Finite Group Databasebeta

← #30597506

Subgroups — #30597506

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×#14519836C211yesmaximal, characteristic
2#21461555C211yesmaximal, characteristic, complemented
3C8×C22⋊#6923C211yesmaximal, characteristic, complemented
4#21461056C211yesmaximal, characteristic
5#21460661C211yesmaximal, characteristic, complemented
6#21460661C211yesmaximal, characteristic, complemented
7C2×#16839832C211yesmaximal, characteristic
8C2×#14519836C412yes—
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#16840607C412yescomplemented
19#16840606C412yescomplemented
20C22×#11758189C411yescharacteristic, complemented
21C22×C8×D61C2211yescharacteristic
22C2×C4×D244C2211yescharacteristic
23#16839832—21no—
24#16839832—21no—
25#16839832—21no—
26#16839832—21no—
27C2×#14519689C411yescharacteristic, complemented
28C2×#14519689C2211yescharacteristic
29C2×#14519688C411yescharacteristic, complemented
30C2×C4⋊C8×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#14519836—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×D244C2×C411yescharacteristic
47C22×C4×D61C2×C411yescharacteristic
48C22×C4×D61C2311yescharacteristic
49C2×#11758189—21no—
50C2×#11758189—21no—
51C2×#11758189—42no—
52C22×#92418C2×C411yescharacteristic
53C22×#92418C2×C411yescharacteristic
54C2×C8×D61—42no—
55C2×C8×D61D411yescharacteristic
56C2×C8×D61D411yescharacteristic
57C2×C8×D61D411yescharacteristic
58C2×C8×D61D411yescharacteristic
59C4×D244—21no—
60C4×D244—21no—
61C4×D244—21no—
62C4×D244—21no—
63C2×C4⋊Dic61C2×C411yescharacteristic
64C2×#11758198C2×C411yescharacteristic
65C2×#11758198C2×C411yescharacteristic
66#14519689—21no—
67#14519689—21no—
68#14519689—21no—
69#14519689—21no—
70#14519688—21no—
71#14519688—21no—
72C22×C8×C61C2×C411yescharacteristic
73C22×C8×C61C2×C411yescharacteristic
74C2×C42×C61C2×C411yescharacteristic
75C4⋊C8×C61—21no—
76C4⋊C8×C61—21no—
77C23×D61C4211yescharacteristic
78C23×D61C22×C411yescharacteristic
79C22×#6923—22no—
80C22×#6923—22no—
81C22×C4×C61C4211yescharacteristic
82C22×C4×C61C4211yescharacteristic
83C22×C4×C61C22×C411yescharacteristic
84C22×Dic61C4211yescharacteristic
85C22×Dic61C22×C411yescharacteristic
86C2×D244—21no—
87C2×D244—21no—
88C2×D244—22no—
89C2×D244—22no—
90C2×C4×D61—21no—
91C2×C4×D61—21no—
92C2×C4×D61—41no—
93C2×C4×D61—41no—
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—
114C2×C8×C61—21no—
115C2×C8×C61—41no—
116C2×C8×C61—41no—
117C2×C8×C61C22⋊C411yescharacteristic
118C2×C8×C61C22⋊C411yescharacteristic
119C42×C61—21no—
120C42×C61—21no—
121#11758198—21no—
122#11758198—21no—
123#11758198—21no—
124#11758198—21no—
125C4⋊Dic61—21no—
126C4⋊Dic61—21no—
127C2×#92418—22no—
128C2×#92418—21no—
129C2×#92418—41no—
130C2×#92418C22⋊C411yescharacteristic
131C2×#92418C22⋊C411yescharacteristic
132#11758189—42no—
133#11758189—42no—
134C8×D61—22no—
135C8×D61—22no—
136C8×D61—41no—
137C8×D61—41no—
138C23×C61C2×C4211yescharacteristic
139C22×D61—21no—
140C22×D61—21no—
141C22×D61—21no—
142C22×D61—41no—
143C22×D61—41no—
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—21no—
160C2×C4×C61—21no—
161C2×C4×C61—21no—
162C2×C4×C61—41no—
163C2×C4×C61C2×C22⋊C411yescharacteristic
164C2×C4×C61#11711yescharacteristic
165C2×Dic61—21no—
166C2×Dic61—41no—
167C2×Dic61—41no—
168C2×Dic61C4×D411yescharacteristic
169C2×Dic61C4×D411yescharacteristic
170D244—42no—
171D244—42no—
172C4×D61—21no—
173C4×D61—21no—
174C4×D61—21no—
175C4×D61—21no—
176C4×D61—41no—
177C4×D61—41no—
178C4×D61—42no—
179C4×D61—41no—
180C4×D61—41no—
181#92420—42no—
182#92420—42no—
183C8×C61—21no—
184C8×C61—21no—
185C8×C61—41no—
186#92418—21no—
187#92418—41no—
188#92418#9912yescomplemented
189#8161—611nomaximal, Sylow
190C22×C61—21no—
191C22×C61—21no—
192C22×C61C4×C22⋊C411yescharacteristic
193C22×C61C4×M1611yescharacteristic
194C22×C61#40511yescharacteristic
195C2×D61—21no—
196C2×D61—21no—
197C2×D61—21no—
198C2×D61—21no—
199C2×D61—42no—
200C2×D61—42no—
201C2×D61—41no—
202C2×D61—41no—
203C2×D61—41no—
204C2×D61—81no—
205C2×D61—81no—
206C2×D61#43512yes—
207C2×D61#43612yes—
208#6923—44no—
209#6923—82no—
210C4×C61—21no—
211C4×C61—41no—
212C4×C61—41no—
213C4×C61C2×#9911yescharacteristic
214C4×C61#41011yescharacteristic
215Dic61—21no—
216Dic61—21no—
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#175311yescharacteristic
228C2×C61C4×#9911yescharacteristic
229C2×C61#175711yescharacteristic
230D61—22no—
231D61—22no—
232D61—81no—
233C22×M16—611no—
234C23×C8—611no—
235C2×C4×D4—611no—
236#435—1221no—
237#435—1221no—
238#435—1221no—
239#435—1221no—
240C2×C4⋊C8#692311yescharacteristic, complemented
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×C4—611no—
260C2×M16—1221no—
261C2×M16—1221no—
262C2×M16—2442no—
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—1221no—
284C2×C42—1221no—
285C2×C42C2×#692311yescharacteristic
286C4⋊C8—21no—
287C4⋊C8—21no—
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—
304C24—611no—
305C2×D4—1222no—
306C2×D4—1221no—
307C2×D4—1221no—
308C2×D4—1222no—
309C22×C4—611no—
310C22×C4—611no—
311C22×C4—611no—
312C22×C4—611no—
313C22×C4—611no—
314C22×C4—611no—
315C22×C4—1222no—
316C22×C4—1221no—
317C22×C4—1221no—
318C22×C4—1222no—
319C22×C4—2441no—
320C22×C4—2441no—
321C22×C4—2441no—
322C22×C4—2441no—
323C22×C4C4×#692311yescharacteristic
324C22×C4C4×#692311yescharacteristic
325C22×C4C22×#692311yescharacteristic
326M16—2442no—
327M16—2442no—
328C2×C8—21no—
329C2×C8—41no—
330C2×C8—41no—
331C2×C8—611no—
332C2×C8—611no—
333C2×C8—1222no—
334C2×C8—1222no—
335C2×C8—1222no—
336C2×C8—1222no—
337C2×C8—1222no—
338C2×C8—1221no—
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—21no—
359C42—21no—
360C42—2441no—
361C42—2441no—
362C42—2441no—
363C42—2441no—
364C23—611no—
365C23—611no—
366C23—612no—
367C23—612no—
368C23—1221no—
369C23—1221no—
370C23—1221no—
371C23—2441no—
372C23—2441no—
373C23—2441no—
374C23—2441no—
375C23C2×C4×#692311yescharacteristic
376D4—2442no—
377D4—2442no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
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—2441no—
394C2×C4—2441no—
395C2×C4—2442no—
396C2×C4—2441no—
397C2×C4—2442no—
398C2×C4—2442no—
399C2×C4—2442no—
400C2×C4—2442no—
401C2×C4—2442no—
402C2×C4—2441no—
403C2×C4—2441no—
404C2×C4—2441no—
405C2×C4C2×C22⋊#692311yescharacteristic
406C2×C4#1451985611yescharacteristic
407C8—21no—
408C8—21no—
409C8—41no—
410C8—612no—
411C8—1221no—
412C8—2442no—
413C8—2442no—
414C8—2441no—
415C22—21no—
416C22—21no—
417C22—612no—
418C22—612no—
419C22—1221no—
420C22—1221no—
421C22—1221no—
422C22—1221no—
423C22—4881no—
424C22—4881no—
425C22—2442no—
426C22—2442no—
427C22—2441no—
428C22—2441no—
429C22—2441no—
430C22C4×C22⋊#692311yescharacteristic
431C22M16×#692311yescharacteristic
432C22#1684072811yescharacteristic
433C4—21no—
434C4—41no—
435C4—41no—
436C4—1221no—
437C4—1221no—
438C4—4882no—
439C4—2444no—
440C4—2441no—
441C4D61⋊#9911yescharacteristic
442C4#1684074311yescharacteristic
443C2—21no—
444C2—21no—
445C2—1222no—
446C2—1222no—
447C2—4881no—
448C2#2146155911yescharacteristic
449C2#2146156411yescharacteristic
450C2#2146157411yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC23×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC2×C4⋊C8×C61C4
socleC22×C61C4×C22⋊C4
prime radicalC22×D244C2×C4
cosocleC22×C4×D61C23
hypercenterC2×C4⋊C8#6923
hypocenterC61#8161
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×C4⋊C8

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. #16840607C4semidirect
19. #16840606C4semidirect
20. C22×#11758189C4semidirect
27. C2×#14519689C4semidirect
29. C2×#14519688C4semidirect
30. C2×C4⋊C8×C61C4semidirect
103. C22⋊#6923M16semidirect
188. #92418#99semidirect
240. C2×C4⋊C8#6923semidirect
256. C61#8161semidirect

Maximal subgroups

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

subgroupindex
C4×#145198362
#214615552
C8×C22⋊#69232
#214610562
#214606612
C2×#168398322
#816161