Finite Group Databasebeta

← #29578397

Subgroups — #29578397

Order 15616.

454 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21446745C211yesmaximal, characteristic
2#21446625C211yesmaximal, characteristic
3#21446578C211yesmaximal, characteristic, complemented
4#21445686C211yesmaximal, characteristic, complemented
5C2×#16839505C211yesmaximal, characteristic
6#21443703C211yesmaximal, characteristic, complemented
7C61×#1277C211yesmaximal, characteristic, complemented
8C2×#14519774C2211yescharacteristic
9C2×#14519711—21no—
10C2×C4⋊#92418C2211yescharacteristic
11C2×#14519699—21no—
12C2×#14519699—21no—
13C2×#14519699—21no—
14C2×#14519699—21no—
15C2×#14519687—21no—
16#16839632C2211yescharacteristic
17C4×C4⋊Dic61C2211yescharacteristic
18#16839525—21no—
19#16839516—21no—
20#16839505C414yescomplemented
21C2×C4⋊C8×C61C2211yescharacteristic
22C2×C4⋊C8×C61C2211yescharacteristic
23C2×C4×C8×C61C2211yescharacteristic
24C22×D244—21no—
25C22×D244—21no—
26C22×D244—21no—
27C22×#92418—21no—
28#14519774—21no—
29#14519774—21no—
30#14519774—21no—
31#14519774C2×C412yes—
32C2×C4⋊Dic61—21no—
33C2×C4⋊Dic61—21no—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61D411yescharacteristic
36C2×C4⋊Dic61D411yescharacteristic
37C2×C4×Dic61—21no—
38#14519711—42no—
39C4⋊#92418—21no—
40C4⋊#92418C2×C412yes—
41#14519699—42no—
42#14519699—42no—
43#14519699—42no—
44#14519699—42no—
45#14519687—42no—
46#14519684—21no—
47C22×C8×C61—21no—
48C22×C8×C61—21no—
49C22×C8×C61D411yescharacteristic
50C22×C8×C61D411yescharacteristic
51C2×C42×C61C2311yescharacteristic
52C4⋊C8×C61—21no—
53C4⋊C8×C61—21no—
54C4⋊C8×C61—21no—
55C4⋊C8×C61C2×C412yes—
56C4×C8×C61—21no—
57C4×C8×C61—21no—
58C23×D61—41no—
59C22×C4×C61C2×D411yescharacteristic
60C22×C4×C61C2×D411yescharacteristic
61C22×C4×C61#4111yescharacteristic
62C22×Dic61—21no—
63C22×Dic61—21no—
64C22×Dic61—41no—
65C2×D244—22no—
66C2×D244—22no—
67C2×D244—22no—
68C2×D244—41no—
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—81no—
80C2×D244—81no—
81C2×C8×C61—21no—
82C2×C8×C61—21no—
83C2×C8×C61—22no—
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×C61—41no—
91C2×C8×C61—41no—
92C2×C8×C61D812yes—
93C42×C61C22×C411yescharacteristic
94C42×C61#4111yescharacteristic
95C42×C61#4111yescharacteristic
96C42×C61#4111yescharacteristic
97C4⋊Dic61—21no—
98C4⋊Dic61—21no—
99C4⋊Dic61—21no—
100C4⋊Dic61—21no—
101C4⋊Dic61—41no—
102C4⋊Dic61—41no—
103C4⋊Dic61—41no—
104C4⋊Dic61—41no—
105C4⋊Dic61—81no—
106C4×Dic61—41no—
107C4×Dic61—41no—
108C2×#92418—22no—
109C2×#92418—41no—
110C2×#92418—41no—
111C23×C61#12111yescharacteristic
112C22×D61—42no—
113C22×D61—81no—
114C22×D61—81no—
115C22×D61—81no—
116C22×D61—81no—
117C22×D61—81no—
118C22×D61—81no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61#11711yescharacteristic
122C2×C4×C61C4×D411yescharacteristic
123C2×C4×C61C4×D411yescharacteristic
124C2×C4×C61#12311yescharacteristic
125C2×C4×C61#12411yescharacteristic
126C2×C4×C61#12611yescharacteristic
127C2×C4×C61C2×D811yescharacteristic
128C2×C4×C61#13511yescharacteristic
129C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
130C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
131C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
132C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C61#13711yescharacteristic
134C2×C4×C61#13711yescharacteristic
135C2×Dic61—41no—
136C2×Dic61—41no—
137C2×Dic61—41no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—81no—
142C2×Dic61—81no—
143C2×Dic61—81no—
144D244—42no—
145D244—42no—
146D244—42no—
147D244—42no—
148D244—82no—
149D244—82no—
150D244—81no—
151D244—81no—
152D244—81no—
153D244—81no—
154C8×C61—22no—
155C8×C61—42no—
156C8×C61—41no—
157C8×C61—81no—
158#92418—42no—
159#9571—611nomaximal, Sylow
160C22×C61#38811yescharacteristic
161C22×C61#45911yescharacteristic
162C22×C61#46411yescharacteristic
163C22×C61#46811yescharacteristic
164C22×C61#46911yescharacteristic
165C22×C61#47111yescharacteristic
166C22×C61#47211yescharacteristic
167C2×D61—82no—
168C2×D61—82no—
169C2×D61—82no—
170C2×D61—161no—
171C2×D61—161no—
172C2×D61—161no—
173C2×D61—161no—
174C4×C61—21no—
175C4×C61—21no—
176C4×C61C4×D811yescharacteristic
177C4×C61#44011yescharacteristic
178C4×C61#44011yescharacteristic
179C4×C61#44211yescharacteristic
180C4×C61#48011yescharacteristic
181C4×C61#48211yescharacteristic
182C4×C61#48911yescharacteristic
183C4×C61#49011yescharacteristic
184Dic61—81no—
185Dic61—81no—
186Dic61—161no—
187#1982—611no—
188#1957—611no—
189#1947—611no—
190#1770—611no—
191C2×#331—611no—
192#1296—611no—
193#1277D6111yescharacteristic, complemented
194C2×C61#168511yescharacteristic
195C2×C61#168711yescharacteristic
196C2×C61#169811yescharacteristic
197C2×C61#170211yescharacteristic
198C2×C61#192511yescharacteristic
199C2×C61#193111yescharacteristic
200C2×C61#193611yescharacteristic
201D61—162no—
202C2×#127—611no—
203C2×#107—1221no—
204C2×C4⋊C8—611no—
205C2×C4⋊C8C2×D6111yescharacteristic
206C2×C4⋊C8C2×D6111yescharacteristic
207C2×#102—1221no—
208C2×#102—1221no—
209C2×#102—1221no—
210C2×#102—1221no—
211C2×#97—1221no—
212C2×C4×C8C2×D6111yescharacteristic
213#384—611no—
214C4×C4⋊C4—611no—
215#340—1221no—
216#336—1221no—
217#331—614no—
218C61#957111yescharacteristic, complemented, Sylow
219C22×D4—1221no—
220C22×D4—1221no—
221C22×D4—1221no—
222C22×C8—21no—
223C22×C8—21no—
224C22×C8—1221no—
225C22×C8D24411yescharacteristic
226C22×C8D24411yescharacteristic
227#127—612no—
228#127—1221no—
229#127—1221no—
230#127—1221no—
231C2×C4⋊C4—611no—
232C2×C4⋊C4—611no—
233C2×C4⋊C4—1221no—
234C2×C4⋊C4—1221no—
235C2×C4⋊C4—1221no—
236C2×C42—1221no—
237C2×C42C22×D6111yescharacteristic
238#107—2442no—
239C4⋊C8—21no—
240C4⋊C8—21no—
241C4⋊C8—21no—
242C4⋊C8—612no—
243C4⋊C8—1221no—
244C4⋊C8C4×D6112yes—
245#102—2442no—
246#102—2442no—
247#102—2442no—
248#102—2442no—
249#97—2442no—
250C4×C8—21no—
251C4×C8—21no—
252#95—1221no—
253C24—2441no—
254C2×D4—1222no—
255C2×D4—1222no—
256C2×D4—1222no—
257C2×D4—4881no—
258C2×D4—4881no—
259C2×D4—2441no—
260C2×D4—2441no—
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—
270C22×C4—1221no—
271C22×C4—1221no—
272C22×C4—2441no—
273C22×C4C2×D24411yescharacteristic
274C22×C4D4×D6111yescharacteristic
275C22×C4#1175822611yescharacteristic
276C2×C8—21no—
277C2×C8—21no—
278C2×C8—22no—
279C2×C8—21no—
280C2×C8—21no—
281C2×C8—21no—
282C2×C8—41no—
283C2×C8—41no—
284C2×C8—41no—
285C2×C8—41no—
286C2×C8—41no—
287C2×C8—1222no—
288C2×C8—2441no—
289C2×C8—2441no—
290C2×C8D48812yes—
291C4⋊C4—1221no—
292C4⋊C4—1221no—
293C4⋊C4—1221no—
294C4⋊C4—1221no—
295C4⋊C4—4881no—
296C4⋊C4—2441no—
297C4⋊C4—2441no—
298C4⋊C4—2441no—
299C4⋊C4—2441no—
300C42—2441no—
301C42—2441no—
302C42C2×C4×D6111yescharacteristic
303C42#1175822211yescharacteristic
304C42#1175822411yescharacteristic
305C42#1175822411yescharacteristic
306C23—4881no—
307C23—4881no—
308C23—4881no—
309C23—4881no—
310C23—4881no—
311C23—4881no—
312C23—2442no—
313C23#1451975211yescharacteristic
314D4—4882no—
315D4—4882no—
316D4—4881no—
317D4—4881no—
318D4—4881no—
319D4—4881no—
320D4—2442no—
321D4—2442no—
322D4—2442no—
323D4—2442no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—4881no—
327C2×C4—4881no—
328C2×C4—4881no—
329C2×C4—2441no—
330C2×C4—2441no—
331C2×C4—2441no—
332C2×C4—2441no—
333C2×C4—2441no—
334C2×C4—2441no—
335C2×C4#1451973511yescharacteristic
336C2×C4#1451973711yescharacteristic
337C2×C4C4×D24411yescharacteristic
338C2×C4#1451976111yescharacteristic
339C2×C4#1451976311yescharacteristic
340C2×C4#1451977211yescharacteristic
341C2×C4C2×D48811yescharacteristic
342C2×C4#1451979911yescharacteristic
343C2×C4#1451980111yescharacteristic
344C2×C4#1451980411yescharacteristic
345C2×C4#1451980411yescharacteristic
346C2×C4#1451980511yescharacteristic
347C2×C4#1451980911yescharacteristic
348C2×C4#1451981011yescharacteristic
349C8—22no—
350C8—41no—
351C8—42no—
352C8—81no—
353C8—2442no—
354C22—9761no—
355C22—9761no—
356C22—9761no—
357C22—9761no—
358C22—4882no—
359C22—4882no—
360C22—4882no—
361C22#1683965411yescharacteristic
362C22#1683995811yescharacteristic
363C22#1683998511yescharacteristic
364C22#1684000911yescharacteristic
365C22#1684001611yescharacteristic
366C22#1684002611yescharacteristic
367C22#1684003311yescharacteristic
368C4—21no—
369C4—21no—
370C4—9761no—
371C4—4881no—
372C4—4881no—
373C4C4×D48811yescharacteristic
374C4#1683986411yescharacteristic
375C4#1683986511yescharacteristic
376C4#1683987111yescharacteristic
377C4#1684007611yescharacteristic
378C4#1684008711yescharacteristic
379C4#1684012311yescharacteristic
380C4#1684012511yescharacteristic
381C2—9762no—
382C2#2144528511yescharacteristic
383C2#2144529911yescharacteristic
384C2#2144536011yescharacteristic
385C2#2144538811yescharacteristic
386C2#2144644011yescharacteristic
387C2#2144648211yescharacteristic
388C2#2144651711yescharacteristic
subgroupG/H
centerC23#14519752
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1277C2
socleC23×C61#121
prime radicalC2×#14519774C22
cosocleC2×C42×C61C23
hypercenter#1277D61
hypocenterC61#9571
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1277

Complements

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

NH ≅ G/Ntype
3. #21446578C2semidirect
4. #21445686C2semidirect
6. #21443703C2semidirect
7. C61×#1277C2semidirect
20. #16839505C4semidirect
193. #1277D61semidirect
218. C61#9571semidirect

Maximal subgroups

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

subgroupindex
#214467452
#214466252
#214465782
#214456862
C2×#168395052
#214437032
C61×#12772
#957161