Finite Group Databasebeta

← #30596655

Subgroups — #30596655

Order 15616.

1026 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#407C211yesmaximal, characteristic
2#21462263C211yesmaximal, characteristic
3#21460681C214yesmaximal, complemented
4#380×D61C211yesmaximal, characteristic
5C2×D61⋊M16C412yescomplemented
6C2×#14519856—21no—
7#16840734—21no—
8#16840733—21no—
9#16840733—21no—
10#16840732—21no—
11D61⋊(C22⋊C8)C412yescomplemented
12D61⋊(C22⋊C8)C2212yes—
13#16840705C412yescomplemented
14#16840704—21no—
15#16840704C2212yes—
16#16840703—21no—
17C4×C22⋊#6923—21no—
18C4×C22⋊#6923C412yescomplemented
19C23×C4×D61C2211yescharacteristic
20C2×C4⋊C4×D61—21no—
21C2×C22⋊C4×D61—21no—
22#16839622C411yescharacteristic, complemented
23#16839621C2212yes—
24#16839620—21no—
25#16839619—21no—
26#95×D61C412yescomplemented
27C61×#380C411yescharacteristic, complemented
28C2×#11758213—22no—
29D61⋊M16—44no—
30C2×#11758217—22no—
31C2×D61⋊C8C2×C414yescomplemented
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×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×C4⋊Dic61—21no—
61C2×#11758196—22no—
62C4⋊C4×D61—44no—
63C2×C22⋊Dic61—21no—
64C2×#11758198—22no—
65C22⋊C4×D61—44no—
66#14519684—22no—
67#14519684C2×C412yes—
68C23×C4×C61C2×C411yescharacteristic
69C2×C4⋊C4×C61—21no—
70C2×C22⋊C4×C61—21no—
71#95×C61C2×C412yes—
72C24×C61C22⋊C411yescharacteristic
73C23×D61—22no—
74C23×D61—22no—
75C23×D61—42no—
76C23×D61—42no—
77C23×D61C22⋊C411yescharacteristic
78C23×D61C22⋊C411yescharacteristic
79C23×D61C22⋊C411yescharacteristic
80C23×D61C4⋊C411yescharacteristic
81C23×D61C4⋊C411yescharacteristic
82C23×D61C2×D411yescharacteristic
83C22×#6923—24no—
84C22×C4×C61—22no—
85C22×C4×C61—42no—
86C22×C4×C61C4211yescharacteristic
87C22×C4×C61C4211yescharacteristic
88C22×C4×C61C22⋊C411yescharacteristic
89C22×C4×C61C4⋊C411yescharacteristic
90C22×C4×C61C4⋊C411yescharacteristic
91C22×C4×C61C22×C411yescharacteristic
92C22×Dic61—22no—
93C22×Dic61—42no—
94C22×Dic61C22⋊C411yescharacteristic
95C22×Dic61C22⋊C411yescharacteristic
96C22×Dic61C22⋊C411yescharacteristic
97C22×Dic61C4⋊C411yescharacteristic
98C22×Dic61C4⋊C411yescharacteristic
99C22×Dic61C2×D411yescharacteristic
100C2×C4×D61—24no—
101C2×C4×D61—24no—
102C2×C4×D61—24no—
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×D61—44no—
115C2×C4×D61C4211yescharacteristic
116C2×C4×D61C4211yescharacteristic
117C2×C4×D61C22⋊C411yescharacteristic
118C2×C4×D61C22⋊C411yescharacteristic
119C2×C4×D61C22⋊C411yescharacteristic
120C2×C4×D61C22⋊C411yescharacteristic
121C2×C4×D61C4⋊C411yescharacteristic
122C2×C4×D61C4⋊C411yescharacteristic
123C2×C4×D61C4⋊C411yescharacteristic
124C2×C4×D61C4⋊C411yescharacteristic
125C2×C4×D61C4⋊C411yescharacteristic
126C2×C4×D61C4⋊C411yescharacteristic
127C2×C4×D61C22×C411yescharacteristic
128C2×C4×D61C22×C411yescharacteristic
129C2×C4×D61C2×D411yescharacteristic
130C2×C4×D61C2×Q811yescharacteristic
131C22⋊#6923—44no—
132C22⋊#6923—44no—
133C22⋊#6923—42no—
134C22⋊#6923—42no—
135#11758217—44no—
136C2×#92420—24no—
137C4⋊#6923—44no—
138C4×#6923—44no—
139#11758213—44no—
140D61⋊C8—44no—
141C4⋊C4×C61—42no—
142C22⋊C4×C61—42no—
143C22⋊Dic61—42no—
144#11758198—44no—
145C4⋊Dic61—42no—
146#11758196—44no—
147C23×C61—21no—
148C23×C61—21no—
149C23×C61—41no—
150C23×C61—41no—
151C23×C61#9511yescharacteristic
152C23×C61#9511yescharacteristic
153C23×C61C2×C22⋊C411yescharacteristic
154C22×D61—21no—
155C22×D61—21no—
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—22no—
165C22×D61—22no—
166C22×D61—41no—
167C22×D61—41no—
168C22×D61—41no—
169C22×D61—41no—
170C22×D61—41no—
171C22×D61—41no—
172C22×D61—48no—
173C22×D61—48no—
174C22×D61#9511yescharacteristic
175C22×D61#9511yescharacteristic
176C22×D61C2×C22⋊C411yescharacteristic
177C22×D61C2×C4⋊C411yescharacteristic
178C22×D61AGL(1,ℤ/8)12yes—
179C22×D61#13712yes—
180C2×#6923—44no—
181C2×#6923—44no—
182C2×#6923—44no—
183C2×C4×C61—22no—
184C2×C4×C61—22no—
185C2×C4×C61—22no—
186C2×C4×C61—41no—
187C2×C4×C61—41no—
188C2×C4×C61—41no—
189C2×C4×C61—42no—
190C2×C4×C61—42no—
191C2×C4×C61—42no—
192C2×C4×C61#9511yescharacteristic
193C2×C4×C61#9511yescharacteristic
194C2×C4×C61C2×C4211yescharacteristic
195C2×C4×C61C2×C4⋊C411yescharacteristic
196C2×Dic61—22no—
197C2×Dic61—22no—
198C2×Dic61—22no—
199C2×Dic61—41no—
200C2×Dic61—41no—
201C2×Dic61—41no—
202C2×Dic61—42no—
203C2×Dic61—42no—
204C2×Dic61—42no—
205C2×Dic61#9511yescharacteristic
206C2×Dic61#9511yescharacteristic
207C2×Dic61C2×C22⋊C411yescharacteristic
208C2×Dic61C2×C4⋊C411yescharacteristic
209C4×D61—22no—
210C4×D61—22no—
211C4×D61—22no—
212C4×D61—22no—
213C4×D61—22no—
214C4×D61—22no—
215C4×D61—22no—
216C4×D61—22no—
217C4×D61—22no—
218C4×D61—41no—
219C4×D61—41no—
220C4×D61—41no—
221C4×D61—41no—
222C4×D61—41no—
223C4×D61—41no—
224C4×D61—88no—
225C4×D61#9914yes—
226#92420—44no—
227#7983—611nomaximal, Sylow
228C22×C61—21no—
229C22×C61—21no—
230C22×C61—21no—
231C22×C61—21no—
232C22×C61—21no—
233C22×C61—21no—
234C22×C61—21no—
235C22×C61—21no—
236C22×C61—42no—
237C22×C61—42no—
238C22×C61C2×#9511yescharacteristic
239C22×C61#41811yescharacteristic
240C22×C61#41911yescharacteristic
241C2×D61—24no—
242C2×D61—24no—
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—42no—
252C2×D61—42no—
253C2×D61—44no—
254C2×D61—44no—
255C2×D61—44no—
256C2×D61—44no—
257C2×D61H(3,ℤ/4)12yes—
258C2×D61#34212yes—
259C2×D61#41712yes—
260C2×D61#42812yes—
261#6923—84no—
262C4×C61—21no—
263C4×C61—21no—
264C4×C61—21no—
265C4×C61—82no—
266C4×C61#34212yes—
267Dic61—21no—
268Dic61—21no—
269Dic61—21no—
270Dic61—82no—
271Dic61C2×#9912yes—
272C2×#407—611no—
273#2280—611no—
274C2×#380—611no—
275#1289—614no—
276C2×C61—21no—
277C2×C61—21no—
278C2×C61—41no—
279C2×C61—41no—
280C2×C61C2×H(3,ℤ/4)11yescharacteristic
281C2×C61#173611yescharacteristic
282C2×C61C2×#34211yescharacteristic
283D61—22no—
284D61—22no—
285D61—22no—
286D61—22no—
287C24×C4—611no—
288C22×M16—612no—
289C2×#117—1221no—
290C22×C4⋊C4—1221no—
291C22×C22⋊C4—1221no—
292#407—1221no—
293#407—1221no—
294#407—1221no—
295#407—1221no—
296C2×C22⋊C8—612no—
297C2×C22⋊C8—612no—
298#381—612no—
299#380—612no—
300#380—611no—
301#380—612no—
302#380—1221no—
303#380—1221no—
304#380—1221no—
305#380#692311yescharacteristic, complemented
306#379—1221no—
307C4×C22⋊C4—612no—
308C4×C22⋊C4—1221no—
309C2×#95—612no—
310C61#798311yescharacteristic, complemented, Sylow
311C25—611no—
312C23×C4—611no—
313C23×C4—611no—
314C23×C4—611no—
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—1222no—
326C23×C4—2444no—
327C23×C4C2×#692311yescharacteristic
328C2×M16—1222no—
329C2×M16—1222no—
330C2×M16—2444no—
331C22×C8—614no—
332#117—2444no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—1222no—
335C2×C4⋊C4—1222no—
336C2×C4⋊C4—1221no—
337C2×C4⋊C4—2444no—
338C2×C22⋊C4—21no—
339C2×C22⋊C4—1222no—
340C2×C22⋊C4—1222no—
341C2×C22⋊C4—1222no—
342C2×C22⋊C4—1222no—
343C2×C22⋊C4—1221no—
344C2×C22⋊C4—2444no—
345C2×C42—1222no—
346C22⋊C8—1222no—
347C22⋊C8—1222no—
348C22⋊C8—1222no—
349C22⋊C8—1222no—
350#95—614no—
351#95—612no—
352#95—1222no—
353#95—1222no—
354#95C2×#692312yes—
355C24—611no—
356C24—611no—
357C24—611no—
358C24—611no—
359C24—611no—
360C24—611no—
361C24—1222no—
362C24—1222no—
363C24—2442no—
364C24—2442no—
365C24C22⋊#692311yescharacteristic
366C22×C4—22no—
367C22×C4—42no—
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—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—1224no—
391C22×C4—1224no—
392C22×C4—1224no—
393C22×C4—1224no—
394C22×C4—1222no—
395C22×C4—2442no—
396C22×C4—2442no—
397C22×C4—2442no—
398C22×C4—2442no—
399C22×C4—2442no—
400C22×C4—2442no—
401C22×C4—2442no—
402C22×C4—2442no—
403C22×C4—2442no—
404C22×C4—2444no—
405C22×C4—2444no—
406C22×C4—2444no—
407C22×C4—2442no—
408C22×C4C4×#692311yescharacteristic
409C22×C4C4×#692311yescharacteristic
410C22×C4C4⋊#692311yescharacteristic
411C22×C4C4⋊#692311yescharacteristic
412C22×C4C22⋊#692311yescharacteristic
413C22×C4C22×#692311yescharacteristic
414M16—2444no—
415M16—2444no—
416C2×C8—1224no—
417C2×C8—2444no—
418C4⋊C4—42no—
419C4⋊C4—2442no—
420C4⋊C4—2444no—
421C4⋊C4—2444no—
422C22⋊C4—42no—
423C22⋊C4—2444no—
424C22⋊C4—2442no—
425C22⋊C4—2442no—
426C22⋊C4—2442no—
427C22⋊C4—2444no—
428C22⋊C4—2444no—
429C42—2444no—
430C23—21no—
431C23—21no—
432C23—41no—
433C23—41no—
434C23—611no—
435C23—611no—
436C23—611no—
437C23—611no—
438C23—612no—
439C23—612no—
440C23—1222no—
441C23—1222no—
442C23—1222no—
443C23—1222no—
444C23—1222no—
445C23—1222no—
446C23—1222no—
447C23—1222no—
448C23—1222no—
449C23—1222no—
450C23—1221no—
451C23—1221no—
452C23—2441no—
453C23—2441no—
454C23—2441no—
455C23—2441no—
456C23—2441no—
457C23—2441no—
458C23—2448no—
459C23—2448no—
460C23(C2×#6923)⋊C411yescharacteristic
461C23(C2×#6923)⋊C411yescharacteristic
462C23C2×C22⋊#692311yescharacteristic
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—611no—
473C2×C4—614no—
474C2×C4—611no—
475C2×C4—611no—
476C2×C4—611no—
477C2×C4—1222no—
478C2×C4—1222no—
479C2×C4—1222no—
480C2×C4—1222no—
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—4888no—
490C2×C4—2441no—
491C2×C4—2441no—
492C2×C4—2441no—
493C2×C4—2441no—
494C2×C4—2441no—
495C2×C4—2441no—
496C2×C4—2441no—
497C2×C4—2441no—
498C2×C4—2441no—
499C2×C4—2442no—
500C2×C4—2442no—
501C2×C4—2444no—
502C2×C4—2444no—
503C2×C4—2444no—
504C2×C4—2442no—
505C2×C4(C2×#6923)⋊C411yescharacteristic
506C2×C4(C2×#6923)⋊C411yescharacteristic
507C2×C4C2×C4×#692311yescharacteristic
508C2×C4C2×C4⋊#692311yescharacteristic
509C8—2444no—
510C22—21no—
511C22—21no—
512C22—21no—
513C22—21no—
514C22—21no—
515C22—21no—
516C22—21no—
517C22—21no—
518C22—42no—
519C22—42no—
520C22—612no—
521C22—612no—
522C22—612no—
523C22—612no—
524C22—1224no—
525C22—1224no—
526C22—1221no—
527C22—1221no—
528C22—1221no—
529C22—1221no—
530C22—1221no—
531C22—1221no—
532C22—1221no—
533C22—1221no—
534C22—2442no—
535C22—2442no—
536C22—2444no—
537C22—2444no—
538C22—2444no—
539C22—2444no—
540C22C2×(C2×#6923)⋊C411yescharacteristic
541C22#1684075411yescharacteristic
542C22#1684075511yescharacteristic
543C4—21no—
544C4—21no—
545C4—21no—
546C4—82no—
547C4—612no—
548C4—1221no—
549C4—1221no—
550C4—1221no—
551C4—4882no—
552C4—4884no—
553C4#1684063912yes—
554C2—21no—
555C2—21no—
556C2—41no—
557C2—41no—
558C2—1222no—
559C2—1222no—
560C2—1222no—
561C2—1222no—
562C2#2146148911yescharacteristic
563C2#2146150611yescharacteristic
564C2C2×#1684063911yescharacteristic
subgroupG/H
centerC22C2×(C2×#6923)⋊C4
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC61×#380C4
socleC22×C61C2×#95
prime radicalC24×D61D4
cosocleC22×C4×D61C23
hypercenter#380#6923
hypocenterC61#7983
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
3. #21460681C2semidirect
5. C2×D61⋊M16C4semidirect
11. D61⋊(C22⋊C8)C4semidirect
13. #16840705C4semidirect
18. C4×C22⋊#6923C4semidirect
22. #16839622C4semidirect
26. #95×D61C4semidirect
27. C61×#380C4semidirect
31. C2×D61⋊C8C2×C4semidirect
43. (C2×#6923)⋊C4C2×C4semidirect
305. #380#6923semidirect
310. C61#7983semidirect

Maximal subgroups

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

subgroupindex
D61⋊#4072
#214622632
#214606812
#380×D612
#798361