Finite Group Databasebeta

← #29596929

Subgroups — #29596929

Order 15616.

456 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#21454720C211yesmaximal, characteristic
2#21447447C211yesmaximal, characteristic, complemented
3C2×#16839545C211yesmaximal, characteristic, complemented
4#21447439C211yesmaximal, characteristic, complemented
5#21443907C211yesmaximal, characteristic, complemented
6#21443906C211yesmaximal, characteristic, complemented
7C2×C61×#504C211yesmaximal, characteristic, complemented
8#16840560C411yescharacteristic
9C2×#14519783C2211yescharacteristic
10C2×#14519717C2211yescharacteristic
11C2×#14519717C2211yescharacteristic
12#16839882—22no—
13#16839877—22no—
14#16839810C411yescharacteristic
15#16839779C411yescharacteristic
16#16839778C411yescharacteristic
17#16839717C2211yescharacteristic
18#16839546—22no—
19#16839545—21no—
20#16839545—21no—
21#16839543—22no—
22C2×#131×C61C2211yescharacteristic
23C61×#504—22no—
24C61×#504—22no—
25C2×M32×C61—21no—
26C2×M32×C61C2211yescharacteristic
27C22×C16×C61—21no—
28C22×C16×C61C2211yescharacteristic
29C2×#11758222C2×C411yescharacteristic
30#14519808—21no—
31#14519807C812yes—
32#14519803—21no—
33#14519802C812yes—
34#14519797—22no—
35#14519783—21no—
36#14519783—21no—
37#14519783—21no—
38#14519783—21no—
39C2×#11758194C2×C411yescharacteristic
40C2×#11758194C2×C411yescharacteristic
41C2×#11758189—21no—
42C2×C8×D61—21no—
43#14519736C2×C411yescharacteristic
44#14519717—21no—
45#14519717—21no—
46#14519717—21no—
47#14519717—21no—
48C2×#11758185—21no—
49C2×#11758185—21no—
50#14519712—22no—
51#14519704—22no—
52#14519703—22no—
53#14519687—21no—
54C8×Dic61—21no—
55C2×#41×C61C2×C411yescharacteristic
56#131×C61—21no—
57#131×C61—21no—
58#131×C61D412yes—
59#131×C61D412yes—
60C2×M16×C61—21no—
61C2×M16×C61C2×C411yescharacteristic
62C22×C8×C61—21no—
63C22×C8×C61C2311yescharacteristic
64M32×C61—24no—
65M32×C61—21no—
66M32×C61D412yes—
67C2×C16×C61—24no—
68C2×C16×C61—21no—
69C2×C16×C61—21no—
70C2×C16×C61—21no—
71C2×C16×C61D411yescharacteristic
72C2×C16×C61D411yescharacteristic
73#41×C61—21no—
74#41×C61—21no—
75#41×C61C22⋊C412yes—
76#41×C61C2×C812yes—
77C2×Q8×C61M1611yescharacteristic
78C2×D4×C61—21no—
79C2×D4×C61M1611yescharacteristic
80C22×C4×C61—21no—
81C22×C4×C61C22×C411yescharacteristic
82C2×C22⋊D61—21no—
83#11758222—21no—
84#11758222—21no—
85#11758222—21no—
86#11758222—21no—
87C2×D244C2×C811yescharacteristic
88C2×C4×D61—21no—
89C2×Dic122C2×C811yescharacteristic
90M16×C61—21no—
91M16×C61—22no—
92M16×C61—22no—
93M16×C61C22⋊C412yes—
94C2×C8×C61—21no—
95C2×C8×C61—22no—
96C2×C8×C61—22no—
97C2×C8×C61C2×D411yescharacteristic
98C2×C8×C61C2×D411yescharacteristic
99C2×C8×C61C2×D411yescharacteristic
100C2×C8×C61C2×D411yescharacteristic
101C2×C8×C61#4111yescharacteristic
102C2×C8×C61#4111yescharacteristic
103C22⋊Dic61—21no—
104#11758202—22no—
105#11758201—22no—
106#11758200—22no—
107#11758199—22no—
108C4⋊Dic61—21no—
109C4×Dic61—21no—
110#11758194—21no—
111#11758194—21no—
112#11758194—21no—
113#11758194C2×C812yes—
114C2×#92418—21no—
115C2×#92418—21no—
116#11758189—41no—
117#11758189—41no—
118C8×D61—41no—
119C8×D61—41no—
120C16×C61—21no—
121C16×C61—22no—
122C16×C61—21no—
123#11758185—41no—
124#11758185—41no—
125C23×C61—21no—
126C23×C61#13111yescharacteristic
127C22×D61—21no—
128Q8×C61—21no—
129Q8×C61C22⋊C812yes—
130D4×C61—22no—
131D4×C61—22no—
132D4×C61—21no—
133D4×C61C22⋊C812yes—
134C2×C4×C61—21no—
135C2×C4×C61—22no—
136C2×C4×C61—22no—
137C2×C4×C61C2×C22⋊C411yescharacteristic
138C2×C4×C61C4×D411yescharacteristic
139C2×C4×C61C4×D411yescharacteristic
140C2×C4×C61C22×C811yescharacteristic
141C2×C4×C61C2×M1611yescharacteristic
142C2×C4×C61#13111yescharacteristic
143C22⋊D61—41no—
144C22⋊D61—41no—
145C2×Dic61—21no—
146C2×Dic61—41no—
147D244—21no—
148D244—21no—
149C4×D61—41no—
150C4×D61—41no—
151Dic122—21no—
152Dic122—21no—
153C8×C61—22no—
154C8×C61#12011yescharacteristic
155C8×C61#12111yescharacteristic
156C8×C61#12111yescharacteristic
157C8×C61#12311yescharacteristic
158#92418—22no—
159#92418—41no—
160#12987—611nomaximal, Sylow
161C22×C61—22no—
162C22×C61—41no—
163C22×C61—42no—
164C22×C61#40811yescharacteristic
165C22×C61C8×D411yescharacteristic
166C22×C61#43511yescharacteristic
167C2×D61—41no—
168C2×D61—81no—
169C4×C61—22no—
170C4×C61#38611yescharacteristic
171C4×C61C2×C22⋊C811yescharacteristic
172C4×C61C8×D411yescharacteristic
173C4×C61#43511yescharacteristic
174Dic61—41no—
175Dic61—81no—
176C2×#504D6111yescharacteristic, complemented
177#2955—611no—
178#2117—611no—
179C2×#350—611no—
180#2115—611no—
181#1379—611no—
182#1378—611no—
183C2×C61—21no—
184C2×C61—21no—
185C2×C61—21no—
186C2×C61—42no—
187C2×C61#186911yescharacteristic
188D61—81no—
189#575—611no—
190C2×#131—611no—
191C2×#131C2×D6111yescharacteristic
192#504—22no—
193#504—22no—
194C2×M32—21no—
195C2×M32—611no—
196C2×M32—611no—
197C2×M32C2×D6111yescharacteristic
198C22×C16—21no—
199C22×C16C2×D6111yescharacteristic
200#444—1222no—
201#443—1222no—
202#430—611no—
203#421—611no—
204#421—611no—
205#405—611no—
206#350—1222no—
207#350—1221no—
208#350—1221no—
209#349—1222no—
210C61#1298711yescharacteristic, complemented, Sylow
211C2×#41—611no—
212C2×#41C4×D6111yescharacteristic
213#137—612no—
214#137—1221no—
215AGL(1,ℤ/8)—612no—
216AGL(1,ℤ/8)—1221no—
217#135—1222no—
218#131—21no—
219#131—21no—
220#131—1221no—
221#131—1221no—
222#131—1221no—
223#131—1221no—
224#131D24412yes—
225#131C22⋊D6112yes—
226C2×M16—21no—
227C2×M16—611no—
228C2×M16—611no—
229C2×M16—1221no—
230C2×M16C4×D6111yescharacteristic
231C22×C8—21no—
232C22×C8—1221no—
233C22×C8C22×D6111yescharacteristic
234#117—611no—
235M32—24no—
236M32—21no—
237M32—1221no—
238M32—1221no—
239M32—1221no—
240M32—1221no—
241M32C22⋊D6112yes—
242C2×C16—24no—
243C2×C16—21no—
244C2×C16—21no—
245C2×C16—21no—
246C2×C16—1221no—
247C2×C16—1221no—
248C2×C16C22⋊D6111yescharacteristic
249C2×C16C22⋊D6111yescharacteristic
250#108—1222no—
251#104—1222no—
252#104—1222no—
253#97—1221no—
254C4×C8—1221no—
255#41—21no—
256#41—21no—
257#41—1221no—
258#41—1221no—
259#41—1221no—
260#41—1221no—
261#41C8×D6112yes—
262#41#1175819812yes—
263C2×Q8—611no—
264C2×Q8#1175818911yescharacteristic
265C2×D4—21no—
266C2×D4—611no—
267C2×D4—1221no—
268C2×D4#1175818911yescharacteristic
269C22×C4—21no—
270C22×C4—1221no—
271C22×C4C2×C4×D6111yescharacteristic
272Q16—1222no—
273SD16—1222no—
274SD16—1222no—
275D8—1222no—
276M16—21no—
277M16—22no—
278M16—22no—
279M16—612no—
280M16—1221no—
281M16—1221no—
282M16—1221no—
283M16—2441no—
284M16—2441no—
285M16#1175819812yes—
286C2×C8—21no—
287C2×C8—22no—
288C2×C8—22no—
289C2×C8—1221no—
290C2×C8—1221no—
291C2×C8—2441no—
292C2×C8—2441no—
293C2×C8C2×D24411yescharacteristic
294C2×C8#1175822211yescharacteristic
295C2×C8#1175822211yescharacteristic
296C2×C8C2×C22⋊D6111yescharacteristic
297C2×C8C2×C22⋊D6111yescharacteristic
298C2×C8C2×C22⋊D6111yescharacteristic
299C4⋊C4—1221no—
300C22⋊C4—1221no—
301C42—1221no—
302C16—21no—
303C16—22no—
304C16—21no—
305C16—2441no—
306C16—2441no—
307C23—21no—
308C23—1221no—
309C23#1451978311yescharacteristic
310Q8—21no—
311Q8—1221no—
312Q8—1221no—
313Q8#1451968912yes—
314D4—22no—
315D4—22no—
316D4—21no—
317D4—1221no—
318D4—1221no—
319D4—2441no—
320D4—2441no—
321D4#1451968912yes—
322C2×C4—21no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—1221no—
326C2×C4—2441no—
327C2×C4—2441no—
328C2×C4—2441no—
329C2×C4C2×#1175819811yescharacteristic
330C2×C4C4×C22⋊D6111yescharacteristic
331C2×C4C4×C22⋊D6111yescharacteristic
332C2×C4C2×C8×D6111yescharacteristic
333C2×C4C2×#1175818911yescharacteristic
334C2×C4#1451978311yescharacteristic
335C8—22no—
336C8—1222no—
337C8—2441no—
338C8#1451974611yescharacteristic
339C8#1451975111yescharacteristic
340C8#1451975111yescharacteristic
341C8#1451976011yescharacteristic
342C22—22no—
343C22—41no—
344C22—42no—
345C22—4881no—
346C22—2441no—
347C22#1683972811yescharacteristic
348C22C8×C22⋊D6111yescharacteristic
349C22#1683983311yescharacteristic
350C4—22no—
351C4—4881no—
352C4—2441no—
353C4#1683964111yescharacteristic
354C4C2×#1451968911yescharacteristic
355C4C8×C22⋊D6111yescharacteristic
356C4#1683983311yescharacteristic
357C2—21no—
358C2—21no—
359C2—21no—
360C2—42no—
361C2—4881no—
362C2#2144611111yescharacteristic
subgroupG/H
centerC8#14519751
commutatorC2×C4×C61C22×C8
FrattiniC22×C8C22×D61
FittingC2×C61×#504C2
socleC2×C61#1869
prime radical#16840560C4
cosocleC22×C8×C61C23
hypercenterC2×#504D61
hypocenterC61#12987
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C8 ◁ C22×C8 ◁ C2×#504

Complements

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

NH ≅ G/Ntype
2. #21447447C2semidirect
3. C2×#16839545C2semidirect
4. #21447439C2semidirect
5. #21443907C2semidirect
6. #21443906C2semidirect
7. C2×C61×#504C2semidirect
176. C2×#504D61semidirect
210. C61#12987semidirect

Maximal subgroups

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

subgroupindex
#214547202
#214474472
C2×#168395452
#214474392
#214439072
#214439062
C2×C61×#5042
#1298761