Finite Group Databasebeta

← #29584585

Subgroups — #29584585

Order 15616.

454 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21446746C211yesmaximal, characteristic
2#21446625C211yesmaximal, characteristic
3#21446582C211yesmaximal, characteristic, complemented
4C2×#16839513C211yesmaximal, characteristic, complemented
5C2×#16839505C211yesmaximal, characteristic
6#21443703C211yesmaximal, characteristic, complemented
7C61×#1939C211yesmaximal, characteristic, complemented
8C2×#14519774C2211yescharacteristic
9C2×#14519708—21no—
10C2×C4⋊#92418C2211yescharacteristic
11C2×C4⋊#92418C2211yescharacteristic
12C2×#14519699—21no—
13C2×#14519699—21no—
14C2×#14519697—21no—
15C2×#14519697—21no—
16#16839632C2211yescharacteristic
17#16839524—21no—
18#16839513—22no—
19#16839505—22no—
20C2×C4⋊C8×C61—21no—
21C2×C4⋊C8×C61C2211yescharacteristic
22C2×C4×C8×C61C2211yescharacteristic
23C4×C4⋊C4×C61C2211yescharacteristic
24C61×#336—21no—
25C22×D244—21no—
26C22×D244—21no—
27C22×D244—21no—
28C22×#92418—21no—
29C22×#92418—21no—
30#14519774—21no—
31#14519774—21no—
32#14519774—21no—
33#14519774Q812yes—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61—21no—
36C2×C4⋊Dic61—21no—
37#14519708—42no—
38C4⋊#92418—21no—
39C4⋊#92418—21no—
40C4⋊#92418—21no—
41C4⋊#92418D412yes—
42#14519699—42no—
43#14519699—42no—
44#14519697—42no—
45#14519697—42no—
46C22×C8×C61—21no—
47C22×C8×C61D411yescharacteristic
48C22×C8×C61D411yescharacteristic
49C2×C4⋊C4×C61D411yescharacteristic
50C2×C4⋊C4×C61D411yescharacteristic
51C2×C42×C61—21no—
52C2×C42×C61C2311yescharacteristic
53C4⋊C8×C61—21no—
54C4⋊C8×C61—21no—
55C4⋊C8×C61—42no—
56C4×C8×C61—21no—
57C4×C8×C61—21no—
58#95×C61—21no—
59C23×D61—41no—
60C22×C4×C61—21no—
61C22×C4×C61—21no—
62C22×C4×C61C2×D411yescharacteristic
63C22×C4×C61C2×D411yescharacteristic
64C22×C4×C61#4111yescharacteristic
65C22×Dic61—41no—
66C2×D244—22no—
67C2×D244—22no—
68C2×D244—22no—
69C2×D244—41no—
70C2×D244—41no—
71C2×D244—41no—
72C2×D244—41no—
73C2×D244—41no—
74C2×D244—41no—
75C2×D244—41no—
76C2×D244—41no—
77C2×D244—41no—
78C2×D244—41no—
79C2×D244—41no—
80C2×D244—81no—
81C2×D244—81no—
82C2×C8×C61—21no—
83C2×C8×C61—21no—
84C2×C8×C61—21no—
85C2×C8×C61—21no—
86C2×C8×C61—21no—
87C2×C8×C61—41no—
88C2×C8×C61—41no—
89C2×C8×C61—41no—
90C2×C8×C61SD1612yes—
91C4⋊C4×C61—21no—
92C4⋊C4×C61—21no—
93C4⋊C4×C61—21no—
94C4⋊C4×C61SD1612yes—
95C42×C61—41no—
96C42×C61—41no—
97C42×C61C2×D411yescharacteristic
98C42×C61C2×Q811yescharacteristic
99C42×C61#4111yescharacteristic
100C42×C61#4111yescharacteristic
101C4⋊Dic61—41no—
102C4⋊Dic61—41no—
103C4⋊Dic61—41no—
104C4⋊Dic61—41no—
105C4⋊Dic61—81no—
106C2×#92418—22no—
107C2×#92418—41no—
108C2×#92418—41no—
109C2×#92418—41no—
110C2×#92418—41no—
111C2×#92418—41no—
112C23×C61#12111yescharacteristic
113C22×D61—42no—
114C22×D61—81no—
115C22×D61—81no—
116C22×D61—81no—
117C22×D61—81no—
118C22×D61—81no—
119C22×D61—81no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—22no—
123C2×C4×C61—41no—
124C2×C4×C61—41no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61#12111yescharacteristic
129C2×C4×C61#12111yescharacteristic
130C2×C4×C61C22⋊Q811yescharacteristic
131C2×C4×C61C22⋊Q811yescharacteristic
132C2×C4×C61C22⋊Q811yescharacteristic
133C2×C4×C61#12611yescharacteristic
134C2×C4×C61C2×SD1611yescharacteristic
135C2×C4×C61C2×SD1611yescharacteristic
136C2×C4×C61#13511yescharacteristic
137C2×C4×C61#13511yescharacteristic
138C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
142C2×Dic61—81no—
143C2×Dic61—81no—
144C2×Dic61—81no—
145D244—42no—
146D244—42no—
147D244—42no—
148D244—42no—
149D244—82no—
150D244—82no—
151D244—81no—
152D244—81no—
153D244—81no—
154D244—81no—
155C8×C61—22no—
156C8×C61—41no—
157C8×C61—81no—
158#92418—42no—
159#92418—81no—
160#10595—611nomaximal, Sylow
161C22×C61#39611yescharacteristic
162C22×C61#46011yescharacteristic
163C22×C61#46311yescharacteristic
164C22×C61#46511yescharacteristic
165C22×C61#46911yescharacteristic
166C22×C61#47111yescharacteristic
167C22×C61#47211yescharacteristic
168C2×D61—82no—
169C2×D61—82no—
170C2×D61—82no—
171C2×D61—161no—
172C2×D61—161no—
173C2×D61—161no—
174C2×D61—161no—
175C4×C61—21no—
176C4×C61—21no—
177C4×C61—42no—
178C4×C61—81no—
179C4×C61#46011yescharacteristic
180C4×C61#46311yescharacteristic
181C4×C61#46511yescharacteristic
182C4×C61#46911yescharacteristic
183C4×C61#47611yescharacteristic
184C4×C61#47611yescharacteristic
185C4×C61#47811yescharacteristic
186C4×C61#47811yescharacteristic
187Dic61—161no—
188#1982—611no—
189#1957—611no—
190#1948—611no—
191#1939D6111yescharacteristic, complemented
192C2×#334—611no—
193C2×#331—611no—
194#1296—611no—
195C2×C61#166611yescharacteristic
196C2×C61#167711yescharacteristic
197C2×C61#168811yescharacteristic
198C2×C61#170111yescharacteristic
199C2×C61#206311yescharacteristic
200C2×C61#206511yescharacteristic
201C2×C61#206511yescharacteristic
202D61—162no—
203C2×#127—611no—
204C2×#106—1221no—
205C2×C4⋊C8—21no—
206C2×C4⋊C8—611no—
207C2×C4⋊C8—611no—
208C2×C4⋊C8C2×D6111yescharacteristic
209C2×#102—1221no—
210C2×#102—1221no—
211C2×#102—1221no—
212C2×#102—1221no—
213C2×C4×C8C2×D6111yescharacteristic
214#384—611no—
215C4×C4⋊C4C2×D6111yescharacteristic
216#340—1221no—
217#336—21no—
218#334—1222no—
219#331—1222no—
220C61#1059511yescharacteristic, complemented, Sylow
221C22×D4—1221no—
222C22×D4—1221no—
223C22×D4—1221no—
224C22×C8—21no—
225C22×C8—1221no—
226C22×C8—1221no—
227C22×C8C22⋊D6111yescharacteristic
228C22×C8C22⋊D6111yescharacteristic
229#127—612no—
230#127—1221no—
231#127—1221no—
232#127—1221no—
233C2×C4⋊C4—1221no—
234C2×C4⋊C4—1221no—
235C2×C4⋊C4—1221no—
236C2×C4⋊C4D24411yescharacteristic
237C2×C4⋊C4D24411yescharacteristic
238C2×C42—21no—
239C2×C42C22×D6111yescharacteristic
240#106—2442no—
241C4⋊C8—21no—
242C4⋊C8—21no—
243C4⋊C8—42no—
244C4⋊C8—612no—
245C4⋊C8—1221no—
246C4⋊C8—1221no—
247C4⋊C8—1221no—
248#102—2442no—
249#102—2442no—
250#102—2442no—
251#102—2442no—
252C4×C8—21no—
253C4×C8—21no—
254#95—21no—
255C24—2441no—
256C2×D4—1222no—
257C2×D4—1222no—
258C2×D4—1222no—
259C2×D4—4881no—
260C2×D4—4881no—
261C2×D4—2441no—
262C2×D4—2441no—
263C2×D4—2441no—
264C2×D4—2441no—
265C2×D4—2441no—
266C2×D4—2441no—
267C2×D4—2441no—
268C2×D4—2441no—
269C2×D4—2441no—
270C2×D4—2441no—
271C2×D4—2441no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—2441no—
275C22×C4C2×D24411yescharacteristic
276C22×C4#1175822211yescharacteristic
277C22×C4C2×C22⋊D6111yescharacteristic
278C2×C8—21no—
279C2×C8—21no—
280C2×C8—21no—
281C2×C8—21no—
282C2×C8—21no—
283C2×C8—41no—
284C2×C8—41no—
285C2×C8—41no—
286C2×C8—1222no—
287C2×C8—2441no—
288C2×C8—2441no—
289C2×C8—2441no—
290C2×C8—2441no—
291C2×C8—2441no—
292C2×C8#1175820112yes—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—21no—
296C4⋊C4—4881no—
297C4⋊C4—2441no—
298C4⋊C4—2441no—
299C4⋊C4—2441no—
300C4⋊C4—2441no—
301C4⋊C4#1175819012yes—
302C42—41no—
303C42—41no—
304C42D4×D6111yescharacteristic
305C42#1175822411yescharacteristic
306C42Q8×D6111yescharacteristic
307C42#1175822611yescharacteristic
308C23—4881no—
309C23—4881no—
310C23—4881no—
311C23—4881no—
312C23—4881no—
313C23—4881no—
314C23—2442no—
315C23#1451975111yescharacteristic
316D4—4882no—
317D4—4882no—
318D4—4881no—
319D4—4881no—
320D4—4881no—
321D4—4881no—
322D4—2442no—
323D4—2442no—
324D4—2442no—
325D4—2442no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—22no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—4881no—
335C2×C4—4881no—
336C2×C4—4881no—
337C2×C4#1451974911yescharacteristic
338C2×C4#1451975211yescharacteristic
339C2×C4#1451975311yescharacteristic
340C2×C4#1451975511yescharacteristic
341C2×C4#1451975711yescharacteristic
342C2×C4#1451977211yescharacteristic
343C2×C4C2×#1175820111yescharacteristic
344C2×C4C2×#1175819011yescharacteristic
345C2×C4#1451979711yescharacteristic
346C2×C4#1451979911yescharacteristic
347C2×C4#1451980211yescharacteristic
348C2×C4#1451980311yescharacteristic
349C2×C4#1451980511yescharacteristic
350C2×C4#1451980511yescharacteristic
351C8—22no—
352C8—41no—
353C8—81no—
354C8—4881no—
355C8—2442no—
356C22—9761no—
357C22—9761no—
358C22—9761no—
359C22—9761no—
360C22—4882no—
361C22—4882no—
362C22—4882no—
363C22#1683968411yescharacteristic
364C22#1683996211yescharacteristic
365C22#1683997711yescharacteristic
366C22#1683999111yescharacteristic
367C22#1684001511yescharacteristic
368C22#1684002511yescharacteristic
369C22#1684003211yescharacteristic
370C4—21no—
371C4—21no—
372C4—42no—
373C4—81no—
374C4—9761no—
375C4#1683996311yescharacteristic
376C4#1683997811yescharacteristic
377C4#1683999311yescharacteristic
378C4#1684001311yescharacteristic
379C4#1684004911yescharacteristic
380C4#1684005311yescharacteristic
381C4#1684005911yescharacteristic
382C4#1684006311yescharacteristic
383C2—9762no—
384C2#2144516711yescharacteristic
385C2#2144522811yescharacteristic
386C2#2144530311yescharacteristic
387C2#2144538011yescharacteristic
388C2#2144717811yescharacteristic
389C2#2144719011yescharacteristic
390C2#2144719211yescharacteristic
subgroupG/H
centerC23#14519751
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1939C2
socleC23×C61#121
prime radicalC2×#14519774C22
hypercenter#1939D61
hypocenterC61#10595
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
3. #21446582C2semidirect
4. C2×#16839513C2semidirect
6. #21443703C2semidirect
7. C61×#1939C2semidirect
191. #1939D61semidirect
220. C61#10595semidirect

Maximal subgroups

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

subgroupindex
#214467462
#214466252
#214465822
C2×#168395132
C2×#168395052
#214437032
C61×#19392
#1059561