Finite Group Databasebeta

← #29579385

Subgroups — #29579385

Order 15616.

394 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456329C211yesmaximal, characteristic
2#21445981C211yesmaximal, characteristic
3#21444384C211yesmaximal, characteristic
4#21444383C211yesmaximal, characteristic
5#21444382C211yesmaximal, characteristic
6#21444103C211yesmaximal, characteristic
7C61×#1518C211yesmaximal, characteristic
8#16840319C2211yescharacteristic
9#16840165C411yescharacteristic, complemented
10#16840165C411yescharacteristic, complemented
11#16840161—21no—
12#16840161—21no—
13#16840158C411yescharacteristic, complemented
14#16840158C411yescharacteristic, complemented
15#16839815C2211yescharacteristic
16#16839798—21no—
17#16839798—21no—
18C2×#14519710—21no—
19C2×#14519708—21no—
20C2×C4×#92418C2211yescharacteristic
21#16839628C2211yescharacteristic
22#16839500—22no—
23#16839499—22no—
24#16839498—22no—
25#16839484—21no—
26C8×#92418—21no—
27C61×#533C2211yescharacteristic
28C61×#431C2211yescharacteristic
29C61×#382C2211yescharacteristic
30C61×#328—22no—
31C22×#92418D411yescharacteristic
32C22×#92418D411yescharacteristic
33#14519777C2×C411yescharacteristic
34#14519777C2×C411yescharacteristic
35#14519769—21no—
36#14519756—21no—
37#14519756—21no—
38C4×Dic122—21no—
39C4×Dic122—21no—
40#14519736—21no—
41C2×C4⋊Dic61—21no—
42#14519710—21no—
43#14519710—21no—
44#14519710—21no—
45#14519710—21no—
46#14519710—42no—
47#14519708—21no—
48#14519708—21no—
49#14519708—21no—
50#14519708—21no—
51#14519708—42no—
52C4⋊#92418—21no—
53C22⋊#92418D412yes—
54C4×#92418—21no—
55C4×#92418C2×C411yescharacteristic
56C4×#92418C2×C411yescharacteristic
57C4×#92418D411yescharacteristic
58C4×#92418D411yescharacteristic
59#14519684—21no—
60#14519684—21no—
61C4⋊Q8×C61C2×C411yescharacteristic
62C4⋊Q8×C61C2×C411yescharacteristic
63#125×C61—21no—
64C22⋊Q8×C61—21no—
65C22⋊Q8×C61—21no—
66C4×Q8×C61—21no—
67C4×Q8×C61—21no—
68#117×C61—21no—
69C2×C4⋊C4×C61—21no—
70C2×C42×C61C2311yescharacteristic
71C4⋊C8×C61—21no—
72C22⋊C8×C61D412yes—
73C4×C8×C61—21no—
74#95×C61—21no—
75#95×C61—21no—
76C2×Q8×C61—21no—
77C2×Q8×C61—21no—
78C22×C4×C61—41no—
79C22×C4×C61C2×D411yescharacteristic
80C22×C4×C61C2×D411yescharacteristic
81C22×C4×C61C2×D411yescharacteristic
82C22×Dic61—41no—
83C2×Dic122—21no—
84C2×Dic122—21no—
85C2×C8×C61—22no—
86C4⋊C4×C61—21no—
87C4⋊C4×C61—21no—
88C4⋊C4×C61—21no—
89C4⋊C4×C61—21no—
90C4⋊C4×C61—41no—
91C4⋊C4×C61—41no—
92C4⋊C4×C61—41no—
93C4⋊C4×C61—41no—
94C22⋊C4×C61—41no—
95C42×C61—41no—
96C42×C61C22×C411yescharacteristic
97C42×C61C2×D411yescharacteristic
98C42×C61#4111yescharacteristic
99C42×C61#4111yescharacteristic
100C22⋊Dic61—41no—
101C4⋊Dic61—21no—
102C4⋊Dic61—21no—
103C4⋊Dic61—21no—
104C4⋊Dic61—21no—
105C4⋊Dic61—41no—
106C4⋊Dic61—41no—
107#11758196—41no—
108#11758196—41no—
109C4×Dic61—41no—
110C2×#92418—22no—
111C2×#92418C22⋊C411yescharacteristic
112C2×#92418C22⋊C411yescharacteristic
113C2×#92418C22⋊C411yescharacteristic
114C2×#92418C22⋊C411yescharacteristic
115C2×#92418SD1612yes—
116C2×#92418SD1612yes—
117C2×#92418Q1612yes—
118C2×#92418Q1612yes—
119C23×C61#12711yescharacteristic
120Q8×C61—81no—
121Q8×C61—81no—
122C2×C4×C61—41no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—81no—
127C2×C4×C61—81no—
128C2×C4×C61—81no—
129C2×C4×C61C2×C22⋊C411yescharacteristic
130C2×C4×C61C4×D411yescharacteristic
131C2×C4×C61C4×D411yescharacteristic
132C2×C4×C61#12111yescharacteristic
133C2×C4×C61#12111yescharacteristic
134C2×C4×C61#12411yescharacteristic
135C2×C4×C61C2×SD1611yescharacteristic
136C2×C4×C61C2×SD1611yescharacteristic
137C2×C4×C61C2×Q1611yescharacteristic
138C2×C4×C61C2×Q1611yescharacteristic
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—81no—
142C2×Dic61—81no—
143C2×Dic61—81no—
144Dic122—81no—
145Dic122—81no—
146C8×C61—42no—
147#92418—42no—
148#92418#10312yes—
149#92418#10312yes—
150#92418#10312yes—
151#92418#10312yes—
152#9755—611nomaximal, Sylow
153C22×C61—21no—
154C22×C61—21no—
155C22×C61#39011yescharacteristic
156C22×C61#49211yescharacteristic
157C22×C61#49411yescharacteristic
158C4×C61—21no—
159C4×C61—21no—
160C4×C61—21no—
161C4×C61—21no—
162C4×C61—81no—
163C4×C61—81no—
164C4×C61—161no—
165C4×C61C2×#10311yescharacteristic
166C4×C61C2×#10311yescharacteristic
167C4×C61#48711yescharacteristic
168C4×C61#48711yescharacteristic
169Dic61—81no—
170Dic61—81no—
171Dic61—161no—
172#3160—611no—
173#1846—611no—
174#1518—611no—
175#1518—611no—
176#1518—611no—
177#1518D6111yescharacteristic
178#1450—611no—
179C2×C61—21no—
180C2×C61—21no—
181C2×C61#195611yescharacteristic
182C2×C61#197611yescharacteristic
183C2×C61#197611yescharacteristic
184#533—611no—
185#533C2×D6111yescharacteristic
186#500—611no—
187#500—611no—
188#499—1221no—
189#499—1221no—
190#498—611no—
191#498—611no—
192#431—611no—
193#431C2×D6111yescharacteristic
194#427—1221no—
195#427—1221no—
196C2×#107—1221no—
197C2×#106—1221no—
198C2×C4×C8—611no—
199#382—611no—
200#382C2×D6111yescharacteristic
201#328—22no—
202#328—1222no—
203#328—1222no—
204#328—1222no—
205#322—1221no—
206C82—1221no—
207C61#975511yescharacteristic, complemented, Sylow
208C22×C8—611no—
209C22×C8—611no—
210C4⋊Q8—611no—
211C4⋊Q8—611no—
212C4⋊Q8C4×D6111yescharacteristic
213C4⋊Q8C4×D6111yescharacteristic
214#125—21no—
215#125—1221no—
216C22⋊Q8—21no—
217C22⋊Q8—21no—
218C22⋊Q8—1221no—
219C22⋊Q8—1221no—
220C4×Q8—21no—
221C4×Q8—21no—
222C4×Q8—1221no—
223C4×Q8—1221no—
224#117—21no—
225#117—1221no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—1221no—
228C2×C42C22×D6111yescharacteristic
229#107—1221no—
230#107—1221no—
231#107—1221no—
232#107—1221no—
233#107—2442no—
234#106—1221no—
235#106—1221no—
236#106—1221no—
237#106—1221no—
238#106—2442no—
239C4⋊C8—21no—
240C4⋊C8—1221no—
241C22⋊C8—612no—
242C22⋊C8C22⋊D6112yes—
243C4×C8—21no—
244C4×C8—611no—
245C4×C8—611no—
246C4×C8—611no—
247C4×C8—611no—
248C4×C8—1221no—
249#95—21no—
250#95—21no—
251#95—1221no—
252#95—1221no—
253C2×Q8—21no—
254C2×Q8—21no—
255C2×Q8—1221no—
256C2×Q8—1221no—
257C22×C4—41no—
258C22×C4—2441no—
259C22×C4D4×D6111yescharacteristic
260C22×C4D4×D6111yescharacteristic
261C22×C4C2×C22⋊D6111yescharacteristic
262C2×C8—22no—
263C2×C8—611no—
264C2×C8—611no—
265C2×C8—611no—
266C2×C8—611no—
267C2×C8—612no—
268C2×C8—612no—
269C2×C8—612no—
270C2×C8—612no—
271C2×C8—1222no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—1221no—
281C4⋊C4—1221no—
282C4⋊C4—1221no—
283C4⋊C4—1221no—
284C4⋊C4—2441no—
285C4⋊C4—2441no—
286C4⋊C4—2441no—
287C4⋊C4—2441no—
288C22⋊C4—41no—
289C22⋊C4—2441no—
290C42—41no—
291C42—2441no—
292C42C2×C4×D6111yescharacteristic
293C42#1175822211yescharacteristic
294C42D4×D6111yescharacteristic
295C42#1175822411yescharacteristic
296C23#1451977311yescharacteristic
297Q8—81no—
298Q8—81no—
299Q8—4881no—
300Q8—4881no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—81no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4—4881no—
309C2×C4—4881no—
310C2×C4—4881no—
311C2×C4—2441no—
312C2×C4—2441no—
313C2×C4C22⋊C4×D6111yescharacteristic
314C2×C4#1451973711yescharacteristic
315C2×C4C4×C22⋊D6111yescharacteristic
316C2×C4#1451974911yescharacteristic
317C2×C4#1451975011yescharacteristic
318C2×C4#1451976311yescharacteristic
319C2×C4SD16×D6111yescharacteristic
320C2×C4SD16×D6111yescharacteristic
321C2×C4Q16×D6111yescharacteristic
322C2×C4Q16×D6111yescharacteristic
323C8—42no—
324C8—612no—
325C8—612no—
326C8—612no—
327C8—612no—
328C8—2442no—
329C22—21no—
330C22—21no—
331C22#1683966211yescharacteristic
332C22#1684013311yescharacteristic
333C22#1684014011yescharacteristic
334C4—21no—
335C4—21no—
336C4—21no—
337C4—21no—
338C4—81no—
339C4—81no—
340C4—161no—
341C4—9761no—
342C4—4881no—
343C4—4881no—
344C4#103×D6111yescharacteristic
345C4#103×D6111yescharacteristic
346C4#1684011111yescharacteristic
347C4#1684011111yescharacteristic
348C2—21no—
349C2—21no—
350C2#2144661911yescharacteristic
351C2#2144671411yescharacteristic
352C2#2144671611yescharacteristic
subgroupG/H
centerC22#16839662
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1518C2
socleC22×C61#390
prime radicalC23×C61#127
cosocleC2×C42×C61C23
hypercenter#1518D61
hypocenterC61#9755
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1518

Complements

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

NH ≅ G/Ntype
9. #16840165C4semidirect
10. #16840165C4semidirect
13. #16840158C4semidirect
14. #16840158C4semidirect
207. C61#9755semidirect

Maximal subgroups

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

subgroupindex
#214563292
#214459812
#214443842
#214443832
#214443822
#214441032
C61×#15182
#975561