Finite Group Databasebeta

← #29583649

Subgroups — #29583649

Order 15616.

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

normal subgroups only

This group has 376 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
1C2×#16840047C211yesmaximal, characteristic
2#21444591C211yesmaximal, characteristic
3#21444505C211yesmaximal, characteristic
4#21444501C211yesmaximal, characteristic
5#21444214C211yesmaximal, characteristic
6#21443714C211yesmaximal, characteristic
7C61×#1801C211yesmaximal, characteristic
8C2×#14519777C2211yescharacteristic
9#16840047—22no—
10#16840047—22no—
11#16839815C2211yescharacteristic
12#16839815C2211yescharacteristic
13C2×#14519708—21no—
14C2×C4⋊#92418C2211yescharacteristic
15C2×#14519701—21no—
16#16839512—22no—
17#16839510—22no—
18#16839507—22no—
19Q8⋊#92418—22no—
20C2×C4×Q8×C61C2211yescharacteristic
21C61×#423C2211yescharacteristic
22C61×#423C2211yescharacteristic
23C2×#101×C61—21no—
24C61×#343—21no—
25C22×Dic122—21no—
26C22×#92418—21no—
27#14519777—21no—
28#14519777—21no—
29#14519777—21no—
30#14519777D412yes—
31C2×C4⋊Dic61—21no—
32C2×C4⋊Dic61—21no—
33#14519708—24no—
34C4⋊#92418—21no—
35C4⋊#92418—21no—
36C4⋊#92418D412yes—
37C4⋊#92418D412yes—
38#14519701—24no—
39C22⋊#92418—21no—
40C22⋊#92418—21no—
41C4×#92418—21no—
42C4×#92418—21no—
43C22×Q8×C61D411yescharacteristic
44C2×M16×C61—21no—
45C2×M16×C61—21no—
46C4×Q8×C61—21no—
47C4×Q8×C61—21no—
48C4×Q8×C61—21no—
49C4×Q8×C61—21no—
50C2×C4⋊C4×C61—21no—
51C2×C4⋊C4×C61D411yescharacteristic
52C2×C42×C61—21no—
53C2×C42×C61C2311yescharacteristic
54C4⋊C8×C61—21no—
55C4⋊C8×C61—21no—
56C4⋊C8×C61—21no—
57C4⋊C8×C61—21no—
58#101×C61—42no—
59C2×Q8×C61—21no—
60C2×Q8×C61—21no—
61C2×Q8×C61—21no—
62C2×Q8×C61—21no—
63C2×Q8×C61—21no—
64C2×Q8×C61SD1612yes—
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61C2×D411yescharacteristic
68C22×C4×C61#4111yescharacteristic
69C22×C4×C61#4111yescharacteristic
70C22×Dic61—41no—
71C2×Dic122—22no—
72C2×Dic122—41no—
73C2×Dic122—82no—
74M16×C61—41no—
75M16×C61—41no—
76M16×C61—41no—
77M16×C61—41no—
78C2×C8×C61—41no—
79C2×C8×C61—41no—
80C4⋊C4×C61—21no—
81C4⋊C4×C61—21no—
82C4⋊C4×C61—41no—
83C4⋊C4×C61—41no—
84C42×C61—41no—
85C42×C61—41no—
86C42×C61C2×D411yescharacteristic
87C42×C61C2×D411yescharacteristic
88C42×C61C2×D411yescharacteristic
89C42×C61#4111yescharacteristic
90C4⋊Dic61—22no—
91C4⋊Dic61—22no—
92C4⋊Dic61—41no—
93C4⋊Dic61—41no—
94C2×#92418—22no—
95C2×#92418—22no—
96C2×#92418—41no—
97C2×#92418—41no—
98C2×#92418—41no—
99C23×C61#12311yescharacteristic
100Q8×C61—22no—
101Q8×C61—22no—
102Q8×C61—41no—
103Q8×C61—41no—
104C2×C4×C61—22no—
105C2×C4×C61—22no—
106C2×C4×C61—41no—
107C2×C4×C61—41no—
108C2×C4×C61—41no—
109C2×C4×C61—41no—
110C2×C4×C61—81no—
111C2×C4×C61#12011yescharacteristic
112C2×C4×C61#12111yescharacteristic
113C2×C4×C61#12111yescharacteristic
114C2×C4×C61#12111yescharacteristic
115C2×C4×C61#12311yescharacteristic
116C2×C4×C61#12411yescharacteristic
117C2×C4×C61C2×SD1611yescharacteristic
118C2×C4×C61#13511yescharacteristic
119C2×C4×C61#13711yescharacteristic
120C2×C4×C61#13711yescharacteristic
121C2×Dic61—42no—
122C2×Dic61—82no—
123Dic122—82no—
124Dic122—82no—
125C8×C61—81no—
126C8×C61—81no—
127#92418—42no—
128#92418—42no—
129#92418—81no—
130#10450—611nomaximal, Sylow
131C22×C61—21no—
132C22×C61—21no—
133C22×C61#39411yescharacteristic
134C22×C61#48311yescharacteristic
135C22×C61#48511yescharacteristic
136C4×C61—21no—
137C4×C61—21no—
138C4×C61—21no—
139C4×C61—42no—
140C4×C61—81no—
141C4×C61#44811yescharacteristic
142C4×C61#45211yescharacteristic
143C4×C61#46511yescharacteristic
144C4×C61#47011yescharacteristic
145C4×C61#47112yes—
146Dic61—82no—
147C2×#475—611no—
148#1801D6111yescharacteristic
149#1570—611no—
150#1549—611no—
151#1548—611no—
152#1479—611no—
153#1301—611no—
154C2×C61—21no—
155C2×C61—21no—
156C2×C61#203511yescharacteristic
157C2×C61#204611yescharacteristic
158C2×C61#204911yescharacteristic
159C2×C4⋊Q8—611no—
160C2×C4×Q8C2×D6111yescharacteristic
161#475—1222no—
162#475—1222no—
163#431—611no—
164#431—611no—
165C2×#106—1221no—
166#423C2×D6111yescharacteristic
167#423C2×D6111yescharacteristic
168C2×C4⋊C8—611no—
169C2×#103—1221no—
170C2×#101—21no—
171#343—21no—
172#334—1222no—
173#333—1222no—
174#332—1222no—
175Q8⋊C8—1222no—
176C61#1045011yescharacteristic, complemented, Sylow
177C22×Q8—1221no—
178C22×Q8C22⋊D6111yescharacteristic
179C2×M16—21no—
180C2×M16—21no—
181C22×C8—1221no—
182C4⋊Q8—612no—
183C4⋊Q8—1221no—
184C4⋊Q8—1221no—
185C4⋊Q8—1221no—
186C4×Q8—21no—
187C4×Q8—21no—
188C4×Q8—21no—
189C4×Q8—21no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—1221no—
192C2×C4⋊C4—1221no—
193C2×C4⋊C4C22⋊D6111yescharacteristic
194C2×C42—21no—
195C2×C42C22×D6111yescharacteristic
196#106—1224no—
197C4⋊C8—21no—
198C4⋊C8—21no—
199C4⋊C8—21no—
200C4⋊C8—21no—
201C4⋊C8—612no—
202C4⋊C8—612no—
203C4⋊C8—1221no—
204C4⋊C8—1221no—
205#103—1224no—
206#101—42no—
207C22⋊C8—1221no—
208C22⋊C8—1221no—
209C4×C8—1221no—
210C4×C8—1221no—
211C2×Q8—21no—
212C2×Q8—21no—
213C2×Q8—21no—
214C2×Q8—21no—
215C2×Q8—21no—
216C2×Q8—1222no—
217C2×Q8—4882no—
218C2×Q8—2441no—
219C2×Q8#1175820012yes—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—2441no—
223C22×C4#1175822211yescharacteristic
224C22×C4#1175822211yescharacteristic
225C22×C4C2×C22⋊D6111yescharacteristic
226M16—41no—
227M16—41no—
228M16—41no—
229M16—41no—
230C2×C8—41no—
231C2×C8—41no—
232C2×C8—1222no—
233C2×C8—1222no—
234C2×C8—2441no—
235C2×C8—2441no—
236C2×C8—2441no—
237C4⋊C4—21no—
238C4⋊C4—21no—
239C4⋊C4—41no—
240C4⋊C4—41no—
241C4⋊C4—1222no—
242C4⋊C4—1222no—
243C4⋊C4—2441no—
244C4⋊C4—2441no—
245C42—41no—
246C42—41no—
247C42D4×D6111yescharacteristic
248C42D4×D6111yescharacteristic
249C42D4×D6111yescharacteristic
250C42#1175822411yescharacteristic
251C23#1451976011yescharacteristic
252Q8—22no—
253Q8—22no—
254Q8—41no—
255Q8—41no—
256Q8—4882no—
257Q8—4882no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—81no—
265C2×C4—4882no—
266C2×C4—2442no—
267C2×C4#1451974511yescharacteristic
268C2×C4#1451974911yescharacteristic
269C2×C4#1451975011yescharacteristic
270C2×C4#1451975011yescharacteristic
271C2×C4#1451975911yescharacteristic
272C2×C4#1451976311yescharacteristic
273C2×C4C2×#1175820011yescharacteristic
274C2×C4#1451979711yescharacteristic
275C2×C4#1451980711yescharacteristic
276C2×C4#1451980811yescharacteristic
277C8—81no—
278C8—81no—
279C8—4881no—
280C8—2442no—
281C8—2442no—
282C22—21no—
283C22—21no—
284C22#1683967711yescharacteristic
285C22#1684009211yescharacteristic
286C22#1684010311yescharacteristic
287C4—21no—
288C4—21no—
289C4—21no—
290C4—42no—
291C4—81no—
292C4—4882no—
293C4#1683990011yescharacteristic
294C4#1683992211yescharacteristic
295C4#1683998911yescharacteristic
296C4#1684001811yescharacteristic
297C4#1684002812yes—
298C2—21no—
299C2—21no—
300C2#2144701511yescharacteristic
301C2#2144707811yescharacteristic
302C2#2144709911yescharacteristic
subgroupG/H
centerC22#16839677
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1801C2
socleC22×C61#394
prime radicalC23×C61#123
hypercenter#1801D61
hypocenterC61#10450
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1801

Complements

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

NH ≅ G/Ntype
176. C61#10450semidirect

Maximal subgroups

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

subgroupindex
C2×#168400472
#214445912
#214445052
#214445012
#214442142
#214437142
C61×#18012
#1045061