Finite Group Databasebeta

← #29590894

Subgroups — #29590894

Order 15616.

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

normal subgroups only

This group has 432 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#21443839C212yesmaximal, complemented
4#21443815C212yesmaximal
5C61×#1820C211yesmaximal, characteristic, complemented
6C2×#14519765C411yescharacteristic, complemented
7#16839815—21no—
8#16839682C411yescharacteristic, complemented
9#16839679C411yescharacteristic, complemented
10#16839674C2211yescharacteristic
11#16839671C2211yescharacteristic
12#16839662—21no—
13#16839653—21no—
14#16839652—21no—
15#16839641—21no—
16#16839608C411yescharacteristic, complemented
17#16839488—21no—
18#16839486C2212yes—
19C2×#117×C61C2211yescharacteristic
20C61×#381—21no—
21C61×#342—21no—
22C61×#342C2212yes—
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
45#117×C61—41no—
46#117×C61—41no—
47C2×C4⋊C4×C61C2×C411yescharacteristic
48C2×C4⋊C4×C61D411yescharacteristic
49C2×C22⋊C4×C61—22no—
50C2×C22⋊C4×C61D411yescharacteristic
51C2×C22⋊C4×C61C2311yescharacteristic
52C2×C42×C61C2×C411yescharacteristic
53C2×C42×C61D411yescharacteristic
54#95×C61—41no—
55#95×C61—41no—
56C24×C61C2×D411yescharacteristic
57C23×D61—21no—
58C22×C4×C61—22no—
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61—41no—
62C22×C4×C61—42no—
63C22×C4×C61C22⋊C411yescharacteristic
64C22×C4×C61C22⋊C411yescharacteristic
65C22×C4×C61C22⋊C411yescharacteristic
66C22×C4×C61C22⋊C411yescharacteristic
67C22×C4×C61C22×C411yescharacteristic
68C22×C4×C61C2×D411yescharacteristic
69C2×C22⋊D61—42no—
70C2×C22⋊D61—42no—
71C2×C22⋊D61—81no—
72C22×Dic61—21no—
73C22×Dic61—21no—
74C22×Dic61—21no—
75C2×D244—41no—
76C2×D244—81no—
77C2×Dic122—41no—
78C2×Dic122—81no—
79C4⋊C4×C61—41no—
80C4⋊C4×C61—41no—
81C22⋊C4×C61—41no—
82C22⋊C4×C61—41no—
83C22⋊C4×C61—42no—
84C22⋊C4×C61—42no—
85C42×C61—21no—
86C42×C61—21no—
87C42×C61—21no—
88C42×C61—21no—
89C22⋊Dic61—81no—
90#11758198—42no—
91#11758198—42no—
92#11758198—42no—
93#11758198—41no—
94#11758198—41no—
95#11758198—81no—
96#11758196—81no—
97C4×Dic61—42no—
98C2×#92418—42no—
99C23×C61—21no—
100C23×C61—21no—
101C23×C61—41no—
102C23×C61—41no—
103C23×C61C2×C22⋊C411yescharacteristic
104C23×C61#13512yes—
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—21no—
121C2×C4×C61—42no—
122C2×C4×C61—42no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—82no—
128C2×C4×C61—82no—
129C2×C4×C61—82no—
130C2×C4×C61#9911yescharacteristic
131C2×C4×C61#9911yescharacteristic
132C22⋊D61—84no—
133C2×Dic61—22no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142D244—82no—
143Dic122—82no—
144#92418—82no—
145#11844—611nomaximal, Sylow
146C22×C61—21no—
147C22×C61—21no—
148C22×C61—22no—
149C22×C61—42no—
150C22×C61—41no—
151C22×C61—41no—
152C22×C61—81no—
153C22×C61C2×#9911yescharacteristic
154C22×C61#41611yescharacteristic
155C22×C61#42111yescharacteristic
156C2×D61—81no—
157C2×D61—81no—
158C2×D61—81no—
159C2×D61—81no—
160C2×D61—81no—
161C2×D61—81no—
162C2×D61—81no—
163C4×C61—21no—
164C4×C61—21no—
165C4×C61—41no—
166C4×C61—41no—
167C4×C61—41no—
168C4×C61—41no—
169C4×C61—41no—
170C4×C61—162no—
171Dic61—42no—
172Dic61—81no—
173Dic61—81no—
174#2610—611no—
175#1820D6111yescharacteristic, complemented
176#1458—611no—
177#1351—612no—
178#1343—612no—
179C2×C61—21no—
180C2×C61—21no—
181C2×C61—42no—
182C2×C61#151611yescharacteristic
183C2×C61#212211yescharacteristic
184C2×C61#212611yescharacteristic
185D61—161no—
186C2×#124—611no—
187C2×#117C2×D6111yescharacteristic
188#431—1221no—
189#395—611no—
190#394—611no—
191#393—611no—
192#392—611no—
193#390—1221no—
194#388—1221no—
195#388—1221no—
196#386—1221no—
197#381—21no—
198#376—611no—
199#342—21no—
200#342C2×D6112yes—
201#324—1221no—
202#323—612no—
203C61#1184411yescharacteristic, complemented, Sylow
204C22×Q8—611no—
205C22×D4—611no—
206C22×D4—1221no—
207C23×C4C22⋊D6111yescharacteristic
208#124—2441no—
209#124—2441no—
210#117—41no—
211#117—41no—
212C2×C4⋊C4—1221no—
213C2×C4⋊C4C4×D6111yescharacteristic
214C2×C4⋊C4D24411yescharacteristic
215C2×C22⋊C4—22no—
216C2×C22⋊C4—1221no—
217C2×C22⋊C4—1221no—
218C2×C22⋊C4—1221no—
219C2×C22⋊C4—1221no—
220C2×C22⋊C4—1221no—
221C2×C22⋊C4—1221no—
222C2×C22⋊C4C22⋊D6111yescharacteristic
223C2×C22⋊C4C22×D6111yescharacteristic
224C2×C42—1221no—
225C2×C42C4×D6111yescharacteristic
226C2×C42D24411yescharacteristic
227C4⋊C8—2441no—
228C22⋊C8—1222no—
229C4×C8—2441no—
230#95—41no—
231#95—41no—
232#95—611no—
233#95—611no—
234#95—1221no—
235#95—1221no—
236#95—1221no—
237C24—1221no—
238C24C2×C22⋊D6111yescharacteristic
239C2×Q8—4881no—
240C2×Q8—2441no—
241C2×D4—4881no—
242C2×D4—4881no—
243C2×D4—2441no—
244C2×D4—2442no—
245C2×D4—2442no—
246C22×C4—22no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—41no—
250C22×C4—42no—
251C22×C4—1221no—
252C22×C4—1221no—
253C22×C4—1221no—
254C22×C4#1175819811yescharacteristic
255C22×C4#1175819811yescharacteristic
256C22×C4#1175819811yescharacteristic
257C22×C4#1175819811yescharacteristic
258C22×C4C2×C4×D6111yescharacteristic
259C22×C4C2×D24411yescharacteristic
260C2×C8—2442no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—4881no—
264C22⋊C4—41no—
265C22⋊C4—41no—
266C22⋊C4—42no—
267C22⋊C4—42no—
268C22⋊C4—4881no—
269C22⋊C4—4881no—
270C22⋊C4—2442no—
271C22⋊C4—2442no—
272C22⋊C4—2442no—
273C22⋊C4—2441no—
274C22⋊C4—2441no—
275C42—21no—
276C42—21no—
277C42—21no—
278C42—21no—
279C42—2442no—
280C23—21no—
281C23—21no—
282C23—41no—
283C23—41no—
284C23—2441no—
285C23—2441no—
286C23—2441no—
287C23—2441no—
288C23—2441no—
289C23—2441no—
290C23—2441no—
291C23C2×#1175819811yescharacteristic
292C23#1451979712yes—
293Q8—4882no—
294D4—4882no—
295D4—4884no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—82no—
312C2×C4—82no—
313C2×C4—82no—
314C2×C4—1222no—
315C2×C4—2441no—
316C2×C4—2441no—
317C2×C4—2441no—
318C2×C4—2441no—
319C2×C4—2441no—
320C2×C4—2441no—
321C2×C4—2441no—
322C2×C4—2441no—
323C2×C4#1451969111yescharacteristic
324C2×C4#1451969111yescharacteristic
325C8—4882no—
326C22—21no—
327C22—21no—
328C22—22no—
329C22—42no—
330C22—41no—
331C22—41no—
332C22—81no—
333C22—4881no—
334C22—4881no—
335C22—4881no—
336C22—4881no—
337C22—4881no—
338C22—4881no—
339C22—4881no—
340C22C2×#1451969111yescharacteristic
341C22#1683975611yescharacteristic
342C22#1683978011yescharacteristic
343C4—21no—
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—41no—
350C4—162no—
351C4—4881no—
352C4—4881no—
353C4—2442no—
354C2—21no—
355C2—21no—
356C2—42no—
357C2—9761no—
358C2#2144437311yescharacteristic
359C2#2144746811yescharacteristic
360C2#2144748211yescharacteristic
subgroupG/H
centerC22C2×#14519691
commutatorC22×C4×C61C22×C4
FrattiniC2×C22⋊C4C22×D61
FittingC61×#1820C2
socleC22×C61C2×#99
prime radical#16839671C22
cosocleC2×C22⋊C4×C61C23
hypercenter#1820D61
hypocenterC61#11844
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1820

Complements

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

NH ≅ G/Ntype
2. #21444133C2semidirect
3. #21443839C2semidirect
5. C61×#1820C2semidirect
6. C2×#14519765C4semidirect
8. #16839682C4semidirect
9. #16839679C4semidirect
16. #16839608C4semidirect
175. #1820D61semidirect
203. C61#11844semidirect

Maximal subgroups

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

subgroupindex
#214515062
#214441332
#214438392
#214438152
C61×#18202
#1184461