Finite Group Databasebeta

← #30596953

Subgroups — #30596953

Order 15616.

1090 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#407C211yesmaximal, characteristic
2#21462263C211yesmaximal, characteristic
3#21460700C214yesmaximal, complemented
4C2×#16839609C211yesmaximal, characteristic
5C2×D61⋊M16C412yescomplemented
6C2×#14519856—21no—
7#16840734—21no—
8#16840733C412yescomplemented
9#16840733C2212yes—
10#16840732—21no—
11D61⋊(C22⋊C8)—21no—
12D61⋊(C22⋊C8)—21no—
13#16840705C412yescomplemented
14#16840704—21no—
15#16840704C412yescomplemented
16#16840703—21no—
17C4×C22⋊#6923—21no—
18C4×C22⋊#6923C2212yes—
19C23×C4×D61C2211yescharacteristic
20C22×#11758198—21no—
21C22×C4×Dic61—21no—
22#16839609—21no—
23#16839609—21no—
24#16839609C412yescomplemented
25#16839609C2212yes—
26C2×#14519684C411yescharacteristic, complemented
27C2×#95×C61C411yescharacteristic, complemented
28C2×#11758213C2×C414yescomplemented
29D61⋊M16—44no—
30C2×#11758217—22no—
31C2×D61⋊C8—22no—
32#14519856—44no—
33C2×C4⋊#6923—22no—
34C2×C22⋊#6923—22no—
35C2×C22⋊#6923—22no—
36C2×C22⋊#6923—22no—
37C2×C4×#6923—22no—
38#14519834—22no—
39#14519834—22no—
40C22⋊#92420—22no—
41C22⋊#92420—22no—
42(C2×#6923)⋊C4—22no—
43(C2×#6923)⋊C4C2×C414yescomplemented
44C24×D61D411yescharacteristic
45C23×Dic61—21no—
46C23×Dic61D411yescharacteristic
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×#11758198—28no—
61C2×#11758198—22no—
62C2×#11758198—22no—
63C2×C4×Dic61—22no—
64C2×C4×Dic61—22no—
65C2×C4×Dic61—44no—
66#14519684—21no—
67#14519684C2×C412yes—
68C23×C4×C61—21no—
69C23×C4×C61C2×C411yescharacteristic
70#95×C61—21no—
71#95×C61C2×C412yes—
72C24×C61C22⋊C411yescharacteristic
73C23×D61—24no—
74C23×D61—42no—
75C23×D61—41no—
76C23×D61—41no—
77C23×D61C22⋊C411yescharacteristic
78C23×D61C22⋊C411yescharacteristic
79C23×D61C22⋊C411yescharacteristic
80C23×D61C4⋊C411yescharacteristic
81C23×D61C4⋊C411yescharacteristic
82C23×D61C2×D411yescharacteristic
83C22×#6923—24no—
84C22×C4×C61—24no—
85C22×C4×C61—22no—
86C22×C4×C61—42no—
87C22×C4×C61—42no—
88C22×C4×C61—42no—
89C22×C4×C61C4211yescharacteristic
90C22×C4×C61C4211yescharacteristic
91C22×C4×C61C22⋊C411yescharacteristic
92C22×C4×C61C4⋊C411yescharacteristic
93C22×C4×C61C4⋊C411yescharacteristic
94C22×C4×C61C22×C411yescharacteristic
95C22×Dic61—24no—
96C22×Dic61—24no—
97C22×Dic61—22no—
98C22×Dic61—42no—
99C22×Dic61—42no—
100C22×Dic61C22⋊C411yescharacteristic
101C22×Dic61C22⋊C411yescharacteristic
102C22×Dic61C22⋊C411yescharacteristic
103C22×Dic61C4⋊C411yescharacteristic
104C22×Dic61C4⋊C411yescharacteristic
105C22×Dic61C2×D411yescharacteristic
106C2×C4×D61—24no—
107C2×C4×D61—24no—
108C2×C4×D61—42no—
109C2×C4×D61—42no—
110C2×C4×D61—42no—
111C2×C4×D61—42no—
112C2×C4×D61—42no—
113C2×C4×D61—42no—
114C2×C4×D61—42no—
115C2×C4×D61—42no—
116C2×C4×D61—42no—
117C2×C4×D61—42no—
118C2×C4×D61C4211yescharacteristic
119C2×C4×D61C4211yescharacteristic
120C2×C4×D61C22⋊C411yescharacteristic
121C2×C4×D61C22⋊C411yescharacteristic
122C2×C4×D61C22⋊C411yescharacteristic
123C2×C4×D61C22⋊C411yescharacteristic
124C2×C4×D61C4⋊C411yescharacteristic
125C2×C4×D61C4⋊C411yescharacteristic
126C2×C4×D61C4⋊C411yescharacteristic
127C2×C4×D61C4⋊C411yescharacteristic
128C2×C4×D61C4⋊C411yescharacteristic
129C2×C4×D61C4⋊C411yescharacteristic
130C2×C4×D61C22×C411yescharacteristic
131C2×C4×D61C22×C411yescharacteristic
132C2×C4×D61C2×D411yescharacteristic
133C2×C4×D61C2×Q811yescharacteristic
134C22⋊#6923—42no—
135C22⋊#6923—42no—
136C22⋊#6923—44no—
137C22⋊#6923—44no—
138#11758217—44no—
139C2×#92420—24no—
140C4⋊#6923—44no—
141C4×#6923—44no—
142#11758213—44no—
143D61⋊C8—44no—
144#11758198—28no—
145#11758198—28no—
146C4×Dic61—44no—
147C4×Dic61—44no—
148C23×C61—22no—
149C23×C61—22no—
150C23×C61—21no—
151C23×C61—21no—
152C23×C61#9511yescharacteristic
153C23×C61#9511yescharacteristic
154C23×C61C2×C22⋊C411yescharacteristic
155C22×D61—22no—
156C22×D61—22no—
157C22×D61—22no—
158C22×D61—21no—
159C22×D61—21no—
160C22×D61—21no—
161C22×D61—21no—
162C22×D61—22no—
163C22×D61—22no—
164C22×D61—22no—
165C22×D61—22no—
166C22×D61—41no—
167C22×D61—41no—
168C22×D61—41no—
169C22×D61—41no—
170C22×D61—41no—
171C22×D61—41no—
172C22×D61—41no—
173C22×D61—41no—
174C22×D61—48no—
175C22×D61—48no—
176C22×D61#9511yescharacteristic
177C22×D61#9511yescharacteristic
178C22×D61#10414yes—
179C22×D61C2×C22⋊C411yescharacteristic
180C22×D61C2×C4⋊C411yescharacteristic
181C2×#6923—44no—
182C2×#6923—44no—
183C2×#6923—44no—
184C2×C4×C61—22no—
185C2×C4×C61—22no—
186C2×C4×C61—24no—
187C2×C4×C61—41no—
188C2×C4×C61—41no—
189C2×C4×C61—41no—
190C2×C4×C61—41no—
191C2×C4×C61—42no—
192C2×C4×C61—48no—
193C2×C4×C61—42no—
194C2×C4×C61#9511yescharacteristic
195C2×C4×C61#9511yescharacteristic
196C2×C4×C61C2×C4211yescharacteristic
197C2×C4×C61C2×C4⋊C411yescharacteristic
198C2×Dic61—22no—
199C2×Dic61—22no—
200C2×Dic61—22no—
201C2×Dic61—22no—
202C2×Dic61—22no—
203C2×Dic61—24no—
204C2×Dic61—42no—
205C2×Dic61—48no—
206C2×Dic61—42no—
207C2×Dic61#9511yescharacteristic
208C2×Dic61#9511yescharacteristic
209C2×Dic61#9914yes—
210C2×Dic61C2×C22⋊C411yescharacteristic
211C2×Dic61C2×C4⋊C411yescharacteristic
212C4×D61—22no—
213C4×D61—22no—
214C4×D61—22no—
215C4×D61—22no—
216C4×D61—22no—
217C4×D61—22no—
218C4×D61—22no—
219C4×D61—22no—
220C4×D61—41no—
221C4×D61—41no—
222C4×D61—41no—
223C4×D61—41no—
224C4×D61—41no—
225C4×D61—41no—
226C4×D61—41no—
227C4×D61—41no—
228#92420—44no—
229#8051—611nomaximal, Sylow
230C22×C61—24no—
231C22×C61—24no—
232C22×C61—21no—
233C22×C61—21no—
234C22×C61—21no—
235C22×C61—21no—
236C22×C61—21no—
237C22×C61—21no—
238C22×C61#33912yes—
239C22×C61#34212yes—
240C22×C61C2×#9511yescharacteristic
241C22×C61#42111yescharacteristic
242C22×C61#42111yescharacteristic
243C2×D61—21no—
244C2×D61—21no—
245C2×D61—21no—
246C2×D61—21no—
247C2×D61—21no—
248C2×D61—21no—
249C2×D61—21no—
250C2×D61—21no—
251C2×D61—21no—
252C2×D61—21no—
253C2×D61—44no—
254C2×D61—42no—
255C2×D61—42no—
256C2×D61—44no—
257C2×D61—42no—
258C2×D61—42no—
259C2×D61—44no—
260C2×D61—44no—
261C2×D61#33912yes—
262C2×D61C2×#10412yes—
263#6923—84no—
264C4×C61—21no—
265C4×C61—21no—
266C4×C61—21no—
267C4×C61—21no—
268C4×C61—44no—
269Dic61—21no—
270Dic61—21no—
271Dic61—44no—
272Dic61#34212yes—
273Dic61C2×#9912yes—
274C2×#407—611no—
275#2280—611no—
276C2×C4×C22⋊C4—611no—
277#1297—614no—
278C2×C61—21no—
279C2×C61—21no—
280C2×C61—22no—
281C2×C61—22no—
282C2×C61C2×#33911yescharacteristic
283C2×C61#173311yescharacteristic
284C2×C61C2×#34211yescharacteristic
285D61—22no—
286D61—22no—
287D61—41no—
288D61—41no—
289C24×C4—611no—
290C22×M16—612no—
291C2×#117—1221no—
292C22×C22⋊C4—1221no—
293C22×C42—1221no—
294#407—612no—
295#407—612no—
296#407—1221no—
297#407—1221no—
298C2×C22⋊C8—1221no—
299C2×C22⋊C8—1221no—
300#381—612no—
301#380—612no—
302#380—1221no—
303#379—1221no—
304C4×C22⋊C4—612no—
305C4×C22⋊C4—612no—
306C4×C22⋊C4—612no—
307C4×C22⋊C4—1221no—
308C4×C22⋊C4—1221no—
309C4×C22⋊C4—1221no—
310C2×#95—611no—
311C2×#95#692311yescharacteristic, complemented
312C61#805111yescharacteristic, complemented, Sylow
313C25—611no—
314C23×C4—21no—
315C23×C4—611no—
316C23×C4—611no—
317C23×C4—611no—
318C23×C4—611no—
319C23×C4—611no—
320C23×C4—611no—
321C23×C4—611no—
322C23×C4—611no—
323C23×C4—611no—
324C23×C4—611no—
325C23×C4—611no—
326C23×C4—611no—
327C23×C4—611no—
328C23×C4—1221no—
329C23×C4—2444no—
330C23×C4C2×#692311yescharacteristic
331C2×M16—614no—
332C2×M16—1222no—
333C2×M16—2444no—
334C22×C8—1222no—
335#117—2444no—
336C2×C4⋊C4—1222no—
337C2×C22⋊C4—1222no—
338C2×C22⋊C4—1222no—
339C2×C22⋊C4—1228no—
340C2×C22⋊C4—1222no—
341C2×C22⋊C4—1222no—
342C2×C22⋊C4—1222no—
343C2×C42—1222no—
344C2×C42—1222no—
345C2×C42—1222no—
346C2×C42—2444no—
347C22⋊C8—1222no—
348C22⋊C8—1222no—
349C22⋊C8—1222no—
350C22⋊C8—1222no—
351#95—21no—
352#95—614no—
353#95—612no—
354#95—1222no—
355#95—1221no—
356#95C2×#692312yes—
357C24—611no—
358C24—611no—
359C24—611no—
360C24—611no—
361C24—611no—
362C24—611no—
363C24—1224no—
364C24—2442no—
365C24—2441no—
366C24—2441no—
367C24C22⋊#692311yescharacteristic
368C22×C4—24no—
369C22×C4—22no—
370C22×C4—42no—
371C22×C4—42no—
372C22×C4—42no—
373C22×C4—611no—
374C22×C4—611no—
375C22×C4—611no—
376C22×C4—611no—
377C22×C4—611no—
378C22×C4—611no—
379C22×C4—611no—
380C22×C4—611no—
381C22×C4—611no—
382C22×C4—611no—
383C22×C4—611no—
384C22×C4—611no—
385C22×C4—611no—
386C22×C4—611no—
387C22×C4—611no—
388C22×C4—611no—
389C22×C4—611no—
390C22×C4—611no—
391C22×C4—611no—
392C22×C4—611no—
393C22×C4—611no—
394C22×C4—611no—
395C22×C4—1224no—
396C22×C4—1224no—
397C22×C4—1224no—
398C22×C4—1224no—
399C22×C4—1222no—
400C22×C4—1224no—
401C22×C4—2442no—
402C22×C4—2442no—
403C22×C4—2442no—
404C22×C4—2442no—
405C22×C4—2442no—
406C22×C4—2442no—
407C22×C4—2442no—
408C22×C4—2442no—
409C22×C4—2442no—
410C22×C4—2442no—
411C22×C4—2442no—
412C22×C4—2442no—
413C22×C4C4×#692311yescharacteristic
414C22×C4C4×#692311yescharacteristic
415C22×C4C4⋊#692311yescharacteristic
416C22×C4C4⋊#692311yescharacteristic
417C22×C4C22⋊#692311yescharacteristic
418C22×C4C22×#692311yescharacteristic
419M16—2444no—
420M16—2444no—
421C2×C8—1224no—
422C2×C8—2444no—
423C4⋊C4—2444no—
424C22⋊C4—1228no—
425C22⋊C4—1228no—
426C22⋊C4—2444no—
427C22⋊C4—2444no—
428C22⋊C4—2442no—
429C22⋊C4—2442no—
430C42—2444no—
431C42—2444no—
432C42—2444no—
433C23—21no—
434C23—21no—
435C23—22no—
436C23—22no—
437C23—611no—
438C23—611no—
439C23—614no—
440C23—611no—
441C23—611no—
442C23—1222no—
443C23—1222no—
444C23—1222no—
445C23—1222no—
446C23—1221no—
447C23—1221no—
448C23—1221no—
449C23—1221no—
450C23—1222no—
451C23—1222no—
452C23—1222no—
453C23—2441no—
454C23—2441no—
455C23—2441no—
456C23—2441no—
457C23—2441no—
458C23—2441no—
459C23—2441no—
460C23—2441no—
461C23—2448no—
462C23—2448no—
463C23(C2×#6923)⋊C411yescharacteristic
464C23(C2×#6923)⋊C411yescharacteristic
465C23C2×C22⋊#692311yescharacteristic
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—24no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—42no—
474C2×C4—48no—
475C2×C4—42no—
476C2×C4—614no—
477C2×C4—611no—
478C2×C4—611no—
479C2×C4—611no—
480C2×C4—611no—
481C2×C4—1222no—
482C2×C4—1222no—
483C2×C4—1222no—
484C2×C4—1222no—
485C2×C4—1222no—
486C2×C4—1222no—
487C2×C4—1222no—
488C2×C4—1222no—
489C2×C4—1222no—
490C2×C4—1222no—
491C2×C4—1222no—
492C2×C4—1222no—
493C2×C4—1222no—
494C2×C4—1224no—
495C2×C4—2441no—
496C2×C4—2441no—
497C2×C4—2441no—
498C2×C4—2441no—
499C2×C4—2441no—
500C2×C4—2441no—
501C2×C4—2441no—
502C2×C4—2441no—
503C2×C4—2444no—
504C2×C4—2444no—
505C2×C4—2444no—
506C2×C4—2442no—
507C2×C4—2448no—
508C2×C4—2442no—
509C2×C4(C2×#6923)⋊C411yescharacteristic
510C2×C4(C2×#6923)⋊C411yescharacteristic
511C2×C4C2×C4×#692311yescharacteristic
512C2×C4C2×C4⋊#692311yescharacteristic
513C8—2444no—
514C22—24no—
515C22—24no—
516C22—21no—
517C22—21no—
518C22—21no—
519C22—21no—
520C22—21no—
521C22—21no—
522C22—612no—
523C22—612no—
524C22—1221no—
525C22—1221no—
526C22—1221no—
527C22—1221no—
528C22—1221no—
529C22—1221no—
530C22—1221no—
531C22—1221no—
532C22—1221no—
533C22—1221no—
534C22—2444no—
535C22—2442no—
536C22—2442no—
537C22—2442no—
538C22—2442no—
539C22—2444no—
540C22—2444no—
541C22—2444no—
542C22#1684063312yes—
543C22#1684063912yes—
544C22C2×(C2×#6923)⋊C411yescharacteristic
545C22#1684076011yescharacteristic
546C22#1684076111yescharacteristic
547C4—21no—
548C4—21no—
549C4—21no—
550C4—21no—
551C4—44no—
552C4—612no—
553C4—612no—
554C4—1221no—
555C4—1221no—
556C4—4884no—
557C4—2444no—
558C2—21no—
559C2—21no—
560C2—22no—
561C2—22no—
562C2—1222no—
563C2—1222no—
564C2—2441no—
565C2—2441no—
566C2C2×#1684063311yescharacteristic
567C2#2146149811yescharacteristic
568C2C2×#1684063911yescharacteristic
subgroupG/H
centerC22C2×(C2×#6923)⋊C4
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC2×#95×C61C4
socleC22×C61C2×#95
prime radicalC24×D61D4
cosocleC22×C4×D61C23
hypercenterC2×#95#6923
hypocenterC61#8051
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
3. #21460700C2semidirect
5. C2×D61⋊M16C4semidirect
8. #16840733C4semidirect
13. #16840705C4semidirect
15. #16840704C4semidirect
24. #16839609C4semidirect
26. C2×#14519684C4semidirect
27. C2×#95×C61C4semidirect
28. C2×#11758213C2×C4semidirect
43. (C2×#6923)⋊C4C2×C4semidirect
311. C2×#95#6923semidirect
312. C61#8051semidirect

Maximal subgroups

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

subgroupindex
D61⋊#4072
#214622632
#214607002
C2×#168396092
#805161