Finite Group Databasebeta

← #30607443

Subgroups — #30607443

Order 15616.

416 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 82 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#21462578C211yesmaximal, characteristic
2#21462167C211yesmaximal, characteristic, complemented
3C2×#16840680C211yesmaximal, characteristic
4#21461938C211yesmaximal, characteristic, complemented
5#21460899C211yesmaximal, characteristic, complemented
6#21460871C211yesmaximal, characteristic, complemented
7#361×D61C211yesmaximal, characteristic
8#16840829—21no—
9C2×#14519852C2211yescharacteristic
10#16840803—21no—
11#16840803—21no—
12D8×#6923—22no—
13#16840777—21no—
14C2×#14519847C2211yescharacteristic
15#16840772C2211yescharacteristic
16#16840754—21no—
17#16840725C2211yescharacteristic
18#16840687—21no—
19#16840686—21no—
20#16840680—22no—
21#16840645—21no—
22C2×D8×D61C2211yescharacteristic
23M32×D61C2211yescharacteristic
24#108×D61C2211yescharacteristic
25#16839576C411yescharacteristic, complemented
26#16839575C411yescharacteristic, complemented
27#16839574C411yescharacteristic, complemented
28C61×#361C411yescharacteristic, complemented
29C2×#11758213—21no—
30D61⋊M16D411yescharacteristic
31D4×#6923—22no—
32D4×#6923—22no—
33D4×#6923—41no—
34D4×#6923—41no—
35#14519856—21no—
36#14519856D411yescharacteristic
37C2×C22⋊#6923—42no—
38#14519852—21no—
39#14519852—21no—
40C2×#11758187—21no—
41#14519848—41no—
42#14519847—21no—
43#14519847—21no—
44#14519847—41no—
45#14519846—21no—
46#14519845D411yescharacteristic
47#14519845D411yescharacteristic
48#14519839—22no—
49#14519839—22no—
50#14519831—21no—
51C8×#6923—21no—
52C2×D4×D61—21no—
53C2×D488C2×C411yescharacteristic
54C2×#11758199—21no—
55D8×D61—21no—
56D8×D61—21no—
57D8×D61D412yes—
58D8×D61Q812yes—
59M16×D61—21no—
60C2×C8×D61C2311yescharacteristic
61#14519717C2×C411yescharacteristic, complemented
62#14519716—21no—
63C16×D61—21no—
64#14519713C2×C411yescharacteristic, complemented
65#14519712—21no—
66C2×D8×C61C2×C411yescharacteristic
67M32×C61C2×C411yescharacteristic, complemented
68#108×C61C2×C411yescharacteristic, complemented
69C23×D61—41no—
70C22×#6923—42no—
71C22×#6923—42no—
72C2×D4×C61—21no—
73C2×C22⋊D61—41no—
74D4×D61—22no—
75D4×D61—22no—
76D4×D61—41no—
77D4×D61—41no—
78C2×D244—21no—
79C2×C4×D61C2×D411yescharacteristic
80C22⋊#6923—42no—
81C22⋊#6923—42no—
82C22⋊#6923—41no—
83C22⋊#6923SD1612yes—
84#11758217—21no—
85C2×#92420—41no—
86C4⋊#6923—21no—
87C4⋊#6923—21no—
88C4⋊#6923—21no—
89C4×#6923—21no—
90C4×#6923—41no—
91#11758213—21no—
92#11758213—41no—
93#11758213—41no—
94D61⋊C8—21no—
95D8×C61—21no—
96D8×C61C4⋊C412yes—
97M16×C61—21no—
98C2×C8×C61C22×C411yescharacteristic
99#11758199—22no—
100#11758199—22no—
101#11758194—21no—
102C2×#92418#4111yescharacteristic
103D488—21no—
104D488C4⋊C412yes—
105#11758189—41no—
106C8×D61—41no—
107C8×D61C2×D411yescharacteristic
108C8×D61C2×D411yescharacteristic
109C8×D61C2×Q811yescharacteristic
110C8×D61#4111yescharacteristic
111#11758187—41no—
112C16×C61—21no—
113#11758185—21no—
114C23×C61—41no—
115C22×D61—41no—
116C22×D61—42no—
117C22×D61—42no—
118C22×D61—161no—
119C22×D61—161no—
120C22×D61C2×SD1611yescharacteristic
121C2×#6923—22no—
122C2×#6923—41no—
123C2×#6923—41no—
124C2×#6923—162no—
125C2×#6923—162no—
126D4×C61—22no—
127D4×C61—41no—
128C2×C4×C61C4×D411yescharacteristic
129C22⋊D61—42no—
130C22⋊D61—42no—
131C2×Dic61#13511yescharacteristic
132D244—22no—
133D244—41no—
134C4×D61#12011yescharacteristic
135C4×D61C22⋊Q811yescharacteristic
136C4×D61AGL(1,ℤ/8)11yescharacteristic
137C4×D61AGL(1,ℤ/8)11yescharacteristic
138#92420—41no—
139#92420—81no—
140C8×C61—41no—
141C8×C61C2×C4⋊C411yescharacteristic
142C8×C61C4×D411yescharacteristic
143#92418—41no—
144#92418C22⋊Q811yescharacteristic
145#92418#12311yescharacteristic
146#12953—611nomaximal, Sylow
147C22×C61—42no—
148C22×C61—161no—
149C22×C61C4×SD1611yescharacteristic
150C2×D61—41no—
151C2×D61—42no—
152C2×D61—82no—
153C2×D61—82no—
154C2×D61—162no—
155C2×D61—161no—
156C2×D61#45011yescharacteristic
157C2×D61#47611yescharacteristic
158#6923—42no—
159#6923—81no—
160#6923—81no—
161C4×C61#38511yescharacteristic
162C4×C61#44211yescharacteristic
163Dic61#44911yescharacteristic
164Dic61#47811yescharacteristic
165#2948—611no—
166#2155—611no—
167C2×#361—611no—
168C2×#361—611no—
169#1953—611no—
170#1389—611no—
171#1378—611no—
172C2×C61—21no—
173C2×C61—82no—
174C2×C61#186411yescharacteristic
175D61—21no—
176D61—21no—
177D61—82no—
178C22×D8—611no—
179#518—1221no—
180C2×M32—611no—
181C2×M32—611no—
182#442—1221no—
183#442—1221no—
184C4×D8—1222no—
185#430—1221no—
186C2×#108—611no—
187C2×#108—611no—
188#427—611no—
189#418—1221no—
190#405—611no—
191#365—1221no—
192#365—1221no—
193#361—611no—
194#361—611no—
195#361—611no—
196#361—1222no—
197#361#692311yescharacteristic, complemented
198#344—1221no—
199C61#1295311yescharacteristic, complemented, Sylow
200C22×D4—1221no—
201C2×D8—612no—
202C2×D8—612no—
203C2×D8—611no—
204C2×D8—1221no—
205C2×D8—1221no—
206C2×D8—1221no—
207C2×D8C2×#692311yescharacteristic
208C2×M16—611no—
209C2×M16—1221no—
210C2×M16—1221no—
211C22×C8—611no—
212C4×D4—1222no—
213C4×D4—1222no—
214C4×D4—2441no—
215C4×D4—2441no—
216#117—611no—
217#117—1221no—
218C2×C22⋊C4—2442no—
219M32—611no—
220M32—1221no—
221M32—1221no—
222M32—1221no—
223M32C2×#692311yescharacteristic, complemented
224C2×C16—1221no—
225C2×C16—1221no—
226#108—611no—
227#108—1221no—
228#108—1221no—
229#108—1221no—
230#108—2441no—
231#108—2441no—
232#108C2×#692311yescharacteristic, complemented
233#107—1221no—
234#106—611no—
235#106—611no—
236#102—1222no—
237#102—1222no—
238#97—1221no—
239C4×C8—1221no—
240C24—2441no—
241C2×D4—21no—
242C2×D4—1222no—
243C2×D4—1222no—
244C2×D4—1221no—
245C2×D4—2441no—
246C2×D4—2441no—
247C2×D4—2441no—
248C22×C4—611no—
249C22×C4—2442no—
250C22×C4—2442no—
251D8—21no—
252D8—612no—
253D8—1222no—
254D8—1222no—
255D8—1221no—
256D8C4⋊#692312yes—
257M16—21no—
258M16—1221no—
259M16—1221no—
260M16—1221no—
261M16—2441no—
262M16—2441no—
263M16—2441no—
264C2×C8—611no—
265C2×C8—611no—
266C2×C8—611no—
267C2×C8—611no—
268C2×C8—611no—
269C2×C8—1221no—
270C2×C8—2441no—
271C2×C8—2441no—
272C2×C8C22×#692311yescharacteristic
273C4⋊C4—1221no—
274C4⋊C4—1221no—
275C4⋊C4—1221no—
276C22⋊C4—612no—
277C22⋊C4—2442no—
278C22⋊C4—2442no—
279C22⋊C4—2441no—
280C42—1221no—
281C42—2441no—
282C16—21no—
283C16—1221no—
284C16—2441no—
285C23—41no—
286C23—611no—
287C23—9761no—
288C23—9761no—
289C23—2442no—
290C23—2442no—
291C23—2441no—
292D4—22no—
293D4—41no—
294D4—1222no—
295D4—2442no—
296D4—2442no—
297D4—2441no—
298C2×C4—611no—
299C2×C4—611no—
300C2×C4—611no—
301C2×C4—611no—
302C2×C4—611no—
303C2×C4—1222no—
304C2×C4—9762no—
305C2×C4—9762no—
306C2×C4—2441no—
307C2×C4—2441no—
308C2×C4D4×#692311yescharacteristic
309C8—41no—
310C8—611no—
311C8—611no—
312C8—4881no—
313C8—2441no—
314C8—2441no—
315C8C2×C4⋊#692311yescharacteristic
316C8D4×#692311yescharacteristic
317C22—42no—
318C22—161no—
319C22—611no—
320C22—611no—
321C22—9761no—
322C22—9762no—
323C22—4882no—
324C22—4882no—
325C22—2441no—
326C22—2442no—
327C22SD16×#692311yescharacteristic
328C4—611no—
329C4—611no—
330C4—4881no—
331C4—4881no—
332C4—2442no—
333C4#1684070911yescharacteristic
334C4#1684080311yescharacteristic
335C2—21no—
336C2—82no—
337C2—1221no—
338C2—1221no—
339C2—4882no—
340C2#2146178411yescharacteristic
subgroupG/H
centerC2#21461784
commutatorC2×C8×C61C22×C4
FrattiniC2×C8C22×#6923
FittingC61×#361C4
socleC2×C61#1864
prime radicalC2×D8×D61C22
cosocleC2×C8×D61C23
hypercenter#361#6923
hypocenterC61#12953
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #361

Complements

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

NH ≅ G/Ntype
2. #21462167C2semidirect
4. #21461938C2semidirect
5. #21460899C2semidirect
6. #21460871C2semidirect
25. #16839576C4semidirect
26. #16839575C4semidirect
27. #16839574C4semidirect
28. C61×#361C4semidirect
61. #14519717C2×C4semidirect
64. #14519713C2×C4semidirect
67. M32×C61C2×C4semidirect
68. #108×C61C2×C4semidirect
197. #361#6923semidirect
199. C61#12953semidirect
223. M32C2×#6923semidirect
232. #108C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214625782
#214621672
C2×#168406802
#214619382
#214608992
#214608712
#361×D612
#1295361