Finite Group Databasebeta

← #29596535

Subgroups — #29596535

Order 15616.

424 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454407C211yesmaximal, characteristic
2#21447608C211yesmaximal, characteristic, complemented
3#21447607C211yesmaximal, characteristic, complemented
4C2×#16839543C211yesmaximal, characteristic
5#21445849C211yesmaximal, characteristic
6#21443926C211yesmaximal, characteristic, complemented
7C61×#1386C211yesmaximal, characteristic, complemented
8C22×#11758189C2211yescharacteristic
9#117×D61—21no—
10C2×#14519717C2211yescharacteristic
11#16839803—21no—
12#16839803—21no—
13#16839801—21no—
14#16839801—21no—
15#16839800C2211yescharacteristic
16#16839798—21no—
17C2×#14519711C2211yescharacteristic
18#16839619—21no—
19#16839590—21no—
20#16839589—21no—
21#16839588—21no—
22#16839587—21no—
23#16839543C414yescomplemented
24#16839524—21no—
25C2×M32×C61C2211yescharacteristic
26C61×#427C2211yescharacteristic
27C2×#106×C61C2211yescharacteristic
28C22×C4×D61D411yescharacteristic
29C2×#11758189—21no—
30C2×#11758189—21no—
31C2×#11758189—21no—
32C2×#11758189—21no—
33C2×#11758189C2×C412yes—
34C2×#11758189Q812yes—
35C22×#92418D411yescharacteristic
36#14519736—21no—
37#14519735—21no—
38#14519735—21no—
39#14519734—41no—
40#14519733—41no—
41C2×C4⋊Dic61—21no—
42C4⋊C4×D61—21no—
43C4⋊C4×D61—21no—
44C2×#11758198—41no—
45C22⋊C4×D61—41no—
46C42×D61—41no—
47#14519717—21no—
48#14519717C2×C412yescomplemented
49C2×#11758185—21no—
50#14519711—21no—
51#14519711—21no—
52#14519711D411yescharacteristic
53#14519711D411yescharacteristic
54#14519710—21no—
55#14519710—21no—
56#14519709—21no—
57#14519708—21no—
58#14519708—21no—
59#14519684—41no—
60C22×C8×C61C2311yescharacteristic
61#117×C61—21no—
62C2×C4⋊C4×C61—21no—
63M32×C61—21no—
64M32×C61C2×C412yescomplemented
65C2×C16×C61—21no—
66#107×C61D411yescharacteristic
67#107×C61D411yescharacteristic
68#106×C61—21no—
69#106×C61—21no—
70#106×C61—21no—
71C23×D61D811yescharacteristic
72C22×C4×C61—41no—
73C22×C4×C61C2×D411yescharacteristic
74C22×Dic61—41no—
75C22×Dic61D811yescharacteristic
76C2×C4×D61—21no—
77C2×C4×D61—21no—
78C2×C4×D61—21no—
79C2×C4×D61—21no—
80C2×C4×D61—41no—
81C2×C4×D61—41no—
82C2×C4×D61C4⋊C412yes—
83C2×C4×D61Q1612yes—
84C2×C8×C61C22×C411yescharacteristic
85C2×C8×C61C2×D411yescharacteristic
86C2×C8×C61C2×D411yescharacteristic
87C2×C8×C61C2×Q811yescharacteristic
88C2×C8×C61#4111yescharacteristic
89C2×C8×C61#4111yescharacteristic
90C4⋊C4×C61—21no—
91C4⋊C4×C61—21no—
92C4⋊C4×C61—41no—
93C4⋊C4×C61—41no—
94C22⋊C4×C61—41no—
95C42×C61—41no—
96C22⋊Dic61—41no—
97#11758198—41no—
98#11758198—41no—
99#11758198—82no—
100C4⋊Dic61—21no—
101C4⋊Dic61—21no—
102C4⋊Dic61—41no—
103C4⋊Dic61—41no—
104#11758196—41no—
105#11758196—41no—
106C4×Dic61—41no—
107C4×Dic61—41no—
108C4×Dic61—41no—
109C2×#92418—21no—
110C2×#92418—21no—
111C2×#92418C4⋊C412yes—
112#11758189—22no—
113#11758189—22no—
114#11758189—22no—
115#11758189—22no—
116C16×C61—22no—
117#11758185—22no—
118C23×C61C2×D811yescharacteristic
119C22×D61—21no—
120C22×D61—21no—
121C22×D61—41no—
122C22×D61—41no—
123C22×D61#10712yes—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—81no—
127C2×C4×C61—81no—
128C2×C4×C61—81no—
129C2×C4×C61C2×C4⋊C411yescharacteristic
130C2×C4×C61#12011yescharacteristic
131C2×C4×C61#12311yescharacteristic
132C2×C4×C61C2×Q1611yescharacteristic
133C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
134C2×C4×C61#13711yescharacteristic
135C2×Dic61—21no—
136C2×Dic61—21no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—81no—
140C2×Dic61—81no—
141C2×Dic61—81no—
142C2×Dic61#10712yes—
143C4×D61—22no—
144C4×D61—22no—
145C4×D61—22no—
146C4×D61—22no—
147C4×D61—82no—
148C4×D61—82no—
149C8×C61C4×D411yescharacteristic
150C8×C61C4×D411yescharacteristic
151C8×C61C22⋊Q811yescharacteristic
152C8×C61C22⋊Q811yescharacteristic
153#92418—22no—
154#12923—611nomaximal, Sylow
155C22×C61—21no—
156C22×C61—21no—
157C22×C61C2×#10711yescharacteristic
158C22×C61#44711yescharacteristic
159C22×C61#48011yescharacteristic
160C2×D61—22no—
161C2×D61—41no—
162C2×D61—41no—
163C2×D61—42no—
164C2×D61—81no—
165C4×C61—81no—
166C4×C61—81no—
167C4×C61—161no—
168C4×C61#38511yescharacteristic
169C4×C61#42811yescharacteristic
170C4×C61#45111yescharacteristic
171C4×C61#48411yescharacteristic
172Dic61—22no—
173Dic61—81no—
174Dic61—81no—
175Dic61—161no—
176#2911—611no—
177#2159—611no—
178#2159—611no—
179C2×#349—611no—
180#1809—611no—
181#1386—611no—
182#1386D6111yescharacteristic, complemented
183C2×C61—21no—
184C2×C61—21no—
185C2×C61#185211yescharacteristic
186C2×C61#219011yescharacteristic
187C2×C61#219111yescharacteristic
188D61—42no—
189C22×M16—611no—
190C2×#117—1221no—
191C2×M32—611no—
192C2×M32C2×D6111yescharacteristic
193#428—1221no—
194#428—1221no—
195#428—1221no—
196#428—1221no—
197#427—611no—
198#427—1221no—
199#427C2×D6111yescharacteristic
200C2×#107—611no—
201C2×#106C2×D6111yescharacteristic
202#380—1221no—
203#367—1221no—
204#367—1221no—
205#366—1221no—
206#366—1221no—
207#349—614no—
208#340—1221no—
209C61#1292311yescharacteristic, complemented, Sylow
210C23×C4—611no—
211C2×M16—612no—
212C2×M16—612no—
213C2×M16—1221no—
214C2×M16—1221no—
215C2×M16—1221no—
216C2×M16—1221no—
217C22×C8—611no—
218C22×C8C22×D6111yescharacteristic
219#117—21no—
220#117—1221no—
221#117—1221no—
222#117—1221no—
223#117—2441no—
224#117—2441no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—1221no—
227C2×C4⋊C4—1221no—
228C2×C4⋊C4—1221no—
229C2×C22⋊C4—2441no—
230C2×C22⋊C4—2441no—
231C2×C42—2441no—
232M32—21no—
233M32—612no—
234M32—1221no—
235M32C4×D6112yescomplemented
236C2×C16—21no—
237C2×C16—1221no—
238#107—611no—
239#107—611no—
240#107—1221no—
241#107—1221no—
242#107—1221no—
243#107—1221no—
244#107D24411yescharacteristic
245#107D24411yescharacteristic
246#106—21no—
247#106—21no—
248#106—21no—
249#106—1221no—
250#106—1221no—
251#106—1221no—
252#95—2441no—
253C24—611no—
254C22×C4—41no—
255C22×C4—611no—
256C22×C4—612no—
257C22×C4—612no—
258C22×C4—1221no—
259C22×C4—1221no—
260C22×C4—1221no—
261C22×C4—1221no—
262C22×C4—2441no—
263C22×C4—2441no—
264C22×C4—2441no—
265C22×C4D4×D6111yescharacteristic
266M16—1222no—
267M16—1222no—
268M16—1222no—
269M16—1222no—
270C2×C8—612no—
271C2×C8—1221no—
272C2×C8—1221no—
273C2×C8C2×C4×D6111yescharacteristic
274C2×C8C2×D24411yescharacteristic
275C2×C8#1175822211yescharacteristic
276C2×C8D4×D6111yescharacteristic
277C2×C8#1175822411yescharacteristic
278C2×C8Q8×D6111yescharacteristic
279C4⋊C4—21no—
280C4⋊C4—21no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—1221no—
284C4⋊C4—1221no—
285C4⋊C4—2441no—
286C4⋊C4—2441no—
287C4⋊C4—2441no—
288C4⋊C4—2441no—
289C22⋊C4—41no—
290C22⋊C4—4882no—
291C22⋊C4—2441no—
292C22⋊C4—2441no—
293C22⋊C4—2441no—
294C42—41no—
295C42—2441no—
296C42—2441no—
297C42—2441no—
298C16—22no—
299C16—1222no—
300C23—612no—
301C23—1221no—
302C23—1221no—
303C23—2441no—
304C23—2441no—
305C23D8×D6111yescharacteristic
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—81no—
309C2×C4—81no—
310C2×C4—81no—
311C2×C4—612no—
312C2×C4—1221no—
313C2×C4—1221no—
314C2×C4—1222no—
315C2×C4—1222no—
316C2×C4—1222no—
317C2×C4—1222no—
318C2×C4—4882no—
319C2×C4—4882no—
320C2×C4—4881no—
321C2×C4—4881no—
322C2×C4—4881no—
323C2×C4—2441no—
324C2×C4—2441no—
325C2×C4C4⋊C4×D6111yescharacteristic
326C2×C4#1451974711yescharacteristic
327C2×C4#1451975911yescharacteristic
328C2×C4Q16×D6111yescharacteristic
329C2×C4#1451980411yescharacteristic
330C2×C4#1451980611yescharacteristic
331C8—1222no—
332C8#1451973711yescharacteristic
333C8C4×D24411yescharacteristic
334C8#1451975511yescharacteristic
335C8#1451975711yescharacteristic
336C22—21no—
337C22—21no—
338C22—1222no—
339C22—4881no—
340C22—2442no—
341C22—2441no—
342C22—2441no—
343C22#107×D6111yescharacteristic
344C22#1683989711yescharacteristic
345C22#1684007411yescharacteristic
346C4—81no—
347C4—81no—
348C4—161no—
349C4—1222no—
350C4—9761no—
351C4—4881no—
352C4—4881no—
353C4#1683963611yescharacteristic
354C4#1683980111yescharacteristic
355C4#1683991911yescharacteristic
356C4#1684009611yescharacteristic
357C2—21no—
358C2—21no—
359C2—2442no—
360C2#2144600811yescharacteristic
361C2#2144776611yescharacteristic
362C2#2144777111yescharacteristic
subgroupG/H
centerC22#16839897
commutatorC2×C8×C61C22×C4
FrattiniC22×C8C22×D61
FittingC61×#1386C2
socleC22×C61#447
prime radicalC23×D61D8
cosocleC22×C8×C61C23
hypercenter#1386D61
hypocenterC61#12923
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #1386

Complements

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

NH ≅ G/Ntype
2. #21447608C2semidirect
3. #21447607C2semidirect
6. #21443926C2semidirect
7. C61×#1386C2semidirect
23. #16839543C4semidirect
48. #14519717C2×C4semidirect
64. M32×C61C2×C4semidirect
182. #1386D61semidirect
209. C61#12923semidirect
235. M32C4×D61semidirect

Maximal subgroups

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

subgroupindex
#214544072
#214476082
#214476072
C2×#168395432
#214458492
#214439262
C61×#13862
#1292361