Finite Group Databasebeta

← #29568917

Subgroups — #29568917

Order 15616.

404 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 85 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#21453783C211yesmaximal, characteristic
2#21447062C211yesmaximal, characteristic
3#21446957C211yesmaximal, characteristic
4#21443645C211yesmaximal, characteristic
5#21443644C211yesmaximal, characteristic
6#21443641C211yesmaximal, characteristic
7C61×#2024C211yesmaximal, characteristic
8C2×#14519701—21no—
9C2×#14519701—21no—
10C2×#14519700—21no—
11#16839695—21no—
12#16839694—21no—
13#16839683—21no—
14#16839669—21no—
15#16839668C2211yescharacteristic
16#16839660C2211yescharacteristic
17#16839659—21no—
18#16839645—21no—
19#16839524—21no—
20#16839517C2211yescharacteristic
21#16839517C2211yescharacteristic
22C2×C4⋊Q8×C61C2211yescharacteristic
23C2×#103×C61—21no—
24C61×#391C2211yescharacteristic
25C61×#340—21no—
26C61×#336C2211yescharacteristic
27C22×Dic122D411yescharacteristic
28C22×#92418—21no—
29C22×#92418—21no—
30C2×C4⋊Dic61—21no—
31C2×C4⋊Dic61—21no—
32C2×C4⋊Dic61D411yescharacteristic
33C2×C4⋊Dic61D411yescharacteristic
34C2×C4⋊Dic61D411yescharacteristic
35C2×#11758196—21no—
36C2×#11758196—21no—
37C2×#11758196—21no—
38C2×C4×Dic61—21no—
39#14519701—42no—
40#14519701—42no—
41#14519700—42no—
42#14519684—21no—
43#14519684—21no—
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48C22×Q8×C61—21no—
49C22×Q8×C61D411yescharacteristic
50C22×C8×C61—21no—
51C4⋊Q8×C61—42no—
52C2×C4⋊C4×C61—21no—
53C2×C4⋊C4×C61—21no—
54C2×C4⋊C4×C61D411yescharacteristic
55C2×C42×C61C2311yescharacteristic
56#103×C61—42no—
57#95×C61—21no—
58#95×C61—21no—
59C2×Q8×C61—21no—
60C2×Q8×C61—22no—
61C2×Q8×C61—41no—
62C2×Q8×C61—41no—
63C2×Q8×C61—41no—
64C2×Q8×C61—41no—
65C2×Q8×C61—41no—
66C2×Q8×C61—41no—
67C2×Q8×C61—41no—
68C2×Q8×C61Q1612yes—
69C22×C4×C61—21no—
70C22×C4×C61—21no—
71C22×C4×C61—41no—
72C22×C4×C61C2×D411yescharacteristic
73C22×C4×C61C2×D411yescharacteristic
74C22×C4×C61C2×D411yescharacteristic
75C22×Dic61—21no—
76C22×Dic61—21no—
77C22×Dic61—21no—
78C22×Dic61—21no—
79C2×Dic122—21no—
80C2×Dic122—21no—
81C2×Dic122—41no—
82C2×Dic122—41no—
83C2×C8×C61—41no—
84C2×C8×C61—41no—
85C2×C8×C61—41no—
86C4⋊C4×C61—22no—
87C4⋊C4×C61—22no—
88C4⋊C4×C61—41no—
89C4⋊C4×C61—41no—
90C4⋊C4×C61—41no—
91C42×C61—41no—
92C4⋊Dic61—21no—
93C4⋊Dic61—41no—
94C4⋊Dic61—41no—
95C4⋊Dic61—81no—
96C4⋊Dic61—81no—
97C4⋊Dic61SD1612yes—
98#11758196—41no—
99#11758196—41no—
100#11758196—81no—
101#11758196—81no—
102C4×Dic61—81no—
103C2×#92418—41no—
104C2×#92418—41no—
105C2×#92418—41no—
106C2×#92418—41no—
107C2×#92418—41no—
108C2×#92418—41no—
109C23×C61#12011yescharacteristic
110Q8×C61—42no—
111Q8×C61—42no—
112Q8×C61—42no—
113Q8×C61—81no—
114Q8×C61—81no—
115Q8×C61—81no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—22no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—42no—
129C2×C4×C61—81no—
130C2×C4×C61—81no—
131C2×C4×C61C2×SD1611yescharacteristic
132C2×C4×C61C2×Q1611yescharacteristic
133C2×C4×C61#13511yescharacteristic
134C2×C4×C61#13711yescharacteristic
135C2×C4×C61#13711yescharacteristic
136C2×C4×C61#13711yescharacteristic
137C2×Dic61—22no—
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—
147C2×Dic61—41no—
148C2×Dic61—41no—
149Dic122—42no—
150Dic122—81no—
151C8×C61—81no—
152#92418—81no—
153#92418—81no—
154#7769—611nomaximal, Sylow
155C22×C61#44811yescharacteristic
156C22×C61#45111yescharacteristic
157C22×C61#45211yescharacteristic
158C22×C61#45411yescharacteristic
159C22×C61#45511yescharacteristic
160C22×C61#45511yescharacteristic
161C22×C61B(4,𝔽2)11yescharacteristic
162C4×C61—21no—
163C4×C61—21no—
164C4×C61—21no—
165C4×C61—21no—
166C4×C61—21no—
167C4×C61—21no—
168C4×C61—42no—
169C4×C61—82no—
170C4×C61—81no—
171Dic61—42no—
172Dic61—81no—
173Dic61—81no—
174Dic61—81no—
175#2806—611no—
176#2043—611no—
177#2024—611no—
178#2024D6111yescharacteristic
179#1272—611no—
180#1272—611no—
181#1271—611no—
182C2×C61#159911yescharacteristic
183C2×C61#160211yescharacteristic
184C2×C61#160611yescharacteristic
185C2×C61#163611yescharacteristic
186C2×C61#164311yescharacteristic
187C2×C61#164511yescharacteristic
188C2×C61#166211yescharacteristic
189C2×C4⋊Q8C2×D6111yescharacteristic
190C2×#103—21no—
191C2×#103—1221no—
192C2×#103—1221no—
193C2×#103—1221no—
194#398—1221no—
195#398—1221no—
196#395—1221no—
197#391—611no—
198#391—1221no—
199#391C2×D6111yescharacteristic
200#389—611no—
201#389—1221no—
202#387—1221no—
203#340—21no—
204#340—1221no—
205#336—611no—
206#336—611no—
207#336C2×D6111yescharacteristic
208C61#776911yescharacteristic, complemented, Sylow
209C22×Q8—21no—
210C22×Q8—611no—
211C22×Q8C22⋊D6111yescharacteristic
212C22×C8—21no—
213C22×C8—1221no—
214C22×C8—1221no—
215C4⋊Q8—42no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
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⋊C4C22⋊D6111yescharacteristic
227C2×C42—1221no—
228C2×C42C22×D6111yescharacteristic
229#103—42no—
230#103—2442no—
231#103—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—
241C2×Q8—21no—
242C2×Q8—22no—
243C2×Q8—41no—
244C2×Q8—41no—
245C2×Q8—41no—
246C2×Q8—41no—
247C2×Q8—41no—
248C2×Q8—41no—
249C2×Q8—41no—
250C2×Q8—1221no—
251C2×Q8—1221no—
252C2×Q8—2441no—
253C2×Q8—2441no—
254C2×Q8#1175820212yes—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—41no—
258C22×C4—1221no—
259C22×C4—1221no—
260C22×C4—1221no—
261C22×C4—1221no—
262C22×C4D4×D6111yescharacteristic
263C22×C4D4×D6111yescharacteristic
264C22×C4C2×C22⋊D6111yescharacteristic
265C2×C8—41no—
266C2×C8—41no—
267C2×C8—41no—
268C2×C8—2441no—
269C2×C8—2441no—
270C2×C8—2441no—
271C2×C8—2441no—
272C2×C8—2441no—
273C2×C8—2441no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—612no—
280C4⋊C4—1221no—
281C4⋊C4—4881no—
282C4⋊C4—4881no—
283C4⋊C4—4881no—
284C4⋊C4—4881no—
285C4⋊C4—2441no—
286C4⋊C4—2441no—
287C4⋊C4—2441no—
288C4⋊C4—2441no—
289C42—41no—
290C42—4881no—
291C23#1451974511yescharacteristic
292Q8—42no—
293Q8—42no—
294Q8—42no—
295Q8—81no—
296Q8—81no—
297Q8—81no—
298Q8—4881no—
299Q8—2442no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—22no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—42no—
312C2×C4—41no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—1222no—
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—
327C2×C4SD16×D6111yescharacteristic
328C2×C4C2×#1175820211yescharacteristic
329C2×C4#1451980011yescharacteristic
330C2×C4#1451980611yescharacteristic
331C2×C4#1451980711yescharacteristic
332C2×C4#1451980911yescharacteristic
333C8—81no—
334C8—4881no—
335C8—4881no—
336C22#1683989911yescharacteristic
337C22#1683991711yescharacteristic
338C22#1683992311yescharacteristic
339C22#1683993311yescharacteristic
340C22#1683993811yescharacteristic
341C22#1683993911yescharacteristic
342C22#1683994811yescharacteristic
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—21no—
349C4—42no—
350C4—81no—
351C4—82no—
352C4—4881no—
353C4—4881no—
354C4—4881no—
355C4—2442no—
356C2#2144475711yescharacteristic
357C2#2144477511yescharacteristic
358C2#2144479811yescharacteristic
359C2#2144497611yescharacteristic
360C2#2144502311yescharacteristic
361C2#2144503911yescharacteristic
362C2#2144514111yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#2024C2
socle, prime radicalC23×C61#120
hypercenter#2024D61
hypocenterC61#7769
LCSG ▷ C2×C42×C61 ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2024

Complements

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

NH ≅ G/Ntype
208. C61#7769semidirect

Maximal subgroups

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

subgroupindex
#214537832
#214470622
#214469572
#214436452
#214436442
#214436412
C61×#20242
#776961