Finite Group Databasebeta

← #29592991

Subgroups — #29592991

Order 15616.

398 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 59 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#21452725C211yesmaximal, characteristic
2#21444810C211yesmaximal, characteristic
3#21444810C211yesmaximal, characteristic
4#21443818C211yesmaximal, characteristic
5#21443818C211yesmaximal, characteristic
6#21443767C211yesmaximal, characteristic
7C61×#2062C211yesmaximal, characteristic
8C2×#14519770—21no—
9#16840090—21no—
10#16840090—21no—
11#16839694—21no—
12#16839692—21no—
13#16839687C2211yescharacteristic
14#16839687C2211yescharacteristic
15#16839661—21no—
16#16839647—21no—
17#16839622—21no—
18#16839499—21no—
19#16839499—21no—
20#16839486C2211yescharacteristic
21#16839486C2211yescharacteristic
22C61×#543C2211yescharacteristic
23C61×#385—21no—
24C61×#385C2211yescharacteristic
25C61×#342—21no—
26C61×#342C2211yescharacteristic
27#14519770—42no—
28#14519770—42no—
29C2×C4⋊Dic61—21no—
30C2×C4⋊Dic61—21no—
31C2×C4⋊Dic61—21no—
32C2×C4⋊Dic61D411yescharacteristic
33C2×C4⋊Dic61D411yescharacteristic
34C2×#11758196—21no—
35C2×#11758196—21no—
36C2×C22⋊Dic61—21no—
37C2×C22⋊Dic61—21no—
38C2×C4×Dic61—21no—
39#14519708—41no—
40#14519708—41no—
41#14519701—41no—
42#14519701—41no—
43C22⋊#92418—21no—
44C22⋊#92418—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49#14519684D411yescharacteristic
50#14519684D411yescharacteristic
51C23×C4×C61D411yescharacteristic
52C22⋊Q8×C61—21no—
53C22⋊Q8×C61—21no—
54C22⋊Q8×C61—41no—
55C22⋊Q8×C61—41no—
56C2×C4⋊C4×C61—21no—
57C2×C4⋊C4×C61—41no—
58C2×C22⋊C4×C61—21no—
59C2×C22⋊C4×C61—21no—
60C2×C22⋊C4×C61D411yescharacteristic
61C2×C22⋊C4×C61C2311yescharacteristic
62#95×C61—21no—
63#95×C61—41no—
64C24×C61C2×D411yescharacteristic
65C2×Q8×C61—21no—
66C2×Q8×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61—21no—
69C22×C4×C61—21no—
70C22×C4×C61—21no—
71C22×C4×C61—42no—
72C22×C4×C61—41no—
73C22×C4×C61—41no—
74C22×C4×C61C2×D411yescharacteristic
75C22×C4×C61C2×D411yescharacteristic
76C22×Dic61—21no—
77C22×Dic61—21no—
78C22×Dic61—21no—
79C22×Dic61—21no—
80C4⋊C4×C61—21no—
81C4⋊C4×C61—21no—
82C4⋊C4×C61—42no—
83C4⋊C4×C61—41no—
84C4⋊C4×C61—41no—
85C4⋊C4×C61—82no—
86C22⋊C4×C61—21no—
87C22⋊C4×C61—22no—
88C22⋊C4×C61—41no—
89C22⋊C4×C61—41no—
90C22⋊C4×C61—41no—
91C22⋊C4×C61—41no—
92C22⋊C4×C61SD1612yes—
93C22⋊Dic61—41no—
94C22⋊Dic61—41no—
95C22⋊Dic61—41no—
96C22⋊Dic61—41no—
97C4⋊Dic61—42no—
98C4⋊Dic61—42no—
99C4⋊Dic61—41no—
100C4⋊Dic61—41no—
101C4⋊Dic61—81no—
102#11758196—42no—
103#11758196—42no—
104C4×Dic61—42no—
105C2×#92418—41no—
106C2×#92418—41no—
107C23×C61—21no—
108C23×C61—21no—
109C23×C61—41no—
110C23×C61—41no—
111C23×C61#12011yescharacteristic
112C23×C61C2×SD1611yescharacteristic
113C23×C61AGL(1,ℤ/8)11yescharacteristic
114Q8×C61—81no—
115Q8×C61—81no—
116C2×C4×C61—22no—
117C2×C4×C61—22no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—41no—
121C2×C4×C61—41no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—42no—
127C2×C4×C61—42no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—81no—
131C2×C4×C61—81no—
132C2×C4×C61—81no—
133C2×C4×C61—81no—
134C2×C4×C61—81no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147#92418—81no—
148#92418—81no—
149#12244—611nomaximal, Sylow
150C22×C61—21no—
151C22×C61—21no—
152C22×C61—21no—
153C22×C61—21no—
154C22×C61—41no—
155C22×C61—41no—
156C22×C61—41no—
157C22×C61—41no—
158C22×C61—81no—
159C22×C61#45011yescharacteristic
160C22×C61#45611yescharacteristic
161C22×C61B(4,𝔽2)11yescharacteristic
162C4×C61—42no—
163C4×C61—41no—
164C4×C61—42no—
165C4×C61—41no—
166C4×C61—82no—
167C4×C61—81no—
168C4×C61—81no—
169Dic61—81no—
170Dic61—81no—
171Dic61—81no—
172Dic61—81no—
173#2722—611no—
174#2062D6111yescharacteristic
175#1608—611no—
176#1608—611no—
177#1344—611no—
178#1344—611no—
179#1326—611no—
180C2×C61—21no—
181C2×C61—21no—
182C2×C61—41no—
183C2×C61—41no—
184C2×C61#160411yescharacteristic
185C2×C61#219711yescharacteristic
186C2×C61#220111yescharacteristic
187#543C2×D6111yescharacteristic
188C2×#126—1221no—
189#483—1221no—
190#483—1221no—
191#398—1221no—
192#398—1221no—
193#397—611no—
194#397—611no—
195#389—1221no—
196#387—1221no—
197#385—21no—
198#385C2×D6111yescharacteristic
199#380—1221no—
200#342—21no—
201#342C2×D6111yescharacteristic
202#328—1221no—
203#328—1221no—
204#323—611no—
205#323—611no—
206C61#1224411yescharacteristic, complemented, Sylow
207C23×C4C22⋊D6111yescharacteristic
208#126—2442no—
209#126—2442no—
210C22⋊Q8—21no—
211C22⋊Q8—21no—
212C22⋊Q8—41no—
213C22⋊Q8—41no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—41no—
216C2×C4⋊C4—611no—
217C2×C4⋊C4—611no—
218C2×C4⋊C4—1221no—
219C2×C4⋊C4—1221no—
220C2×C4⋊C4—1221no—
221C2×C4⋊C4—1221no—
222C2×C4⋊C4—1221no—
223C2×C22⋊C4—21no—
224C2×C22⋊C4—21no—
225C2×C22⋊C4—1221no—
226C2×C22⋊C4—1221no—
227C2×C22⋊C4C22⋊D6111yescharacteristic
228C2×C22⋊C4C22×D6111yescharacteristic
229C2×C42—1221no—
230#106—2441no—
231#106—2441no—
232#103—2441no—
233#103—2441no—
234C22⋊C8—1221no—
235C22⋊C8—1221no—
236#95—21no—
237#95—41no—
238#95—611no—
239#95—611no—
240#95—1221no—
241#95—1221no—
242#95—1221no—
243#95—1221no—
244C24C2×C22⋊D6111yescharacteristic
245C2×Q8—21no—
246C2×Q8—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—42no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4—1221no—
255C22×C4—1221no—
256C22×C4—1221no—
257C22×C4—1221no—
258C22×C4D4×D6111yescharacteristic
259C22×C4D4×D6111yescharacteristic
260C2×C8—2441no—
261C2×C8—2441no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—42no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—82no—
268C4⋊C4—4881no—
269C4⋊C4—2441no—
270C4⋊C4—2441no—
271C4⋊C4—2442no—
272C4⋊C4—2442no—
273C4⋊C4—2442no—
274C4⋊C4—2442no—
275C22⋊C4—21no—
276C22⋊C4—22no—
277C22⋊C4—41no—
278C22⋊C4—41no—
279C22⋊C4—41no—
280C22⋊C4—41no—
281C22⋊C4—2441no—
282C22⋊C4—2441no—
283C22⋊C4—2441no—
284C22⋊C4—2441no—
285C22⋊C4#1175820112yes—
286C42—2442no—
287C23—21no—
288C23—21no—
289C23—41no—
290C23—41no—
291C23#1451974511yescharacteristic
292C23C2×#1175820111yescharacteristic
293C23#1451980211yescharacteristic
294Q8—81no—
295Q8—81no—
296C2×C4—22no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—22no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—42no—
307C2×C4—42no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—81no—
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—2441no—
327C8—4881no—
328C8—4881no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—21no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—81no—
338C22#1683991211yescharacteristic
339C22#1683994411yescharacteristic
340C22#1683994811yescharacteristic
341C4—42no—
342C4—41no—
343C4—42no—
344C4—41no—
345C4—82no—
346C4—81no—
347C4—81no—
348C4—4881no—
349C4—4881no—
350C4—4881no—
351C4—4881no—
352C2—21no—
353C2—21no—
354C2—41no—
355C2—41no—
356C2#2144478711yescharacteristic
357C2#2144780711yescharacteristic
358C2#2144783011yescharacteristic
subgroupG/H
centerC22#16839948
commutator, cosocleC2×C22⋊C4×C61C23
FrattiniC2×C22⋊C4C22×D61
FittingC61×#2062C2
socleC22×C61B(4,𝔽2)
prime radicalC24×C61C2×D4
hypercenter#2062D61
hypocenterC61#12244
LCSG ▷ C2×C22⋊C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #2062

Complements

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

NH ≅ G/Ntype
206. C61#12244semidirect

Maximal subgroups

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

subgroupindex
#214527252
#214448102
#214438182
#214437672
C61×#20622
#1224461