Finite Group Databasebeta

← #29589255

Subgroups — #29589255

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#21454516C211yesmaximal, characteristic
2#21447428C211yesmaximal, characteristic, complemented
3C22⋊C16×D61C211yesmaximal, characteristic, complemented
4#21443760C211yesmaximal, characteristic, complemented
5#21443760C211yesmaximal, characteristic, complemented
6#21443745C211yesmaximal, characteristic, complemented
7C61×#1315C211yesmaximal, characteristic, complemented
8C2×#14519784C411yescharacteristic
9C22×C8×D61C2211yescharacteristic
10#16840269C411yescharacteristic
11C2×#14519716—21no—
12C2×C16×D61—21no—
13#16839836—21no—
14#16839836—21no—
15#16839825—21no—
16#16839825—21no—
17#16839788C2211yescharacteristic
18#16839725C411yescharacteristic
19#16839720C411yescharacteristic
20C22⋊#11758185C2211yescharacteristic
21C22⋊#11758185C2211yescharacteristic
22#16839541—21no—
23#16839541—21no—
24C61×#408C2211yescharacteristic
25C61×C22⋊C16C2211yescharacteristic
26C61×C22⋊C16C2211yescharacteristic
27C22×C4×D61C2×C411yescharacteristic
28#14519784—42no—
29C2×#11758194—21no—
30C2×#11758194C2×C411yescharacteristic
31C22×#92418—21no—
32C22×#92418C2×C411yescharacteristic
33C2×C8×D61—42no—
34C2×C8×D61D411yescharacteristic
35C2×C8×D61D411yescharacteristic
36C2×C8×D61D411yescharacteristic
37C2×C8×D61D411yescharacteristic
38#14519758—21no—
39#14519753C811yescharacteristic
40#14519753C811yescharacteristic
41#14519748C811yescharacteristic
42#14519748C811yescharacteristic
43#14519745—21no—
44C4×C22⋊D61—21no—
45C4×C22⋊D61—21no—
46#14519736C2×C411yescharacteristic
47#14519716—42no—
48C2×#11758185—21no—
49C2×#11758185—21no—
50C16×D61—42no—
51#14519706—21no—
52#14519706—21no—
53#14519689—21no—
54#14519689—21no—
55#14519687—21no—
56C8×Dic61—21no—
57C2×#41×C61C2×C411yescharacteristic
58C2×M16×C61C2×C411yescharacteristic
59C22×C8×C61C2311yescharacteristic
60C2×C16×C61—21no—
61C2×C16×C61—21no—
62C22⋊C8×C61—21no—
63C22⋊C8×C61—21no—
64C23×D61M1611yescharacteristic
65#41×C61—41no—
66#41×C61—41no—
67C2×Q8×C61C2×C811yescharacteristic
68C2×D4×C61—21no—
69C2×D4×C61C2×C811yescharacteristic
70C22×C4×C61—21no—
71C22×C4×C61C22×C411yescharacteristic
72C2×C22⋊D61—21no—
73C2×C22⋊D61—21no—
74C22×Dic61M1611yescharacteristic
75C2×C4×D61—41no—
76C2×C4×D61—41no—
77C2×C4×D61C22⋊C411yescharacteristic
78C2×C4×D61C22⋊C411yescharacteristic
79C2×C4×D61C2×C811yescharacteristic
80C2×C4×D61C2×C811yescharacteristic
81M16×C61—41no—
82C2×C8×C61—21no—
83C2×C8×C61—41no—
84C2×C8×C61C2×D411yescharacteristic
85C2×C8×C61C2×D411yescharacteristic
86C22⋊Dic61—21no—
87C22⋊Dic61—21no—
88C22⋊Dic61—21no—
89#11758198—21no—
90#11758198—21no—
91C4⋊Dic61C2×C811yescharacteristic
92C4⋊Dic61C2×C811yescharacteristic
93#11758196—21no—
94#11758196—21no—
95C4×Dic61—21no—
96#11758194—42no—
97#11758194—41no—
98C2×#92418—22no—
99C2×#92418—21no—
100C2×#92418—42no—
101C2×#92418C22⋊C411yescharacteristic
102C2×#92418C22⋊C411yescharacteristic
103C8×D61—22no—
104C8×D61—22no—
105C8×D61—41no—
106C8×D61—41no—
107C16×C61—41no—
108C16×C61—41no—
109#11758185—41no—
110#11758185—41no—
111C23×C61—21no—
112C23×C61C2×M1611yescharacteristic
113C22×D61—22no—
114C22×D61—41no—
115C22×D61—41no—
116C22×D61C22⋊C811yescharacteristic
117C22×D61C22⋊C811yescharacteristic
118Q8×C61—41no—
119D4×C61—41no—
120D4×C61—42no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61C2×C22⋊C411yescharacteristic
127C2×C4×C61C22×C811yescharacteristic
128C22⋊D61—42no—
129C22⋊D61—42no—
130C2×Dic61—21no—
131C2×Dic61—21no—
132C2×Dic61—41no—
133C2×Dic61C22⋊C811yescharacteristic
134C2×Dic61C22⋊C811yescharacteristic
135C4×D61—21no—
136C4×D61—21no—
137C4×D61—21no—
138C4×D61—21no—
139C4×D61—41no—
140C4×D61—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×C61—41no—
152C22×C61—41no—
153C22×C61—41no—
154C22×C61C2×C22⋊C811yescharacteristic
155C2×D61—21no—
156C2×D61—21no—
157C2×D61—21no—
158C2×D61—21no—
159C2×D61—21no—
160C2×D61—44no—
161C2×D61#35012yes—
162C4×C61—21no—
163C4×C61—41no—
164C4×C61C2×#9911yescharacteristic
165C4×C61#41311yescharacteristic
166Dic61—21no—
167Dic61—21no—
168Dic61—41no—
169Dic61—41no—
170#2929—611no—
171#2112—611no—
172C2×C22⋊C16—611no—
173#1323—611no—
174#1323—611no—
175#1315—611no—
176#1315D6111yescharacteristic, complemented
177C2×C61—41no—
178C2×C61—81no—
179C2×C61#145911yescharacteristic
180C2×C61C2×#35011yescharacteristic
181C2×C61#211711yescharacteristic
182D61—22no—
183D61—41no—
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#424—611no—
194#408C2×D6111yescharacteristic
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×#41C4×D6111yescharacteristic
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#117—611no—
227M32—2442no—
228C2×C16—21no—
229C2×C16—21no—
230C2×C16—1221no—
231C2×C16—1221no—
232C2×C16—2442no—
233C4⋊C8—1221no—
234C4⋊C8—1221no—
235C22⋊C8—21no—
236C22⋊C8—21no—
237C22⋊C8—1221no—
238C22⋊C8—1221no—
239#97—1221no—
240C4×C8—1221no—
241C24—611no—
242#41—41no—
243#41—41no—
244C2×Q8C8×D6111yescharacteristic
245C2×D4—21no—
246C2×D4—1221no—
247C2×D4—1221no—
248C2×D4C8×D6111yescharacteristic
249C22×C4—21no—
250C22×C4—611no—
251C22×C4—611no—
252C22×C4—611no—
253C22×C4—611no—
254C22×C4—611no—
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—611no—
275C4⋊C4—611no—
276C4⋊C4—1221no—
277C4⋊C4—1221no—
278C22⋊C4—1221no—
279C22⋊C4—1221no—
280C22⋊C4—1221no—
281C22⋊C4—1221no—
282C22⋊C4—1221no—
283C42—1221no—
284C16—41no—
285C16—41no—
286C16—2441no—
287C16—2441no—
288C23—21no—
289C23—611no—
290C23—611no—
291C23—1222no—
292C23—2441no—
293C23—2441no—
294C23M16×D6111yescharacteristic
295Q8—41no—
296D4—41no—
297D4—42no—
298D4—2442no—
299D4—2442no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—611no—
306C2×C4—611no—
307C2×C4—1221no—
308C2×C4—1221no—
309C2×C4—1221no—
310C2×C4—1221no—
311C2×C4—1221no—
312C2×C4—1221no—
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—41no—
328C22—41no—
329C22—41no—
330C22—612no—
331C22—1221no—
332C22—1221no—
333C22—1221no—
334C22—1221no—
335C22—1221no—
336C22—2444no—
337C22C22⋊C8×D6111yescharacteristic
338C4—21no—
339C4—41no—
340C4—1221no—
341C4—1221no—
342C4—2441no—
343C4—2441no—
344C4#99×D6111yescharacteristic
345C4#1683974311yescharacteristic
346C2—41no—
347C2—81no—
348C2—1222no—
349C2—2441no—
350C2#2144413411yescharacteristic
351C2#350×D6111yescharacteristic
352C2#2144744511yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D61
commutatorC2×C4×C61C22×C8
FrattiniC22×C8C22×D61
FittingC61×#1315C2
socleC22×C61C2×C22⋊C8
prime radical#16840269C4
cosocleC22×C8×C61C23
hypercenter#1315D61
hypocenterC61#11470
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1315

Complements

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

NH ≅ G/Ntype
2. #21447428C2semidirect
3. C22⋊C16×D61C2semidirect
4. #21443760C2semidirect
5. #21443760C2semidirect
6. #21443745C2semidirect
7. C61×#1315C2semidirect
176. #1315D61semidirect
203. C61#11470semidirect

Maximal subgroups

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

subgroupindex
#214545162
#214474282
C22⋊C16×D612
#214437602
#214437452
C61×#13152
#1147061