Finite Group Databasebeta

← #29570163

Subgroups — #29570163

Order 15616.

906 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839724C211yesmaximal, characteristic
2#407×D61C211yesmaximal, characteristic
3C2×C22⋊C8×D61C211yesmaximal, characteristic
4#21443707C211yesmaximal, characteristic, complemented
5#21443707C211yesmaximal, characteristic, complemented
6#21443706C211yesmaximal, characteristic, complemented
7C61×#1298C211yesmaximal, characteristic, complemented
8C23×C4×D61C2211yescharacteristic
9C22×#11758189—21no—
10C2×M16×D61C412yes—
11C22×C8×D61—21no—
12#16839726C2211yescharacteristic
13#16839725C412yes—
14#16839724—21no—
15#16839724—21no—
16#16839724—21no—
17#16839724—21no—
18#16839724C412yes—
19#16839724C412yes—
20C2×C22⋊#92418C2211yescharacteristic
21C2×C22⋊#92418C2211yescharacteristic
22C2×#14519689—21no—
23C2×#14519689—21no—
24C22⋊C8×D61—21no—
25C22⋊C8×D61—21no—
26C22⋊C8×D61—21no—
27C22⋊C8×D61—21no—
28C22⋊C8×D61C412yes—
29C22⋊C8×D61C412yes—
30C61×#407C2211yescharacteristic
31C2×C22⋊C8×C61C2211yescharacteristic
32C2×C22⋊C8×C61C2211yescharacteristic
33C24×D61Q811yescharacteristic
34C23×Dic61Q811yescharacteristic
35C22×C4×D61—44no—
36C22×C4×D61C2×C411yescharacteristic
37C22×C4×D61C2×C411yescharacteristic
38C22×C4×D61C2×C411yescharacteristic
39C22×C4×D61C2×C411yescharacteristic
40C22×C4×D61C2×C411yescharacteristic
41C22×C4×D61C2×C411yescharacteristic
42C22×C4×D61D411yescharacteristic
43C22×C4×D61D411yescharacteristic
44C22×C4×D61D411yescharacteristic
45C22×C4×D61D411yescharacteristic
46C22×C4×D61D411yescharacteristic
47C22×C4×D61D411yescharacteristic
48C2×#11758194C2×C412yes—
49C2×#11758189—22no—
50C2×#11758189—22no—
51C2×#11758189—22no—
52C2×#11758189—44no—
53M16×D61—44no—
54C22×#92418—21no—
55C22×#92418—21no—
56C2×C8×D61—22no—
57C2×C8×D61—22no—
58C2×C8×D61—22no—
59C2×C8×D61—44no—
60C22⋊#92418—21no—
61C22⋊#92418—21no—
62C22⋊#92418—21no—
63C22⋊#92418—21no—
64C22⋊#92418C2×C412yes—
65C22⋊#92418C2×C412yes—
66#14519689—22no—
67#14519689—22no—
68#14519689—22no—
69#14519689—22no—
70#14519689—22no—
71#14519689—22no—
72C23×C4×C61C2311yescharacteristic
73C2×M16×C61C2×C412yes—
74C22×C8×C61—21no—
75C22×C8×C61—21no—
76C22⋊C8×C61—21no—
77C22⋊C8×C61—21no—
78C22⋊C8×C61—21no—
79C22⋊C8×C61—21no—
80C22⋊C8×C61C2×C412yes—
81C22⋊C8×C61C2×C412yes—
82C24×C61C2×Q811yescharacteristic
83C23×D61—24no—
84C23×D61—42no—
85C23×D61—42no—
86C23×D61C4⋊C411yescharacteristic
87C23×D61C4⋊C411yescharacteristic
88C23×D61C4⋊C411yescharacteristic
89C23×D61C4⋊C411yescharacteristic
90C23×D61C4⋊C411yescharacteristic
91C23×D61C4⋊C411yescharacteristic
92C22×C4×C61—42no—
93C22×C4×C61C22×C411yescharacteristic
94C22×C4×C61C22×C411yescharacteristic
95C22×C4×C61C22×C411yescharacteristic
96C22×C4×C61C2×D411yescharacteristic
97C22×C4×C61C2×D411yescharacteristic
98C22×C4×C61C2×D411yescharacteristic
99C22×Dic61—42no—
100C22×Dic61C4⋊C411yescharacteristic
101C22×Dic61C4⋊C411yescharacteristic
102C22×Dic61C4⋊C411yescharacteristic
103C22×Dic61C4⋊C411yescharacteristic
104C22×Dic61C4⋊C411yescharacteristic
105C22×Dic61C4⋊C411yescharacteristic
106C2×C4×D61—24no—
107C2×C4×D61—24no—
108C2×C4×D61—24no—
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×D61C4211yescharacteristic
121C2×C4×D61C4211yescharacteristic
122C2×C4×D61C22⋊C411yescharacteristic
123C2×C4×D61C22⋊C411yescharacteristic
124C2×C4×D61C22⋊C411yescharacteristic
125C2×C4×D61C22⋊C411yescharacteristic
126C2×C4×D61C22⋊C411yescharacteristic
127C2×C4×D61C22⋊C411yescharacteristic
128C2×C4×D61C22⋊C411yescharacteristic
129C2×C4×D61C22⋊C411yescharacteristic
130C2×C4×D61C22⋊C411yescharacteristic
131C2×C4×D61C22⋊C411yescharacteristic
132C2×C4×D61C22⋊C411yescharacteristic
133C2×C4×D61C22⋊C411yescharacteristic
134M16×C61—42no—
135C2×C8×C61—22no—
136C2×C8×C61—22no—
137C2×C8×C61—22no—
138C2×C8×C61—42no—
139C2×C8×C61—42no—
140#11758194—42no—
141C2×#92418—22no—
142C2×#92418—22no—
143C2×#92418—22no—
144C2×#92418—42no—
145C2×#92418—42no—
146#11758189—44no—
147#11758189—44no—
148#11758189—44no—
149C8×D61—44no—
150C8×D61—44no—
151C8×D61—44no—
152C23×C61—22no—
153C23×C61—22no—
154C23×C61—41no—
155C23×C61C2×C4⋊C411yescharacteristic
156C23×C61C2×C4⋊C411yescharacteristic
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#9511yescharacteristic
179C22×D61#9511yescharacteristic
180C22×D61#10814yes—
181C2×C4×C61—22no—
182C2×C4×C61—22no—
183C2×C4×C61—22no—
184C2×C4×C61—41no—
185C2×C4×C61—41no—
186C2×C4×C61—41no—
187C2×C4×C61C2×C4211yescharacteristic
188C2×C4×C61C2×C22⋊C411yescharacteristic
189C2×C4×C61C2×C22⋊C411yescharacteristic
190C2×C4×C61C2×C22⋊C411yescharacteristic
191C2×Dic61—22no—
192C2×Dic61—22no—
193C2×Dic61—22no—
194C2×Dic61—41no—
195C2×Dic61—41no—
196C2×Dic61—41no—
197C2×Dic61#9511yescharacteristic
198C2×Dic61#9511yescharacteristic
199C2×Dic61#9511yescharacteristic
200C2×Dic61#9511yescharacteristic
201C4×D61—22no—
202C4×D61—22no—
203C4×D61—22no—
204C4×D61—22no—
205C4×D61—22no—
206C4×D61—22no—
207C4×D61—22no—
208C4×D61—22no—
209C4×D61—22no—
210C4×D61—41no—
211C4×D61—41no—
212C4×D61—41no—
213C4×D61—41no—
214C4×D61—41no—
215C4×D61—41no—
216C4×D61#9914yes—
217C8×C61—42no—
218C8×C61—42no—
219C8×C61—42no—
220#92418—42no—
221#92418—42no—
222#92418—42no—
223#8057—611nomaximal, Sylow
224C22×C61—21no—
225C22×C61—21no—
226C22×C61—21no—
227C22×C61—21no—
228C22×C61—21no—
229C22×C61—21no—
230C22×C61—21no—
231C22×C61—44no—
232C22×C61C2×#9511yescharacteristic
233C22×C61C2×#10812yes—
234C22×C61#43012yes—
235C2×D61—28no—
236C2×D61—21no—
237C2×D61—21no—
238C2×D61—21no—
239C2×D61—21no—
240C2×D61—21no—
241C2×D61—21no—
242C2×D61—21no—
243C2×D61—21no—
244C2×D61—21no—
245C2×D61—44no—
246C2×D61—44no—
247C2×D61—44no—
248C2×D61—44no—
249C2×D61—44no—
250C2×D61#34112yes—
251C2×D61#34112yes—
252C2×D61#34212yes—
253C4×C61—21no—
254C4×C61—21no—
255C4×C61—21no—
256C4×C61C2×#9912yes—
257Dic61—21no—
258Dic61—21no—
259Dic61—21no—
260Dic61#34212yes—
261C2×#407—611no—
262C2×#407—611no—
263C22×C22⋊C8—611no—
264#1298—611no—
265#1298—611no—
266#1298—611no—
267#1298D6111yescharacteristic, complemented
268C2×C61—22no—
269C2×C61—22no—
270C2×C61—41no—
271C2×C61C2×#34111yescharacteristic
272C2×C61#173811yescharacteristic
273C2×C61C2×#34211yescharacteristic
274D61—22no—
275D61—22no—
276D61—22no—
277D61—41no—
278C24×C4—611no—
279C22×M16—612no—
280C22×M16—1221no—
281C23×C8—1221no—
282#407—612no—
283#407—612no—
284#407—611no—
285#407—612no—
286#407—1221no—
287#407—1221no—
288#407—1221no—
289#407—1221no—
290#407C2×D6111yescharacteristic
291C2×C22⋊C8—611no—
292C2×C22⋊C8—611no—
293C2×C22⋊C8—612no—
294C2×C22⋊C8—612no—
295C2×C22⋊C8—1221no—
296C2×C22⋊C8—1221no—
297C2×C22⋊C8—1221no—
298C2×C22⋊C8—1221no—
299C2×C22⋊C8—1221no—
300C2×C22⋊C8—1221no—
301C2×C22⋊C8C2×D6111yescharacteristic
302C2×C22⋊C8C2×D6111yescharacteristic
303C61#805711yescharacteristic, complemented, Sylow
304C25—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—611no—
315C23×C4—611no—
316C23×C4—611no—
317C23×C4—611no—
318C23×C4—2444no—
319C23×C4C22×D6111yescharacteristic
320C2×M16—612no—
321C2×M16—1222no—
322C2×M16—1222no—
323C2×M16—1222no—
324C2×M16—2444no—
325C2×M16—2444no—
326C2×M16C4×D6112yes—
327C22×C8—21no—
328C22×C8—21no—
329C22×C8—1222no—
330C22×C8—1222no—
331C22×C8—1222no—
332C22×C8—1221no—
333C22×C8—1221no—
334C22×C8—2444no—
335C22⋊C8—21no—
336C22⋊C8—21no—
337C22⋊C8—21no—
338C22⋊C8—21no—
339C22⋊C8—612no—
340C22⋊C8—612no—
341C22⋊C8—1222no—
342C22⋊C8—1222no—
343C22⋊C8—1222no—
344C22⋊C8—1222no—
345C22⋊C8—1222no—
346C22⋊C8—1222no—
347C22⋊C8—1221no—
348C22⋊C8—1221no—
349C22⋊C8—1221no—
350C22⋊C8—1221no—
351C22⋊C8C4×D6112yes—
352C22⋊C8C4×D6112yes—
353C24—611no—
354C24—611no—
355C24—611no—
356C24—611no—
357C24—611no—
358C24—611no—
359C24—1224no—
360C24—2442no—
361C24—2442no—
362C24Q8×D6111yescharacteristic
363C22×C4—42no—
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—1224no—
387C22×C4—1224no—
388C22×C4—1224no—
389C22×C4—2442no—
390C22×C4—2442no—
391C22×C4—2442no—
392C22×C4—2442no—
393C22×C4—2442no—
394C22×C4—2442no—
395C22×C4—2442no—
396C22×C4—2442no—
397C22×C4—2442no—
398C22×C4—2442no—
399C22×C4C2×C4×D6111yescharacteristic
400C22×C4C2×C4×D6111yescharacteristic
401C22×C4C2×C4×D6111yescharacteristic
402C22×C4D4×D6111yescharacteristic
403C22×C4D4×D6111yescharacteristic
404C22×C4D4×D6111yescharacteristic
405M16—42no—
406M16—2444no—
407M16—2444no—
408M16—2444no—
409M16—2442no—
410C2×C8—22no—
411C2×C8—22no—
412C2×C8—22no—
413C2×C8—42no—
414C2×C8—42no—
415C2×C8—1222no—
416C2×C8—1222no—
417C2×C8—1222no—
418C2×C8—2444no—
419C2×C8—2444no—
420C2×C8—2444no—
421C2×C8—2442no—
422C2×C8—2442no—
423C23—22no—
424C23—22no—
425C23—41no—
426C23—611no—
427C23—611no—
428C23—611no—
429C23—614no—
430C23—611no—
431C23—1222no—
432C23—1222no—
433C23—1222no—
434C23—1222no—
435C23—1222no—
436C23—1222no—
437C23—1222no—
438C23—1222no—
439C23—1222no—
440C23—1222no—
441C23—2441no—
442C23—2441no—
443C23—2441no—
444C23—2441no—
445C23—2441no—
446C23—2441no—
447C23—2441no—
448C23—24416no—
449C23C4⋊C4×D6111yescharacteristic
450C23C4⋊C4×D6111yescharacteristic
451C23C4⋊C4×D6111yescharacteristic
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—22no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—611no—
459C2×C4—614no—
460C2×C4—611no—
461C2×C4—611no—
462C2×C4—611no—
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—1222no—
473C2×C4—1222no—
474C2×C4—1222no—
475C2×C4—2441no—
476C2×C4—2441no—
477C2×C4—2441no—
478C2×C4—2441no—
479C2×C4—2441no—
480C2×C4—2441no—
481C2×C4—2441no—
482C2×C4—2441no—
483C2×C4—2441no—
484C2×C4C42×D6111yescharacteristic
485C2×C4C22⋊C4×D6111yescharacteristic
486C2×C4C22⋊C4×D6111yescharacteristic
487C2×C4C22⋊C4×D6111yescharacteristic
488C8—42no—
489C8—42no—
490C8—42no—
491C8—2442no—
492C8—2442no—
493C8—2442no—
494C22—21no—
495C22—21no—
496C22—21no—
497C22—21no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—44no—
502C22—612no—
503C22—612no—
504C22—612no—
505C22—1228no—
506C22—1221no—
507C22—1221no—
508C22—1221no—
509C22—1221no—
510C22—1221no—
511C22—1221no—
512C22—1221no—
513C22—1221no—
514C22—1221no—
515C22—2444no—
516C22—2444no—
517C22—2444no—
518C22—2444no—
519C22—2444no—
520C22#95×D6111yescharacteristic
521C22#108×D6112yes—
522C22#1683980912yes—
523C4—21no—
524C4—21no—
525C4—21no—
526C4—612no—
527C4—1221no—
528C4—1221no—
529C4—1221no—
530C4#99×D6112yes—
531C2—22no—
532C2—22no—
533C2—41no—
534C2—1222no—
535C2—1222no—
536C2—1222no—
537C2—2441no—
538C2#341×D6111yescharacteristic
539C2#2144554411yescharacteristic
540C2#342×D6111yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D61
commutatorC2×C4×C61C2×C42
FrattiniC23×C4C22×D61
FittingC61×#1298C2
socleC22×C61C2×#95
prime radicalC24×D61Q8
cosocleC23×C4×C61C23
hypercenter#1298D61
hypocenterC61#8057
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1298

Complements

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

NH ≅ G/Ntype
4. #21443707C2semidirect
5. #21443707C2semidirect
6. #21443706C2semidirect
7. C61×#1298C2semidirect
267. #1298D61semidirect
303. C61#8057semidirect

Maximal subgroups

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

subgroupindex
C2×#168397242
#407×D612
C2×C22⋊C8×D612
#214437072
#214437062
C61×#12982
#805761