Finite Group Databasebeta

← #30597281

Subgroups — #30597281

Order 15616.

606 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462495C211yesmaximal, characteristic
2#21462495C211yesmaximal, characteristic
3#21460720C214yesmaximal
4#21448221C211yesmaximal, characteristic
5#16840783—21no—
6#16840783—21no—
7#16840782—21no—
8#16840782C412yescomplemented
9#16840779—21no—
10#16840779—21no—
11#16840778—21no—
12#16840778C412yescomplemented
13#16840765—21no—
14#16840765C412yescomplemented
15#16840732C2212yes—
16#16840732C2212yes—
17C4×#11758217—21no—
18C4×#11758217C412yescomplemented
19C2×#14519733C412yes—
20C22×C4×Dic61C2211yescharacteristic
21#16839631—21no—
22#16839626—21no—
23#16839622C411yescharacteristic
24#16839620C2212yes—
25C4⋊C4×Dic61—21no—
26#16839613—21no—
27C61×#380C411yescharacteristic
28C2×#11758217—22no—
29C2×#11758217C2×C414yes—
30#14519844—22no—
31#14519844—22no—
32C4⋊#92420—22no—
33C4⋊#92420—22no—
34C22⋊#92420—22no—
35C22⋊#92420—22no—
36C22⋊#92420—22no—
37C22⋊#92420C2×C414yes—
38#14519832—22no—
39#14519832—22no—
40C4×#92420—22no—
41C4×#92420—22no—
42C23×Dic61C2×C411yescharacteristic
43C23×Dic61C2311yescharacteristic
44#14519733—44no—
45C2×C4⋊Dic61—21no—
46C2×#11758196—22no—
47C2×#11758196—22no—
48C2×C22⋊Dic61C2×C412yes—
49C2×C4×Dic61—22no—
50C2×C4×Dic61C2×C411yescharacteristic
51C2×C4×Dic61C2×C411yescharacteristic
52C2×C4×Dic61C2×C411yescharacteristic
53C2×C4×Dic61C2×C411yescharacteristic
54C2×C4×Dic61D411yescharacteristic
55C2×C4×Dic61D411yescharacteristic
56C2×C4×Dic61D411yescharacteristic
57C2×C4×Dic61D411yescharacteristic
58C2×C4×Dic61D411yescharacteristic
59C2×C4×Dic61D411yescharacteristic
60C2×C4×Dic61Q811yescharacteristic
61C2×C4×Dic61Q811yescharacteristic
62#14519684—21no—
63#14519684—22no—
64C23×C4×C61C2×C411yescharacteristic
65C2×C4⋊C4×C61—21no—
66C2×C22⋊C4×C61C2×C412yes—
67#95×C61—21no—
68C24×C61C22×C411yescharacteristic
69C22×C4×C61—22no—
70C22×C4×C61—42no—
71C22×C4×C61C4211yescharacteristic
72C22×C4×C61C4211yescharacteristic
73C22×C4×C61C22⋊C411yescharacteristic
74C22×C4×C61C22⋊C411yescharacteristic
75C22×C4×C61C4⋊C411yescharacteristic
76C22×C4×C61C4⋊C411yescharacteristic
77C22×Dic61—22no—
78C22×Dic61—22no—
79C22×Dic61—22no—
80C22×Dic61—42no—
81C22×Dic61C4211yescharacteristic
82C22×Dic61C4211yescharacteristic
83C22×Dic61C22⋊C411yescharacteristic
84C22×Dic61C22⋊C411yescharacteristic
85C22×Dic61C4⋊C411yescharacteristic
86C22×Dic61C4⋊C411yescharacteristic
87C22×Dic61C22×C411yescharacteristic
88C22×Dic61C22×C411yescharacteristic
89C22×Dic61C2×D411yescharacteristic
90C22×Dic61C2×D411yescharacteristic
91C22×Dic61C2×D411yescharacteristic
92C22×Dic61C2×Q811yescharacteristic
93#11758217—44no—
94#11758217—44no—
95C2×#92420—24no—
96C2×#92420—24no—
97C4⋊C4×C61—42no—
98C22⋊C4×C61—42no—
99C22⋊Dic61—42no—
100C4⋊Dic61—42no—
101#11758196—44no—
102#11758196—44no—
103C4×Dic61—44no—
104C4×Dic61C22⋊C411yescharacteristic
105C4×Dic61C22⋊C411yescharacteristic
106C4×Dic61C22⋊C411yescharacteristic
107C4×Dic61C22⋊C411yescharacteristic
108C4×Dic61C22⋊C411yescharacteristic
109C4×Dic61C22⋊C411yescharacteristic
110C4×Dic61C22⋊C411yescharacteristic
111C4×Dic61C22⋊C411yescharacteristic
112C4×Dic61C4⋊C411yescharacteristic
113C4×Dic61C4⋊C411yescharacteristic
114C4×Dic61C4⋊C411yescharacteristic
115C4×Dic61C4⋊C411yescharacteristic
116C4×Dic61C4⋊C411yescharacteristic
117C4×Dic61C4⋊C411yescharacteristic
118C4×Dic61C4⋊C411yescharacteristic
119C4×Dic61C4⋊C411yescharacteristic
120C23×C61—21no—
121C23×C61—21no—
122C23×C61—41no—
123C23×C61—41no—
124C23×C61C2×C4211yescharacteristic
125C23×C61C2×C22⋊C411yescharacteristic
126C23×C61C2×C4⋊C411yescharacteristic
127C2×C4×C61—22no—
128C2×C4×C61—22no—
129C2×C4×C61—22no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—42no—
134C2×C4×C61—42no—
135C2×C4×C61—42no—
136C2×C4×C61#9511yescharacteristic
137C2×C4×C61#9511yescharacteristic
138C2×C4×C61#9511yescharacteristic
139C2×C4×C61#9511yescharacteristic
140C2×Dic61—21no—
141C2×Dic61—21no—
142C2×Dic61—22no—
143C2×Dic61—22no—
144C2×Dic61—22no—
145C2×Dic61—22no—
146C2×Dic61—22no—
147C2×Dic61—22no—
148C2×Dic61—22no—
149C2×Dic61—41no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—42no—
153C2×Dic61—42no—
154C2×Dic61—42no—
155C2×Dic61#9511yescharacteristic
156C2×Dic61#9511yescharacteristic
157C2×Dic61#9511yescharacteristic
158C2×Dic61#9511yescharacteristic
159C2×Dic61#10012yes—
160C2×Dic61#10112yes—
161C2×Dic61C2×C22⋊C411yescharacteristic
162C2×Dic61C2×C22⋊C411yescharacteristic
163C2×Dic61C2×C4⋊C411yescharacteristic
164C2×Dic61C2×C4⋊C411yescharacteristic
165#92420—44no—
166#92420—44no—
167#8109—611nomaximal, Sylow
168C22×C61—21no—
169C22×C61—21no—
170C22×C61—21no—
171C22×C61—21no—
172C22×C61—21no—
173C22×C61—21no—
174C22×C61—21no—
175C22×C61—21no—
176C22×C61—42no—
177C22×C61—42no—
178C22×C61C2×#9511yescharacteristic
179C22×C61C2×#10011yescharacteristic
180C22×C61C2×#10111yescharacteristic
181C4×C61—21no—
182C4×C61—21no—
183C4×C61—21no—
184C4×C61—82no—
185C4×C61#34412yes—
186Dic61—21no—
187Dic61—21no—
188Dic61—21no—
189Dic61—21no—
190Dic61—21no—
191Dic61—82no—
192Dic61#34312yes—
193Dic61#34312yes—
194Dic61#41012yes—
195#2920—611no—
196#2920—611no—
197#2285—611no—
198#1305—614no—
199C2×C61—21no—
200C2×C61—21no—
201C2×C61—41no—
202C2×C61—41no—
203C2×C61#174011yescharacteristic
204C2×C61C2×#34311yescharacteristic
205C2×C61C2×#34411yescharacteristic
206C2×#117—612no—
207C22×C42—611no—
208#432—612no—
209#432—1221no—
210#432—1221no—
211#432—1221no—
212#431—612no—
213#431—1221no—
214#431—1221no—
215#431—1221no—
216#423—612no—
217#423—1221no—
218#407—612no—
219#407—612no—
220C4×M16—612no—
221C4×M16—1221no—
222#384—1221no—
223#382—1221no—
224#380—611no—
225#380—612no—
226#380#692311yescharacteristic
227C4×C4⋊C4—1221no—
228C4×C4⋊C4—1221no—
229C61#810911yescharacteristic, complemented, Sylow
230C23×C4—611no—
231C23×C4—611no—
232C23×C4C2×#692311yescharacteristic
233C2×M16—614no—
234C2×M16—1222no—
235#117—2444no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—1222no—
238C2×C4⋊C4—1222no—
239C2×C4⋊C4—1221no—
240C2×C22⋊C4—612no—
241C2×C22⋊C4C2×#692312yes—
242C2×C42—611no—
243C2×C42—611no—
244C2×C42—611no—
245C2×C42—611no—
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—1222no—
255C4⋊C8—1222no—
256C4⋊C8—1222no—
257C4⋊C8—1222no—
258C4⋊C8—1222no—
259C22⋊C8—614no—
260C22⋊C8—1222no—
261C22⋊C8—1222no—
262C22⋊C8—1222no—
263#97—1222no—
264#97—1222no—
265C4×C8—1222no—
266C4×C8—1222no—
267#95—21no—
268#95—1222no—
269#95—1221no—
270C24C22×#692311yescharacteristic
271C22×C4—22no—
272C22×C4—42no—
273C22×C4—611no—
274C22×C4—611no—
275C22×C4—611no—
276C22×C4—611no—
277C22×C4—611no—
278C22×C4—611no—
279C22×C4—611no—
280C22×C4—611no—
281C22×C4—611no—
282C22×C4—611no—
283C22×C4—611no—
284C22×C4—611no—
285C22×C4—1222no—
286C22×C4—1222no—
287C22×C4—1222no—
288C22×C4—2442no—
289C22×C4C4×#692311yescharacteristic
290C22×C4C4×#692311yescharacteristic
291C22×C4C4⋊#692311yescharacteristic
292C22×C4C4⋊#692311yescharacteristic
293C22×C4C22⋊#692311yescharacteristic
294C22×C4C22⋊#692311yescharacteristic
295M16—2444no—
296M16—2444no—
297C2×C8—1224no—
298C2×C8—1224no—
299C4⋊C4—42no—
300C4⋊C4—2442no—
301C4⋊C4—2444no—
302C4⋊C4—2444no—
303C22⋊C4—42no—
304C22⋊C4—2442no—
305C42—611no—
306C42—611no—
307C42—611no—
308C42—611no—
309C42—611no—
310C42—611no—
311C42—611no—
312C42—611no—
313C42—611no—
314C42—611no—
315C42—611no—
316C42—611no—
317C42—611no—
318C42—611no—
319C42—611no—
320C42—611no—
321C42—2444no—
322C23—21no—
323C23—21no—
324C23—41no—
325C23—41no—
326C23C2×C4×#692311yescharacteristic
327C23C2×C22⋊#692311yescharacteristic
328C23C2×C4⋊#692311yescharacteristic
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—42no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—612no—
339C2×C4—612no—
340C2×C4—611no—
341C2×C4—611no—
342C2×C4—611no—
343C2×C4—611no—
344C2×C4—611no—
345C2×C4—611no—
346C2×C4—611no—
347C2×C4—611no—
348C2×C4—1222no—
349C2×C4—1222no—
350C2×C4—1222no—
351C2×C4—1222no—
352C2×C4—1222no—
353C2×C4—1222no—
354C2×C4—1222no—
355C2×C4—1221no—
356C2×C4—1221no—
357C2×C4—2441no—
358C2×C4—2441no—
359C2×C4—2441no—
360C2×C4—2442no—
361C2×C4—2442no—
362C2×C4—2442no—
363C2×C4(C2×#6923)⋊C411yescharacteristic
364C2×C4(C2×#6923)⋊C411yescharacteristic
365C2×C4(C2×#6923)⋊C411yescharacteristic
366C2×C4(C2×#6923)⋊C411yescharacteristic
367C8—2444no—
368C8—2444no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—42no—
378C22—42no—
379C22C2×(C2×#6923)⋊C411yescharacteristic
380C22D61⋊#10011yescharacteristic
381C22D61⋊#10111yescharacteristic
382C4—21no—
383C4—21no—
384C4—21no—
385C4—82no—
386C4—612no—
387C4—612no—
388C4—612no—
389C4—1221no—
390C4—1221no—
391C4—1221no—
392C4—1221no—
393C4—1221no—
394C4—4882no—
395C4#1684064312yes—
396C2—21no—
397C2—21no—
398C2—41no—
399C2—41no—
400C2#2146151711yescharacteristic
401C2#2146152211yescharacteristic
402C2C2×#1684064311yescharacteristic
subgroupG/H
centerC22C2×(C2×#6923)⋊C4
commutatorC23×C61C2×C42
FrattiniC24C22×#6923
FittingC61×#380C4
socleC22×C61C2×#95
prime radicalC24×C61C22×C4
cosocleC23×Dic61C23
hypercenter#380#6923
hypocenterC61#8109
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
8. #16840782C4semidirect
12. #16840778C4semidirect
14. #16840765C4semidirect
18. C4×#11758217C4semidirect
229. C61#8109semidirect

Maximal subgroups

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

subgroupindex
#214624952
#214607202
#214482212
#810961