Finite Group Databasebeta

← #29584238

Subgroups — #29584238

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×#16840109C211yesmaximal, characteristic
2#21446767C211yesmaximal, characteristic, complemented
3#21446746C211yesmaximal, characteristic
4C2×#16839510C211yesmaximal, characteristic, complemented
5C2×#16839505C211yesmaximal, characteristic
6#21443654C211yesmaximal, characteristic, complemented
7C61×#1939C211yesmaximal, characteristic, complemented
8C2×#14519777C2211yescharacteristic
9C2×#14519774C2211yescharacteristic
10#16840109—22no—
11#16840109—22no—
12C2×C4⋊#92418C2211yescharacteristic
13C2×C4⋊#92418C2211yescharacteristic
14C2×#14519699—21no—
15C2×#14519699—21no—
16C2×#14519697—21no—
17C2×#14519697—21no—
18#16839524—21no—
19#16839524—21no—
20#16839510—22no—
21#16839505—22no—
22C2×C4⋊C8×C61—21no—
23C2×C4⋊C8×C61C2211yescharacteristic
24C2×C4×C8×C61C2211yescharacteristic
25C4×C4⋊C4×C61C2211yescharacteristic
26C61×#336—21no—
27C22×Dic122—21no—
28C22×D244—21no—
29C22×D244—21no—
30C22×D244—21no—
31C22×#92418—21no—
32C22×#92418—21no—
33#14519777—21no—
34#14519777—21no—
35#14519777—21no—
36#14519777D412yes—
37#14519774—21no—
38#14519774—21no—
39#14519774—21no—
40#14519774D412yes—
41C2×C4⋊Dic61—21no—
42C2×C4⋊Dic61—21no—
43C4⋊#92418—21no—
44C4⋊#92418—21no—
45C4⋊#92418—21no—
46C4⋊#92418—21no—
47#14519699—24no—
48#14519699—24no—
49#14519697—42no—
50#14519697—42no—
51C22×C8×C61—21no—
52C22×C8×C61D411yescharacteristic
53C22×C8×C61D411yescharacteristic
54C2×C4⋊C4×C61D411yescharacteristic
55C2×C4⋊C4×C61D411yescharacteristic
56C2×C42×C61—21no—
57C2×C42×C61C2311yescharacteristic
58C4⋊C8×C61—21no—
59C4⋊C8×C61—21no—
60C4⋊C8×C61—42no—
61C4×C8×C61—21no—
62C4×C8×C61—21no—
63#95×C61—21no—
64C23×D61—41no—
65C22×C4×C61—21no—
66C22×C4×C61—21no—
67C22×C4×C61C2×D411yescharacteristic
68C22×C4×C61C2×D411yescharacteristic
69C22×C4×C61#4111yescharacteristic
70C22×Dic61—41no—
71C2×D244—22no—
72C2×D244—22no—
73C2×D244—22no—
74C2×D244—41no—
75C2×D244—41no—
76C2×D244—41no—
77C2×D244—41no—
78C2×D244—41no—
79C2×D244—41no—
80C2×D244—41no—
81C2×D244—41no—
82C2×D244—41no—
83C2×D244—41no—
84C2×D244—41no—
85C2×D244—81no—
86C2×D244—81no—
87C2×Dic122—22no—
88C2×Dic122—41no—
89C2×Dic122—81no—
90C2×Dic122—81no—
91C2×C8×C61—21no—
92C2×C8×C61—21no—
93C2×C8×C61—21no—
94C2×C8×C61—21no—
95C2×C8×C61—21no—
96C2×C8×C61—21no—
97C2×C8×C61—41no—
98C2×C8×C61—41no—
99C2×C8×C61—41no—
100C4⋊C4×C61—21no—
101C4⋊C4×C61—21no—
102C4⋊C4×C61—21no—
103C4⋊C4×C61SD1612yes—
104C42×C61—41no—
105C42×C61—41no—
106C42×C61C2×D411yescharacteristic
107C42×C61C2×D411yescharacteristic
108C42×C61#4111yescharacteristic
109C42×C61#4111yescharacteristic
110C4⋊Dic61—22no—
111C4⋊Dic61—22no—
112C4⋊Dic61—41no—
113C4⋊Dic61—41no—
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—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—22no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61#12011yescharacteristic
137C2×C4×C61#12111yescharacteristic
138C2×C4×C61#12111yescharacteristic
139C2×C4×C61#12311yescharacteristic
140C2×C4×C61#12311yescharacteristic
141C2×C4×C61#12411yescharacteristic
142C2×C4×C61C2×SD1611yescharacteristic
143C2×C4×C61#13511yescharacteristic
144C2×C4×C61#13511yescharacteristic
145C2×C4×C61#13511yescharacteristic
146C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
148C2×C4×C61#13711yescharacteristic
149C2×C4×C61#13711yescharacteristic
150C2×Dic61—42no—
151C2×Dic61—81no—
152C2×Dic61—81no—
153D244—42no—
154D244—42no—
155D244—42no—
156D244—42no—
157D244—82no—
158D244—82no—
159D244—81no—
160D244—81no—
161D244—81no—
162D244—81no—
163Dic122—82no—
164Dic122—82no—
165C8×C61—41no—
166C8×C61—41no—
167C8×C61—81no—
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#44911yescharacteristic
190C4×C61#45211yescharacteristic
191C4×C61#46011yescharacteristic
192C4×C61#46111yescharacteristic
193C4×C61#46311yescharacteristic
194C4×C61#46411yescharacteristic
195C4×C61#48811yescharacteristic
196C4×C61#48911yescharacteristic
197Dic61—82no—
198C2×#486—611no—
199#1987—611no—
200#1982—611no—
201#1939D6111yescharacteristic, complemented
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⋊Q8—611no—
214C2×#127—611no—
215#486—1222no—
216#486—1222no—
217C2×C4⋊C8—21no—
218C2×C4⋊C8—611no—
219C2×C4⋊C8—611no—
220C2×C4⋊C8C2×D6111yescharacteristic
221C2×#102—1221no—
222C2×#102—1221no—
223C2×#102—1221no—
224C2×#102—1221no—
225C2×C4×C8C2×D6111yescharacteristic
226C4×C4⋊C4C2×D6111yescharacteristic
227#340—1221no—
228#340—1221no—
229#336—21no—
230#333—1222no—
231#331—1222no—
232C61#1053911yescharacteristic, complemented, Sylow
233C22×Q8—1221no—
234C22×D4—1221no—
235C22×D4—1221no—
236C22×D4—1221no—
237C22×C8—21no—
238C22×C8—1221no—
239C22×C8—1221no—
240C22×C8C22⋊D6111yescharacteristic
241C22×C8C22⋊D6111yescharacteristic
242C4⋊Q8—612no—
243C4⋊Q8—1221no—
244C4⋊Q8—1221no—
245C4⋊Q8—1221no—
246#127—612no—
247#127—1221no—
248#127—1221no—
249#127—1221no—
250C2×C4⋊C4—1221no—
251C2×C4⋊C4—1221no—
252C2×C4⋊C4D24411yescharacteristic
253C2×C4⋊C4D24411yescharacteristic
254C2×C42—21no—
255C2×C42C22×D6111yescharacteristic
256C4⋊C8—21no—
257C4⋊C8—21no—
258C4⋊C8—42no—
259C4⋊C8—1221no—
260C4⋊C8—1221no—
261C4⋊C8—1221no—
262C4⋊C8—1221no—
263#102—1224no—
264#102—1224no—
265#102—2442no—
266#102—2442no—
267C4×C8—21no—
268C4×C8—21no—
269#95—21no—
270C24—2441no—
271C2×Q8—1222no—
272C2×Q8—4881no—
273C2×Q8—4881no—
274C2×Q8—2441no—
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—2441no—
294C22×C4C2×D24411yescharacteristic
295C22×C4#1175822211yescharacteristic
296C22×C4C2×C22⋊D6111yescharacteristic
297C2×C8—21no—
298C2×C8—21no—
299C2×C8—21no—
300C2×C8—21no—
301C2×C8—21no—
302C2×C8—21no—
303C2×C8—41no—
304C2×C8—41no—
305C2×C8—41no—
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—21no—
315C4⋊C4—1222no—
316C4⋊C4—1222no—
317C4⋊C4—2441no—
318C4⋊C4—2441no—
319C4⋊C4#1175819012yes—
320C42—41no—
321C42—41no—
322C42D4×D6111yescharacteristic
323C42D4×D6111yescharacteristic
324C42#1175822611yescharacteristic
325C42#1175822611yescharacteristic
326C23—4881no—
327C23—4881no—
328C23—4881no—
329C23—4881no—
330C23—4881no—
331C23—4881no—
332C23—2442no—
333C23#1451975111yescharacteristic
334Q8—4882no—
335Q8—4882no—
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—4881no—
355C2×C4—4881no—
356C2×C4—2442no—
357C2×C4#1451974511yescharacteristic
358C2×C4#1451975211yescharacteristic
359C2×C4#1451975211yescharacteristic
360C2×C4#1451976211yescharacteristic
361C2×C4#1451976211yescharacteristic
362C2×C4#1451976611yescharacteristic
363C2×C4C2×#1175819011yescharacteristic
364C2×C4#1451979711yescharacteristic
365C2×C4#1451979711yescharacteristic
366C2×C4#1451979911yescharacteristic
367C2×C4#1451980311yescharacteristic
368C2×C4#1451980511yescharacteristic
369C2×C4#1451980811yescharacteristic
370C2×C4#1451981011yescharacteristic
371C8—41no—
372C8—41no—
373C8—81no—
374C8—4881no—
375C8—4881no—
376C22—9761no—
377C22—9761no—
378C22—9761no—
379C22—9761no—
380C22—4882no—
381C22—4882no—
382C22—4882no—
383C22#1683967911yescharacteristic
384C22#1683997711yescharacteristic
385C22#1683998411yescharacteristic
386C22#1683999111yescharacteristic
387C22#1684000811yescharacteristic
388C22#1684003211yescharacteristic
389C22#1684003211yescharacteristic
390C4—21no—
391C4—21no—
392C4—42no—
393C4—81no—
394C4—4882no—
395C4#1683990511yescharacteristic
396C4#1683992211yescharacteristic
397C4#1683996311yescharacteristic
398C4#1683996811yescharacteristic
399C4#1683997811yescharacteristic
400C4#1683998511yescharacteristic
401C4#1684011911yescharacteristic
402C4#1684012411yescharacteristic
403C2—9762no—
404C2#2144522811yescharacteristic
405C2#2144523511yescharacteristic
406C2#2144535211yescharacteristic
407C2#2144535911yescharacteristic
408C2#2144706011yescharacteristic
409C2#2144707511yescharacteristic
410C2#2144713711yescharacteristic
subgroupG/H
centerC23#14519751
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1939C2
socleC23×C61#121
prime radicalC2×#14519774C22
hypercenter#1939D61
hypocenterC61#10539
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1939

Complements

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

NH ≅ G/Ntype
2. #21446767C2semidirect
4. C2×#16839510C2semidirect
6. #21443654C2semidirect
7. C61×#1939C2semidirect
201. #1939D61semidirect
232. C61#10539semidirect

Maximal subgroups

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

subgroupindex
C2×#168401092
#214467672
#214467462
C2×#168395102
C2×#168395052
#214436542
C61×#19392
#1053961