Finite Group Databasebeta

← #29573902

Subgroups — #29573902

Order 15616.

446 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454928C211yesmaximal, characteristic
2C4×#14519705C211yesmaximal, characteristic
3#21444569C211yesmaximal, characteristic, complemented
4#21444204C211yesmaximal, characteristic
5#21443669C211yesmaximal, characteristic, complemented
6#21443652C211yesmaximal, characteristic, complemented
7C61×#1831C211yesmaximal, characteristic, complemented
8C4×#11758222C2211yescharacteristic
9#16839886—21no—
10#16839827—21no—
11C8×C22⋊D61—22no—
12#16839815C2211yescharacteristic
13#16839815C2211yescharacteristic
14#16839814—21no—
15C4⋊C8×D61—21no—
16C2×#14519705C411yescharacteristic
17C2×#14519705C411yescharacteristic
18C4×#11758194C2211yescharacteristic
19#16839522C411yescharacteristic
20#16839522C411yescharacteristic
21#16839514—21no—
22#16839512—21no—
23#16839492—21no—
24#16839489—21no—
25C2×C4⋊C8×C61C2211yescharacteristic
26C2×C4⋊C8×C61C2211yescharacteristic
27C43×C61C2211yescharacteristic
28C61×#336—22no—
29C2×#11758222C2×C411yescharacteristic
30C2×#11758194C2×C411yescharacteristic
31C2×#11758194C2×C411yescharacteristic
32C2×C8×D61—22no—
33C4×Dic122D411yescharacteristic
34C4×Dic122Q811yescharacteristic
35C4×D244D411yescharacteristic
36C4×D244Q811yescharacteristic
37C4×C22⋊D61—21no—
38C4×C22⋊D61—21no—
39#14519736C2×C411yescharacteristic
40#14519734—21no—
41C42×D61—21no—
42C4⋊#92418—21no—
43C4⋊#92418D411yescharacteristic
44C4⋊#92418D411yescharacteristic
45#14519706—22no—
46#14519705—22no—
47#14519705C814yescomplemented
48C22⋊#92418—21no—
49C22⋊#92418—21no—
50#14519689—22no—
51#14519688—21no—
52C4×#92418—21no—
53C4×#92418—21no—
54C4×#92418—21no—
55C8×Dic61—22no—
56C22×C8×C61—21no—
57C22×C8×C61D412yes—
58C2×C42×C61—21no—
59C2×C42×C61—21no—
60C2×C42×C61C2×C411yescharacteristic
61C2×C42×C61C2×C411yescharacteristic
62C2×C42×C61C2311yescharacteristic
63C4⋊C8×C61—21no—
64C4⋊C8×C61—21no—
65C4⋊C8×C61—21no—
66C4⋊C8×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61—21no—
69C22×C4×C61C22×C411yescharacteristic
70C22×C4×C61C2×D411yescharacteristic
71C22×C4×C61#4111yescharacteristic
72C2×C22⋊D61—21no—
73#11758222—21no—
74#11758222—21no—
75#11758222C2×C812yes—
76#11758222M1612yes—
77C2×D244C4⋊C411yescharacteristic
78C2×C4×D61—21no—
79C2×C4×D61—21no—
80C2×C4×D61—21no—
81C2×Dic122C4⋊C411yescharacteristic
82C2×C8×C61—22no—
83C2×C8×C61—42no—
84C2×C8×C61—42no—
85C2×C8×C61—41no—
86C42×C61—21no—
87C42×C61—21no—
88C42×C61—21no—
89C42×C61—41no—
90C42×C61—41no—
91C42×C61—42no—
92C42×C61C2×C812yescomplemented
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—21no—
105C4×Dic61—21no—
106C4×Dic61—21no—
107#11758194—21no—
108#11758194—21no—
109#11758194—21no—
110#11758194C2×C812yescomplemented
111C2×#92418—21no—
112C2×#92418—21no—
113C2×#92418—21no—
114C2×#92418—21no—
115C2×#92418—41no—
116C8×D61—82no—
117C23×C61C4×D411yescharacteristic
118C22×D61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—22no—
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×C61C2×C4⋊C411yescharacteristic
129C2×C4×C61C4×D411yescharacteristic
130C2×C4×C61#12011yescharacteristic
131C2×C4×C61C22⋊Q811yescharacteristic
132C2×C4×C61C22⋊Q811yescharacteristic
133C2×C4×C61#12311yescharacteristic
134C2×C4×C61C22×C811yescharacteristic
135C2×C4×C61C2×M1611yescharacteristic
136C2×C4×C61#13111yescharacteristic
137C2×C4×C61#13111yescharacteristic
138C22⋊D61—22no—
139C22⋊D61—22no—
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—21no—
143D244—21no—
144D244C4⋊C812yes—
145C4×D61—22no—
146C4×D61—22no—
147C4×D61—41no—
148C4×D61—41no—
149C4×D61—81no—
150Dic122—21no—
151Dic122C4⋊C812yes—
152C8×C61—42no—
153C8×C61—81no—
154#92418—22no—
155#92418—41no—
156#92418—41no—
157#92418—41no—
158#92418—81no—
159#8840—611nomaximal, Sylow
160C22×C61—21no—
161C22×C61—21no—
162C22×C61#38511yescharacteristic
163C22×C61C8×D411yescharacteristic
164C22×C61#43511yescharacteristic
165C2×D61—22no—
166C2×D61—41no—
167C2×D61—41no—
168C4×C61—21no—
169C4×C61—21no—
170C4×C61—21no—
171C4×C61—42no—
172C4×C61—42no—
173C4×C61C2×C4⋊C811yescharacteristic
174C4×C61#42411yescharacteristic
175C4×C61C8×D411yescharacteristic
176C4×C61#43511yescharacteristic
177C4×C61#45411yescharacteristic
178C4×C61#45511yescharacteristic
179Dic61—22no—
180Dic61—41no—
181Dic61—41no—
182#2988—611no—
183#1831D6111yescharacteristic, complemented
184C4×#104—611no—
185#1565—611no—
186#1477—611no—
187#1283—611no—
188#1276—611no—
189C2×C61—21no—
190C2×C61—21no—
191C2×C61#185011yescharacteristic
192C2×C61#186011yescharacteristic
193C2×C61#186111yescharacteristic
194D61—42no—
195C4×#41—611no—
196C8×Q8—1221no—
197C8×D4—1221no—
198C8×D4—1222no—
199#431—611no—
200#431—611no—
201#431—1221no—
202C2×C4⋊C8—1221no—
203C2×C4⋊C8C2×D6111yescharacteristic
204C2×C4⋊C8C2×D6111yescharacteristic
205C2×#104—611no—
206C2×#104—611no—
207C4×M16—611no—
208C43C2×D6111yescharacteristic
209#339—611no—
210#339—611no—
211#336—22no—
212#335—1221no—
213#334—1221no—
214Q8⋊C8—1221no—
215D4⋊C8—1221no—
216C61#884011yescharacteristic, complemented, Sylow
217C2×#41—611no—
218C2×M16—611no—
219C2×M16—611no—
220C22×C8—21no—
221C22×C8—1222no—
222C22×C8C22⋊D6112yes—
223C4×Q8—611no—
224C4×Q8—611no—
225C4×D4—611no—
226C4×D4—611no—
227C4×D4—1221no—
228C4×D4—1221no—
229#117—611no—
230#117—1221no—
231C2×C42—21no—
232C2×C42—21no—
233C2×C42—1221no—
234C2×C42C4×D6111yescharacteristic
235C2×C42C4×D6111yescharacteristic
236C2×C42C22×D6111yescharacteristic
237C4⋊C8—21no—
238C4⋊C8—21no—
239C4⋊C8—21no—
240C4⋊C8—21no—
241C4⋊C8—611no—
242C4⋊C8—611no—
243C4⋊C8—1222no—
244C4⋊C8—1221no—
245#104—614no—
246#104—1222no—
247C22⋊C8—1222no—
248C22⋊C8—1221no—
249C22⋊C8—1221no—
250#97—1221no—
251C4×C8—1222no—
252C4×C8—1221no—
253C4×C8—1221no—
254C4×C8—1221no—
255#41—612no—
256#41—612no—
257#41—1221no—
258#41—1221no—
259C2×Q8—611no—
260C2×D4—611no—
261C2×D4—1221no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—1221no—
265C22×C4—1221no—
266C22×C4—1221no—
267C22×C4C2×C4×D6111yescharacteristic
268C22×C4#1175822211yescharacteristic
269C22×C4C2×C22⋊D6111yescharacteristic
270M16—612no—
271M16—1221no—
272M16—1221no—
273M16—1221no—
274C2×C8—22no—
275C2×C8—42no—
276C2×C8—42no—
277C2×C8—41no—
278C2×C8—1221no—
279C2×C8—1221no—
280C2×C8—1221no—
281C2×C8—1221no—
282C2×C8—4882no—
283C2×C8—2441no—
284C4⋊C4—611no—
285C4⋊C4—611no—
286C4⋊C4—1221no—
287C4⋊C4—1221no—
288C22⋊C4—1221no—
289C22⋊C4—1221no—
290C22⋊C4—1221no—
291C42—21no—
292C42—21no—
293C42—21no—
294C42—41no—
295C42—41no—
296C42—42no—
297C42—1221no—
298C42—1221no—
299C42—1221no—
300C42C8×D6112yescomplemented
301C42D4×D6111yescharacteristic
302C42D4×D6111yescharacteristic
303C42Q8×D6111yescharacteristic
304C42#1175822611yescharacteristic
305C23—1221no—
306C23C4×C22⋊D6111yescharacteristic
307Q8—612no—
308Q8—1221no—
309D4—612no—
310D4—1222no—
311D4—1222no—
312D4—1221no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—1221no—
323C2×C4—1222no—
324C2×C4—1222no—
325C2×C4—1221no—
326C2×C4—1221no—
327C2×C4—4881no—
328C2×C4—2441no—
329C2×C4—2441no—
330C2×C4C4⋊C4×D6111yescharacteristic
331C2×C4#1451973911yescharacteristic
332C2×C4#1451974511yescharacteristic
333C2×C4#1451975311yescharacteristic
334C2×C4#1451975511yescharacteristic
335C2×C4#1451976211yescharacteristic
336C2×C4C2×C8×D6111yescharacteristic
337C2×C4M16×D6111yescharacteristic
338C2×C4#1451978311yescharacteristic
339C2×C4#1451978511yescharacteristic
340C8—42no—
341C8—81no—
342C8—1222no—
343C8—4881no—
344C8—2441no—
345C8—2441no—
346C8—2441no—
347C22—21no—
348C22—21no—
349C22—1222no—
350C22—2441no—
351C22—2441no—
352C22#1683963311yescharacteristic
353C22C8×C22⋊D6111yescharacteristic
354C22#1683983111yescharacteristic
355C4—21no—
356C4—21no—
357C4—21no—
358C4—42no—
359C4—42no—
360C4—1222no—
361C4—2441no—
362C4—2441no—
363C4C4⋊C8×D6111yescharacteristic
364C4#1683978711yescharacteristic
365C4#1683982711yescharacteristic
366C4#1683983211yescharacteristic
367C4#1683993411yescharacteristic
368C4#1683993911yescharacteristic
369C2—21no—
370C2—21no—
371C2—2442no—
372C2#2144599511yescharacteristic
373C2#2144605111yescharacteristic
374C2#2144605811yescharacteristic
subgroupG/H
centerC2×C4#14519745
commutatorC2×C4×C61C22×C8
FrattiniC2×C42C22×D61
FittingC61×#1831C2
socleC22×C61#385
prime radicalC2×#11758222C2×C4
cosocleC2×C42×C61C23
hypercenter#1831D61
hypocenterC61#8840
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1831

Complements

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

NH ≅ G/Ntype
3. #21444569C2semidirect
5. #21443669C2semidirect
6. #21443652C2semidirect
7. C61×#1831C2semidirect
47. #14519705C8semidirect
92. C42×C61C2×C8semidirect
110. #11758194C2×C8semidirect
183. #1831D61semidirect
216. C61#8840semidirect
300. C42C8×D61semidirect

Maximal subgroups

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

subgroupindex
#214549282
C4×#145197052
#214445692
#214442042
#214436692
#214436522
C61×#18312
#884061