Finite Group Databasebeta

← #30615194

Subgroups — #30615194

Order 15616.

1262 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462495C212yesmaximal
2#21461718C212yesmaximal
3#21461686C214yesmaximal, complemented
4#21461653C212yesmaximal
5#21461572C214yesmaximal, complemented
6C22×#14519742C211yesmaximal, characteristic
7#16840783—22no—
8#16840782—22no—
9#16840779—22no—
10#16840778—22no—
11#16840765C2214yes—
12C2×#14519838C2218yes—
13#16840732C2214yes—
14C4×#11758217C2214yes—
15#16840642C2218yes—
16C23×Dic122C2211yescharacteristic
17C2×#14519742—22no—
18C2×#14519742—22no—
19C2×#14519742—22no—
20C2×#14519742—22no—
21C2×#14519742C412yes—
22C2×#14519742C412yes—
23C2×#14519742C2212yes—
24C2×#14519742C2212yes—
25C22×#11758196C411yescharacteristic
26C22×#11758196C2211yescharacteristic
27C22×C4×Dic61C411yescharacteristic
28C22×C4×Dic61C411yescharacteristic
29C22×C4×Dic61C2211yescharacteristic
30C22×C4⋊C4×C61C411yescharacteristic
31C2×#11758217C2318yes—
32#14519844—24no—
33C4⋊#92420—24no—
34#14519838—216no—
35C22⋊#92420—24no—
36C22⋊#92420—24no—
37#14519832—24no—
38C4×#92420—24no—
39C22×Dic122—22no—
40C22×Dic122—22no—
41C22×Dic122—28no—
42C22×Dic122C2×C412yes—
43C22×Dic122C2312yes—
44C23×Dic61C2×C411yescharacteristic
45C23×Dic61C2×C411yescharacteristic
46C23×Dic61C2×C411yescharacteristic
47C23×Dic61C2311yescharacteristic
48#14519742—24no—
49#14519742—24no—
50#14519742—24no—
51#14519742—24no—
52#14519742—24no—
53#14519742—24no—
54#14519742—24no—
55#14519742—24no—
56C2×#11758196—22no—
57C2×#11758196—22no—
58C2×#11758196—22no—
59C2×#11758196—22no—
60C2×#11758196C2×C412yes—
61C2×#11758196C2×C412yes—
62C2×#11758196C2×C412yes—
63C2×#11758196C2312yes—
64C2×C4×Dic61—21no—
65C2×C4×Dic61—21no—
66C2×C4×Dic61—21no—
67C2×C4×Dic61—21no—
68C2×C4×Dic61—21no—
69C2×C4×Dic61—21no—
70C2×C4×Dic61—21no—
71C2×C4×Dic61—21no—
72C2×C4×Dic61C2×C412yes—
73C2×C4×Dic61C2×C412yes—
74C2×C4×Dic61C2×C412yes—
75C2×C4×Dic61C2×C412yes—
76C2×C4×Dic61C2×C411yescharacteristic
77C2×C4×Dic61C2×C411yescharacteristic
78C2×C4×Dic61D412yes—
79C2×C4×Dic61D412yes—
80C2×C4×Dic61D412yes—
81C2×C4×Dic61D412yes—
82C2×C4×Dic61C2311yescharacteristic
83C2×C4×Dic61C2311yescharacteristic
84C23×C4×C61C2×C411yescharacteristic
85C23×C4×C61C2×C411yescharacteristic
86C23×C4×C61C2×C411yescharacteristic
87C2×C4⋊C4×C61—22no—
88C2×C4⋊C4×C61—22no—
89C2×C4⋊C4×C61C2×C412yes—
90C2×C4⋊C4×C61C2×C412yes—
91C24×C61C22×C411yescharacteristic
92C22×C4×C61—21no—
93C22×C4×C61—21no—
94C22×C4×C61—24no—
95C22×C4×C61—21no—
96C22×C4×C61—21no—
97C22×C4×C61—42no—
98C22×C4×C61—42no—
99C22×C4×C61C22⋊C412yes—
100C22×C4×C61C22⋊C412yes—
101C22×C4×C61C22×C412yes—
102C22×C4×C61C22×C412yes—
103C22×C4×C61C22×C411yescharacteristic
104C22×C4×C61C22×C411yescharacteristic
105C22×Dic61—21no—
106C22×Dic61—21no—
107C22×Dic61—24no—
108C22×Dic61—24no—
109C22×Dic61—24no—
110C22×Dic61—21no—
111C22×Dic61—21no—
112C22×Dic61—42no—
113C22×Dic61C22⋊C411yescharacteristic
114C22×Dic61C22⋊C411yescharacteristic
115C22×Dic61C22⋊C411yescharacteristic
116C22×Dic61C22⋊C411yescharacteristic
117C22×Dic61C22×C411yescharacteristic
118C22×Dic61C22×C411yescharacteristic
119C22×Dic61C22×C411yescharacteristic
120C22×Dic61C22×C412yes—
121C22×Dic61C22×C412yes—
122C22×Dic61C2×D412yes—
123C22×Dic61C2×D412yes—
124C22×Dic61C2411yescharacteristic
125C2×Dic122—216no—
126C2×Dic122—216no—
127C2×Dic122—24no—
128C2×Dic122—24no—
129C2×Dic122—24no—
130C2×Dic122—24no—
131C2×Dic122—24no—
132C2×Dic122#4118yes—
133#11758217—216no—
134C2×#92420—28no—
135C4⋊C4×C61—24no—
136C4⋊C4×C61—24no—
137#11758196—24no—
138#11758196—24no—
139#11758196—24no—
140#11758196—24no—
141C4×Dic61—22no—
142C4×Dic61—22no—
143C4×Dic61—22no—
144C4×Dic61—22no—
145C4×Dic61—22no—
146C4×Dic61—22no—
147C4×Dic61—22no—
148C4×Dic61—22no—
149C4×Dic61C22⋊C412yes—
150C4×Dic61C22⋊C412yes—
151C4×Dic61C22⋊C412yes—
152C4×Dic61C22⋊C412yes—
153C4×Dic61C2×D412yes—
154C4×Dic61C2×D412yes—
155C4×Dic61C2×D412yes—
156C4×Dic61C2×D412yes—
157C23×C61—22no—
158C23×C61—22no—
159C23×C61—22no—
160C23×C61C2×C22⋊C411yescharacteristic
161C23×C61C2×C22⋊C411yescharacteristic
162C23×C61C23×C411yescharacteristic
163C2×C4×C61—24no—
164C2×C4×C61—24no—
165C2×C4×C61—22no—
166C2×C4×C61—22no—
167C2×C4×C61—24no—
168C2×C4×C61—22no—
169C2×C4×C61—42no—
170C2×C4×C61—41no—
171C2×C4×C61—41no—
172C2×C4×C61—42no—
173C2×C4×C61—42no—
174C2×C4×C61—42no—
175C2×C4×C61C2×C22⋊C412yes—
176C2×C4×C61C2×C22⋊C412yes—
177C2×C4×C61#11714yes—
178C2×Dic61—24no—
179C2×Dic61—24no—
180C2×Dic61—22no—
181C2×Dic61—22no—
182C2×Dic61—22no—
183C2×Dic61—22no—
184C2×Dic61—24no—
185C2×Dic61—24no—
186C2×Dic61—22no—
187C2×Dic61—22no—
188C2×Dic61—22no—
189C2×Dic61—22no—
190C2×Dic61—22no—
191C2×Dic61—42no—
192C2×Dic61—42no—
193C2×Dic61—42no—
194C2×Dic61#10114yescomplemented
195C2×Dic61C2×C22⋊C411yescharacteristic
196C2×Dic61C2×C22⋊C411yescharacteristic
197C2×Dic61C2×C22⋊C412yes—
198C2×Dic61C2×C22⋊C411yescharacteristic
199C2×Dic61C2×C22⋊C411yescharacteristic
200C2×Dic61#11714yes—
201C2×Dic61C22×D412yes—
202C2×Dic61C2×#4114yes—
203Dic122—216no—
204Dic122—216no—
205#92420—48no—
206#20727—611nomaximal, Sylow
207C22×C61—28no—
208C22×C61—21no—
209C22×C61—21no—
210C22×C61—21no—
211C22×C61—21no—
212C22×C61—21no—
213C22×C61—21no—
214C22×C61C2×#10112yes—
215C22×C61#41312yes—
216C22×C61C22×C22⋊C411yescharacteristic
217C22×C61C2×#11712yes—
218C4×C61—22no—
219C4×C61—22no—
220C4×C61—24no—
221C4×C61—42no—
222Dic61—21no—
223Dic61—21no—
224Dic61—22no—
225Dic61—24no—
226Dic61—42no—
227Dic61C2×#10112yes—
228Dic61C2×#10112yes—
229Dic61#52514yes—
230C22×C4×Q8—611no—
231#2920—612no—
232#1821—612no—
233#1801—614no—
234#1784—612no—
235C4×#101—614no—
236C2×C61—22no—
237C2×C61—22no—
238C2×C61—22no—
239C2×C61#228011yescharacteristic
240C2×C61C22×#10111yescharacteristic
241C2×C61C2×#41311yescharacteristic
242C23×Q8—611no—
243C2×C4×Q8—612no—
244C2×C4×Q8—612no—
245C2×C4×Q8—612no—
246C2×C4×Q8—612no—
247C2×C4×Q8—1222no—
248C2×C4×Q8—1222no—
249C2×C4×Q8—1222no—
250C2×C4×Q8—1222no—
251C22×C4⋊C4—611no—
252C22×C4⋊C4—611no—
253C22×C4⋊C4#692311yescharacteristic
254C22×C42—611no—
255C22×C42—611no—
256C22×C42—611no—
257#432—1222no—
258#432—1222no—
259#431—1222no—
260#431—1222no—
261#423—614no—
262C2×#101—618no—
263#407—614no—
264C4×M16—614no—
265#343—618no—
266C61#2072711yescharacteristic, complemented, Sylow
267C22×Q8—612no—
268C22×Q8—612no—
269C22×Q8—1222no—
270C22×Q8—1222no—
271C22×Q8—1228no—
272C23×C4—611no—
273C23×C4—611no—
274C23×C4—611no—
275C23×C4—611no—
276C23×C4C2×#692311yescharacteristic
277C23×C4C2×#692311yescharacteristic
278C23×C4C2×#692311yescharacteristic
279C2×M16—618no—
280C4×Q8—1224no—
281C4×Q8—1224no—
282C4×Q8—1224no—
283C4×Q8—1224no—
284C4×Q8—1224no—
285C4×Q8—1224no—
286C4×Q8—1224no—
287C4×Q8—1224no—
288C2×C4⋊C4—22no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—612no—
291C2×C4⋊C4—612no—
292C2×C4⋊C4—612no—
293C2×C4⋊C4—612no—
294C2×C4⋊C4—1222no—
295C2×C4⋊C4—1222no—
296C2×C4⋊C4—1222no—
297C2×C4⋊C4—1222no—
298C2×C4⋊C4C2×#692312yes—
299C2×C4⋊C4C2×#692312yes—
300C2×C42—612no—
301C2×C42—612no—
302C2×C42—612no—
303C2×C42—612no—
304C2×C42—611no—
305C2×C42—611no—
306C2×C42—611no—
307C2×C42—611no—
308C2×C42—612no—
309C2×C42—612no—
310C2×C42—612no—
311C2×C42—612no—
312C2×C42—1221no—
313C2×C42—1221no—
314C2×C42—1221no—
315C2×C42—1221no—
316C2×C42—1221no—
317C2×C42—1221no—
318C2×C42—1221no—
319C2×C42—1221no—
320C4⋊C8—1224no—
321C4⋊C8—1224no—
322#101—12216no—
323C22⋊C8—1224no—
324C22⋊C8—1224no—
325#97—1224no—
326C4×C8—1224no—
327C24C22×#692311yescharacteristic
328C2×Q8—618no—
329C2×Q8—1224no—
330C2×Q8—1224no—
331C2×Q8—1224no—
332C2×Q8—1224no—
333C2×Q8—12216no—
334C2×Q8—12216no—
335C2×Q8—1224no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—24no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—42no—
342C22×C4—42no—
343C22×C4—611no—
344C22×C4—611no—
345C22×C4—612no—
346C22×C4—612no—
347C22×C4—611no—
348C22×C4—611no—
349C22×C4—611no—
350C22×C4—611no—
351C22×C4—611no—
352C22×C4—611no—
353C22×C4—612no—
354C22×C4—612no—
355C22×C4—1224no—
356C22×C4—1224no—
357C22×C4—1224no—
358C22×C4—1221no—
359C22×C4—1221no—
360C22×C4—1221no—
361C22×C4—1221no—
362C22×C4—2442no—
363C22×C4C22⋊#692312yes—
364C22×C4C22⋊#692312yes—
365C22×C4C22×#692312yes—
366C22×C4C22×#692312yes—
367C22×C4C22×#692311yescharacteristic
368C22×C4C22×#692311yescharacteristic
369M16—12216no—
370C2×C8—1228no—
371C4⋊C4—24no—
372C4⋊C4—24no—
373C4⋊C4—1224no—
374C4⋊C4—1224no—
375C4⋊C4—1224no—
376C4⋊C4—1224no—
377C42—612no—
378C42—612no—
379C42—612no—
380C42—612no—
381C42—612no—
382C42—612no—
383C42—612no—
384C42—612no—
385C42—1222no—
386C42—1222no—
387C42—1222no—
388C42—1222no—
389C42—1222no—
390C42—1222no—
391C42—1222no—
392C42—1222no—
393C23—22no—
394C23—22no—
395C23—22no—
396C23C2×C22⋊#692311yescharacteristic
397C23C2×C22⋊#692311yescharacteristic
398C23C23×#692311yescharacteristic
399Q8—12216no—
400Q8—12216no—
401C2×C4—24no—
402C2×C4—24no—
403C2×C4—24no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—42no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—614no—
414C2×C4—611no—
415C2×C4—611no—
416C2×C4—612no—
417C2×C4—614no—
418C2×C4—611no—
419C2×C4—611no—
420C2×C4—612no—
421C2×C4—614no—
422C2×C4—1222no—
423C2×C4—1222no—
424C2×C4—1222no—
425C2×C4—1222no—
426C2×C4—1224no—
427C2×C4—1224no—
428C2×C4—1224no—
429C2×C4—1224no—
430C2×C4—1222no—
431C2×C4—1222no—
432C2×C4—1222no—
433C2×C4—1222no—
434C2×C4—1222no—
435C2×C4—2442no—
436C2×C4—2442no—
437C2×C4—2442no—
438C2×C4C2×C22⋊#692312yes—
439C2×C4C2×C22⋊#692312yes—
440C2×C4#1451985614yes—
441C8—2448no—
442C22—28no—
443C22—21no—
444C22—21no—
445C22—21no—
446C22—21no—
447C22—21no—
448C22—21no—
449C22D61⋊#10112yes—
450C22#1684074912yes—
451C22C22×C22⋊#692311yescharacteristic
452C22C2×#1451985612yes—
453C4—22no—
454C4—22no—
455C4—24no—
456C4—42no—
457C4—612no—
458C4—612no—
459C4—614no—
460C4—1221no—
461C4—1221no—
462C4—1222no—
463C4—1224no—
464C4—2442no—
465C2—22no—
466C2—22no—
467C2—22no—
468C2#2146226311yescharacteristic
469C2C2×D61⋊#10111yescharacteristic
470C2C2×#1684074911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC22×C4⋊C4×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC24×C61C22×C4
cosocleC22×Dic61C24
hypercenterC22×C4⋊C4#6923
hypocenterC61#20727
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #21461686C2semidirect
5. #21461572C2semidirect
194. C2×Dic61#101semidirect
266. C61#20727semidirect

Maximal subgroups

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

subgroupindex
#214624952
#214617182
#214616862
#214616532
#214615722
C22×#145197422
#2072761