Finite Group Databasebeta

← #29569017

Subgroups — #29569017

Order 15616.

424 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 81 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#21453774C211yesmaximal, characteristic
2#21447153C211yesmaximal, characteristic
3#21447148C211yesmaximal, characteristic
4#21446918C211yesmaximal, characteristic
5#21443643C211yesmaximal, characteristic
6#21443641C211yesmaximal, characteristic
7C61×#1272C211yesmaximal, characteristic
8C22×#11758202—21no—
9C2×#14519777C2211yescharacteristic
10C2×#14519711—21no—
11C2×#14519709—21no—
12C2×#14519700—21no—
13#16839704—21no—
14#16839702—21no—
15#16839681—21no—
16#16839660C2211yescharacteristic
17#16839660C2211yescharacteristic
18#16839659—21no—
19#16839645—21no—
20#16839643—21no—
21#16839525—21no—
22#16839525—21no—
23#16839517C2211yescharacteristic
24C61×#391C2211yescharacteristic
25C61×#336C2211yescharacteristic
26C61×#336C2211yescharacteristic
27C22×Dic122—21no—
28C2×#11758202—42no—
29C2×#11758202—42no—
30C2×#11758202—42no—
31C22×#92418—21no—
32#14519777—42no—
33C2×C4⋊Dic61—21no—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61D411yescharacteristic
36C2×C4⋊Dic61D411yescharacteristic
37C2×C4⋊Dic61D411yescharacteristic
38C2×C4⋊Dic61D411yescharacteristic
39C2×#11758196—21no—
40C2×#11758196—21no—
41C2×#11758196—21no—
42C2×#11758196—21no—
43C2×C4×Dic61—21no—
44#14519711—42no—
45#14519709—42no—
46#14519700—42no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54C22×Q8×C61D411yescharacteristic
55C22×C8×C61—21no—
56C22×C8×C61—21no—
57C2×C4⋊C4×C61D411yescharacteristic
58C2×C42×C61C2311yescharacteristic
59#95×C61—21no—
60#95×C61—21no—
61C2×Q8×C61—21no—
62C2×Q8×C61—21no—
63C2×Q8×C61—41no—
64C2×Q8×C61—41no—
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61C2×D411yescharacteristic
68C22×C4×C61C2×D411yescharacteristic
69C22×C4×C61C2×D411yescharacteristic
70C22×Dic61—21no—
71C22×Dic61—21no—
72C22×Dic61—21no—
73C22×Dic61—21no—
74C22×Dic61—41no—
75C2×Dic122—22no—
76C2×Dic122—41no—
77C2×Dic122—41no—
78C2×Dic122—41no—
79C2×Dic122—41no—
80C2×Dic122—41no—
81C2×C8×C61—22no—
82C2×C8×C61—22no—
83C2×C8×C61—41no—
84C2×C8×C61—41no—
85C2×C8×C61—41no—
86C2×C8×C61—41no—
87C4⋊C4×C61—41no—
88C42×C61—41no—
89#11758202—48no—
90C4⋊Dic61—21no—
91C4⋊Dic61—22no—
92C4⋊Dic61—22no—
93C4⋊Dic61—21no—
94C4⋊Dic61—21no—
95C4⋊Dic61—41no—
96C4⋊Dic61—41no—
97C4⋊Dic61—41no—
98C4⋊Dic61—41no—
99C4⋊Dic61Q1612yescomplemented
100#11758196—41no—
101#11758196—41no—
102#11758196—41no—
103#11758196—41no—
104#11758196—81no—
105#11758196—81no—
106C4×Dic61—81no—
107C2×#92418—22no—
108C2×#92418—41no—
109C2×#92418—41no—
110C23×C61#12011yescharacteristic
111Q8×C61—42no—
112Q8×C61—81no—
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×C61C2×Q1611yescharacteristic
126C2×C4×C61#13511yescharacteristic
127C2×C4×C61#13511yescharacteristic
128C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
129C2×C4×C61#13711yescharacteristic
130C2×C4×C61#13711yescharacteristic
131C2×Dic61—22no—
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—41no—
143C2×Dic61—42no—
144C2×Dic61—81no—
145C2×Dic61—81no—
146Dic122—42no—
147Dic122—42no—
148Dic122—81no—
149Dic122—81no—
150C8×C61—42no—
151C8×C61—42no—
152#92418—42no—
153#7783—611nomaximal, Sylow
154C22×C61#44911yescharacteristic
155C22×C61#45111yescharacteristic
156C22×C61#45211yescharacteristic
157C22×C61#45311yescharacteristic
158C22×C61#45611yescharacteristic
159C22×C61#45611yescharacteristic
160C22×C61B(4,𝔽2)11yescharacteristic
161C4×C61—21no—
162C4×C61—21no—
163C4×C61—21no—
164C4×C61—21no—
165C4×C61—21no—
166C4×C61—21no—
167C4×C61—81no—
168C4×C61—81no—
169Dic61—42no—
170Dic61—82no—
171Dic61—81no—
172Dic61—81no—
173Dic61—81no—
174#2805—611no—
175#2058—611no—
176#2057—611no—
177#2016—611no—
178#1272D6111yescharacteristic
179#1271—611no—
180#1271—611no—
181C2×C61#160011yescharacteristic
182C2×C61#160311yescharacteristic
183C2×C61#160511yescharacteristic
184C2×C61#163211yescharacteristic
185C2×C61#164811yescharacteristic
186C2×C61#165211yescharacteristic
187C2×C61#166011yescharacteristic
188C22×Q16—1221no—
189C2×C4⋊Q8—611no—
190C2×#107—1221no—
191C2×#106—1221no—
192C2×#103—1221no—
193#400—1221no—
194#400—1221no—
195#395—1221no—
196#391C2×D6111yescharacteristic
197#389—611no—
198#389—611no—
199#389—1221no—
200#387—1221no—
201#387—1221no—
202#340—1221no—
203#340—1221no—
204#336—611no—
205#336C2×D6111yescharacteristic
206#336C2×D6111yescharacteristic
207C61#778311yescharacteristic, complemented, Sylow
208C22×Q8—1221no—
209C22×Q8D24411yescharacteristic
210C2×Q16—2442no—
211C2×Q16—2442no—
212C2×Q16—2442no—
213C22×C8—21no—
214C22×C8—21no—
215C22×C8—1221no—
216C4⋊Q8—2442no—
217C2×C4⋊C4—611no—
218C2×C4⋊C4—611no—
219C2×C4⋊C4—611no—
220C2×C4⋊C4—611no—
221C2×C4⋊C4—1221no—
222C2×C4⋊C4—1221no—
223C2×C4⋊C4—1221no—
224C2×C4⋊C4—1221no—
225C2×C4⋊C4—1221no—
226C2×C4⋊C4—1221no—
227C2×C4⋊C4D24411yescharacteristic
228C2×C42—1221no—
229C2×C42C22×D6111yescharacteristic
230#107—2442no—
231#106—2442no—
232#103—2442no—
233#95—21no—
234#95—21no—
235#95—1221no—
236#95—1221no—
237#95—1221no—
238#95—1221no—
239#95—1221no—
240#95—1221no—
241#95—1221no—
242C2×Q8—21no—
243C2×Q8—21no—
244C2×Q8—41no—
245C2×Q8—41no—
246C2×Q8—1222no—
247C2×Q8—2441no—
248C2×Q8—2441no—
249C2×Q8—2441no—
250C2×Q8—2441no—
251C2×Q8—2441no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—1221no—
255C22×C4—1221no—
256C22×C4—1221no—
257C22×C4—1221no—
258C22×C4—2441no—
259C22×C4C2×D24411yescharacteristic
260C22×C4D4×D6111yescharacteristic
261C22×C4D4×D6111yescharacteristic
262Q16—2448no—
263C2×C8—22no—
264C2×C8—22no—
265C2×C8—41no—
266C2×C8—41no—
267C2×C8—41no—
268C2×C8—41no—
269C2×C8—1222no—
270C2×C8—2441no—
271C2×C8—2441no—
272C4⋊C4—41no—
273C4⋊C4—612no—
274C4⋊C4—1222no—
275C4⋊C4—1222no—
276C4⋊C4—1221no—
277C4⋊C4—1221no—
278C4⋊C4—1221no—
279C4⋊C4—4881no—
280C4⋊C4—4881no—
281C4⋊C4—2441no—
282C4⋊C4—2441no—
283C4⋊C4—2441no—
284C4⋊C4—2441no—
285C4⋊C4—2441no—
286C4⋊C4—2441no—
287C4⋊C4—2441no—
288C4⋊C4—2441no—
289C42—41no—
290C42—4881no—
291C23#1451974711yescharacteristic
292Q8—42no—
293Q8—81no—
294Q8—4881no—
295Q8—4881no—
296Q8—2442no—
297Q8—2442no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—1222no—
311C2×C4—4881no—
312C2×C4—4881no—
313C2×C4—2441no—
314C2×C4—2441no—
315C2×C4—2442no—
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×C4Q16×D6111yescharacteristic
326C2×C4#1451979811yescharacteristic
327C2×C4#1451979911yescharacteristic
328C2×C4#1451980511yescharacteristic
329C2×C4#1451980611yescharacteristic
330C2×C4#1451980911yescharacteristic
331C8—42no—
332C8—42no—
333C8—2442no—
334C22#1683990911yescharacteristic
335C22#1683991911yescharacteristic
336C22#1683992711yescharacteristic
337C22#1683993211yescharacteristic
338C22#1683994611yescharacteristic
339C22#1683994611yescharacteristic
340C22#1683995011yescharacteristic
341C4—21no—
342C4—21no—
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—81no—
348C4—81no—
349C4—4882no—
350C4—4881no—
351C4—4881no—
352C4—4881no—
353C4—2442no—
354C2#2144476711yescharacteristic
355C2#2144478511yescharacteristic
356C2#2144479411yescharacteristic
357C2#2144495411yescharacteristic
358C2#2144506311yescharacteristic
359C2#2144509111yescharacteristic
360C2#2144513111yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1272C2
socle, prime radicalC23×C61#120
hypercenter#1272D61
hypocenterC61#7783
LCSG ▷ C2×C42×C61 ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
99. C4⋊Dic61Q16semidirect
207. C61#7783semidirect

Maximal subgroups

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

subgroupindex
#214537742
#214471532
#214471482
#214469182
#214436432
#214436412
C61×#12722
#778361