Finite Group Databasebeta

← #29590761

Subgroups — #29590761

Order 15616.

386 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 87 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#21445899C211yesmaximal, characteristic
2#21444149C211yesmaximal, characteristic
3#21443849C212yesmaximal, complemented
4#21443846C212yesmaximal, complemented
5C61×#2627C211yesmaximal, characteristic
6#16839726—21no—
7#16839726—21no—
8#16839531—21no—
9#16839531C2212yes—
10#16839488—21no—
11#16839488C2212yes—
12C2×C22⋊Q8×C61C411yescharacteristic
13C22×C4⋊C4×C61C2211yescharacteristic
14C61×#400C411yescharacteristic
15C61×#400C2211yescharacteristic
16C61×#398—21no—
17C61×#398—21no—
18C61×#395C411yescharacteristic
19C61×#395C2211yescharacteristic
20C61×#385—21no—
21C61×#381—21no—
22C61×#380C411yescharacteristic
23C2×#11758194—22no—
24C2×#11758194—41no—
25C22⋊#92418—22no—
26C22⋊#92418—41no—
27C22⋊#92418—41no—
28C22⋊#92418—41no—
29C22×Q8×C61C2×C411yescharacteristic
30C23×C4×C61C2×C411yescharacteristic
31C23×C4×C61D411yescharacteristic
32C23×C4×C61D411yescharacteristic
33C22⋊Q8×C61—41no—
34C22⋊Q8×C61—41no—
35C2×C4⋊C4×C61—21no—
36C2×C4⋊C4×C61—21no—
37C2×C4⋊C4×C61—21no—
38C2×C4⋊C4×C61—21no—
39C2×C4⋊C4×C61—41no—
40C2×C4⋊C4×C61—41no—
41C2×C4⋊C4×C61C2×C411yescharacteristic
42C2×C4⋊C4×C61C2×C411yescharacteristic
43C2×C4⋊C4×C61D411yescharacteristic
44C2×C4⋊C4×C61D411yescharacteristic
45C2×C4⋊C4×C61C2311yescharacteristic
46C2×C22⋊C4×C61—21no—
47C2×C22⋊C4×C61—21no—
48#95×C61—21no—
49#95×C61—21no—
50#95×C61—21no—
51#95×C61—21no—
52#95×C61—21no—
53#95×C61—21no—
54#95×C61C2×C411yescharacteristic
55#95×C61C2×C411yescharacteristic
56C24×C61C22⋊C411yescharacteristic
57C2×Q8×C61—41no—
58C2×Q8×C61—81no—
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61—21no—
62C22×C4×C61—21no—
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61—22no—
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61—21no—
69C22×C4×C61—21no—
70C22×C4×C61—41no—
71C22×C4×C61—81no—
72C22×C4×C61—81no—
73C22×C4×C61C22⋊C411yescharacteristic
74C22×C4×C61C22⋊C411yescharacteristic
75C22×C4×C61C22⋊C411yescharacteristic
76C22×C4×C61C22×C411yescharacteristic
77C22×C4×C61C2×D411yescharacteristic
78C22×C4×C61C2×D411yescharacteristic
79C4⋊C4×C61—41no—
80C4⋊C4×C61—41no—
81C4⋊C4×C61—41no—
82C4⋊C4×C61—41no—
83C4⋊C4×C61—42no—
84C4⋊C4×C61—41no—
85C4⋊C4×C61—81no—
86C4⋊C4×C61—81no—
87C4⋊C4×C61—81no—
88C22⋊C4×C61—42no—
89C22⋊C4×C61—41no—
90C22⋊C4×C61—41no—
91#11758194—42no—
92#11758194—42no—
93#11758194—82no—
94C2×#92418—42no—
95C2×#92418—42no—
96C23×C61—21no—
97C23×C61—21no—
98C23×C61—41no—
99C23×C61—41no—
100C23×C61#9911yescharacteristic
101C23×C61#9911yescharacteristic
102C23×C61C2×C22⋊C411yescharacteristic
103Q8×C61—82no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—21no—
109C2×C4×C61—21no—
110C2×C4×C61—21no—
111C2×C4×C61—21no—
112C2×C4×C61—21no—
113C2×C4×C61—42no—
114C2×C4×C61—42no—
115C2×C4×C61—42no—
116C2×C4×C61—41no—
117C2×C4×C61—41no—
118C2×C4×C61—41no—
119C2×C4×C61—41no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—42no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—81no—
132C2×C4×C61—81no—
133C2×C4×C61—81no—
134C2×C4×C61#13712yes—
135#92418—82no—
136#92418—82no—
137#11817—611nomaximal, Sylow
138C22×C61—21no—
139C22×C61—21no—
140C22×C61—21no—
141C22×C61—21no—
142C22×C61—21no—
143C22×C61—21no—
144C22×C61—21no—
145C22×C61—21no—
146C22×C61—42no—
147C22×C61—42no—
148C22×C61C2×#9911yescharacteristic
149C22×C61#41911yescharacteristic
150C22×C61#42111yescharacteristic
151C4×C61—22no—
152C4×C61—41no—
153C4×C61—41no—
154C4×C61—41no—
155C4×C61—41no—
156C4×C61—41no—
157C4×C61—81no—
158C4×C61—81no—
159C4×C61—81no—
160C4×C61—81no—
161#2627D6111yescharacteristic
162#1821—611no—
163#1463—611no—
164#1354—612no—
165#1353—612no—
166C2×C61—21no—
167C2×C61—21no—
168C2×C61—41no—
169C2×C61—41no—
170C2×C61#151111yescharacteristic
171C2×C61#212111yescharacteristic
172C2×C61#213311yescharacteristic
173C2×C22⋊Q8Dic6111yescharacteristic
174C22×C4⋊C4C2×D6111yescharacteristic
175#407—1221no—
176#407—1221no—
177#400Dic6111yescharacteristic
178#400C2×D6111yescharacteristic
179#398—21no—
180#398—21no—
181#395Dic6111yescharacteristic
182#395C2×D6111yescharacteristic
183#385—21no—
184#381—21no—
185#380Dic6111yescharacteristic
186#343—612no—
187#343—1221no—
188#324—612no—
189#324—1221no—
190C61#1181711yescharacteristic, complemented, Sylow
191C22×Q8C2×Dic6111yescharacteristic
192C23×C4C2×Dic6111yescharacteristic
193C23×C4C22⋊D6111yescharacteristic
194C23×C4C22⋊D6111yescharacteristic
195C2×M16—1222no—
196C2×M16—2441no—
197C22⋊Q8—41no—
198C22⋊Q8—41no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—41no—
204C2×C4⋊C4—41no—
205C2×C4⋊C4C2×Dic6111yescharacteristic
206C2×C4⋊C4C2×Dic6111yescharacteristic
207C2×C4⋊C4C22⋊D6111yescharacteristic
208C2×C4⋊C4C22⋊D6111yescharacteristic
209C2×C4⋊C4C22×D6111yescharacteristic
210C2×C22⋊C4—21no—
211C2×C22⋊C4—21no—
212C22⋊C8—1222no—
213C22⋊C8—2441no—
214C22⋊C8—2441no—
215C22⋊C8—2441no—
216#95—21no—
217#95—21no—
218#95—21no—
219#95—21no—
220#95—21no—
221#95—21no—
222#95C2×Dic6111yescharacteristic
223#95C2×Dic6111yescharacteristic
224C24C22⋊Dic6111yescharacteristic
225C2×Q8—41no—
226C2×Q8—81no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—22no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—41no—
239C22×C4—81no—
240C22×C4—81no—
241C22×C4C22⋊Dic6111yescharacteristic
242C22×C4C22⋊Dic6111yescharacteristic
243C22×C4C22⋊Dic6111yescharacteristic
244C22×C4C22×Dic6111yescharacteristic
245C22×C4C2×C22⋊D6111yescharacteristic
246C22×C4C2×C22⋊D6111yescharacteristic
247M16—4882no—
248M16—2442no—
249M16—2442no—
250C2×C8—2442no—
251C2×C8—2442no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—42no—
258C4⋊C4—81no—
259C4⋊C4—81no—
260C4⋊C4—81no—
261C22⋊C4—42no—
262C22⋊C4—41no—
263C22⋊C4—41no—
264C23—21no—
265C23—21no—
266C23—41no—
267C23—41no—
268C23#1451969211yescharacteristic
269C23#1451969211yescharacteristic
270C23C2×C22⋊Dic6111yescharacteristic
271Q8—82no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—42no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4—81no—
302C2×C4#1451980812yes—
303C8—4882no—
304C8—4882no—
305C22—21no—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22—21no—
312C22—21no—
313C22—42no—
314C22—42no—
315C22C2×#1451969211yescharacteristic
316C22#1683977111yescharacteristic
317C22#1683977911yescharacteristic
318C4—22no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—81no—
325C4—81no—
326C4—81no—
327C4—81no—
328C2—21no—
329C2—21no—
330C2—41no—
331C2—41no—
332C2#2144435211yescharacteristic
333C2#2144746511yescharacteristic
334C2#2144750811yescharacteristic
subgroupG/H
centerC22C2×#14519692
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#2627C2
socleC22×C61C2×#99
prime radicalC24×C61C22⋊C4
cosocleC2×C4⋊C4×C61C23
hypercenter#2627D61
hypocenterC61#11817
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ #2627

Complements

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

NH ≅ G/Ntype
3. #21443849C2semidirect
4. #21443846C2semidirect
190. C61#11817semidirect

Maximal subgroups

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

subgroupindex
#214458992
#214441492
#214438492
#214438462
C61×#26272
#1181761