Finite Group Databasebeta

← #29590929

Subgroups — #29590929

Order 15616.

418 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 79 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#21451506C211yesmaximal, characteristic
2#21444133C211yesmaximal, characteristic, complemented
3#21443848C212yesmaximal, complemented
4#21443821C212yesmaximal, complemented
5C61×#1822C211yesmaximal, characteristic, complemented
6C2×#14519765C411yescharacteristic
7#16839815—21no—
8#16839682C2211yescharacteristic
9#16839679C2211yescharacteristic
10#16839674C411yescharacteristic
11#16839671C411yescharacteristic
12#16839662—21no—
13#16839653—21no—
14#16839652—21no—
15#16839641—21no—
16#16839608C411yescharacteristic
17#16839488C2212yes—
18#16839486—21no—
19C2×#117×C61C2211yescharacteristic
20C61×#407—21no—
21C61×#343—21no—
22C61×#343C2212yes—
23C22×Dic122C2×C411yescharacteristic
24C22×D244C2×C411yescharacteristic
25C22×C22⋊D61—21no—
26#14519765—41no—
27#14519765—41no—
28C2×#11758196—21no—
29C2×C22⋊Dic61—21no—
30C2×#11758198—21no—
31C2×#11758198—21no—
32C2×#11758198—21no—
33C2×#11758198—21no—
34C2×#11758198—21no—
35C2×C4×Dic61—21no—
36C4⋊#92418—41no—
37C22⋊#92418—22no—
38C4×#92418—41no—
39#14519684—21no—
40#14519684—21no—
41#14519684—21no—
42#14519684C2×C411yescharacteristic
43#14519684C2×C411yescharacteristic
44C23×C4×C61D411yescharacteristic
45C2×M16×C61—22no—
46#117×C61—41no—
47#117×C61—41no—
48C2×C4⋊C4×C61D411yescharacteristic
49C2×C4⋊C4×C61C2311yescharacteristic
50C2×C22⋊C4×C61C2×C411yescharacteristic
51C2×C22⋊C4×C61D411yescharacteristic
52C2×C42×C61C2×C411yescharacteristic
53C2×C42×C61D411yescharacteristic
54C22⋊C8×C61—41no—
55C22⋊C8×C61—41no—
56C24×C61C22⋊C411yescharacteristic
57C23×D61—21no—
58C22×C4×C61—21no—
59C22×C4×C61—21no—
60C22×C4×C61—22no—
61C22×C4×C61—41no—
62C22×C4×C61C22⋊C411yescharacteristic
63C22×C4×C61C22⋊C411yescharacteristic
64C22×C4×C61C22⋊C411yescharacteristic
65C22×C4×C61C22×C411yescharacteristic
66C22×C4×C61C2×D411yescharacteristic
67C22×C4×C61C2×D411yescharacteristic
68C2×C22⋊D61—42no—
69C2×C22⋊D61—42no—
70C2×C22⋊D61—81no—
71C22×Dic61—21no—
72C22×Dic61—21no—
73C22×Dic61—21no—
74C2×D244—41no—
75C2×D244—81no—
76C2×Dic122—41no—
77C2×Dic122—81no—
78M16×C61—42no—
79M16×C61—42no—
80C2×C8×C61—42no—
81C4⋊C4×C61—41no—
82C4⋊C4×C61—41no—
83C22⋊C4×C61—41no—
84C22⋊C4×C61—41no—
85C42×C61—21no—
86C42×C61—21no—
87C42×C61—21no—
88C42×C61—21no—
89C22⋊Dic61—81no—
90#11758198—42no—
91#11758198—42no—
92#11758198—41no—
93#11758198—41no—
94#11758198—42no—
95#11758198—81no—
96#11758196—81no—
97C4×Dic61—42no—
98C2×#92418—42no—
99C23×C61—21no—
100C23×C61—21no—
101C23×C61—21no—
102C23×C61—41no—
103C23×C61—41no—
104C23×C61C2×C22⋊C411yescharacteristic
105C22×D61—41no—
106C22×D61—41no—
107C22×D61—41no—
108C22×D61—41no—
109C22×D61—41no—
110C22×D61—41no—
111C22×D61—41no—
112C2×C4×C61—21no—
113C2×C4×C61—21no—
114C2×C4×C61—21no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—42no—
121C2×C4×C61—42no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61#9911yescharacteristic
127C2×C4×C61#9911yescharacteristic
128C2×C4×C61#13512yes—
129C22⋊D61—84no—
130C2×Dic61—22no—
131C2×Dic61—41no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139D244—82no—
140Dic122—82no—
141C8×C61—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×C61C2×#9911yescharacteristic
152C22×C61#41611yescharacteristic
153C22×C61#42111yescharacteristic
154C2×D61—81no—
155C2×D61—81no—
156C2×D61—81no—
157C2×D61—81no—
158C2×D61—81no—
159C2×D61—81no—
160C2×D61—81no—
161C4×C61—22no—
162C4×C61—21no—
163C4×C61—21no—
164C4×C61—41no—
165C4×C61—41no—
166C4×C61—41no—
167C4×C61—41no—
168Dic61—42no—
169Dic61—81no—
170Dic61—81no—
171#2610—611no—
172#1822D6111yescharacteristic, complemented
173#1458—611no—
174#1354—612no—
175#1345—612no—
176C2×C61—21no—
177C2×C61—21no—
178C2×C61—81no—
179C2×C61#151611yescharacteristic
180C2×C61#212211yescharacteristic
181C2×C61#213211yescharacteristic
182D61—161no—
183C2×#124—611no—
184C2×#117C2×D6111yescharacteristic
185#431—1221no—
186#407—21no—
187#395—611no—
188#394—611no—
189#393—611no—
190#392—611no—
191#390—1221no—
192#388—1221no—
193#388—1221no—
194#386—1221no—
195#376—611no—
196#343—21no—
197#343C2×D6112yes—
198#324—612no—
199#323—1221no—
200C61#1185111yescharacteristic, complemented, Sylow
201C22×Q8—611no—
202C22×D4—611no—
203C22×D4—1221no—
204C23×C4C22⋊D6111yescharacteristic
205C2×M16—22no—
206#124—2441no—
207#124—2441no—
208#117—41no—
209#117—41no—
210C2×C4⋊C4—1221no—
211C2×C4⋊C4C22⋊D6111yescharacteristic
212C2×C4⋊C4C22×D6111yescharacteristic
213C2×C22⋊C4—1221no—
214C2×C22⋊C4—1221no—
215C2×C22⋊C4—1221no—
216C2×C22⋊C4—1221no—
217C2×C22⋊C4—1221no—
218C2×C22⋊C4—1221no—
219C2×C22⋊C4C4×D6111yescharacteristic
220C2×C22⋊C4D24411yescharacteristic
221C2×C42—1221no—
222C2×C42C4×D6111yescharacteristic
223C2×C42D24411yescharacteristic
224C4⋊C8—2441no—
225C22⋊C8—41no—
226C22⋊C8—41no—
227C22⋊C8—1222no—
228C4×C8—2441no—
229#95—611no—
230#95—611no—
231#95—1221no—
232#95—1221no—
233#95—1221no—
234C24—1221no—
235C24#1175819811yescharacteristic
236C2×Q8—4881no—
237C2×Q8—2441no—
238C2×D4—4881no—
239C2×D4—4881no—
240C2×D4—2441no—
241C2×D4—2442no—
242C2×D4—2442no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—22no—
246C22×C4—41no—
247C22×C4—1221no—
248C22×C4—1221no—
249C22×C4—1221no—
250C22×C4#1175819811yescharacteristic
251C22×C4#1175819811yescharacteristic
252C22×C4#1175819811yescharacteristic
253C22×C4C2×C4×D6111yescharacteristic
254C22×C4C2×D24411yescharacteristic
255C22×C4C2×C22⋊D6111yescharacteristic
256M16—42no—
257M16—42no—
258C2×C8—42no—
259C2×C8—2442no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—4881no—
263C22⋊C4—41no—
264C22⋊C4—41no—
265C22⋊C4—4881no—
266C22⋊C4—4881no—
267C22⋊C4—2442no—
268C22⋊C4—2442no—
269C22⋊C4—2441no—
270C22⋊C4—2441no—
271C22⋊C4—2442no—
272C42—21no—
273C42—21no—
274C42—21no—
275C42—21no—
276C42—2442no—
277C23—21no—
278C23—21no—
279C23—21no—
280C23—41no—
281C23—41no—
282C23—2441no—
283C23—2441no—
284C23—2441no—
285C23—2441no—
286C23—2441no—
287C23—2441no—
288C23—2441no—
289C23C2×#1175819811yescharacteristic
290Q8—4882no—
291D4—4882no—
292D4—4884no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—1222no—
308C2×C4—2441no—
309C2×C4—2441no—
310C2×C4—2441no—
311C2×C4—2441no—
312C2×C4—2441no—
313C2×C4—2441no—
314C2×C4—2441no—
315C2×C4—2441no—
316C2×C4#1451969111yescharacteristic
317C2×C4#1451969111yescharacteristic
318C2×C4#1451979712yes—
319C8—82no—
320C8—4882no—
321C22—21no—
322C22—21no—
323C22—42no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—81no—
328C22—4881no—
329C22—4881no—
330C22—4881no—
331C22—4881no—
332C22—4881no—
333C22—4881no—
334C22—4881no—
335C22C2×#1451969111yescharacteristic
336C22#1683975611yescharacteristic
337C22#1683978011yescharacteristic
338C4—22no—
339C4—21no—
340C4—21no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—4881no—
346C4—4881no—
347C4—2442no—
348C2—21no—
349C2—21no—
350C2—81no—
351C2—9761no—
352C2#2144437311yescharacteristic
353C2#2144747011yescharacteristic
354C2#2144750211yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC22×C4×C61C22×C4
FrattiniC2×C4⋊C4C22×D61
FittingC61×#1822C2
socleC22×C61C2×#99
prime radical#16839671C4
cosocleC2×C4⋊C4×C61C23
hypercenter#1822D61
hypocenterC61#11851
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1822

Complements

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

NH ≅ G/Ntype
2. #21444133C2semidirect
3. #21443848C2semidirect
4. #21443821C2semidirect
5. C61×#1822C2semidirect
172. #1822D61semidirect
200. C61#11851semidirect

Maximal subgroups

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

subgroupindex
#214515062
#214441332
#214438482
#214438212
C61×#18222
#1185161