Finite Group Databasebeta

← #29574672

Subgroups — #29574672

Order 15616.

566 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
1#21454899C211yesmaximal, characteristic, complemented
2C4×#14519765C211yesmaximal, characteristic
3#21444211C211yesmaximal, characteristic
4#21444209C211yesmaximal, characteristic
5#21444142C211yesmaximal, characteristic, complemented
6#21443652C211yesmaximal, characteristic, complemented
7C61×#1276C211yesmaximal, characteristic, complemented
8C2×#14519765C411yescharacteristic
9C2×C4×Dic122C2211yescharacteristic
10C2×C4×D244C2211yescharacteristic
11C8×Dic122—22no—
12#16839886—22no—
13#16839815C2211yescharacteristic
14#16839815C2211yescharacteristic
15#16839812—22no—
16#16839668C411yescharacteristic
17#16839664C411yescharacteristic
18#16839653—22no—
19#16839628C411yescharacteristic
20C4×#11758198—22no—
21#16839491—22no—
22#16839489—22no—
23#16839487—22no—
24C61×#431C2211yescharacteristic
25C61×#431C2211yescharacteristic
26C43×C61C2211yescharacteristic
27C22×Dic122C2×C411yescharacteristic
28C22×D244C2×C411yescharacteristic
29C22×C4×D61—21no—
30#14519765—22no—
31#14519765C814yescomplemented
32C4×Dic122—21no—
33C4×Dic122—21no—
34C4×Dic122—21no—
35C4×Dic122—21no—
36C4×D244—21no—
37C4×D244—21no—
38C4×D244—21no—
39C4×D244—21no—
40C2×C4⋊Dic61C2×C411yescharacteristic
41C2×C4⋊Dic61C2×C411yescharacteristic
42C2×#11758196D412yes—
43C2×#11758198—22no—
44C2×#11758198—21no—
45C2×#11758198—22no—
46C2×C4×Dic61D412yes—
47C4⋊#92418—21no—
48C4⋊#92418D412yes—
49#14519706—24no—
50C22⋊#92418—21no—
51C22⋊#92418—21no—
52C4×#92418—21no—
53C4×#92418—21no—
54C8×Dic61—24no—
55#14519684—22no—
56#14519684—22no—
57C2×C42×C61—21no—
58C2×C42×C61—21no—
59C2×C42×C61C2×C411yescharacteristic
60C2×C42×C61C2×C411yescharacteristic
61C2×C42×C61C2311yescharacteristic
62C4⋊C8×C61—21no—
63C4⋊C8×C61D412yes—
64C22⋊C8×C61—21no—
65C22⋊C8×C61—21no—
66C4×C8×C61—21no—
67C4×C8×C61—21no—
68C23×D61—21no—
69C22×C4×C61—21no—
70C22×C4×C61—21no—
71C22×C4×C61C22×C411yescharacteristic
72C22×C4×C61C2×D411yescharacteristic
73C22×C4×C61C2×D411yescharacteristic
74C22×Dic61—21no—
75C22×Dic61C22⋊C412yes—
76C22×Dic61C22⋊C412yes—
77C2×D244—21no—
78C2×D244—21no—
79C2×D244—21no—
80C2×D244—21no—
81C2×D244—21no—
82C2×D244C2×C812yes—
83C2×C4×D61—44no—
84C2×C4×D61—41no—
85C2×C4×D61—41no—
86C2×Dic122—21no—
87C2×Dic122—21no—
88C2×Dic122—21no—
89C2×Dic122—21no—
90C2×Dic122C2×C812yes—
91C2×Dic122M1612yes—
92C2×C8×C61—22no—
93C2×C8×C61—41no—
94C42×C61—21no—
95C42×C61—21no—
96C42×C61—21no—
97C42×C61—42no—
98C42×C61—42no—
99C42×C61C2×C812yes—
100C42×C61C2×D411yescharacteristic
101C42×C61C2×D411yescharacteristic
102C42×C61#4111yescharacteristic
103C42×C61#4111yescharacteristic
104#11758198—28no—
105#11758198—44no—
106#11758198—41no—
107#11758198—41no—
108C4⋊Dic61—21no—
109C4⋊Dic61—21no—
110C4⋊Dic61—21no—
111C4⋊Dic61—21no—
112#11758196—22no—
113#11758196—22no—
114C4×Dic61—22no—
115C4×Dic61—22no—
116C2×#92418—22no—
117C2×#92418—41no—
118C23×C61C2×C22⋊C411yescharacteristic
119C22×D61—22no—
120C22×D61—42no—
121C22×D61—42no—
122C22×D61—41no—
123C22×D61—41no—
124C2×C4×C61—22no—
125C2×C4×C61—22no—
126C2×C4×C61—22no—
127C2×C4×C61—41no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61C4×D411yescharacteristic
133C2×C4×C61C4×D411yescharacteristic
134C2×C4×C61#12011yescharacteristic
135C2×C4×C61#12111yescharacteristic
136C2×C4×C61#12111yescharacteristic
137C2×C4×C61#12311yescharacteristic
138C2×C4×C61C22×C811yescharacteristic
139C2×C4×C61C2×M1611yescharacteristic
140C2×C4×C61#13111yescharacteristic
141C2×C4×C61#13111yescharacteristic
142C2×Dic61—22no—
143C2×Dic61—22no—
144C2×Dic61—22no—
145C2×Dic61—42no—
146C2×Dic61—42no—
147C2×Dic61—41no—
148C2×Dic61C22⋊C814yes—
149D244—22no—
150D244—22no—
151D244—41no—
152D244—41no—
153C4×D61—82no—
154C4×D61—82no—
155Dic122—22no—
156Dic122—22no—
157Dic122—22no—
158Dic122—22no—
159C8×C61—42no—
160C8×C61—81no—
161#92418—42no—
162#92418—81no—
163#8960—611nomaximal, Sylow
164C22×C61—21no—
165C22×C61—21no—
166C22×C61#38611yescharacteristic
167C22×C61C2×C22⋊C811yescharacteristic
168C22×C61#40811yescharacteristic
169C2×D61—44no—
170C2×D61—42no—
171C2×D61—82no—
172C2×D61—81no—
173C2×D61—81no—
174C4×C61—21no—
175C4×C61—21no—
176C4×C61—21no—
177C4×C61—42no—
178C4×C61—42no—
179C4×C61C8×D411yescharacteristic
180C4×C61C8×D411yescharacteristic
181C4×C61#43511yescharacteristic
182C4×C61#43511yescharacteristic
183C4×C61#45412yes—
184Dic61—24no—
185Dic61—42no—
186Dic61—81no—
187#2982—611no—
188C4×#124—611no—
189#1478—611no—
190#1478—611no—
191#1461—611no—
192#1276—611no—
193#1276D6111yescharacteristic, complemented
194C2×C61—21no—
195C2×C61—21no—
196C2×C61#186911yescharacteristic
197C2×C61#188411yescharacteristic
198C2×C61#188811yescharacteristic
199D61—82no—
200C2×#124—611no—
201C2×C4×Q8—611no—
202C2×C4×D4—611no—
203C8×Q8—1222no—
204C8×Q8—1222no—
205#431—611no—
206#431—611no—
207#431—1222no—
208#431C2×D6111yescharacteristic
209#431C2×D6111yescharacteristic
210#391—611no—
211#390—611no—
212#388—1222no—
213#382—611no—
214C4×C22⋊C4—1222no—
215C43C2×D6111yescharacteristic
216D4⋊C8—1222no—
217D4⋊C8—1222no—
218#324—1222no—
219C61#896011yescharacteristic, complemented, Sylow
220C22×Q8—611no—
221C22×D4—611no—
222C23×C4—1221no—
223#124—614no—
224#124—1222no—
225C4×Q8—1221no—
226C4×Q8—1221no—
227C4×Q8—1221no—
228C4×Q8—1221no—
229C4×D4—1221no—
230C4×D4—1221no—
231C4×D4—1221no—
232C4×D4—1221no—
233C2×C4⋊C4—611no—
234C2×C4⋊C4—612no—
235C2×C4⋊C4—611no—
236C2×C22⋊C4—1222no—
237C2×C22⋊C4—1222no—
238C2×C22⋊C4—1221no—
239C2×C42—21no—
240C2×C42—21no—
241C2×C42—612no—
242C2×C42C4×D6111yescharacteristic
243C2×C42C4×D6111yescharacteristic
244C2×C42C22×D6111yescharacteristic
245C4⋊C8—21no—
246C4⋊C8—612no—
247C4⋊C8—1224no—
248C4⋊C8—1221no—
249C4⋊C8D24412yes—
250C22⋊C8—21no—
251C22⋊C8—21no—
252C22⋊C8—1221no—
253C22⋊C8—1221no—
254C4×C8—21no—
255C4×C8—21no—
256C4×C8—1224no—
257C4×C8—1221no—
258C4×C8—1221no—
259#95—1222no—
260#95—1222no—
261C24—1221no—
262C2×Q8—612no—
263C2×Q8—612no—
264C2×Q8—1221no—
265C2×Q8—1221no—
266C2×Q8—1221no—
267C2×Q8—1221no—
268C2×D4—612no—
269C2×D4—1221no—
270C2×D4—1221no—
271C2×D4—1221no—
272C2×D4—1221no—
273C2×D4—1221no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—612no—
277C22×C4—612no—
278C22×C4—1221no—
279C22×C4—2444no—
280C22×C4—2441no—
281C22×C4—2441no—
282C22×C4C2×C4×D6111yescharacteristic
283C22×C4D4×D6111yescharacteristic
284C22×C4D4×D6111yescharacteristic
285C2×C8—22no—
286C2×C8—41no—
287C2×C8—1222no—
288C2×C8—2441no—
289C4⋊C4—1221no—
290C4⋊C4—1221no—
291C4⋊C4—1222no—
292C4⋊C4—1222no—
293C4⋊C4—1221no—
294C4⋊C4—1221no—
295C22⋊C4—1228no—
296C22⋊C4—2444no—
297C22⋊C4—2441no—
298C22⋊C4—2441no—
299C42—21no—
300C42—21no—
301C42—21no—
302C42—42no—
303C42—42no—
304C42—1222no—
305C42—1222no—
306C42C8×D6112yes—
307C42C2×D24411yescharacteristic
308C42#1175822211yescharacteristic
309C42D4×D6111yescharacteristic
310C42#1175822611yescharacteristic
311C23—1222no—
312C23—2442no—
313C23—2442no—
314C23—2441no—
315C23—2441no—
316C23C22⋊C4×D6111yescharacteristic
317Q8—1222no—
318Q8—1222no—
319Q8—1222no—
320Q8—1222no—
321D4—1222no—
322D4—1222no—
323D4—2441no—
324D4—2441no—
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—614no—
334C2×C4—1222no—
335C2×C4—1222no—
336C2×C4—1222no—
337C2×C4—4882no—
338C2×C4—4882no—
339C2×C4—2442no—
340C2×C4—2441no—
341C2×C4—2442no—
342C2×C4#1451973911yescharacteristic
343C2×C4C4×D24411yescharacteristic
344C2×C4#1451974711yescharacteristic
345C2×C4#1451975011yescharacteristic
346C2×C4#1451975211yescharacteristic
347C2×C4#1451976211yescharacteristic
348C2×C4C2×C8×D6111yescharacteristic
349C2×C4M16×D6111yescharacteristic
350C2×C4#1451978311yescharacteristic
351C2×C4#1451978511yescharacteristic
352C8—42no—
353C8—81no—
354C8—4881no—
355C8—2442no—
356C22—21no—
357C22—21no—
358C22—4882no—
359C22—4881no—
360C22—4881no—
361C22—2444no—
362C22—2442no—
363C22#1683964011yescharacteristic
364C22C22⋊C8×D6111yescharacteristic
365C22#1683972711yescharacteristic
366C4—21no—
367C4—21no—
368C4—21no—
369C4—42no—
370C4—42no—
371C4—1224no—
372C4—4881no—
373C4—2442no—
374C4#1683982711yescharacteristic
375C4C8×D24411yescharacteristic
376C4#1683983211yescharacteristic
377C4#1683983511yescharacteristic
378C4#1683993612yes—
379C2—21no—
380C2—21no—
381C2—4882no—
382C2#2144611011yescharacteristic
383C2#2144620111yescharacteristic
384C2#2144622111yescharacteristic
subgroupG/H
centerC2×C4#14519747
commutatorC2×C4×C61C22×C8
FrattiniC2×C42C22×D61
FittingC61×#1276C2
socleC22×C61#386
prime radicalC22×D244C2×C4
cosocleC2×C42×C61C23
hypercenter#1276D61
hypocenterC61#8960
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1276

Complements

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

NH ≅ G/Ntype
1. #21454899C2semidirect
5. #21444142C2semidirect
6. #21443652C2semidirect
7. C61×#1276C2semidirect
31. #14519765C8semidirect
193. #1276D61semidirect
219. C61#8960semidirect

Maximal subgroups

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

subgroupindex
#214548992
C4×#145197652
#214442112
#214442092
#214441422
#214436522
C61×#12762
#896061