Finite Group Databasebeta

← #29573066

Subgroups — #29573066

Order 15616.

542 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839827C211yesmaximal, characteristic
2#21445978C211yesmaximal, characteristic, complemented
3#21445820C211yesmaximal, characteristic
4#21445816C211yesmaximal, characteristic
5C2×#16839514C211yesmaximal, characteristic, complemented
6#21443703C211yesmaximal, characteristic, complemented
7C61×#1296C211yesmaximal, characteristic, complemented
8C22×C8×D61—21no—
9C2×C4×D244C2211yescharacteristic
10#16839827—22no—
11#16839827C414yescomplemented
12C2×#14519710—21no—
13C2×#14519710—21no—
14C2×C4⋊#92418C2211yescharacteristic
15C2×#14519699—21no—
16C2×#14519697—21no—
17C2×#14519689—21no—
18C2×C4×#92418C2211yescharacteristic
19#16839632C2211yescharacteristic
20#16839525—21no—
21#16839524—21no—
22#16839514—22no—
23C2×C4⋊C8×C61C2211yescharacteristic
24C2×C4⋊C8×C61C2211yescharacteristic
25C61×#384C2211yescharacteristic
26C22×D244D411yescharacteristic
27C22×C4×D61—21no—
28C22×#92418—21no—
29C22×#92418D411yescharacteristic
30C22×#92418D411yescharacteristic
31C2×C8×D61—24no—
32C2×C8×D61—42no—
33C2×C8×D61—42no—
34C4×D244—21no—
35C4×D244—21no—
36C4×D244C2×C412yes—
37C4×D244Q812yes—
38C2×C4⋊Dic61—21no—
39C2×C4⋊Dic61—21no—
40C2×C4⋊Dic61—21no—
41C2×C4⋊Dic61D411yescharacteristic
42C2×#11758198—21no—
43#14519710—42no—
44#14519710—42no—
45C4⋊#92418—21no—
46C4⋊#92418—21no—
47#14519699—42no—
48#14519697—42no—
49#14519689—24no—
50C4×#92418C2×C412yes—
51C4×#92418D412yes—
52C22×C8×C61—21no—
53C22×C8×C61—21no—
54C2×C4⋊C4×C61—21no—
55C2×C4⋊C4×C61—21no—
56C2×C4⋊C4×C61—21no—
57C2×C42×C61C2311yescharacteristic
58C4⋊C8×C61—21no—
59C4⋊C8×C61—21no—
60C4⋊C8×C61—21no—
61C4⋊C8×C61C2×C412yes—
62C23×D61—21no—
63C22×C4×C61—41no—
64C22×C4×C61C2×D411yescharacteristic
65C22×C4×C61C2×D411yescharacteristic
66C22×C4×C61#4111yescharacteristic
67C22×Dic61—21no—
68C22×Dic61—41no—
69C2×D244—21no—
70C2×D244—21no—
71C2×D244—21no—
72C2×D244C4⋊C412yes—
73C2×D244D812yes—
74C2×D244Q1612yes—
75C2×C4×D61—22no—
76C2×C4×D61—22no—
77C2×C4×D61—41no—
78C2×C4×D61—41no—
79C2×C4×D61—41no—
80C2×C4×D61—41no—
81C2×C8×C61—22no—
82C2×C8×C61—41no—
83C2×C8×C61—41no—
84C2×C8×C61—41no—
85C2×C8×C61—41no—
86C2×C8×C61—41no—
87C4⋊C4×C61—41no—
88C4⋊C4×C61—41no—
89C4⋊C4×C61—41no—
90C4⋊C4×C61—41no—
91C4⋊C4×C61—81no—
92C42×C61C22×C411yescharacteristic
93C42×C61C2×D411yescharacteristic
94C42×C61C2×Q811yescharacteristic
95C42×C61#4111yescharacteristic
96#11758198—22no—
97#11758198—22no—
98C4⋊Dic61—21no—
99C4⋊Dic61—41no—
100C4⋊Dic61—41no—
101C4⋊Dic61—41no—
102C4⋊Dic61—41no—
103C4⋊Dic61—81no—
104C4⋊Dic61C4⋊C412yes—
105C2×#92418—21no—
106C2×#92418—21no—
107C2×#92418—41no—
108C2×#92418—41no—
109C2×#92418—41no—
110C2×#92418C22⋊C412yes—
111C2×#92418C22⋊C412yes—
112C2×#92418D812yes—
113C2×#92418SD1612yes—
114C8×D61—48no—
115C23×C61#12111yescharacteristic
116C22×D61—22no—
117C22×D61—22no—
118C22×D61—22no—
119C22×D61—41no—
120C22×D61—41no—
121C22×D61—41no—
122C22×D61—41no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—81no—
126C2×C4×C61—81no—
127C2×C4×C61—81no—
128C2×C4×C61C2×C22⋊C411yescharacteristic
129C2×C4×C61C2×C4⋊C411yescharacteristic
130C2×C4×C61#11711yescharacteristic
131C2×C4×C61#12111yescharacteristic
132C2×C4×C61C22⋊Q811yescharacteristic
133C2×C4×C61C22⋊Q811yescharacteristic
134C2×C4×C61C2×D811yescharacteristic
135C2×C4×C61C2×D811yescharacteristic
136C2×C4×C61C2×SD1611yescharacteristic
137C2×C4×C61C2×Q1611yescharacteristic
138C2×C4×C61#13511yescharacteristic
139C2×C4×C61#13511yescharacteristic
140C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C61#13711yescharacteristic
142C2×Dic61—22no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—81no—
146C2×Dic61—81no—
147C2×Dic61—81no—
148D244—22no—
149D244—22no—
150D244—22no—
151D244#10714yescomplemented
152C4×D61—42no—
153C4×D61—42no—
154C4×D61—42no—
155C4×D61—42no—
156C8×C61—42no—
157C8×C61—81no—
158#92418—22no—
159#92418—81no—
160#92418#10214yescomplemented
161#8644—611nomaximal, Sylow
162C22×C61#38011yescharacteristic
163C22×C61#45911yescharacteristic
164C22×C61#46111yescharacteristic
165C22×C61#46611yescharacteristic
166C22×C61#46711yescharacteristic
167C22×C61#47211yescharacteristic
168C22×C61#47311yescharacteristic
169C2×D61—24no—
170C2×D61—42no—
171C2×D61—42no—
172C2×D61—42no—
173C2×D61—42no—
174C2×D61—42no—
175C2×D61—42no—
176C4×C61—21no—
177C4×C61—21no—
178C4×C61—161no—
179C4×C61C2×#10211yescharacteristic
180C4×C61#41711yescharacteristic
181C4×C61C2×#10711yescharacteristic
182C4×C61#42711yescharacteristic
183C4×C61#46611yescharacteristic
184C4×C61#46711yescharacteristic
185C4×C61#47411yescharacteristic
186C4×C61#47611yescharacteristic
187Dic61—42no—
188Dic61—161no—
189C2×C8×D4—611no—
190#1845—611no—
191#1802—611no—
192#1802—611no—
193C2×#335—611no—
194#1296—611no—
195#1296D6111yescharacteristic, complemented
196C2×C61#166711yescharacteristic
197C2×C61#166911yescharacteristic
198C2×C61#167311yescharacteristic
199C2×C61#167511yescharacteristic
200C2×C61#180211yescharacteristic
201C2×C61#180811yescharacteristic
202C2×C61#181611yescharacteristic
203D61—44no—
204C23×C8—1221no—
205C2×C4×D4—611no—
206C8×D4—614no—
207C8×D4—1222no—
208C2×#107—1221no—
209C2×#107—1221no—
210C2×C4⋊C8—611no—
211C2×C4⋊C8C2×D6111yescharacteristic
212C2×C4⋊C8C2×D6111yescharacteristic
213C2×#102—1221no—
214C2×#102—1221no—
215C2×C22⋊C8—1221no—
216C2×C4×C8—611no—
217#384—611no—
218#384C2×D6111yescharacteristic
219#340—1221no—
220#340—1221no—
221#335—1222no—
222C61#864411yescharacteristic, complemented, Sylow
223C22×D4—611no—
224C23×C4—1221no—
225C22×C8—21no—
226C22×C8—21no—
227C22×C8—611no—
228C22×C8—611no—
229C22×C8—1224no—
230C22×C8—1221no—
231C22×C8—2442no—
232C22×C8—2442no—
233C4×D4—612no—
234C4×D4—612no—
235C4×D4—1221no—
236C4×D4—1221no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—611no—
241C2×C4⋊C4—1221no—
242C2×C4⋊C4—1221no—
243C2×C4⋊C4—1221no—
244C2×C22⋊C4—1221no—
245C2×C42C22×D6111yescharacteristic
246#107—2442no—
247#107—2442no—
248C4⋊C8—21no—
249C4⋊C8—21no—
250C4⋊C8—21no—
251C4⋊C8—1221no—
252C4⋊C8—1221no—
253C4⋊C8C4×D6112yes—
254#102—2442no—
255#102—2442no—
256C22⋊C8—1224no—
257C4×C8—612no—
258C4×C8—612no—
259C24—1221no—
260C2×D4—612no—
261C2×D4—612no—
262C2×D4—612no—
263C2×D4—1221no—
264C2×D4—1221no—
265C2×D4—1221no—
266C22×C4—41no—
267C22×C4—1221no—
268C22×C4—1222no—
269C22×C4—1222no—
270C22×C4—2441no—
271C22×C4—2441no—
272C22×C4—2441no—
273C22×C4—2441no—
274C22×C4—2441no—
275C22×C4#1175822211yescharacteristic
276C22×C4D4×D6111yescharacteristic
277C22×C4D4×D6111yescharacteristic
278C2×C8—22no—
279C2×C8—41no—
280C2×C8—41no—
281C2×C8—41no—
282C2×C8—41no—
283C2×C8—41no—
284C2×C8—612no—
285C2×C8—612no—
286C2×C8—612no—
287C2×C8—612no—
288C2×C8—1221no—
289C2×C8—1221no—
290C2×C8—2448no—
291C2×C8—2441no—
292C2×C8—2441no—
293C2×C8—2441no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—81no—
299C4⋊C4—612no—
300C4⋊C4—1221no—
301C4⋊C4—4881no—
302C4⋊C4—2441no—
303C4⋊C4—2441no—
304C4⋊C4—2441no—
305C4⋊C4—2441no—
306C22⋊C4—1222no—
307C22⋊C4—1222no—
308C42C2×C4×D6111yescharacteristic
309C42#1175822211yescharacteristic
310C42D4×D6111yescharacteristic
311C42Q8×D6111yescharacteristic
312C23—1222no—
313C23—1222no—
314C23—1222no—
315C23—2441no—
316C23—2441no—
317C23—2441no—
318C23—2441no—
319C23#1451975011yescharacteristic
320D4—614no—
321D4—1222no—
322D4—1222no—
323D4—1222no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—81no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—1222no—
330C2×C4—4881no—
331C2×C4—4881no—
332C2×C4—4881no—
333C2×C4—2441no—
334C2×C4—2441no—
335C2×C4—2442no—
336C2×C4—2442no—
337C2×C4—2442no—
338C2×C4—2442no—
339C2×C4C22⋊C4×D6111yescharacteristic
340C2×C4C4⋊C4×D6111yescharacteristic
341C2×C4#1451973411yescharacteristic
342C2×C4#1451975011yescharacteristic
343C2×C4#1451975511yescharacteristic
344C2×C4#1451975511yescharacteristic
345C2×C4D8×D6111yescharacteristic
346C2×C4D8×D6111yescharacteristic
347C2×C4SD16×D6111yescharacteristic
348C2×C4Q16×D6111yescharacteristic
349C2×C4#1451979811yescharacteristic
350C2×C4#1451979811yescharacteristic
351C2×C4#1451980411yescharacteristic
352C2×C4#1451980911yescharacteristic
353C8—42no—
354C8—81no—
355C8—614no—
356C8—1222no—
357C8—4881no—
358C22—1224no—
359C22—2442no—
360C22—2442no—
361C22—2442no—
362C22—2442no—
363C22—2442no—
364C22—2442no—
365C22#1683962111yescharacteristic
366C22#1683995611yescharacteristic
367C22#1683996611yescharacteristic
368C22#1683999711yescharacteristic
369C22#1684000211yescharacteristic
370C22#1684003111yescharacteristic
371C22#1684003611yescharacteristic
372C4—21no—
373C4—21no—
374C4—161no—
375C4—9761no—
376C4—2442no—
377C4#102×D6111yescharacteristic
378C4#1683976211yescharacteristic
379C4#107×D6111yescharacteristic
380C4#1683979711yescharacteristic
381C4#1683999711yescharacteristic
382C4#1684000211yescharacteristic
383C4#1684004111yescharacteristic
384C4#1684005111yescharacteristic
385C2—2444no—
386C2#2144517311yescharacteristic
387C2#2144518311yescharacteristic
388C2#2144520711yescharacteristic
389C2#2144521711yescharacteristic
390C2#2144581811yescharacteristic
391C2#2144584711yescharacteristic
392C2#2144588211yescharacteristic
subgroupG/H
centerC23#14519750
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1296C2
socleC23×C61#121
prime radicalC22×D244D4
cosocleC2×C42×C61C23
hypercenter#1296D61
hypocenterC61#8644
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
2. #21445978C2semidirect
5. C2×#16839514C2semidirect
6. #21443703C2semidirect
7. C61×#1296C2semidirect
11. #16839827C4semidirect
151. D244#107semidirect
160. #92418#102semidirect
195. #1296D61semidirect
222. C61#8644semidirect

Maximal subgroups

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

subgroupindex
C2×#168398272
#214459782
#214458202
#214458162
C2×#168395142
#214437032
C61×#12962
#864461