Finite Group Databasebeta

← #29576561

Subgroups — #29576561

Order 15616.

560 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456737C211yesmaximal, characteristic
2#21454565C211yesmaximal, characteristic, complemented
3#21444497C211yesmaximal, characteristic, complemented
4C2×#16839506C211yesmaximal, characteristic, complemented
5#21443714C211yesmaximal, characteristic, complemented
6#21443670C211yesmaximal, characteristic, complemented
7C61×#1965C211yesmaximal, characteristic, complemented
8C2×#14519785—21no—
9#16840312C2211yescharacteristic
10#16840138—21no—
11#16840108—21no—
12#16839954—22no—
13#16839896C414yes—
14#16839841—21no—
15#16839835—22no—
16C8×D244—21no—
17#16839815C2211yescharacteristic
18C2×C4⋊#92418C2211yescharacteristic
19C2×C4⋊#92418C2211yescharacteristic
20#16839730—21no—
21#16839509—21no—
22#16839506—21no—
23#16839506—21no—
24#16839505—21no—
25C2×#127×C61C2211yescharacteristic
26C61×#423C2211yescharacteristic
27C2×#100×C61—21no—
28C2×#100×C61—21no—
29C4×M16×C61C2211yescharacteristic
30C2×#11758222—21no—
31C2×#11758199—24no—
32#14519785—42no—
33#14519785—42no—
34C2×#11758189—22no—
35C22×#92418—21no—
36C22×#92418—21no—
37C2×C8×D61—22no—
38#14519777D411yescharacteristic
39#14519774D411yescharacteristic
40#14519765—21no—
41#14519751—21no—
42#14519751C2×C412yes—
43C4×D244—21no—
44C4×D244D412yes—
45C4⋊#92418—21no—
46C4⋊#92418—21no—
47C4⋊#92418—21no—
48C4⋊#92418—21no—
49C4⋊#92418D411yescharacteristic
50C4⋊#92418D411yescharacteristic
51#14519698—24no—
52C22⋊#92418C2×C412yes—
53#14519689—22no—
54#14519689—22no—
55C4×#92418—21no—
56C22×D4×C61—21no—
57C22×D4×C61—21no—
58C22×D4×C61C2×C412yes—
59C2×M16×C61—21no—
60C2×M16×C61D411yescharacteristic
61C2×M16×C61D411yescharacteristic
62#127×C61—21no—
63#127×C61—21no—
64#127×C61—21no—
65#127×C61—21no—
66C2×C42×C61C2311yescharacteristic
67C4⋊C8×C61—21no—
68C4⋊C8×C61—21no—
69#100×C61—42no—
70#100×C61—42no—
71#97×C61—21no—
72C4×C8×C61—21no—
73C24×C61—22no—
74C2×D4×C61—22no—
75C2×D4×C61—22no—
76C2×D4×C61—41no—
77C2×D4×C61—41no—
78C2×D4×C61—41no—
79C2×D4×C61—41no—
80C2×D4×C61—41no—
81C2×D4×C61—41no—
82C2×D4×C61—41no—
83C2×D4×C61—41no—
84C2×D4×C61—81no—
85C2×D4×C61—81no—
86C2×D4×C61—82no—
87C22×C4×C61C22×C411yescharacteristic
88C22×C4×C61C2×D411yescharacteristic
89C22×C4×C61#4111yescharacteristic
90C2×C22⋊D61—22no—
91#11758222—41no—
92#11758222—41no—
93#11758222—41no—
94#11758222—41no—
95C2×D244—21no—
96C2×D244—21no—
97C2×D244C22⋊C412yes—
98C2×C4×D61—22no—
99C2×Dic122—21no—
100M16×C61—21no—
101M16×C61—21no—
102M16×C61—21no—
103M16×C61—41no—
104M16×C61—41no—
105M16×C61D812yescomplemented
106C2×C8×C61—21no—
107C2×C8×C61—21no—
108C2×C8×C61—41no—
109C42×C61C2×D411yescharacteristic
110C42×C61C2×D411yescharacteristic
111C42×C61C2×D411yescharacteristic
112C42×C61#4111yescharacteristic
113#11758199—84no—
114#11758198—22no—
115#11758198—22no—
116C4⋊Dic61—21no—
117C4⋊Dic61C22⋊C412yes—
118C2×#92418—22no—
119C2×#92418—21no—
120C2×#92418—21no—
121C2×#92418—41no—
122C2×#92418—41no—
123C2×#92418—41no—
124C2×#92418—81no—
125#11758189—44no—
126C8×D61—44no—
127C23×C61—42no—
128C23×C61—42no—
129C23×C61—42no—
130C23×C61—82no—
131C23×C61—82no—
132C23×C61C4×D411yescharacteristic
133C22×D61—22no—
134D4×C61—44no—
135D4×C61—82no—
136D4×C61—82no—
137D4×C61—81no—
138D4×C61—81no—
139D4×C61—81no—
140D4×C61—81no—
141D4×C61—81no—
142D4×C61—81no—
143C2×C4×C61—21no—
144C2×C4×C61—21no—
145C2×C4×C61—41no—
146C2×C4×C61C2×C22⋊C411yescharacteristic
147C2×C4×C61C4×D411yescharacteristic
148C2×C4×C61#12011yescharacteristic
149C2×C4×C61#12111yescharacteristic
150C2×C4×C61#12111yescharacteristic
151C2×C4×C61#12311yescharacteristic
152C2×C4×C61C2×D811yescharacteristic
153C2×C4×C61#13511yescharacteristic
154C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
155C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
156C22⋊D61—42no—
157C22⋊D61—42no—
158C2×Dic61—22no—
159D244—42no—
160D244—41no—
161D244—41no—
162D244—41no—
163D244—41no—
164C4×D61—42no—
165C4×D61—42no—
166Dic122—41no—
167Dic122—41no—
168C8×C61—22no—
169C8×C61—41no—
170C8×C61—81no—
171#92418—42no—
172#92418—41no—
173#92418—41no—
174#92418—81no—
175#9273—611nomaximal, Sylow
176C22×C61—21no—
177C22×C61—21no—
178C22×C61—82no—
179C22×C61—82no—
180C22×C61—82no—
181C22×C61—162no—
182C22×C61—162no—
183C22×C61#38611yescharacteristic
184C22×C61C4×D811yescharacteristic
185C22×C61#44211yescharacteristic
186C2×D61—42no—
187C2×D61—42no—
188C2×D61—42no—
189C4×C61—21no—
190C4×C61—21no—
191C4×C61—21no—
192C4×C61#44711yescharacteristic
193C4×C61#44911yescharacteristic
194C4×C61#45911yescharacteristic
195C4×C61#46311yescharacteristic
196C4×C61#47111yescharacteristic
197C4×C61#47211yescharacteristic
198Dic61—42no—
199#3205—611no—
200#2935—611no—
201#1965D6111yescharacteristic, complemented
202#1547—611no—
203C2×#331—611no—
204#1301—611no—
205#1283—611no—
206C2×C61—21no—
207C2×C61—21no—
208C2×C61—162no—
209C2×C61#187911yescharacteristic
210C2×C61#190711yescharacteristic
211C2×C61#191411yescharacteristic
212D61—82no—
213C2×#131—1221no—
214#532—611no—
215C2×#127C2×D6111yescharacteristic
216#493—1221no—
217#486—1221no—
218#459—1222no—
219#447—614no—
220#436—1221no—
221#435—1222no—
222C8×D4—1221no—
223#431—611no—
224#423C2×D6111yescharacteristic
225C2×C4⋊C8—611no—
226C2×C4⋊C8—611no—
227C2×#100—21no—
228C2×#100—21no—
229#408—1221no—
230C4×M16C2×D6111yescharacteristic
231#332—1221no—
232#331—1221no—
233#331—1221no—
234#331—1221no—
235C61#927311yescharacteristic, complemented, Sylow
236C2×#41—1221no—
237C22×D4—21no—
238C22×D4—21no—
239C22×D4C4×D6112yes—
240C2×D8—1224no—
241#131—2442no—
242#131—2442no—
243C2×M16—21no—
244C2×M16—1222no—
245C2×M16C22⋊D6111yescharacteristic
246C2×M16C22⋊D6111yescharacteristic
247C22×C8—1222no—
248C22×C8—1221no—
249C22×C8—1221no—
250C4⋊Q8—611no—
251#127—21no—
252#127—21no—
253#127—21no—
254#127—21no—
255#127—611no—
256#124—1221no—
257#121—612no—
258#121—1221no—
259C4×D4—612no—
260C4×D4—1221no—
261C2×C42C22×D6111yescharacteristic
262C4⋊C8—21no—
263C4⋊C8—21no—
264C4⋊C8—611no—
265C4⋊C8—611no—
266C4⋊C8—1221no—
267C4⋊C8—1221no—
268C4⋊C8—1221no—
269C4⋊C8—1221no—
270#102—1224no—
271#100—42no—
272#100—42no—
273C22⋊C8—612no—
274C22⋊C8—1222no—
275C22⋊C8—1222no—
276#97—21no—
277C4×C8—21no—
278C4×C8—1221no—
279C24—22no—
280#41—2441no—
281#41—2441no—
282#41—2441no—
283#41—2441no—
284C2×Q8—1221no—
285C2×D4—22no—
286C2×D4—22no—
287C2×D4—41no—
288C2×D4—41no—
289C2×D4—41no—
290C2×D4—41no—
291C2×D4—41no—
292C2×D4—41no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—81no—
296C2×D4—81no—
297C2×D4—82no—
298C2×D4—612no—
299C2×D4—1222no—
300C2×D4—1221no—
301C2×D4—1221no—
302C22×C4—1222no—
303C22×C4C2×C4×D6111yescharacteristic
304C22×C4#1175822211yescharacteristic
305C22×C4C2×C22⋊D6111yescharacteristic
306D8—4884no—
307M16—21no—
308M16—21no—
309M16—21no—
310M16—41no—
311M16—41no—
312M16—2444no—
313M16#1175819912yescomplemented
314C2×C8—21no—
315C2×C8—21no—
316C2×C8—41no—
317C2×C8—1222no—
318C2×C8—1221no—
319C2×C8—1221no—
320C2×C8—4881no—
321C2×C8—2444no—
322C2×C8—2441no—
323C2×C8—2441no—
324C2×C8—2441no—
325C4⋊C4—612no—
326C4⋊C4—1221no—
327C22⋊C4—1222no—
328C22⋊C4—1222no—
329C42D4×D6111yescharacteristic
330C42D4×D6111yescharacteristic
331C42D4×D6111yescharacteristic
332C42#1175822411yescharacteristic
333C23—42no—
334C23—42no—
335C23—42no—
336C23—82no—
337C23—82no—
338C23—1222no—
339C23C4×C22⋊D6111yescharacteristic
340Q8—2441no—
341Q8—2441no—
342D4—44no—
343D4—82no—
344D4—82no—
345D4—81no—
346D4—81no—
347D4—81no—
348D4—81no—
349D4—81no—
350D4—81no—
351D4—2442no—
352D4—2442no—
353D4—2442no—
354D4—2441no—
355D4—2441no—
356D4—2441no—
357D4—2441no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—41no—
361C2×C4—1222no—
362C2×C4—2442no—
363C2×C4—2442no—
364C2×C4C22⋊C4×D6111yescharacteristic
365C2×C4#1451973711yescharacteristic
366C2×C4#1451974511yescharacteristic
367C2×C4#1451974811yescharacteristic
368C2×C4#1451975011yescharacteristic
369C2×C4#1451975911yescharacteristic
370C2×C4C2×#1175819911yescharacteristic
371C2×C4#1451979711yescharacteristic
372C2×C4#1451980211yescharacteristic
373C2×C4#1451980311yescharacteristic
374C8—22no—
375C8—41no—
376C8—81no—
377C8—4881no—
378C8—2442no—
379C8—2441no—
380C8—2441no—
381C22—21no—
382C22—21no—
383C22—82no—
384C22—82no—
385C22—82no—
386C22—162no—
387C22—162no—
388C22—2442no—
389C22—2442no—
390C22—2442no—
391C22#1683963811yescharacteristic
392C22C4×#1175819911yescharacteristic
393C22#1683987211yescharacteristic
394C4—21no—
395C4—21no—
396C4—21no—
397C4—2442no—
398C4#1683989511yescharacteristic
399C4#1683990511yescharacteristic
400C4#1683995411yescharacteristic
401C4#1683997411yescharacteristic
402C4#1684002411yescharacteristic
403C4#1684003111yescharacteristic
404C2—21no—
405C2—21no—
406C2—162no—
407C2—4882no—
408C2#2144617011yescharacteristic
409C2#2144632411yescharacteristic
410C2#2144636311yescharacteristic
subgroupG/H
centerC22#16839638
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1965C2
socleC22×C61#386
prime radical#21456737C2
cosocleC2×C42×C61C23
hypercenter#1965D61
hypocenterC61#9273
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1965

Complements

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

NH ≅ G/Ntype
2. #21454565C2semidirect
3. #21444497C2semidirect
4. C2×#16839506C2semidirect
5. #21443714C2semidirect
6. #21443670C2semidirect
7. C61×#1965C2semidirect
105. M16×C61D8semidirect
201. #1965D61semidirect
235. C61#9273semidirect
313. M16#11758199semidirect

Maximal subgroups

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

subgroupindex
#214567372
#214545652
#214444972
C2×#168395062
#214437142
#214436702
C61×#19652
#927361