Finite Group Databasebeta

← #29573893

Subgroups — #29573893

Order 15616.

466 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454927C211yesmaximal, characteristic
2#21445970C211yesmaximal, characteristic, complemented
3C4×#14519703C211yesmaximal, characteristic
4#21444204C211yesmaximal, characteristic
5#21443670C211yesmaximal, characteristic, complemented
6#21443651C211yesmaximal, characteristic, complemented
7C61×#1565C211yesmaximal, characteristic, complemented
8C4×#11758222C2211yescharacteristic
9C8×Dic122—21no—
10C8×D244—21no—
11#16839825—22no—
12#16839815C2211yescharacteristic
13#16839814—21no—
14C2×C4⋊#92418C2211yescharacteristic
15C2×#14519706—22no—
16C4⋊C8×D61—21no—
17C2×#14519703C411yescharacteristic
18C2×#14519703C411yescharacteristic
19C42×Dic61C2211yescharacteristic
20#16839523C411yescharacteristic
21#16839523C411yescharacteristic
22#16839492—21no—
23#16839489—21no—
24C61×#431C2211yescharacteristic
25C2×C4⋊C8×C61C2211yescharacteristic
26C4×M16×C61C2211yescharacteristic
27C61×#335—21no—
28C61×#334—21no—
29C2×#11758222C2×C411yescharacteristic
30C22×#92418D412yes—
31C2×C8×D61—22no—
32C4×Dic122D411yescharacteristic
33C4×Dic122Q811yescharacteristic
34C4×D244D411yescharacteristic
35C4×D244Q811yescharacteristic
36C4×C22⋊D61—21no—
37C4×C22⋊D61—21no—
38#14519736C2×C411yescharacteristic
39#14519734—21no—
40C2×C4×Dic61—21no—
41C2×C4×Dic61—21no—
42C2×C4×Dic61C2×C411yescharacteristic
43C2×C4×Dic61C2×C411yescharacteristic
44C42×D61—21no—
45C4⋊#92418—21no—
46C4⋊#92418—21no—
47C4⋊#92418—21no—
48#14519706—22no—
49#14519706—44no—
50#14519703—22no—
51#14519703C814yescomplemented
52C22⋊#92418—21no—
53#14519689—22no—
54C4×#92418—21no—
55C8×Dic61—22no—
56C2×M16×C61C2×C411yescharacteristic
57C2×M16×C61C2×C411yescharacteristic
58C22×C8×C61—21no—
59C2×C42×C61C2311yescharacteristic
60C4⋊C8×C61—21no—
61C4⋊C8×C61—21no—
62C4⋊C8×C61D411yescharacteristic
63C4⋊C8×C61D411yescharacteristic
64C22⋊C8×C61—21no—
65#97×C61—21no—
66C4×C8×C61—21no—
67C4×C8×C61—21no—
68C22×C4×C61C22×C411yescharacteristic
69C22×C4×C61C2×D411yescharacteristic
70C22×C4×C61#4111yescharacteristic
71C2×C22⋊D61—21no—
72C22×Dic61—21no—
73C22×Dic61—21no—
74#11758222—21no—
75#11758222—21no—
76#11758222C2×C812yes—
77#11758222M1612yes—
78C2×D244C4⋊C411yescharacteristic
79C2×C4×D61—21no—
80C2×C4×D61—21no—
81C2×C4×D61—21no—
82C2×Dic122C4⋊C411yescharacteristic
83M16×C61—21no—
84M16×C61—21no—
85M16×C61—21no—
86M16×C61C2×C812yescomplemented
87C2×C8×C61—21no—
88C2×C8×C61—21no—
89C2×C8×C61—21no—
90C2×C8×C61—21no—
91C2×C8×C61—42no—
92C2×C8×C61—41no—
93C42×C61C2×D411yescharacteristic
94C42×C61C2×D411yescharacteristic
95C42×C61C2×Q811yescharacteristic
96C42×C61#4111yescharacteristic
97C22⋊Dic61—21no—
98#11758198—21no—
99#11758198—21no—
100C4⋊Dic61C4⋊C411yescharacteristic
101C4⋊Dic61C4⋊C411yescharacteristic
102#11758196—21no—
103#11758196—21no—
104C4×Dic61—22no—
105C4×Dic61—22no—
106C4×Dic61—21no—
107C4×Dic61—21no—
108C4×Dic61—21no—
109C4×Dic61—21no—
110C4×Dic61—21no—
111C4×Dic61—21no—
112C4×Dic61—42no—
113C4×Dic61C2×C812yescomplemented
114C2×#92418—22no—
115C2×#92418—42no—
116C2×#92418—41no—
117C8×D61—82no—
118C23×C61C4×D411yescharacteristic
119C22×D61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—41no—
123C2×C4×C61C2×C4⋊C411yescharacteristic
124C2×C4×C61C4×D411yescharacteristic
125C2×C4×C61#12011yescharacteristic
126C2×C4×C61C22⋊Q811yescharacteristic
127C2×C4×C61C22⋊Q811yescharacteristic
128C2×C4×C61#12311yescharacteristic
129C2×C4×C61C22×C811yescharacteristic
130C2×C4×C61C2×M1611yescharacteristic
131C2×C4×C61#13111yescharacteristic
132C2×C4×C61#13111yescharacteristic
133C22⋊D61—22no—
134C22⋊D61—22no—
135C2×Dic61—22no—
136C2×Dic61—22no—
137C2×Dic61—21no—
138C2×Dic61—22no—
139C2×Dic61—22no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144D244—21no—
145D244C4⋊C812yescomplemented
146C4×D61—22no—
147C4×D61—22no—
148C4×D61—41no—
149C4×D61—41no—
150C4×D61—81no—
151Dic122—21no—
152Dic122C4⋊C812yescomplemented
153C8×C61—22no—
154C8×C61—41no—
155C8×C61—41no—
156C8×C61—41no—
157C8×C61—81no—
158#92418—42no—
159#92418—81no—
160#8839—611nomaximal, Sylow
161C22×C61—21no—
162C22×C61—21no—
163C22×C61#38511yescharacteristic
164C22×C61C8×D411yescharacteristic
165C22×C61#43511yescharacteristic
166C2×D61—22no—
167C2×D61—41no—
168C2×D61—41no—
169C4×C61—21no—
170C4×C61—21no—
171C4×C61—21no—
172C4×C61C2×C4⋊C811yescharacteristic
173C4×C61#42411yescharacteristic
174C4×C61C8×D411yescharacteristic
175C4×C61#43511yescharacteristic
176C4×C61#45311yescharacteristic
177C4×C61#45611yescharacteristic
178Dic61—24no—
179Dic61—22no—
180Dic61—42no—
181Dic61—41no—
182Dic61—41no—
183#2988—611no—
184#1842—611no—
185C4×#104—611no—
186#1565D6111yescharacteristic, complemented
187#1477—611no—
188#1283—611no—
189#1276—611no—
190C2×C61—21no—
191C2×C61—21no—
192C2×C61#185011yescharacteristic
193C2×C61#185911yescharacteristic
194C2×C61#186111yescharacteristic
195D61—42no—
196C4×#41—611no—
197C8×Q8—1221no—
198C8×D4—1221no—
199C8×D4—1222no—
200#431—611no—
201#431—1221no—
202#431C2×D6111yescharacteristic
203C2×C4⋊C8—611no—
204C2×C4⋊C8—1221no—
205C2×C4⋊C8—1222no—
206C2×C4⋊C8C2×D6111yescharacteristic
207C2×#104—611no—
208C2×#104—611no—
209C4×M16C2×D6111yescharacteristic
210C43—611no—
211#339—611no—
212#339—611no—
213#335—21no—
214#334—21no—
215Q8⋊C8—1221no—
216D4⋊C8—1221no—
217C61#883911yescharacteristic, complemented, Sylow
218C2×#41—611no—
219C2×M16C4×D6111yescharacteristic
220C2×M16C4×D6111yescharacteristic
221C22×C8—21no—
222C22×C8—612no—
223C22×C8—1222no—
224C4×Q8—611no—
225C4×Q8—611no—
226C4×D4—611no—
227C4×D4—611no—
228C4×D4—1221no—
229C4×D4—1221no—
230#117—611no—
231#117—1221no—
232C2×C42—611no—
233C2×C42—611no—
234C2×C42—1221no—
235C2×C42—1221no—
236C2×C42—1221no—
237C2×C42C22×D6111yescharacteristic
238C4⋊C8—21no—
239C4⋊C8—21no—
240C4⋊C8—1222no—
241C4⋊C8—1221no—
242C4⋊C8—1221no—
243C4⋊C8—1221no—
244C4⋊C8—2444no—
245C4⋊C8C22⋊D6111yescharacteristic
246C4⋊C8C22⋊D6111yescharacteristic
247#104—614no—
248#104—1222no—
249C22⋊C8—21no—
250C22⋊C8—1222no—
251C22⋊C8—1221no—
252#97—21no—
253C4×C8—21no—
254C4×C8—21no—
255C4×C8—1222no—
256C4×C8—1221no—
257#41—612no—
258#41—612no—
259#41—1221no—
260#41—1221no—
261C2×Q8—611no—
262C2×D4—611no—
263C2×D4—1221no—
264C22×C4—1221no—
265C22×C4—1221no—
266C22×C4—1221no—
267C22×C4—1221no—
268C22×C4—1221no—
269C22×C4C2×C4×D6111yescharacteristic
270C22×C4D4×D6111yescharacteristic
271C22×C4#1175822611yescharacteristic
272M16—21no—
273M16—21no—
274M16—21no—
275M16C8×D6112yescomplemented
276C2×C8—21no—
277C2×C8—21no—
278C2×C8—21no—
279C2×C8—21no—
280C2×C8—42no—
281C2×C8—41no—
282C2×C8—1222no—
283C2×C8—4882no—
284C2×C8—2441no—
285C2×C8—2442no—
286C4⋊C4—611no—
287C4⋊C4—611no—
288C4⋊C4—1221no—
289C4⋊C4—1221no—
290C22⋊C4—1221no—
291C22⋊C4—1221no—
292C22⋊C4—1221no—
293C42—612no—
294C42—1222no—
295C42—1222no—
296C42—1221no—
297C42—1221no—
298C42—1221no—
299C42—1221no—
300C42—1221no—
301C42—1221no—
302C42—2442no—
303C42#1175822211yescharacteristic
304C42D4×D6111yescharacteristic
305C42Q8×D6111yescharacteristic
306C42C2×C22⋊D6111yescharacteristic
307C23—1221no—
308C23#1451973911yescharacteristic
309Q8—612no—
310Q8—1221no—
311D4—612no—
312D4—1222no—
313D4—1222no—
314D4—1221no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—41no—
318C2×C4—1222no—
319C2×C4—1222no—
320C2×C4—1222no—
321C2×C4—1221no—
322C2×C4—1222no—
323C2×C4—1222no—
324C2×C4—1222no—
325C2×C4—1221no—
326C2×C4—1221no—
327C2×C4—4881no—
328C2×C4—2441no—
329C2×C4—2441no—
330C2×C4—2441no—
331C2×C4—2441no—
332C2×C4C4⋊C4×D6111yescharacteristic
333C2×C4C4×C22⋊D6111yescharacteristic
334C2×C4#1451974511yescharacteristic
335C2×C4#1451975311yescharacteristic
336C2×C4#1451975511yescharacteristic
337C2×C4#1451976211yescharacteristic
338C2×C4C2×C8×D6111yescharacteristic
339C2×C4M16×D6111yescharacteristic
340C2×C4#1451978311yescharacteristic
341C2×C4#1451978511yescharacteristic
342C8—22no—
343C8—41no—
344C8—41no—
345C8—41no—
346C8—81no—
347C8—4881no—
348C8—2442no—
349C22—21no—
350C22—21no—
351C22—1222no—
352C22—2441no—
353C22—2441no—
354C22#1683963311yescharacteristic
355C22#1683982711yescharacteristic
356C22#1683983211yescharacteristic
357C4—21no—
358C4—21no—
359C4—21no—
360C4—1224no—
361C4—1222no—
362C4—2442no—
363C4—2441no—
364C4—2441no—
365C4C4⋊C8×D6111yescharacteristic
366C4#1683978711yescharacteristic
367C4C8×C22⋊D6111yescharacteristic
368C4#1683983111yescharacteristic
369C4#1683992811yescharacteristic
370C4#1683994311yescharacteristic
371C2—21no—
372C2—21no—
373C2—2442no—
374C2#2144599511yescharacteristic
375C2#2144604211yescharacteristic
376C2#2144605611yescharacteristic
subgroupG/H
centerC2×C4#14519745
commutatorC2×C4×C61C22×C8
FrattiniC2×C42C22×D61
FittingC61×#1565C2
socleC22×C61#385
prime radicalC2×#11758222C2×C4
cosocleC2×C42×C61C23
hypercenter#1565D61
hypocenterC61#8839
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1565

Complements

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

NH ≅ G/Ntype
2. #21445970C2semidirect
5. #21443670C2semidirect
6. #21443651C2semidirect
7. C61×#1565C2semidirect
51. #14519703C8semidirect
86. M16×C61C2×C8semidirect
113. C4×Dic61C2×C8semidirect
145. D244C4⋊C8semidirect
152. Dic122C4⋊C8semidirect
186. #1565D61semidirect
217. C61#8839semidirect
275. M16C8×D61semidirect

Maximal subgroups

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

subgroupindex
#214549272
#214459702
C4×#145197032
#214442042
#214436702
#214436512
C61×#15652
#883961