Finite Group Databasebeta

← #29574657

Subgroups — #29574657

Order 15616.

586 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454842C211yesmaximal, characteristic
2C4×#14519765C211yesmaximal, characteristic
3#21444215C211yesmaximal, characteristic, complemented
4#21444213C211yesmaximal, characteristic, complemented
5#21444139C211yesmaximal, characteristic
6#21443652C211yesmaximal, characteristic, complemented
7C61×#1276C211yesmaximal, 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#16839653—22no—
19#16839628C411yescharacteristic
20C4×#11758198—22no—
21#16839494—22no—
22#16839492—22no—
23#16839485—22no—
24C61×#431C2211yescharacteristic
25C61×#431C2211yescharacteristic
26C43×C61C2211yescharacteristic
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⋊Dic61C2×C411yescharacteristic
42C2×C4⋊Dic61C2×C411yescharacteristic
43C2×#11758196—21no—
44C2×#11758198—22no—
45C2×#11758198—22no—
46C2×#11758198D412yes—
47C2×C4×Dic61—21no—
48C4⋊#92418—21no—
49C4⋊#92418D412yes—
50C22⋊#92418—21no—
51C22⋊#92418—21no—
52#14519689—24no—
53C4×#92418—21no—
54C4×#92418—21no—
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×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—44no—
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×C61—42no—
98C42×C61—42no—
99C42×C61C2×C812yescomplemented
100C42×C61C2×D411yescharacteristic
101C42×C61C2×D411yescharacteristic
102C42×C61#4111yescharacteristic
103C42×C61#4111yescharacteristic
104#11758198—28no—
105#11758198—22no—
106#11758198—22no—
107#11758198—44no—
108C4⋊Dic61—21no—
109C4⋊Dic61—21no—
110C4⋊Dic61—21no—
111C4⋊Dic61—21no—
112#11758196—41no—
113#11758196—41no—
114C4×Dic61—41no—
115C4×Dic61—41no—
116C2×#92418—22no—
117C2×#92418—41no—
118C8×D61—84no—
119C23×C61C2×C22⋊C411yescharacteristic
120C22×D61—22no—
121C22×D61—22no—
122C22×D61—42no—
123C22×D61—42no—
124C22×D61C22⋊C814yes—
125C2×C4×C61—22no—
126C2×C4×C61—22no—
127C2×C4×C61—22no—
128C2×C4×C61—41no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61C4×D411yescharacteristic
134C2×C4×C61C4×D411yescharacteristic
135C2×C4×C61#12011yescharacteristic
136C2×C4×C61#12111yescharacteristic
137C2×C4×C61#12111yescharacteristic
138C2×C4×C61#12311yescharacteristic
139C2×C4×C61C22×C811yescharacteristic
140C2×C4×C61C2×M1611yescharacteristic
141C2×C4×C61#13111yescharacteristic
142C2×C4×C61#13111yescharacteristic
143C2×Dic61—22no—
144C2×Dic61—22no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—42no—
148C2×Dic61—42no—
149C2×Dic61—41no—
150D244—22no—
151D244—22no—
152D244—22no—
153D244—22no—
154C4×D61—44no—
155C4×D61—82no—
156Dic122—22no—
157Dic122—22no—
158Dic122—41no—
159Dic122—41no—
160C8×C61—42no—
161C8×C61—81no—
162#92418—42no—
163#92418—81no—
164#8957—611nomaximal, Sylow
165C22×C61—21no—
166C22×C61—21no—
167C22×C61#38611yescharacteristic
168C22×C61C2×C22⋊C811yescharacteristic
169C22×C61#40811yescharacteristic
170C2×D61—24no—
171C2×D61—42no—
172C2×D61—42no—
173C2×D61—44no—
174C2×D61—82no—
175C4×C61—21no—
176C4×C61—21no—
177C4×C61—21no—
178C4×C61—42no—
179C4×C61—42no—
180C4×C61C8×D411yescharacteristic
181C4×C61C8×D411yescharacteristic
182C4×C61#43511yescharacteristic
183C4×C61#43511yescharacteristic
184C4×C61#45512yes—
185Dic61—42no—
186Dic61—42no—
187Dic61—81no—
188#2972—611no—
189C4×#124—611no—
190#1479—611no—
191#1479—611no—
192#1460—611no—
193#1276—611no—
194#1276D6111yescharacteristic, complemented
195C2×C61—21no—
196C2×C61—21no—
197C2×C61#186911yescharacteristic
198C2×C61#188411yescharacteristic
199C2×C61#188511yescharacteristic
200D61—44no—
201C2×#124—611no—
202C2×C4×Q8—611no—
203C2×C4×D4—611no—
204C8×D4—1222no—
205C8×D4—1222no—
206#431—611no—
207#431—611no—
208#431C2×D6111yescharacteristic
209#431C2×D6111yescharacteristic
210C2×C22⋊C8—1222no—
211#391—611no—
212#390—611no—
213#388—1222no—
214#382—611no—
215C4×C22⋊C4—1222no—
216C43C2×D6111yescharacteristic
217Q8⋊C8—1222no—
218Q8⋊C8—1222no—
219#323—1222no—
220C61#895711yescharacteristic, complemented, Sylow
221C22×Q8—611no—
222C22×D4—611no—
223C23×C4—612no—
224C22×C8—1224no—
225#124—614no—
226#124—1222no—
227C4×Q8—1221no—
228C4×Q8—1221no—
229C4×Q8—1221no—
230C4×Q8—1221no—
231C4×D4—1221no—
232C4×D4—1221no—
233C4×D4—1221no—
234C4×D4—1221no—
235C2×C4⋊C4—611no—
236C2×C4⋊C4—611no—
237C2×C4⋊C4—1221no—
238C2×C22⋊C4—612no—
239C2×C22⋊C4—1222no—
240C2×C22⋊C4—1222no—
241C2×C42—21no—
242C2×C42—21no—
243C2×C42—1221no—
244C2×C42C4×D6111yescharacteristic
245C2×C42C4×D6111yescharacteristic
246C2×C42C22×D6111yescharacteristic
247C4⋊C8—21no—
248C4⋊C8—612no—
249C4⋊C8—1221no—
250C4⋊C8D24412yes—
251C22⋊C8—21no—
252C22⋊C8—21no—
253C22⋊C8—1224no—
254C22⋊C8—1221no—
255C22⋊C8—1221no—
256C4×C8—21no—
257C4×C8—21no—
258C4×C8—1221no—
259C4×C8—1221no—
260#95—1222no—
261#95—1222no—
262C24—612no—
263C2×Q8—612no—
264C2×Q8—1221no—
265C2×Q8—1221no—
266C2×Q8—1221no—
267C2×Q8—1221no—
268C2×Q8—1221no—
269C2×D4—612no—
270C2×D4—612no—
271C2×D4—1221no—
272C2×D4—1221no—
273C2×D4—1221no—
274C2×D4—1221no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—612no—
278C22×C4—1221no—
279C22×C4—1222no—
280C22×C4—1222no—
281C22×C4—1221no—
282C22×C4—2444no—
283C22×C4C2×C4×D6111yescharacteristic
284C22×C4D4×D6111yescharacteristic
285C22×C4D4×D6111yescharacteristic
286C2×C8—22no—
287C2×C8—41no—
288C2×C8—1222no—
289C2×C8—4884no—
290C2×C8—2441no—
291C4⋊C4—1221no—
292C4⋊C4—1221no—
293C4⋊C4—1221no—
294C4⋊C4—1221no—
295C4⋊C4—2441no—
296C4⋊C4—2441no—
297C22⋊C4—1228no—
298C22⋊C4—1222no—
299C22⋊C4—1222no—
300C22⋊C4—2444no—
301C42—21no—
302C42—21no—
303C42—21no—
304C42—42no—
305C42—42no—
306C42—2441no—
307C42—2441no—
308C42C8×D6112yescomplemented
309C42C2×D24411yescharacteristic
310C42#1175822211yescharacteristic
311C42D4×D6111yescharacteristic
312C42#1175822611yescharacteristic
313C23—614no—
314C23—1222no—
315C23—1222no—
316C23—2442no—
317C23—2442no—
318C23C22⋊C4×D6111yescharacteristic
319Q8—1222no—
320Q8—1222no—
321Q8—2441no—
322Q8—2441no—
323D4—1222no—
324D4—1222no—
325D4—1222no—
326D4—1222no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—1222no—
336C2×C4—1222no—
337C2×C4—4882no—
338C2×C4—2442no—
339C2×C4—2441no—
340C2×C4—2441no—
341C2×C4—2441no—
342C2×C4—2444no—
343C2×C4—2442no—
344C2×C4#1451973911yescharacteristic
345C2×C4C4×D24411yescharacteristic
346C2×C4#1451974711yescharacteristic
347C2×C4#1451975011yescharacteristic
348C2×C4#1451975211yescharacteristic
349C2×C4#1451976211yescharacteristic
350C2×C4C2×C8×D6111yescharacteristic
351C2×C4M16×D6111yescharacteristic
352C2×C4#1451978311yescharacteristic
353C2×C4#1451978511yescharacteristic
354C8—42no—
355C8—81no—
356C8—4881no—
357C8—2442no—
358C22—21no—
359C22—21no—
360C22—1224no—
361C22—4882no—
362C22—2444no—
363C22—2442no—
364C22—2442no—
365C22#1683964011yescharacteristic
366C22C22⋊C8×D6111yescharacteristic
367C22#1683972711yescharacteristic
368C4—21no—
369C4—21no—
370C4—21no—
371C4—42no—
372C4—42no—
373C4—4881no—
374C4—2442no—
375C4—2442no—
376C4#1683982711yescharacteristic
377C4C8×D24411yescharacteristic
378C4#1683983211yescharacteristic
379C4#1683983511yescharacteristic
380C4#1683994112yes—
381C2—21no—
382C2—21no—
383C2—2444no—
384C2#2144611011yescharacteristic
385C2#2144620111yescharacteristic
386C2#2144620611yescharacteristic
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#8957
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
3. #21444215C2semidirect
4. #21444213C2semidirect
6. #21443652C2semidirect
7. C61×#1276C2semidirect
32. #14519765C8semidirect
91. C2×Dic122C2×C8semidirect
99. C42×C61C2×C8semidirect
194. #1276D61semidirect
220. C61#8957semidirect
308. C42C8×D61semidirect

Maximal subgroups

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

subgroupindex
#214548422
C4×#145197652
#214442152
#214442132
#214441392
#214436522
C61×#12762
#895761