2211yescharacteristic
10#16840171—21no—
11#16840131—21no—
12#16840098—21no—
13#16840093—21no—
14#16840070—21no—
15#16840070—21no—
16#16839819C2211yescharacteristic
17C4×C4⋊Dic61C2211yescharacteristic
18#16839525—21no—
19#16839525—21no—
20#16839509—21no—
21#16839507—21no—
22#16839500—22no—
23#16839487—22no—
24C61×#432C2211yescharacteristic
25C61×#431C2211yescharacteristic
26C2×C4⋊C8×C61C2211yescharacteristic
27C61×#335—21no—
28C61×#334—21no—
29#14519777D411yescharacteristic
30#14519777D411yescharacteristic
31#14519769—21no—
32#14519769—21no—
33#14519769—21no—
34#14519769—21no—
35#14519769—21no—
36#14519756—21no—
37#14519756—21no—
38C4×Dic122—21no—
39C4×Dic122—21no—
40#14519736—21no—
41C2×C4⋊Dic61—21no—
42C2×C4⋊Dic61D411yescharacteristic
43C2×C4⋊Dic61D411yescharacteristic
44C2×#11758196—21no—
45C2×#11758196—21no—
46C2×C4×Dic61—21no—
47#14519711—21no—
48#14519711—21no—
49#14519709—21no—
50#14519709—21no—
51C4⋊#92418—21no—
52#14519702—21no—
53#14519702—21no—
54#14519702—21no—
55#14519702—21no—
56C22⋊#92418—21no—
57#14519688—21no—
58#14519684—21no—
59C22×C8×C61—21no—
60C2×C42×C61C2311yescharacteristic
61C4⋊C8×C61—21no—
62C4⋊C8×C61—21no—
63C4⋊C8×C61—21no—
64C4⋊C8×C61D411yescharacteristic
65C4⋊C8×C61D411yescharacteristic
66C22⋊C8×C61—21no—
67C22⋊C8×C61D412yes—
68#97×C61—21no—
69C4×C8×C61—21no—
70C22×C4×C61C2×D411yescharacteristic
71C22×C4×C61C2×D411yescharacteristic
72C22×C4×C61#4111yescharacteristic
73C22×Dic61—21no—
74C22×Dic61—21no—
75C22×Dic61—41no—
76C2×Dic122—21no—
77C2×Dic122—21no—
78C2×C8×C61—21no—
79C2×C8×C61—21no—
80C2×C8×C61—22no—
81C2×C8×C61—42no—
82C2×C8×C61—41no—
83C42×C61C2×D411yescharacteristic
84C42×C61C2×D411yescharacteristic
85C42×C61#4111yescharacteristic
86C42×C61#4111yescharacteristic
87C22⋊Dic61—41no—
88C4⋊Dic61—22no—
89C4⋊Dic61—21no—
90C4⋊Dic61—21no—
91C4⋊Dic61—21no—
92C4⋊Dic61—21no—
93C4⋊Dic61—21no—
94C4⋊Dic61—21no—
95C4⋊Dic61—21no—
96C4⋊Dic61—21no—
97C4⋊Dic61—41no—
98#11758196—41no—
99#11758196—41no—
100#11758196—41no—
101#11758196—41no—
102#11758196—41no—
103#11758196—41no—
104C4×Dic61—41no—
105C4×Dic61—81no—
106C2×#92418—41no—
107C23×C61#12111yescharacteristic
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—41no—
113C2×C4×C61#12011yescharacteristic
114C2×C4×C61#12111yescharacteristic
115C2×C4×C61#12111yescharacteristic
116C2×C4×C61#12311yescharacteristic
117C2×C4×C61#12311yescharacteristic
118C2×C4×C61#12411yescharacteristic
119C2×Dic61—42no—
120C2×Dic61—41no—
121C2×Dic61—41no—
122C2×Dic61—41no—
123C2×Dic61—41no—
124C2×Dic61—41no—
125C2×Dic61—41no—
126C2×Dic61—81no—
127C2×Dic61—81no—
128C2×Dic61—81no—
129Dic122—41no—
130Dic122—41no—
131Dic122—81no—
132C8×C61—42no—
133C8×C61—41no—
134C8×C61—41no—
135C8×C61—81no—
136#92418—81no—
137#10511—611nomaximal, Sylow
138C22×C61—21no—
139C22×C61—21no—
140C22×C61#39411yescharacteristic
141C22×C61#47111yescharacteristic
142C22×C61#47311yescharacteristic
143C4×C61—21no—
144C4×C61—21no—
145C4×C61—21no—
146C4×C61—21no—
147C4×C61—21no—
148C4×C61#45411yescharacteristic
149C4×C61#45611yescharacteristic
150Dic61—82no—
151Dic61—81no—
152Dic61—81no—
153Dic61—81no—
154Dic61—81no—
155#3236—611no—
156#1989—611no—
157#1573D6111yescharacteristic
158#1552—611no—
159#1503—611no—
160#1470—611no—
161#1285—611no—
162C2×C61—21no—
163C2×C61—21no—
164C2×C61#203811yescharacteristic
165C2×C61#205211yescharacteristic
166C2×C61#205311yescharacteristic
167#533—611no—
168C2×#125—611no—
169#501—1221no—
170#491—1221no—
171#484—1221no—
172#483—1221no—
173#479—1221no—
174#479—1221no—
175#432—611no—
176#432C2×D6111yescharacteristic
177#431C2×D6111yescharacteristic
178C2×C4⋊C8C2×D6111yescharacteristic
179C4×C4⋊C4—611no—
180#340—1221no—
181#340—1221no—
182#335—21no—
183#334—21no—
184#332—1221no—
185#332—1221no—
186#328—1222no—
187#324—1222no—
188C61#1051111yescharacteristic, complemented, Sylow
189C22×C8—21no—
190C4⋊Q8—611no—
191C4⋊Q8—611no—
192#125—1221no—
193#125—1221no—
194#125—1221no—
195#125—1221no—
196#125—1221no—
197C22⋊Q8—1221no—
198C22⋊Q8—1221no—
199C4×Q8—1221no—
200C4×Q8—1221no—
201#117—1221no—
202C2×C4⋊C4—611no—
203C2×C4⋊C4—611no—
204C2×C4⋊C4—1221no—
205C2×C4⋊C4—1221no—
206C2×C4⋊C4—1221no—
207C2×C42—1221no—
208C2×C42C22×D6111yescharacteristic
209#107—1221no—
210#107—1221no—
211#106—1221no—
212#106—1221no—
213C4⋊C8—21no—
214C4⋊C8—21no—
215C4⋊C8—21no—
216C4⋊C8—1221no—
217C4⋊C8C22⋊D6111yescharacteristic
218C4⋊C8C22⋊D6111yescharacteristic
219#103—1221no—
220#103—1221no—
221#103—1221no—
222#103—1221no—
223C22⋊C8—21no—
224C22⋊C8—1221no—
225C22⋊C8D24412yes—
226#97—21no—
227#97—1221no—
228C4×C8—21no—
229#95—1221no—
230C2×Q8—1221no—
231C2×Q8—1221no—
232C22×C4—1221no—
233C22×C4—1221no—
234C22×C4—2441no—
235C22×C4C2×D24411yescharacteristic
236C22×C4D4×D6111yescharacteristic
237C22×C4#1175822611yescharacteristic
238C2×C8—21no—
239C2×C8—21no—
240C2×C8—22no—
241C2×C8—42no—
242C2×C8—41no—
243C2×C8—2441no—
244C4⋊C4—1222no—
245C4⋊C4—1221no—
246C4⋊C4—1221no—
247C4⋊C4—1221no—
248C4⋊C4—1221no—
249C4⋊C4—1221no—
250C4⋊C4—1221no—
251C4⋊C4—1221no—
252C4⋊C4—1221no—
253C4⋊C4—2441no—
254C4⋊C4—2441no—
255C4⋊C4—2441no—
256C4⋊C4—2441no—
257C4⋊C4—2441no—
258C4⋊C4—2441no—
259C4⋊C4—2441no—
260C22⋊C4—2441no—
261C42—4881no—
262C42—2441no—
263C42#1175822211yescharacteristic
264C42D4×D6111yescharacteristic
265C42#1175822611yescharacteristic
266C42C2×C22⋊D6111yescharacteristic
267C23#1451975211yescharacteristic
268Q8—4881no—
269Q8—2441no—
270Q8—2441no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—41no—
276C2×C4—4881no—
277C2×C4—4881no—
278C2×C4—4881no—
279C2×C4—2442no—
280C2×C4—2441no—
281C2×C4—2441no—
282C2×C4—2441no—
283C2×C4—2441no—
284C2×C4—2441no—
285C2×C4—2441no—
286C2×C4#1451974511yescharacteristic
287C2×C4#1451975111yescharacteristic
288C2×C4#1451975211yescharacteristic
289C2×C4#1451976211yescharacteristic
290C2×C4#1451976211yescharacteristic
291C2×C4#1451976611yescharacteristic
292C8—42no—
293C8—41no—
294C8—41no—
295C8—81no—
296C8—4881no—
297C22—21no—
298C22—21no—
299C22#1683967911yescharacteristic
300C22#1684002611yescharacteristic
301C22#1684003811yescharacteristic
302C4—21no—
303C4—21no—
304C4—21no—
305C4—21no—
306C4—21no—
307C4—4882no—
308C4—4881no—
309C4—4881no—
310C4—4881no—
311C4—4881no—
312C4#1683993311yescharacteristic
313C4#1683994311yescharacteristic
314C2—21no—
315C2—21no—
316C2#2144703811yescharacteristic
317C2#2144712011yescharacteristic
318C2#2144712511yescharacteristic
subgroupG/H
centerC22#16839679
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1573C2
socleC22×C61#394
prime radicalC23×C61#121
hypercenter#1573D61
hypocenterC61#10511
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1573

Complements

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

NH ≅ G/Ntype
188. C61#10511semidirect

Maximal subgroups

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

subgroupindex
#214570272
#214467742
#214445172
#214443192
#214441742
#214436762
C61×#15732
#1051161