Finite Group Databasebeta

← #29589257

Subgroups — #29589257

Order 15616.

392 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 89 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#21454512C211yesmaximal, characteristic
2#21447428C211yesmaximal, characteristic, complemented
3C22⋊C16×D61C211yesmaximal, characteristic, complemented
4#21443761C211yesmaximal, characteristic, complemented
5#21443744C211yesmaximal, characteristic, complemented
6#21443744C211yesmaximal, characteristic, complemented
7C61×#1323C211yesmaximal, characteristic, complemented
8C2×#14519785C411yescharacteristic
9C22×C8×D61C2211yescharacteristic
10#16840274C411yescharacteristic
11C2×#14519716—21no—
12C2×C16×D61—21no—
13#16839832—21no—
14#16839832—21no—
15#16839827—21no—
16#16839827—21no—
17#16839728C2211yescharacteristic
18#16839725C411yescharacteristic
19#16839718C411yescharacteristic
20C22⋊#11758185C2211yescharacteristic
21C22⋊#11758185C2211yescharacteristic
22#16839541—21no—
23#16839541—21no—
24C61×#424C2211yescharacteristic
25C61×C22⋊C16C2211yescharacteristic
26C61×C22⋊C16C2211yescharacteristic
27C2×#11758222C2×C411yescharacteristic
28C22×C4×D61C2×C411yescharacteristic
29#14519785—42no—
30C2×#11758194C2×C411yescharacteristic
31C2×#11758189—21no—
32C22×#92418C2×C411yescharacteristic
33C2×C8×D61—21no—
34C2×C8×D61—42no—
35C2×C8×D61D411yescharacteristic
36C2×C8×D61D411yescharacteristic
37C2×C8×D61D411yescharacteristic
38C2×C8×D61D411yescharacteristic
39#14519761—21no—
40#14519757C811yescharacteristic
41#14519757C811yescharacteristic
42#14519752C811yescharacteristic
43#14519752C811yescharacteristic
44#14519747—21no—
45C4×D244—21no—
46C4×D244—21no—
47#14519716—42no—
48C2×#11758185—21no—
49C2×#11758185—21no—
50C16×D61—42no—
51#14519689—21no—
52#14519689—21no—
53#14519689—21no—
54#14519689—21no—
55#14519688—21no—
56C4×#92418—21no—
57C2×M16×C61C2×C411yescharacteristic
58C22×C8×C61C2311yescharacteristic
59#117×C61C2×C411yescharacteristic
60C2×C16×C61—21no—
61C2×C16×C61—21no—
62C4⋊C8×C61—21no—
63C4⋊C8×C61—21no—
64C23×D61M1611yescharacteristic
65C22×C4×C61C22×C411yescharacteristic
66C2×C22⋊D61—21no—
67C22×Dic61M1611yescharacteristic
68#11758222—41no—
69#11758222—41no—
70C2×D244—21no—
71C2×D244—21no—
72C2×D244C2×C811yescharacteristic
73C2×C4×D61—21no—
74C2×C4×D61—41no—
75C2×C4×D61—41no—
76C2×C4×D61C22⋊C411yescharacteristic
77C2×C4×D61C22⋊C411yescharacteristic
78C2×C4×D61C2×C811yescharacteristic
79C2×C4×D61C2×C811yescharacteristic
80C2×Dic122C2×C811yescharacteristic
81M16×C61—41no—
82C2×C8×C61—21no—
83C2×C8×C61—41no—
84C2×C8×C61C2×D411yescharacteristic
85C2×C8×C61C2×D411yescharacteristic
86C4⋊C4×C61C2×C811yescharacteristic
87C4⋊C4×C61C2×C811yescharacteristic
88C22⋊C4×C61—21no—
89C42×C61—21no—
90#11758198—21no—
91#11758198—21no—
92#11758198—21no—
93#11758198—21no—
94C4⋊Dic61—21no—
95C4⋊Dic61—21no—
96#11758194—41no—
97C2×#92418—22no—
98C2×#92418—21no—
99C2×#92418C22⋊C411yescharacteristic
100C2×#92418C22⋊C411yescharacteristic
101#11758189—42no—
102C8×D61—22no—
103C8×D61—22no—
104C8×D61—41no—
105C8×D61—41no—
106C8×D61—42no—
107C16×C61—41no—
108C16×C61—41no—
109#11758185—41no—
110#11758185—41no—
111C23×C61C2×M1611yescharacteristic
112C22×D61—22no—
113C22×D61—21no—
114C22×D61—41no—
115C22×D61—41no—
116C22×D61C22⋊C811yescharacteristic
117C22×D61C22⋊C811yescharacteristic
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61C2×C22⋊C411yescharacteristic
123C2×C4×C61C22×C811yescharacteristic
124C22⋊D61—42no—
125C2×Dic61—21no—
126C2×Dic61—41no—
127C2×Dic61C22⋊C811yescharacteristic
128C2×Dic61C22⋊C811yescharacteristic
129D244—41no—
130D244—42no—
131D244—42no—
132C4×D61—21no—
133C4×D61—21no—
134C4×D61—21no—
135C4×D61—21no—
136C4×D61—41no—
137C4×D61—41no—
138C4×D61—41no—
139C4×D61—41no—
140Dic122—41no—
141C8×C61—21no—
142C8×C61—21no—
143C8×C61—41no—
144#92418—21no—
145#92418—41no—
146#92418#9912yes—
147#11470—611nomaximal, Sylow
148C22×C61—21no—
149C22×C61—21no—
150C22×C61—21no—
151C22×C61C2×C22⋊C811yescharacteristic
152C2×D61—21no—
153C2×D61—21no—
154C2×D61—21no—
155C2×D61—21no—
156C2×D61—21no—
157C2×D61—44no—
158C2×D61—41no—
159C2×D61—41no—
160C2×D61—41no—
161C2×D61#35012yes—
162C4×C61—21no—
163C4×C61—41no—
164C4×C61—41no—
165C4×C61C2×#9911yescharacteristic
166C4×C61#41311yescharacteristic
167Dic61—21no—
168Dic61—21no—
169Dic61—41no—
170#2929—611no—
171#2112—611no—
172C2×C22⋊C16—611no—
173#1323—611no—
174#1323D6111yescharacteristic, complemented
175#1315—611no—
176#1315—611no—
177C2×C61—41no—
178C2×C61#145911yescharacteristic
179C2×C61C2×#35011yescharacteristic
180C2×C61#211711yescharacteristic
181D61—22no—
182D61—41no—
183D61—81no—
184C2×#131—611no—
185C23×C8—611no—
186#525—611no—
187C2×M32—1221no—
188C22×C16—1221no—
189#435—1221no—
190#435—1221no—
191C8×D4—1221no—
192C8×D4—1221no—
193#424C2×D6111yescharacteristic
194#408—611no—
195#407—611no—
196#405—611no—
197C22⋊C16—611no—
198C22⋊C16—611no—
199C22⋊C16—1221no—
200C22⋊C16—1221no—
201C22⋊C16C2×D6111yescharacteristic
202C22⋊C16C2×D6111yescharacteristic
203C61#1147011yescharacteristic, complemented, Sylow
204C2×#41—611no—
205C23×C4—611no—
206#131—2442no—
207C2×M16—611no—
208C2×M16—1221no—
209C2×M16C4×D6111yescharacteristic
210C22×C8—611no—
211C22×C8—611no—
212C22×C8—611no—
213C22×C8—611no—
214C22×C8—611no—
215C22×C8—1221no—
216C22×C8—2442no—
217C22×C8C22×D6111yescharacteristic
218#123—1221no—
219C22⋊Q8—611no—
220C22⋊Q8—611no—
221#121—611no—
222#121—611no—
223#120—1221no—
224C4×D4—1221no—
225C4×D4—1221no—
226#117C4×D6111yescharacteristic
227M32—2442no—
228C2×C16—21no—
229C2×C16—21no—
230C2×C16—1221no—
231C2×C16—1221no—
232C2×C16—2442no—
233C4⋊C8—21no—
234C4⋊C8—21no—
235C22⋊C8—1221no—
236C22⋊C8—1221no—
237C22⋊C8—1221no—
238C22⋊C8—1221no—
239#97—1221no—
240C4×C8—1221no—
241C24—611no—
242#41—2441no—
243#41—2441no—
244C2×Q8—611no—
245C2×D4—611no—
246C2×D4—1221no—
247C2×D4—1221no—
248C2×D4—1221no—
249C22×C4—611no—
250C22×C4—611no—
251C22×C4—611no—
252C22×C4—611no—
253C22×C4—611no—
254C22×C4—1221no—
255C22×C4—2441no—
256C22×C4—2441no—
257C22×C4C2×C4×D6111yescharacteristic
258M16—41no—
259M16—2442no—
260M16—2441no—
261C2×C8—21no—
262C2×C8—41no—
263C2×C8—611no—
264C2×C8—611no—
265C2×C8—1222no—
266C2×C8—1222no—
267C2×C8—1222no—
268C2×C8—1221no—
269C2×C8—2441no—
270C2×C8—2441no—
271C2×C8—2442no—
272C2×C8D4×D6111yescharacteristic
273C2×C8D4×D6111yescharacteristic
274C4⋊C4—1221no—
275C4⋊C4—1221no—
276C4⋊C4C8×D6111yescharacteristic
277C4⋊C4C8×D6111yescharacteristic
278C22⋊C4—21no—
279C22⋊C4—1221no—
280C22⋊C4—1221no—
281C22⋊C4—1221no—
282C22⋊C4—1221no—
283C42—21no—
284C16—41no—
285C16—41no—
286C16—2441no—
287C16—2441no—
288C23—611no—
289C23—611no—
290C23—1222no—
291C23—1221no—
292C23—2441no—
293C23—2441no—
294C23M16×D6111yescharacteristic
295Q8—2441no—
296D4—2441no—
297D4—2442no—
298D4—2442no—
299D4—2442no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—611no—
305C2×C4—611no—
306C2×C4—1221no—
307C2×C4—1221no—
308C2×C4—1221no—
309C2×C4—1221no—
310C2×C4—1221no—
311C2×C4—2441no—
312C2×C4—2441no—
313C2×C4—2441no—
314C2×C4—2441no—
315C2×C4—2441no—
316C2×C4C22⋊C4×D6111yescharacteristic
317C2×C4C2×C8×D6111yescharacteristic
318C8—21no—
319C8—21no—
320C8—41no—
321C8—612no—
322C8—1221no—
323C8—2441no—
324C22—21no—
325C22—21no—
326C22—21no—
327C22—612no—
328C22—1221no—
329C22—1221no—
330C22—1221no—
331C22—1221no—
332C22—1221no—
333C22—2444no—
334C22—2441no—
335C22—2441no—
336C22—2441no—
337C22C22⋊C8×D6111yescharacteristic
338C4—21no—
339C4—41no—
340C4—41no—
341C4—1221no—
342C4—1221no—
343C4—2441no—
344C4#99×D6111yescharacteristic
345C4#1683974511yescharacteristic
346C2—41no—
347C2—1222no—
348C2—4881no—
349C2—2441no—
350C2#2144413611yescharacteristic
351C2#350×D6111yescharacteristic
352C2#2144744511yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D61
commutatorC2×C4×C61C22×C8
FrattiniC22×C8C22×D61
FittingC61×#1323C2
socleC22×C61C2×C22⋊C8
prime radical#16840274C4
cosocleC22×C8×C61C23
hypercenter#1323D61
hypocenterC61#11470
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1323

Complements

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

NH ≅ G/Ntype
2. #21447428C2semidirect
3. C22⋊C16×D61C2semidirect
4. #21443761C2semidirect
5. #21443744C2semidirect
6. #21443744C2semidirect
7. C61×#1323C2semidirect
174. #1323D61semidirect
203. C61#11470semidirect

Maximal subgroups

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

subgroupindex
#214545122
#214474282
C22⋊C16×D612
#214437612
#214437442
C61×#13232
#1147061