Finite Group Databasebeta

← #29590097

Subgroups — #29590097

Order 15616.

348 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 75 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#21454724C211yesmaximal, characteristic
2#21447630C211yesmaximal, characteristic, complemented
3#21444117C211yesmaximal, characteristic, complemented
4#21443796C211yesmaximal, characteristic, complemented
5#21443792C211yesmaximal, characteristic, complemented
6#21443791C211yesmaximal, characteristic, complemented
7C61×#1336C211yesmaximal, characteristic, complemented
8#16840559C411yescharacteristic
9#16840527—21no—
10#16839884C411yescharacteristic
11#16839883C411yescharacteristic
12#16839882—21no—
13#16839880C2211yescharacteristic
14#16839876—21no—
15#16839813—21no—
16#16839809C411yescharacteristic
17#104×D61—21no—
18C4×#11758189C2211yescharacteristic
19#16839583C2211yescharacteristic, complemented
20#16839543—21no—
21#16839539—21no—
22#16839483—21no—
23C8×#92418C2211yescharacteristic, complemented
24C61×#443C2211yescharacteristic
25C61×#364C2211yescharacteristic, complemented
26C61×#322C2211yescharacteristic, complemented
27#41×D61—21no—
28#14519809—21no—
29#14519806—21no—
30#14519804—21no—
31#14519801—21no—
32#14519799C2×C411yescharacteristic
33#14519797—21no—
34#14519785—21no—
35#14519785—41no—
36#14519784—21no—
37#14519783—21no—
38#14519783—41no—
39C2×#11758189—41no—
40C2×#11758189C2×C411yescharacteristic
41C2×#11758189D411yescharacteristic
42M16×D61—21no—
43M16×D61—41no—
44C42×D61D411yescharacteristic
45#14519717—21no—
46#14519713C2×C411yescharacteristic
47#14519712—21no—
48#14519706—22no—
49#14519705—21no—
50#14519704—21no—
51#14519703—21no—
52#14519689—22no—
53#14519687C2×C411yescharacteristic
54#14519687D411yescharacteristic
55C4×#92418—21no—
56C4×#92418D411yescharacteristic
57#135×C61C2×C411yescharacteristic
58#131×C61—21no—
59M32×C61—21no—
60#108×C61C2×C411yescharacteristic
61#104×C61—21no—
62C4×C8×C61—21no—
63C4×C8×C61C2311yescharacteristic
64#41×C61—21no—
65#11758226—21no—
66Q8×D61—21no—
67#11758224—21no—
68#11758224—41no—
69D4×D61—21no—
70D4×D61—41no—
71#11758222—21no—
72#11758222—41no—
73C2×C4×D61—21no—
74C2×C4×D61—41no—
75C2×C4×D61C22⋊C411yescharacteristic
76Q16×C61M1611yescharacteristic
77SD16×C61—21no—
78D8×C61M1611yescharacteristic
79M16×C61—21no—
80M16×C61—41no—
81C2×C8×C61—22no—
82C2×C8×C61—41no—
83C2×C8×C61C22×C411yescharacteristic
84C2×C8×C61C2×D411yescharacteristic
85C42×C61C2×D411yescharacteristic
86#11758202—21no—
87#11758201—21no—
88#11758200—21no—
89#11758199—21no—
90C4×Dic61—21no—
91C4×Dic61C22⋊C411yescharacteristic
92#11758194—21no—
93#11758194—41no—
94C2×#92418—22no—
95C2×#92418—41no—
96C2×#92418C22⋊C411yescharacteristic
97C2×#92418C22⋊C411yescharacteristic
98Dic244M1611yescharacteristic
99D488M1611yescharacteristic
100#11758190—21no—
101#11758189—21no—
102#11758189—21no—
103#11758189—21no—
104#11758189—21no—
105#11758189—41no—
106#11758189—41no—
107#11758189—41no—
108C8×D61—41no—
109C8×D61—41no—
110C8×D61—41no—
111C16×C61—41no—
112#11758185—41no—
113C22×D61—41no—
114C22×D61#10411yescharacteristic
115Q8×C61—21no—
116D4×C61—21no—
117D4×C61—41no—
118C2×C4×C61—21no—
119C2×C4×C61—41no—
120C2×C4×C61C2×C22⋊C411yescharacteristic
121C22⋊D61—41no—
122C22⋊D61—41no—
123C22⋊D61—41no—
124C2×Dic61—21no—
125C2×Dic61—41no—
126C2×Dic61#10411yescharacteristic
127D244—21no—
128D244—41no—
129C4×D61—21no—
130C4×D61—21no—
131C4×D61—41no—
132C4×D61—42no—
133C4×D61—41no—
134C4×D61—41no—
135Dic122—21no—
136Dic122—41no—
137C8×C61—42no—
138C8×C61—41no—
139C8×C61C2×M1611yescharacteristic
140C8×C61C2×M1611yescharacteristic
141C8×C61AGL(1,ℤ/8)11yescharacteristic
142C8×C61AGL(1,ℤ/8)11yescharacteristic
143#92418—21no—
144#92418—21no—
145#92418—42no—
146#92418—41no—
147#11670—611nomaximal, Sylow
148C22×C61—41no—
149C22×C61C2×#10411yescharacteristic
150C2×D61—21no—
151C2×D61—41no—
152C2×D61—41no—
153C2×D61—161no—
154C4×C61—22no—
155C4×C61—41no—
156C4×C61#40711yescharacteristic
157C4×C61#41811yescharacteristic
158Dic61—21no—
159Dic61—41no—
160Dic61—41no—
161#2956—611no—
162#2165—611no—
163#1453—611no—
164#1336—611no—
165#1336D6111yescharacteristic, complemented
166#1335—611no—
167#1335—611no—
168C2×C61—21no—
169C2×C61—81no—
170C2×C61#149011yescharacteristic
171D61—41no—
172D61—81no—
173#575—611no—
174#568—1221no—
175#444—611no—
176#444—611no—
177#444—1221no—
178#443—611no—
179#443—1221no—
180#443C2×D6111yescharacteristic
181#431—1221no—
182#430—611no—
183C2×#104—1221no—
184C4×M16—611no—
185#364—611no—
186#364C2×D6111yescharacteristic, complemented
187#349—1221no—
188#347—1221no—
189#322—1221no—
190#322C2×D6111yescharacteristic, complemented
191C82—611no—
192C61#1167011yescharacteristic, complemented, Sylow
193C2×#41—1221no—
194#137—1221no—
195#137—1221no—
196AGL(1,ℤ/8)—1221no—
197AGL(1,ℤ/8)—1221no—
198#135—611no—
199#135—1221no—
200#135C4×D6111yescharacteristic
201#131—21no—
202#131—1221no—
203#131—1221no—
204#131—1221no—
205#131—2441no—
206#131—2441no—
207C2×M16—611no—
208C2×M16—611no—
209C2×M16—1221no—
210C2×M16—2441no—
211C2×M16—2441no—
212C2×C42—611no—
213M32—21no—
214M32—1221no—
215#108—611no—
216#108—1221no—
217#108C4×D6111yescharacteristic
218C4⋊C8—1222no—
219#104—21no—
220#104—1221no—
221#104—1221no—
222#104—1221no—
223C22⋊C8—1222no—
224#97—611no—
225#97—611no—
226C4×C8—21no—
227C4×C8—611no—
228C4×C8—1221no—
229C4×C8C22×D6111yescharacteristic
230#41—21no—
231#41—1221no—
232#41—1221no—
233#41—1221no—
234#41—2441no—
235#41—2441no—
236C2×Q8—1221no—
237C2×D4—1221no—
238C2×D4—2441no—
239C22×C4—611no—
240C22×C4—1221no—
241C22×C4—2441no—
242Q16—611no—
243Q16—1221no—
244Q16#1175818911yescharacteristic
245SD16—21no—
246SD16—1221no—
247SD16—1221no—
248SD16—1221no—
249D8—611no—
250D8—1221no—
251D8#1175818911yescharacteristic
252M16—21no—
253M16—41no—
254M16—1221no—
255M16—1221no—
256M16—1221no—
257M16—1221no—
258M16—1221no—
259M16—2441no—
260M16—2441no—
261M16—2441no—
262M16—2441no—
263C2×C8—22no—
264C2×C8—41no—
265C2×C8—611no—
266C2×C8—611no—
267C2×C8—1222no—
268C2×C8—2441no—
269C2×C8—2441no—
270C2×C8—2441no—
271C2×C8—2441no—
272C2×C8C2×C4×D6111yescharacteristic
273C2×C8D4×D6111yescharacteristic
274C42—611no—
275C42—1221no—
276C42D4×D6111yescharacteristic
277C16—41no—
278C16—2441no—
279C23—611no—
280C23—2441no—
281Q8—21no—
282Q8—1221no—
283Q8—2441no—
284D4—21no—
285D4—41no—
286D4—1221no—
287D4—2441no—
288D4—2441no—
289D4—2441no—
290D4—2441no—
291C2×C4—21no—
292C2×C4—41no—
293C2×C4—611no—
294C2×C4—1221no—
295C2×C4—1221no—
296C2×C4—1221no—
297C2×C4—2442no—
298C2×C4—2441no—
299C2×C4—2441no—
300C2×C4—2441no—
301C2×C4—2441no—
302C2×C4C22⋊C4×D6111yescharacteristic
303C8—42no—
304C8—41no—
305C8—1221no—
306C8—1221no—
307C8—2442no—
308C8—2441no—
309C8M16×D6111yescharacteristic
310C8C2×#1175818911yescharacteristic
311C8#1451980111yescharacteristic
312C8#1451980411yescharacteristic
313C22—41no—
314C22—1221no—
315C22—9761no—
316C22—2441no—
317C22—2441no—
318C22#104×D6111yescharacteristic
319C4—22no—
320C4—41no—
321C4—1221no—
322C4—2441no—
323C4—2441no—
324C4#1683972411yescharacteristic
325C4#1683976511yescharacteristic
326C2—21no—
327C2—81no—
328C2—4881no—
329C2—2441no—
330C2#2144426011yescharacteristic
subgroupG/H
centerC4#16839765
commutatorC2×C8×C61C22×C4
FrattiniC4×C8C22×D61
FittingC61×#1336C2
socleC2×C61#1490
prime radical#16840559C4
cosocleC4×C8×C61C23
hypercenter#1336D61
hypocenterC61#11670
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C8 ◁ C4×C8 ◁ #1336

Complements

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

NH ≅ G/Ntype
2. #21447630C2semidirect
3. #21444117C2semidirect
4. #21443796C2semidirect
5. #21443792C2semidirect
6. #21443791C2semidirect
7. C61×#1336C2semidirect
19. #16839583C22semidirect
23. C8×#92418C22semidirect
25. C61×#364C22semidirect
26. C61×#322C22semidirect
165. #1336D61semidirect
186. #364C2×D61semidirect
190. #322C2×D61semidirect
192. C61#11670semidirect

Maximal subgroups

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

subgroupindex
#214547242
#214476302
#214441172
#214437962
#214437922
#214437912
C61×#13362
#1167061