Finite Group Databasebeta

← #29572886

Subgroups — #29572886

Order 15616.

462 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14519785C211yesmaximal, characteristic
2#21444565C211yesmaximal, characteristic, complemented
3C2×#16839512C211yesmaximal, characteristic, complemented
4#21444207C211yesmaximal, characteristic
5#21444204C211yesmaximal, characteristic
6#21443670C211yesmaximal, characteristic, complemented
7C61×#1283C211yesmaximal, characteristic, complemented
8C2×#14519785C411yescharacteristic
9C2×#14519785C411yescharacteristic
10C4×#11758222C2211yescharacteristic
11#16839815C2211yescharacteristic
12C2×C4⋊#92418C2211yescharacteristic
13#16839720C411yescharacteristic
14#16839720C411yescharacteristic
15#16839719—21no—
16#16839719—21no—
17C4×#11758189—21no—
18C2×C4×#92418C2211yescharacteristic
19C4×C8×D61—21no—
20#16839514—21no—
21#16839512—21no—
22#16839512—21no—
23#16839512—21no—
24#16839494—21no—
25#16839492—21no—
26#16839491—21no—
27#16839489—21no—
28C61×#431C2211yescharacteristic
29C2×C4⋊C8×C61C2211yescharacteristic
30C4×M16×C61C2211yescharacteristic
31C2×#11758222C2×C411yescharacteristic
32#14519785—22no—
33#14519785—22no—
34#14519785—22no—
35#14519785C814yescomplemented
36C2×#11758189—21no—
37C2×#11758189—21no—
38C22×#92418—21no—
39C22×#92418C2×C411yescharacteristic
40C22×#92418C2×C411yescharacteristic
41C2×C8×D61—21no—
42C2×C8×D61—21no—
43C4×Dic122D411yescharacteristic
44C4×Dic122Q811yescharacteristic
45C4×D244D411yescharacteristic
46C4×D244Q811yescharacteristic
47C4×C22⋊D61—21no—
48C4×C22⋊D61—21no—
49#14519736C2×C411yescharacteristic
50#14519734—21no—
51C42×D61—21no—
52C4⋊#92418—21no—
53C4⋊#92418—21no—
54C4⋊#92418—21no—
55C22⋊#92418—21no—
56#14519687—21no—
57#14519687—21no—
58C4×#92418—21no—
59C4×#92418D411yescharacteristic
60C4×#92418D411yescharacteristic
61C4×#92418D411yescharacteristic
62C4×#92418D411yescharacteristic
63C8×Dic61—21no—
64C8×Dic61—21no—
65C2×M16×C61C2×C411yescharacteristic
66C2×M16×C61C2×C411yescharacteristic
67C22×C8×C61—21no—
68C2×C42×C61C2311yescharacteristic
69C4⋊C8×C61—21no—
70C4⋊C8×C61—21no—
71C4⋊C8×C61—21no—
72C22⋊C8×C61—21no—
73#97×C61—21no—
74C4×C8×C61—21no—
75C4×C8×C61—21no—
76C22×C4×C61C22×C411yescharacteristic
77C22×C4×C61#4111yescharacteristic
78C22×C4×C61#4111yescharacteristic
79C2×C22⋊D61—21no—
80#11758222—21no—
81#11758222—21no—
82#11758222C2×C812yes—
83#11758222M1612yes—
84C2×D244C4⋊C411yescharacteristic
85C2×C4×D61—21no—
86C2×C4×D61—21no—
87C2×C4×D61—21no—
88C2×Dic122C4⋊C411yescharacteristic
89M16×C61—21no—
90M16×C61—21no—
91M16×C61C2×C812yes—
92M16×C61M1612yes—
93C2×C8×C61—21no—
94C2×C8×C61—21no—
95C2×C8×C61—41no—
96C2×C8×C61—41no—
97C2×C8×C61—81no—
98C42×C61C2×D411yescharacteristic
99C42×C61C2×D411yescharacteristic
100C42×C61C2×D411yescharacteristic
101C42×C61C2×Q811yescharacteristic
102C22⋊Dic61—21no—
103#11758198—21no—
104#11758198—21no—
105C4⋊Dic61C4⋊C411yescharacteristic
106C4⋊Dic61C4⋊C411yescharacteristic
107#11758196—21no—
108#11758196—21no—
109C4×Dic61—21no—
110C4×Dic61—21no—
111C4×Dic61—21no—
112C2×#92418—21no—
113C2×#92418—21no—
114C2×#92418—41no—
115C2×#92418—41no—
116C2×#92418—81no—
117C2×#92418C22⋊C411yescharacteristic
118C2×#92418C22⋊C411yescharacteristic
119C2×#92418C22⋊C411yescharacteristic
120C2×#92418C22⋊C411yescharacteristic
121C2×#92418C2×C812yes—
122C2×#92418M1612yes—
123#11758189—24no—
124#11758189—24no—
125C8×D61—24no—
126C8×D61—24no—
127C23×C61#11711yescharacteristic
128C22×D61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—41no—
132C2×C4×C61C2×C22⋊C411yescharacteristic
133C2×C4×C61C2×C4⋊C411yescharacteristic
134C2×C4×C61#12111yescharacteristic
135C2×C4×C61#12111yescharacteristic
136C2×C4×C61C22⋊Q811yescharacteristic
137C2×C4×C61C22⋊Q811yescharacteristic
138C2×C4×C61C22×C811yescharacteristic
139C2×C4×C61C2×M1611yescharacteristic
140C2×C4×C61C2×M1611yescharacteristic
141C2×C4×C61C2×M1611yescharacteristic
142C22⋊D61—22no—
143C22⋊D61—22no—
144C2×Dic61—21no—
145C2×Dic61—21no—
146C2×Dic61—21no—
147D244—21no—
148D244C4⋊C812yes—
149C4×D61—22no—
150C4×D61—22no—
151C4×D61—42no—
152C4×D61—41no—
153C4×D61—41no—
154Dic122—21no—
155Dic122C4⋊C812yes—
156C8×C61—22no—
157C8×C61—22no—
158C8×C61—81no—
159C8×C61—81no—
160#92418—21no—
161#92418—21no—
162#92418—81no—
163#92418—81no—
164#92418C22⋊C812yes—
165#92418C22⋊C812yes—
166#8604—611nomaximal, Sylow
167C22×C61—21no—
168C22×C61—21no—
169C22×C61#38011yescharacteristic
170C22×C61#43111yescharacteristic
171C22×C61#43211yescharacteristic
172C2×D61—22no—
173C2×D61—41no—
174C2×D61—41no—
175C4×C61—21no—
176C4×C61—21no—
177C4×C61—21no—
178C4×C61C2×C22⋊C811yescharacteristic
179C4×C61#40711yescharacteristic
180C4×C61C2×C4⋊C811yescharacteristic
181C4×C61#42311yescharacteristic
182C4×C61#47111yescharacteristic
183C4×C61#47111yescharacteristic
184Dic61—22no—
185Dic61—41no—
186Dic61—41no—
187C4×#131—611no—
188#1564—611no—
189C2×#334—611no—
190#1477—611no—
191#1477—611no—
192#1283—611no—
193#1283D6111yescharacteristic, complemented
194C2×C61—21no—
195C2×C61—21no—
196C2×C61#179711yescharacteristic
197C2×C61#181411yescharacteristic
198C2×C61#181511yescharacteristic
199D61—42no—
200C2×#131—611no—
201C2×#131—611no—
202C4×#41—611no—
203#431—611no—
204#431C2×D6111yescharacteristic
205C2×C4⋊C8—611no—
206C2×C4⋊C8C2×D6111yescharacteristic
207#405—611no—
208#405—611no—
209#405—1221no—
210#405—1221no—
211C4×M16—1221no—
212C4×M16C2×D6111yescharacteristic
213C2×C4×C8—611no—
214C2×C4×C8—1221no—
215#335—1221no—
216#334—1221no—
217#334—1221no—
218#334—1221no—
219Q8⋊C8—1221no—
220Q8⋊C8—1221no—
221D4⋊C8—1221no—
222D4⋊C8—1221no—
223C61#860411yescharacteristic, complemented, Sylow
224C2×#41—611no—
225#131—614no—
226#131—1222no—
227#131—1222no—
228#131—1222no—
229C2×M16—1221no—
230C2×M16—1221no—
231C2×M16C4×D6111yescharacteristic
232C2×M16C4×D6111yescharacteristic
233C22×C8—21no—
234C22×C8—611no—
235C22×C8—611no—
236C22×C8—1221no—
237C22×C8—1221no—
238C22×C8—1221no—
239C4×Q8—611no—
240C4×Q8—611no—
241C4×D4—611no—
242C4×D4—611no—
243C4×D4—1221no—
244C4×D4—1221no—
245#117—611no—
246#117—1221no—
247C2×C42—1221no—
248C2×C42C22×D6111yescharacteristic
249C4⋊C8—21no—
250C4⋊C8—21no—
251C4⋊C8—21no—
252C4⋊C8—1221no—
253C4⋊C8—1221no—
254C4⋊C8—1221no—
255C22⋊C8—21no—
256C22⋊C8—1221no—
257#97—21no—
258#97—1221no—
259#97—1221no—
260C4×C8—21no—
261C4×C8—21no—
262C4×C8—611no—
263C4×C8—611no—
264C4×C8—611no—
265C4×C8—611no—
266C4×C8—1221no—
267C4×C8—1221no—
268C4×C8—1221no—
269#41—612no—
270#41—612no—
271#41—1221no—
272#41—1221no—
273C2×Q8—611no—
274C2×D4—611no—
275C2×D4—1221no—
276C22×C4—1221no—
277C22×C4—1221no—
278C22×C4—1221no—
279C22×C4C2×C4×D6111yescharacteristic
280C22×C4#1175822211yescharacteristic
281C22×C4#1175822211yescharacteristic
282M16—21no—
283M16—21no—
284M16—1224no—
285M16—1224no—
286M16C8×D6112yes—
287M16#1175818912yes—
288C2×C8—21no—
289C2×C8—21no—
290C2×C8—41no—
291C2×C8—41no—
292C2×C8—81no—
293C2×C8—611no—
294C2×C8—611no—
295C2×C8—612no—
296C2×C8—612no—
297C2×C8—611no—
298C2×C8—611no—
299C2×C8—1224no—
300C2×C8—1224no—
301C2×C8—1221no—
302C2×C8—1221no—
303C2×C8—4881no—
304C2×C8—2441no—
305C2×C8—2441no—
306C4⋊C4—611no—
307C4⋊C4—611no—
308C4⋊C4—1221no—
309C4⋊C4—1221no—
310C22⋊C4—1221no—
311C22⋊C4—1221no—
312C22⋊C4—1221no—
313C42—1221no—
314C42—1221no—
315C42—1221no—
316C42D4×D6111yescharacteristic
317C42D4×D6111yescharacteristic
318C42D4×D6111yescharacteristic
319C42Q8×D6111yescharacteristic
320C23—1221no—
321C23#1451973411yescharacteristic
322Q8—612no—
323Q8—1221no—
324D4—612no—
325D4—1222no—
326D4—1222no—
327D4—1221no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—41no—
331C2×C4—1221no—
332C2×C4—1222no—
333C2×C4—1222no—
334C2×C4—1221no—
335C2×C4—1221no—
336C2×C4—2442no—
337C2×C4—2441no—
338C2×C4—2441no—
339C2×C4C22⋊C4×D6111yescharacteristic
340C2×C4C4⋊C4×D6111yescharacteristic
341C2×C4#1451975011yescharacteristic
342C2×C4#1451975011yescharacteristic
343C2×C4#1451975511yescharacteristic
344C2×C4#1451975511yescharacteristic
345C2×C4C2×C8×D6111yescharacteristic
346C2×C4M16×D6111yescharacteristic
347C2×C4M16×D6111yescharacteristic
348C2×C4C2×#1175818911yescharacteristic
349C8—22no—
350C8—22no—
351C8—81no—
352C8—81no—
353C8—612no—
354C8—612no—
355C8—1221no—
356C8—1221no—
357C8—4881no—
358C8—4881no—
359C22—21no—
360C22—21no—
361C22—1222no—
362C22—2441no—
363C22—2441no—
364C22#1683962111yescharacteristic
365C22#1683981311yescharacteristic
366C22#1683981711yescharacteristic
367C4—21no—
368C4—21no—
369C4—21no—
370C4—1222no—
371C4—2441no—
372C4—2441no—
373C4C22⋊C8×D6111yescharacteristic
374C4#1683972411yescharacteristic
375C4C4⋊C8×D6111yescharacteristic
376C4#1683978411yescharacteristic
377C4#1684002411yescharacteristic
378C4#1684002811yescharacteristic
379C2—21no—
380C2—21no—
381C2—2442no—
382C2#2144579811yescharacteristic
383C2#2144587211yescharacteristic
384C2#2144587711yescharacteristic
subgroupG/H
centerC2×C4#14519750
commutatorC2×C4×C61C22×C8
FrattiniC2×C42C22×D61
FittingC61×#1283C2
socleC22×C61#380
prime radicalC2×#11758222C2×C4
cosocleC2×C42×C61C23
hypercenter#1283D61
hypocenterC61#8604
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1283

Complements

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

NH ≅ G/Ntype
2. #21444565C2semidirect
3. C2×#16839512C2semidirect
6. #21443670C2semidirect
7. C61×#1283C2semidirect
35. #14519785C8semidirect
193. #1283D61semidirect
223. C61#8604semidirect

Maximal subgroups

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

subgroupindex
C4×#145197852
#214445652
C2×#168395122
#214442072
#214442042
#214436702
C61×#12832
#860461