Finite Group Databasebeta

← #29575507

Subgroups — #29575507

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#21454842C211yesmaximal, characteristic
2#21448530C211yesmaximal, characteristic
3#21444215C211yesmaximal, characteristic, complemented
4#21444213C211yesmaximal, characteristic, complemented
5#21444139C211yesmaximal, characteristic
6#21443648C211yesmaximal, characteristic, complemented
7C61×#1274C211yesmaximal, characteristic, complemented
8C2×#14519765C411yescharacteristic
9C2×C4×Dic122C2211yescharacteristic
10C2×C4×D244C2211yescharacteristic
11C8×D244—22no—
12#16839827—22no—
13#16839815C2211yescharacteristic
14#16839815C2211yescharacteristic
15C22⋊C8×D61—22no—
16#16839668C411yescharacteristic
17#16839664C411yescharacteristic
18#16839654—22no—
19#16839636—22no—
20#16839632C411yescharacteristic
21#16839494—22no—
22#16839492—22no—
23#16839485—22no—
24C61×#431C2211yescharacteristic
25C61×#431C2211yescharacteristic
26C61×#376C2211yescharacteristic
27C22×Dic122C2×C411yescharacteristic
28C22×D244C2×C411yescharacteristic
29C22×C4×D61D412yes—
30C2×C8×D61—24no—
31#14519765—22no—
32#14519765C814yescomplemented
33C4×Dic122—21no—
34C4×Dic122—21no—
35C4×Dic122—21no—
36C4×Dic122—21no—
37C4×D244—21no—
38C4×D244—21no—
39C4×D244—21no—
40C4×D244—21no—
41C2×C4⋊Dic61—22no—
42C2×C4⋊Dic61C2×C411yescharacteristic
43C2×C4⋊Dic61C2×C411yescharacteristic
44C2×#11758196—21no—
45C2×#11758198—22no—
46C2×#11758198—22no—
47C2×#11758198D412yes—
48C2×C4×Dic61—21no—
49C4⋊#92418—21no—
50C4⋊#92418—21no—
51C22⋊#92418—21no—
52C22⋊#92418—21no—
53#14519689—24no—
54C4×#92418—21no—
55C4×#92418D412yes—
56#14519684—22no—
57C2×C42×C61C2×C411yescharacteristic
58C2×C42×C61C2×C411yescharacteristic
59C2×C42×C61C2311yescharacteristic
60C4⋊C8×C61—21no—
61C4⋊C8×C61—21no—
62C22⋊C8×C61—21no—
63C22⋊C8×C61—21no—
64C4×C8×C61—21no—
65C4×C8×C61D412yes—
66#95×C61—21no—
67#95×C61—21no—
68C23×D61C22⋊C412yes—
69C22×C4×C61—21no—
70C22×C4×C61—21no—
71C22×C4×C61C22×C411yescharacteristic
72C22×C4×C61C2×D411yescharacteristic
73C22×C4×C61C2×D411yescharacteristic
74C22×Dic61—21no—
75C22×Dic61—21no—
76C22×Dic61C22⋊C412yes—
77C2×D244—21no—
78C2×D244—21no—
79C2×D244—21no—
80C2×D244—21no—
81C2×D244C2×C812yes—
82C2×D244M1612yes—
83C2×C4×D61—22no—
84C2×C4×D61—22no—
85C2×C4×D61—82no—
86C2×Dic122—21no—
87C2×Dic122—21no—
88C2×Dic122—21no—
89C2×Dic122—21no—
90C2×Dic122—21no—
91C2×Dic122C2×C812yescomplemented
92C2×C8×C61—22no—
93C2×C8×C61—41no—
94C42×C61—21no—
95C42×C61—21no—
96C42×C61—21no—
97C42×C61C2×C812yescomplemented
98C42×C61C2×D411yescharacteristic
99C42×C61C2×D411yescharacteristic
100C42×C61#4111yescharacteristic
101C42×C61#4111yescharacteristic
102#11758198—28no—
103#11758198—22no—
104#11758198—22no—
105#11758198—82no—
106C4⋊Dic61—21no—
107C4⋊Dic61—21no—
108C4⋊Dic61—21no—
109C4⋊Dic61—21no—
110C4⋊Dic61—82no—
111#11758196—41no—
112#11758196—41no—
113C4×Dic61—41no—
114C4×Dic61—41no—
115C2×#92418—22no—
116C2×#92418—41no—
117C8×D61—84no—
118C23×C61C2×C22⋊C411yescharacteristic
119C22×D61—22no—
120C22×D61—22no—
121C22×D61—42no—
122C22×D61—42no—
123C22×D61C22⋊C814yes—
124C2×C4×C61—22no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
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—41no—
145C2×Dic61—41no—
146C2×Dic61—42no—
147C2×Dic61—42no—
148C2×Dic61—41no—
149D244—22no—
150D244—22no—
151D244—22no—
152D244—22no—
153C4×D61—44no—
154C4×D61—82no—
155Dic122—22no—
156Dic122—22no—
157Dic122—41no—
158Dic122—41no—
159C8×C61—42no—
160C8×C61—81no—
161#92418—42no—
162#92418—81no—
163#9099—611nomaximal, Sylow
164C22×C61—21no—
165C22×C61—21no—
166C22×C61#38611yescharacteristic
167C22×C61C2×C22⋊C811yescharacteristic
168C22×C61#40811yescharacteristic
169C2×D61—24no—
170C2×D61—42no—
171C2×D61—42no—
172C2×D61—44no—
173C2×D61—82no—
174C4×C61—21no—
175C4×C61—21no—
176C4×C61—21no—
177C4×C61—21no—
178C4×C61—42no—
179C4×C61—81no—
180C4×C61C8×D411yescharacteristic
181C4×C61C8×D411yescharacteristic
182C4×C61#43511yescharacteristic
183C4×C61#43511yescharacteristic
184Dic61—42no—
185Dic61—42no—
186Dic61—81no—
187#2972—611no—
188#2326—611no—
189#1479—611no—
190#1479—611no—
191#1460—611no—
192#1274—611no—
193#1274D6111yescharacteristic, complemented
194C2×C61—21no—
195C2×C61—21no—
196C2×C61#186911yescharacteristic
197C2×C61#190911yescharacteristic
198C2×C61#191111yescharacteristic
199D61—44no—
200C2×#124—611no—
201C2×C4×Q8—611no—
202C2×C4×D4—611no—
203C8×D4—1222no—
204C8×D4—1222no—
205#431—611no—
206#431—611no—
207#431C2×D6111yescharacteristic
208#431C2×D6111yescharacteristic
209C2×C22⋊C8—1222no—
210#391—611no—
211#390—611no—
212#388—1222no—
213#385—1222no—
214#384—611no—
215#376C2×D6111yescharacteristic
216Q8⋊C8—1222no—
217Q8⋊C8—1222no—
218#323—1222no—
219C61#909911yescharacteristic, complemented, Sylow
220C22×Q8—611no—
221C22×D4—611no—
222C23×C4—612no—
223C22×C8—1224no—
224#124—614no—
225#124—1222no—
226C4×Q8—1221no—
227C4×Q8—1221no—
228C4×Q8—1221no—
229C4×Q8—1221no—
230C4×D4—1221no—
231C4×D4—1221no—
232C4×D4—1221no—
233C4×D4—1221no—
234C2×C4⋊C4—611no—
235C2×C4⋊C4—611no—
236C2×C4⋊C4—1222no—
237C2×C4⋊C4—1221no—
238C2×C22⋊C4—612no—
239C2×C22⋊C4—1222no—
240C2×C22⋊C4—1222no—
241C2×C42—1221no—
242C2×C42C4×D6111yescharacteristic
243C2×C42C4×D6111yescharacteristic
244C2×C42C22×D6111yescharacteristic
245C4⋊C8—21no—
246C4⋊C8—21no—
247C4⋊C8—1221no—
248C4⋊C8—1221no—
249C22⋊C8—21no—
250C22⋊C8—21no—
251C22⋊C8—1224no—
252C22⋊C8—1221no—
253C22⋊C8—1221no—
254C4×C8—21no—
255C4×C8—612no—
256C4×C8—1221no—
257C4×C8D24412yes—
258#95—21no—
259#95—21no—
260#95—1222no—
261C24—612no—
262C2×Q8—612no—
263C2×Q8—1221no—
264C2×Q8—1221no—
265C2×Q8—1221no—
266C2×Q8—1221no—
267C2×Q8—1221no—
268C2×D4—612no—
269C2×D4—612no—
270C2×D4—1221no—
271C2×D4—1221no—
272C2×D4—1221no—
273C2×D4—1221no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—612no—
277C22×C4—1221no—
278C22×C4—1222no—
279C22×C4—1222no—
280C22×C4—1221no—
281C22×C4—4882no—
282C22×C4C2×C4×D6111yescharacteristic
283C22×C4D4×D6111yescharacteristic
284C22×C4D4×D6111yescharacteristic
285C2×C8—22no—
286C2×C8—41no—
287C2×C8—1222no—
288C2×C8—4884no—
289C2×C8—2441no—
290C4⋊C4—1221no—
291C4⋊C4—1221no—
292C4⋊C4—1221no—
293C4⋊C4—1221no—
294C4⋊C4—4882no—
295C4⋊C4—2441no—
296C4⋊C4—2441no—
297C22⋊C4—1228no—
298C22⋊C4—1222no—
299C22⋊C4—1222no—
300C22⋊C4—4882no—
301C42—21no—
302C42—21no—
303C42—21no—
304C42—2441no—
305C42—2441no—
306C42C8×D6112yescomplemented
307C42C2×D24411yescharacteristic
308C42#1175822211yescharacteristic
309C42D4×D6111yescharacteristic
310C42#1175822611yescharacteristic
311C23—614no—
312C23—1222no—
313C23—1222no—
314C23—2442no—
315C23—2442no—
316C23C22⋊C4×D6111yescharacteristic
317Q8—1222no—
318Q8—1222no—
319Q8—2441no—
320Q8—2441no—
321D4—1222no—
322D4—1222no—
323D4—1222no—
324D4—1222no—
325C2×C4—22no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—1222no—
334C2×C4—1222no—
335C2×C4—4882no—
336C2×C4—2444no—
337C2×C4—2442no—
338C2×C4—2441no—
339C2×C4—2441no—
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—1224no—
359C22—4882no—
360C22—2444no—
361C22—2442no—
362C22—2442no—
363C22#1683964011yescharacteristic
364C22C22⋊C8×D6111yescharacteristic
365C22#1683972711yescharacteristic
366C4—21no—
367C4—21no—
368C4—21no—
369C4—21no—
370C4—42no—
371C4—81no—
372C4—4881no—
373C4—2442no—
374C4—2442no—
375C4#1683982711yescharacteristic
376C4C8×D24411yescharacteristic
377C4#1683983211yescharacteristic
378C4#1683983511yescharacteristic
379C2—21no—
380C2—21no—
381C2—2444no—
382C2#2144611011yescharacteristic
383C2#2144634011yescharacteristic
384C2#2144635011yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC2×C4×C61C22×C8
FrattiniC2×C42C22×D61
FittingC61×#1274C2
socleC22×C61#386
prime radicalC22×D244C2×C4
cosocleC2×C42×C61C23
hypercenter#1274D61
hypocenterC61#9099
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1274

Complements

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

NH ≅ G/Ntype
3. #21444215C2semidirect
4. #21444213C2semidirect
6. #21443648C2semidirect
7. C61×#1274C2semidirect
32. #14519765C8semidirect
91. C2×Dic122C2×C8semidirect
97. C42×C61C2×C8semidirect
193. #1274D61semidirect
219. C61#9099semidirect
306. C42C8×D61semidirect

Maximal subgroups

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

subgroupindex
#214548422
#214485302
#214442152
#214442132
#214441392
#214436482
C61×#12742
#909961