Finite Group Databasebeta

← #29576001

Subgroups — #29576001

Order 15616.

478 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 103 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#21451679C211yesmaximal, characteristic
2C4×#14519696C211yesmaximal, characteristic, complemented
3#21444418C212yesmaximal
4#21443685C212yesmaximal, complemented
5C61×#2983C211yesmaximal, characteristic, complemented
6C2×#14519765C2211yescharacteristic
7C2×#14519696—21no—
8C4×#11758194C2212yes—
9#16839697—21no—
10#16839682C411yescharacteristic
11#16839682C411yescharacteristic
12#16839679C411yescharacteristic
13#16839679C411yescharacteristic
14#16839673—21no—
15#16839653—21no—
16#16839653—21no—
17#16839630C2211yescharacteristic
18#16839531—21no—
19#16839501—24no—
20C2×C4×Q8×C61C2211yescharacteristic
21C61×#446—24no—
22C61×#432—21no—
23C61×#432C2212yes—
24C61×#431—21no—
25C22×Dic122C2×C411yescharacteristic
26C22×D244C2×C411yescharacteristic
27C2×#11758194—22no—
28#14519765—22no—
29#14519765—22no—
30C2×#11758196—21no—
31C2×#11758196—21no—
32C2×#11758198—21no—
33C2×#11758198—21no—
34C2×#11758198—21no—
35C2×#11758198—21no—
36C2×#11758198—21no—
37C2×#11758198—21no—
38#14519696—24no—
39#14519688—22no—
40C4×#92418—22no—
41#14519684—21no—
42#14519684—21no—
43#14519684—21no—
44#14519684—21no—
45#14519684C2×C411yescharacteristic
46#14519684C2×C411yescharacteristic
47C22×Q8×C61D411yescharacteristic
48C4×Q8×C61—22no—
49C4×Q8×C61—22no—
50C2×C4⋊C4×C61C2×C411yescharacteristic
51C2×C4⋊C4×C61C2×C411yescharacteristic
52C2×C4⋊C4×C61D411yescharacteristic
53C2×C42×C61D411yescharacteristic
54C2×C42×C61D411yescharacteristic
55C2×C42×C61C2311yescharacteristic
56C4⋊C8×C61—22no—
57C4⋊C8×C61—22no—
58C4⋊C8×C61—22no—
59C22⋊C8×C61—22no—
60#97×C61—22no—
61#97×C61D414yes—
62C4×C8×C61—22no—
63C23×D61—21no—
64C2×Q8×C61—22no—
65C2×Q8×C61—22no—
66C2×Q8×C61—41no—
67C22×C4×C61C22⋊C411yescharacteristic
68C22×C4×C61C22⋊C411yescharacteristic
69C22×C4×C61C22⋊C411yescharacteristic
70C22×C4×C61C22⋊C411yescharacteristic
71C22×C4×C61C22×C411yescharacteristic
72C22×C4×C61C2×D411yescharacteristic
73C22×C4×C61C2×D411yescharacteristic
74C22×Dic61—21no—
75C22×Dic61—21no—
76C22×Dic61—21no—
77C2×D244—22no—
78C2×D244—81no—
79C2×Dic122—22no—
80C2×Dic122—81no—
81C2×C8×C61—24no—
82C4⋊C4×C61—22no—
83C4⋊C4×C61—22no—
84C4⋊C4×C61—22no—
85C42×C61—21no—
86C42×C61—21no—
87C42×C61—21no—
88C42×C61—21no—
89C42×C61C2×D412yes—
90C42×C61#4112yes—
91#11758198—42no—
92#11758198—42no—
93#11758198—41no—
94#11758198—42no—
95#11758198—41no—
96#11758198—81no—
97#11758198—81no—
98#11758196—81no—
99#11758196—81no—
100#11758194—24no—
101#11758194—42no—
102C2×#92418—42no—
103C23×C61C2×C22⋊C411yescharacteristic
104C22×D61—41no—
105C22×D61—41no—
106C22×D61—41no—
107C22×D61—41no—
108C22×D61—41no—
109C22×D61—41no—
110C22×D61—41no—
111Q8×C61—44no—
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—41no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61#10412yes—
126C2×C4×C61C4×D412yes—
127C2×C4×C61#12011yescharacteristic
128C2×C4×C61#12112yes—
129C2×C4×C61#12311yescharacteristic
130C2×Dic61—41no—
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—44no—
142#92418—44no—
143#9188—611nomaximal, Sylow
144C22×C61—21no—
145C22×C61—21no—
146C22×C61#38611yescharacteristic
147C22×C61C2×#10411yescharacteristic
148C22×C61#42111yescharacteristic
149C2×D61—81no—
150C2×D61—81no—
151C2×D61—81no—
152C2×D61—81no—
153C2×D61—81no—
154C2×D61—81no—
155C2×D61—81no—
156C4×C61—22no—
157C4×C61—22no—
158C4×C61—21no—
159C4×C61—21no—
160C4×C61—22no—
161C4×C61—41no—
162C4×C61—41no—
163C4×C61—41no—
164Dic61—81no—
165Dic61—81no—
166Dic61—81no—
167#2983D6111yescharacteristic, complemented
168#2632—611no—
169C4×#101—611no—
170#1527—612no—
171#1288—612no—
172C2×C61—21no—
173C2×C61—21no—
174C2×C61#187111yescharacteristic
175C2×C61#191211yescharacteristic
176C2×C61#191411yescharacteristic
177D61—161no—
178C2×#124—611no—
179C2×C4×Q8C2×D6111yescharacteristic
180#446—24no—
181#432—21no—
182#432C2×D6112yes—
183#431—21no—
184C2×#101—1221no—
185C4×M16—612no—
186#399—1221no—
187#395—611no—
188#395—611no—
189#394—611no—
190#394—611no—
191#393—1221no—
192#388—1221no—
193#388—1221no—
194#383—611no—
195#343—1221no—
196#329—1224no—
197C61#918811yescharacteristic, complemented, Sylow
198C22×Q8—611no—
199C22×Q8D24411yescharacteristic
200C22×D4—611no—
201C2×M16—1222no—
202#124—1222no—
203#124—1222no—
204C4×Q8—22no—
205C4×Q8—22no—
206C2×C4⋊C4—1221no—
207C2×C4⋊C4—1221no—
208C2×C4⋊C4C4×D6111yescharacteristic
209C2×C4⋊C4C4×D6111yescharacteristic
210C2×C4⋊C4D24411yescharacteristic
211C2×C22⋊C4—1221no—
212C2×C22⋊C4—1221no—
213C2×C22⋊C4—1221no—
214C2×C22⋊C4—1221no—
215C2×C22⋊C4—1221no—
216C2×C22⋊C4—1221no—
217C2×C42C22⋊D6111yescharacteristic
218C2×C42C22⋊D6111yescharacteristic
219C2×C42C22×D6111yescharacteristic
220C4⋊C8—22no—
221C4⋊C8—22no—
222C4⋊C8—22no—
223#101—1224no—
224C22⋊C8—22no—
225#97—22no—
226#97—1222no—
227#97C22⋊D6114yes—
228C4×C8—22no—
229C4×C8—1222no—
230#95—611no—
231#95—611no—
232#95—1221no—
233#95—1221no—
234#95—1221no—
235#95—1221no—
236C24—1221no—
237C2×Q8—22no—
238C2×Q8—22no—
239C2×Q8—41no—
240C2×Q8—1222no—
241C2×Q8—4881no—
242C2×D4—1222no—
243C2×D4—4881no—
244C22×C4—1221no—
245C22×C4—1221no—
246C22×C4—1221no—
247C22×C4#1175819811yescharacteristic
248C22×C4#1175819811yescharacteristic
249C22×C4#1175819811yescharacteristic
250C22×C4#1175819811yescharacteristic
251C22×C4C2×C4×D6111yescharacteristic
252C22×C4C2×D24411yescharacteristic
253C22×C4C2×C22⋊D6111yescharacteristic
254M16—1224no—
255M16—2442no—
256C2×C8—24no—
257C2×C8—2442no—
258C4⋊C4—22no—
259C4⋊C4—22no—
260C4⋊C4—22no—
261C4⋊C4—4881no—
262C4⋊C4—4881no—
263C22⋊C4—4881no—
264C22⋊C4—4881no—
265C22⋊C4—2442no—
266C22⋊C4—2442no—
267C22⋊C4—2441no—
268C22⋊C4—2442no—
269C22⋊C4—2441no—
270C42—21no—
271C42—21no—
272C42—21no—
273C42—21no—
274C42#1175822212yes—
275C42C2×C22⋊D6112yes—
276C23—2441no—
277C23—2441no—
278C23—2441no—
279C23—2441no—
280C23—2441no—
281C23—2441no—
282C23—2441no—
283C23C2×#1175819811yescharacteristic
284Q8—44no—
285Q8—4882no—
286D4—4882no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—2441no—
301C2×C4—2441no—
302C2×C4—2441no—
303C2×C4—2441no—
304C2×C4—2441no—
305C2×C4—2441no—
306C2×C4—2441no—
307C2×C4—2441no—
308C2×C4—2441no—
309C2×C4#1451970312yes—
310C2×C4C4×C22⋊D6112yes—
311C2×C4#1451974611yescharacteristic
312C2×C4#1451975112yes—
313C2×C4#1451976011yescharacteristic
314C8—44no—
315C8—2444no—
316C22—21no—
317C22—21no—
318C22—4881no—
319C22—4881no—
320C22—4881no—
321C22—4881no—
322C22—4881no—
323C22—4881no—
324C22—4881no—
325C22#1683964111yescharacteristic
326C22C2×#1451970311yescharacteristic
327C22#1683977811yescharacteristic
328C4—21no—
329C4—21no—
330C4—22no—
331C4—22no—
332C4—22no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—4881no—
337C4—4881no—
338C4—4881no—
339C2—21no—
340C2—21no—
341C2—9761no—
342C2#2144612111yescharacteristic
343C2#2144635611yescharacteristic
344C2#2144636611yescharacteristic
subgroupG/H
centerC22#16839641
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#2983C2
socleC22×C61#386
prime radicalC22×D244C2×C4
cosocleC2×C42×C61C23
hypercenter#2983D61
hypocenterC61#9188
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2983

Complements

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

NH ≅ G/Ntype
2. C4×#14519696C2semidirect
4. #21443685C2semidirect
5. C61×#2983C2semidirect
167. #2983D61semidirect
197. C61#9188semidirect

Maximal subgroups

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

subgroupindex
#214516792
C4×#145196962
#214444182
#214436852
C61×#29832
#918861