Finite Group Databasebeta

← #30596659

Subgroups — #30596659

Order 15616.

1026 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#407C211yesmaximal, characteristic
2C2×#16840704C211yesmaximal, characteristic
3#21460681C214yesmaximal, complemented
4#21448199C211yesmaximal, characteristic
5C2×D61⋊M16C412yescomplemented
6C22×C4⋊#6923—21no—
7C22×C22⋊#6923—21no—
8#16840734—21no—
9#16840733—21no—
10#16840733—21no—
11#16840732—21no—
12D61⋊(C22⋊C8)C412yescomplemented
13D61⋊(C22⋊C8)C2212yes—
14#16840704—21no—
15#16840704—21no—
16#16840704C412yescomplemented
17#16840704C2212yes—
18C2×(C2×#6923)⋊C4C412yescomplemented
19C23×C4×D61C2211yescharacteristic
20C2×#14519733—21no—
21#16839625C411yescharacteristic, complemented
22#16839621—21no—
23#16839621C2212yes—
24#16839617—21no—
25#16839609—21no—
26#16839609C412yescomplemented
27C61×#381C411yescharacteristic, complemented
28C23×#6923—22no—
29C2×#11758213—22no—
30D61⋊M16—44no—
31C2×#11758217—22no—
32C2×D61⋊C8C2×C414yescomplemented
33C2×C4⋊#6923—22no—
34C2×C4⋊#6923—22no—
35C2×C4⋊#6923—44no—
36C2×C22⋊#6923—22no—
37C2×C22⋊#6923—22no—
38C2×C22⋊#6923—44no—
39#14519834—22no—
40#14519834—22no—
41C22⋊#92420—22no—
42C22⋊#92420—22no—
43(C2×#6923)⋊C4—22no—
44(C2×#6923)⋊C4C2×C414yes—
45C24×D61D411yescharacteristic
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
60#14519733—44no—
61C2×#11758196—22no—
62C2×C22⋊Dic61—21no—
63C2×#11758198—22no—
64C2×#11758198—22no—
65C2×C4×Dic61—22no—
66#14519684—21no—
67#14519684C2×C412yescomplemented
68C23×C4×C61C2×C411yescharacteristic
69C2×C22⋊C4×C61—21no—
70#95×C61—21no—
71#95×C61C2×C412yescomplemented
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×#6923—44no—
85C22×#6923—44no—
86C22×#6923—44no—
87C22×C4×C61—22no—
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—22no—
97C22×Dic61C22⋊C411yescharacteristic
98C22×Dic61C22⋊C411yescharacteristic
99C22×Dic61C22⋊C411yescharacteristic
100C22×Dic61C4⋊C411yescharacteristic
101C22×Dic61C4⋊C411yescharacteristic
102C22×Dic61C2×D411yescharacteristic
103C2×C4×D61—24no—
104C2×C4×D61—24no—
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—42no—
113C2×C4×D61—42no—
114C2×C4×D61—42no—
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—
133#11758217—44no—
134C2×#92420—24no—
135C4⋊#6923—44no—
136C4⋊#6923—44no—
137#11758213—44no—
138D61⋊C8—44no—
139C22⋊C4×C61—42no—
140C22⋊Dic61—42no—
141#11758198—44no—
142#11758198—42no—
143#11758198—42no—
144#11758196—44no—
145C4×Dic61—44no—
146C23×C61—22no—
147C23×C61—22no—
148C23×C61—41no—
149C23×C61#9511yescharacteristic
150C23×C61#9511yescharacteristic
151C23×C61C2×C22⋊C411yescharacteristic
152C22×D61—22no—
153C22×D61—22no—
154C22×D61—21no—
155C22×D61—21no—
156C22×D61—22no—
157C22×D61—22no—
158C22×D61—22no—
159C22×D61—22no—
160C22×D61—21no—
161C22×D61—21no—
162C22×D61—22no—
163C22×D61—22no—
164C22×D61—41no—
165C22×D61—41no—
166C22×D61—41no—
167C22×D61—41no—
168C22×D61—41no—
169C22×D61—41no—
170C22×D61—41no—
171C22×D61—48no—
172C22×D61—48no—
173C22×D61#9511yescharacteristic
174C22×D61#9511yescharacteristic
175C22×D61C2×C22⋊C411yescharacteristic
176C22×D61C2×C4⋊C411yescharacteristic
177C22×D61AGL(1,ℤ/8)12yes—
178C22×D61#13712yes—
179C2×#6923—44no—
180C2×#6923—44no—
181C2×#6923—44no—
182C2×#6923—88no—
183C2×C4×C61—22no—
184C2×C4×C61—22no—
185C2×C4×C61—41no—
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—22no—
200C2×Dic61—22no—
201C2×Dic61—42no—
202C2×Dic61—42no—
203C2×Dic61—42no—
204C2×Dic61#9511yescharacteristic
205C2×Dic61#9511yescharacteristic
206C2×Dic61#9914yes—
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—41no—
218C4×D61—41no—
219C4×D61—41no—
220C4×D61—41no—
221C4×D61—41no—
222C4×D61—41no—
223C4×D61—41no—
224C4×D61—41no—
225#92420—44no—
226#7983—611nomaximal, Sylow
227C22×C61—21no—
228C22×C61—21no—
229C22×C61—21no—
230C22×C61—21no—
231C22×C61—21no—
232C22×C61—21no—
233C22×C61—21no—
234C22×C61—44no—
235C22×C61#34212yes—
236C22×C61C2×#9511yescharacteristic
237C22×C61#41712yes—
238C2×D61—24no—
239C2×D61—24no—
240C2×D61—21no—
241C2×D61—21no—
242C2×D61—21no—
243C2×D61—21no—
244C2×D61—21no—
245C2×D61—21no—
246C2×D61—21no—
247C2×D61—21no—
248C2×D61—21no—
249C2×D61—42no—
250C2×D61—42no—
251C2×D61—44no—
252C2×D61—44no—
253C2×D61—44no—
254C2×D61—42no—
255C2×D61—42no—
256C2×D61H(3,ℤ/4)12yes—
257C2×D61#41811yescharacteristic
258C2×D61#41911yescharacteristic
259C2×D61#42812yes—
260#6923—84no—
261C4×C61—21no—
262C4×C61—21no—
263C4×C61—21no—
264C4×C61—21no—
265C4×C61—82no—
266Dic61—21no—
267Dic61—21no—
268Dic61—82no—
269Dic61#34212yes—
270Dic61C2×#9912yes—
271C2×#407—611no—
272#2280—611no—
273C2×#380—611no—
274#1289—614no—
275C2×C61—22no—
276C2×C61—22no—
277C2×C61—41no—
278C2×C61C2×H(3,ℤ/4)11yescharacteristic
279C2×C61#173611yescharacteristic
280C2×C61C2×#34211yescharacteristic
281D61—21no—
282D61—22no—
283D61—21no—
284D61—22no—
285D61—41no—
286C24×C4—611no—
287C22×M16—612no—
288C2×#117—1221no—
289C22×C4⋊C4—1221no—
290C22×C22⋊C4—1221no—
291#407—1221no—
292#407—1221no—
293#407—1221no—
294#407—1221no—
295C2×C22⋊C8—612no—
296C2×C22⋊C8—612no—
297#381—611no—
298#381#692311yescharacteristic, complemented
299#380—612no—
300#380—612no—
301#380—612no—
302#380—1221no—
303#380—1221no—
304#380—1221no—
305#379—1221no—
306C4×C22⋊C4—612no—
307C4×C22⋊C4—1221no—
308C2×#95—612no—
309C61#798311yescharacteristic, complemented, Sylow
310C25—611no—
311C23×C4—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—1222no—
325C23×C4—2444no—
326C23×C4C2×#692311yescharacteristic
327C2×M16—1222no—
328C2×M16—1222no—
329C2×M16—2444no—
330C22×C8—614no—
331#117—2444no—
332C2×C4⋊C4—1222no—
333C2×C4⋊C4—1222no—
334C2×C4⋊C4—1222no—
335C2×C4⋊C4—2444no—
336C2×C22⋊C4—21no—
337C2×C22⋊C4—1222no—
338C2×C22⋊C4—1222no—
339C2×C22⋊C4—1222no—
340C2×C22⋊C4—1222no—
341C2×C22⋊C4—1221no—
342C2×C22⋊C4—2444no—
343C2×C42—1222no—
344C22⋊C8—1222no—
345C22⋊C8—1222no—
346C22⋊C8—1222no—
347C22⋊C8—1222no—
348#95—21no—
349#95—614no—
350#95—612no—
351#95—1222no—
352#95—1221no—
353#95C2×#692312yescomplemented
354C24—611no—
355C24—611no—
356C24—611no—
357C24—611no—
358C24—611no—
359C24—611no—
360C24—1222no—
361C24—1222no—
362C24—2442no—
363C24—2442no—
364C24C22⋊#692311yescharacteristic
365C22×C4—22no—
366C22×C4—42no—
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—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—1224no—
390C22×C4—1224no—
391C22×C4—1224no—
392C22×C4—1224no—
393C22×C4—1222no—
394C22×C4—2442no—
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×C4C4×#692311yescharacteristic
408C22×C4C4×#692311yescharacteristic
409C22×C4C4⋊#692311yescharacteristic
410C22×C4C4⋊#692311yescharacteristic
411C22×C4C22⋊#692311yescharacteristic
412C22×C4C22×#692311yescharacteristic
413M16—2444no—
414M16—2444no—
415C2×C8—1224no—
416C2×C8—2444no—
417C4⋊C4—2444no—
418C4⋊C4—2444no—
419C4⋊C4—2444no—
420C22⋊C4—42no—
421C22⋊C4—2442no—
422C22⋊C4—2442no—
423C22⋊C4—2444no—
424C22⋊C4—2442no—
425C22⋊C4—2444no—
426C22⋊C4—2444no—
427C42—2444no—
428C23—22no—
429C23—22no—
430C23—41no—
431C23—611no—
432C23—611no—
433C23—611no—
434C23—612no—
435C23—612no—
436C23—611no—
437C23—1221no—
438C23—1222no—
439C23—1221no—
440C23—1221no—
441C23—1222no—
442C23—1222no—
443C23—1221no—
444C23—1222no—
445C23—1222no—
446C23—1222no—
447C23—1222no—
448C23—1222no—
449C23—2441no—
450C23—2441no—
451C23—2441no—
452C23—2441no—
453C23—2441no—
454C23—2441no—
455C23—2441no—
456C23—2448no—
457C23—2448no—
458C23(C2×#6923)⋊C411yescharacteristic
459C23(C2×#6923)⋊C411yescharacteristic
460C23C2×C22⋊#692311yescharacteristic
461C2×C4—22no—
462C2×C4—22no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—614no—
471C2×C4—611no—
472C2×C4—611no—
473C2×C4—611no—
474C2×C4—611no—
475C2×C4—1222no—
476C2×C4—1222no—
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—4888no—
489C2×C4—2441no—
490C2×C4—2441no—
491C2×C4—2441no—
492C2×C4—2441no—
493C2×C4—2441no—
494C2×C4—2441no—
495C2×C4—2441no—
496C2×C4—2441no—
497C2×C4—2442no—
498C2×C4—2442no—
499C2×C4—2444no—
500C2×C4—2444no—
501C2×C4—2444no—
502C2×C4—2442no—
503C2×C4(C2×#6923)⋊C411yescharacteristic
504C2×C4(C2×#6923)⋊C411yescharacteristic
505C2×C4C2×C4×#692311yescharacteristic
506C2×C4C2×C4⋊#692311yescharacteristic
507C8—2444no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—21no—
513C22—21no—
514C22—21no—
515C22—44no—
516C22—611no—
517C22—611no—
518C22—612no—
519C22—612no—
520C22—1224no—
521C22—1224no—
522C22—1221no—
523C22—1221no—
524C22—1221no—
525C22—1221no—
526C22—1221no—
527C22—1221no—
528C22—1221no—
529C22—1221no—
530C22—1221no—
531C22—2442no—
532C22—2442no—
533C22—2444no—
534C22—2444no—
535C22—2444no—
536C22—2442no—
537C22—2442no—
538C22#1684063912yes—
539C22C2×(C2×#6923)⋊C411yescharacteristic
540C22#1684075312yes—
541C4—21no—
542C4—21no—
543C4—21no—
544C4—21no—
545C4—82no—
546C4—612no—
547C4—612no—
548C4—1221no—
549C4—1221no—
550C4—4882no—
551C4—4884no—
552C2—22no—
553C2—22no—
554C2—41no—
555C2—1221no—
556C2—1221no—
557C2—1222no—
558C2—1222no—
559C2—2441no—
560C2#2146148911yescharacteristic
561C2#2146150811yescharacteristic
562C2C2×#1684063911yescharacteristic
subgroupG/H
centerC22C2×(C2×#6923)⋊C4
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC61×#381C4
socleC22×C61C2×#95
prime radicalC24×D61D4
cosocleC22×C4×D61C23
hypercenter#381#6923
hypocenterC61#7983
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #381

Complements

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

NH ≅ G/Ntype
3. #21460681C2semidirect
5. C2×D61⋊M16C4semidirect
12. D61⋊(C22⋊C8)C4semidirect
16. #16840704C4semidirect
18. C2×(C2×#6923)⋊C4C4semidirect
21. #16839625C4semidirect
26. #16839609C4semidirect
27. C61×#381C4semidirect
32. C2×D61⋊C8C2×C4semidirect
67. #14519684C2×C4semidirect
71. #95×C61C2×C4semidirect
298. #381#6923semidirect
309. C61#7983semidirect
353. #95C2×#6923semidirect

Maximal subgroups

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

subgroupindex
D61⋊#4072
C2×#168407042
#214606812
#214481992
#798361