Finite Group Databasebeta

← #29600432

Subgroups — #29600432

Order 15616.

304 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 67 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#21456902C211yesmaximal, characteristic
2#21447514C211yesmaximal, characteristic
3#21443991C212yesmaximal, complemented
4#21443987C212yesmaximal, complemented
5C61×#2133C211yesmaximal, characteristic
6#16840374C411yescharacteristic
7#16840157C411yescharacteristic
8#16840141C2211yescharacteristic
9#16840130C2211yescharacteristic
10#16840116C411yescharacteristic
11#16839981—21no—
12#16839969—21no—
13#16839924—21no—
14#16839918—21no—
15#16839823C411yescharacteristic
16#16839746—21no—
17#16839561—21no—
18#16839561C2212yes—
19C61×#536C2211yescharacteristic
20C2×#101×C61—21no—
21C61×#356C2212yes—
22C61×#355—21no—
23C2×#11758202—21no—
24C2×#11758202—21no—
25C2×#11758202—21no—
26C2×#11758200—21no—
27C2×#11758194—41no—
28#14519777C2×C411yescharacteristic
29#14519770—41no—
30#14519769C2×C411yescharacteristic
31#14519767—41no—
32#14519756—21no—
33C4×Dic122—21no—
34C4⋊#92418—21no—
35#14519701—21no—
36#14519701—21no—
37#14519701—21no—
38#14519698—21no—
39#14519696—22no—
40#14519694—41no—
41C22⋊#92418—21no—
42#14519688C2×C411yescharacteristic
43C4×#92418C2×C411yescharacteristic
44C2×#41×C61D411yescharacteristic
45C22×Q8×C61D411yescharacteristic
46C2×M16×C61—41no—
47C4⋊Q8×C61D411yescharacteristic
48C4⋊Q8×C61C2311yescharacteristic
49#124×C61C2×C411yescharacteristic
50#124×C61D411yescharacteristic
51#123×C61—41no—
52C22⋊Q8×C61—41no—
53#117×C61C2×C411yescharacteristic
54#101×C61—22no—
55#101×C61—41no—
56#41×C61—81no—
57C2×Q8×C61—21no—
58C2×Q8×C61—81no—
59C2×Q8×C61C22⋊C411yescharacteristic
60C2×Q8×C61C2×D411yescharacteristic
61C2×Q8×C61C2×D411yescharacteristic
62C2×D4×C61—21no—
63C2×D4×C61C22⋊C411yescharacteristic
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61C22⋊C411yescharacteristic
67C2×Dic122—21no—
68M16×C61—42no—
69M16×C61—81no—
70C2×C8×C61—81no—
71C4⋊C4×C61—21no—
72C4⋊C4×C61—41no—
73C4⋊C4×C61—41no—
74C22⋊C4×C61—21no—
75C22⋊C4×C61—41no—
76C22⋊C4×C61—41no—
77C42×C61C22⋊C411yescharacteristic
78C42×C61C22×C411yescharacteristic
79C22⋊Dic61—41no—
80#11758202—81no—
81#11758202—81no—
82#11758202—81no—
83#11758200—81no—
84C4⋊Dic61—21no—
85C4⋊Dic61—41no—
86#11758196—41no—
87#11758196—41no—
88#11758196—41no—
89C4×Dic61—41no—
90#11758194—42no—
91#11758194—81no—
92C2×#92418—21no—
93C2×#92418—21no—
94C2×#92418—81no—
95C23×C61—21no—
96C23×C61#9911yescharacteristic
97Q8×C61—41no—
98Q8×C61—41no—
99Q8×C61—41no—
100Q8×C61—81no—
101D4×C61—41no—
102D4×C61—81no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—41no—
109C2×C4×C61—41no—
110C2×C4×C61—41no—
111C2×C4×C61—41no—
112C2×C4×C61—41no—
113C2×C4×C61#9911yescharacteristic
114C2×C4×C61C2×C22⋊C411yescharacteristic
115C2×Dic61—41no—
116C2×Dic61—41no—
117Dic122—41no—
118Dic122—41no—
119C8×C61—82no—
120#92418—41no—
121#92418—41no—
122#92418—82no—
123#13612—611nomaximal, Sylow
124C22×C61—21no—
125C22×C61—41no—
126C22×C61—41no—
127C22×C61—81no—
128C22×C61C2×#9911yescharacteristic
129C4×C61—21no—
130C4×C61—21no—
131C4×C61—41no—
132C4×C61—41no—
133C4×C61—41no—
134C4×C61—41no—
135C4×C61—41no—
136Dic61—81no—
137Dic61—81no—
138#3223—611no—
139#2135—611no—
140#2133D6111yescharacteristic
141#1413—612no—
142#1411—612no—
143C2×C61—21no—
144C2×C61—41no—
145C2×C61—81no—
146C2×C61#212711yescharacteristic
147#541—611no—
148#536C2×D6111yescharacteristic
149#497—611no—
150#494—611no—
151#491—611no—
152#488—611no—
153#464—1221no—
154#462—1221no—
155#452—1221no—
156#451—1221no—
157#433—611no—
158#413—1221no—
159C2×#101—21no—
160#356—612no—
161#356—1221no—
162#356C2×D6112yes—
163#355—21no—
164C61#1361211yescharacteristic, complemented, Sylow
165C2×#41D24411yescharacteristic
166C22×Q8C22⋊D6111yescharacteristic
167C2×Q16—1221no—
168C2×Q16—1221no—
169C2×Q16—1221no—
170C2×SD16—1221no—
171C2×M16—41no—
172C2×M16—2441no—
173C4⋊Q8—611no—
174C4⋊Q8D24411yescharacteristic
175C4⋊Q8C22×D6111yescharacteristic
176#126—2441no—
177#125—611no—
178#125—2441no—
179#124C4×D6111yescharacteristic
180#124C22⋊D6111yescharacteristic
181#123—41no—
182C22⋊Q8—41no—
183C22⋊Q8—1221no—
184C4×Q8—1221no—
185#117C4×D6111yescharacteristic
186C4⋊C8—1221no—
187#103—1221no—
188#103—1221no—
189#103—1221no—
190#102—1221no—
191#101—22no—
192#101—41no—
193#101—1222no—
194#100—2441no—
195C22⋊C8—1221no—
196#97—611no—
197C4×C8—611no—
198#41—81no—
199C2×Q8—21no—
200C2×Q8—81no—
201C2×Q8—1221no—
202C2×Q8#1175819811yescharacteristic
203C2×Q8C2×D24411yescharacteristic
204C2×Q8C2×C22⋊D6111yescharacteristic
205C2×D4—21no—
206C2×D4#1175819811yescharacteristic
207C22×C4—21no—
208C22×C4—21no—
209C22×C4#1175819811yescharacteristic
210Q16—4881no—
211Q16—4881no—
212Q16—4881no—
213SD16—4881no—
214M16—42no—
215M16—81no—
216M16—4881no—
217M16—2442no—
218C2×C8—81no—
219C2×C8—1221no—
220C2×C8—1221no—
221C2×C8—4881no—
222C4⋊C4—21no—
223C4⋊C4—41no—
224C4⋊C4—41no—
225C4⋊C4—1221no—
226C4⋊C4—2441no—
227C4⋊C4—2441no—
228C4⋊C4—2441no—
229C4⋊C4—2441no—
230C22⋊C4—21no—
231C22⋊C4—41no—
232C22⋊C4—41no—
233C22⋊C4—2441no—
234C42—2441no—
235C42#1175819811yescharacteristic
236C42C2×C4×D6111yescharacteristic
237C23—21no—
238C23#1451969111yescharacteristic
239Q8—41no—
240Q8—41no—
241Q8—41no—
242Q8—81no—
243Q8—2441no—
244Q8—2441no—
245D4—41no—
246D4—81no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—2441no—
258C2×C4—2441no—
259C2×C4#1451969111yescharacteristic
260C2×C4C2×#1175819811yescharacteristic
261C8—82no—
262C8—4882no—
263C8—2441no—
264C8—2441no—
265C22—21no—
266C22—41no—
267C22—41no—
268C22—81no—
269C22C2×#1451969111yescharacteristic
270C4—21no—
271C4—21no—
272C4—41no—
273C4—41no—
274C4—41no—
275C4—41no—
276C4—41no—
277C4—4881no—
278C4—4881no—
279C2—21no—
280C2—41no—
281C2—81no—
282C2#2144748611yescharacteristic
subgroupG/H
centerC2#21447486
commutatorC42×C61C22×C4
FrattiniC4⋊Q8C22×D61
FittingC61×#2133C2
socleC2×C61#2127
prime radicalC2×#41×C61D4
cosocleC4⋊Q8×C61C23
hypercenter#2133D61
hypocenterC61#13612
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C22×C4 ◁ #536 ◁ #2133

Complements

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

NH ≅ G/Ntype
3. #21443991C2semidirect
4. #21443987C2semidirect
164. C61#13612semidirect

Maximal subgroups

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

subgroupindex
#214569022
#214475142
#214439912
#214439872
C61×#21332
#1361261