Finite Group Databasebeta

← #30596978

Subgroups — #30596978

Order 15616.

906 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#407C211yesmaximal, characteristic
2C2×D61⋊(C22⋊C8)C211yesmaximal, characteristic
3#21460701C214yesmaximal, complemented
4C2×#16839725C211yesmaximal, characteristic
5C2×D61⋊M16—21no—
6C22×D61⋊C8—21no—
7#16840734C412yes—
8#16840733—21no—
9#16840733C412yes—
10#16840732—21no—
11C2×#14519834C412yes—
12D61⋊(C22⋊C8)—21no—
13D61⋊(C22⋊C8)—21no—
14D61⋊(C22⋊C8)—21no—
15D61⋊(C22⋊C8)C412yes—
16D61⋊(C22⋊C8)C2212yes—
17D61⋊(C22⋊C8)C2212yes—
18C2×C22⋊#92420—21no—
19C23×C4×D61C2211yescharacteristic
20C22×#11758194C411yescharacteristic
21#16839725—21no—
22#16839725—21no—
23#16839725C412yes—
24#16839725C2212yes—
25C2×#14519689—21no—
26C2×#14519689—21no—
27C22×M16×C61C411yescharacteristic
28C2×#11758213—22no—
29D61⋊M16—42no—
30D61⋊M16—42no—
31C2×#11758217—22no—
32C2×D61⋊C8—22no—
33C2×D61⋊C8—22no—
34C2×D61⋊C8—22no—
35C2×D61⋊C8—42no—
36C2×D61⋊C8—42no—
37C22×#92420—22no—
38#14519834—22no—
39#14519834—22no—
40#14519834C2×C414yes—
41#14519834C2×C414yes—
42C22⋊#92420—22no—
43C22⋊#92420—22no—
44C22⋊#92420—22no—
45C22⋊#92420—22no—
46C24×D61Q811yescharacteristic
47C23×Dic61D411yescharacteristic
48C22×C4×D61—42no—
49C22×C4×D61—42no—
50C22×C4×D61C2×C411yescharacteristic
51C22×C4×D61C2×C411yescharacteristic
52C22×C4×D61C2×C411yescharacteristic
53C22×C4×D61C2×C411yescharacteristic
54C22×C4×D61C2×C411yescharacteristic
55C22×C4×D61D411yescharacteristic
56C22×C4×D61D411yescharacteristic
57C22×C4×D61D411yescharacteristic
58C22×C4×D61D411yescharacteristic
59C22×C4×D61D411yescharacteristic
60C22×C4×D61Q811yescharacteristic
61C22×C4×D61C2311yescharacteristic
62C2×#11758194—21no—
63C2×#11758194—42no—
64C2×#11758194C2×C412yes—
65C22×#92418—21no—
66#14519689—22no—
67#14519689—22no—
68#14519689—22no—
69#14519689—22no—
70C23×C4×C61C2×C411yescharacteristic
71C2×M16×C61—21no—
72C2×M16×C61—42no—
73C2×M16×C61C2×C412yes—
74C22×C8×C61—21no—
75C24×C61C4⋊C411yescharacteristic
76C23×D61—24no—
77C23×D61—42no—
78C23×D61—42no—
79C23×D61C4⋊C411yescharacteristic
80C23×D61C4⋊C411yescharacteristic
81C23×D61C4⋊C411yescharacteristic
82C23×D61C4⋊C411yescharacteristic
83C23×D61C4⋊C411yescharacteristic
84C23×D61C2×Q811yescharacteristic
85C22×C4×C61—22no—
86C22×C4×C61—22no—
87C22×C4×C61C4211yescharacteristic
88C22×C4×C61C4211yescharacteristic
89C22×C4×C61C22⋊C411yescharacteristic
90C22×C4×C61C22⋊C411yescharacteristic
91C22×C4×C61C4⋊C411yescharacteristic
92C22×C4×C61C22×C411yescharacteristic
93C22×Dic61—42no—
94C22×Dic61C22⋊C411yescharacteristic
95C22×Dic61C22⋊C411yescharacteristic
96C22×Dic61C22⋊C411yescharacteristic
97C22×Dic61C22⋊C411yescharacteristic
98C22×Dic61C4⋊C411yescharacteristic
99C22×Dic61C2×D411yescharacteristic
100C2×C4×D61—22no—
101C2×C4×D61—22no—
102C2×C4×D61—22no—
103C2×C4×D61—22no—
104C2×C4×D61—42no—
105C2×C4×D61—42no—
106C2×C4×D61—41no—
107C2×C4×D61—41no—
108C2×C4×D61—42no—
109C2×C4×D61—41no—
110C2×C4×D61—41no—
111C2×C4×D61—41no—
112C2×C4×D61—41no—
113C2×C4×D61—42no—
114C2×C4×D61—41no—
115C2×C4×D61—41no—
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×D61C22⋊C411yescharacteristic
125C2×C4×D61C22⋊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×D411yescharacteristic
134#11758217—44no—
135C2×#92420—24no—
136C2×#92420—24no—
137C2×#92420—44no—
138#11758213—44no—
139D61⋊C8—44no—
140D61⋊C8—42no—
141D61⋊C8—42no—
142D61⋊C8—42no—
143D61⋊C8—42no—
144M16×C61—42no—
145M16×C61—42no—
146C2×C8×C61—22no—
147C2×C8×C61—42no—
148#11758194—42no—
149#11758194—42no—
150C2×#92418—22no—
151C2×#92418—42no—
152C23×C61—22no—
153C23×C61—22no—
154C23×C61—41no—
155C23×C61#9511yescharacteristic
156C23×C61#9511yescharacteristic
157C23×C61C2×C4⋊C411yescharacteristic
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—22no—
167C22×D61—22no—
168C22×D61—41no—
169C22×D61—41no—
170C22×D61—41no—
171C22×D61—41no—
172C22×D61—41no—
173C22×D61—41no—
174C22×D61—41no—
175C22×D61—416no—
176C22×D61#9511yescharacteristic
177C22×D61#9511yescharacteristic
178C22×D61#10814yes—
179C22×D61C2×C4⋊C411yescharacteristic
180C22×D61C2×C4⋊C411yescharacteristic
181C2×C4×C61—22no—
182C2×C4×C61—22no—
183C2×C4×C61—22no—
184C2×C4×C61—21no—
185C2×C4×C61—21no—
186C2×C4×C61—21no—
187C2×C4×C61—21no—
188C2×C4×C61#9511yescharacteristic
189C2×C4×C61#9511yescharacteristic
190C2×C4×C61#9912yes—
191C2×C4×C61#9912yes—
192C2×C4×C61C2×C4211yescharacteristic
193C2×C4×C61C2×C22⋊C411yescharacteristic
194C2×Dic61—22no—
195C2×Dic61—22no—
196C2×Dic61—41no—
197C2×Dic61—41no—
198C2×Dic61—41no—
199C2×Dic61—41no—
200C2×Dic61#9511yescharacteristic
201C2×Dic61#9511yescharacteristic
202C2×Dic61C2×C22⋊C411yescharacteristic
203C2×Dic61C2×C22⋊C411yescharacteristic
204C4×D61—22no—
205C4×D61—22no—
206C4×D61—22no—
207C4×D61—22no—
208C4×D61—21no—
209C4×D61—21no—
210C4×D61—21no—
211C4×D61—21no—
212C4×D61—21no—
213C4×D61—21no—
214C4×D61—21no—
215C4×D61—21no—
216C4×D61—41no—
217C4×D61—41no—
218C4×D61—41no—
219C4×D61—41no—
220C4×D61—41no—
221C4×D61—41no—
222C4×D61—41no—
223C4×D61—41no—
224#92420—44no—
225#92420—44no—
226C8×C61—42no—
227#92418—42no—
228#8057—611nomaximal, Sylow
229C22×C61—21no—
230C22×C61—21no—
231C22×C61—21no—
232C22×C61—21no—
233C22×C61—21no—
234C22×C61—21no—
235C22×C61—21no—
236C22×C61—44no—
237C22×C61#34112yes—
238C22×C61#34212yes—
239C22×C61C2×#9511yescharacteristic
240C2×D61—28no—
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—21no—
250C2×D61—44no—
251C2×D61—44no—
252C2×D61—44no—
253C2×D61—44no—
254C2×D61—44no—
255C2×D61#34112yes—
256C2×D61C2×#10812yes—
257C2×D61#43012yes—
258C4×C61—21no—
259C4×C61—21no—
260C4×C61#34212yes—
261C4×C61C2×#9911yescharacteristic
262C4×C61C2×#9911yescharacteristic
263Dic61—21no—
264Dic61—21no—
265Dic61—21no—
266Dic61—21no—
267C2×#407—611no—
268C2×#407—611no—
269C22×C22⋊C8—611no—
270#1298—614no—
271C2×C61—22no—
272C2×C61—22no—
273C2×C61—41no—
274C2×C61C2×#34111yescharacteristic
275C2×C61#173811yescharacteristic
276C2×C61C2×#34211yescharacteristic
277D61—22no—
278D61—22no—
279D61—22no—
280D61—41no—
281C24×C4—611no—
282C22×M16—611no—
283C22×M16—1221no—
284C22×M16#692311yescharacteristic
285C23×C8—1221no—
286#407—612no—
287#407—612no—
288#407—612no—
289#407—612no—
290#407—1221no—
291#407—1221no—
292#407—1221no—
293#407—1221no—
294C2×C22⋊C8—612no—
295C2×C22⋊C8—612no—
296C2×C22⋊C8—612no—
297C2×C22⋊C8—612no—
298C2×C22⋊C8—1221no—
299C2×C22⋊C8—1221no—
300C2×C22⋊C8—1221no—
301C2×C22⋊C8—1221no—
302C2×C22⋊C8—1221no—
303C2×C22⋊C8—1221no—
304C61#805711yescharacteristic, complemented, Sylow
305C25—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—611no—
315C23×C4—611no—
316C23×C4—611no—
317C23×C4—611no—
318C23×C4—611no—
319C23×C4—2442no—
320C23×C4—2442no—
321C23×C4C2×#692311yescharacteristic
322C2×M16—21no—
323C2×M16—42no—
324C2×M16—612no—
325C2×M16—1222no—
326C2×M16—1222no—
327C2×M16—1221no—
328C2×M16—2442no—
329C2×M16—2442no—
330C2×M16—2442no—
331C2×M16C2×#692312yes—
332C22×C8—21no—
333C22×C8—1222no—
334C22×C8—1222no—
335C22×C8—1222no—
336C22×C8—1222no—
337C22×C8—1221no—
338C22×C8—2442no—
339C22×C8—2442no—
340C22⋊C8—614no—
341C22⋊C8—614no—
342C22⋊C8—1222no—
343C22⋊C8—1222no—
344C22⋊C8—1222no—
345C22⋊C8—1222no—
346C22⋊C8—1222no—
347C22⋊C8—1222no—
348C22⋊C8—1222no—
349C22⋊C8—1222no—
350C22⋊C8—1222no—
351C22⋊C8—1222no—
352C24—611no—
353C24—611no—
354C24—611no—
355C24—611no—
356C24—611no—
357C24—611no—
358C24—1224no—
359C24—2442no—
360C24—2442no—
361C24C4⋊#692311yescharacteristic
362C22×C4—22no—
363C22×C4—22no—
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—611no—
379C22×C4—611no—
380C22×C4—611no—
381C22×C4—611no—
382C22×C4—611no—
383C22×C4—611no—
384C22×C4—611no—
385C22×C4—611no—
386C22×C4—1222no—
387C22×C4—1222no—
388C22×C4—1222no—
389C22×C4—1222no—
390C22×C4—2441no—
391C22×C4—2441no—
392C22×C4—2441no—
393C22×C4—2441no—
394C22×C4—2441no—
395C22×C4—2441no—
396C22×C4—2441no—
397C22×C4—2441no—
398C22×C4—2442no—
399C22×C4—2442no—
400C22×C4—2442no—
401C22×C4—2442no—
402C22×C4—2442no—
403C22×C4—2442no—
404C22×C4—2442no—
405C22×C4C4×#692311yescharacteristic
406C22×C4C4×#692311yescharacteristic
407C22×C4C4⋊#692311yescharacteristic
408C22×C4C22⋊#692311yescharacteristic
409C22×C4C22⋊#692311yescharacteristic
410C22×C4C22×#692311yescharacteristic
411M16—42no—
412M16—42no—
413M16—2444no—
414M16—2444no—
415M16—2442no—
416M16—2442no—
417C2×C8—22no—
418C2×C8—42no—
419C2×C8—1224no—
420C2×C8—1224no—
421C2×C8—1222no—
422C2×C8—2442no—
423C2×C8—2442no—
424C2×C8—2442no—
425C2×C8—2444no—
426C2×C8—2444no—
427C2×C8—2442no—
428C2×C8—2442no—
429C23—22no—
430C23—22no—
431C23—41no—
432C23—611no—
433C23—611no—
434C23—611no—
435C23—614no—
436C23—611no—
437C23—1222no—
438C23—1222no—
439C23—1222no—
440C23—1222no—
441C23—1222no—
442C23—1222no—
443C23—1222no—
444C23—1222no—
445C23—1222no—
446C23—1222no—
447C23—2441no—
448C23—2441no—
449C23—2441no—
450C23—2441no—
451C23—2441no—
452C23—2441no—
453C23—2441no—
454C23—24416no—
455C23(C2×#6923)⋊C411yescharacteristic
456C23(C2×#6923)⋊C411yescharacteristic
457C23C2×C4⋊#692311yescharacteristic
458C2×C4—22no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—611no—
466C2×C4—611no—
467C2×C4—611no—
468C2×C4—611no—
469C2×C4—1222no—
470C2×C4—1222no—
471C2×C4—1221no—
472C2×C4—1221no—
473C2×C4—1221no—
474C2×C4—1221no—
475C2×C4—1221no—
476C2×C4—1221no—
477C2×C4—1221no—
478C2×C4—1221no—
479C2×C4—1222no—
480C2×C4—1222no—
481C2×C4—1222no—
482C2×C4—1222no—
483C2×C4—2441no—
484C2×C4—2441no—
485C2×C4—2441no—
486C2×C4—2441no—
487C2×C4—2441no—
488C2×C4—2441no—
489C2×C4—2441no—
490C2×C4—2441no—
491C2×C4—2441no—
492C2×C4—2441no—
493C2×C4—2441no—
494C2×C4—2441no—
495C2×C4(C2×#6923)⋊C411yescharacteristic
496C2×C4(C2×#6923)⋊C411yescharacteristic
497C2×C4#1451983512yes—
498C2×C4#1451983612yes—
499C2×C4C2×C4×#692311yescharacteristic
500C2×C4C2×C22⋊#692311yescharacteristic
501C8—42no—
502C8—2444no—
503C8—2444no—
504C8—2442no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—44no—
513C22—612no—
514C22—612no—
515C22—612no—
516C22—1228no—
517C22—1221no—
518C22—1221no—
519C22—1221no—
520C22—1221no—
521C22—1221no—
522C22—1221no—
523C22—1221no—
524C22—1221no—
525C22—1221no—
526C22—2444no—
527C22—2444no—
528C22—2444no—
529C22—2444no—
530C22—2444no—
531C22#1684063712yes—
532C22#1684064012yes—
533C22C2×(C2×#6923)⋊C411yescharacteristic
534C4—21no—
535C4—21no—
536C4—1221no—
537C4—1221no—
538C4—1221no—
539C4—1221no—
540C4#1684064012yes—
541C4C2×#1451983511yescharacteristic
542C4C2×#1451983611yescharacteristic
543C2—22no—
544C2—22no—
545C2—41no—
546C2—1222no—
547C2—1222no—
548C2—1222no—
549C2—2441no—
550C2C2×#1684063711yescharacteristic
551C2#2146151211yescharacteristic
552C2C2×#1684064011yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC22×M16×C61C4
socleC22×C61C2×#95
prime radicalC24×D61Q8
cosocleC22×C4×D61C23
hypercenterC22×M16#6923
hypocenterC61#8057
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×M16

Complements

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

NH ≅ G/Ntype
3. #21460701C2semidirect
304. C61#8057semidirect

Maximal subgroups

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

subgroupindex
D61⋊#4072
C2×D61⋊(C22⋊C8)2
#214607012
C2×#168397252
#805761