Finite Group Databasebeta

← #29596883

Subgroups — #29596883

Order 15616.

456 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454720C211yesmaximal, characteristic
2#21447448C211yesmaximal, characteristic, complemented
3C2×#16839546C211yesmaximal, characteristic, complemented
4#21447434C211yesmaximal, characteristic, complemented
5#21443909C211yesmaximal, characteristic, complemented
6#21443904C211yesmaximal, characteristic, complemented
7C61×#3407C211yesmaximal, characteristic, complemented
8#16840560C411yescharacteristic
9C2×#14519783C2211yescharacteristic
10C2×#14519717C2211yescharacteristic
11C22×#11758185C2211yescharacteristic
12#16839882—22no—
13#16839877—22no—
14#16839810C411yescharacteristic
15#16839779C411yescharacteristic
16#16839778C411yescharacteristic
17#16839717C2211yescharacteristic
18#16839547—22no—
19#16839546—22no—
20#16839541—22no—
21C2×#131×C61C2211yescharacteristic
22C61×#504—22no—
23C61×#504—22no—
24C2×M32×C61—22no—
25C2×M32×C61C2211yescharacteristic
26C2×M32×C61C2211yescharacteristic
27C2×#11758222C2×C411yescharacteristic
28#14519808—21no—
29#14519807C812yes—
30#14519803—21no—
31#14519802C812yes—
32#14519797—22no—
33#14519783—21no—
34#14519783—21no—
35#14519783—21no—
36#14519783—21no—
37C2×#11758194C2×C411yescharacteristic
38C2×#11758194C2×C411yescharacteristic
39C2×#11758189—21no—
40C2×C8×D61—21no—
41#14519736C2×C411yescharacteristic
42#14519717—21no—
43#14519717—21no—
44C2×#11758185—21no—
45C2×#11758185—21no—
46C2×#11758185—21no—
47C2×#11758185—21no—
48#14519712—22no—
49#14519704—22no—
50#14519703—22no—
51#14519687—21no—
52C8×Dic61—21no—
53C2×#41×C61C2×C411yescharacteristic
54#131×C61—21no—
55#131×C61—21no—
56#131×C61D412yes—
57#131×C61D412yes—
58C2×M16×C61—21no—
59C2×M16×C61C2×C411yescharacteristic
60C22×C8×C61—21no—
61C22×C8×C61C2311yescharacteristic
62M32×C61—24no—
63M32×C61—21no—
64M32×C61—21no—
65M32×C61—21no—
66M32×C61D412yes—
67C2×C16×C61—24no—
68C2×C16×C61—21no—
69C2×C16×C61D412yes—
70#41×C61—21no—
71#41×C61—21no—
72#41×C61C22⋊C412yes—
73#41×C61C2×C812yes—
74C2×Q8×C61M1611yescharacteristic
75C2×D4×C61—21no—
76C2×D4×C61M1611yescharacteristic
77C22×C4×C61—21no—
78C22×C4×C61C22×C411yescharacteristic
79C2×C22⋊D61—21no—
80#11758222—21no—
81#11758222—21no—
82#11758222—21no—
83#11758222—21no—
84C2×D244C2×C811yescharacteristic
85C2×C4×D61—21no—
86C2×Dic122C2×C811yescharacteristic
87M16×C61—21no—
88M16×C61—22no—
89M16×C61—22no—
90M16×C61C22⋊C412yes—
91C2×C8×C61—21no—
92C2×C8×C61—22no—
93C2×C8×C61—22no—
94C2×C8×C61C2×D411yescharacteristic
95C2×C8×C61C2×D411yescharacteristic
96C2×C8×C61C2×D411yescharacteristic
97C2×C8×C61C2×D411yescharacteristic
98C2×C8×C61#4111yescharacteristic
99C2×C8×C61#4111yescharacteristic
100C22⋊Dic61—21no—
101#11758202—22no—
102#11758201—22no—
103#11758200—22no—
104#11758199—22no—
105C4⋊Dic61—21no—
106C4×Dic61—21no—
107#11758194—21no—
108#11758194—21no—
109#11758194—21no—
110#11758194C2×C812yes—
111C2×#92418—21no—
112C2×#92418—21no—
113#11758189—41no—
114#11758189—41no—
115C8×D61—41no—
116C8×D61—41no—
117C16×C61—22no—
118C16×C61—22no—
119#11758185—41no—
120#11758185—41no—
121C23×C61—21no—
122C23×C61#13111yescharacteristic
123C22×D61—21no—
124Q8×C61—21no—
125Q8×C61C22⋊C812yes—
126D4×C61—22no—
127D4×C61—22no—
128D4×C61—21no—
129D4×C61C22⋊C812yes—
130C2×C4×C61—21no—
131C2×C4×C61—22no—
132C2×C4×C61—22no—
133C2×C4×C61C2×C22⋊C411yescharacteristic
134C2×C4×C61C4×D411yescharacteristic
135C2×C4×C61C4×D411yescharacteristic
136C2×C4×C61C22×C811yescharacteristic
137C2×C4×C61C2×M1611yescharacteristic
138C2×C4×C61#13111yescharacteristic
139C22⋊D61—41no—
140C22⋊D61—41no—
141C2×Dic61—21no—
142C2×Dic61—41no—
143D244—21no—
144D244—21no—
145C4×D61—41no—
146C4×D61—41no—
147Dic122—21no—
148Dic122—21no—
149C8×C61—22no—
150C8×C61#12011yescharacteristic
151C8×C61#12111yescharacteristic
152C8×C61#12111yescharacteristic
153C8×C61#12311yescharacteristic
154#92418—22no—
155#92418—41no—
156#12979—611nomaximal, Sylow
157C22×C61—22no—
158C22×C61—41no—
159C22×C61—81no—
160C22×C61#40811yescharacteristic
161C22×C61C8×D411yescharacteristic
162C22×C61#43511yescharacteristic
163C2×D61—42no—
164C2×D61—41no—
165C4×C61—22no—
166C4×C61#38611yescharacteristic
167C4×C61C2×C22⋊C811yescharacteristic
168C4×C61C8×D411yescharacteristic
169C4×C61#43511yescharacteristic
170Dic61—41no—
171Dic61—81no—
172#3407D6111yescharacteristic, complemented
173#2955—611no—
174#2117—611no—
175C2×#350—611no—
176#2113—611no—
177#1379—611no—
178#1378—611no—
179C2×C61—21no—
180C2×C61—21no—
181C2×C61—21no—
182C2×C61—42no—
183C2×C61#186911yescharacteristic
184D61—81no—
185#575—611no—
186C2×#131—611no—
187C2×#131C2×D6111yescharacteristic
188#504—22no—
189#504—22no—
190C2×M32—22no—
191C2×M32—611no—
192C2×M32C2×D6111yescharacteristic
193C2×M32C2×D6111yescharacteristic
194C22×C16—611no—
195#444—1222no—
196#443—1222no—
197#430—611no—
198#421—611no—
199#421—611no—
200#405—611no—
201#350—1222no—
202#350—1222no—
203C22⋊C16—1222no—
204C61#1297911yescharacteristic, complemented, Sylow
205C2×#41—611no—
206C2×#41C4×D6111yescharacteristic
207#137—612no—
208#137—1221no—
209AGL(1,ℤ/8)—612no—
210AGL(1,ℤ/8)—1221no—
211#135—1222no—
212#131—21no—
213#131—21no—
214#131—1221no—
215#131—1221no—
216#131—1221no—
217#131—1221no—
218#131D24412yes—
219#131C22⋊D6112yes—
220C2×M16—21no—
221C2×M16—611no—
222C2×M16—611no—
223C2×M16—1221no—
224C2×M16C4×D6111yescharacteristic
225C22×C8—21no—
226C22×C8—1221no—
227C22×C8C22×D6111yescharacteristic
228#117—611no—
229M32—24no—
230M32—21no—
231M32—21no—
232M32—21no—
233M32—1221no—
234M32—1221no—
235M32C22⋊D6112yes—
236C2×C16—24no—
237C2×C16—21no—
238C2×C16—1221no—
239C2×C16—1221no—
240C2×C16—1221no—
241C2×C16—1221no—
242C2×C16C22⋊D6112yes—
243#108—1222no—
244#104—1222no—
245#104—1222no—
246#97—1221no—
247C4×C8—1221no—
248#41—21no—
249#41—21no—
250#41—1221no—
251#41—1221no—
252#41—1221no—
253#41—1221no—
254#41C8×D6112yes—
255#41#1175819812yes—
256C2×Q8—611no—
257C2×Q8#1175818911yescharacteristic
258C2×D4—21no—
259C2×D4—611no—
260C2×D4—1221no—
261C2×D4#1175818911yescharacteristic
262C22×C4—21no—
263C22×C4—1221no—
264C22×C4C2×C4×D6111yescharacteristic
265Q16—1222no—
266SD16—1222no—
267SD16—1222no—
268D8—1222no—
269M16—21no—
270M16—22no—
271M16—22no—
272M16—612no—
273M16—1221no—
274M16—1221no—
275M16—1221no—
276M16—2441no—
277M16—2441no—
278M16#1175819812yes—
279C2×C8—21no—
280C2×C8—22no—
281C2×C8—22no—
282C2×C8—1221no—
283C2×C8—1221no—
284C2×C8—2441no—
285C2×C8—2441no—
286C2×C8C2×D24411yescharacteristic
287C2×C8#1175822211yescharacteristic
288C2×C8#1175822211yescharacteristic
289C2×C8C2×C22⋊D6111yescharacteristic
290C2×C8C2×C22⋊D6111yescharacteristic
291C2×C8C2×C22⋊D6111yescharacteristic
292C4⋊C4—1221no—
293C22⋊C4—1221no—
294C42—1221no—
295C16—22no—
296C16—22no—
297C16—2441no—
298C16—2441no—
299C23—21no—
300C23—1221no—
301C23#1451978311yescharacteristic
302Q8—21no—
303Q8—1221no—
304Q8—1221no—
305Q8#1451968912yes—
306D4—22no—
307D4—22no—
308D4—21no—
309D4—1221no—
310D4—1221no—
311D4—2441no—
312D4—2441no—
313D4#1451968912yes—
314C2×C4—21no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—1221no—
318C2×C4—2441no—
319C2×C4—2441no—
320C2×C4—2441no—
321C2×C4C2×#1175819811yescharacteristic
322C2×C4C4×C22⋊D6111yescharacteristic
323C2×C4C4×C22⋊D6111yescharacteristic
324C2×C4C2×C8×D6111yescharacteristic
325C2×C4C2×#1175818911yescharacteristic
326C2×C4#1451978311yescharacteristic
327C8—22no—
328C8—1222no—
329C8—2441no—
330C8#1451974611yescharacteristic
331C8#1451975111yescharacteristic
332C8#1451975111yescharacteristic
333C8#1451976011yescharacteristic
334C22—22no—
335C22—41no—
336C22—81no—
337C22—2442no—
338C22—2441no—
339C22#1683972811yescharacteristic
340C22C8×C22⋊D6111yescharacteristic
341C22#1683983311yescharacteristic
342C4—22no—
343C4—4881no—
344C4—2441no—
345C4#1683964111yescharacteristic
346C4C2×#1451968911yescharacteristic
347C4C8×C22⋊D6111yescharacteristic
348C4#1683983311yescharacteristic
349C2—21no—
350C2—21no—
351C2—21no—
352C2—42no—
353C2—4881no—
354C2#2144611111yescharacteristic
subgroupG/H
centerC8#14519746
commutatorC2×C4×C61C22×C8
FrattiniC22×C8C22×D61
FittingC61×#3407C2
socleC2×C61#1869
prime radical#16840560C4
cosocleC22×C8×C61C23
hypercenter#3407D61
hypocenterC61#12979
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C8 ◁ C22×C8 ◁ #3407

Complements

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

NH ≅ G/Ntype
2. #21447448C2semidirect
3. C2×#16839546C2semidirect
4. #21447434C2semidirect
5. #21443909C2semidirect
6. #21443904C2semidirect
7. C61×#3407C2semidirect
172. #3407D61semidirect
204. C61#12979semidirect

Maximal subgroups

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

subgroupindex
#214547202
#214474482
C2×#168395462
#214474342
#214439092
#214439042
C61×#34072
#1297961