Finite Group Databasebeta

← #30597505

Subgroups — #30597505

Order 15616.

568 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14519835C211yesmaximal, characteristic
2#21461555C211yesmaximal, characteristic, complemented
3C8×C22⋊#6923C211yesmaximal, characteristic, complemented
4#21461054C211yesmaximal, characteristic
5#21460661C211yesmaximal, characteristic, complemented
6#21460661C211yesmaximal, characteristic, complemented
7C2×#16839831C211yesmaximal, characteristic
8C2×#14519835C412yes—
9D61⋊(C22⋊C8)C2211yescharacteristic
10D61⋊(C22⋊C8)C2211yescharacteristic
11C2×#14519831—21no—
12C2×C8×#6923—21no—
13C4×C22⋊#6923C2211yescharacteristic
14C4×C22⋊#6923C2211yescharacteristic
15#16840640C412yes—
16(C2×#6923)⋊C8—21no—
17(C2×#6923)⋊C8—21no—
18#16840608C412yescomplemented
19#16840605C412yescomplemented
20C22×C8×D61C2211yescharacteristic
21C2×C4×C22⋊D61C2211yescharacteristic
22#16839831—21no—
23#16839831—21no—
24#16839831—21no—
25#16839831—21no—
26C2×#14519706C411yescharacteristic, complemented
27C2×C22⋊#92418C411yescharacteristic, complemented
28C2×#14519689C2211yescharacteristic
29C2×#14519687C411yescharacteristic, complemented
30C22×M16×C61C411yescharacteristic, complemented
31C2×D61⋊C8—21no—
32C2×D61⋊C8—21no—
33C2×C22⋊#6923C2×C412yes—
34C2×C22⋊#6923C2×C412yes—
35C2×C4×#6923—21no—
36C2×C4×#6923—21no—
37#14519835—24no—
38#14519834—21no—
39#14519834—21no—
40C22⋊#92420C2×C412yes—
41C22⋊#92420C2×C412yes—
42#14519831—42no—
43C8×#6923—42no—
44(C2×#6923)⋊C4—21no—
45(C2×#6923)⋊C4—21no—
46C22×C22⋊D61C2×C411yescharacteristic
47C22×C4×D61C2311yescharacteristic
48C22×#92418C2×C411yescharacteristic
49C22×#92418C2×C411yescharacteristic
50C2×C8×D61—42no—
51C2×C8×D61D411yescharacteristic
52C2×C8×D61D411yescharacteristic
53C2×C8×D61D411yescharacteristic
54C2×C8×D61D411yescharacteristic
55C4×C22⋊D61—21no—
56C4×C22⋊D61—21no—
57C4×C22⋊D61—21no—
58C4×C22⋊D61—21no—
59C2×#11758196C2×C411yescharacteristic
60C2×C22⋊Dic61C2×C411yescharacteristic
61C2×#11758198C2×C411yescharacteristic
62C2×C4×Dic61C2×C411yescharacteristic
63#14519706—21no—
64#14519706—21no—
65C22⋊#92418—21no—
66C22⋊#92418—21no—
67#14519689—21no—
68#14519689—21no—
69#14519687—21no—
70#14519687—21no—
71C23×C4×C61C2×C411yescharacteristic
72C2×M16×C61—21no—
73C2×M16×C61—21no—
74C2×M16×C61—42no—
75C22×C8×C61C2×C411yescharacteristic
76C22×C8×C61C2×C411yescharacteristic
77C24×C61C4211yescharacteristic
78C23×D61C22×C411yescharacteristic
79C22×#6923—22no—
80C22×#6923—22no—
81C22×C4×C61—21no—
82C22×C4×C61—21no—
83C22×C4×C61—41no—
84C22×C4×C61—41no—
85C22×C4×C61C4211yescharacteristic
86C22×C4×C61C22×C411yescharacteristic
87C2×C22⋊D61—21no—
88C2×C22⋊D61—21no—
89C2×C22⋊D61—22no—
90C2×C22⋊D61—22no—
91C22×Dic61C4211yescharacteristic
92C22×Dic61C4211yescharacteristic
93C22×Dic61C22×C411yescharacteristic
94C2×C4×D61—41no—
95C2×C4×D61—41no—
96C2×C4×D61C2×D411yescharacteristic
97C2×C4×D61C2×D411yescharacteristic
98C2×C4×D61#4111yescharacteristic
99C2×C4×D61#4111yescharacteristic
100C22⋊#6923—22no—
101C22⋊#6923—22no—
102C22⋊#6923—22no—
103C22⋊#6923M1614yescomplemented
104C2×#92420—22no—
105C2×#92420—22no—
106C4×#6923—41no—
107C4×#6923—41no—
108C4×#6923—41no—
109C4×#6923—41no—
110D61⋊C8—41no—
111D61⋊C8—41no—
112D61⋊C8—41no—
113D61⋊C8—41no—
114M16×C61—42no—
115M16×C61—42no—
116C2×C8×C61—22no—
117C2×C8×C61—21no—
118C2×C8×C61—41no—
119C2×C8×C61C22⋊C411yescharacteristic
120C2×C8×C61C22⋊C411yescharacteristic
121C22⋊Dic61—21no—
122C22⋊Dic61—21no—
123#11758198—21no—
124#11758198—21no—
125#11758196—21no—
126#11758196—21no—
127C4×Dic61—21no—
128C4×Dic61—21no—
129C2×#92418—21no—
130C2×#92418—41no—
131C2×#92418—41no—
132C2×#92418C22⋊C411yescharacteristic
133C2×#92418C22⋊C411yescharacteristic
134C8×D61—22no—
135C8×D61—22no—
136C8×D61—41no—
137C8×D61—41no—
138C23×C61—21no—
139C23×C61—21no—
140C23×C61—21no—
141C23×C61—41no—
142C23×C61—41no—
143C23×C61C2×C4211yescharacteristic
144C22×D61—41no—
145C22×D61—41no—
146C22×D61C4×D411yescharacteristic
147C22×D61C4×D411yescharacteristic
148C22×D61C2×M1612yes—
149C22×D61#13112yes—
150C2×#6923—24no—
151C2×#6923—42no—
152C2×#6923—42no—
153C2×#6923—42no—
154C2×#6923—42no—
155C2×#6923—42no—
156C2×C4×C61—21no—
157C2×C4×C61—21no—
158C2×C4×C61—21no—
159C2×C4×C61—42no—
160C2×C4×C61—41no—
161C2×C4×C61—41no—
162C2×C4×C61—41no—
163C2×C4×C61C2×C22⋊C411yescharacteristic
164C2×C4×C61#11711yescharacteristic
165C22⋊D61—42no—
166C22⋊D61—42no—
167C2×Dic61—21no—
168C2×Dic61—21no—
169C2×Dic61—21no—
170C2×Dic61—21no—
171C2×Dic61—41no—
172C2×Dic61—41no—
173C2×Dic61C4×D411yescharacteristic
174C2×Dic61C4×D411yescharacteristic
175C4×D61—21no—
176C4×D61—21no—
177C4×D61—21no—
178C4×D61—21no—
179C4×D61—41no—
180C4×D61—41no—
181#92420—42no—
182#92420—42no—
183C8×C61—21no—
184C8×C61—41no—
185C8×C61#9912yescomplemented
186#92418—21no—
187#92418—21no—
188#92418—41no—
189#8161—611nomaximal, Sylow
190C22×C61—21no—
191C22×C61—21no—
192C22×C61—41no—
193C22×C61—41no—
194C22×C61—41no—
195C22×C61—81no—
196C22×C61—81no—
197C22×C61C4×C22⋊C411yescharacteristic
198C22×C61C4×M1611yescharacteristic
199C22×C61#40511yescharacteristic
200C2×D61—21no—
201C2×D61—21no—
202C2×D61—21no—
203C2×D61—21no—
204C2×D61—42no—
205C2×D61—42no—
206C2×D61#43512yes—
207C2×D61#43612yes—
208#6923—44no—
209#6923—82no—
210C4×C61—21no—
211C4×C61—41no—
212C4×C61C2×#9911yescharacteristic
213C4×C61#41011yescharacteristic
214Dic61—21no—
215Dic61—21no—
216Dic61—41no—
217Dic61—41no—
218C2×#435—611no—
219C4×#99—611no—
220#1752—611no—
221C8×C22⋊C4—611no—
222#1459—611no—
223#1282—611no—
224#1282—611no—
225C2×C61—21no—
226C2×C61—21no—
227C2×C61—81no—
228C2×C61#175311yescharacteristic
229C2×C61C4×#9911yescharacteristic
230C2×C61#175711yescharacteristic
231D61—22no—
232D61—22no—
233C22×M16#692311yescharacteristic, complemented
234C23×C8—611no—
235C2×C4×D4—611no—
236#435—1221no—
237#435—1221no—
238#435—1221no—
239#435—1221no—
240C2×C4⋊C8—611no—
241C2×#99—612no—
242C2×C22⋊C8—611no—
243C2×C22⋊C8—611no—
244C2×C22⋊C8—611no—
245C2×C22⋊C8—611no—
246C2×#97—611no—
247C2×#97—1221no—
248C2×C4×C8—1221no—
249C4×C22⋊C4—611no—
250C4×C22⋊C4—611no—
251#342—612no—
252#336—1221no—
253#336—1221no—
254#324—612no—
255#323—612no—
256C61#816111yescharacteristic, complemented, Sylow
257C22×D4—611no—
258C23×C4—611no—
259C23×C4C2×#692311yescharacteristic
260C2×M16—21no—
261C2×M16—21no—
262C2×M16—42no—
263C22×C8—611no—
264C22×C8—611no—
265C22×C8—611no—
266C22×C8—611no—
267C22×C8—611no—
268C22×C8—611no—
269C22×C8—1221no—
270C22×C8—1221no—
271C22×C8—2442no—
272C22×C8C2×#692311yescharacteristic
273C22×C8C2×#692311yescharacteristic
274C4×D4—1221no—
275C4×D4—1221no—
276C4×D4—1221no—
277C4×D4—1221no—
278C2×C4⋊C4—611no—
279C2×C22⋊C4—612no—
280C2×C22⋊C4—611no—
281C2×C22⋊C4—611no—
282C2×C22⋊C4—612no—
283C2×C42—611no—
284C2×C42—1221no—
285C2×C42—1221no—
286C4⋊C8—1221no—
287C4⋊C8—1221no—
288#99—1224no—
289C22⋊C8—612no—
290C22⋊C8—612no—
291C22⋊C8—1221no—
292C22⋊C8—1221no—
293C22⋊C8—1221no—
294C22⋊C8—1221no—
295C22⋊C8—1221no—
296C22⋊C8—1221no—
297#97—1221no—
298#97—1221no—
299#97—2442no—
300C4×C8—2442no—
301#95—1221no—
302#95—1221no—
303C24—611no—
304C24C4×#692311yescharacteristic
305C2×D4—1222no—
306C2×D4—1221no—
307C2×D4—1221no—
308C2×D4—1222no—
309C22×C4—21no—
310C22×C4—21no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4—611no—
314C22×C4—611no—
315C22×C4—611no—
316C22×C4—611no—
317C22×C4—611no—
318C22×C4—611no—
319C22×C4—611no—
320C22×C4—1222no—
321C22×C4—1222no—
322C22×C4—2441no—
323C22×C4—2441no—
324C22×C4C4×#692311yescharacteristic
325C22×C4C22×#692311yescharacteristic
326M16—42no—
327M16—42no—
328C2×C8—22no—
329C2×C8—21no—
330C2×C8—41no—
331C2×C8—611no—
332C2×C8—611no—
333C2×C8—1222no—
334C2×C8—1222no—
335C2×C8—1222no—
336C2×C8—1222no—
337C2×C8—1221no—
338C2×C8—2441no—
339C2×C8—2441no—
340C2×C8—2441no—
341C2×C8—2441no—
342C2×C8—2441no—
343C2×C8—2441no—
344C2×C8—2441no—
345C2×C8—2441no—
346C2×C8C22⋊#692311yescharacteristic
347C2×C8C22⋊#692311yescharacteristic
348C4⋊C4—1221no—
349C4⋊C4—1221no—
350C22⋊C4—614no—
351C22⋊C4—1221no—
352C22⋊C4—1221no—
353C22⋊C4—1221no—
354C22⋊C4—1221no—
355C22⋊C4—1222no—
356C22⋊C4—1222no—
357C22⋊C4—1222no—
358C42—1221no—
359C42—1221no—
360C42—2441no—
361C42—2441no—
362C42—2441no—
363C42—2441no—
364C23—21no—
365C23—21no—
366C23—21no—
367C23—41no—
368C23—41no—
369C23—611no—
370C23—611no—
371C23—612no—
372C23—612no—
373C23—2441no—
374C23—2441no—
375C23C2×C4×#692311yescharacteristic
376D4—2442no—
377D4—2442no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—42no—
382C2×C4—41no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—611no—
386C2×C4—611no—
387C2×C4—1221no—
388C2×C4—1221no—
389C2×C4—1221no—
390C2×C4—1221no—
391C2×C4—1224no—
392C2×C4—1221no—
393C2×C4—1221no—
394C2×C4—1221no—
395C2×C4—1221no—
396C2×C4—2441no—
397C2×C4—2441no—
398C2×C4—2441no—
399C2×C4—2442no—
400C2×C4—2442no—
401C2×C4—2442no—
402C2×C4—2442no—
403C2×C4—2442no—
404C2×C4—2441no—
405C2×C4C2×C22⋊#692311yescharacteristic
406C2×C4#1451985611yescharacteristic
407C8—21no—
408C8—41no—
409C8—1221no—
410C8—1221no—
411C8—2442no—
412C8—2442no—
413C8—2441no—
414C8#1451983512yescomplemented
415C22—21no—
416C22—21no—
417C22—41no—
418C22—41no—
419C22—41no—
420C22—81no—
421C22—81no—
422C22—612no—
423C22—612no—
424C22—1221no—
425C22—1221no—
426C22—1221no—
427C22—1221no—
428C22—2442no—
429C22—2442no—
430C22C4×C22⋊#692311yescharacteristic
431C22M16×#692311yescharacteristic
432C22#1684072811yescharacteristic
433C4—21no—
434C4—41no—
435C4—1221no—
436C4—1221no—
437C4—4882no—
438C4—2444no—
439C4—2441no—
440C4—2441no—
441C4C2×#1451983511yescharacteristic
442C4#1684074111yescharacteristic
443C2—21no—
444C2—21no—
445C2—81no—
446C2—1222no—
447C2—1222no—
448C2#2146155911yescharacteristic
449C2C4×#1451983511yescharacteristic
450C2#2146157511yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC23×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC22×M16×C61C4
socleC22×C61C4×C22⋊C4
prime radicalC22×C22⋊D61C2×C4
cosocleC22×C4×D61C23
hypercenterC22×M16#6923
hypocenterC61#8161
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C22×M16

Complements

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

NH ≅ G/Ntype
2. #21461555C2semidirect
3. C8×C22⋊#6923C2semidirect
5. #21460661C2semidirect
6. #21460661C2semidirect
18. #16840608C4semidirect
19. #16840605C4semidirect
26. C2×#14519706C4semidirect
27. C2×C22⋊#92418C4semidirect
29. C2×#14519687C4semidirect
30. C22×M16×C61C4semidirect
103. C22⋊#6923M16semidirect
185. C8×C61#99semidirect
233. C22×M16#6923semidirect
256. C61#8161semidirect
414. C8#14519835semidirect

Maximal subgroups

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

subgroupindex
C4×#145198352
#214615552
C8×C22⋊#69232
#214610542
#214606612
C2×#168398312
#816161