Finite Group Databasebeta

← #30596349

Subgroups — #30596349

Order 15616.

666 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840783C211yesmaximal, characteristic
2C2×#16840783C211yesmaximal, characteristic
3#21460662C214yesmaximal
4C4×#14519733C211yesmaximal, characteristic
5#16840783—21no—
6#16840783—21no—
7#16840783—21no—
8#16840783—21no—
9#16840783—21no—
10#16840783—21no—
11#16840783C412yescomplemented
12#16840783C412yescomplemented
13C2×C4⋊#92420—21no—
14C2×C4⋊#92420C412yescomplemented
15C2×C22⋊#92420C2212yes—
16C2×C22⋊#92420C2212yes—
17C2×#14519832—21no—
18C2×#14519832C412yescomplemented
19C2×#14519733C412yes—
20C22×C4×Dic61C2211yescharacteristic
21C4×#11758196—21no—
22#16839613—21no—
23C22⋊C4×Dic61C2212yes—
24C4×C22⋊Dic61C411yescharacteristic
25#16839607—21no—
26C42×Dic61—21no—
27C4×C22⋊C4×C61C411yescharacteristic
28C22×#92420—22no—
29C22×#92420C2×C414yes—
30C4⋊#92420—22no—
31C4⋊#92420—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—
40#14519832—22no—
41#14519832—22no—
42C23×Dic61C2×C411yescharacteristic
43C23×Dic61C2311yescharacteristic
44#14519733—24no—
45#14519733—24no—
46C2×#11758196—22no—
47C2×C22⋊Dic61C2×C412yes—
48C2×C4×Dic61—22no—
49C2×C4×Dic61—21no—
50C2×C4×Dic61—22no—
51C2×C4×Dic61C2×C411yescharacteristic
52C2×C4×Dic61C2×C411yescharacteristic
53C2×C4×Dic61C2×C411yescharacteristic
54C2×C4×Dic61C2×C411yescharacteristic
55C2×C4×Dic61D411yescharacteristic
56C2×C4×Dic61D411yescharacteristic
57C2×C4×Dic61D411yescharacteristic
58C2×C4×Dic61D411yescharacteristic
59C2×C4×Dic61D411yescharacteristic
60C2×C4×Dic61D411yescharacteristic
61C2×C4×Dic61Q811yescharacteristic
62C2×C4×Dic61Q811yescharacteristic
63#14519684—21no—
64#14519684—22no—
65C23×C4×C61C2×C411yescharacteristic
66C2×C22⋊C4×C61C2×C412yes—
67C2×C42×C61—21no—
68#95×C61—21no—
69C24×C61C22×C411yescharacteristic
70C22×C4×C61—22no—
71C22×C4×C61—42no—
72C22×C4×C61C4211yescharacteristic
73C22×C4×C61C4211yescharacteristic
74C22×C4×C61C22⋊C411yescharacteristic
75C22×C4×C61C22⋊C411yescharacteristic
76C22×C4×C61C4⋊C411yescharacteristic
77C22×C4×C61C4⋊C411yescharacteristic
78C22×Dic61—22no—
79C22×Dic61—22no—
80C22×Dic61—22no—
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
94C2×#92420—24no—
95C2×#92420—24no—
96C2×#92420—44no—
97C2×#92420—44no—
98C22⋊C4×C61—22no—
99C22⋊C4×C61M1614yes—
100C42×C61—42no—
101C22⋊Dic61—22no—
102C22⋊Dic61M1614yes—
103#11758196—28no—
104C4×Dic61—28no—
105C4×Dic61—44no—
106C4×Dic61—42no—
107C4×Dic61C22⋊C411yescharacteristic
108C4×Dic61C22⋊C411yescharacteristic
109C4×Dic61C22⋊C411yescharacteristic
110C4×Dic61C22⋊C411yescharacteristic
111C4×Dic61C22⋊C411yescharacteristic
112C4×Dic61C22⋊C411yescharacteristic
113C4×Dic61C22⋊C411yescharacteristic
114C4×Dic61C22⋊C411yescharacteristic
115C4×Dic61C4⋊C411yescharacteristic
116C4×Dic61C4⋊C411yescharacteristic
117C4×Dic61C4⋊C411yescharacteristic
118C4×Dic61C4⋊C411yescharacteristic
119C4×Dic61C4⋊C411yescharacteristic
120C4×Dic61C4⋊C411yescharacteristic
121C4×Dic61C4⋊C411yescharacteristic
122C4×Dic61C4⋊C411yescharacteristic
123C23×C61—41no—
124C23×C61—41no—
125C23×C61C2×C4211yescharacteristic
126C23×C61C2×C22⋊C411yescharacteristic
127C23×C61C2×C4⋊C411yescharacteristic
128C23×C61C2×M1612yes—
129C23×C61C2×M1612yes—
130C2×C4×C61—22no—
131C2×C4×C61—22no—
132C2×C4×C61—22no—
133C2×C4×C61—24no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—42no—
138C2×C4×C61—42no—
139C2×C4×C61#9511yescharacteristic
140C2×C4×C61#9511yescharacteristic
141C2×C4×C61#9511yescharacteristic
142C2×C4×C61#9511yescharacteristic
143C2×Dic61—22no—
144C2×Dic61—22no—
145C2×Dic61—22no—
146C2×Dic61—22no—
147C2×Dic61—21no—
148C2×Dic61—21no—
149C2×Dic61—21no—
150C2×Dic61—21no—
151C2×Dic61—22no—
152C2×Dic61—22no—
153C2×Dic61—22no—
154C2×Dic61—24no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61—41no—
158C2×Dic61—42no—
159C2×Dic61—42no—
160C2×Dic61#9511yescharacteristic
161C2×Dic61#9511yescharacteristic
162C2×Dic61#9511yescharacteristic
163C2×Dic61#9511yescharacteristic
164C2×Dic61C2×C22⋊C411yescharacteristic
165C2×Dic61C2×C22⋊C411yescharacteristic
166C2×Dic61C2×C4⋊C411yescharacteristic
167C2×Dic61C2×C4⋊C411yescharacteristic
168#92420—44no—
169#92420—44no—
170#7930—611nomaximal, Sylow
171C22×C61—21no—
172C22×C61—21no—
173C22×C61—21no—
174C22×C61—21no—
175C22×C61—21no—
176C22×C61—21no—
177C22×C61—42no—
178C22×C61—42no—
179C22×C61C2×#9511yescharacteristic
180C22×C61C4×M1612yes—
181C22×C61#40712yes—
182C22×C61#42311yescharacteristic
183C22×C61#42311yescharacteristic
184C4×C61—21no—
185C4×C61—21no—
186C4×C61—21no—
187C4×C61—44no—
188C4×C61#34412yes—
189Dic61—21no—
190Dic61—21no—
191Dic61—21no—
192Dic61—21no—
193Dic61—21no—
194Dic61—21no—
195Dic61—21no—
196Dic61—44no—
197Dic61#41012yes—
198C2×#432—611no—
199C2×#432—611no—
200C4×#117—611no—
201#1282—614no—
202C2×C61—22no—
203C2×C61—22no—
204C2×C61—21no—
205C2×C61—21no—
206C2×C61#172811yescharacteristic
207C2×C61#174011yescharacteristic
208C2×C61C2×#34411yescharacteristic
209C2×#117—612no—
210C22×C42—611no—
211#432—612no—
212#432—612no—
213#432—1221no—
214#432—1221no—
215#432—1221no—
216#432—1221no—
217#432—1221no—
218#432—1221no—
219C2×C4⋊C8—612no—
220C2×C4⋊C8—1221no—
221C2×C22⋊C8—612no—
222C2×C22⋊C8—612no—
223C2×#97—612no—
224C2×#97—1221no—
225C4×C4⋊C4—1221no—
226C4×C4⋊C4—1221no—
227C4×C22⋊C4—611no—
228C4×C22⋊C4—612no—
229C4×C22⋊C4#692311yescharacteristic
230#376—1221no—
231C43—1221no—
232C61#793011yescharacteristic, complemented, Sylow
233C23×C4—611no—
234C23×C4—611no—
235C23×C4C2×#692311yescharacteristic
236C22×C8—614no—
237C22×C8—1222no—
238#117—1224no—
239#117—1224no—
240C2×C4⋊C4—1222no—
241C2×C22⋊C4—612no—
242C2×C22⋊C4C2×#692312yes—
243C2×C42—21no—
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—611no—
255C2×C42—611no—
256C2×C42—1222no—
257C2×C42—1222no—
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—
269#97—1222no—
270#97—1222no—
271#95—21no—
272#95—1222no—
273#95—1221no—
274C24C22×#692311yescharacteristic
275C22×C4—22no—
276C22×C4—42no—
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—1222no—
291C22×C4—1222no—
292C22×C4—2442no—
293C22×C4C4×#692311yescharacteristic
294C22×C4C4×#692311yescharacteristic
295C22×C4C4⋊#692311yescharacteristic
296C22×C4C4⋊#692311yescharacteristic
297C22×C4C22⋊#692311yescharacteristic
298C22×C4C22⋊#692311yescharacteristic
299C2×C8—1224no—
300C2×C8—1224no—
301C2×C8—2444no—
302C2×C8—2444no—
303C4⋊C4—1228no—
304C22⋊C4—22no—
305C22⋊C4—614no—
306C22⋊C4—1222no—
307C22⋊C4#1175821314yes—
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—1228no—
326C42—2442no—
327C42—2444no—
328C23—41no—
329C23—41no—
330C23C2×C4×#692311yescharacteristic
331C23C2×C22⋊#692311yescharacteristic
332C23C2×C4⋊#692311yescharacteristic
333C23D61⋊M1612yes—
334C23C2×#1175821312yes—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—24no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—611no—
345C2×C4—611no—
346C2×C4—611no—
347C2×C4—611no—
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—1222no—
359C2×C4—1221no—
360C2×C4—1221no—
361C2×C4—1221no—
362C2×C4—1221no—
363C2×C4—1224no—
364C2×C4—2441no—
365C2×C4—2441no—
366C2×C4—2441no—
367C2×C4—2442no—
368C2×C4—2442no—
369C2×C4(C2×#6923)⋊C411yescharacteristic
370C2×C4(C2×#6923)⋊C411yescharacteristic
371C2×C4(C2×#6923)⋊C411yescharacteristic
372C2×C4(C2×#6923)⋊C411yescharacteristic
373C8—2444no—
374C8—2444no—
375C22—21no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—21no—
381C22—42no—
382C22—42no—
383C22C2×(C2×#6923)⋊C411yescharacteristic
384C22C4×#1175821312yes—
385C22#1684073312yes—
386C22#1684076611yescharacteristic
387C22#1684076711yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—44no—
392C4—612no—
393C4—1221no—
394C4—1221no—
395C4—1221no—
396C4—1221no—
397C4—1221no—
398C4—1221no—
399C4—1221no—
400C4—2444no—
401C4#1684064312yes—
402C2—22no—
403C2—22no—
404C2—21no—
405C2—21no—
406C2#2146148311yescharacteristic
407C2#2146151711yescharacteristic
408C2C2×#1684064311yescharacteristic
subgroupG/H
centerC22C2×(C2×#6923)⋊C4
commutatorC23×C61C2×C42
FrattiniC24C22×#6923
FittingC4×C22⋊C4×C61C4
socleC22×C61C2×#95
prime radicalC24×C61C22×C4
cosocleC23×Dic61C23
hypercenterC4×C22⋊C4#6923
hypocenterC61#7930
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
11. #16840783C4semidirect
12. #16840783C4semidirect
14. C2×C4⋊#92420C4semidirect
18. C2×#14519832C4semidirect
232. C61#7930semidirect

Maximal subgroups

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

subgroupindex
C2×#168407832
#214606622
C4×#145197332
#793061