Finite Group Databasebeta

← #29599702

Subgroups — #29599702

Order 15616.

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

normal subgroups only

This group has 384 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#21453805C211yesmaximal, characteristic
2#21446036C211yesmaximal, characteristic
3#21446036C211yesmaximal, characteristic
4#21446033C211yesmaximal, characteristic
5#21443945C211yesmaximal, characteristic
6#21443945C211yesmaximal, characteristic
7C61×#1394C211yesmaximal, characteristic
8#16840240C2211yescharacteristic
9#16839804—21no—
10#16839804—21no—
11#16839802—21no—
12C2×#14519696C2211yescharacteristic
13#16839704—21no—
14#16839696—21no—
15#16839695—21no—
16#16839669C2211yescharacteristic
17#16839669C2211yescharacteristic
18#16839659—21no—
19#16839646—21no—
20#16839645—21no—
21#16839523—21no—
22#16839523—21no—
23#16839522—21no—
24C2×#101×C61C2211yescharacteristic
25C2×#101×C61C2211yescharacteristic
26C61×#391C2211yescharacteristic
27C2×#11758194—21no—
28Q8×Dic61—41no—
29Q8×Dic61—41no—
30#14519736—21no—
31#14519736—21no—
32#14519736—21no—
33C2×C4⋊Dic61—21no—
34C2×C4⋊Dic61D411yescharacteristic
35C2×C4⋊Dic61D411yescharacteristic
36C2×#11758196—21no—
37C2×#11758196—21no—
38C2×#11758196—21no—
39C2×#11758196—21no—
40C2×C4×Dic61D411yescharacteristic
41C2×C4×Dic61D411yescharacteristic
42#14519711—41no—
43#14519711—41no—
44#14519710—41no—
45#14519709—41no—
46#14519709—41no—
47#14519708—41no—
48#14519696—21no—
49#14519696Q812yes—
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54#14519684—21no—
55#14519684—21no—
56#14519684—21no—
57C22×Q8×C61C2311yescharacteristic
58C2×M16×C61—21no—
59C2×M16×C61—21no—
60C2×C4⋊C4×C61D411yescharacteristic
61C2×C42×C61D411yescharacteristic
62#101×C61—21no—
63#101×C61—21no—
64#101×C61Q812yes—
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—22no—
85M16×C61—41no—
86M16×C61—41no—
87C2×C8×C61—41no—
88C2×C8×C61—41no—
89C4⋊C4×C61—41no—
90C42×C61—41no—
91C22⋊Dic61—41no—
92C4⋊Dic61—21no—
93C4⋊Dic61—21no—
94C4⋊Dic61—21no—
95C4⋊Dic61—21no—
96C4⋊Dic61—21no—
97C4⋊Dic61—21no—
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—
107C4×Dic61—41no—
108C4×Dic61—41no—
109C4×Dic61—41no—
110#11758194—22no—
111#11758194—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×C61C22⋊Q811yescharacteristic
131C2×C4×C61C22⋊Q811yescharacteristic
132C2×C4×C61C22⋊Q811yescharacteristic
133C2×C4×C61C4⋊Q811yescharacteristic
134C2×C4×C61C4⋊Q811yescharacteristic
135C2×C4×C61C4⋊Q811yescharacteristic
136C2×Dic61—22no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—42no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C8×C61—42no—
150C8×C61—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—
166Dic61—42no—
167Dic61—81no—
168Dic61—81no—
169Dic61—81no—
170Dic61—81no—
171Dic61—81no—
172#2809—611no—
173#1857—611no—
174#1857—611no—
175#1857—611no—
176#1394—611no—
177#1394—611no—
178#1394D6111yescharacteristic
179C2×C61—21no—
180C2×C61—21no—
181C2×C61#206211yescharacteristic
182C2×C61#220311yescharacteristic
183C2×C61#220411yescharacteristic
184#519—611no—
185#428—1221no—
186#428—1221no—
187#428—1221no—
188C2×#101—611no—
189C2×#101C2×D6111yescharacteristic
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—1221no—
201#339—1221no—
202#339—1221no—
203C61#1346511yescharacteristic, complemented, Sylow
204C22×Q8C22×D6111yescharacteristic
205C2×M16—21no—
206C2×M16—21no—
207C2×M16—1221no—
208C4×Q8—2441no—
209C4×Q8—2441no—
210#117—1221no—
211#117—1221no—
212#117—1221no—
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⋊C4D24411yescharacteristic
221C2×C42—611no—
222C2×C42—611no—
223C2×C42D24411yescharacteristic
224#107—2441no—
225#107—2441no—
226#107—2441no—
227#106—2441no—
228#106—2441no—
229#106—2441no—
230#101—21no—
231#101—21no—
232#101—612no—
233#101—1221no—
234#101Dic12212yes—
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×Q8C2×Dic12211yescharacteristic
249C2×Q8#1175822411yescharacteristic
250C2×Q8Q8×D6111yescharacteristic
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—1221no—
254C22×C4—1221no—
255C22×C4—1221no—
256C22×C4—1221no—
257C22×C4C2×D24411yescharacteristic
258C22×C4D4×D6111yescharacteristic
259C22×C4D4×D6111yescharacteristic
260M16—22no—
261M16—22no—
262M16—41no—
263M16—41no—
264M16—1222no—
265M16—2441no—
266C2×C8—41no—
267C2×C8—41no—
268C2×C8—2441no—
269C4⋊C4—41no—
270C4⋊C4—1221no—
271C4⋊C4—1221no—
272C4⋊C4—1221no—
273C4⋊C4—1221no—
274C4⋊C4—1221no—
275C4⋊C4—1221no—
276C4⋊C4—4881no—
277C4⋊C4—4881no—
278C4⋊C4—2441no—
279C4⋊C4—2441no—
280C4⋊C4—2442no—
281C4⋊C4—2442no—
282C4⋊C4—2442no—
283C22⋊C4—2441no—
284C42—41no—
285C42—2441no—
286C42—2441no—
287C42—2441no—
288C42—2441no—
289C42—2441no—
290C23#1451974711yescharacteristic
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—1222no—
308C2×C4—2441no—
309C2×C4—2441no—
310C2×C4—2441no—
311C2×C4—2441no—
312C2×C4—2442no—
313C2×C4—2441no—
314C2×C4—2441no—
315C2×C4—2441no—
316C2×C4—2441no—
317C2×C4—2441no—
318C2×C4—2441no—
319C2×C4—2441no—
320C2×C4#1451975411yescharacteristic
321C2×C4#1451975411yescharacteristic
322C2×C4#1451975711yescharacteristic
323C2×C4#1451977611yescharacteristic
324C2×C4#1451977611yescharacteristic
325C2×C4#1451977711yescharacteristic
326C8—42no—
327C8—42no—
328C8—2442no—
329C22—21no—
330C22—21no—
331C22#1683968311yescharacteristic
332C22#1683995011yescharacteristic
333C22#1683995311yescharacteristic
334C4—21no—
335C4—21no—
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—81no—
341C4—81no—
342C4—4881no—
343C4—4881no—
344C4—4881no—
345C4—4881no—
346C4—4881no—
347C4—2442no—
348C2—21no—
349C2—21no—
350C2#2144717311yescharacteristic
351C2#2144784111yescharacteristic
352C2#2144784611yescharacteristic
subgroupG/H
centerC22#16839950
commutator, cosocleC22×Q8×C61C23
FrattiniC22×Q8C22×D61
FittingC61×#1394C2
socleC22×C61B(4,𝔽2)
prime radicalC23×C61#120
hypercenter#1394D61
hypocenterC61#13465
LCSG ▷ C22×Q8×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ #1394

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
#214460362
#214460332
#214439452
C61×#13942
#1346561