Finite Group Databasebeta

← #30596252

Subgroups — #30596252

Order 15616.

1058 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#407C211yesmaximal, characteristic
2C2×C4×C22⋊#6923C211yesmaximal, characteristic
3#21460656C214yesmaximal, complemented
4#407×D61C211yesmaximal, characteristic
5C2×D61⋊M16—21no—
6C22×C22⋊#6923C412yes—
7C22×C4×#6923C412yes—
8#16840734—21no—
9#16840733—21no—
10#16840733C412yescomplemented
11#16840732C412yescomplemented
12D61⋊(C22⋊C8)—21no—
13D61⋊(C22⋊C8)C2212yes—
14C4×C22⋊#6923—21no—
15C4×C22⋊#6923—21no—
16C4×C22⋊#6923—21no—
17C4×C22⋊#6923—21no—
18C2×(C2×#6923)⋊C4C2212yes—
19C23×C4×D61C2211yescharacteristic
20C2×M16×D61—21no—
21#16839726C411yescharacteristic, complemented
22#16839725—21no—
23#16839724—21no—
24#16839724C412yescomplemented
25C22⋊C8×D61—21no—
26C22⋊C8×D61C2212yes—
27C61×#407C411yescharacteristic, complemented
28C23×#6923C2×C414yes—
29C2×#11758213—22no—
30D61⋊M16—44no—
31C2×#11758217—22no—
32C2×D61⋊C8—22no—
33C2×C22⋊#6923—22no—
34C2×C22⋊#6923—22no—
35C2×C22⋊#6923—28no—
36C2×C4×#6923—22no—
37C2×C4×#6923—22no—
38C2×C4×#6923—44no—
39#14519834—22no—
40#14519834—22no—
41C22⋊#92420—22no—
42C22⋊#92420C2×C414yes—
43(C2×#6923)⋊C4—22no—
44(C2×#6923)⋊C4—22no—
45C24×D61C2×C411yescharacteristic
46C23×Dic61C2×C411yescharacteristic
47C22×C4×D61—44no—
48C22×C4×D61C2×C411yescharacteristic
49C22×C4×D61C2×C411yescharacteristic
50C22×C4×D61C2×C411yescharacteristic
51C22×C4×D61D411yescharacteristic
52C22×C4×D61D411yescharacteristic
53C22×C4×D61D411yescharacteristic
54C22×C4×D61D411yescharacteristic
55C22×C4×D61D411yescharacteristic
56C22×C4×D61D411yescharacteristic
57C22×C4×D61Q811yescharacteristic
58C22×C4×D61Q811yescharacteristic
59C22×C4×D61C2311yescharacteristic
60C2×#11758194—21no—
61C2×#11758189—22no—
62M16×D61—44no—
63C2×C8×D61—22no—
64C22⋊#92418—21no—
65C22⋊#92418C2×C412yes—
66#14519689—22no—
67#14519689—22no—
68C23×C4×C61C2×C411yescharacteristic
69C2×M16×C61—21no—
70C22⋊C8×C61—21no—
71C22⋊C8×C61C2×C412yes—
72C24×C61C4211yescharacteristic
73C23×D61—24no—
74C23×D61—42no—
75C23×D61—42no—
76C23×D61C4211yescharacteristic
77C23×D61C22⋊C411yescharacteristic
78C23×D61C22⋊C411yescharacteristic
79C23×D61C4⋊C411yescharacteristic
80C23×D61C4⋊C411yescharacteristic
81C23×D61C22×C411yescharacteristic
82C22×#6923—24no—
83C22×#6923—24no—
84C22×#6923—44no—
85C22×#6923—44no—
86C22×#6923M1618yescomplemented
87C22×C4×C61—42no—
88C22×C4×C61C4211yescharacteristic
89C22×C4×C61C22⋊C411yescharacteristic
90C22×C4×C61C22⋊C411yescharacteristic
91C22×C4×C61C4⋊C411yescharacteristic
92C22×C4×C61C4⋊C411yescharacteristic
93C22×C4×C61C22×C411yescharacteristic
94C22×Dic61—42no—
95C22×Dic61C4211yescharacteristic
96C22×Dic61C22⋊C411yescharacteristic
97C22×Dic61C22⋊C411yescharacteristic
98C22×Dic61C4⋊C411yescharacteristic
99C22×Dic61C4⋊C411yescharacteristic
100C22×Dic61C22×C411yescharacteristic
101C2×C4×D61—24no—
102C2×C4×D61—24no—
103C2×C4×D61—24no—
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—42no—
113C2×C4×D61C22⋊C411yescharacteristic
114C2×C4×D61C22⋊C411yescharacteristic
115C2×C4×D61C22⋊C411yescharacteristic
116C2×C4×D61C22⋊C411yescharacteristic
117C2×C4×D61C22⋊C411yescharacteristic
118C2×C4×D61C22⋊C411yescharacteristic
119C2×C4×D61C4⋊C411yescharacteristic
120C2×C4×D61C4⋊C411yescharacteristic
121C2×C4×D61C4⋊C411yescharacteristic
122C2×C4×D61C4⋊C411yescharacteristic
123C2×C4×D61C4⋊C411yescharacteristic
124C2×C4×D61C4⋊C411yescharacteristic
125C2×C4×D61C2×D411yescharacteristic
126C2×C4×D61C2×D411yescharacteristic
127C2×C4×D61C2×D411yescharacteristic
128C2×C4×D61C2×Q811yescharacteristic
129C22⋊#6923—28no—
130C22⋊#6923—28no—
131#11758217—44no—
132C2×#92420—24no—
133C4×#6923—44no—
134C4×#6923—44no—
135#11758213—44no—
136D61⋊C8—44no—
137M16×C61—42no—
138C2×C8×C61—22no—
139#11758194—42no—
140C2×#92418—22no—
141#11758189—44no—
142C8×D61—44no—
143C23×C61—22no—
144C23×C61—41no—
145C23×C61—41no—
146C23×C61#9511yescharacteristic
147C23×C61#9511yescharacteristic
148C23×C61C2×C4211yescharacteristic
149C22×D61—22no—
150C22×D61—22no—
151C22×D61—22no—
152C22×D61—22no—
153C22×D61—22no—
154C22×D61—22no—
155C22×D61—22no—
156C22×D61—22no—
157C22×D61—22no—
158C22×D61—22no—
159C22×D61—22no—
160C22×D61—41no—
161C22×D61—41no—
162C22×D61—41no—
163C22×D61—41no—
164C22×D61—41no—
165C22×D61—41no—
166C22×D61—48no—
167C22×D61—48no—
168C22×D61#9511yescharacteristic
169C22×D61#9511yescharacteristic
170C22×D61C2×C22⋊C411yescharacteristic
171C22×D61C2×C4⋊C411yescharacteristic
172C22×D61C2×M1614yes—
173C2×#6923—28no—
174C2×#6923—48no—
175C2×#6923—44no—
176C2×#6923—44no—
177C2×#6923—48no—
178C2×C4×C61—22no—
179C2×C4×C61—22no—
180C2×C4×C61—22no—
181C2×C4×C61—41no—
182C2×C4×C61—41no—
183C2×C4×C61—41no—
184C2×C4×C61#9511yescharacteristic
185C2×C4×C61#9511yescharacteristic
186C2×C4×C61C2×C22⋊C411yescharacteristic
187C2×C4×C61C2×C4⋊C411yescharacteristic
188C2×Dic61—22no—
189C2×Dic61—22no—
190C2×Dic61—22no—
191C2×Dic61—41no—
192C2×Dic61—41no—
193C2×Dic61—41no—
194C2×Dic61#9511yescharacteristic
195C2×Dic61#9511yescharacteristic
196C2×Dic61C2×C22⋊C411yescharacteristic
197C2×Dic61C2×C4⋊C411yescharacteristic
198C4×D61—22no—
199C4×D61—22no—
200C4×D61—22no—
201C4×D61—22no—
202C4×D61—22no—
203C4×D61—22no—
204C4×D61—22no—
205C4×D61—22no—
206C4×D61—22no—
207C4×D61—41no—
208C4×D61—41no—
209C4×D61—41no—
210C4×D61—41no—
211C4×D61—41no—
212C4×D61—41no—
213C4×D61#9914yes—
214#92420—44no—
215C8×C61—42no—
216#92418—42no—
217#7911—611nomaximal, Sylow
218C22×C61—21no—
219C22×C61—21no—
220C22×C61—21no—
221C22×C61—21no—
222C22×C61—21no—
223C22×C61—21no—
224C22×C61—21no—
225C22×C61—21no—
226C22×C61—44no—
227C22×C61C2×#9511yescharacteristic
228C22×C61C4×M1612yes—
229C2×D61—21no—
230C2×D61—21no—
231C2×D61—24no—
232C2×D61—24no—
233C2×D61—21no—
234C2×D61—21no—
235C2×D61—21no—
236C2×D61—21no—
237C2×D61—21no—
238C2×D61—21no—
239C2×D61—44no—
240C2×D61—44no—
241C2×D61—44no—
242C2×D61—44no—
243C2×D61—44no—
244C2×D61#40712yes—
245C2×D61C2×#9912yes—
246C2×D61#41312yes—
247C2×D61#42312yes—
248#6923—48no—
249C4×C61—21no—
250C4×C61—21no—
251C4×C61—21no—
252C4×C61#34212yes—
253Dic61—21no—
254Dic61—21no—
255Dic61—21no—
256Dic61#34212yes—
257C2×#407—611no—
258C2×#407—611no—
259C2×C4×C22⋊C4—611no—
260#1280—614no—
261C2×C61—22no—
262C2×C61—41no—
263C2×C61—41no—
264C2×C61#172811yescharacteristic
265C2×C61C2×#34211yescharacteristic
266C2×C61#174211yescharacteristic
267D61—22no—
268D61—41no—
269D61—41no—
270D61#146514yes—
271C24×C4—611no—
272C22×M16—1221no—
273C22×M16—1221no—
274C22×C22⋊C4—612no—
275C22×C42—612no—
276#407—612no—
277#407—612no—
278#407—611no—
279#407—612no—
280#407—1221no—
281#407—1221no—
282#407—1221no—
283#407—1221no—
284#407#692311yescharacteristic, complemented
285C2×C22⋊C8—612no—
286C2×C22⋊C8—612no—
287C2×C22⋊C8—1221no—
288C2×C22⋊C8—1221no—
289C4×C22⋊C4—1221no—
290C4×C22⋊C4—1221no—
291C4×C22⋊C4—1221no—
292C4×C22⋊C4—1221no—
293C2×#95—612no—
294C61#791111yescharacteristic, complemented, Sylow
295C25—611no—
296C23×C4—611no—
297C23×C4—611no—
298C23×C4—611no—
299C23×C4—611no—
300C23×C4—611no—
301C23×C4—611no—
302C23×C4—611no—
303C23×C4—611no—
304C23×C4—611no—
305C23×C4—611no—
306C23×C4—611no—
307C23×C4—611no—
308C23×C4—611no—
309C23×C4—614no—
310C23×C4—2444no—
311C23×C4C2×#692311yescharacteristic
312C2×M16—21no—
313C2×M16—1222no—
314C2×M16—1222no—
315C2×M16—1222no—
316C2×M16—1221no—
317C2×M16—2444no—
318C2×M16—2444no—
319C22×C8—1222no—
320C22×C8—1222no—
321C2×C22⋊C4—1228no—
322C2×C22⋊C4—1222no—
323C2×C22⋊C4—1222no—
324C2×C42—1222no—
325C2×C42—1222no—
326C2×C42—2444no—
327C22⋊C8—21no—
328C22⋊C8—614no—
329C22⋊C8—612no—
330C22⋊C8—1222no—
331C22⋊C8—1222no—
332C22⋊C8—1222no—
333C22⋊C8—1222no—
334C22⋊C8—1222no—
335C22⋊C8—1221no—
336C22⋊C8C2×#692312yes—
337#95—1222no—
338#95—1222no—
339C24—611no—
340C24—611no—
341C24—611no—
342C24—611no—
343C24—611no—
344C24—611no—
345C24—1224no—
346C24—2442no—
347C24—2442no—
348C24C4×#692311yescharacteristic
349C22×C4—42no—
350C22×C4—611no—
351C22×C4—611no—
352C22×C4—611no—
353C22×C4—611no—
354C22×C4—611no—
355C22×C4—611no—
356C22×C4—611no—
357C22×C4—611no—
358C22×C4—611no—
359C22×C4—611no—
360C22×C4—611no—
361C22×C4—611no—
362C22×C4—611no—
363C22×C4—611no—
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—618no—
373C22×C4—1224no—
374C22×C4—1224no—
375C22×C4—1224no—
376C22×C4—1224no—
377C22×C4—1224no—
378C22×C4—2442no—
379C22×C4—2442no—
380C22×C4—2442no—
381C22×C4—2442no—
382C22×C4—2442no—
383C22×C4—2442no—
384C22×C4—2442no—
385C22×C4—2442no—
386C22×C4—2442no—
387C22×C4—2442no—
388C22×C4—2444no—
389C22×C4—2444no—
390C22×C4C4×#692311yescharacteristic
391C22×C4C4⋊#692311yescharacteristic
392C22×C4C4⋊#692311yescharacteristic
393C22×C4C22⋊#692311yescharacteristic
394C22×C4C22⋊#692311yescharacteristic
395C22×C4C22×#692311yescharacteristic
396M16—42no—
397M16—2444no—
398M16—2442no—
399M16—2444no—
400M16—2444no—
401C2×C8—22no—
402C2×C8—1224no—
403C2×C8—1222no—
404C2×C8—2444no—
405C2×C8—2444no—
406C22⋊C4—1228no—
407C22⋊C4—1228no—
408C42—2444no—
409C42—2444no—
410C23—22no—
411C23—41no—
412C23—41no—
413C23—611no—
414C23—614no—
415C23—611no—
416C23—611no—
417C23—611no—
418C23—1222no—
419C23—1222no—
420C23—1222no—
421C23—1222no—
422C23—1222no—
423C23—1222no—
424C23—1222no—
425C23—1222no—
426C23—1222no—
427C23—1222no—
428C23—1222no—
429C23—2441no—
430C23—2441no—
431C23—2441no—
432C23—2441no—
433C23—2441no—
434C23—2441no—
435C23—2448no—
436C23—2448no—
437C23(C2×#6923)⋊C411yescharacteristic
438C23(C2×#6923)⋊C411yescharacteristic
439C23C2×C4×#692311yescharacteristic
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—611no—
447C2×C4—614no—
448C2×C4—611no—
449C2×C4—611no—
450C2×C4—611no—
451C2×C4—1222no—
452C2×C4—1222no—
453C2×C4—1222no—
454C2×C4—1222no—
455C2×C4—1222no—
456C2×C4—1222no—
457C2×C4—1222no—
458C2×C4—1222no—
459C2×C4—1222no—
460C2×C4—1222no—
461C2×C4—1222no—
462C2×C4—1222no—
463C2×C4—1228no—
464C2×C4—2441no—
465C2×C4—2441no—
466C2×C4—2441no—
467C2×C4—2441no—
468C2×C4—2441no—
469C2×C4—2441no—
470C2×C4—2441no—
471C2×C4—2441no—
472C2×C4—2441no—
473C2×C4—2444no—
474C2×C4—2444no—
475C2×C4—2448no—
476C2×C4—2448no—
477C2×C4(C2×#6923)⋊C411yescharacteristic
478C2×C4(C2×#6923)⋊C411yescharacteristic
479C2×C4C2×C22⋊#692311yescharacteristic
480C2×C4C2×C4⋊#692311yescharacteristic
481C8—42no—
482C8—2442no—
483C8—2444no—
484C22—21no—
485C22—21no—
486C22—21no—
487C22—21no—
488C22—21no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—44no—
493C22—612no—
494C22—612no—
495C22—612no—
496C22—612no—
497C22—1224no—
498C22—1224no—
499C22—1221no—
500C22—1221no—
501C22—1221no—
502C22—1221no—
503C22—1221no—
504C22—1221no—
505C22—1221no—
506C22—1221no—
507C22—2444no—
508C22—2444no—
509C22—2444no—
510C22—2444no—
511C22—2444no—
512C22C2×(C2×#6923)⋊C411yescharacteristic
513C22M16×#692312yes—
514C4—21no—
515C4—21no—
516C4—21no—
517C4—612no—
518C4—1221no—
519C4—1221no—
520C4—1221no—
521C4—2448no—
522C4#1684063912yes—
523C2—22no—
524C2—41no—
525C2—41no—
526C2—614no—
527C2—1222no—
528C2—2441no—
529C2—2441no—
530C2#2146148111yescharacteristic
531C2C2×#1684063911yescharacteristic
532C2#2146152311yescharacteristic
subgroupG/H
centerC22C2×(C2×#6923)⋊C4
commutatorC23×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC61×#407C4
socleC22×C61C2×#95
prime radicalC24×D61C2×C4
cosocleC22×C4×D61C23
hypercenter#407#6923
hypocenterC61#7911
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
3. #21460656C2semidirect
10. #16840733C4semidirect
11. #16840732C4semidirect
21. #16839726C4semidirect
24. #16839724C4semidirect
27. C61×#407C4semidirect
86. C22×#6923M16semidirect
284. #407#6923semidirect
294. C61#7911semidirect

Maximal subgroups

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

subgroupindex
D61⋊#4072
C2×C4×C22⋊#69232
#214606562
#407×D612
#791161