Finite Group Databasebeta

← #30615204

Subgroups — #30615204

Order 15616.

1166 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462501C212yesmaximal
2#21461720C212yesmaximal
3#21461686C212yesmaximal, complemented
4#21461685C212yesmaximal, complemented
5#21461654C212yesmaximal
6#21461572C212yesmaximal, complemented
7C4×#14519838C212yesmaximal, complemented
8C2×#16840238C211yesmaximal, characteristic
9#16840787—28no—
10#16840765C2214yes—
11C2×#14519838C2214yes—
12C2×#14519838C2214yes—
13#16840734C2214yes—
14C4×#11758217C2214yes—
15#16840642C2214yes—
16#16840642C2214yes—
17C22×Q8×D61C2211yescharacteristic
18#16840238—28no—
19C2×Q8×Dic61C411yescharacteristic
20C2×C4×Dic122C411yescharacteristic
21C2×C4×Dic122C2211yescharacteristic
22C2×C4×Dic122C2211yescharacteristic
23C2×#14519742C411yescharacteristic
24C2×#14519742C2211yescharacteristic
25C2×#14519742C2211yescharacteristic
26C2×#14519735C411yescharacteristic
27C2×#14519735C411yescharacteristic
28C2×#14519735C2211yescharacteristic
29C2×#14519734C411yescharacteristic
30C2×#14519734C411yescharacteristic
31C2×#14519734C2211yescharacteristic
32C2×C4×Q8×C61C411yescharacteristic
33C2×#11758217C2318yes—
34#14519844—24no—
35C4⋊#92420—24no—
36#14519838—28no—
37#14519838—28no—
38#14519834—28no—
39#14519832—24no—
40C4×#92420—24no—
41C22×Dic122C2×C411yescharacteristic
42C22×Dic122C2311yescharacteristic
43C22×Dic122C2311yescharacteristic
44C2×Q8×D61—24no—
45C2×Q8×D61—24no—
46C2×Q8×D61—24no—
47C22×C4×D61C2×C411yescharacteristic
48C22×C4×D61C2×C411yescharacteristic
49C22×C4×D61C2311yescharacteristic
50Q8×Dic61—24no—
51C4×Dic122—24no—
52C4×Dic122—24no—
53C4×Dic122—24no—
54#14519742—24no—
55#14519742—24no—
56#14519742—24no—
57#14519735—24no—
58#14519735—24no—
59#14519735D418yes—
60#14519734—24no—
61#14519734—24no—
62#14519734—24no—
63C2×C4⋊Dic61C2×C411yescharacteristic
64C2×C4⋊Dic61C2×C411yescharacteristic
65C2×C4⋊Dic61C2×C411yescharacteristic
66C2×#11758196C2×C411yescharacteristic
67C2×#11758196C2×C411yescharacteristic
68C2×#11758196C2×C411yescharacteristic
69C2×#11758196C2×C411yescharacteristic
70C2×#11758196C2311yescharacteristic
71C2×#11758196C2311yescharacteristic
72C2×#11758198C2×C411yescharacteristic
73C2×#11758198C2×C411yescharacteristic
74C2×#11758198C2×C411yescharacteristic
75C2×#11758198C2×C411yescharacteristic
76C2×C4×Dic61C2×C411yescharacteristic
77C2×C4×Dic61C2×C411yescharacteristic
78C2×C4×Dic61C2×C411yescharacteristic
79C2×C4×Dic61C2×C411yescharacteristic
80C2×C4×Dic61C2×C411yescharacteristic
81C2×C4×Dic61C2×C411yescharacteristic
82C2×C4×Dic61C2×C411yescharacteristic
83C2×C4×Dic61C2311yescharacteristic
84C2×C4×Dic61C2311yescharacteristic
85C22×Q8×C61C2×C411yescharacteristic
86C4×Q8×C61—24no—
87C2×C4⋊C4×C61C2×C411yescharacteristic
88C2×C4⋊C4×C61C2×C411yescharacteristic
89C2×C4⋊C4×C61C2×C411yescharacteristic
90C2×C42×C61C2×C411yescharacteristic
91C2×C42×C61C2×C411yescharacteristic
92C2×C42×C61C2×C411yescharacteristic
93C23×D61C22×C411yescharacteristic
94C2×Q8×C61—22no—
95C2×Q8×C61—22no—
96C2×Q8×C61—22no—
97C22×C4×C61C22×C411yescharacteristic
98C22×C4×C61C22×C411yescharacteristic
99C22×C4×C61C22×C411yescharacteristic
100C22×C4×C61C22×C411yescharacteristic
101C22×C4×C61C22×C411yescharacteristic
102C22×C4×C61C22×C411yescharacteristic
103C22×C4×C61C22×C411yescharacteristic
104C22×Dic61C22×C411yescharacteristic
105C22×Dic61C22×C411yescharacteristic
106C22×Dic61C22×C411yescharacteristic
107C22×Dic61C22×C411yescharacteristic
108C22×Dic61C22×C411yescharacteristic
109C22×Dic61C22×C411yescharacteristic
110C22×Dic61C2411yescharacteristic
111Q8×D61—232no—
112C2×C4×D61—22no—
113C2×C4×D61—22no—
114C2×C4×D61—22no—
115C2×C4×D61—22no—
116C2×C4×D61—22no—
117C2×C4×D61—22no—
118C2×C4×D61—22no—
119C2×C4×D61—22no—
120C2×C4×D61C2×D414yes—
121C2×Dic122—22no—
122C2×Dic122—22no—
123C2×Dic122—22no—
124C2×Dic122—22no—
125C2×Dic122—22no—
126C2×Dic122—22no—
127C2×Dic122—22no—
128C2×Dic122#4114yes—
129C2×Dic122#4114yes—
130#11758217—28no—
131#11758217—28no—
132C2×#92420—28no—
133C4⋊C4×C61—22no—
134C4⋊C4×C61—22no—
135C4⋊C4×C61C22⋊C414yes—
136C42×C61—22no—
137C42×C61—22no—
138C42×C61—22no—
139#11758198—22no—
140#11758198—22no—
141#11758198C22⋊C414yes—
142#11758198C22⋊C414yes—
143C4⋊Dic61—22no—
144C4⋊Dic61—22no—
145C4⋊Dic61C22⋊C414yes—
146#11758196—22no—
147#11758196—22no—
148#11758196—22no—
149#11758196—22no—
150#11758196—22no—
151#11758196—22no—
152C4×Dic61—22no—
153C4×Dic61—22no—
154C4×Dic61—22no—
155C4×Dic61—22no—
156C4×Dic61—22no—
157C4×Dic61—22no—
158C4×Dic61—22no—
159C4×Dic61C2×D414yes—
160C4×Dic61C2×D414yes—
161C23×C61C23×C411yescharacteristic
162C22×D61—21no—
163C22×D61—21no—
164C22×D61—41no—
165C22×D61—41no—
166C22×D61C2×C22⋊C412yes—
167Q8×C61—28no—
168C2×C4×C61—21no—
169C2×C4×C61—21no—
170C2×C4×C61—21no—
171C2×C4×C61—21no—
172C2×C4×C61—21no—
173C2×C4×C61—21no—
174C2×C4×C61—21no—
175C2×C4×C61—21no—
176C2×C4×C61—41no—
177C2×C4×C61—41no—
178C2×C4×C61—41no—
179C2×C4×C61—41no—
180C2×C4×C61C2×C22⋊C412yes—
181C2×C4×C61C2×C22⋊C412yes—
182C2×C4×C61C2×C22⋊C412yes—
183C2×C4×C61#11712yes—
184C2×C4×C61#11712yes—
185C2×Dic61—21no—
186C2×Dic61—21no—
187C2×Dic61—21no—
188C2×Dic61—21no—
189C2×Dic61—21no—
190C2×Dic61—21no—
191C2×Dic61—41no—
192C2×Dic61—41no—
193C2×Dic61—41no—
194C2×Dic61—41no—
195C2×Dic61C2×C22⋊C412yes—
196C2×Dic61C2×C22⋊C412yes—
197C2×Dic61#11712yes—
198C2×Dic61#11712yes—
199C2×Dic61C22×D412yes—
200C2×Dic61C2×#4112yes—
201C2×Dic61C2×#4112yes—
202C4×D61—28no—
203C4×D61—28no—
204C4×D61—28no—
205Dic122—28no—
206Dic122—28no—
207Dic122—28no—
208#92420—48no—
209#20730—611nomaximal, Sylow
210C22×C61—21no—
211C22×C61—21no—
212C22×C61C22×C22⋊C411yescharacteristic
213C22×C61C2×#11711yescharacteristic
214C22×C61C2×#11711yescharacteristic
215C2×D61—22no—
216C2×D61—22no—
217C2×D61—22no—
218C2×D61—42no—
219C2×D61—42no—
220C4×C61—22no—
221C4×C61—22no—
222C4×C61—22no—
223C4×C61—22no—
224C4×C61—22no—
225C4×C61—41no—
226C4×C61—41no—
227Dic61—22no—
228Dic61—22no—
229Dic61—22no—
230Dic61—22no—
231Dic61—41no—
232Dic61—41no—
233Dic61#52514yes—
234C2×#519—611no—
235#2921—612no—
236#1822—612no—
237#1801—612no—
238#1801—612no—
239#1784—612no—
240C4×#101—612no—
241C4×#101—612no—
242C2×C61—21no—
243C2×C61—21no—
244C2×C61#228011yescharacteristic
245C2×C61#288911yescharacteristic
246C2×C61#288911yescharacteristic
247D61—42no—
248C23×Q8—611no—
249#519—1228no—
250C2×C4×Q8—611no—
251C2×C4×Q8—611no—
252C2×C4×Q8—611no—
253C2×C4×Q8—611no—
254C2×C4×Q8—611no—
255C2×C4×Q8—611no—
256C2×C4×Q8—611no—
257C2×C4×Q8#692311yescharacteristic
258C2×#117—611no—
259C2×#117—611no—
260C2×#117—611no—
261C2×#117—611no—
262C2×#117—611no—
263C2×#117—611no—
264#433—1228no—
265#423—614no—
266C2×#101—614no—
267C2×#101—614no—
268#407—614no—
269C4×M16—614no—
270#343—614no—
271#343—614no—
272C61#2073011yescharacteristic, complemented, Sylow
273C22×Q8—611no—
274C22×Q8—611no—
275C22×Q8—611no—
276C22×Q8—1224no—
277C22×Q8—1224no—
278C22×Q8—1224no—
279C22×Q8C2×#692311yescharacteristic
280C23×C4—611no—
281C23×C4—611no—
282C23×C4—611no—
283C2×M16—618no—
284C4×Q8—24no—
285C4×Q8—1224no—
286C4×Q8—1224no—
287C4×Q8—1224no—
288C4×Q8—1224no—
289C4×Q8—1224no—
290C4×Q8—1224no—
291C4×Q8—1224no—
292#117—618no—
293#117—1224no—
294#117—1224no—
295#117—1224no—
296#117—1224no—
297#117—1224no—
298C2×C4⋊C4—611no—
299C2×C4⋊C4—611no—
300C2×C4⋊C4—611no—
301C2×C4⋊C4—611no—
302C2×C4⋊C4—611no—
303C2×C4⋊C4—611no—
304C2×C4⋊C4—611no—
305C2×C4⋊C4—611no—
306C2×C4⋊C4—611no—
307C2×C4⋊C4C2×#692311yescharacteristic
308C2×C4⋊C4C2×#692311yescharacteristic
309C2×C4⋊C4C2×#692311yescharacteristic
310C2×C22⋊C4—611no—
311C2×C22⋊C4—611no—
312C2×C22⋊C4—611no—
313C2×C22⋊C4—611no—
314C2×C42—611no—
315C2×C42—611no—
316C2×C42—611no—
317C2×C42—611no—
318C2×C42—611no—
319C2×C42—611no—
320C2×C42—611no—
321C2×C42—611no—
322C2×C42—611no—
323C2×C42C2×#692311yescharacteristic
324C2×C42C2×#692311yescharacteristic
325C2×C42C2×#692311yescharacteristic
326C4⋊C8—1224no—
327C4⋊C8—1224no—
328#101—1228no—
329#101—1228no—
330C22⋊C8—1228no—
331#97—1224no—
332C4×C8—1224no—
333C24—611no—
334C2×Q8—22no—
335C2×Q8—22no—
336C2×Q8—22no—
337C2×Q8—614no—
338C2×Q8—614no—
339C2×Q8—1222no—
340C2×Q8—1222no—
341C2×Q8—1222no—
342C2×Q8—1222no—
343C2×Q8—1222no—
344C2×Q8—1222no—
345C2×Q8—12232no—
346C2×Q8—1222no—
347C22×C4—611no—
348C22×C4—611no—
349C22×C4—611no—
350C22×C4—611no—
351C22×C4—611no—
352C22×C4—614no—
353C22×C4—611no—
354C22×C4—611no—
355C22×C4—1222no—
356C22×C4—1222no—
357C22×C4—1222no—
358C22×C4—1222no—
359C22×C4—1222no—
360C22×C4—1222no—
361C22×C4—1222no—
362C22×C4—1222no—
363C22×C4C22×#692311yescharacteristic
364C22×C4C22×#692311yescharacteristic
365C22×C4C22×#692311yescharacteristic
366C22×C4C22×#692311yescharacteristic
367C22×C4C22×#692311yescharacteristic
368C22×C4C22×#692311yescharacteristic
369C22×C4C22×#692311yescharacteristic
370M16—1228no—
371M16—1228no—
372C2×C8—1228no—
373C4⋊C4—22no—
374C4⋊C4—22no—
375C4⋊C4—614no—
376C4⋊C4—1222no—
377C4⋊C4—1222no—
378C4⋊C4—1222no—
379C4⋊C4—1222no—
380C4⋊C4—1222no—
381C4⋊C4—1222no—
382C4⋊C4—1222no—
383C4⋊C4—1222no—
384C4⋊C4C22⋊#692314yes—
385C22⋊C4—614no—
386C22⋊C4—614no—
387C22⋊C4—1222no—
388C22⋊C4—1222no—
389C42—22no—
390C42—22no—
391C42—22no—
392C42—614no—
393C42—614no—
394C42—1222no—
395C42—1222no—
396C42—1222no—
397C42—1222no—
398C42—1222no—
399C42—1222no—
400C42—1222no—
401C23—612no—
402C23—1221no—
403C23—1221no—
404C23—2441no—
405C23—2441no—
406C23C23×#692311yescharacteristic
407Q8—28no—
408Q8—1228no—
409Q8—1228no—
410Q8—1228no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—612no—
424C2×C4—612no—
425C2×C4—612no—
426C2×C4—612no—
427C2×C4—612no—
428C2×C4—612no—
429C2×C4—612no—
430C2×C4—1228no—
431C2×C4—1228no—
432C2×C4—1228no—
433C2×C4—1221no—
434C2×C4—1221no—
435C2×C4—1221no—
436C2×C4—1221no—
437C2×C4—1221no—
438C2×C4—1221no—
439C2×C4—2441no—
440C2×C4—2441no—
441C2×C4—2441no—
442C2×C4—2441no—
443C2×C4C2×C22⋊#692312yes—
444C2×C4C2×C22⋊#692312yes—
445C2×C4C2×C22⋊#692312yes—
446C2×C4#1451985612yes—
447C2×C4#1451985612yes—
448C8—2448no—
449C22—21no—
450C22—21no—
451C22—1222no—
452C22—1222no—
453C22—1222no—
454C22—2442no—
455C22—2442no—
456C22C22×C22⋊#692311yescharacteristic
457C22C2×#1451985611yescharacteristic
458C22C2×#1451985611yescharacteristic
459C4—22no—
460C4—22no—
461C4—22no—
462C4—22no—
463C4—22no—
464C4—41no—
465C4—41no—
466C4—614no—
467C4—1222no—
468C4—1222no—
469C4—1222no—
470C4—1222no—
471C4—2441no—
472C4—2441no—
473C2—21no—
474C2—21no—
475C2—2442no—
476C2#2146226311yescharacteristic
477C2#2146243111yescharacteristic
478C2#2146243211yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×C4×Q8×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC23×D61C22×C4
cosocleC22×Dic61C24
hypercenterC2×C4×Q8#6923
hypocenterC61#20730
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C4⋊C4 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
3. #21461686C2semidirect
4. #21461685C2semidirect
6. #21461572C2semidirect
7. C4×#14519838C2semidirect
272. C61#20730semidirect

Maximal subgroups

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

subgroupindex
#214625012
#214617202
#214616862
#214616852
#214616542
#214615722
C4×#145198382
C2×#168402382
#2073061