Finite Group Databasebeta

← #29599701

Subgroups — #29599701

Order 15616.

384 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 384 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#21453805C211yesmaximal, characteristic
2#21446034C211yesmaximal, characteristic
3#21446034C211yesmaximal, characteristic
4#21443946C211yesmaximal, characteristic
5#21443945C211yesmaximal, characteristic
6#21443945C211yesmaximal, characteristic
7C61×#1857C211yesmaximal, characteristic
8#16839805—21no—
9#16839805—21no—
10C2×#14519696C2211yescharacteristic
11C2×#14519696C2211yescharacteristic
12#16839704—21no—
13#16839696—21no—
14#16839695—21no—
15#16839669C2211yescharacteristic
16#16839669C2211yescharacteristic
17#16839659—21no—
18#16839646—21no—
19#16839645—21no—
20#16839521—21no—
21#16839521—21no—
22C61×#519C2211yescharacteristic
23C61×#428—21no—
24C2×#101×C61C2211yescharacteristic
25C61×#391C2211yescharacteristic
26C61×#339—21no—
27C2×#11758194—21no—
28C2×#11758194—21no—
29C2×C4⋊Dic61—21no—
30C2×C4⋊Dic61D411yescharacteristic
31C2×C4⋊Dic61D411yescharacteristic
32C2×#11758196—21no—
33C2×#11758196—21no—
34C2×#11758196—21no—
35C2×#11758196—21no—
36C2×C4×Dic61D411yescharacteristic
37C2×C4×Dic61D411yescharacteristic
38#14519710—41no—
39#14519710—41no—
40#14519708—41no—
41#14519708—41no—
42#14519696—21no—
43#14519696—21no—
44#14519696Q812yes—
45#14519696Q812yes—
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53C22×Q8×C61C2311yescharacteristic
54C2×M16×C61—21no—
55C4×Q8×C61—41no—
56C4×Q8×C61—41no—
57#117×C61—21no—
58#117×C61—21no—
59#117×C61—21no—
60C2×C4⋊C4×C61D411yescharacteristic
61C2×C42×C61D411yescharacteristic
62#107×C61—41no—
63#106×C61—41no—
64#101×C61—21no—
65#101×C61Q812yes—
66#95×C61—21no—
67#95×C61—21no—
68C2×Q8×C61—41no—
69C2×Q8×C61—41no—
70C2×Q8×C61C2×Q811yescharacteristic
71C2×Q8×C61C2×Q811yescharacteristic
72C2×Q8×C61C2×Q811yescharacteristic
73C2×Q8×C61#4111yescharacteristic
74C22×C4×C61—21no—
75C22×C4×C61—21no—
76C22×C4×C61C2×D411yescharacteristic
77C22×C4×C61C2×D411yescharacteristic
78C22×C4×C61C2×D411yescharacteristic
79C22×Dic61—21no—
80C22×Dic61—21no—
81C22×Dic61—21no—
82C22×Dic61—21no—
83M16×C61—22no—
84M16×C61—41no—
85C2×C8×C61—41no—
86C4⋊C4×C61—21no—
87C4⋊C4×C61—21no—
88C4⋊C4×C61—21no—
89C4⋊C4×C61—21no—
90C4⋊C4×C61—21no—
91C4⋊C4×C61—21no—
92C4⋊C4×C61—41no—
93C22⋊C4×C61—41no—
94C42×C61—41no—
95C42×C61—41no—
96C42×C61—41no—
97C42×C61—41no—
98C4⋊Dic61—42no—
99C4⋊Dic61—41no—
100C4⋊Dic61—41no—
101#11758196—42no—
102#11758196—42no—
103#11758196—81no—
104#11758196—81no—
105C4×Dic61—41no—
106C4×Dic61—41no—
107#11758194—22no—
108#11758194—22no—
109#11758194—41no—
110#11758194—41no—
111C2×#92418—41no—
112C2×#92418—41no—
113C23×C61#12011yescharacteristic
114Q8×C61—41no—
115Q8×C61—41no—
116Q8×C61—41no—
117Q8×C61—41no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61C22⋊Q811yescharacteristic
133C2×C4×C61C22⋊Q811yescharacteristic
134C2×C4×C61C22⋊Q811yescharacteristic
135C2×C4×C61C4⋊Q811yescharacteristic
136C2×C4×C61C4⋊Q811yescharacteristic
137C2×C4×C61C4⋊Q811yescharacteristic
138C2×Dic61—22no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—42no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C8×C61—42no—
150#92418—42no—
151#92418—42no—
152#13465—611nomaximal, Sylow
153C22×C61—21no—
154C22×C61—21no—
155C22×C61#39511yescharacteristic
156C22×C61B(4,𝔽2)11yescharacteristic
157C22×C61#45811yescharacteristic
158C4×C61—21no—
159C4×C61—21no—
160C4×C61—21no—
161C4×C61—21no—
162C4×C61—21no—
163C4×C61—21no—
164C4×C61—81no—
165C4×C61—81no—
166C4×C61—81no—
167C4×C61—81no—
168Dic61—42no—
169Dic61—81no—
170Dic61—81no—
171Dic61—81no—
172#2809—611no—
173#1857—611no—
174#1857—611no—
175#1857D6111yescharacteristic
176#1394—611no—
177#1394—611no—
178#1394—611no—
179C2×C61—21no—
180C2×C61—21no—
181C2×C61#206211yescharacteristic
182C2×C61#220311yescharacteristic
183C2×C61#220411yescharacteristic
184#519C2×D6111yescharacteristic
185#428—21no—
186#428—1221no—
187#428—1221no—
188C2×#101—611no—
189C2×#101—611no—
190C2×#101C2×D6111yescharacteristic
191#400—1221no—
192#398—1221no—
193#398—1221no—
194#391—611no—
195#391—611no—
196#391C2×D6111yescharacteristic
197#389—1221no—
198#387—1221no—
199#387—1221no—
200#339—21no—
201#339—1221no—
202#339—1221no—
203C61#1346511yescharacteristic, complemented, Sylow
204C22×Q8C22×D6111yescharacteristic
205C2×M16—21no—
206C2×M16—1221no—
207C2×M16—1221no—
208C4×Q8—41no—
209C4×Q8—41no—
210#117—21no—
211#117—21no—
212#117—21no—
213C2×C4⋊C4—611no—
214C2×C4⋊C4—611no—
215C2×C4⋊C4—1221no—
216C2×C4⋊C4—1221no—
217C2×C4⋊C4—1221no—
218C2×C4⋊C4—1221no—
219C2×C4⋊C4—1221no—
220C2×C4⋊C4C22⋊D6111yescharacteristic
221C2×C42—611no—
222C2×C42—611no—
223C2×C42C22⋊D6111yescharacteristic
224#107—41no—
225#107—2441no—
226#107—2441no—
227#106—41no—
228#106—2441no—
229#106—2441no—
230#101—21no—
231#101—612no—
232#101—612no—
233#101—1221no—
234#101—1221no—
235#101Dic12212yes—
236#95—21no—
237#95—21no—
238#95—1221no—
239#95—1221no—
240#95—1221no—
241#95—1221no—
242#95—1221no—
243#95—1221no—
244#95—1221no—
245C2×Q8—41no—
246C2×Q8—41no—
247C2×Q8C2×Dic12211yescharacteristic
248C2×Q8#1175822211yescharacteristic
249C2×Q8Q8×D6111yescharacteristic
250C2×Q8Q8×D6111yescharacteristic
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—1221no—
254C22×C4—1221no—
255C22×C4—1221no—
256C22×C4—1221no—
257C22×C4D4×D6111yescharacteristic
258C22×C4D4×D6111yescharacteristic
259C22×C4C2×C22⋊D6111yescharacteristic
260M16—22no—
261M16—41no—
262M16—1222no—
263M16—1222no—
264M16—2441no—
265M16—2441no—
266C2×C8—41no—
267C2×C8—2441no—
268C2×C8—2441no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—41no—
276C4⋊C4—4881no—
277C4⋊C4—4881no—
278C4⋊C4—2441no—
279C4⋊C4—2441no—
280C4⋊C4—2442no—
281C4⋊C4—2442no—
282C4⋊C4—2442no—
283C22⋊C4—41no—
284C42—41no—
285C42—41no—
286C42—41no—
287C42—41no—
288C42—2441no—
289C42—2441no—
290C23#1451974511yescharacteristic
291Q8—41no—
292Q8—41no—
293Q8—41no—
294Q8—41no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—1222no—
310C2×C4—2441no—
311C2×C4—2441no—
312C2×C4—2441no—
313C2×C4—2441no—
314C2×C4—2442no—
315C2×C4—2441no—
316C2×C4—2441no—
317C2×C4—2441no—
318C2×C4—2441no—
319C2×C4—2441no—
320C2×C4#1451975511yescharacteristic
321C2×C4#1451975511yescharacteristic
322C2×C4#1451975611yescharacteristic
323C2×C4#1451977511yescharacteristic
324C2×C4#1451977611yescharacteristic
325C2×C4#1451977611yescharacteristic
326C8—42no—
327C8—2442no—
328C8—2442no—
329C22—21no—
330C22—21no—
331C22#1683968211yescharacteristic
332C22#1683994811yescharacteristic
333C22#1683995111yescharacteristic
334C4—21no—
335C4—21no—
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—81no—
341C4—81no—
342C4—81no—
343C4—81no—
344C4—4881no—
345C4—4881no—
346C4—4881no—
347C4—2442no—
348C2—21no—
349C2—21no—
350C2#2144717211yescharacteristic
351C2#2144783811yescharacteristic
352C2#2144784311yescharacteristic
subgroupG/H
centerC22#16839948
commutator, cosocleC22×Q8×C61C23
FrattiniC22×Q8C22×D61
FittingC61×#1857C2
socleC22×C61B(4,𝔽2)
prime radicalC23×C61#120
hypercenter#1857D61
hypocenterC61#13465
LCSG ▷ C22×Q8×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ #1857

Complements

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

NH ≅ G/Ntype
203. C61#13465semidirect

Maximal subgroups

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

subgroupindex
#214538052
#214460342
#214439462
#214439452
C61×#18572
#1346561