Finite Group Databasebeta

← #30596804

Subgroups — #30596804

Order 15616.

1122 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D61⋊(C22⋊C8)C211yesmaximal, characteristic
2#21462263C211yesmaximal, characteristic
3#21460693C214yesmaximal, complemented
4C4×C22⋊C4×D61C211yesmaximal, characteristic
5C22×D61⋊C8—21no—
6C2×#14519856C412yescomplemented
7C2×#14519834C412yescomplemented
8D61⋊(C22⋊C8)—21no—
9D61⋊(C22⋊C8)—21no—
10D61⋊(C22⋊C8)C412yescomplemented
11D61⋊(C22⋊C8)C2212yes—
12C2×C22⋊#92420—21no—
13#16840705—21no—
14#16840704C412yescomplemented
15#16840704C2212yes—
16#16840703—21no—
17C4×C22⋊#6923—21no—
18C4×C22⋊#6923—21no—
19C23×C4×D61C2211yescharacteristic
20C2×C22⋊C4×D61—21no—
21C2×C42×D61—21no—
22C22⋊C4×Dic61—21no—
23C4×#11758198—21no—
24C4×C22⋊Dic61C411yescharacteristic, complemented
25#16839609C412yescomplemented
26#95×D61C2212yes—
27C4×C22⋊C4×C61C411yescharacteristic, complemented
28C2×D61⋊C8—22no—
29C2×D61⋊C8—22no—
30C2×D61⋊C8—44no—
31C22×#92420—22no—
32#14519856—44no—
33C2×C4⋊#6923C2×C414yes—
34C2×C22⋊#6923—22no—
35C2×C22⋊#6923—22no—
36C2×C22⋊#6923—22no—
37C2×C4×#6923—22no—
38#14519834—22no—
39#14519834C2×C414yes—
40C22⋊#92420—22no—
41C22⋊#92420—22no—
42(C2×#6923)⋊C4—22no—
43(C2×#6923)⋊C4—22no—
44C24×D61D411yescharacteristic
45C23×Dic61D411yescharacteristic
46C22×C4×D61—22no—
47C22×C4×D61—44no—
48C22×C4×D61C2×C411yescharacteristic
49C22×C4×D61C2×C411yescharacteristic
50C22×C4×D61C2×C411yescharacteristic
51C22×C4×D61C2×C411yescharacteristic
52C22×C4×D61C2×C411yescharacteristic
53C22×C4×D61D411yescharacteristic
54C22×C4×D61D411yescharacteristic
55C22×C4×D61D411yescharacteristic
56C22×C4×D61D411yescharacteristic
57C22×C4×D61Q811yescharacteristic
58C22×C4×D61Q811yescharacteristic
59C22×C4×D61C2311yescharacteristic
60C2×C22⋊Dic61—21no—
61C2×#11758198—22no—
62C22⋊C4×D61—28no—
63C2×C4×Dic61—21no—
64C2×C4×Dic61—22no—
65C42×D61—44no—
66#14519684—22no—
67#14519684C2×C412yes—
68C23×C4×C61C2×C411yescharacteristic
69C2×C22⋊C4×C61—21no—
70C2×C42×C61—21no—
71#95×C61C2×C412yes—
72C24×C61C22⋊C411yescharacteristic
73C23×D61—24no—
74C23×D61—24no—
75C23×D61—42no—
76C23×D61C22⋊C411yescharacteristic
77C23×D61C22⋊C411yescharacteristic
78C23×D61C22⋊C411yescharacteristic
79C23×D61C4⋊C411yescharacteristic
80C23×D61C4⋊C411yescharacteristic
81C23×D61C2×D411yescharacteristic
82C22×#6923—24no—
83C22×C4×C61—22no—
84C22×C4×C61—42no—
85C22×C4×C61C4211yescharacteristic
86C22×C4×C61C4211yescharacteristic
87C22×C4×C61C22⋊C411yescharacteristic
88C22×C4×C61C4⋊C411yescharacteristic
89C22×C4×C61C4⋊C411yescharacteristic
90C22×C4×C61C22×C411yescharacteristic
91C22×Dic61—22no—
92C22×Dic61—42no—
93C22×Dic61C22⋊C411yescharacteristic
94C22×Dic61C22⋊C411yescharacteristic
95C22×Dic61C22⋊C411yescharacteristic
96C22×Dic61C4⋊C411yescharacteristic
97C22×Dic61C4⋊C411yescharacteristic
98C22×Dic61C2×D411yescharacteristic
99C2×C4×D61—24no—
100C2×C4×D61—24no—
101C2×C4×D61—24no—
102C2×C4×D61—28no—
103C2×C4×D61—42no—
104C2×C4×D61—42no—
105C2×C4×D61—42no—
106C2×C4×D61—42no—
107C2×C4×D61—42no—
108C2×C4×D61—42no—
109C2×C4×D61—42no—
110C2×C4×D61—42no—
111C2×C4×D61—42no—
112C2×C4×D61—44no—
113C2×C4×D61—44no—
114C2×C4×D61C4211yescharacteristic
115C2×C4×D61C4211yescharacteristic
116C2×C4×D61C22⋊C411yescharacteristic
117C2×C4×D61C22⋊C411yescharacteristic
118C2×C4×D61C22⋊C411yescharacteristic
119C2×C4×D61C22⋊C411yescharacteristic
120C2×C4×D61C4⋊C411yescharacteristic
121C2×C4×D61C4⋊C411yescharacteristic
122C2×C4×D61C4⋊C411yescharacteristic
123C2×C4×D61C4⋊C411yescharacteristic
124C2×C4×D61C4⋊C411yescharacteristic
125C2×C4×D61C4⋊C411yescharacteristic
126C2×C4×D61C22×C411yescharacteristic
127C2×C4×D61C22×C411yescharacteristic
128C2×C4×D61C2×D411yescharacteristic
129C2×C4×D61C2×Q811yescharacteristic
130C22⋊#6923—44no—
131C22⋊#6923—44no—
132C22⋊#6923—44no—
133C2×#92420—24no—
134C2×#92420—44no—
135C4⋊#6923—44no—
136C4×#6923—44no—
137D61⋊C8—44no—
138D61⋊C8—44no—
139C22⋊C4×C61—24no—
140C42×C61—42no—
141C22⋊Dic61—24no—
142#11758198—28no—
143C4×Dic61—44no—
144C4×Dic61—42no—
145C23×C61—22no—
146C23×C61—22no—
147C23×C61—41no—
148C23×C61#9511yescharacteristic
149C23×C61#9511yescharacteristic
150C23×C61C2×C22⋊C411yescharacteristic
151C22×D61—22no—
152C22×D61—22no—
153C22×D61—22no—
154C22×D61—22no—
155C22×D61—22no—
156C22×D61—22no—
157C22×D61—22no—
158C22×D61—22no—
159C22×D61—22no—
160C22×D61—22no—
161C22×D61—22no—
162C22×D61—22no—
163C22×D61—22no—
164C22×D61—41no—
165C22×D61—41no—
166C22×D61—41no—
167C22×D61—416no—
168C22×D61#9511yescharacteristic
169C22×D61#9511yescharacteristic
170C22×D61#10414yes—
171C22×D61C2×C22⋊C411yescharacteristic
172C22×D61C2×C4⋊C411yescharacteristic
173C22×D61#13514yes—
174C2×#6923—44no—
175C2×#6923—44no—
176C2×#6923—44no—
177C2×C4×C61—22no—
178C2×C4×C61—22no—
179C2×C4×C61—22no—
180C2×C4×C61—24no—
181C2×C4×C61—41no—
182C2×C4×C61—41no—
183C2×C4×C61—41no—
184C2×C4×C61—42no—
185C2×C4×C61—42no—
186C2×C4×C61#9511yescharacteristic
187C2×C4×C61#9511yescharacteristic
188C2×C4×C61C2×C4211yescharacteristic
189C2×C4×C61C2×C4⋊C411yescharacteristic
190C2×Dic61—22no—
191C2×Dic61—22no—
192C2×Dic61—22no—
193C2×Dic61—24no—
194C2×Dic61—41no—
195C2×Dic61—41no—
196C2×Dic61—41no—
197C2×Dic61—42no—
198C2×Dic61—42no—
199C2×Dic61#9511yescharacteristic
200C2×Dic61#9511yescharacteristic
201C2×Dic61C2×C22⋊C411yescharacteristic
202C2×Dic61C2×C4⋊C411yescharacteristic
203C4×D61—22no—
204C4×D61—22no—
205C4×D61—22no—
206C4×D61—22no—
207C4×D61—22no—
208C4×D61—22no—
209C4×D61—22no—
210C4×D61—22no—
211C4×D61—22no—
212C4×D61—41no—
213C4×D61—41no—
214C4×D61—41no—
215C4×D61—41no—
216C4×D61—41no—
217C4×D61—41no—
218C4×D61—416no—
219C4×D61#9914yes—
220#92420—44no—
221#8012—611nomaximal, Sylow
222C22×C61—21no—
223C22×C61—21no—
224C22×C61—21no—
225C22×C61—21no—
226C22×C61—21no—
227C22×C61—21no—
228C22×C61—21no—
229C22×C61—44no—
230C22×C61#33912yes—
231C22×C61C2×#9511yescharacteristic
232C22×C61#41612yes—
233C2×D61—21no—
234C2×D61—21no—
235C2×D61—21no—
236C2×D61—21no—
237C2×D61—28no—
238C2×D61—28no—
239C2×D61—21no—
240C2×D61—21no—
241C2×D61—21no—
242C2×D61—44no—
243C2×D61—44no—
244C2×D61—44no—
245C2×D61—44no—
246C2×D61#33912yes—
247C2×D61C2×#9912yes—
248C2×D61#41612yes—
249C2×D61C2×#10412yes—
250C2×D61#42712yes—
251#6923—84no—
252C4×C61—21no—
253C4×C61—21no—
254C4×C61—21no—
255C4×C61—44no—
256C4×C61#34212yes—
257Dic61—21no—
258Dic61—21no—
259Dic61—21no—
260Dic61—44no—
261Dic61#34212yes—
262C22×C22⋊C8—611no—
263#2280—611no—
264C2×C4×C22⋊C4—611no—
265#1294—614no—
266C2×C61—22no—
267C2×C61—22no—
268C2×C61—41no—
269C2×C61C2×#33911yescharacteristic
270C2×C61#173511yescharacteristic
271C2×C61C2×#34211yescharacteristic
272D61—22no—
273D61—22no—
274D61—41no—
275D61#150114yes—
276C24×C4—611no—
277C23×C8—1221no—
278C2×#117—612no—
279C22×C22⋊C4—1221no—
280C22×C42—1221no—
281C2×C22⋊C8—612no—
282C2×C22⋊C8—612no—
283C2×C22⋊C8—612no—
284C2×C22⋊C8—1221no—
285C2×C22⋊C8—1221no—
286C2×C22⋊C8—1221no—
287#381—1221no—
288#380—612no—
289#380—612no—
290#379—1221no—
291C4×C22⋊C4—611no—
292C4×C22⋊C4—612no—
293C4×C22⋊C4—1221no—
294C4×C22⋊C4—1221no—
295C4×C22⋊C4—1221no—
296C4×C22⋊C4—1221no—
297C4×C22⋊C4#692311yescharacteristic, complemented
298C2×#95—612no—
299C61#801211yescharacteristic, complemented, Sylow
300C25—611no—
301C23×C4—611no—
302C23×C4—611no—
303C23×C4—611no—
304C23×C4—611no—
305C23×C4—611no—
306C23×C4—611no—
307C23×C4—611no—
308C23×C4—611no—
309C23×C4—611no—
310C23×C4—611no—
311C23×C4—611no—
312C23×C4—611no—
313C23×C4—611no—
314C23×C4—1222no—
315C23×C4—2444no—
316C23×C4C2×#692311yescharacteristic
317C22×C8—1222no—
318C22×C8—1222no—
319C22×C8—1222no—
320C22×C8—2444no—
321#117—2444no—
322C2×C4⋊C4—614no—
323C2×C22⋊C4—21no—
324C2×C22⋊C4—1228no—
325C2×C22⋊C4—1222no—
326C2×C22⋊C4—1221no—
327C2×C22⋊C4—1222no—
328C2×C22⋊C4—1222no—
329C2×C22⋊C4—1222no—
330C2×C42—21no—
331C2×C42—1222no—
332C2×C42—1222no—
333C2×C42—1221no—
334C2×C42—2444no—
335C22⋊C8—614no—
336C22⋊C8—1222no—
337C22⋊C8—1222no—
338C22⋊C8—1222no—
339#95—612no—
340#95—1222no—
341#95—1222no—
342#95—1222no—
343#95C2×#692312yes—
344C24—611no—
345C24—611no—
346C24—611no—
347C24—611no—
348C24—611no—
349C24—611no—
350C24—1224no—
351C24—1224no—
352C24—2442no—
353C24C22⋊#692311yescharacteristic
354C22×C4—22no—
355C22×C4—42no—
356C22×C4—611no—
357C22×C4—611no—
358C22×C4—611no—
359C22×C4—611no—
360C22×C4—611no—
361C22×C4—611no—
362C22×C4—611no—
363C22×C4—611no—
364C22×C4—611no—
365C22×C4—611no—
366C22×C4—611no—
367C22×C4—611no—
368C22×C4—611no—
369C22×C4—611no—
370C22×C4—611no—
371C22×C4—611no—
372C22×C4—611no—
373C22×C4—611no—
374C22×C4—611no—
375C22×C4—611no—
376C22×C4—611no—
377C22×C4—611no—
378C22×C4—1224no—
379C22×C4—1224no—
380C22×C4—1224no—
381C22×C4—1228no—
382C22×C4—1222no—
383C22×C4—1224no—
384C22×C4—2442no—
385C22×C4—2442no—
386C22×C4—2442no—
387C22×C4—2442no—
388C22×C4—2442no—
389C22×C4—2442no—
390C22×C4—2442no—
391C22×C4—2442no—
392C22×C4—2442no—
393C22×C4—2444no—
394C22×C4—2444no—
395C22×C4—2442no—
396C22×C4C4×#692311yescharacteristic
397C22×C4C4×#692311yescharacteristic
398C22×C4C4⋊#692311yescharacteristic
399C22×C4C4⋊#692311yescharacteristic
400C22×C4C22⋊#692311yescharacteristic
401C22×C4C22×#692311yescharacteristic
402C2×C8—1224no—
403C2×C8—2444no—
404C2×C8—2444no—
405C2×C8—2444no—
406C4⋊C4—2444no—
407C22⋊C4—24no—
408C22⋊C4—1228no—
409C22⋊C4—1224no—
410C22⋊C4—2444no—
411C22⋊C4—2444no—
412C22⋊C4—2444no—
413C42—42no—
414C42—2442no—
415C42—2444no—
416C42—2444no—
417C23—22no—
418C23—22no—
419C23—41no—
420C23—611no—
421C23—614no—
422C23—614no—
423C23—611no—
424C23—611no—
425C23—611no—
426C23—1222no—
427C23—1222no—
428C23—1222no—
429C23—1222no—
430C23—1222no—
431C23—1222no—
432C23—1222no—
433C23—1222no—
434C23—1222no—
435C23—1222no—
436C23—1222no—
437C23—1222no—
438C23—1222no—
439C23—2441no—
440C23—2441no—
441C23—2441no—
442C23—24416no—
443C23(C2×#6923)⋊C411yescharacteristic
444C23(C2×#6923)⋊C411yescharacteristic
445C23C2×C22⋊#692311yescharacteristic
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—24no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—611no—
456C2×C4—614no—
457C2×C4—611no—
458C2×C4—611no—
459C2×C4—611no—
460C2×C4—1222no—
461C2×C4—1222no—
462C2×C4—1222no—
463C2×C4—1222no—
464C2×C4—1222no—
465C2×C4—1222no—
466C2×C4—1222no—
467C2×C4—1222no—
468C2×C4—1222no—
469C2×C4—1222no—
470C2×C4—1222no—
471C2×C4—1222no—
472C2×C4—1224no—
473C2×C4—2441no—
474C2×C4—2441no—
475C2×C4—2441no—
476C2×C4—2441no—
477C2×C4—2441no—
478C2×C4—2441no—
479C2×C4—24416no—
480C2×C4—2441no—
481C2×C4—2441no—
482C2×C4—2441no—
483C2×C4—2444no—
484C2×C4—2444no—
485C2×C4—2444no—
486C2×C4—2442no—
487C2×C4—2442no—
488C2×C4(C2×#6923)⋊C411yescharacteristic
489C2×C4(C2×#6923)⋊C411yescharacteristic
490C2×C4C2×C4×#692311yescharacteristic
491C2×C4C2×C4⋊#692311yescharacteristic
492C8—2444no—
493C22—21no—
494C22—21no—
495C22—21no—
496C22—21no—
497C22—21no—
498C22—21no—
499C22—21no—
500C22—44no—
501C22—612no—
502C22—612no—
503C22—612no—
504C22—612no—
505C22—612no—
506C22—1228no—
507C22—1228no—
508C22—1221no—
509C22—1221no—
510C22—1221no—
511C22—1221no—
512C22—1221no—
513C22—1221no—
514C22—1221no—
515C22—2444no—
516C22—2444no—
517C22—2444no—
518C22—2444no—
519C22#1684063312yes—
520C22C2×(C2×#6923)⋊C411yescharacteristic
521C22#1684075212yes—
522C4—21no—
523C4—21no—
524C4—21no—
525C4—44no—
526C4—612no—
527C4—1221no—
528C4—1221no—
529C4—1221no—
530C4—4884no—
531C4—2444no—
532C4#1684063912yes—
533C2—22no—
534C2—22no—
535C2—41no—
536C2—614no—
537C2—1222no—
538C2—1222no—
539C2—2441no—
540C2C2×#1684063311yescharacteristic
541C2#2146150411yescharacteristic
542C2C2×#1684063911yescharacteristic
subgroupG/H
centerC2×C4(C2×#6923)⋊C4
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC4×C22⋊C4×C61C4
socleC22×C61C2×#95
prime radicalC24×D61D4
cosocleC22×C4×D61C23
hypercenterC4×C22⋊C4#6923
hypocenterC61#8012
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. #21460693C2semidirect
6. C2×#14519856C4semidirect
7. C2×#14519834C4semidirect
10. D61⋊(C22⋊C8)C4semidirect
14. #16840704C4semidirect
24. C4×C22⋊Dic61C4semidirect
25. #16839609C4semidirect
27. C4×C22⋊C4×C61C4semidirect
297. C4×C22⋊C4#6923semidirect
299. C61#8012semidirect

Maximal subgroups

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

subgroupindex
C2×D61⋊(C22⋊C8)2
#214622632
#214606932
C4×C22⋊C4×D612
#801261