Finite Group Databasebeta

← #29576557

Subgroups — #29576557

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#21456739C211yesmaximal, characteristic
2#21454565C211yesmaximal, characteristic, complemented
3#21446659C211yesmaximal, characteristic, complemented
4#21444494C211yesmaximal, characteristic, complemented
5C2×#16839505C211yesmaximal, characteristic, complemented
6#21443715C211yesmaximal, characteristic, complemented
7C61×#1283C211yesmaximal, characteristic, complemented
8C2×#14519785—21no—
9#16840312C2211yescharacteristic
10C2×#14519774C2211yescharacteristic
11#16840139—21no—
12#16840109—21no—
13#16839958—22no—
14#16839898C414yes—
15#16839841—21no—
16#16839835—22no—
17C8×D244—21no—
18#16839786C2211yescharacteristic
19C2×C4⋊#92418C2211yescharacteristic
20C2×#14519693—21no—
21C2×#14519693—21no—
22#16839730—21no—
23#16839507—21no—
24#16839505—21no—
25#16839505—21no—
26#16839505—21no—
27C61×#431C2211yescharacteristic
28C2×C4⋊C8×C61C2211yescharacteristic
29C4×M16×C61C2211yescharacteristic
30C2×#11758222—21no—
31C22×D244—21no—
32C22×D244—21no—
33C22×D244C2×C412yes—
34C2×D488—24no—
35#14519785—42no—
36#14519785—42no—
37C2×#11758194—21no—
38C2×#11758189—22no—
39C22×#92418—21no—
40C2×C8×D61—22no—
41#14519777D411yescharacteristic
42#14519774—21no—
43#14519774—21no—
44#14519774—21no—
45#14519774—21no—
46#14519774D411yescharacteristic
47#14519765—21no—
48#14519751—21no—
49#14519751C2×C412yes—
50C4×D244—21no—
51C4×D244D412yes—
52C4⋊#92418—21no—
53C4⋊#92418—21no—
54C4⋊#92418—21no—
55C4⋊#92418D411yescharacteristic
56C4⋊#92418D411yescharacteristic
57#14519699—24no—
58#14519693—42no—
59#14519693—42no—
60#14519689—22no—
61#14519689—22no—
62C2×M16×C61D411yescharacteristic
63C2×M16×C61D411yescharacteristic
64C22×C8×C61—21no—
65C2×C42×C61C2311yescharacteristic
66C4⋊C8×C61—21no—
67C4⋊C8×C61—21no—
68C4⋊C8×C61—21no—
69C22⋊C8×C61C2×C412yes—
70#97×C61—21no—
71C4×C8×C61—21no—
72C4×C8×C61—21no—
73C23×D61—22no—
74C22×C4×C61C22×C411yescharacteristic
75C22×C4×C61C2×D411yescharacteristic
76C22×C4×C61#4111yescharacteristic
77C2×C22⋊D61—22no—
78#11758222—41no—
79#11758222—41no—
80#11758222—41no—
81#11758222—41no—
82C2×D244—22no—
83C2×D244—21no—
84C2×D244—21no—
85C2×D244—22no—
86C2×D244—41no—
87C2×D244—41no—
88C2×D244—41no—
89C2×D244—41no—
90C2×D244—41no—
91C2×D244—41no—
92C2×D244—41no—
93C2×D244—41no—
94C2×D244—82no—
95C2×D244—81no—
96C2×D244—81no—
97C2×D244C22⋊C412yes—
98C2×C4×D61—22no—
99C2×Dic122—21no—
100M16×C61—21no—
101M16×C61—21no—
102M16×C61—21no—
103M16×C61D812yescomplemented
104C2×C8×C61—21no—
105C2×C8×C61—22no—
106C2×C8×C61—21no—
107C2×C8×C61—41no—
108C2×C8×C61—81no—
109C42×C61C2×D411yescharacteristic
110C42×C61C2×D411yescharacteristic
111C42×C61C2×D411yescharacteristic
112C42×C61#4111yescharacteristic
113#11758198—22no—
114#11758198—22no—
115C4⋊Dic61—21no—
116C4⋊Dic61C22⋊C412yes—
117#11758194—41no—
118#11758194—41no—
119C2×#92418—21no—
120C2×#92418—21no—
121C2×#92418—41no—
122C2×#92418—41no—
123C2×#92418—41no—
124D488—84no—
125#11758189—44no—
126C8×D61—44no—
127C23×C61C4×D411yescharacteristic
128C22×D61—22no—
129C22×D61—42no—
130C22×D61—42no—
131C22×D61—42no—
132C22×D61—82no—
133C22×D61—82no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—41no—
137C2×C4×C61C2×C22⋊C411yescharacteristic
138C2×C4×C61C4×D411yescharacteristic
139C2×C4×C61#12011yescharacteristic
140C2×C4×C61#12111yescharacteristic
141C2×C4×C61#12111yescharacteristic
142C2×C4×C61#12311yescharacteristic
143C2×C4×C61C2×D811yescharacteristic
144C2×C4×C61#13511yescharacteristic
145C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
146C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
147C22⋊D61—42no—
148C22⋊D61—42no—
149C2×Dic61—22no—
150D244—42no—
151D244—44no—
152D244—41no—
153D244—41no—
154D244—41no—
155D244—41no—
156D244—82no—
157D244—82no—
158D244—81no—
159D244—81no—
160D244—81no—
161D244—81no—
162D244—81no—
163D244—81no—
164C4×D61—42no—
165C4×D61—42no—
166Dic122—41no—
167Dic122—41no—
168C8×C61—22no—
169C8×C61—42no—
170C8×C61—41no—
171C8×C61—81no—
172#92418—41no—
173#92418—41no—
174#92418—81no—
175#9273—611nomaximal, Sylow
176C22×C61—21no—
177C22×C61—21no—
178C22×C61#38611yescharacteristic
179C22×C61C4×D811yescharacteristic
180C22×C61#44211yescharacteristic
181C2×D61—42no—
182C2×D61—42no—
183C2×D61—42no—
184C2×D61—82no—
185C2×D61—82no—
186C2×D61—82no—
187C2×D61—162no—
188C2×D61—162no—
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#1965—611no—
202#1547—611no—
203C2×#331—611no—
204#1301—611no—
205#1283D6111yescharacteristic, complemented
206C2×C61—21no—
207C2×C61—21no—
208C2×C61#187911yescharacteristic
209C2×C61#190711yescharacteristic
210C2×C61#191411yescharacteristic
211D61—82no—
212D61—162no—
213C2×#131—1221no—
214#532—611no—
215C2×#127—611no—
216#493—1221no—
217#486—1221no—
218#459—1222no—
219#447—614no—
220#436—1221no—
221#435—1222no—
222C8×D4—1221no—
223#431C2×D6111yescharacteristic
224#423—611no—
225C2×C4⋊C8—611no—
226C2×C4⋊C8C2×D6111yescharacteristic
227C2×#100—1221no—
228C2×#100—1221no—
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—612no—
238C22×D4—1221no—
239C22×D4—1221no—
240C2×D8—1224no—
241#131—2442no—
242#131—2442no—
243C2×M16—1222no—
244C2×M16—1221no—
245C2×M16D24411yescharacteristic
246C2×M16D24411yescharacteristic
247C22×C8—21no—
248C22×C8—1222no—
249C22×C8—1221no—
250C4⋊Q8—611no—
251#127—611no—
252#127—1221no—
253#127—1221no—
254#127—1221no—
255#127—1221no—
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—21no—
265C4⋊C8—611no—
266C4⋊C8—611no—
267C4⋊C8—1221no—
268C4⋊C8—1221no—
269C4⋊C8—1221no—
270#102—1224no—
271#100—2442no—
272#100—2442no—
273C22⋊C8—1222no—
274C22⋊C8—1222no—
275C22⋊C8C4×D6112yes—
276#97—21no—
277C4×C8—21no—
278C4×C8—21no—
279C24—1222no—
280#41—2441no—
281#41—2441no—
282#41—2441no—
283#41—2441no—
284C2×Q8—1221no—
285C2×D4—612no—
286C2×D4—1222no—
287C2×D4—1222no—
288C2×D4—1222no—
289C2×D4—1221no—
290C2×D4—1221no—
291C2×D4—4881no—
292C2×D4—4881no—
293C2×D4—4882no—
294C2×D4—2441no—
295C2×D4—2441no—
296C2×D4—2441no—
297C2×D4—2441no—
298C2×D4—2441no—
299C2×D4—2441no—
300C2×D4—2441no—
301C2×D4—2441no—
302C22×C4—1222no—
303C22×C4C2×C4×D6111yescharacteristic
304C22×C4C2×D24411yescharacteristic
305C22×C4#1175822211yescharacteristic
306D8—4884no—
307M16—21no—
308M16—21no—
309M16—21no—
310M16—2444no—
311M16—2441no—
312M16—2441no—
313M16D48812yescomplemented
314C2×C8—21no—
315C2×C8—22no—
316C2×C8—21no—
317C2×C8—41no—
318C2×C8—81no—
319C2×C8—1221no—
320C2×C8—1221no—
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#1175822611yescharacteristic
333C23—1222no—
334C23—4882no—
335C23—4882no—
336C23—2442no—
337C23—2442no—
338C23—2442no—
339C23C4×D24411yescharacteristic
340Q8—2441no—
341Q8—2441no—
342D4—4882no—
343D4—4882no—
344D4—4881no—
345D4—4881no—
346D4—4881no—
347D4—4881no—
348D4—4881no—
349D4—4881no—
350D4—2444no—
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#1451973911yescharacteristic
366C2×C4#1451974711yescharacteristic
367C2×C4#1451975011yescharacteristic
368C2×C4#1451975211yescharacteristic
369C2×C4#1451976211yescharacteristic
370C2×C4C2×D48811yescharacteristic
371C2×C4#1451979911yescharacteristic
372C2×C4#1451980511yescharacteristic
373C2×C4#1451980511yescharacteristic
374C8—22no—
375C8—42no—
376C8—41no—
377C8—81no—
378C8—4881no—
379C8—2441no—
380C8—2441no—
381C22—21no—
382C22—21no—
383C22—9762no—
384C22—9762no—
385C22—4882no—
386C22—4882no—
387C22—4882no—
388C22—2442no—
389C22—2442no—
390C22—2442no—
391C22#1683964011yescharacteristic
392C22C4×D48811yescharacteristic
393C22#1683987511yescharacteristic
394C4—21no—
395C4—21no—
396C4—21no—
397C4—2442no—
398C4#1683989811yescharacteristic
399C4#1683990911yescharacteristic
400C4#1683995811yescharacteristic
401C4#1683997811yescharacteristic
402C4#1684002811yescharacteristic
403C4#1684003111yescharacteristic
404C2—21no—
405C2—21no—
406C2—9762no—
407C2—4882no—
408C2#2144616611yescharacteristic
409C2#2144632811yescharacteristic
410C2#2144636511yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1283C2
socleC22×C61#386
prime radical#21456739C2
cosocleC2×C42×C61C23
hypercenter#1283D61
hypocenterC61#9273
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1283

Complements

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

NH ≅ G/Ntype
2. #21454565C2semidirect
3. #21446659C2semidirect
4. #21444494C2semidirect
5. C2×#16839505C2semidirect
6. #21443715C2semidirect
7. C61×#1283C2semidirect
103. M16×C61D8semidirect
205. #1283D61semidirect
235. C61#9273semidirect
313. M16D488semidirect

Maximal subgroups

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

subgroupindex
#214567392
#214545652
#214466592
#214444942
C2×#168395052
#214437152
C61×#12832
#927361