Finite Group Databasebeta

← #29569203

Subgroups — #29569203

Order 15616.

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

normal subgroups only

This group has 380 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#21453796C211yesmaximal, characteristic
2#21447228C211yesmaximal, characteristic, complemented
3#21447223C211yesmaximal, characteristic
4#21443644C211yesmaximal, characteristic, complemented
5#21443642C211yesmaximal, characteristic, complemented
6#21443639C211yesmaximal, characteristic
7C61×#2099C211yesmaximal, characteristic, complemented
8C2×#14519700—21no—
9C2×#14519697—21no—
10#16839688—21no—
11#16839679—21no—
12#16839675—21no—
13#16839668C2211yescharacteristic
14#16839664C2211yescharacteristic
15#16839654—21no—
16#16839652—21no—
17#16839648—21no—
18#16839524—21no—
19#16839524—21no—
20#16839517C2211yescharacteristic
21#16839517C2211yescharacteristic
22C61×#389C2211yescharacteristic
23C61×#384C2211yescharacteristic
24C61×#340—21no—
25C61×#340—21no—
26C61×#336C2211yescharacteristic
27C22×Dic122D411yescharacteristic
28C22×D244D411yescharacteristic
29C22×#92418—21no—
30C22×#92418—21no—
31C2×C4⋊Dic61D411yescharacteristic
32C2×C4⋊Dic61D411yescharacteristic
33C2×#11758198—21no—
34C2×#11758198—21no—
35C2×#11758198—21no—
36C2×#11758198—21no—
37C2×#11758198—21no—
38C2×#11758198—21no—
39C2×C4×Dic61—21no—
40#14519700—42no—
41#14519697—42no—
42#14519684—21no—
43#14519684—21no—
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47C22×C8×C61—21no—
48C2×C4⋊C4×C61—21no—
49C2×C4⋊C4×C61—21no—
50C2×C4⋊C4×C61—21no—
51C2×C4⋊C4×C61—21no—
52C2×C4⋊C4×C61D411yescharacteristic
53C2×C4⋊C4×C61D411yescharacteristic
54C2×C42×C61C2311yescharacteristic
55#95×C61—21no—
56C23×D61—21no—
57C22×C4×C61—21no—
58C22×C4×C61—21no—
59C22×C4×C61—41no—
60C22×C4×C61C2×D411yescharacteristic
61C22×C4×C61C2×D411yescharacteristic
62C22×C4×C61C2×D411yescharacteristic
63C22×Dic61—21no—
64C22×Dic61—21no—
65C22×Dic61—21no—
66C2×D244—21no—
67C2×D244—21no—
68C2×D244—41no—
69C2×D244—41no—
70C2×Dic122—21no—
71C2×Dic122—21no—
72C2×Dic122—41no—
73C2×Dic122—41no—
74C2×C8×C61—41no—
75C2×C8×C61—41no—
76C2×C8×C61—41no—
77C4⋊C4×C61—21no—
78C4⋊C4×C61—21no—
79C4⋊C4×C61—41no—
80C4⋊C4×C61—42no—
81C4⋊C4×C61—41no—
82C4⋊C4×C61—41no—
83C4⋊C4×C61—41no—
84C4⋊C4×C61—41no—
85C4⋊C4×C61—41no—
86C4⋊C4×C61—41no—
87C42×C61—41no—
88#11758198—41no—
89#11758198—41no—
90#11758198—41no—
91#11758198—41no—
92#11758198—81no—
93#11758198—81no—
94#11758198—81no—
95#11758198—81no—
96C4⋊Dic61—41no—
97C4⋊Dic61—41no—
98C4×Dic61—81no—
99C2×#92418—41no—
100C2×#92418—41no—
101C2×#92418—41no—
102C2×#92418—41no—
103C2×#92418—41no—
104C2×#92418—41no—
105C23×C61#12011yescharacteristic
106C22×D61—41no—
107C22×D61—41no—
108C22×D61—41no—
109C22×D61—41no—
110C22×D61—41no—
111C22×D61—41no—
112C22×D61—41no—
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—41no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61—81no—
126C2×C4×C61—81no—
127C2×C4×C61—81no—
128C2×C4×C61#13511yescharacteristic
129C2×C4×C61#13511yescharacteristic
130C2×C4×C61#13511yescharacteristic
131C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
132C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C61#13711yescharacteristic
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143D244—42no—
144D244—81no—
145Dic122—42no—
146Dic122—81no—
147C8×C61—81no—
148#92418—81no—
149#92418—81no—
150#7811—611nomaximal, Sylow
151C22×C61#44911yescharacteristic
152C22×C61#44911yescharacteristic
153C22×C61#45211yescharacteristic
154C22×C61#45411yescharacteristic
155C22×C61#45511yescharacteristic
156C22×C61#45511yescharacteristic
157C22×C61#45811yescharacteristic
158C2×D61—81no—
159C2×D61—81no—
160C2×D61—81no—
161C2×D61—81no—
162C2×D61—81no—
163C2×D61—81no—
164C2×D61—81no—
165C4×C61—21no—
166C4×C61—21no—
167C4×C61—21no—
168C4×C61—21no—
169C4×C61—21no—
170C4×C61—21no—
171C4×C61—81no—
172C4×C61—81no—
173C4×C61—161no—
174Dic61—81no—
175Dic61—81no—
176Dic61—81no—
177#2808—611no—
178#2099D6111yescharacteristic, complemented
179#2072—611no—
180#2071—611no—
181#1272—611no—
182#1271—611no—
183#1270—611no—
184C2×C61#161211yescharacteristic
185C2×C61#161211yescharacteristic
186C2×C61#161511yescharacteristic
187C2×C61#162811yescharacteristic
188C2×C61#164011yescharacteristic
189C2×C61#164611yescharacteristic
190C2×C61#166211yescharacteristic
191D61—161no—
192C2×#103—1221no—
193C2×#102—1221no—
194#397—1221no—
195#394—1221no—
196#393—1221no—
197#391—611no—
198#390—611no—
199#389C2×D6111yescharacteristic
200#388—1221no—
201#388—1221no—
202#387—1221no—
203#384C2×D6111yescharacteristic
204#340—21no—
205#340—21no—
206#340—1221no—
207#340—1221no—
208#336—611no—
209#336—611no—
210#336C2×D6111yescharacteristic
211C61#781111yescharacteristic, complemented, Sylow
212C22×Q8—611no—
213C22×D4—611no—
214C22×C8—21no—
215C22×C8—1221no—
216C22×C8—1221no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—611no—
222C2×C4⋊C4—611no—
223C2×C4⋊C4C22⋊D6111yescharacteristic
224C2×C4⋊C4C22⋊D6111yescharacteristic
225C2×C22⋊C4—1221no—
226C2×C22⋊C4—1221no—
227C2×C22⋊C4—1221no—
228C2×C22⋊C4—1221no—
229C2×C22⋊C4—1221no—
230C2×C22⋊C4—1221no—
231C2×C42—1221no—
232C2×C42C22×D6111yescharacteristic
233#103—2442no—
234#102—2442no—
235#95—21no—
236#95—1221no—
237#95—1221no—
238#95—1221no—
239#95—1221no—
240#95—1221no—
241C24—1221no—
242C2×Q8—1221no—
243C2×Q8—1221no—
244C2×Q8—2441no—
245C2×Q8—2441no—
246C2×D4—1221no—
247C2×D4—1221no—
248C2×D4—2441no—
249C2×D4—2441no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—41no—
253C22×C4—1221no—
254C22×C4—1221no—
255C22×C4—1221no—
256C22×C4D4×D6111yescharacteristic
257C22×C4D4×D6111yescharacteristic
258C22×C4C2×C22⋊D6111yescharacteristic
259C2×C8—41no—
260C2×C8—41no—
261C2×C8—41no—
262C2×C8—2441no—
263C2×C8—2441no—
264C2×C8—2441no—
265C2×C8—2441no—
266C2×C8—2441no—
267C2×C8—2441no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—41no—
271C4⋊C4—42no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—2441no—
279C4⋊C4—2441no—
280C22⋊C4—4881no—
281C22⋊C4—4881no—
282C22⋊C4—4881no—
283C22⋊C4—4881no—
284C22⋊C4—2441no—
285C22⋊C4—2441no—
286C22⋊C4—2441no—
287C22⋊C4—2441no—
288C42—41no—
289C42—4881no—
290C23—2441no—
291C23—2441no—
292C23—2441no—
293C23—2441no—
294C23—2441no—
295C23—2441no—
296C23—2441no—
297C23#1451974511yescharacteristic
298Q8—4881no—
299Q8—2442no—
300D4—4881no—
301D4—2442no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—2441no—
318C2×C4—2441no—
319C2×C4—2441no—
320C2×C4—2441no—
321C2×C4—2441no—
322C2×C4—2441no—
323C2×C4—2441no—
324C2×C4—2441no—
325C2×C4—2441no—
326C2×C4#1451979611yescharacteristic
327C2×C4#1451979711yescharacteristic
328C2×C4#1451979811yescharacteristic
329C2×C4#1451980111yescharacteristic
330C2×C4#1451980411yescharacteristic
331C2×C4#1451980811yescharacteristic
332C8—81no—
333C8—4881no—
334C8—4881no—
335C22—4881no—
336C22—4881no—
337C22—4881no—
338C22—4881no—
339C22—4881no—
340C22—4881no—
341C22—4881no—
342C22#1683990411yescharacteristic
343C22#1683990611yescharacteristic
344C22#1683992211yescharacteristic
345C22#1683993411yescharacteristic
346C22#1683993811yescharacteristic
347C22#1683993811yescharacteristic
348C22#1683995111yescharacteristic
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—21no—
355C4—81no—
356C4—81no—
357C4—161no—
358C4—4881no—
359C4—4881no—
360C4—4881no—
361C2—9761no—
362C2#2144483011yescharacteristic
363C2#2144483211yescharacteristic
364C2#2144484811yescharacteristic
365C2#2144492611yescharacteristic
366C2#2144500411yescharacteristic
367C2#2144504611yescharacteristic
368C2#2144514011yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#2099C2
socleC23×C61#120
prime radicalC22×D244D4
hypercenter#2099D61
hypocenterC61#7811
LCSG ▷ C2×C42×C61 ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2099

Complements

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

NH ≅ G/Ntype
2. #21447228C2semidirect
4. #21443644C2semidirect
5. #21443642C2semidirect
7. C61×#2099C2semidirect
178. #2099D61semidirect
211. C61#7811semidirect

Maximal subgroups

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

subgroupindex
#214537962
#214472282
#214472232
#214436442
#214436422
#214436392
C61×#20992
#781161