Finite Group Databasebeta

← #29575251

Subgroups — #29575251

Order 15616.

500 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456379C211yesmaximal, characteristic
2#21454562C211yesmaximal, characteristic
3#21446764C211yesmaximal, characteristic, complemented
4#21444315C211yesmaximal, characteristic
5#21443658C211yesmaximal, characteristic, complemented
6#21443655C211yesmaximal, characteristic, complemented
7C61×#1481C211yesmaximal, characteristic, complemented
8C2×#14519783—21no—
9#16840312C2211yescharacteristic
10#16840158C411yescharacteristic, complemented
11#16840136C411yescharacteristic, complemented
12#16840112C411yescharacteristic, complemented
13#16840110C411yescharacteristic, complemented
14#16839993—22no—
15C4×#11758201—22no—
16#16839839—21no—
17#16839832—22no—
18#16839827—21no—
19#16839728—21no—
20C4×#11758194C2211yescharacteristic
21C2×C4×#92418C2211yescharacteristic
22C4×C4⋊Dic61C2211yescharacteristic
23#16839521—21no—
24#16839521—21no—
25#16839497—22no—
26C61×#533C2211yescharacteristic
27C61×#431C2211yescharacteristic
28C2×C4⋊C8×C61C2211yescharacteristic
29C61×Q8⋊C8—21no—
30C61×Q8⋊C8—21no—
31C2×#11758222—21no—
32C2×#11758201—22no—
33#14519783—42no—
34#14519783—42no—
35C2×#11758194D411yescharacteristic
36C2×#11758194D411yescharacteristic
37C2×#11758189—22no—
38C22×#92418—21no—
39C2×C8×D61—22no—
40#14519777C2×C411yescharacteristic
41#14519774C2×C411yescharacteristic
42#14519765—21no—
43#14519751—21no—
44#14519751D412yes—
45C4×D244—21no—
46C4×D244D412yes—
47C2×C4⋊Dic61—21no—
48C2×C4×Dic61—21no—
49#14519708—22no—
50#14519701—22no—
51#14519697—22no—
52#14519689—22no—
53#14519689—22no—
54#14519688—21no—
55C4×#92418—21no—
56C4×#92418—21no—
57C4×#92418C2×C411yescharacteristic
58C4×#92418C2×C411yescharacteristic
59#14519684—21no—
60C22×C8×C61—21no—
61C4⋊Q8×C61C2×C411yescharacteristic
62C4⋊Q8×C61C2×C411yescharacteristic
63#125×C61—21no—
64C22⋊Q8×C61—21no—
65C22⋊Q8×C61—21no—
66C4×Q8×C61—21no—
67C4×Q8×C61—21no—
68#117×C61—21no—
69C2×C42×C61C2311yescharacteristic
70C4⋊C8×C61—21no—
71C4⋊C8×C61—21no—
72C4⋊C8×C61D411yescharacteristic
73C4⋊C8×C61D411yescharacteristic
74C22⋊C8×C61—21no—
75C4×C8×C61—21no—
76C2×Q8×C61—21no—
77C2×Q8×C61—21no—
78C22×C4×C61C2×D411yescharacteristic
79C22×C4×C61C2×D411yescharacteristic
80C22×C4×C61#4111yescharacteristic
81C2×C22⋊D61—22no—
82C22×Dic61—41no—
83#11758222—41no—
84#11758222—41no—
85#11758222—41no—
86#11758222—41no—
87C2×D244—21no—
88C2×D244—21no—
89C2×D244C22⋊C412yes—
90C2×C4×D61—22no—
91C2×Dic122—21no—
92C2×C8×C61—21no—
93C2×C8×C61—21no—
94C2×C8×C61—41no—
95C2×C8×C61—41no—
96C2×C8×C61—41no—
97C4⋊C4×C61—21no—
98C4⋊C4×C61—21no—
99C4⋊C4×C61—21no—
100C4⋊C4×C61—21no—
101C4⋊C4×C61—41no—
102C4⋊C4×C61—41no—
103C22⋊C4×C61—41no—
104C42×C61—41no—
105C42×C61C22×C411yescharacteristic
106C42×C61C2×D411yescharacteristic
107C42×C61C2×D411yescharacteristic
108C42×C61#4111yescharacteristic
109#11758201—44no—
110#11758198—22no—
111#11758198—22no—
112C4⋊Dic61—21no—
113C4⋊Dic61—22no—
114C4⋊Dic61—41no—
115C4⋊Dic61C22⋊C412yes—
116C4×Dic61—41no—
117C4×Dic61—41no—
118#11758194—21no—
119#11758194—21no—
120#11758194—21no—
121#11758194SD1612yescomplemented
122C2×#92418—21no—
123C2×#92418—21no—
124C2×#92418—21no—
125C2×#92418—21no—
126C2×#92418—42no—
127#11758189—44no—
128C8×D61—44no—
129C23×C61#12111yescharacteristic
130C22×D61—22no—
131Q8×C61—42no—
132Q8×C61—41no—
133Q8×C61—41no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61C2×C22⋊C411yescharacteristic
140C2×C4×C61C4×D411yescharacteristic
141C2×C4×C61C4×D411yescharacteristic
142C2×C4×C61#12011yescharacteristic
143C2×C4×C61#12111yescharacteristic
144C2×C4×C61#12311yescharacteristic
145C2×C4×C61C2×SD1611yescharacteristic
146C2×C4×C61#13511yescharacteristic
147C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
148C2×C4×C61#13711yescharacteristic
149C22⋊D61—42no—
150C22⋊D61—42no—
151C2×Dic61—22no—
152C2×Dic61—42no—
153C2×Dic61—81no—
154C2×Dic61—81no—
155D244—42no—
156D244—41no—
157D244—41no—
158D244—41no—
159D244—41no—
160C4×D61—42no—
161C4×D61—42no—
162Dic122—41no—
163Dic122—41no—
164C8×C61—41no—
165C8×C61—41no—
166C8×C61—81no—
167#92418—22no—
168#92418—22no—
169#92418—41no—
170#92418—41no—
171#9055—611nomaximal, Sylow
172C22×C61—21no—
173C22×C61—21no—
174C22×C61#38611yescharacteristic
175C22×C61#46111yescharacteristic
176C22×C61#46311yescharacteristic
177C2×D61—42no—
178C2×D61—42no—
179C2×D61—42no—
180C4×C61—21no—
181C4×C61—21no—
182C4×C61—21no—
183C4×C61—81no—
184C4×C61—81no—
185C4×C61C4×SD1611yescharacteristic
186C4×C61#44011yescharacteristic
187C4×C61#44311yescharacteristic
188C4×C61#44411yescharacteristic
189C4×C61#45011yescharacteristic
190C4×C61#45211yescharacteristic
191Dic61—42no—
192Dic61—82no—
193#3167—611no—
194#2935—611no—
195#1986—611no—
196#1502—611no—
197#1481D6111yescharacteristic, complemented
198#1279—611no—
199#1278—611no—
200C2×C61—21no—
201C2×C61—21no—
202C2×C61#187611yescharacteristic
203C2×C61#187711yescharacteristic
204C2×C61#188411yescharacteristic
205D61—82no—
206C2×#131—1221no—
207#533C2×D6111yescharacteristic
208#532—611no—
209#498—611no—
210#492—611no—
211#487—611no—
212#486—611no—
213#465—1222no—
214C4×SD16—1222no—
215#436—1221no—
216#435—1222no—
217C8×D4—1221no—
218#431C2×D6111yescharacteristic
219C2×C4⋊C8C2×D6111yescharacteristic
220#408—1221no—
221C4×M16—611no—
222C2×C4×C8—611no—
223C4×C4⋊C4—611no—
224#339—1221no—
225#339—1221no—
226#327—1222no—
227Q8⋊C8—21no—
228Q8⋊C8—21no—
229C61#905511yescharacteristic, complemented, Sylow
230C2×#41—1221no—
231C2×SD16—1222no—
232#131—2442no—
233#131—2442no—
234C2×M16—611no—
235C2×M16—611no—
236C2×M16—1222no—
237C22×C8—21no—
238C22×C8—1222no—
239C22×C8—1221no—
240C4⋊Q8—611no—
241C4⋊Q8C4×D6111yescharacteristic
242C4⋊Q8C4×D6111yescharacteristic
243#127—611no—
244#125—21no—
245#124—1221no—
246C22⋊Q8—21no—
247C22⋊Q8—21no—
248#121—612no—
249#121—1221no—
250C4×Q8—21no—
251C4×Q8—21no—
252C4×D4—612no—
253C4×D4—1221no—
254#117—21no—
255C2×C4⋊C4—1221no—
256C2×C42—1221no—
257C2×C42C22×D6111yescharacteristic
258#106—1222no—
259C4⋊C8—21no—
260C4⋊C8—21no—
261C4⋊C8C22⋊D6111yescharacteristic
262C4⋊C8C22⋊D6111yescharacteristic
263#103—1222no—
264#102—1222no—
265C22⋊C8—21no—
266C22⋊C8—1222no—
267C22⋊C8—1222no—
268#97—1221no—
269C4×C8—21no—
270C4×C8—611no—
271C4×C8—611no—
272C4×C8—1221no—
273C4×C8—1221no—
274#95—1221no—
275#41—2441no—
276#41—2441no—
277#41—2441no—
278#41—2441no—
279C2×Q8—21no—
280C2×Q8—21no—
281C2×Q8—1221no—
282C2×D4—612no—
283C2×D4—1222no—
284C2×D4—1221no—
285C2×D4—1221no—
286C22×C4—1222no—
287C22×C4—2441no—
288C22×C4#1175822211yescharacteristic
289C22×C4D4×D6111yescharacteristic
290C22×C4D4×D6111yescharacteristic
291SD16—2444no—
292M16—612no—
293M16—1221no—
294M16—1221no—
295M16—1221no—
296M16—2444no—
297C2×C8—21no—
298C2×C8—21no—
299C2×C8—41no—
300C2×C8—41no—
301C2×C8—41no—
302C2×C8—1221no—
303C2×C8—1221no—
304C2×C8—1221no—
305C2×C8—1221no—
306C2×C8—2444no—
307C2×C8—2442no—
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—21no—
311C4⋊C4—21no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C4⋊C4—612no—
315C4⋊C4—1222no—
316C4⋊C4—1221no—
317C4⋊C4—2441no—
318C22⋊C4—41no—
319C22⋊C4—1222no—
320C22⋊C4—1222no—
321C42—41no—
322C42—2441no—
323C42—2441no—
324C42C2×C4×D6111yescharacteristic
325C42D4×D6111yescharacteristic
326C42#1175822411yescharacteristic
327C42C2×C22⋊D6111yescharacteristic
328C23—1222no—
329C23#1451975011yescharacteristic
330Q8—42no—
331Q8—41no—
332Q8—41no—
333Q8—2441no—
334Q8—2441no—
335D4—2442no—
336D4—2442no—
337D4—2442no—
338D4—2441no—
339D4—2441no—
340D4—2441no—
341D4—2441no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—1222no—
348C2×C4—4881no—
349C2×C4—4881no—
350C2×C4—2442no—
351C2×C4—2442no—
352C2×C4—2442no—
353C2×C4C22⋊C4×D6111yescharacteristic
354C2×C4#1451973711yescharacteristic
355C2×C4C4×C22⋊D6111yescharacteristic
356C2×C4#1451974511yescharacteristic
357C2×C4#1451974811yescharacteristic
358C2×C4#1451975911yescharacteristic
359C2×C4SD16×D6111yescharacteristic
360C2×C4#1451980011yescharacteristic
361C2×C4#1451980411yescharacteristic
362C2×C4#1451980911yescharacteristic
363C8—41no—
364C8—41no—
365C8—81no—
366C8—1222no—
367C8—1222no—
368C8—2441no—
369C8—2441no—
370C22—21no—
371C22—21no—
372C22—2442no—
373C22—2442no—
374C22—2442no—
375C22#1683963811yescharacteristic
376C22#1683996611yescharacteristic
377C22#1683998011yescharacteristic
378C4—21no—
379C4—21no—
380C4—21no—
381C4—81no—
382C4—81no—
383C4—4882no—
384C4—2442no—
385C4#1683984711yescharacteristic
386C4#1683986511yescharacteristic
387C4#1683987711yescharacteristic
388C4#1683988211yescharacteristic
389C4#1683991111yescharacteristic
390C4#1683992311yescharacteristic
391C2—21no—
392C2—21no—
393C2—4882no—
394C2#2144614911yescharacteristic
395C2#2144615011yescharacteristic
396C2#2144619911yescharacteristic
subgroupG/H
centerC2×C4#14519745
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1481C2
socleC22×C61#386
prime radical#16840312C22
cosocleC2×C42×C61C23
hypercenter#1481D61
hypocenterC61#9055
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1481

Complements

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

NH ≅ G/Ntype
3. #21446764C2semidirect
5. #21443658C2semidirect
6. #21443655C2semidirect
7. C61×#1481C2semidirect
10. #16840158C4semidirect
11. #16840136C4semidirect
12. #16840112C4semidirect
13. #16840110C4semidirect
121. #11758194SD16semidirect
197. #1481D61semidirect
229. C61#9055semidirect

Maximal subgroups

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

subgroupindex
#214563792
#214545622
#214467642
#214443152
#214436582
#214436552
C61×#14812
#905561