Finite Group Databasebeta

← #29596123

Subgroups — #29596123

Order 15616.

400 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839878C211yesmaximal, characteristic
2C2×#16839582C211yesmaximal, characteristic, complemented
3#21447569C211yesmaximal, characteristic
4#21447566C211yesmaximal, characteristic
5#21445989C211yesmaximal, characteristic, complemented
6#21443922C211yesmaximal, characteristic, complemented
7C61×#1385C211yesmaximal, characteristic, complemented
8C2×#14519799C2211yescharacteristic
9C2×#14519785—21no—
10C2×#14519717C2211yescharacteristic
11#16839878—21no—
12#16839878—21no—
13#16839878C412yes—
14#16839878C412yes—
15C2×#14519713C2211yescharacteristic
16C2×#14519712—21no—
17#16839785—21no—
18C2×#14519703—21no—
19C2×C8×Dic61C2211yescharacteristic
20#16839582—21no—
21#16839582—21no—
22#16839579—21no—
23#16839577—21no—
24#16839576—21no—
25#16839574—21no—
26C2×M32×C61C2211yescharacteristic
27C2×#108×C61C2211yescharacteristic
28C2×#108×C61C2211yescharacteristic
29C2×#11758222—21no—
30#14519799—21no—
31#14519799—21no—
32#14519799C2×C412yes—
33#14519799Q812yes—
34C2×Dic244D411yescharacteristic
35C2×#11758190—21no—
36C2×D488D411yescharacteristic
37#14519785—22no—
38#14519785—22no—
39#14519785—41no—
40#14519785—41no—
41C2×#11758194—21no—
42C2×#11758189—41no—
43C22×#92418D411yescharacteristic
44C2×C8×D61—41no—
45C2×C4×Dic61D411yescharacteristic
46#14519717—21no—
47#14519717—21no—
48C2×#11758185—21no—
49#14519713—21no—
50#14519713—21no—
51#14519712—41no—
52#14519712—41no—
53#14519706—42no—
54#14519703—22no—
55#14519703—22no—
56C8×Dic61C2×C411yescharacteristic
57C8×Dic61C2×C411yescharacteristic
58C8×Dic61D411yescharacteristic
59C8×Dic61D411yescharacteristic
60C2×M16×C61—21no—
61C2×M16×C61—21no—
62C22×C8×C61C2311yescharacteristic
63M32×C61—21no—
64M32×C61—21no—
65C2×C16×C61—21no—
66#108×C61—21no—
67#108×C61—21no—
68#108×C61—21no—
69#108×C61C2×C412yes—
70C22×C4×C61C2×D411yescharacteristic
71C2×C22⋊D61—41no—
72C22×Dic61—21no—
73#11758222—22no—
74#11758222—22no—
75#11758222—41no—
76#11758222—41no—
77C2×D244—21no—
78C2×C4×D61—41no—
79C2×Dic122—21no—
80M16×C61—22no—
81M16×C61—41no—
82M16×C61—41no—
83M16×C61—41no—
84C2×C8×C61—41no—
85C2×C8×C61—41no—
86C2×C8×C61C22×C411yescharacteristic
87C2×C8×C61C2×D411yescharacteristic
88C2×C8×C61C2×D411yescharacteristic
89C2×C8×C61C2×Q811yescharacteristic
90C2×C8×C61#4111yescharacteristic
91C2×C8×C61#4111yescharacteristic
92C4×Dic61—21no—
93C4×Dic61C22⋊C411yescharacteristic
94C4×Dic61C22⋊C411yescharacteristic
95#11758194—41no—
96#11758194—41no—
97C2×#92418—41no—
98C2×#92418C22⋊C411yescharacteristic
99C2×#92418C22⋊C411yescharacteristic
100C2×#92418D811yescharacteristic
101C2×#92418D811yescharacteristic
102C2×#92418SD1611yescharacteristic
103C2×#92418SD1611yescharacteristic
104Dic244—21no—
105Dic244C4⋊C412yes—
106D488—21no—
107D488C4⋊C412yes—
108#11758190—22no—
109#11758190—22no—
110#11758189—42no—
111#11758189—42no—
112C8×D61—42no—
113C8×D61—42no—
114C16×C61—41no—
115#11758185—41no—
116C23×C61#13711yescharacteristic
117C22×D61—41no—
118C2×C4×C61C2×C22⋊C411yescharacteristic
119C2×C4×C61#12111yescharacteristic
120C2×C4×C61C22⋊Q811yescharacteristic
121C2×C4×C61C2×D811yescharacteristic
122C2×C4×C61C2×SD1611yescharacteristic
123C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
124C22⋊D61—42no—
125C22⋊D61—42no—
126C2×Dic61—21no—
127C2×Dic61—21no—
128C2×Dic61—42no—
129C2×Dic61—41no—
130D244—22no—
131D244—41no—
132C4×D61—42no—
133C4×D61—42no—
134Dic122—22no—
135Dic122—41no—
136C8×C61—42no—
137C8×C61—81no—
138C8×C61C2×C4⋊C411yescharacteristic
139C8×C61#11711yescharacteristic
140C8×C61#12111yescharacteristic
141C8×C61C22⋊Q811yescharacteristic
142#92418—81no—
143#92418#10211yescharacteristic
144#92418#10211yescharacteristic
145#92418#10211yescharacteristic
146#92418#10211yescharacteristic
147#12825—611nomaximal, Sylow
148C22×C61—41no—
149C22×C61#41711yescharacteristic
150C22×C61#46111yescharacteristic
151C22×C61#47411yescharacteristic
152C2×D61—42no—
153C2×D61—82no—
154C4×C61#38011yescharacteristic
155C4×C61C2×#10211yescharacteristic
156C4×C61#45911yescharacteristic
157C4×C61#47611yescharacteristic
158Dic61—22no—
159Dic61—41no—
160Dic61—42no—
161C2×#443—611no—
162C2×#364—611no—
163#2148—611no—
164#2148—611no—
165#1848—611no—
166#1385—611no—
167#1385D6111yescharacteristic, complemented
168C2×C61—21no—
169C2×C61—21no—
170C2×C61—21no—
171C2×C61#180211yescharacteristic
172D61—82no—
173C2×#135—611no—
174C2×#131—1221no—
175C2×M32—611no—
176C2×M32C2×D6111yescharacteristic
177#443—612no—
178#443—612no—
179#443—1221no—
180#443—1221no—
181C2×#108—611no—
182C2×#108—1221no—
183C2×#108C2×D6111yescharacteristic
184C2×#108C2×D6111yescharacteristic
185#423—1221no—
186C2×#104—1221no—
187C2×C4×C8—611no—
188#364—1221no—
189#364—1221no—
190#362—1221no—
191#362—1221no—
192#361—1221no—
193#361—1221no—
194C61#1282511yescharacteristic, complemented, Sylow
195C2×#41—1221no—
196#135—612no—
197#135—612no—
198#135—1221no—
199#135—1221no—
200C2×Q16—611no—
201C2×SD16—1221no—
202C2×D8—611no—
203#131—1222no—
204#131—1222no—
205#131—2441no—
206#131—2441no—
207C2×M16—21no—
208C2×M16—21no—
209C2×M16—1221no—
210C2×M16—2441no—
211C22×C8—611no—
212C22×C8—2441no—
213C22×C8C22×D6111yescharacteristic
214C2×C42—611no—
215M32—21no—
216M32—21no—
217M32—1221no—
218M32—1221no—
219C2×C16—21no—
220C2×C16—1221no—
221#108—21no—
222#108—21no—
223#108—21no—
224#108—1221no—
225#108—1221no—
226#108—2441no—
227#108—2441no—
228#108C4×D6112yes—
229C4⋊C8—2442no—
230#104—1222no—
231#104—1222no—
232C4×C8—611no—
233C4×C8—611no—
234C4×C8—611no—
235C4×C8—611no—
236#41—1222no—
237#41—1222no—
238#41—2441no—
239#41—2441no—
240C2×Q8—1221no—
241C2×D4—1221no—
242C2×D4—2441no—
243C22×C4—1221no—
244C22×C4—2441no—
245C22×C4D4×D6111yescharacteristic
246Q16—612no—
247Q16—1221no—
248SD16—1222no—
249SD16—1222no—
250D8—612no—
251D8—1221no—
252M16—22no—
253M16—41no—
254M16—41no—
255M16—41no—
256M16—2442no—
257M16—2442no—
258M16—2441no—
259M16—2441no—
260C2×C8—41no—
261C2×C8—41no—
262C2×C8—611no—
263C2×C8—611no—
264C2×C8—611no—
265C2×C8—611no—
266C2×C8—611no—
267C2×C8—611no—
268C2×C8—2442no—
269C2×C8—2442no—
270C2×C8—2441no—
271C2×C8C2×C4×D6111yescharacteristic
272C2×C8#1175822211yescharacteristic
273C2×C8#1175822211yescharacteristic
274C2×C8D4×D6111yescharacteristic
275C2×C8D4×D6111yescharacteristic
276C2×C8Q8×D6111yescharacteristic
277C42—611no—
278C42—611no—
279C42—1221no—
280C16—41no—
281C16—2441no—
282C23—2441no—
283C23#1451980911yescharacteristic
284Q8—1222no—
285Q8—2441no—
286D4—1222no—
287D4—2442no—
288D4—2442no—
289D4—2441no—
290C2×C4—1221no—
291C2×C4—1221no—
292C2×C4—2442no—
293C2×C4—2441no—
294C2×C4—2442no—
295C2×C4—2442no—
296C2×C4C22⋊C4×D6111yescharacteristic
297C2×C4#1451975011yescharacteristic
298C2×C4#1451975511yescharacteristic
299C2×C4D8×D6111yescharacteristic
300C2×C4SD16×D6111yescharacteristic
301C2×C4#1451980411yescharacteristic
302C8—42no—
303C8—81no—
304C8—611no—
305C8—611no—
306C8—611no—
307C8—611no—
308C8—4881no—
309C8C4⋊C4×D6111yescharacteristic
310C8#1451973411yescharacteristic
311C8#1451975011yescharacteristic
312C8#1451975511yescharacteristic
313C22—41no—
314C22—4882no—
315C22—2442no—
316C22#1683976211yescharacteristic
317C22#1683996611yescharacteristic
318C22#1684004111yescharacteristic
319C4—1222no—
320C4—2441no—
321C4—2442no—
322C4#1683962111yescharacteristic
323C4#102×D6111yescharacteristic
324C4#1683995611yescharacteristic
325C4#1684005111yescharacteristic
326C2—21no—
327C2—21no—
328C2—21no—
329C2—4882no—
330C2#2144581811yescharacteristic
subgroupG/H
centerC4#16840051
commutatorC2×C8×C61C22×C4
FrattiniC22×C8C22×D61
FittingC61×#1385C2
socleC2×C61#1802
prime radicalC2×#14519799C22
cosocleC22×C8×C61C23
hypercenter#1385D61
hypocenterC61#12825
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×C8 ◁ #1385

Complements

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

NH ≅ G/Ntype
2. C2×#16839582C2semidirect
5. #21445989C2semidirect
6. #21443922C2semidirect
7. C61×#1385C2semidirect
167. #1385D61semidirect
194. C61#12825semidirect

Maximal subgroups

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

subgroupindex
C2×#168398782
C2×#168395822
#214475692
#214475662
#214459892
#214439222
C61×#13852
#1282561