Finite Group Databasebeta

← #30596958

Subgroups — #30596958

Order 15616.

696 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462498C211yesmaximal, characteristic
2#21462266C211yesmaximal, characteristic
3#21460700C214yesmaximal
4C4×#14519735C211yesmaximal, characteristic
5#16840785—21no—
6#16840782—21no—
7#16840780—21no—
8#16840779—21no—
9#16840767C412yescomplemented
10#16840733C2212yes—
11C4×#11758213C412yescomplemented
12#16840707C412yescomplemented
13#16840706C412yescomplemented
14#16840705—21no—
15#16840704—21no—
16C4×C4⋊#6923—21no—
17C4×C22⋊#6923C2212yes—
18#16840698—21no—
19C2×#14519735—21no—
20C2×C42×D61C2211yescharacteristic
21C4⋊C4×Dic61—21no—
22C4×C4⋊Dic61C411yescharacteristic, complemented
23C4×#11758198—21no—
24#16839609C2212yes—
25#16839607C412yescomplemented
26C42×Dic61—21no—
27C4×C4⋊C4×C61C411yescharacteristic, complemented
28C2×#11758213C2×C414yes—
29C2×C4⋊#6923—22no—
30C2×C22⋊#6923—22no—
31C2×C4×#6923—22no—
32#14519844—22no—
33#14519844—22no—
34#14519834—22no—
35C22⋊#92420—22no—
36#14519832—22no—
37C4×#92420—22no—
38(C2×#6923)⋊C4—22no—
39(C2×#6923)⋊C4—22no—
40(C2×#6923)⋊C4—22no—
41(C2×#6923)⋊C4C2×C414yes—
42C22×C4×D61D411yescharacteristic
43C22×C4×D61D411yescharacteristic
44C22×C4×D61C2311yescharacteristic
45#14519735—28no—
46C2×C4⋊Dic61—21no—
47C2×#11758198—22no—
48C2×C4×Dic61—22no—
49C2×C4×Dic61—21no—
50C2×C4×Dic61—22no—
51C2×C4×Dic61C2×C411yescharacteristic
52C2×C4×Dic61D411yescharacteristic
53C2×C4×Dic61D411yescharacteristic
54C42×D61C2×C411yescharacteristic
55C42×D61C2×C411yescharacteristic
56C42×D61C2×C411yescharacteristic
57C42×D61C2×C411yescharacteristic
58C42×D61D411yescharacteristic
59C42×D61D411yescharacteristic
60C42×D61Q811yescharacteristic
61C42×D61Q811yescharacteristic
62#14519684—22no—
63#14519684C2×C412yes—
64C2×C4⋊C4×C61—21no—
65C2×C42×C61—21no—
66C2×C42×C61C2×C411yescharacteristic
67#95×C61C2×C412yes—
68C23×D61C2×D411yescharacteristic
69C22×#6923—24no—
70C22×C4×C61—22no—
71C22×C4×C61C22⋊C411yescharacteristic
72C22×C4×C61C22⋊C411yescharacteristic
73C22×C4×C61C22×C411yescharacteristic
74C22×Dic61—22no—
75C22×Dic61C22⋊C411yescharacteristic
76C22×Dic61C22⋊C411yescharacteristic
77C22×Dic61C2×D411yescharacteristic
78C2×C4×D61—24no—
79C2×C4×D61—42no—
80C2×C4×D61—41no—
81C2×C4×D61—41no—
82C2×C4×D61C22⋊C411yescharacteristic
83C2×C4×D61C22⋊C411yescharacteristic
84C2×C4×D61C22⋊C411yescharacteristic
85C2×C4×D61C22⋊C411yescharacteristic
86C2×C4×D61C4⋊C411yescharacteristic
87C2×C4×D61C4⋊C411yescharacteristic
88C2×C4×D61C4⋊C411yescharacteristic
89C2×C4×D61C4⋊C411yescharacteristic
90C2×C4×D61C22×C411yescharacteristic
91C2×C4×D61C22×C411yescharacteristic
92C2×C4×D61C2×D411yescharacteristic
93C2×C4×D61C2×Q811yescharacteristic
94C22⋊#6923—42no—
95C22⋊#6923—42no—
96C2×#92420—24no—
97C4⋊#6923—44no—
98C4×#6923—44no—
99#11758213—44no—
100C4⋊C4×C61—24no—
101C42×C61—42no—
102C42×C61C4211yescharacteristic
103C42×C61C4211yescharacteristic
104C42×C61C4⋊C411yescharacteristic
105C42×C61C4⋊C411yescharacteristic
106#11758198—28no—
107C4⋊Dic61—24no—
108C4×Dic61—28no—
109C4×Dic61—44no—
110C4×Dic61—42no—
111C4×Dic61C4211yescharacteristic
112C4×Dic61C4211yescharacteristic
113C4×Dic61C22⋊C411yescharacteristic
114C4×Dic61C22⋊C411yescharacteristic
115C4×Dic61C22⋊C411yescharacteristic
116C4×Dic61C22⋊C411yescharacteristic
117C4×Dic61C4⋊C411yescharacteristic
118C4×Dic61C4⋊C411yescharacteristic
119C4×Dic61C4⋊C411yescharacteristic
120C4×Dic61C4⋊C411yescharacteristic
121C4×Dic61C4⋊C411yescharacteristic
122C4×Dic61C4⋊C411yescharacteristic
123C23×C61C2×C22⋊C411yescharacteristic
124C22×D61—21no—
125C22×D61—21no—
126C22×D61—22no—
127C22×D61—41no—
128C22×D61C2×C22⋊C411yescharacteristic
129C22×D61C2×C4⋊C411yescharacteristic
130C2×#6923—44no—
131C2×#6923—44no—
132C2×#6923—44no—
133C2×C4×C61—21no—
134C2×C4×C61—21no—
135C2×C4×C61—22no—
136C2×C4×C61—24no—
137C2×C4×C61—41no—
138C2×C4×C61—42no—
139C2×C4×C61—42no—
140C2×C4×C61#9511yescharacteristic
141C2×C4×C61#9511yescharacteristic
142C2×C4×C61#9511yescharacteristic
143C2×C4×C61#9511yescharacteristic
144C2×C4×C61C2×C4211yescharacteristic
145C2×C4×C61C2×C4⋊C411yescharacteristic
146C2×Dic61—21no—
147C2×Dic61—21no—
148C2×Dic61—22no—
149C2×Dic61—22no—
150C2×Dic61—24no—
151C2×Dic61—42no—
152C2×Dic61—42no—
153C2×Dic61#9511yescharacteristic
154C2×Dic61#9511yescharacteristic
155C2×Dic61#9511yescharacteristic
156C2×Dic61#9511yescharacteristic
157C2×Dic61C2×C22⋊C411yescharacteristic
158C2×Dic61C2×C4⋊C411yescharacteristic
159C4×D61—22no—
160C4×D61—22no—
161C4×D61—22no—
162C4×D61—22no—
163C4×D61—22no—
164C4×D61—41no—
165C4×D61—41no—
166C4×D61—41no—
167C4×D61—41no—
168C4×D61—41no—
169C4×D61—41no—
170C4×D61#10414yes—
171#92420—44no—
172#8052—611nomaximal, Sylow
173C22×C61—21no—
174C22×C61—21no—
175C22×C61C2×#9511yescharacteristic
176C22×C61#42111yescharacteristic
177C22×C61#42111yescharacteristic
178C2×D61—21no—
179C2×D61—21no—
180C2×D61—21no—
181C2×D61—21no—
182C2×D61—21no—
183C2×D61—42no—
184C2×D61—42no—
185C2×D61C2×#10412yes—
186#6923—84no—
187C4×C61—21no—
188C4×C61—21no—
189C4×C61—21no—
190C4×C61—21no—
191C4×C61—21no—
192C4×C61—44no—
193C4×C61#33912yes—
194Dic61—21no—
195Dic61—21no—
196Dic61—21no—
197Dic61—21no—
198Dic61—44no—
199Dic61#33912yes—
200Dic61#41012yes—
201#2920—611no—
202#2283—611no—
203C4×#117—611no—
204#1297—614no—
205C2×C61—21no—
206C2×C61—21no—
207C2×C61C2×#33911yescharacteristic
208C2×C61#173311yescharacteristic
209C2×C61#174011yescharacteristic
210D61—22no—
211D61—41no—
212C2×#117—1221no—
213C22×C42—611no—
214#432—1221no—
215#432—1221no—
216#431—1221no—
217#431—1221no—
218#423—612no—
219#407—612no—
220C4×M16—612no—
221#383—612no—
222#382—612no—
223#381—1221no—
224#380—1221no—
225C4×C4⋊C4—611no—
226C4×C4⋊C4—1221no—
227C4×C4⋊C4—1221no—
228C4×C4⋊C4#692311yescharacteristic, complemented
229C4×C22⋊C4—612no—
230C4×C22⋊C4—612no—
231C4×C22⋊C4—1221no—
232#376—612no—
233#376—1221no—
234C43—1221no—
235C61#805211yescharacteristic, complemented, Sylow
236C23×C4—611no—
237C23×C4—611no—
238C23×C4—611no—
239C2×M16—614no—
240#117—1228no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—1221no—
243C2×C4⋊C4—1222no—
244C2×C22⋊C4—1222no—
245C2×C22⋊C4—1222no—
246C2×C42—21no—
247C2×C42—611no—
248C2×C42—611no—
249C2×C42—611no—
250C2×C42—611no—
251C2×C42—611no—
252C2×C42—611no—
253C2×C42—611no—
254C2×C42—611no—
255C2×C42—611no—
256C2×C42—611no—
257C2×C42—611no—
258C2×C42—1222no—
259C2×C42—1222no—
260C2×C42—1222no—
261C2×C42—1221no—
262C2×C42C2×#692311yescharacteristic
263C4⋊C8—1222no—
264C4⋊C8—1222no—
265C22⋊C8—1222no—
266C22⋊C8—1222no—
267#97—1222no—
268C4×C8—1222no—
269#95—614no—
270#95—612no—
271#95—1222no—
272#95—1222no—
273#95—1222no—
274#95—1222no—
275#95C2×#692312yes—
276C24—611no—
277C22×C4—22no—
278C22×C4—611no—
279C22×C4—611no—
280C22×C4—611no—
281C22×C4—611no—
282C22×C4—611no—
283C22×C4—611no—
284C22×C4—611no—
285C22×C4—611no—
286C22×C4—611no—
287C22×C4—611no—
288C22×C4—611no—
289C22×C4—611no—
290C22×C4—611no—
291C22×C4—611no—
292C22×C4—611no—
293C22×C4—1224no—
294C22×C4—1222no—
295C22×C4—1224no—
296C22×C4—2441no—
297C22×C4—2441no—
298C22×C4—2442no—
299C22×C4C22⋊#692311yescharacteristic
300C22×C4C22⋊#692311yescharacteristic
301C22×C4C22×#692311yescharacteristic
302M16—2444no—
303C2×C8—1224no—
304C4⋊C4—24no—
305C4⋊C4—1224no—
306C4⋊C4—2444no—
307C22⋊C4—1228no—
308C22⋊C4—2442no—
309C22⋊C4—2442no—
310C42—42no—
311C42—611no—
312C42—611no—
313C42—611no—
314C42—611no—
315C42—611no—
316C42—611no—
317C42—611no—
318C42—611no—
319C42—611no—
320C42—611no—
321C42—611no—
322C42—611no—
323C42—1228no—
324C42—2442no—
325C42—2444no—
326C42—2444no—
327C42C4×#692311yescharacteristic
328C42C4×#692311yescharacteristic
329C42C4⋊#692311yescharacteristic
330C42C4⋊#692311yescharacteristic
331C23—611no—
332C23—611no—
333C23—1222no—
334C23—1221no—
335C23—1221no—
336C23—2441no—
337C23C2×C22⋊#692311yescharacteristic
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—22no—
341C2×C4—24no—
342C2×C4—41no—
343C2×C4—42no—
344C2×C4—42no—
345C2×C4—611no—
346C2×C4—611no—
347C2×C4—614no—
348C2×C4—611no—
349C2×C4—611no—
350C2×C4—611no—
351C2×C4—611no—
352C2×C4—1222no—
353C2×C4—1222no—
354C2×C4—1222no—
355C2×C4—1222no—
356C2×C4—1222no—
357C2×C4—1222no—
358C2×C4—1221no—
359C2×C4—1221no—
360C2×C4—1222no—
361C2×C4—1224no—
362C2×C4—2441no—
363C2×C4—2441no—
364C2×C4—2441no—
365C2×C4—2441no—
366C2×C4—2441no—
367C2×C4—2441no—
368C2×C4—2444no—
369C2×C4—2444no—
370C2×C4—2444no—
371C2×C4—2442no—
372C2×C4—2442no—
373C2×C4(C2×#6923)⋊C411yescharacteristic
374C2×C4(C2×#6923)⋊C411yescharacteristic
375C2×C4(C2×#6923)⋊C411yescharacteristic
376C2×C4(C2×#6923)⋊C411yescharacteristic
377C2×C4C2×C4×#692311yescharacteristic
378C2×C4C2×C4⋊#692311yescharacteristic
379C8—2444no—
380C22—21no—
381C22—21no—
382C22—612no—
383C22—1221no—
384C22—1221no—
385C22—1221no—
386C22—1221no—
387C22—1221no—
388C22—2442no—
389C22—2442no—
390C22C2×(C2×#6923)⋊C411yescharacteristic
391C22#1684076011yescharacteristic
392C22#1684076111yescharacteristic
393C4—21no—
394C4—21no—
395C4—21no—
396C4—21no—
397C4—21no—
398C4—44no—
399C4—612no—
400C4—612no—
401C4—1221no—
402C4—1221no—
403C4—1221no—
404C4—1221no—
405C4—4884no—
406C4—2444no—
407C4#1684063312yes—
408C2—21no—
409C2—21no—
410C2—1222no—
411C2—2441no—
412C2C2×#1684063311yescharacteristic
413C2#2146149811yescharacteristic
414C2#2146151711yescharacteristic
subgroupG/H
centerC22C2×(C2×#6923)⋊C4
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC4×C4⋊C4×C61C4
socleC22×C61C2×#95
prime radicalC23×D61C2×D4
cosocleC22×C4×D61C23
hypercenterC4×C4⋊C4#6923
hypocenterC61#8052
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
9. #16840767C4semidirect
11. C4×#11758213C4semidirect
12. #16840707C4semidirect
13. #16840706C4semidirect
22. C4×C4⋊Dic61C4semidirect
25. #16839607C4semidirect
27. C4×C4⋊C4×C61C4semidirect
228. C4×C4⋊C4#6923semidirect
235. C61#8052semidirect

Maximal subgroups

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

subgroupindex
#214624982
#214622662
#214607002
C4×#145197352
#805261