Finite Group Databasebeta

← #29584235

Subgroups — #29584235

Order 15616.

490 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
1C2×#16840110C211yesmaximal, characteristic
2#21446746C211yesmaximal, characteristic
3#21446538C211yesmaximal, characteristic, complemented
4C2×#16839511C211yesmaximal, characteristic, complemented
5C2×#16839505C211yesmaximal, characteristic
6#21443653C211yesmaximal, characteristic, complemented
7C61×#1987C211yesmaximal, characteristic, complemented
8C2×#14519774C2211yescharacteristic
9#16840110—22no—
10#16840110—22no—
11C2×C4⋊#92418—21no—
12C2×C4⋊#92418C2211yescharacteristic
13C2×C4⋊#92418C2211yescharacteristic
14C2×#14519697—21no—
15C2×#14519697—21no—
16C2×#14519697—21no—
17C2×#14519697—21no—
18C2×C4×#92418C2211yescharacteristic
19#16839517—21no—
20#16839511—22no—
21#16839505—22no—
22C2×C4⋊Q8×C61C2211yescharacteristic
23C2×C4⋊C8×C61C2211yescharacteristic
24C4×C4⋊C4×C61C2211yescharacteristic
25C61×#340—21no—
26C61×#340—21no—
27C22×D244—21no—
28C22×D244—21no—
29C22×D244—21no—
30C22×#92418—21no—
31C22×#92418—21no—
32C22×#92418D411yescharacteristic
33C22×#92418D411yescharacteristic
34#14519774—21no—
35#14519774—21no—
36#14519774—21no—
37#14519774D412yes—
38C4⋊#92418—21no—
39C4⋊#92418—21no—
40C4⋊#92418—21no—
41C4⋊#92418—21no—
42C4⋊#92418—42no—
43#14519697—24no—
44#14519697—24no—
45#14519697—42no—
46#14519697—42no—
47C4×#92418—21no—
48C4×#92418—21no—
49C22×Q8×C61—21no—
50C22×C8×C61—21no—
51C4⋊Q8×C61—21no—
52C4⋊Q8×C61—21no—
53C4⋊Q8×C61—21no—
54C4⋊Q8×C61D412yes—
55C2×C4⋊C4×C61—21no—
56C2×C4⋊C4×C61—21no—
57C2×C4⋊C4×C61D411yescharacteristic
58C2×C4⋊C4×C61D411yescharacteristic
59C2×C42×C61—21no—
60C2×C42×C61C2311yescharacteristic
61C4⋊C8×C61—21no—
62C4⋊C8×C61—21no—
63#95×C61—21no—
64C23×D61—41no—
65C2×Q8×C61—22no—
66C2×Q8×C61—41no—
67C2×Q8×C61—81no—
68C2×Q8×C61—81no—
69C22×C4×C61—21no—
70C22×C4×C61—21no—
71C22×C4×C61—41no—
72C22×C4×C61C2×D411yescharacteristic
73C22×C4×C61C2×D411yescharacteristic
74C22×C4×C61#4111yescharacteristic
75C2×D244—22no—
76C2×D244—22no—
77C2×D244—22no—
78C2×D244—41no—
79C2×D244—41no—
80C2×D244—41no—
81C2×D244—41no—
82C2×D244—41no—
83C2×D244—41no—
84C2×D244—41no—
85C2×D244—41no—
86C2×D244—41no—
87C2×D244—41no—
88C2×D244—41no—
89C2×D244—81no—
90C2×D244—81no—
91C2×C8×C61—41no—
92C2×C8×C61—41no—
93C2×C8×C61—41no—
94C4⋊C4×C61—21no—
95C4⋊C4×C61—22no—
96C4⋊C4×C61—22no—
97C4⋊C4×C61—21no—
98C4⋊C4×C61—21no—
99C4⋊C4×C61—41no—
100C4⋊C4×C61—41no—
101C4⋊C4×C61SD1612yes—
102C42×C61—41no—
103C42×C61—41no—
104C42×C61C2×D411yescharacteristic
105C42×C61C2×D411yescharacteristic
106C42×C61#4111yescharacteristic
107C42×C61#4111yescharacteristic
108C2×#92418—21no—
109C2×#92418—21no—
110C2×#92418—21no—
111C2×#92418—21no—
112C2×#92418—21no—
113C2×#92418—21no—
114C2×#92418—41no—
115C2×#92418—41no—
116C2×#92418—41no—
117C2×#92418—41no—
118C2×#92418—41no—
119C2×#92418—41no—
120C23×C61#12111yescharacteristic
121C22×D61—42no—
122C22×D61—81no—
123C22×D61—81no—
124C22×D61—81no—
125C22×D61—81no—
126C22×D61—81no—
127C22×D61—81no—
128Q8×C61—82no—
129Q8×C61—82no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—22no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—42no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61—81no—
140C2×C4×C61—81no—
141C2×C4×C61#12011yescharacteristic
142C2×C4×C61#12111yescharacteristic
143C2×C4×C61#12111yescharacteristic
144C2×C4×C61#12311yescharacteristic
145C2×C4×C61#12311yescharacteristic
146C2×C4×C61#12411yescharacteristic
147C2×C4×C61C2×SD1611yescharacteristic
148C2×C4×C61#13511yescharacteristic
149C2×C4×C61#13511yescharacteristic
150C2×C4×C61#13511yescharacteristic
151C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
152C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C61#13711yescharacteristic
154C2×C4×C61#13711yescharacteristic
155D244—42no—
156D244—42no—
157D244—42no—
158D244—42no—
159D244—82no—
160D244—82no—
161D244—81no—
162D244—81no—
163D244—81no—
164D244—81no—
165C8×C61—81no—
166#92418—41no—
167#92418—41no—
168#92418—81no—
169#92418—81no—
170#10539—611nomaximal, Sylow
171C22×C61#39411yescharacteristic
172C22×C61#46311yescharacteristic
173C22×C61#46411yescharacteristic
174C22×C61#46511yescharacteristic
175C22×C61#46811yescharacteristic
176C22×C61#47211yescharacteristic
177C22×C61#47211yescharacteristic
178C2×D61—82no—
179C2×D61—82no—
180C2×D61—82no—
181C2×D61—161no—
182C2×D61—161no—
183C2×D61—161no—
184C2×D61—161no—
185C4×C61—21no—
186C4×C61—21no—
187C4×C61—42no—
188C4×C61—81no—
189C4×C61—82no—
190C4×C61#44911yescharacteristic
191C4×C61#45211yescharacteristic
192C4×C61#46011yescharacteristic
193C4×C61#46111yescharacteristic
194C4×C61#46311yescharacteristic
195C4×C61#46411yescharacteristic
196C4×C61#48811yescharacteristic
197C4×C61#48911yescharacteristic
198C2×#486—611no—
199#1987D6111yescharacteristic, complemented
200#1982—611no—
201#1939—611no—
202C2×#333—611no—
203C2×#331—611no—
204#1277—611no—
205C2×C61#167711yescharacteristic
206C2×C61#167811yescharacteristic
207C2×C61#169711yescharacteristic
208C2×C61#169811yescharacteristic
209C2×C61#204211yescharacteristic
210C2×C61#204511yescharacteristic
211C2×C61#205511yescharacteristic
212D61—162no—
213C2×C4⋊Q8C2×D6111yescharacteristic
214C2×#127—611no—
215#486—1222no—
216#486—1222no—
217C2×C4⋊C8—611no—
218C2×C4⋊C8—611no—
219C2×C4⋊C8—1221no—
220C2×C4⋊C8C2×D6111yescharacteristic
221C2×#102—1221no—
222C2×#102—1221no—
223C2×#102—1221no—
224C2×#102—1221no—
225C2×C4×C8—611no—
226C4×C4⋊C4C2×D6111yescharacteristic
227#340—21no—
228#340—21no—
229#336—1221no—
230#333—1222no—
231#331—1222no—
232C61#1053911yescharacteristic, complemented, Sylow
233C22×Q8—21no—
234C22×D4—1221no—
235C22×D4—1221no—
236C22×D4—1221no—
237C22×C8—21no—
238C22×C8—611no—
239C22×C8—611no—
240C22×C8—1221no—
241C22×C8—1221no—
242C4⋊Q8—21no—
243C4⋊Q8—21no—
244C4⋊Q8—21no—
245C4⋊Q8D24412yes—
246#127—612no—
247#127—1221no—
248#127—1221no—
249#127—1221no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4C22⋊D6111yescharacteristic
253C2×C4⋊C4C22⋊D6111yescharacteristic
254C2×C42—21no—
255C2×C42C22×D6111yescharacteristic
256C4⋊C8—21no—
257C4⋊C8—21no—
258C4⋊C8—1221no—
259C4⋊C8—1221no—
260C4⋊C8—1221no—
261C4⋊C8—1221no—
262C4⋊C8—2442no—
263#102—1224no—
264#102—1224no—
265#102—2442no—
266#102—2442no—
267C4×C8—1221no—
268C4×C8—1221no—
269#95—21no—
270C24—2441no—
271C2×Q8—22no—
272C2×Q8—41no—
273C2×Q8—81no—
274C2×Q8—81no—
275C2×D4—1222no—
276C2×D4—1222no—
277C2×D4—1222no—
278C2×D4—4881no—
279C2×D4—4881no—
280C2×D4—2441no—
281C2×D4—2441no—
282C2×D4—2441no—
283C2×D4—2441no—
284C2×D4—2441no—
285C2×D4—2441no—
286C2×D4—2441no—
287C2×D4—2441no—
288C2×D4—2441no—
289C2×D4—2441no—
290C2×D4—2441no—
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—41no—
294C22×C4D4×D6111yescharacteristic
295C22×C4#1175822411yescharacteristic
296C22×C4C2×C22⋊D6111yescharacteristic
297C2×C8—41no—
298C2×C8—41no—
299C2×C8—41no—
300C2×C8—1221no—
301C2×C8—1221no—
302C2×C8—1221no—
303C2×C8—1221no—
304C2×C8—1221no—
305C2×C8—1221no—
306C2×C8—2441no—
307C2×C8—2441no—
308C2×C8—2441no—
309C2×C8—2441no—
310C2×C8—2441no—
311C2×C8—2441no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—22no—
315C4⋊C4—22no—
316C4⋊C4—21no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4#1175820112yes—
320C42—41no—
321C42—41no—
322C42C2×D24411yescharacteristic
323C42#1175822211yescharacteristic
324C42D4×D6111yescharacteristic
325C42#1175822411yescharacteristic
326C23—4881no—
327C23—4881no—
328C23—4881no—
329C23—4881no—
330C23—4881no—
331C23—4881no—
332C23—2442no—
333C23#1451974911yescharacteristic
334Q8—82no—
335Q8—82no—
336D4—4882no—
337D4—4882no—
338D4—4881no—
339D4—4881no—
340D4—4881no—
341D4—4881no—
342D4—2442no—
343D4—2442no—
344D4—2442no—
345D4—2442no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—22no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—42no—
355C2×C4—81no—
356C2×C4—81no—
357C2×C4#1451974711yescharacteristic
358C2×C4#1451974811yescharacteristic
359C2×C4#1451975111yescharacteristic
360C2×C4#1451975911yescharacteristic
361C2×C4#1451976111yescharacteristic
362C2×C4#1451976311yescharacteristic
363C2×C4C2×#1175820111yescharacteristic
364C2×C4#1451979711yescharacteristic
365C2×C4#1451979811yescharacteristic
366C2×C4#1451980011yescharacteristic
367C2×C4#1451980211yescharacteristic
368C2×C4#1451980411yescharacteristic
369C2×C4#1451980811yescharacteristic
370C2×C4#1451980911yescharacteristic
371C8—81no—
372C8—4881no—
373C8—4881no—
374C8—2441no—
375C8—2441no—
376C22—9761no—
377C22—9761no—
378C22—9761no—
379C22—9761no—
380C22—4882no—
381C22—4882no—
382C22—4882no—
383C22#1683967811yescharacteristic
384C22#1683997911yescharacteristic
385C22#1683998611yescharacteristic
386C22#1683999311yescharacteristic
387C22#1684001011yescharacteristic
388C22#1684003011yescharacteristic
389C22#1684003011yescharacteristic
390C4—21no—
391C4—21no—
392C4—42no—
393C4—82no—
394C4—81no—
395C4#1683991011yescharacteristic
396C4#1683992711yescharacteristic
397C4#1683996211yescharacteristic
398C4#1683996411yescharacteristic
399C4#1683997411yescharacteristic
400C4#1683998411yescharacteristic
401C4#1684011811yescharacteristic
402C4#1684012311yescharacteristic
403C2—9762no—
404C2#2144523011yescharacteristic
405C2#2144523711yescharacteristic
406C2#2144535411yescharacteristic
407C2#2144536111yescharacteristic
408C2#2144705711yescharacteristic
409C2#2144707411yescharacteristic
410C2#2144713411yescharacteristic
subgroupG/H
centerC23#14519749
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1987C2
socleC23×C61#121
prime radicalC2×#14519774C22
hypercenter#1987D61
hypocenterC61#10539
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1987

Complements

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

NH ≅ G/Ntype
3. #21446538C2semidirect
4. C2×#16839511C2semidirect
6. #21443653C2semidirect
7. C61×#1987C2semidirect
199. #1987D61semidirect
232. C61#10539semidirect

Maximal subgroups

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

subgroupindex
C2×#168401102
#214467462
#214465382
C2×#168395112
C2×#168395052
#214436532
C61×#19872
#1053961