Finite Group Databasebeta

← #29834669

Subgroups — #29834669

Order 15616.

598 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456330C211yesmaximal, characteristic, complemented
2C4×D8×D61C211yesmaximal, characteristic
3#21447975C212yesmaximal, complemented
4#21447974C212yesmaximal, complemented
5#21447963C211yesmaximal, characteristic, complemented
6#21447957C211yesmaximal, characteristic, complemented
7#21447956C211yesmaximal, characteristic, complemented
8#21447606C212yesmaximal, complemented
9#21447573C211yesmaximal, characteristic, complemented
10#21447533C212yesmaximal
11C61×#2226C211yesmaximal, characteristic, complemented
12C2×D8×D61C2211yescharacteristic
13#16840317—21no—
14C4×D4×D61—21no—
15C2×#14519716C2212yes—
16#16840167C2211yescharacteristic, complemented
17#16840163—21no—
18#16840163C2212yescomplemented
19#16840158—21no—
20C4×D488C2211yescharacteristic
21D8×Dic61C2211yescharacteristic
22#16839844C2211yescharacteristic
23C4×#11758199—21no—
24#16839842—21no—
25#16839799—21no—
26#16839799C2212yes—
27#107×D61C2211yescharacteristic
28#102×D61—21no—
29C4×C8×D61C2211yescharacteristic
30#16839589C2212yescomplemented
31#16839588C2212yescomplemented
32#16839587C2212yescomplemented
33C4⋊#11758185C2211yescharacteristic, complemented
34#16839580C2212yescomplemented
35#16839564C2212yes—
36#16839563C2212yes—
37#16839562C2212yes—
38C61×#500C2211yescharacteristic, complemented
39C4×D8×C61C2211yescharacteristic
40C61×#367C2212yescomplemented
41C61×C4⋊C16C2211yescharacteristic, complemented
42C61×#357C2212yes—
43C2×D4×D61—21no—
44C22×C4×D61—41no—
45C2×D488C2311yescharacteristic
46C2×#11758199—21no—
47D8×D61—22no—
48D8×D61Q814yescomplemented
49C2×C8×D61D411yescharacteristic
50C2×C8×D61C2311yescharacteristic
51#14519777—21no—
52#14519768—22no—
53#14519757—41no—
54#14519753—41no—
55Q8×Dic61—41no—
56#14519742—41no—
57C4×D244—21no—
58D4×Dic61—21no—
59#14519739—21no—
60C4×C22⋊D61—41no—
61#14519737—41no—
62#14519735—22no—
63C4⋊C4×D61—21no—
64C22⋊C4×D61—41no—
65C42×D61D411yescharacteristic
66#14519716—24no—
67C2×#11758185C2312yes—
68#14519711—21no—
69#14519711C2311yescharacteristic
70#14519711C2312yes—
71#14519710—21no—
72#14519708—22no—
73#14519708—22no—
74#14519699—21no—
75#14519698—21no—
76#14519697—21no—
77C4×#92418D411yescharacteristic
78C8×Dic61D411yescharacteristic
79C8×Dic61C2311yescharacteristic
80C2×D8×C61C2311yescharacteristic
81C4⋊Q8×C61—21no—
82C4×D4×C61—21no—
83C2×C16×C61C2312yes—
84#107×C61—21no—
85#107×C61C2312yes—
86#107×C61C2311yescharacteristic
87#102×C61—21no—
88C4×C8×C61C2311yescharacteristic
89C23×D61—41no—
90C2×Q8×C61—41no—
91C2×D4×C61—21no—
92C22×C4×C61—41no—
93C2×C22⋊D61—41no—
94C22×Dic61—41no—
95D4×D61—24no—
96D4×D61—42no—
97C2×D244—21no—
98C2×C4×D61—41no—
99C2×C4×D61—41no—
100C2×C4×D61—41no—
101C2×C4×D61—84no—
102C2×C4×D61D811yescharacteristic
103C2×C4×D61D811yescharacteristic
104C2×C4×D61C2×D411yescharacteristic
105C2×Dic122—41no—
106D8×C61—21no—
107D8×C61C2×Q812yes—
108C2×C8×C61C2×D411yescharacteristic
109C2×C8×C61C2411yescharacteristic
110C4⋊C4×C61—21no—
111C4⋊C4×C61—22no—
112C4⋊C4×C61—41no—
113C22⋊C4×C61—41no—
114C42×C61C2×D411yescharacteristic
115C22⋊Dic61—41no—
116#11758199—24no—
117#11758198—42no—
118#11758198—41no—
119#11758198—41no—
120C4⋊Dic61—21no—
121C4⋊Dic61—22no—
122C4⋊Dic61—41no—
123C4⋊Dic61—42no—
124#11758196—41no—
125#11758196—42no—
126C4×Dic61—42no—
127C4×Dic61D811yescharacteristic
128C4×Dic61D811yescharacteristic
129C4×Dic61C2×D411yescharacteristic
130C2×#92418C2×D411yescharacteristic
131C2×#92418C2×D411yescharacteristic
132D488—21no—
133D488C2×Q812yes—
134C8×D61—22no—
135C8×D61C2×Q812yes—
136C8×D61#4112yes—
137C16×C61—22no—
138#11758185—22no—
139C23×C61—41no—
140C22×D61—41no—
141C22×D61—44no—
142C22×D61—82no—
143C22×D61—82no—
144C22×D61C2×D811yescharacteristic
145Q8×C61—82no—
146D4×C61—22no—
147D4×C61—41no—
148C2×C4×C61—42no—
149C2×C4×C61—41no—
150C2×C4×C61—82no—
151C2×C4×C61C2×D811yescharacteristic
152C2×C4×C61C2×D811yescharacteristic
153C2×C4×C61C22×D411yescharacteristic
154C22⋊D61—44no—
155C2×Dic61—42no—
156C2×Dic61—41no—
157C2×Dic61—82no—
158C2×Dic61C2×D811yescharacteristic
159C2×Dic61C2×D811yescharacteristic
160C2×Dic61C2×D811yescharacteristic
161D244—22no—
162D244—41no—
163C4×D61—22no—
164C4×D61—41no—
165C4×D61—82no—
166C4×D61—82no—
167C4×D61—82no—
168C4×D61C22⋊Q812yes—
169C4×D61#13712yes—
170Dic122—82no—
171C8×C61—21no—
172C8×C61C22×Q811yescharacteristic
173C8×C61C2×#4111yescharacteristic
174#92418—21no—
175#92418C22⋊Q812yes—
176#33627—611nomaximal, Sylow
177C22×C61—42no—
178C22×C61—81no—
179C22×C61—81no—
180C22×C61C22×D811yescharacteristic
181C2×D61—21no—
182C2×D61—21no—
183C2×D61—42no—
184C2×D61—88no—
185C2×D61—81no—
186C2×D61—81no—
187C2×D61#47412yes—
188C4×C61—21no—
189C4×C61—81no—
190C4×C61—82no—
191C4×C61#50912yes—
192C4×C61C2×C22⋊Q811yescharacteristic
193C4×C61C2×#13711yescharacteristic
194Dic61—21no—
195Dic61—21no—
196Dic61—82no—
197Dic61—81no—
198Dic61#47412yes—
199#3160—611no—
200C2×C4×D8—611no—
201#2228—612no—
202#2228—612no—
203#2226—611no—
204#2226D6111yescharacteristic, complemented
205#2224—611no—
206#2224—611no—
207#2159—612no—
208#2150—611no—
209#2140—612no—
210C2×C61—82no—
211C2×C61C2×#47411yescharacteristic
212C2×C61C2×#50911yescharacteristic
213C2×C61#341411yescharacteristic
214D61—22no—
215D61—82no—
216C22×D8—611no—
217#533—1221no—
218C2×C4×D4—1221no—
219C2×M32—612no—
220#500—611no—
221#500C2×D6111yescharacteristic, complemented
222#499—612no—
223#499—1221no—
224#498—1221no—
225C4×D8—611no—
226C4×D8—611no—
227C4×D8—611no—
228C4×D8—1221no—
229C4×D8—1221no—
230C4×D8C2×D6111yescharacteristic
231#427—612no—
232#427—1221no—
233C2×#107—611no—
234C2×#102—1221no—
235C2×C4×C8—611no—
236#367—612no—
237#367C2×D6112yescomplemented
238#366—612no—
239#366—612no—
240C4⋊C16—612no—
241C4⋊C16—611no—
242C4⋊C16C2×D6111yescharacteristic, complemented
243#357—612no—
244#357—612no—
245#357—612no—
246#357C2×D6112yes—
247C61#3362711yescharacteristic, complemented, Sylow
248C22×D4—1221no—
249C23×C4—2441no—
250C2×D8—614no—
251C2×D8—611no—
252C2×D8—1222no—
253C2×D8—1221no—
254C2×D8C22×D6111yescharacteristic
255C22×C8—611no—
256C22×C8—611no—
257C4⋊Q8—21no—
258C4⋊Q8—1221no—
259#125—1222no—
260C22⋊Q8—2441no—
261C22⋊Q8—2441no—
262C4×Q8—2441no—
263C4×Q8—2441no—
264C4×D4—21no—
265C4×D4—1221no—
266C4×D4—1221no—
267C4×D4—1221no—
268C4×D4—2441no—
269C4×D4—2441no—
270#117—1222no—
271C2×C4⋊C4—1221no—
272C2×C22⋊C4—2441no—
273C2×C42—611no—
274M32—1224no—
275C2×C16—612no—
276C2×C16C22×D6112yes—
277#107—21no—
278#107—612no—
279#107—611no—
280#107—1221no—
281#107—1221no—
282#107C22×D6112yes—
283#107C22×D6111yescharacteristic
284#106—1222no—
285#106—1222no—
286#102—21no—
287#102—1221no—
288#102—1221no—
289#102—1221no—
290C4×C8—611no—
291C4×C8—611no—
292C4×C8—611no—
293C4×C8C22×D6111yescharacteristic
294C24—2441no—
295C2×Q8—41no—
296C2×Q8—2441no—
297C2×D4—21no—
298C2×D4—1224no—
299C2×D4—1221no—
300C2×D4—2442no—
301C2×D4—2441no—
302C22×C4—41no—
303C22×C4—611no—
304C22×C4—611no—
305C22×C4—611no—
306C22×C4—4884no—
307C22×C4—2441no—
308C22×C4—2441no—
309C22×C4—2441no—
310C22×C4—2441no—
311D8—21no—
312D8—612no—
313D8—1224no—
314D8—1221no—
315D8Q8×D6112yes—
316C2×C8—611no—
317C2×C8—612no—
318C2×C8—612no—
319C2×C8—611no—
320C2×C8—1222no—
321C2×C8D4×D6111yescharacteristic
322C2×C8C23×D6111yescharacteristic
323C4⋊C4—21no—
324C4⋊C4—22no—
325C4⋊C4—41no—
326C4⋊C4—1221no—
327C4⋊C4—1222no—
328C4⋊C4—2441no—
329C4⋊C4—2442no—
330C4⋊C4—2442no—
331C4⋊C4—2441no—
332C22⋊C4—41no—
333C22⋊C4—2441no—
334C22⋊C4—2442no—
335C22⋊C4—2441no—
336C22⋊C4—2441no—
337C42—611no—
338C42—611no—
339C42—611no—
340C42—2442no—
341C42D4×D6111yescharacteristic
342C16—22no—
343C16—1222no—
344C23—41no—
345C23—611no—
346C23—4882no—
347C23—4882no—
348C23—2444no—
349C23—2441no—
350Q8—82no—
351Q8—4882no—
352D4—22no—
353D4—41no—
354D4—1222no—
355D4—2444no—
356D4—2441no—
357C2×C4—42no—
358C2×C4—41no—
359C2×C4—82no—
360C2×C4—611no—
361C2×C4—612no—
362C2×C4—612no—
363C2×C4—611no—
364C2×C4—611no—
365C2×C4—1222no—
366C2×C4—4882no—
367C2×C4—4882no—
368C2×C4—4882no—
369C2×C4—4882no—
370C2×C4—2441no—
371C2×C4—2442no—
372C2×C4—2441no—
373C2×C4D8×D6111yescharacteristic
374C2×C4D8×D6111yescharacteristic
375C2×C4C2×D4×D6111yescharacteristic
376C8—21no—
377C8—612no—
378C8—1221no—
379C8C2×Q8×D6111yescharacteristic
380C8#41×D6111yescharacteristic
381C22—42no—
382C22—81no—
383C22—81no—
384C22—612no—
385C22—1221no—
386C22—1221no—
387C22—4888no—
388C22—4881no—
389C22—4881no—
390C22—2442no—
391C22C2×D8×D6111yescharacteristic
392C4—21no—
393C4—82no—
394C4—81no—
395C4—612no—
396C4—1221no—
397C4—1221no—
398C4—4881no—
399C4—4882no—
400C4#1684019912yes—
401C4C22⋊Q8×D6111yescharacteristic
402C4#137×D6111yescharacteristic
403C2—82no—
404C2—1222no—
405C2—4882no—
406C2#474×D6111yescharacteristic
407C2C2×#1684019911yescharacteristic
408C2#2145895111yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2226C2
socleC22×C61C22×D8
prime radicalC2×D8×D61C22
hypercenter#2226D61
hypocenterC61#33627
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2226

Complements

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

NH ≅ G/Ntype
1. #21456330C2semidirect
3. #21447975C2semidirect
4. #21447974C2semidirect
5. #21447963C2semidirect
6. #21447957C2semidirect
7. #21447956C2semidirect
8. #21447606C2semidirect
9. #21447573C2semidirect
11. C61×#2226C2semidirect
16. #16840167C22semidirect
18. #16840163C22semidirect
30. #16839589C22semidirect
31. #16839588C22semidirect
32. #16839587C22semidirect
33. C4⋊#11758185C22semidirect
34. #16839580C22semidirect
38. C61×#500C22semidirect
40. C61×#367C22semidirect
41. C61×C4⋊C16C22semidirect
48. D8×D61Q8semidirect
204. #2226D61semidirect
221. #500C2×D61semidirect
237. #367C2×D61semidirect
242. C4⋊C16C2×D61semidirect
247. C61#33627semidirect

Maximal subgroups

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

subgroupindex
#214563302
C4×D8×D612
#214479752
#214479742
#214479632
#214479572
#214479562
#214476062
#214475732
#214475332
C61×#22262
#3362761