Finite Group Databasebeta

← #30597229

Subgroups — #30597229

Order 15616.

742 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462498C211yesmaximal, characteristic
2#21462497C211yesmaximal, characteristic
3#21460717C214yesmaximal, complemented
4C4×C4⋊C4×D61C211yesmaximal, characteristic
5#16840785—21no—
6#16840785C412yescomplemented
7#16840784C412yescomplemented
8#16840782—21no—
9#16840781C412yescomplemented
10#16840780—21no—
11#16840780—21no—
12#16840779C2212yes—
13#16840767C412yescomplemented
14#16840765C2212yes—
15#16840734—21no—
16#16840733—21no—
17C4×#11758213—21no—
18C4×#11758217—21no—
19C2×C4⋊C4×D61—21no—
20C2×C42×D61—21no—
21C2×C42×D61C2211yescharacteristic
22C4⋊C4×Dic61—21no—
23C4×#11758196—21no—
24C4×C4⋊Dic61C411yescharacteristic
25#16839613C2212yes—
26#95×D61C412yes—
27C4×C4⋊C4×C61C411yescharacteristic
28C2×#11758213—22no—
29C2×#11758217—22no—
30#14519844—22no—
31#14519844—22no—
32#14519844C2×C414yescomplemented
33C4⋊#92420C2×C414yescomplemented
34#14519834—22no—
35#14519834—22no—
36#14519834—22no—
37C22⋊#92420—22no—
38#14519832—22no—
39#14519832—22no—
40C4×#92420—22no—
41C4×#92420—22no—
42C22×C4×D61—22no—
43C22×C4×D61C2×C411yescharacteristic
44C22×C4×D61D411yescharacteristic
45C22×C4×D61D411yescharacteristic
46C2×C4⋊Dic61—21no—
47C2×#11758196—22no—
48C4⋊C4×D61—28no—
49C2×C4×Dic61—21no—
50C2×C4×Dic61—22no—
51C2×C4×Dic61D411yescharacteristic
52C2×C4×Dic61D411yescharacteristic
53C2×C4×Dic61C2311yescharacteristic
54C42×D61—44no—
55C42×D61C2×C411yescharacteristic
56C42×D61C2×C411yescharacteristic
57C42×D61C2×C411yescharacteristic
58C42×D61C2×C411yescharacteristic
59C42×D61D411yescharacteristic
60C42×D61D411yescharacteristic
61C42×D61Q811yescharacteristic
62C42×D61Q811yescharacteristic
63#14519684—22no—
64#14519684C2×C412yes—
65C2×C4⋊C4×C61—21no—
66C2×C42×C61—21no—
67C2×C42×C61C2×C411yescharacteristic
68#95×C61C2×C412yes—
69C23×D61C22⋊C411yescharacteristic
70C22×C4×C61—22no—
71C22×C4×C61C22⋊C411yescharacteristic
72C22×C4×C61C22⋊C411yescharacteristic
73C22×C4×C61C22×C411yescharacteristic
74C22×Dic61—22no—
75C22×Dic61C22⋊C411yescharacteristic
76C22×Dic61C2×D411yescharacteristic
77C22×Dic61C2×D411yescharacteristic
78C2×C4×D61—22no—
79C2×C4×D61—22no—
80C2×C4×D61—24no—
81C2×C4×D61—28no—
82C2×C4×D61—42no—
83C2×C4×D61—44no—
84C2×C4×D61—44no—
85C2×C4×D61C4211yescharacteristic
86C2×C4×D61C4211yescharacteristic
87C2×C4×D61C22⋊C411yescharacteristic
88C2×C4×D61C22⋊C411yescharacteristic
89C2×C4×D61C22⋊C411yescharacteristic
90C2×C4×D61C22⋊C411yescharacteristic
91C2×C4×D61C4⋊C411yescharacteristic
92C2×C4×D61C4⋊C411yescharacteristic
93C2×C4×D61C4⋊C411yescharacteristic
94C2×C4×D61C4⋊C411yescharacteristic
95C2×C4×D61C4⋊C411yescharacteristic
96C2×C4×D61C4⋊C411yescharacteristic
97#11758217—42no—
98#11758217—42no—
99C2×#92420—24no—
100C2×#92420—24no—
101#11758213—44no—
102C4⋊C4×C61—24no—
103C42×C61—42no—
104C42×C61C4211yescharacteristic
105C42×C61C4211yescharacteristic
106C42×C61C4⋊C411yescharacteristic
107C42×C61C4⋊C411yescharacteristic
108C4⋊Dic61—24no—
109#11758196—28no—
110C4×Dic61—42no—
111C4×Dic61—44no—
112C4×Dic61C22⋊C411yescharacteristic
113C4×Dic61C22⋊C411yescharacteristic
114C4×Dic61C22⋊C411yescharacteristic
115C4×Dic61C22⋊C411yescharacteristic
116C4×Dic61C4⋊C411yescharacteristic
117C4×Dic61C4⋊C411yescharacteristic
118C4×Dic61C4⋊C411yescharacteristic
119C4×Dic61C4⋊C411yescharacteristic
120C4×Dic61C22×C411yescharacteristic
121C4×Dic61C22×C411yescharacteristic
122C4×Dic61C2×D411yescharacteristic
123C4×Dic61C2×Q811yescharacteristic
124C23×C61C2×C22⋊C411yescharacteristic
125C22×D61—21no—
126C22×D61—21no—
127C22×D61—22no—
128C22×D61—22no—
129C22×D61#9511yescharacteristic
130C22×D61#9511yescharacteristic
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—22no—
134C2×C4×C61—24no—
135C2×C4×C61—41no—
136C2×C4×C61—42no—
137C2×C4×C61—42no—
138C2×C4×C61#9511yescharacteristic
139C2×C4×C61#9511yescharacteristic
140C2×C4×C61#9511yescharacteristic
141C2×C4×C61#9511yescharacteristic
142C2×C4×C61C2×C4211yescharacteristic
143C2×C4×C61C2×C4⋊C411yescharacteristic
144C2×Dic61—22no—
145C2×Dic61—24no—
146C2×Dic61—41no—
147C2×Dic61—42no—
148C2×Dic61—42no—
149C2×Dic61#9511yescharacteristic
150C2×Dic61#9511yescharacteristic
151C2×Dic61C2×C22⋊C411yescharacteristic
152C2×Dic61C2×C22⋊C411yescharacteristic
153C2×Dic61C2×C4⋊C411yescharacteristic
154C2×Dic61C2×C4⋊C411yescharacteristic
155C2×Dic61AGL(1,ℤ/8)12yes—
156C2×Dic61#13712yes—
157C4×D61—22no—
158C4×D61—22no—
159C4×D61—22no—
160C4×D61—22no—
161C4×D61—22no—
162C4×D61—22no—
163C4×D61—22no—
164C4×D61—22no—
165C4×D61—22no—
166C4×D61—41no—
167C4×D61—41no—
168C4×D61—416no—
169C4×D61#10414yes—
170#92420—44no—
171#92420—44no—
172#8098—611nomaximal, Sylow
173C22×C61—21no—
174C22×C61—21no—
175C22×C61C2×#9511yescharacteristic
176C22×C61#41811yescharacteristic
177C22×C61#41911yescharacteristic
178C2×D61—24no—
179C2×D61—24no—
180C2×D61—21no—
181C2×D61—21no—
182C2×D61—21no—
183C2×D61—21no—
184C2×D61#33912yes—
185C2×D61#34412yes—
186C4×C61—21no—
187C4×C61—21no—
188C4×C61—21no—
189C4×C61—21no—
190C4×C61—21no—
191C4×C61—44no—
192C4×C61#33912yes—
193Dic61—21no—
194Dic61—21no—
195Dic61—21no—
196Dic61—44no—
197Dic61#41712yes—
198Dic61C2×#10412yes—
199Dic61#42812yes—
200#2920—611no—
201#2920—611no—
202C2×C4×C4⋊C4—611no—
203#1303—614no—
204C2×C61—21no—
205C2×C61—21no—
206C2×C61C2×#33911yescharacteristic
207C2×C61#173611yescharacteristic
208C2×C61C2×#34411yescharacteristic
209D61—22no—
210D61—22no—
211C22×C4⋊C4—1221no—
212C22×C42—611no—
213C22×C42—1221no—
214#432—612no—
215#432—612no—
216#432—1221no—
217#432—1221no—
218#431—612no—
219#431—612no—
220#431—1221no—
221#431—1221no—
222#423—612no—
223#423—612no—
224#407—1221no—
225#407—1221no—
226C4×M16—1221no—
227C4×M16—1221no—
228C4×C4⋊C4—611no—
229C4×C4⋊C4—612no—
230C4×C4⋊C4—1221no—
231C4×C4⋊C4—1221no—
232C4×C4⋊C4#692311yescharacteristic
233C2×#95—612no—
234C61#809811yescharacteristic, complemented, Sylow
235C23×C4—611no—
236C23×C4—611no—
237C23×C4—611no—
238C23×C4—1222no—
239C2×M16—1222no—
240C2×M16—1222no—
241C2×C4⋊C4—21no—
242C2×C4⋊C4—1228no—
243C2×C4⋊C4—1222no—
244C2×C4⋊C4—1221no—
245C2×C42—21no—
246C2×C42—611no—
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—1222no—
258C2×C42—1221no—
259C2×C42—2444no—
260C2×C42C2×#692311yescharacteristic
261C4⋊C8—614no—
262C4⋊C8—614no—
263C4⋊C8—1222no—
264C4⋊C8—1222no—
265C22⋊C8—1222no—
266C22⋊C8—1222no—
267C22⋊C8—1222no—
268C22⋊C8—1222no—
269#97—1222no—
270#97—1222no—
271C4×C8—1222no—
272C4×C8—1222no—
273#95—612no—
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—1222no—
294C22×C4—1224no—
295C22×C4—1222no—
296C22×C4—1228no—
297C22×C4—1222no—
298C22×C4—2442no—
299C22×C4—2444no—
300C22×C4—2444no—
301C22×C4C22⋊#692311yescharacteristic
302C22×C4C22⋊#692311yescharacteristic
303C22×C4C22×#692311yescharacteristic
304M16—2444no—
305M16—2442no—
306M16—2442no—
307C2×C8—1224no—
308C2×C8—1224no—
309C4⋊C4—24no—
310C4⋊C4—1228no—
311C4⋊C4—1224no—
312C42—42no—
313C42—611no—
314C42—611no—
315C42—611no—
316C42—611no—
317C42—611no—
318C42—611no—
319C42—611no—
320C42—611no—
321C42—611no—
322C42—611no—
323C42—611no—
324C42—611no—
325C42—2442no—
326C42—2444no—
327C42C4×#692311yescharacteristic
328C42C4×#692311yescharacteristic
329C42C4⋊#692311yescharacteristic
330C42C4⋊#692311yescharacteristic
331C23—611no—
332C23—611no—
333C23—1222no—
334C23—1222no—
335C23—1221no—
336C23—1221no—
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—612no—
346C2×C4—612no—
347C2×C4—611no—
348C2×C4—611no—
349C2×C4—611no—
350C2×C4—614no—
351C2×C4—611no—
352C2×C4—611no—
353C2×C4—611no—
354C2×C4—1222no—
355C2×C4—1222no—
356C2×C4—1222no—
357C2×C4—1222no—
358C2×C4—1222no—
359C2×C4—1222no—
360C2×C4—1222no—
361C2×C4—1222no—
362C2×C4—1222no—
363C2×C4—1222no—
364C2×C4—1224no—
365C2×C4—2441no—
366C2×C4—2441no—
367C2×C4—24416no—
368C2×C4—2441no—
369C2×C4—2442no—
370C2×C4—2442no—
371C2×C4(C2×#6923)⋊C411yescharacteristic
372C2×C4(C2×#6923)⋊C411yescharacteristic
373C2×C4(C2×#6923)⋊C411yescharacteristic
374C2×C4(C2×#6923)⋊C411yescharacteristic
375C2×C4C2×C4×#692311yescharacteristic
376C2×C4C2×C4⋊#692311yescharacteristic
377C8—2444no—
378C8—2444no—
379C22—21no—
380C22—21no—
381C22—612no—
382C22—612no—
383C22—1224no—
384C22—1224no—
385C22—1221no—
386C22—1221no—
387C22—1221no—
388C22—1221no—
389C22C2×(C2×#6923)⋊C411yescharacteristic
390C22#1684075411yescharacteristic
391C22#1684075511yescharacteristic
392C4—21no—
393C4—21no—
394C4—21no—
395C4—21no—
396C4—21no—
397C4—44no—
398C4—612no—
399C4—612no—
400C4—612no—
401C4—1221no—
402C4—1221no—
403C4—1221no—
404C4—2444no—
405C4#1684063312yes—
406C2—21no—
407C2—21no—
408C2—1222no—
409C2—1222no—
410C2C2×#1684063311yescharacteristic
411C2#2146150611yescharacteristic
412C2#2146152711yescharacteristic
subgroupG/H
centerC22C2×(C2×#6923)⋊C4
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC4×C4⋊C4×C61C4
socleC22×C61C2×#95
prime radicalC23×D61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC4×C4⋊C4#6923
hypocenterC61#8098
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
3. #21460717C2semidirect
6. #16840785C4semidirect
7. #16840784C4semidirect
9. #16840781C4semidirect
13. #16840767C4semidirect
32. #14519844C2×C4semidirect
33. C4⋊#92420C2×C4semidirect
234. C61#8098semidirect

Maximal subgroups

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

subgroupindex
#214624982
#214624972
#214607172
C4×C4⋊C4×D612
#809861