Finite Group Databasebeta

← #29573191

Subgroups — #29573191

Order 15616.

432 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454780C211yesmaximal, characteristic
2#21445840C211yesmaximal, characteristic
3#21445836C211yesmaximal, characteristic
4C4×#14519708C211yesmaximal, characteristic, complemented
5#21444577C211yesmaximal, characteristic, complemented
6#21443721C211yesmaximal, characteristic, complemented
7C61×#1303C211yesmaximal, characteristic, complemented
8C4×#11758222C2211yescharacteristic
9#16839889C411yescharacteristic, complemented
10#16839889C411yescharacteristic, complemented
11#16839839C411yescharacteristic, complemented
12#16839839C411yescharacteristic, complemented
13#16839830—21no—
14#16839830—21no—
15#16839813—21no—
16C2×#14519708—21no—
17#16839786C2211yescharacteristic
18C2×#14519705—21no—
19C2×#14519703—21no—
20C4×#11758189—21no—
21C2×C4×#92418C2211yescharacteristic
22C4×C4⋊Dic61C2211yescharacteristic
23#16839524—21no—
24#16839523—21no—
25#16839522—21no—
26#16839514—21no—
27#16839514—21no—
28C61×#431C2211yescharacteristic
29C61×#423C2211yescharacteristic
30C4×C4⋊C4×C61C2211yescharacteristic
31C2×#11758222D411yescharacteristic
32C2×#11758194—21no—
33C2×#11758189—21no—
34C2×#11758189—21no—
35C22×#92418D411yescharacteristic
36C22×#92418D411yescharacteristic
37C4×Dic122C2×C411yescharacteristic
38C4×Dic122Q811yescharacteristic
39C4×D244C2×C411yescharacteristic
40C4×D244Q811yescharacteristic
41C4×C22⋊D61—21no—
42C4×C22⋊D61—21no—
43#14519736D411yescharacteristic
44#14519734—21no—
45C2×C4⋊Dic61—21no—
46C2×C4×Dic61—21no—
47C42×D61—21no—
48#14519708—24no—
49C4⋊#92418—21no—
50C4⋊#92418—21no—
51#14519706—21no—
52#14519706—21no—
53#14519705—42no—
54#14519703—42no—
55#14519689—21no—
56#14519689—21no—
57#14519687—21no—
58#14519687—21no—
59C4×#92418C2×C411yescharacteristic
60C4×#92418C2×C411yescharacteristic
61C4×#92418D411yescharacteristic
62C4×#92418D411yescharacteristic
63#14519684—21no—
64C2×M16×C61—21no—
65C2×C4⋊C4×C61—21no—
66C2×C42×C61—21no—
67C2×C42×C61C2311yescharacteristic
68C4⋊C8×C61—21no—
69C4⋊C8×C61—21no—
70C4⋊C8×C61C2×C411yescharacteristic
71C4⋊C8×C61C2×C411yescharacteristic
72C22⋊C8×C61—21no—
73C4×C8×C61—21no—
74#95×C61—21no—
75C22×C4×C61—41no—
76C22×C4×C61C2×D411yescharacteristic
77C22×C4×C61C2×D411yescharacteristic
78C22×C4×C61#4111yescharacteristic
79C2×C22⋊D61—21no—
80C22×Dic61—41no—
81#11758222—21no—
82#11758222—21no—
83#11758222—21no—
84#11758222—21no—
85C2×D244C4⋊C411yescharacteristic
86C2×C4×D61—21no—
87C2×C4×D61—21no—
88C2×C4×D61—21no—
89C2×Dic122C4⋊C411yescharacteristic
90M16×C61—41no—
91M16×C61—41no—
92C2×C8×C61—21no—
93C2×C8×C61—21no—
94C2×C8×C61—41no—
95C4⋊C4×C61—22no—
96C4⋊C4×C61—41no—
97C42×C61—41no—
98C42×C61—41no—
99C42×C61C22×C411yescharacteristic
100C42×C61C2×D411yescharacteristic
101C42×C61C2×Q811yescharacteristic
102C42×C61#4111yescharacteristic
103C22⋊Dic61—21no—
104#11758198—21no—
105#11758198—21no—
106C4⋊Dic61—22no—
107C4⋊Dic61—41no—
108C4⋊Dic61C4⋊C411yescharacteristic
109C4⋊Dic61C4⋊C411yescharacteristic
110#11758196—21no—
111#11758196—21no—
112C4×Dic61—21no—
113C4×Dic61—21no—
114C4×Dic61—21no—
115C4×Dic61—41no—
116C4×Dic61—41no—
117#11758194—41no—
118#11758194—41no—
119C2×#92418—22no—
120C2×#92418—41no—
121C2×#92418—41no—
122C2×#92418C22⋊C411yescharacteristic
123C2×#92418C22⋊C411yescharacteristic
124C2×#92418C22⋊C411yescharacteristic
125C2×#92418C22⋊C411yescharacteristic
126#11758189—42no—
127#11758189—42no—
128C23×C61#12111yescharacteristic
129C22×D61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—41no—
133C2×C4×C61—42no—
134C2×C4×C61—81no—
135C2×C4×C61—81no—
136C2×C4×C61C2×C22⋊C411yescharacteristic
137C2×C4×C61C2×C4⋊C411yescharacteristic
138C2×C4×C61#11711yescharacteristic
139C2×C4×C61#12111yescharacteristic
140C2×C4×C61C22⋊Q811yescharacteristic
141C2×C4×C61C22⋊Q811yescharacteristic
142C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
144C2×C4×C61#13711yescharacteristic
145C2×C4×C61#13711yescharacteristic
146C22⋊D61—41no—
147C22⋊D61—41no—
148C2×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—21no—
151C2×Dic61—42no—
152C2×Dic61—81no—
153C2×Dic61—81no—
154D244—21no—
155D244—21no—
156C4×D61—42no—
157C4×D61—41no—
158C4×D61—41no—
159C4×D61—41no—
160C4×D61—41no—
161Dic122—21no—
162Dic122—21no—
163C8×C61—41no—
164C8×C61—41no—
165C8×C61—81no—
166#92418—21no—
167#92418—21no—
168#92418—21no—
169#92418—81no—
170#92418#10412yescomplemented
171#8669—611nomaximal, Sylow
172C22×C61—21no—
173C22×C61—21no—
174C22×C61#38011yescharacteristic
175C22×C61#46811yescharacteristic
176C22×C61#46811yescharacteristic
177C2×D61—41no—
178C2×D61—41no—
179C2×D61—41no—
180C4×C61—21no—
181C4×C61—21no—
182C4×C61—21no—
183C4×C61—82no—
184C4×C61C2×#10411yescharacteristic
185C4×C61#42111yescharacteristic
186C4×C61#42811yescharacteristic
187C4×C61#42811yescharacteristic
188C4×C61#46911yescharacteristic
189C4×C61#47011yescharacteristic
190Dic61—41no—
191Dic61—41no—
192Dic61—41no—
193Dic61—82no—
194#2965—611no—
195#1806—611no—
196#1806—611no—
197C4×#106—611no—
198#1567—611no—
199#1303—611no—
200#1303D6111yescharacteristic, complemented
201C2×C61—21no—
202C2×C61—21no—
203C2×C61#180611yescharacteristic
204C2×C61#180911yescharacteristic
205C2×C61#181411yescharacteristic
206D61—81no—
207C4×#41—611no—
208#446—611no—
209#446—611no—
210#436—611no—
211#436—611no—
212#435—1221no—
213#435—1221no—
214#431—1221no—
215#431C2×D6111yescharacteristic
216C2×#106—1221no—
217#423—611no—
218#423C2×D6111yescharacteristic
219C2×#104—1221no—
220C2×#104—1221no—
221C4×M16—1221no—
222C2×C4×C8—611no—
223C4×C4⋊C4—611no—
224C4×C4⋊C4C2×D6111yescharacteristic
225#340—1221no—
226#339—1221no—
227#339—1221no—
228#335—1221no—
229#335—1221no—
230C61#866911yescharacteristic, complemented, Sylow
231C2×#41—611no—
232C2×M16—21no—
233C2×M16—1221no—
234C2×M16—1221no—
235C2×M16—1221no—
236C22×C8—611no—
237C22×C8—611no—
238C4×Q8—611no—
239C4×Q8—611no—
240C4×D4—611no—
241C4×D4—611no—
242C4×D4—1221no—
243C4×D4—1221no—
244#117—611no—
245#117—1221no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—1221no—
248C2×C42—21no—
249C2×C42—1221no—
250C2×C42—1221no—
251C2×C42C22×D6111yescharacteristic
252#106—1224no—
253C4⋊C8—21no—
254C4⋊C8—21no—
255C4⋊C8—1221no—
256C4⋊C8—1221no—
257C4⋊C8—1221no—
258C4⋊C8—1221no—
259C4⋊C8C4×D6111yescharacteristic
260C4⋊C8C4×D6111yescharacteristic
261#104—2442no—
262#104—2442no—
263C22⋊C8—21no—
264C22⋊C8—1221no—
265C22⋊C8—1221no—
266#97—1221no—
267#97—1221no—
268C4×C8—21no—
269C4×C8—611no—
270C4×C8—611no—
271C4×C8—611no—
272C4×C8—611no—
273#95—21no—
274#95—1221no—
275#41—1221no—
276#41—1221no—
277#41—1221no—
278#41—1221no—
279C2×Q8—611no—
280C2×D4—611no—
281C2×D4—1221no—
282C22×C4—41no—
283C22×C4—1221no—
284C22×C4—1221no—
285C22×C4—1221no—
286C22×C4—2441no—
287C22×C4#1175822211yescharacteristic
288C22×C4D4×D6111yescharacteristic
289C22×C4D4×D6111yescharacteristic
290M16—41no—
291M16—41no—
292M16—2442no—
293M16—2442no—
294M16—2441no—
295M16—2441no—
296C2×C8—21no—
297C2×C8—21no—
298C2×C8—41no—
299C2×C8—611no—
300C2×C8—611no—
301C2×C8—611no—
302C2×C8—611no—
303C2×C8—1222no—
304C2×C8—2441no—
305C2×C8—2441no—
306C4⋊C4—22no—
307C4⋊C4—41no—
308C4⋊C4—611no—
309C4⋊C4—611no—
310C4⋊C4—1222no—
311C4⋊C4—1221no—
312C4⋊C4—1221no—
313C4⋊C4—2441no—
314C22⋊C4—1221no—
315C22⋊C4—1221no—
316C22⋊C4—1221no—
317C42—41no—
318C42—41no—
319C42—1221no—
320C42—1221no—
321C42—1221no—
322C42—2441no—
323C42—2441no—
324C42C2×C4×D6111yescharacteristic
325C42#1175822211yescharacteristic
326C42D4×D6111yescharacteristic
327C42Q8×D6111yescharacteristic
328C23—1221no—
329C23#1451975011yescharacteristic
330Q8—1221no—
331Q8—1221no—
332D4—1221no—
333D4—1221no—
334D4—2441no—
335D4—2441no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—41no—
339C2×C4—42no—
340C2×C4—81no—
341C2×C4—81no—
342C2×C4—1221no—
343C2×C4—1221no—
344C2×C4—1221no—
345C2×C4—4881no—
346C2×C4—4881no—
347C2×C4—2442no—
348C2×C4—2442no—
349C2×C4—2441no—
350C2×C4—2441no—
351C2×C4—2441no—
352C2×C4—2441no—
353C2×C4C22⋊C4×D6111yescharacteristic
354C2×C4C4⋊C4×D6111yescharacteristic
355C2×C4#1451973411yescharacteristic
356C2×C4#1451975011yescharacteristic
357C2×C4#1451975511yescharacteristic
358C2×C4#1451975511yescharacteristic
359C2×C4#1451980111yescharacteristic
360C2×C4#1451980411yescharacteristic
361C2×C4#1451980611yescharacteristic
362C2×C4#1451980911yescharacteristic
363C8—41no—
364C8—41no—
365C8—81no—
366C8—612no—
367C8—1221no—
368C8—1221no—
369C8—1221no—
370C8—4881no—
371C22—21no—
372C22—21no—
373C22—2441no—
374C22—2441no—
375C22—2441no—
376C22#1683962111yescharacteristic
377C22#1684000711yescharacteristic
378C22#1684001111yescharacteristic
379C4—21no—
380C4—21no—
381C4—21no—
382C4—82no—
383C4—4882no—
384C4—2441no—
385C4—2441no—
386C4—2441no—
387C4#104×D6111yescharacteristic
388C4#1683977711yescharacteristic
389C4#1683980111yescharacteristic
390C4#1683980311yescharacteristic
391C4#1684001411yescharacteristic
392C4#1684001911yescharacteristic
393C2—21no—
394C2—21no—
395C2—4881no—
396C2#2144583811yescharacteristic
397C2#2144585111yescharacteristic
398C2#2144587211yescharacteristic
subgroupG/H
centerC2×C4#14519750
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1303C2
socleC22×C61#380
prime radicalC2×#11758222D4
cosocleC2×C42×C61C23
hypercenter#1303D61
hypocenterC61#8669
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1303

Complements

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

NH ≅ G/Ntype
4. C4×#14519708C2semidirect
5. #21444577C2semidirect
6. #21443721C2semidirect
7. C61×#1303C2semidirect
9. #16839889C4semidirect
10. #16839889C4semidirect
11. #16839839C4semidirect
12. #16839839C4semidirect
170. #92418#104semidirect
200. #1303D61semidirect
230. C61#8669semidirect

Maximal subgroups

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

subgroupindex
#214547802
#214458402
#214458362
C4×#145197082
#214445772
#214437212
C61×#13032
#866961