Finite Group Databasebeta

← #29590931

Subgroups — #29590931

Order 15616.

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

normal subgroups only

This group has 418 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#21445902C211yesmaximal, characteristic, complemented
2#21444133C211yesmaximal, characteristic, complemented
3#21443849C212yesmaximal, complemented
4#21443822C212yesmaximal, complemented
5C61×#2610C211yesmaximal, characteristic
6#16839815—21no—
7#16839726—21no—
8#16839531—21no—
9#16839531C2212yes—
10#16839488C2212yes—
11#16839486—21no—
12C2×#124×C61C411yescharacteristic
13C2×#117×C61C2211yescharacteristic
14C61×#395C2211yescharacteristic
15C61×#394C2211yescharacteristic
16C61×#393C411yescharacteristic
17C61×#392C411yescharacteristic
18C61×#390—21no—
19C61×#388—21no—
20C61×#388—21no—
21C61×#386—21no—
22C61×#376C411yescharacteristic
23C2×#11758194—22no—
24C4⋊#92418—41no—
25C22⋊#92418—22no—
26C22⋊#92418—41no—
27C22⋊#92418—41no—
28C4×#92418—41no—
29C22×Q8×C61C2×C411yescharacteristic
30C22×D4×C61—21no—
31C22×D4×C61C2×C411yescharacteristic
32C23×C4×C61D411yescharacteristic
33#124×C61—41no—
34#124×C61—41no—
35#117×C61—41no—
36#117×C61—41no—
37C2×C4⋊C4×C61—21no—
38C2×C4⋊C4×C61D411yescharacteristic
39C2×C4⋊C4×C61C2311yescharacteristic
40C2×C22⋊C4×C61—21no—
41C2×C22⋊C4×C61—21no—
42C2×C22⋊C4×C61—21no—
43C2×C22⋊C4×C61—21no—
44C2×C22⋊C4×C61—21no—
45C2×C22⋊C4×C61—21no—
46C2×C22⋊C4×C61C2×C411yescharacteristic
47C2×C22⋊C4×C61D411yescharacteristic
48C2×C42×C61—21no—
49C2×C42×C61C2×C411yescharacteristic
50C2×C42×C61D411yescharacteristic
51#95×C61—21no—
52#95×C61—21no—
53#95×C61—21no—
54#95×C61C2×C411yescharacteristic
55#95×C61C2×C411yescharacteristic
56C24×C61—21no—
57C24×C61C22⋊C411yescharacteristic
58C2×Q8×C61—41no—
59C2×Q8×C61—81no—
60C2×D4×C61—42no—
61C2×D4×C61—41no—
62C2×D4×C61—42no—
63C2×D4×C61—81no—
64C2×D4×C61—81no—
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61—22no—
69C22×C4×C61—21no—
70C22×C4×C61—21no—
71C22×C4×C61—41no—
72C22×C4×C61C22⋊C411yescharacteristic
73C22×C4×C61C22⋊C411yescharacteristic
74C22×C4×C61C22⋊C411yescharacteristic
75C22×C4×C61C22×C411yescharacteristic
76C22×C4×C61C2×D411yescharacteristic
77C22×C4×C61C2×D411yescharacteristic
78C4⋊C4×C61—41no—
79C4⋊C4×C61—41no—
80C4⋊C4×C61—81no—
81C22⋊C4×C61—41no—
82C22⋊C4×C61—41no—
83C22⋊C4×C61—42no—
84C22⋊C4×C61—42no—
85C22⋊C4×C61—41no—
86C22⋊C4×C61—41no—
87C22⋊C4×C61—42no—
88C22⋊C4×C61—81no—
89C22⋊C4×C61—81no—
90C42×C61—21no—
91C42×C61—21no—
92C42×C61—21no—
93C42×C61—21no—
94C42×C61—42no—
95#11758194—42no—
96#11758194—42no—
97C2×#92418—42no—
98C2×#92418—42no—
99C23×C61—21no—
100C23×C61—21no—
101C23×C61—21no—
102C23×C61—41no—
103C23×C61—41no—
104C23×C61—41no—
105C23×C61—41no—
106C23×C61—41no—
107C23×C61—41no—
108C23×C61—41no—
109C23×C61—41no—
110C23×C61—41no—
111C23×C61C2×C22⋊C411yescharacteristic
112Q8×C61—82no—
113D4×C61—84no—
114D4×C61—82no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—22no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—42no—
125C2×C4×C61—42no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61#9911yescharacteristic
139C2×C4×C61#9911yescharacteristic
140C2×C4×C61#13512yes—
141#92418—82no—
142#92418—82no—
143#11851—611nomaximal, Sylow
144C22×C61—21no—
145C22×C61—21no—
146C22×C61—42no—
147C22×C61—41no—
148C22×C61—41no—
149C22×C61—41no—
150C22×C61—81no—
151C22×C61—81no—
152C22×C61—81no—
153C22×C61—81no—
154C22×C61—81no—
155C22×C61—81no—
156C22×C61—81no—
157C22×C61—81no—
158C22×C61C2×#9911yescharacteristic
159C22×C61#41611yescharacteristic
160C22×C61#42111yescharacteristic
161C4×C61—22no—
162C4×C61—21no—
163C4×C61—21no—
164C4×C61—42no—
165C4×C61—41no—
166C4×C61—41no—
167C4×C61—41no—
168C4×C61—41no—
169C4×C61—81no—
170C4×C61—81no—
171#2610D6111yescharacteristic
172#1822—611no—
173#1458—611no—
174#1354—612no—
175#1345—612no—
176C2×C61—21no—
177C2×C61—21no—
178C2×C61—81no—
179C2×C61—161no—
180C2×C61#151611yescharacteristic
181C2×C61#212211yescharacteristic
182C2×C61#213211yescharacteristic
183C2×#124Dic6111yescharacteristic
184C2×#117C2×D6111yescharacteristic
185#431—1221no—
186#407—1221no—
187#395C2×D6111yescharacteristic
188#394C2×D6111yescharacteristic
189#393Dic6111yescharacteristic
190#392Dic6111yescharacteristic
191#390—21no—
192#388—21no—
193#388—21no—
194#386—21no—
195#376Dic6111yescharacteristic
196#343—612no—
197#343—1221no—
198#324—612no—
199#323—1221no—
200C61#1185111yescharacteristic, complemented, Sylow
201C22×Q8C2×Dic6111yescharacteristic
202C22×D4—21no—
203C22×D4C2×Dic6111yescharacteristic
204C23×C4C22⋊D6111yescharacteristic
205C2×M16—1222no—
206#124—41no—
207#124—41no—
208#117—41no—
209#117—41no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4C22⋊D6111yescharacteristic
212C2×C4⋊C4C22×D6111yescharacteristic
213C2×C22⋊C4—21no—
214C2×C22⋊C4—21no—
215C2×C22⋊C4—21no—
216C2×C22⋊C4—21no—
217C2×C22⋊C4—21no—
218C2×C22⋊C4—21no—
219C2×C22⋊C4C2×Dic6111yescharacteristic
220C2×C22⋊C4C22⋊D6111yescharacteristic
221C2×C42—21no—
222C2×C42C2×Dic6111yescharacteristic
223C2×C42C22⋊D6111yescharacteristic
224C4⋊C8—2441no—
225C22⋊C8—1222no—
226C22⋊C8—2441no—
227C22⋊C8—2441no—
228C4×C8—2441no—
229#95—21no—
230#95—21no—
231#95—21no—
232#95C2×Dic6111yescharacteristic
233#95C2×Dic6111yescharacteristic
234C24—21no—
235C24C22⋊Dic6111yescharacteristic
236C2×Q8—41no—
237C2×Q8—81no—
238C2×D4—41no—
239C2×D4—42no—
240C2×D4—42no—
241C2×D4—81no—
242C2×D4—81no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—22no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—41no—
250C22×C4C22⋊Dic6111yescharacteristic
251C22×C4C22⋊Dic6111yescharacteristic
252C22×C4C22⋊Dic6111yescharacteristic
253C22×C4C22×Dic6111yescharacteristic
254C22×C4C2×C22⋊D6111yescharacteristic
255C22×C4C2×C22⋊D6111yescharacteristic
256M16—2442no—
257M16—2442no—
258C2×C8—2442no—
259C2×C8—2442no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—81no—
263C22⋊C4—41no—
264C22⋊C4—41no—
265C22⋊C4—42no—
266C22⋊C4—42no—
267C22⋊C4—41no—
268C22⋊C4—41no—
269C22⋊C4—42no—
270C22⋊C4—81no—
271C22⋊C4—81no—
272C42—21no—
273C42—21no—
274C42—21no—
275C42—21no—
276C42—42no—
277C23—21no—
278C23—21no—
279C23—21no—
280C23—41no—
281C23—41no—
282C23—41no—
283C23—41no—
284C23—41no—
285C23—41no—
286C23—41no—
287C23—41no—
288C23—41no—
289C23C2×C22⋊Dic6111yescharacteristic
290Q8—82no—
291D4—84no—
292D4—82no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—22no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4#1451969211yescharacteristic
317C2×C4#1451969211yescharacteristic
318C2×C4#1451979712yes—
319C8—4882no—
320C8—4882no—
321C22—21no—
322C22—21no—
323C22—42no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—81no—
328C22—81no—
329C22—81no—
330C22—81no—
331C22—81no—
332C22—81no—
333C22—81no—
334C22—81no—
335C22C2×#1451969211yescharacteristic
336C22#1683975811yescharacteristic
337C22#1683977911yescharacteristic
338C4—22no—
339C4—21no—
340C4—21no—
341C4—42no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—81no—
347C4—81no—
348C2—21no—
349C2—21no—
350C2—81no—
351C2—161no—
352C2#2144437511yescharacteristic
353C2#2144746911yescharacteristic
354C2#2144750411yescharacteristic
subgroupG/H
centerC22C2×#14519692
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#2610C2
socleC22×C61C2×#99
prime radicalC61×#392C4
cosocleC2×C4⋊C4×C61C23
hypercenter#2610D61
hypocenterC61#11851
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #2610

Complements

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

NH ≅ G/Ntype
1. #21445902C2semidirect
2. #21444133C2semidirect
3. #21443849C2semidirect
4. #21443822C2semidirect
200. C61#11851semidirect

Maximal subgroups

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

subgroupindex
#214459022
#214441332
#214438492
#214438222
C61×#26102
#1185161