Finite Group Databasebeta

← #30597256

Subgroups — #30597256

Order 15616.

606 conjugacy classes of subgroups.

The subgroup lattice has 408 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#21448222C211yesmaximal, characteristic
5#16840783—21no—
6#16840783C412yescomplemented
7#16840782—21no—
8#16840782—21no—
9#16840779—21no—
10#16840779C412yescomplemented
11#16840778—21no—
12#16840778—21no—
13#16840765—21no—
14#16840765C412yescomplemented
15#16840732C2212yes—
16#16840732C2212yes—
17C4×#11758217—21no—
18C4×#11758217C412yescomplemented
19C2×#14519736C411yescharacteristic
20C22×C4×Dic61C2211yescharacteristic
21#16839631—21no—
22#16839627—21no—
23#16839620C412yes—
24#16839620C2212yes—
25C4×#11758196—21no—
26C4×#11758196—21no—
27C2×#117×C61C411yescharacteristic
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#14519736—42no—
45C2×C4⋊Dic61—21no—
46C2×#11758196—22no—
47C2×#11758196—22no—
48C2×C22⋊Dic61C2×C412yes—
49C2×C4×Dic61—21no—
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—22no—
63#14519684—22no—
64C23×C4×C61C2×C411yescharacteristic
65#117×C61—42no—
66C2×C4⋊C4×C61—21no—
67C2×C22⋊C4×C61C2×C412yes—
68C2×C42×C61—21no—
69C24×C61C22×C411yescharacteristic
70C22×C4×C61—22no—
71C22×C4×C61—22no—
72C22×C4×C61—22no—
73C22×C4×C61C4211yescharacteristic
74C22×C4×C61C4211yescharacteristic
75C22×C4×C61C22⋊C411yescharacteristic
76C22×C4×C61C22⋊C411yescharacteristic
77C22×C4×C61C4⋊C411yescharacteristic
78C22×C4×C61C4⋊C411yescharacteristic
79C22×Dic61—22no—
80C22×Dic61—42no—
81C22×Dic61—42no—
82C22×Dic61C4211yescharacteristic
83C22×Dic61C4211yescharacteristic
84C22×Dic61C22⋊C411yescharacteristic
85C22×Dic61C22⋊C411yescharacteristic
86C22×Dic61C4⋊C411yescharacteristic
87C22×Dic61C4⋊C411yescharacteristic
88C22×Dic61C22×C411yescharacteristic
89C22×Dic61C22×C411yescharacteristic
90C22×Dic61C2×D411yescharacteristic
91C22×Dic61C2×D411yescharacteristic
92C22×Dic61C2×D411yescharacteristic
93C22×Dic61C2×Q811yescharacteristic
94#11758217—44no—
95#11758217—44no—
96C2×#92420—24no—
97C2×#92420—24no—
98C4⋊C4×C61—42no—
99C22⋊C4×C61—42no—
100C42×C61—42no—
101C22⋊Dic61—42no—
102C4⋊Dic61—42no—
103#11758196—44no—
104#11758196—44no—
105C4×Dic61—42no—
106C4×Dic61C22⋊C411yescharacteristic
107C4×Dic61C22⋊C411yescharacteristic
108C4×Dic61C22⋊C411yescharacteristic
109C4×Dic61C22⋊C411yescharacteristic
110C4×Dic61C22⋊C411yescharacteristic
111C4×Dic61C22⋊C411yescharacteristic
112C4×Dic61C22⋊C411yescharacteristic
113C4×Dic61C22⋊C411yescharacteristic
114C4×Dic61C4⋊C411yescharacteristic
115C4×Dic61C4⋊C411yescharacteristic
116C4×Dic61C4⋊C411yescharacteristic
117C4×Dic61C4⋊C411yescharacteristic
118C4×Dic61C4⋊C411yescharacteristic
119C4×Dic61C4⋊C411yescharacteristic
120C4×Dic61C4⋊C411yescharacteristic
121C4×Dic61C4⋊C411yescharacteristic
122C23×C61—21no—
123C23×C61—21no—
124C23×C61—41no—
125C23×C61—41no—
126C23×C61C2×C4211yescharacteristic
127C23×C61C2×C22⋊C411yescharacteristic
128C23×C61C2×C4⋊C411yescharacteristic
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—22no—
132C2×C4×C61—22no—
133C2×C4×C61—22no—
134C2×C4×C61—22no—
135C2×C4×C61—42no—
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×C61#10012yes—
143C2×C4×C61#10112yes—
144C2×Dic61—22no—
145C2×Dic61—22no—
146C2×Dic61—22no—
147C2×Dic61—22no—
148C2×Dic61—22no—
149C2×Dic61—22no—
150C2×Dic61—41no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61—42no—
157C2×Dic61—42no—
158C2×Dic61—42no—
159C2×Dic61#9511yescharacteristic
160C2×Dic61#9511yescharacteristic
161C2×Dic61#9511yescharacteristic
162C2×Dic61#9511yescharacteristic
163C2×Dic61C2×C22⋊C411yescharacteristic
164C2×Dic61C2×C22⋊C411yescharacteristic
165C2×Dic61C2×C4⋊C411yescharacteristic
166C2×Dic61C2×C4⋊C411yescharacteristic
167#92420—44no—
168#92420—44no—
169#8105—611nomaximal, Sylow
170C22×C61—21no—
171C22×C61—21no—
172C22×C61—21no—
173C22×C61—21no—
174C22×C61—21no—
175C22×C61—21no—
176C22×C61—21no—
177C22×C61—21no—
178C22×C61—42no—
179C22×C61—42no—
180C22×C61C2×#9511yescharacteristic
181C22×C61C2×#10011yescharacteristic
182C22×C61C2×#10111yescharacteristic
183C4×C61—21no—
184C4×C61—21no—
185C4×C61—82no—
186C4×C61#34312yes—
187C4×C61#34312yes—
188Dic61—21no—
189Dic61—21no—
190Dic61—21no—
191Dic61—21no—
192Dic61—21no—
193Dic61—21no—
194Dic61—82no—
195Dic61#34412yes—
196Dic61#41012yes—
197#2920—611no—
198#2920—611no—
199#2285—611no—
200#1305—614no—
201C2×C61—21no—
202C2×C61—21no—
203C2×C61—41no—
204C2×C61—41no—
205C2×C61#174011yescharacteristic
206C2×C61C2×#34311yescharacteristic
207C2×C61C2×#34411yescharacteristic
208C2×#117—611no—
209C2×#117#692311yescharacteristic
210C22×C42—611no—
211#432—612no—
212#432—1221no—
213#432—1221no—
214#432—1221no—
215#431—612no—
216#431—1221no—
217#431—1221no—
218#431—1221no—
219#423—612no—
220#423—1221no—
221#407—612no—
222#407—612no—
223C4×M16—612no—
224C4×M16—1221no—
225#384—1221no—
226#382—1221no—
227#380—612no—
228#380—612no—
229C4×C4⋊C4—1221no—
230C4×C4⋊C4—1221no—
231C61#810511yescharacteristic, complemented, Sylow
232C23×C4—611no—
233C23×C4—611no—
234C23×C4C2×#692311yescharacteristic
235C2×M16—614no—
236C2×M16—1222no—
237#117—42no—
238#117—2442no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—1222no—
241C2×C4⋊C4—1222no—
242C2×C4⋊C4—1221no—
243C2×C22⋊C4—612no—
244C2×C22⋊C4C2×#692312yes—
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—611no—
258C2×C42—1221no—
259C4⋊C8—1222no—
260C4⋊C8—1222no—
261C4⋊C8—1222no—
262C4⋊C8—1222no—
263C22⋊C8—614no—
264C22⋊C8—1222no—
265C22⋊C8—1222no—
266C22⋊C8—1222no—
267#97—1222no—
268#97—1222no—
269C4×C8—1222no—
270C4×C8—1222no—
271#95—1222no—
272#95—1222no—
273C24C22×#692311yescharacteristic
274C22×C4—22no—
275C22×C4—22no—
276C22×C4—22no—
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—611no—
286C22×C4—611no—
287C22×C4—611no—
288C22×C4—611no—
289C22×C4—1222no—
290C22×C4—2442no—
291C22×C4—2442no—
292C22×C4C4×#692311yescharacteristic
293C22×C4C4×#692311yescharacteristic
294C22×C4C4⋊#692311yescharacteristic
295C22×C4C4⋊#692311yescharacteristic
296C22×C4C22⋊#692311yescharacteristic
297C22×C4C22⋊#692311yescharacteristic
298M16—2444no—
299M16—2444no—
300C2×C8—1224no—
301C2×C8—1224no—
302C4⋊C4—42no—
303C4⋊C4—2442no—
304C4⋊C4—2444no—
305C4⋊C4—2444no—
306C22⋊C4—42no—
307C22⋊C4—2442no—
308C42—42no—
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—611no—
322C42—611no—
323C42—611no—
324C42—611no—
325C42—2442no—
326C23—21no—
327C23—21no—
328C23—41no—
329C23—41no—
330C23C2×C4×#692311yescharacteristic
331C23C2×C22⋊#692311yescharacteristic
332C23C2×C4⋊#692311yescharacteristic
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—611no—
343C2×C4—611no—
344C2×C4—611no—
345C2×C4—611no—
346C2×C4—611no—
347C2×C4—611no—
348C2×C4—611no—
349C2×C4—611no—
350C2×C4—1222no—
351C2×C4—1222no—
352C2×C4—1222no—
353C2×C4—1222no—
354C2×C4—1222no—
355C2×C4—1222no—
356C2×C4—2441no—
357C2×C4—2441no—
358C2×C4—2441no—
359C2×C4—2441no—
360C2×C4—2441no—
361C2×C4—2441no—
362C2×C4—2442no—
363C2×C4—2442no—
364C2×C4—2442no—
365C2×C4(C2×#6923)⋊C411yescharacteristic
366C2×C4(C2×#6923)⋊C411yescharacteristic
367C2×C4(C2×#6923)⋊C411yescharacteristic
368C2×C4(C2×#6923)⋊C411yescharacteristic
369C2×C4#1451983712yes—
370C2×C4#1451983812yes—
371C8—2444no—
372C8—2444no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—42no—
382C22—42no—
383C22C2×(C2×#6923)⋊C411yescharacteristic
384C22C2×#1451983711yescharacteristic
385C22C2×#1451983811yescharacteristic
386C4—21no—
387C4—21no—
388C4—82no—
389C4—612no—
390C4—612no—
391C4—1221no—
392C4—1221no—
393C4—1221no—
394C4—1221no—
395C4—1221no—
396C4—1221no—
397C4—4882no—
398C4#1684064212yes—
399C4#1684064212yes—
400C2—21no—
401C2—21no—
402C2—41no—
403C2—41no—
404C2#2146151711yescharacteristic
405C2C2×#1684064211yescharacteristic
406C2#2146152711yescharacteristic
subgroupG/H
centerC2×C4(C2×#6923)⋊C4
commutatorC23×C61C2×C42
FrattiniC24C22×#6923
FittingC2×#117×C61C4
socleC22×C61C2×#95
prime radicalC24×C61C22×C4
cosocleC23×Dic61C23
hypercenterC2×#117#6923
hypocenterC61#8105
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
6. #16840783C4semidirect
10. #16840779C4semidirect
14. #16840765C4semidirect
18. C4×#11758217C4semidirect
231. C61#8105semidirect

Maximal subgroups

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

subgroupindex
#214624952
#214607202
#214482222
#810561