Finite Group Databasebeta

← #30600381

Subgroups — #30600381

Order 15616.

644 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519844C211yesmaximal, characteristic
2#21461675C211yesmaximal, characteristic
3C2×#16840621C212yesmaximal, complemented
4#21460697C212yesmaximal, complemented
5#21454169C211yesmaximal, characteristic
6C23×#92420—21no—
7C2×#14519844—21no—
8C2×#14519844—24no—
9C2×#14519844C2212yes—
10C2×#14519844C2212yes—
11C2×C22⋊#92420—21no—
12#16840628—21no—
13#16840621—24no—
14C2×#14519776C2211yescharacteristic
15C2×#14519754—21no—
16C22×C4×Dic61C2211yescharacteristic
17#16839666—21no—
18#16839661C411yescharacteristic
19#16839659—21no—
20#16839658C411yescharacteristic
21#16839631C2211yescharacteristic
22#16839622C411yescharacteristic
23#16839620—21no—
24C61×#380C411yescharacteristic
25C22×#92420—24no—
26C22×#92420—22no—
27C22×#92420—22no—
28C22×#92420—42no—
29C22×#92420—42no—
30#14519844—24no—
31#14519844—22no—
32#14519844—22no—
33#14519844—22no—
34#14519844D414yes—
35C22⋊#92420—42no—
36C22×Dic122—21no—
37C23×Dic61D411yescharacteristic
38C23×Dic61D411yescharacteristic
39#14519776—22no—
40#14519776—22no—
41#14519754—42no—
42#14519754—42no—
43C2×C4⋊Dic61—21no—
44C2×C4⋊Dic61C2×C411yescharacteristic
45C2×C4⋊Dic61C2×C411yescharacteristic
46C2×#11758196—21no—
47C2×#11758196—21no—
48C2×#11758196—21no—
49C2×#11758196—21no—
50C2×C22⋊Dic61—21no—
51C2×C4×Dic61—22no—
52C2×C4×Dic61—22no—
53C2×C4×Dic61C2×C411yescharacteristic
54C2×C4×Dic61D411yescharacteristic
55C2×C4×Dic61D411yescharacteristic
56C2×C4×Dic61C2311yescharacteristic
57#14519684—21no—
58#14519684—21no—
59#14519684—21no—
60C23×C4×C61C2×C411yescharacteristic
61C2×C4⋊C4×C61C2×C411yescharacteristic
62C2×C4⋊C4×C61C2×C411yescharacteristic
63C2×C22⋊C4×C61—21no—
64#95×C61—21no—
65C24×C61C22⋊C411yescharacteristic
66C22×C4×C61—22no—
67C22×C4×C61—22no—
68C22×C4×C61—21no—
69C22×C4×C61—21no—
70C22×C4×C61—41no—
71C22×C4×C61C22⋊C411yescharacteristic
72C22×C4×C61C22×C411yescharacteristic
73C22×Dic61—21no—
74C22×Dic61—22no—
75C22×Dic61—21no—
76C22×Dic61—22no—
77C22×Dic61—21no—
78C22×Dic61—21no—
79C22×Dic61—21no—
80C22×Dic61—21no—
81C22×Dic61C22⋊C411yescharacteristic
82C22×Dic61C22⋊C411yescharacteristic
83C22×Dic61D812yes—
84C22×Dic61SD1612yes—
85C22×Dic61SD1612yes—
86C22×Dic61Q1612yes—
87C22×Dic61C2×D411yescharacteristic
88C22×Dic61C2×D411yescharacteristic
89C2×Dic122—41no—
90C2×Dic122—41no—
91C2×Dic122—41no—
92C2×Dic122—41no—
93C2×Dic122—41no—
94C2×Dic122—41no—
95C2×#92420—24no—
96C2×#92420—48no—
97C2×#92420—42no—
98C2×#92420—42no—
99C2×#92420—42no—
100C2×#92420—42no—
101C2×#92420—42no—
102C4⋊C4×C61—22no—
103C4⋊C4×C61—41no—
104C22⋊C4×C61—42no—
105C22⋊Dic61—42no—
106C4⋊Dic61—22no—
107C4⋊Dic61—42no—
108C4⋊Dic61—41no—
109#11758196—42no—
110#11758196—42no—
111#11758196—41no—
112#11758196—41no—
113#11758196—42no—
114C4×Dic61—22no—
115C4×Dic61—21no—
116C4×Dic61—22no—
117C4×Dic61—21no—
118C4×Dic61C2×D412yes—
119C4×Dic61#4112yes—
120C23×C61—21no—
121C23×C61—21no—
122C23×C61—21no—
123C23×C61—21no—
124C23×C61#10112yes—
125C23×C61#10212yes—
126C23×C61#10312yes—
127C23×C61C2×C22⋊C411yescharacteristic
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—21no—
131C2×C4×C61—21no—
132C2×C4×C61—21no—
133C2×C4×C61—44no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61—41no—
140C2×C4×C61C4×D412yes—
141C2×Dic61—21no—
142C2×Dic61—21no—
143C2×Dic61—21no—
144C2×Dic61—21no—
145C2×Dic61—22no—
146C2×Dic61—22no—
147C2×Dic61—24no—
148C2×Dic61—24no—
149C2×Dic61—22no—
150C2×Dic61—22no—
151C2×Dic61—41no—
152C2×Dic61—41no—
153C2×Dic61—41no—
154C2×Dic61—41no—
155C2×Dic61—41no—
156C2×Dic61—41no—
157C2×Dic61#10212yes—
158C2×Dic61#10312yes—
159C2×Dic61#12011yescharacteristic
160C2×Dic61#12112yes—
161C2×Dic61#12311yescharacteristic
162C2×Dic61C2×D811yescharacteristic
163C2×Dic61C2×SD1611yescharacteristic
164C2×Dic61C2×SD1611yescharacteristic
165C2×Dic61C2×Q1611yescharacteristic
166C2×Dic61#13512yes—
167C2×Dic61AGL(1,ℤ/8)11yescharacteristic
168C2×Dic61#13711yescharacteristic
169Dic122—81no—
170Dic122—81no—
171Dic122—81no—
172Dic122—81no—
173#92420—44no—
174#92420—82no—
175#9131—611nomaximal, Sylow
176C22×C61—22no—
177C22×C61—22no—
178C22×C61—22no—
179C22×C61—22no—
180C22×C61—22no—
181C22×C61—22no—
182C22×C61#33214yescomplemented
183C22×C61#38611yescharacteristic
184C22×C61C2×#10111yescharacteristic
185C22×C61#41311yescharacteristic
186C22×C61C2×#10211yescharacteristic
187C22×C61C2×#10311yescharacteristic
188C22×C61#41611yescharacteristic
189C22×C61#41711yescharacteristic
190C4×C61—22no—
191C4×C61—41no—
192C4×C61—81no—
193C4×C61—81no—
194Dic61—22no—
195Dic61—22no—
196Dic61—81no—
197Dic61—81no—
198Dic61#44711yescharacteristic
199Dic61#44811yescharacteristic
200Dic61#46512yes—
201Dic61#46712yes—
202Dic61#48011yescharacteristic
203Dic61#48111yescharacteristic
204C22×C4⋊C8—611no—
205#2857—611no—
206#1797—611no—
207C2×#332—612no—
208#1296—612no—
209C2×C61—24no—
210C2×C61C2×#33211yescharacteristic
211C2×C61#154011yescharacteristic
212C2×C61#155011yescharacteristic
213C2×C61#155211yescharacteristic
214C2×C61#187411yescharacteristic
215C2×C61#189211yescharacteristic
216C2×C61#190111yescharacteristic
217C23×C8—1221no—
218C2×C4⋊Q8—611no—
219C2×C22⋊Q8—1221no—
220C22×C42—611no—
221C2×C4⋊C8—612no—
222C2×C4⋊C8—612no—
223C2×C4⋊C8—1224no—
224C2×C4⋊C8—1221no—
225C2×C22⋊C8—1221no—
226#391—1221no—
227#389—611no—
228#389—611no—
229#389—1221no—
230#384—611no—
231#380—611no—
232#380—1221no—
233#380#692311yescharacteristic
234#336—1221no—
235#332—1224no—
236C61#913111yescharacteristic, complemented, Sylow
237C22×Q8—1221no—
238C23×C4—611no—
239C23×C4—611no—
240C23×C4C2×#692311yescharacteristic
241C22×C8—1222no—
242C22×C8—1224no—
243C22×C8—1222no—
244C22×C8—2442no—
245C22×C8—2442no—
246C4⋊Q8—1222no—
247C4⋊Q8—1222no—
248C22⋊Q8—2442no—
249C22⋊Q8—2442no—
250C2×C4⋊C4—611no—
251C2×C4⋊C4—611no—
252C2×C4⋊C4—1221no—
253C2×C4⋊C4—1221no—
254C2×C4⋊C4—1221no—
255C2×C4⋊C4—1221no—
256C2×C4⋊C4—1221no—
257C2×C4⋊C4C2×#692311yescharacteristic
258C2×C4⋊C4C2×#692311yescharacteristic
259C2×C22⋊C4—21no—
260C2×C22⋊C4—1221no—
261C2×C42—611no—
262C2×C42—611no—
263C2×C42—611no—
264C2×C42—611no—
265C2×C42—1222no—
266C2×C42—1222no—
267C4⋊C8—614no—
268C4⋊C8—1222no—
269C4⋊C8—1222no—
270C4⋊C8—1222no—
271C4⋊C8—1224no—
272C22⋊C8—2442no—
273#95—21no—
274#95—1221no—
275#95—1221no—
276#95—1221no—
277C24C22⋊#692311yescharacteristic
278C2×Q8—2441no—
279C2×Q8—2441no—
280C2×Q8—2441no—
281C2×Q8—2441no—
282C2×Q8—2441no—
283C2×Q8—2441no—
284C22×C4—22no—
285C22×C4—22no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—41no—
289C22×C4—611no—
290C22×C4—611no—
291C22×C4—612no—
292C22×C4—612no—
293C22×C4—612no—
294C22×C4—612no—
295C22×C4—611no—
296C22×C4—611no—
297C22×C4—1221no—
298C22×C4—1222no—
299C22×C4—1221no—
300C22×C4—1221no—
301C22×C4—1222no—
302C22×C4—1221no—
303C22×C4—1221no—
304C22×C4—1221no—
305C22×C4C22⋊#692311yescharacteristic
306C22×C4C22×#692311yescharacteristic
307C2×C8—1224no—
308C2×C8—2442no—
309C2×C8—2442no—
310C2×C8—2442no—
311C2×C8—2442no—
312C2×C8—2442no—
313C2×C8—2448no—
314C4⋊C4—22no—
315C4⋊C4—41no—
316C4⋊C4—1222no—
317C4⋊C4—2441no—
318C4⋊C4—2442no—
319C4⋊C4—2441no—
320C4⋊C4—2441no—
321C4⋊C4—2442no—
322C4⋊C4—2442no—
323C4⋊C4—2442no—
324C22⋊C4—42no—
325C22⋊C4—2442no—
326C42—612no—
327C42—612no—
328C42—1221no—
329C42—1222no—
330C42—1221no—
331C42—1222no—
332C23—21no—
333C23—21no—
334C23—21no—
335C23—21no—
336C23#1451983812yes—
337C23#1451983912yes—
338C23#1451984012yes—
339C23C2×C22⋊#692311yescharacteristic
340Q8—4881no—
341Q8—4881no—
342Q8—4881no—
343Q8—4881no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—44no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—611no—
357C2×C4—612no—
358C2×C4—611no—
359C2×C4—611no—
360C2×C4—611no—
361C2×C4—611no—
362C2×C4—611no—
363C2×C4—612no—
364C2×C4—611no—
365C2×C4—611no—
366C2×C4—612no—
367C2×C4—612no—
368C2×C4—1222no—
369C2×C4—1222no—
370C2×C4—1222no—
371C2×C4—1222no—
372C2×C4—1224no—
373C2×C4—1224no—
374C2×C4—1221no—
375C2×C4—1221no—
376C2×C4—1221no—
377C2×C4—1221no—
378C2×C4—2441no—
379C2×C4—2441no—
380C2×C4—2441no—
381C2×C4—2441no—
382C2×C4—2441no—
383C2×C4—2441no—
384C2×C4D4×#692312yes—
385C8—4882no—
386C8—2444no—
387C22—22no—
388C22—22no—
389C22—22no—
390C22—22no—
391C22—22no—
392C22—22no—
393C22#1684062114yescomplemented
394C22#1684071011yescharacteristic
395C22C2×#1451983811yescharacteristic
396C22#1684074911yescharacteristic
397C22C2×#1451983911yescharacteristic
398C22C2×#1451984011yescharacteristic
399C22#1684075211yescharacteristic
400C22#1684075311yescharacteristic
401C4—22no—
402C4—41no—
403C4—81no—
404C4—81no—
405C4—611no—
406C4—611no—
407C4—611no—
408C4—611no—
409C4—612no—
410C4—612no—
411C4—1222no—
412C4—1222no—
413C4—4881no—
414C4—4881no—
415C2—24no—
416C2C2×#1684062111yescharacteristic
417C2#2146131711yescharacteristic
418C2#2146133711yescharacteristic
419C2#2146134011yescharacteristic
420C2#2146180611yescharacteristic
421C2#2146183211yescharacteristic
422C2#2146184611yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#380C4
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#380#6923
hypocenterC61#9131
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
3. C2×#16840621C2semidirect
4. #21460697C2semidirect
182. C22×C61#332semidirect
236. C61#9131semidirect
393. C22#16840621semidirect

Maximal subgroups

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

subgroupindex
C22×#145198442
#214616752
C2×#168406212
#214606972
#214541692
#913161