Finite Group Databasebeta

← #29600428

Subgroups — #29600428

Order 15616.

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

normal subgroups only

This group has 316 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#21456881C211yesmaximal, characteristic
2#21447512C211yesmaximal, characteristic, complemented
3#21447507C211yesmaximal, characteristic, complemented
4#21443992C211yesmaximal, characteristic, complemented
5#21443985C211yesmaximal, characteristic, complemented
6#21443985C211yesmaximal, characteristic, complemented
7C61×#1413C211yesmaximal, characteristic, complemented
8#16840368C411yescharacteristic
9#16840337C2211yescharacteristic
10#16840151C411yescharacteristic
11#16840136C2211yescharacteristic
12#16840119C411yescharacteristic
13#16839980—21no—
14#16839966—21no—
15#16839910—21no—
16#16839902—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×#11758190—21no—
30C2×#11758201—21no—
31C2×#11758201—21no—
32C2×D488—21no—
33M16×D61—41no—
34M16×D61—41no—
35#14519775D411yescharacteristic
36#14519774C2×C411yescharacteristic
37#14519766D411yescharacteristic
38#14519765C2×C411yescharacteristic
39#14519762—41no—
40#14519762—41no—
41#14519755—41no—
42#14519752—21no—
43#14519752—41no—
44#14519739—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×D244—21no—
68C2×D244—41no—
69C2×D244—41no—
70C2×D244C22⋊C411yescharacteristic
71C2×C4×D61—21no—
72C2×C4×D61—21no—
73C2×C4×D61—41no—
74C2×C4×D61C22⋊C411yescharacteristic
75C2×Dic122—21no—
76C2×Dic122C22⋊C411yescharacteristic
77M16×C61—41no—
78M16×C61—41no—
79C2×C8×C61—21no—
80C4⋊C4×C61—21no—
81C4⋊C4×C61—41no—
82C4⋊C4×C61—41no—
83C42×C61C22×C411yescharacteristic
84#11758201—81no—
85#11758201—81no—
86#11758198—21no—
87#11758198—41no—
88#11758198—41no—
89#11758198—41no—
90#11758198—41no—
91#11758196—21no—
92#11758196—41no—
93C4×Dic61C22⋊C411yescharacteristic
94#11758194—41no—
95#11758194—41no—
96C2×#92418—21no—
97D488—81no—
98#11758190—81no—
99#11758189—81no—
100#11758189—81no—
101C8×D61—81no—
102C8×D61—81no—
103C22×D61—21no—
104C22×D61—41no—
105C22×D61#9911yescharacteristic
106Q8×C61—41no—
107Q8×C61—41no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—41no—
112C2×C4×C61C2×C22⋊C411yescharacteristic
113C2×Dic61—21no—
114C2×Dic61—21no—
115C2×Dic61#9911yescharacteristic
116D244—41no—
117D244—41no—
118D244—41no—
119D244—81no—
120D244—161no—
121D244—161no—
122C4×D61—41no—
123C4×D61—41no—
124C4×D61—41no—
125C4×D61—41no—
126C4×D61—41no—
127C4×D61—161no—
128Dic122—41no—
129Dic122—81no—
130C8×C61—41no—
131C8×C61—81no—
132C8×C61—81no—
133#92418—41no—
134#92418—81no—
135#92418—81no—
136#13611—611nomaximal, Sylow
137C22×C61C2×#9911yescharacteristic
138C2×D61—21no—
139C2×D61—41no—
140C2×D61—41no—
141C2×D61—81no—
142C2×D61—81no—
143C2×D61—81no—
144C2×D61—81no—
145C4×C61—21no—
146C4×C61—41no—
147C4×C61—41no—
148C4×C61—41no—
149C4×C61—81no—
150Dic61—21no—
151Dic61—41no—
152Dic61—41no—
153#3221—611no—
154#2135—611no—
155#2133—611no—
156#1413—611no—
157#1413D6111yescharacteristic, complemented
158#1410—611no—
159#1410—611no—
160C2×C61—21no—
161C2×C61#212711yescharacteristic
162D61—41no—
163D61—81no—
164D61—161no—
165#540—611no—
166#536—611no—
167#496—611no—
168#492—611no—
169#491C2×D6111yescharacteristic
170#488—611no—
171#463—1221no—
172#461—1221no—
173#449—1221no—
174#448—1221no—
175#433—611no—
176#413—1221no—
177C2×#101—1221no—
178#356—611no—
179#356—611no—
180#356—1221no—
181#356C2×D6111yescharacteristic
182#356C2×D6111yescharacteristic
183#355—1221no—
184C61#1361111yescharacteristic, complemented, Sylow
185C2×#41—611no—
186C22×Q8—611no—
187C2×SD16—1221no—
188C2×SD16—1221no—
189C2×SD16—1221no—
190C2×D8—1221no—
191C2×M16—2441no—
192C2×M16—2441no—
193C4⋊Q8—611no—
194C4⋊Q8C22×D6111yescharacteristic
195#127—611no—
196#125C4×D6111yescharacteristic
197#124—611no—
198#124—611no—
199#123—2441no—
200#123—2441no—
201C22⋊Q8—2441no—
202#121—1221no—
203#121—2441no—
204C4×D4—1221no—
205#117—611no—
206C4⋊C8—1221no—
207#103—21no—
208#103—21no—
209#103—1221no—
210#102—1221no—
211#101—21no—
212#101—21no—
213#101—1221no—
214#101—1221no—
215#101—2441no—
216#100—2441no—
217C22⋊C8—1221no—
218#97C4×D6111yescharacteristic
219C4×C8—611no—
220#41—4881no—
221C2×Q8—611no—
222C2×Q8—1221no—
223C2×Q8—4881no—
224C2×Q8D4×D6111yescharacteristic
225C2×Q8D4×D6111yescharacteristic
226C2×D4—611no—
227C2×D4—1221no—
228C2×D4—1221no—
229C2×D4—2441no—
230C2×D4—2441no—
231C22×C4—611no—
232C22×C4—1221no—
233C22×C4—1221no—
234C22×C4—2441no—
235SD16—4881no—
236SD16—4881no—
237SD16—4881no—
238D8—4881no—
239M16—41no—
240M16—41no—
241M16—4881no—
242M16—4881no—
243M16—2441no—
244M16—2441no—
245C2×C8—21no—
246C2×C8—1221no—
247C2×C8—4881no—
248C2×C8—4881no—
249C4⋊C4—21no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—1221no—
253C4⋊C4—2441no—
254C22⋊C4—1221no—
255C22⋊C4—2441no—
256C22⋊C4—2441no—
257C22⋊C4—2441no—
258C22⋊C4—2441no—
259C42—611no—
260C42C2×C4×D6111yescharacteristic
261C23—611no—
262C23—1221no—
263C23—2441no—
264Q8—41no—
265Q8—41no—
266Q8—4881no—
267Q8—2441no—
268D4—9761no—
269D4—9761no—
270D4—4881no—
271D4—2441no—
272D4—2441no—
273D4—2441no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—41no—
278C2×C4—611no—
279C2×C4—1221no—
280C2×C4—1221no—
281C2×C4—9761no—
282C2×C4—2441no—
283C2×C4—2441no—
284C2×C4—2441no—
285C2×C4—2441no—
286C2×C4—2441no—
287C2×C4C22⋊C4×D6111yescharacteristic
288C8—41no—
289C8—81no—
290C8—81no—
291C8—4881no—
292C8—4881no—
293C8—2441no—
294C22—1221no—
295C22—4881no—
296C22—4881no—
297C22—4881no—
298C22—4881no—
299C22—2441no—
300C22—2441no—
301C22#99×D6111yescharacteristic
302C4—21no—
303C4—41no—
304C4—41no—
305C4—41no—
306C4—81no—
307C4—1221no—
308C4—2441no—
309C4—2441no—
310C2—21no—
311C2—9761no—
312C2—4881no—
313C2—2441no—
314C2#2144748711yescharacteristic
subgroupG/H
centerC2#21447487
commutatorC42×C61C22×C4
FrattiniC4⋊Q8C22×D61
FittingC61×#1413C2
socleC2×C61#2127
prime radical#21456881C2
cosocleC4⋊Q8×C61C23
hypercenter#1413D61
hypocenterC61#13611
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
2. #21447512C2semidirect
3. #21447507C2semidirect
4. #21443992C2semidirect
5. #21443985C2semidirect
6. #21443985C2semidirect
7. C61×#1413C2semidirect
157. #1413D61semidirect
184. C61#13611semidirect

Maximal subgroups

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

subgroupindex
#214568812
#214475122
#214475072
#214439922
#214439852
C61×#14132
#1361161