Finite Group Databasebeta

← #29568613

Subgroups — #29568613

Order 15616.

372 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 93 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#21454202C211yesmaximal, characteristic
2#21445961C211yesmaximal, characteristic
3#21445671C211yesmaximal, characteristic
4#21443644C211yesmaximal, characteristic
5#21443644C211yesmaximal, characteristic
6#21443642C211yesmaximal, characteristic
7C61×#1271C211yesmaximal, characteristic
8C2×#14519706—21no—
9C2×#14519687—21no—
10#16839668C2211yescharacteristic
11#16839667C411yescharacteristic
12#16839667C411yescharacteristic
13#16839661C411yescharacteristic
14#16839658C411yescharacteristic
15#16839648—21no—
16#16839645—21no—
17#16839643—21no—
18#16839629—21no—
19C42×Dic61C2211yescharacteristic
20#16839517C2211yescharacteristic
21#16839517C2211yescharacteristic
22#16839516—21no—
23#16839516—21no—
24C61×#389C2211yescharacteristic
25C61×#336C2211yescharacteristic
26C61×#336C2211yescharacteristic
27C22×Dic122C2×C411yescharacteristic
28C22×#92418—21no—
29C22×#92418—21no—
30C2×C4⋊Dic61—21no—
31C2×C4⋊Dic61C2×C411yescharacteristic
32C2×#11758196—21no—
33C2×C4×Dic61C2×C411yescharacteristic
34C2×C4×Dic61C2×C411yescharacteristic
35C2×C4×Dic61D411yescharacteristic
36C2×C4×Dic61D411yescharacteristic
37C2×C4×Dic61D411yescharacteristic
38C2×C4×Dic61D411yescharacteristic
39#14519706—24no—
40#14519687—42no—
41#14519684—21no—
42#14519684—21no—
43#14519684—21no—
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49C22×C8×C61—21no—
50C22×C8×C61—21no—
51C2×C4⋊C4×C61—21no—
52C2×C4⋊C4×C61C2×C411yescharacteristic
53C2×C4⋊C4×C61C2×C411yescharacteristic
54C2×C42×C61C2311yescharacteristic
55#95×C61—21no—
56C22×C4×C61—21no—
57C22×C4×C61—21no—
58C22×C4×C61C22×C411yescharacteristic
59C22×C4×C61C2×D411yescharacteristic
60C22×C4×C61C2×D411yescharacteristic
61C22×Dic61—21no—
62C22×Dic61—21no—
63C22×Dic61C22⋊C411yescharacteristic
64C22×Dic61C22⋊C411yescharacteristic
65C22×Dic61C22⋊C411yescharacteristic
66C22×Dic61C22⋊C411yescharacteristic
67C2×Dic122—21no—
68C2×Dic122—21no—
69C2×Dic122—41no—
70C2×Dic122—41no—
71C2×C8×C61—22no—
72C2×C8×C61—41no—
73C2×C8×C61—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—41no—
81C4⋊C4×C61—41no—
82C42×C61—41no—
83C4⋊Dic61—42no—
84C4⋊Dic61—41no—
85#11758196—42no—
86C4×Dic61—21no—
87C4×Dic61—21no—
88C4×Dic61—21no—
89C4×Dic61—21no—
90C4×Dic61—21no—
91C4×Dic61—21no—
92C4×Dic61—22no—
93C4×Dic61—41no—
94C4×Dic61—41no—
95C2×#92418—22no—
96C2×#92418—41no—
97C2×#92418—41no—
98C2×#92418—41no—
99C2×#92418—41no—
100C2×#92418—41no—
101C23×C61C2×C22⋊C411yescharacteristic
102C2×C4×C61—21no—
103C2×C4×C61—21no—
104C2×C4×C61—21no—
105C2×C4×C61—21no—
106C2×C4×C61—21no—
107C2×C4×C61—21no—
108C2×C4×C61—41no—
109C2×C4×C61—41no—
110C2×C4×C61—41no—
111C2×C4×C61—41no—
112C2×C4×C61—41no—
113C2×C4×C61—41no—
114C2×C4×C61#13111yescharacteristic
115C2×C4×C61#13111yescharacteristic
116C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
117C2×C4×C61#13711yescharacteristic
118C2×C4×C61#13711yescharacteristic
119C2×C4×C61#13711yescharacteristic
120C2×Dic61—21no—
121C2×Dic61—21no—
122C2×Dic61—21no—
123C2×Dic61—21no—
124C2×Dic61—21no—
125C2×Dic61—21no—
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—21no—
129C2×Dic61—21no—
130C2×Dic61—21no—
131C2×Dic61—41no—
132C2×Dic61—41no—
133C2×Dic61—41no—
134C2×Dic61—41no—
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61#10412yes—
138Dic122—81no—
139Dic122—81no—
140C8×C61—42no—
141C8×C61—81no—
142#92418—42no—
143#92418—81no—
144#7713—611nomaximal, Sylow
145C22×C61#40811yescharacteristic
146C22×C61#41011yescharacteristic
147C22×C61#41311yescharacteristic
148C22×C61#41711yescharacteristic
149C22×C61#41911yescharacteristic
150C22×C61C2×#10411yescharacteristic
151C22×C61#42111yescharacteristic
152C4×C61—21no—
153C4×C61—21no—
154C4×C61—21no—
155C4×C61—21no—
156C4×C61—21no—
157C4×C61—21no—
158C4×C61—81no—
159C4×C61—81no—
160Dic61—22no—
161Dic61—41no—
162Dic61—41no—
163Dic61—41no—
164Dic61—81no—
165Dic61—81no—
166#2863—611no—
167#1839—611no—
168#1767—611no—
169#1272—611no—
170#1272—611no—
171#1271—611no—
172#1271D6111yescharacteristic
173C2×C61#147311yescharacteristic
174C2×C61#148511yescharacteristic
175C2×C61#149511yescharacteristic
176C2×C61#150911yescharacteristic
177C2×C61#151511yescharacteristic
178C2×C61#153211yescharacteristic
179C2×C61#155911yescharacteristic
180C2×C4⋊C8—1221no—
181C2×#97—1221no—
182#391—611no—
183#391—611no—
184#391—611no—
185#389—611no—
186#389—611no—
187#389C2×D6111yescharacteristic
188#387—1221no—
189#387—1221no—
190#387—1221no—
191#383—1221no—
192C43—611no—
193#336—611no—
194#336—611no—
195#336—1221no—
196#336—1221no—
197#336C2×D6111yescharacteristic
198#336C2×D6111yescharacteristic
199C61#771311yescharacteristic, complemented, Sylow
200C22×Q8—611no—
201C22×C8—21no—
202C22×C8—21no—
203C22×C8—1221no—
204C22×C8—1221no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—611no—
207C2×C4⋊C4—1221no—
208C2×C4⋊C4—1221no—
209C2×C4⋊C4C4×D6111yescharacteristic
210C2×C4⋊C4C4×D6111yescharacteristic
211C2×C42—611no—
212C2×C42—611no—
213C2×C42—611no—
214C2×C42—611no—
215C2×C42—611no—
216C2×C42—611no—
217C2×C42C22×D6111yescharacteristic
218C4⋊C8—1224no—
219#97—2442no—
220#95—21no—
221#95—1221no—
222#95—1221no—
223#95—1221no—
224#95—1221no—
225#95—1221no—
226#95—1221no—
227#95—1221no—
228#95—1221no—
229C2×Q8—1221no—
230C2×Q8—1221no—
231C2×Q8—2441no—
232C2×Q8—2441no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—611no—
236C22×C4—611no—
237C22×C4—611no—
238C22×C4—611no—
239C22×C4—1221no—
240C22×C4—1221no—
241C22×C4C2×C4×D6111yescharacteristic
242C22×C4D4×D6111yescharacteristic
243C22×C4D4×D6111yescharacteristic
244C2×C8—22no—
245C2×C8—41no—
246C2×C8—41no—
247C2×C8—41no—
248C2×C8—41no—
249C2×C8—41no—
250C2×C8—1222no—
251C2×C8—2441no—
252C2×C8—2441no—
253C2×C8—2441no—
254C2×C8—2441no—
255C2×C8—2441no—
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—2441no—
262C4⋊C4—2442no—
263C4⋊C4—2442no—
264C42—41no—
265C42—1222no—
266C42—1221no—
267C42—1221no—
268C42—1221no—
269C42—1221no—
270C42—1221no—
271C42—1221no—
272C42—2441no—
273C42—2441no—
274C23C22⋊C4×D6111yescharacteristic
275Q8—4881no—
276Q8—4881no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—612no—
290C2×C4—1221no—
291C2×C4—1221no—
292C2×C4—1221no—
293C2×C4—1221no—
294C2×C4—1221no—
295C2×C4—1221no—
296C2×C4—1221no—
297C2×C4—1221no—
298C2×C4—1221no—
299C2×C4—1221no—
300C2×C4—1221no—
301C2×C4—2441no—
302C2×C4—2441no—
303C2×C4—2441no—
304C2×C4—2441no—
305C2×C4—2441no—
306C2×C4—2441no—
307C2×C4#1451978311yescharacteristic
308C2×C4#1451978511yescharacteristic
309C2×C4#1451980111yescharacteristic
310C2×C4#1451980611yescharacteristic
311C2×C4#1451980611yescharacteristic
312C2×C4#1451980911yescharacteristic
313C8—42no—
314C8—81no—
315C8—4881no—
316C8—2442no—
317C22#1683972711yescharacteristic
318C22#1683973411yescharacteristic
319C22#1683974511yescharacteristic
320C22#1683976011yescharacteristic
321C22#1683976911yescharacteristic
322C22#104×D6111yescharacteristic
323C22#1683977711yescharacteristic
324C4—21no—
325C4—21no—
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—81no—
331C4—81no—
332C4—1222no—
333C4—4881no—
334C4—4881no—
335C4—2441no—
336C4—2441no—
337C4—2441no—
338C2#2144418711yescharacteristic
339C2#2144423811yescharacteristic
340C2#2144428111yescharacteristic
341C2#2144434111yescharacteristic
342C2#2144436811yescharacteristic
343C2#2144443811yescharacteristic
344C2#2144454811yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1271C2
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1271D61
hypocenterC61#7713
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
199. C61#7713semidirect

Maximal subgroups

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

subgroupindex
#214542022
#214459612
#214456712
#214436442
#214436422
C61×#12712
#771361