Finite Group Databasebeta

← #29569206

Subgroups — #29569206

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#21453799C211yesmaximal, characteristic
2#21447378C211yesmaximal, characteristic, complemented
3#21447229C211yesmaximal, characteristic, complemented
4#21447222C211yesmaximal, characteristic
5#21443644C211yesmaximal, characteristic, complemented
6#21443641C211yesmaximal, characteristic, complemented
7C61×#1270C211yesmaximal, characteristic
8C2×#14519702—21no—
9C2×#14519698—21no—
10#16839687—21no—
11#16839676—21no—
12#16839674—21no—
13#16839668C2211yescharacteristic
14#16839660C2211yescharacteristic
15#16839655—21no—
16#16839655—21no—
17#16839643—21no—
18#16839632C2211yescharacteristic
19#16839525—21no—
20#16839525—21no—
21#16839525—21no—
22#16839524—21no—
23#16839517C2211yescharacteristic
24C61×#390C2211yescharacteristic
25C61×#336C2211yescharacteristic
26C61×#336C2211yescharacteristic
27C22×Dic122D411yescharacteristic
28C22×#92418—21no—
29C2×C4⋊Dic61—21no—
30C2×C4⋊Dic61—21no—
31C2×C4⋊Dic61—21no—
32C2×C4⋊Dic61D411yescharacteristic
33C2×C4⋊Dic61D411yescharacteristic
34C2×C4⋊Dic61D411yescharacteristic
35C2×#11758196—21no—
36C2×C22⋊Dic61—21no—
37C2×C22⋊Dic61—21no—
38C2×C22⋊Dic61—21no—
39C2×C22⋊Dic61—21no—
40C2×C4×Dic61—21no—
41#14519702—42no—
42#14519698—42no—
43#14519684—21no—
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49C22×D4×C61D411yescharacteristic
50C22×C8×C61—21no—
51C22×C8×C61—21no—
52C2×C4⋊C4×C61D411yescharacteristic
53C2×C22⋊C4×C61—21no—
54C2×C22⋊C4×C61—21no—
55C2×C42×C61C2311yescharacteristic
56C24×C61—21no—
57C2×D4×C61—21no—
58C2×D4×C61—21no—
59C2×D4×C61—41no—
60C2×D4×C61—41no—
61C22×C4×C61—21no—
62C22×C4×C61C2×D411yescharacteristic
63C22×C4×C61C2×D411yescharacteristic
64C22×C4×C61C2×D411yescharacteristic
65C22×Dic61—21no—
66C22×Dic61—21no—
67C22×Dic61—21no—
68C22×Dic61—21no—
69C22×Dic61—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—
77C2×C8×C61—41no—
78C2×C8×C61—41no—
79C2×C8×C61—41no—
80C4⋊C4×C61—41no—
81C22⋊C4×C61—41no—
82C22⋊C4×C61—41no—
83C22⋊C4×C61—41no—
84C22⋊C4×C61—41no—
85C42×C61—41no—
86C22⋊Dic61—81no—
87C22⋊Dic61—81no—
88C22⋊Dic61—81no—
89C22⋊Dic61—81no—
90C4⋊Dic61—21no—
91C4⋊Dic61—21no—
92C4⋊Dic61—41no—
93C4⋊Dic61—41no—
94C4⋊Dic61—42no—
95C4⋊Dic61—41no—
96C4⋊Dic61—41no—
97C4⋊Dic61—41no—
98C4⋊Dic61—41no—
99#11758196—41no—
100#11758196—41no—
101C4×Dic61—81no—
102C2×#92418—41no—
103C2×#92418—41no—
104C2×#92418—41no—
105C23×C61—41no—
106C23×C61—41no—
107C23×C61—41no—
108C23×C61—41no—
109C23×C61—41no—
110C23×C61—41no—
111C23×C61—41no—
112C23×C61#12011yescharacteristic
113D4×C61—42no—
114D4×C61—81no—
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#13511yescharacteristic
125C2×C4×C61#13511yescharacteristic
126C2×C4×C61#13511yescharacteristic
127C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
128C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
129C2×C4×C61#13711yescharacteristic
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—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—81no—
143C2×Dic61—81no—
144C2×Dic61—81no—
145Dic122—42no—
146Dic122—81no—
147C8×C61—81no—
148C8×C61—81no—
149#92418—81no—
150#7811—611nomaximal, Sylow
151C22×C61—81no—
152C22×C61—81no—
153C22×C61—81no—
154C22×C61—81no—
155C22×C61—81no—
156C22×C61—81no—
157C22×C61—81no—
158C22×C61#44911yescharacteristic
159C22×C61#44911yescharacteristic
160C22×C61#45211yescharacteristic
161C22×C61#45411yescharacteristic
162C22×C61#45511yescharacteristic
163C22×C61#45511yescharacteristic
164C22×C61#45811yescharacteristic
165C4×C61—21no—
166C4×C61—21no—
167C4×C61—21no—
168C4×C61—21no—
169C4×C61—21no—
170C4×C61—21no—
171C4×C61—81no—
172Dic61—81no—
173Dic61—81no—
174Dic61—81no—
175Dic61—81no—
176Dic61—161no—
177#2808—611no—
178#2099—611no—
179#2072—611no—
180#2071—611no—
181#1272—611no—
182#1271—611no—
183#1270D6111yescharacteristic
184C2×C61—161no—
185C2×C61#161211yescharacteristic
186C2×C61#161211yescharacteristic
187C2×C61#161511yescharacteristic
188C2×C61#162811yescharacteristic
189C2×C61#164011yescharacteristic
190C2×C61#164611yescharacteristic
191C2×C61#166211yescharacteristic
192C2×#103—1221no—
193C2×#102—1221no—
194#397—1221no—
195#394—1221no—
196#393—1221no—
197#391—611no—
198#390C2×D6111yescharacteristic
199#389—611no—
200#388—1221no—
201#388—1221no—
202#387—1221no—
203#384—611no—
204#340—1221no—
205#340—1221no—
206#340—1221no—
207#340—1221no—
208#336—611no—
209#336C2×D6111yescharacteristic
210#336C2×D6111yescharacteristic
211C61#781111yescharacteristic, complemented, Sylow
212C22×Q8—611no—
213C22×D4D24411yescharacteristic
214C22×C8—21no—
215C22×C8—21no—
216C22×C8—1221no—
217C2×C4⋊C4—611no—
218C2×C4⋊C4—611no—
219C2×C4⋊C4—611no—
220C2×C4⋊C4—1221no—
221C2×C4⋊C4—1221no—
222C2×C4⋊C4—1221no—
223C2×C4⋊C4—1221no—
224C2×C4⋊C4D24411yescharacteristic
225C2×C22⋊C4—21no—
226C2×C22⋊C4—21no—
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—1221no—
236#95—1221no—
237#95—1221no—
238#95—1221no—
239#95—1221no—
240#95—1221no—
241C24—21no—
242C2×Q8—1221no—
243C2×Q8—1221no—
244C2×Q8—2441no—
245C2×Q8—2441no—
246C2×D4—21no—
247C2×D4—21no—
248C2×D4—41no—
249C2×D4—41no—
250C22×C4—21no—
251C22×C4—1221no—
252C22×C4—1221no—
253C22×C4—1221no—
254C22×C4—1221no—
255C22×C4—2441no—
256C22×C4C2×D24411yescharacteristic
257C22×C4D4×D6111yescharacteristic
258C22×C4D4×D6111yescharacteristic
259C2×C8—41no—
260C2×C8—41no—
261C2×C8—41no—
262C2×C8—41no—
263C2×C8—41no—
264C2×C8—41no—
265C2×C8—2441no—
266C2×C8—2441no—
267C2×C8—2441no—
268C4⋊C4—41no—
269C4⋊C4—1221no—
270C4⋊C4—1221no—
271C4⋊C4—2442no—
272C4⋊C4—2441no—
273C4⋊C4—2441no—
274C4⋊C4—2441no—
275C4⋊C4—2441no—
276C4⋊C4—2441no—
277C4⋊C4—2441no—
278C4⋊C4—2441no—
279C4⋊C4—2441no—
280C22⋊C4—41no—
281C22⋊C4—41no—
282C22⋊C4—41no—
283C22⋊C4—41no—
284C22⋊C4—4881no—
285C22⋊C4—4881no—
286C22⋊C4—4881no—
287C22⋊C4—4881no—
288C42—41no—
289C42—4881no—
290C23—41no—
291C23—41no—
292C23—41no—
293C23—41no—
294C23—41no—
295C23—41no—
296C23—41no—
297C23#1451974711yescharacteristic
298Q8—4881no—
299Q8—2442no—
300D4—42no—
301D4—81no—
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—4881no—
312C2×C4—4881no—
313C2×C4—4881no—
314C2×C4—2441no—
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—2441no—
324C2×C4—2441no—
325C2×C4—2441no—
326C2×C4#1451979611yescharacteristic
327C2×C4#1451979811yescharacteristic
328C2×C4#1451979911yescharacteristic
329C2×C4#1451980111yescharacteristic
330C2×C4#1451980511yescharacteristic
331C2×C4#1451980611yescharacteristic
332C8—81no—
333C8—81no—
334C8—4881no—
335C22—81no—
336C22—81no—
337C22—81no—
338C22—81no—
339C22—81no—
340C22—81no—
341C22—81no—
342C22#1683990811yescharacteristic
343C22#1683990911yescharacteristic
344C22#1683992511yescharacteristic
345C22#1683993611yescharacteristic
346C22#1683994111yescharacteristic
347C22#1683994211yescharacteristic
348C22#1683995311yescharacteristic
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—21no—
355C4—81no—
356C4—9761no—
357C4—4881no—
358C4—4881no—
359C4—4881no—
360C4—4881no—
361C2—161no—
362C2#2144483411yescharacteristic
363C2#2144483511yescharacteristic
364C2#2144485111yescharacteristic
365C2#2144493111yescharacteristic
366C2#2144500611yescharacteristic
367C2#2144504911yescharacteristic
368C2#2144514411yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1270C2
socleC23×C61#120
prime radicalC22×D4×C61D4
hypercenter#1270D61
hypocenterC61#7811
LCSG ▷ C2×C42×C61 ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1270

Complements

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

NH ≅ G/Ntype
2. #21447378C2semidirect
3. #21447229C2semidirect
5. #21443644C2semidirect
6. #21443641C2semidirect
211. C61#7811semidirect

Maximal subgroups

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

subgroupindex
#214537992
#214473782
#214472292
#214472222
#214436442
#214436412
C61×#12702
#781161