Finite Group Databasebeta

← #29600433

Subgroups — #29600433

Order 15616.

304 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 57 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#21456903C211yesmaximal, characteristic
2#21447512C211yesmaximal, characteristic
3#21447507C211yesmaximal, characteristic
4#21443992C211yesmaximal, characteristic, complemented
5#21443987C211yesmaximal, characteristic, complemented
6#21443987C211yesmaximal, characteristic, complemented
7C61×#1413C211yesmaximal, characteristic, complemented
8#16840375C411yescharacteristic
9#16840337C2211yescharacteristic
10#16840156C411yescharacteristic
11#16840141C2211yescharacteristic
12#16840119C411yescharacteristic
13#16839987—21no—
14#16839971—21no—
15#16839927—21no—
16#16839919—21no—
17#16839824C411yescharacteristic
18#16839745—21no—
19#101×D61—21no—
20#16839561C2211yescharacteristic
21#16839561C2211yescharacteristic
22#16839560—21no—
23#16839558—21no—
24C61×#491C2211yescharacteristic
25C61×#356C2211yescharacteristic
26C61×#356C2211yescharacteristic
27C2×#11758226D411yescharacteristic
28C2×Q8×D61D411yescharacteristic
29C2×Dic244—21no—
30C2×#11758202—21no—
31C2×#11758202—21no—
32C2×#11758190—21no—
33M16×D61—41no—
34M16×D61—41no—
35#14519777C2×C411yescharacteristic
36#14519775D411yescharacteristic
37#14519772—41no—
38#14519768—41no—
39#14519766D411yescharacteristic
40#14519765C2×C411yescharacteristic
41#14519762—41no—
42#14519757—21no—
43#14519755—41no—
44#14519742—21no—
45#14519734C2×C411yescharacteristic
46#14519706—21no—
47#14519700—21no—
48#14519697—21no—
49#14519696—21no—
50#14519696—21no—
51#14519695—41no—
52#14519693—41no—
53#14519689—21no—
54C4×#92418C2×C411yescharacteristic
55C4⋊Q8×C61C2311yescharacteristic
56#125×C61C2×C411yescharacteristic
57#103×C61—21no—
58#103×C61—21no—
59#101×C61—21no—
60#101×C61—21no—
61#97×C61C2×C411yescharacteristic
62C2×Q8×C61C2×D411yescharacteristic
63C2×Q8×C61C2×D411yescharacteristic
64#11758226—81no—
65Q8×D61—81no—
66C2×D244—21no—
67C2×D244C22⋊C411yescharacteristic
68C2×C4×D61—21no—
69C2×C4×D61—21no—
70C2×C4×D61C22⋊C411yescharacteristic
71C2×Dic122—21no—
72C2×Dic122—21no—
73C2×Dic122C22⋊C411yescharacteristic
74M16×C61—41no—
75M16×C61—41no—
76C2×C8×C61—21no—
77C4⋊C4×C61—21no—
78C4⋊C4×C61—41no—
79C4⋊C4×C61—41no—
80C42×C61C22×C411yescharacteristic
81#11758202—81no—
82#11758202—81no—
83#11758198—21no—
84#11758198—41no—
85#11758198—41no—
86#11758198—41no—
87C4⋊Dic61—41no—
88C4⋊Dic61—41no—
89#11758196—21no—
90#11758196—41no—
91#11758196—41no—
92C4×Dic61—41no—
93C4×Dic61C22⋊C411yescharacteristic
94#11758194—41no—
95#11758194—41no—
96C2×#92418—21no—
97Dic244—81no—
98#11758190—81no—
99#11758189—81no—
100#11758189—81no—
101C8×D61—81no—
102C8×D61—81no—
103C22×D61—21no—
104C22×D61#9911yescharacteristic
105Q8×C61—41no—
106Q8×C61—41no—
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—41no—
111C2×C4×C61C2×C22⋊C411yescharacteristic
112C2×Dic61—21no—
113C2×Dic61—21no—
114C2×Dic61—41no—
115C2×Dic61#9911yescharacteristic
116D244—41no—
117D244—81no—
118C4×D61—41no—
119C4×D61—41no—
120C4×D61—41no—
121C4×D61—41no—
122C4×D61—41no—
123Dic122—41no—
124Dic122—41no—
125Dic122—41no—
126Dic122—81no—
127C8×C61—41no—
128C8×C61—81no—
129C8×C61—81no—
130#92418—41no—
131#92418—81no—
132#92418—81no—
133#13612—611nomaximal, Sylow
134C22×C61C2×#9911yescharacteristic
135C2×D61—21no—
136C2×D61—41no—
137C2×D61—41no—
138C2×D61—81no—
139C4×C61—21no—
140C4×C61—41no—
141C4×C61—41no—
142C4×C61—41no—
143C4×C61—81no—
144Dic61—21no—
145Dic61—41no—
146Dic61—41no—
147Dic61—81no—
148#3223—611no—
149#2135—611no—
150#2133—611no—
151#1413—611no—
152#1413D6111yescharacteristic, complemented
153#1411—611no—
154#1411—611no—
155C2×C61—21no—
156C2×C61#212711yescharacteristic
157D61—41no—
158D61—81no—
159#541—611no—
160#536—611no—
161#497—611no—
162#494—611no—
163#491C2×D6111yescharacteristic
164#488—611no—
165#464—1221no—
166#462—1221no—
167#452—1221no—
168#451—1221no—
169#433—611no—
170#413—1221no—
171C2×#101—1221no—
172#356—611no—
173#356—611no—
174#356—1221no—
175#356C2×D6111yescharacteristic
176#356C2×D6111yescharacteristic
177#355—1221no—
178C61#1361211yescharacteristic, complemented, Sylow
179C2×#41—611no—
180C22×Q8—611no—
181C2×Q16—1221no—
182C2×Q16—1221no—
183C2×Q16—1221no—
184C2×SD16—1221no—
185C2×M16—2441no—
186C2×M16—2441no—
187C4⋊Q8—611no—
188C4⋊Q8—611no—
189C4⋊Q8C22×D6111yescharacteristic
190#126—2441no—
191#125—2441no—
192#125C4×D6111yescharacteristic
193#124—611no—
194#124—611no—
195#123—2441no—
196C22⋊Q8—1221no—
197C22⋊Q8—2441no—
198C4×Q8—1221no—
199#117—611no—
200C4⋊C8—1221no—
201#103—21no—
202#103—21no—
203#103—1221no—
204#102—1221no—
205#101—21no—
206#101—21no—
207#101—1221no—
208#101—1221no—
209#101—2441no—
210#100—2441no—
211C22⋊C8—1221no—
212#97C4×D6111yescharacteristic
213C4×C8—611no—
214#41—4881no—
215C2×Q8—611no—
216C2×Q8—1221no—
217C2×Q8—1221no—
218C2×Q8—4881no—
219C2×Q8D4×D6111yescharacteristic
220C2×Q8D4×D6111yescharacteristic
221C2×D4—611no—
222C2×D4—1221no—
223C22×C4—611no—
224C22×C4—1221no—
225C22×C4—1221no—
226Q16—4881no—
227Q16—4881no—
228Q16—4881no—
229SD16—4881no—
230M16—41no—
231M16—41no—
232M16—4881no—
233M16—4881no—
234M16—2441no—
235M16—2441no—
236C2×C8—21no—
237C2×C8—1221no—
238C2×C8—4881no—
239C2×C8—4881no—
240C4⋊C4—21no—
241C4⋊C4—41no—
242C4⋊C4—41no—
243C4⋊C4—1221no—
244C4⋊C4—2441no—
245C4⋊C4—2441no—
246C4⋊C4—2441no—
247C4⋊C4—2441no—
248C22⋊C4—1221no—
249C22⋊C4—2441no—
250C22⋊C4—2441no—
251C22⋊C4—2441no—
252C42—611no—
253C42—2441no—
254C42C2×C4×D6111yescharacteristic
255C23—611no—
256C23—1221no—
257Q8—41no—
258Q8—41no—
259Q8—4881no—
260Q8—2441no—
261Q8—2441no—
262Q8—2441no—
263D4—4881no—
264D4—2441no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—41no—
269C2×C4—611no—
270C2×C4—1221no—
271C2×C4—1221no—
272C2×C4—2441no—
273C2×C4—2441no—
274C2×C4—2441no—
275C2×C4—2441no—
276C2×C4—2441no—
277C2×C4—2441no—
278C2×C4C22⋊C4×D6111yescharacteristic
279C8—41no—
280C8—81no—
281C8—81no—
282C8—4881no—
283C8—4881no—
284C8—2441no—
285C22—1221no—
286C22—4881no—
287C22—2441no—
288C22—2441no—
289C22#99×D6111yescharacteristic
290C4—21no—
291C4—41no—
292C4—41no—
293C4—41no—
294C4—81no—
295C4—1221no—
296C4—4881no—
297C4—2441no—
298C4—2441no—
299C2—21no—
300C2—4881no—
301C2—2441no—
302C2#2144748711yescharacteristic
subgroupG/H
centerC2#21447487
commutatorC42×C61C22×C4
FrattiniC4⋊Q8C22×D61
FittingC61×#1413C2
socleC2×C61#2127
prime radicalC2×#11758226D4
cosocleC4⋊Q8×C61C23
hypercenter#1413D61
hypocenterC61#13612
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C4⋊Q8 ◁ #1413

Complements

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

NH ≅ G/Ntype
4. #21443992C2semidirect
5. #21443987C2semidirect
6. #21443987C2semidirect
7. C61×#1413C2semidirect
152. #1413D61semidirect
178. C61#13612semidirect

Maximal subgroups

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

subgroupindex
#214569032
#214475122
#214475072
#214439922
#214439872
C61×#14132
#1361261