Finite Group Databasebeta

← #29576318

Subgroups — #29576318

Order 15616.

686 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839924C211yesmaximal, characteristic
2#21454268C211yesmaximal, characteristic
3#21444338C211yesmaximal, characteristic, complemented
4#21444184C211yesmaximal, characteristic, complemented
5#21443695C211yesmaximal, characteristic, complemented
6#21443667C211yesmaximal, characteristic, complemented
7C61×#1789C211yesmaximal, characteristic
8C22×#11758202C411yescharacteristic, complemented
9C22×#11758200C411yescharacteristic, complemented
10C2×#14519784—21no—
11C2×#14519756C2211yescharacteristic
12#16839924—21no—
13#16839924—21no—
14#16839924—21no—
15#16839924—21no—
16C2×#14519701C411yescharacteristic, complemented
17C2×#14519698C411yescharacteristic, complemented
18#16839729—22no—
19#16839729—21no—
20#16839726—21no—
21#16839726C2211yescharacteristic
22C2×C22⋊#92418—21no—
23C2×C22⋊#92418C2211yescharacteristic
24C2×C22⋊#92418C2211yescharacteristic
25#16839498—22no—
26#16839487—21no—
27#16839487—21no—
28C22×#41×C61C2211yescharacteristic
29C2×#104×C61—21no—
30C2×#104×C61—21no—
31C61×#407C2211yescharacteristic
32C4×C22⋊C4×C61C2211yescharacteristic
33C22×Dic122C2×C411yescharacteristic
34C2×#11758202—21no—
35C2×#11758202—21no—
36C2×#11758202—42no—
37C2×#11758200—21no—
38C2×#11758200—21no—
39C2×#11758200—42no—
40#14519784—42no—
41#14519784—42no—
42C2×#11758194—22no—
43C2×#11758194—21no—
44C22×#92418—22no—
45C22×#92418—21no—
46C22×#92418C2×C411yescharacteristic
47C22×#92418C2×C411yescharacteristic
48#14519756—21no—
49#14519756—21no—
50#14519756—21no—
51#14519756—21no—
52C2×C4⋊Dic61C2×C411yescharacteristic
53C2×#11758196—21no—
54C2×C22⋊Dic61—21no—
55#14519701—21no—
56#14519701—21no—
57#14519698—21no—
58#14519698—21no—
59C22⋊#92418—22no—
60C22⋊#92418—22no—
61C22⋊#92418—21no—
62C22⋊#92418—21no—
63C22⋊#92418—21no—
64C22⋊#92418—21no—
65C22⋊#92418D411yescharacteristic
66C22⋊#92418D411yescharacteristic
67C22⋊#92418D412yes—
68C2×#41×C61—21no—
69C2×#41×C61—21no—
70C2×#41×C61—42no—
71C2×#41×C61—42no—
72C2×#41×C61D411yescharacteristic
73C2×#41×C61D411yescharacteristic
74C2×#41×C61D411yescharacteristic
75C2×#41×C61D411yescharacteristic
76C22×Q8×C61C2×C411yescharacteristic
77C22×D4×C61—21no—
78C22×D4×C61C2×C411yescharacteristic
79C23×C4×C61—21no—
80C23×C4×C61C2311yescharacteristic
81C2×M16×C61—21no—
82C2×C22⋊C4×C61—21no—
83C2×C42×C61—21no—
84#104×C61—42no—
85#104×C61—42no—
86C22⋊C8×C61—21no—
87C22⋊C8×C61—21no—
88#95×C61—21no—
89C24×C61—21no—
90C24×C61#4111yescharacteristic
91#41×C61—22no—
92#41×C61—22no—
93#41×C61—22no—
94#41×C61—22no—
95#41×C61—41no—
96#41×C61—41no—
97#41×C61—41no—
98#41×C61—41no—
99#41×C61—44no—
100#41×C61—44no—
101C2×Q8×C61—21no—
102C2×Q8×C61—22no—
103C2×Q8×C61—41no—
104C2×Q8×C61C22⋊C411yescharacteristic
105C2×Q8×C61C22⋊C411yescharacteristic
106C2×D4×C61—21no—
107C2×D4×C61—22no—
108C2×D4×C61—21no—
109C2×D4×C61—21no—
110C2×D4×C61—21no—
111C2×D4×C61—21no—
112C2×D4×C61—41no—
113C2×D4×C61—44no—
114C2×D4×C61C22⋊C411yescharacteristic
115C2×D4×C61C22⋊C411yescharacteristic
116C22×C4×C61—21no—
117C22×C4×C61—21no—
118C22×C4×C61—21no—
119C22×C4×C61—21no—
120C22×C4×C61—21no—
121C22×C4×C61—41no—
122C22×C4×C61—41no—
123C22×C4×C61—44no—
124C22×C4×C61—41no—
125C22×C4×C61C22×C411yescharacteristic
126C22×C4×C61C2×D411yescharacteristic
127C22×C4×C61C2×D411yescharacteristic
128C22×C4×C61C2×D411yescharacteristic
129C22×C4×C61C2×D411yescharacteristic
130C22×C4×C61#4111yescharacteristic
131C22×Dic61—21no—
132C22×Dic61—21no—
133C2×Dic122—21no—
134C2×Dic122—21no—
135C2×Dic122—41no—
136C2×Dic122—41no—
137M16×C61—41no—
138M16×C61—41no—
139C2×C8×C61—41no—
140C22⋊C4×C61—22no—
141C22⋊C4×C61—41no—
142C42×C61—41no—
143C42×C61—41no—
144C22⋊Dic61—41no—
145C22⋊Dic61—41no—
146#11758202—42no—
147#11758202—42no—
148#11758200—42no—
149#11758200—42no—
150C4⋊Dic61—21no—
151C4⋊Dic61—21no—
152#11758196—41no—
153#11758196—41no—
154#11758194—44no—
155#11758194—41no—
156#11758194—41no—
157C2×#92418—21no—
158C2×#92418—21no—
159C2×#92418—21no—
160C2×#92418—22no—
161C2×#92418—21no—
162C2×#92418—44no—
163C2×#92418—41no—
164C2×#92418—41no—
165C2×#92418—41no—
166C2×#92418—41no—
167C23×C61—21no—
168C23×C61—21no—
169C23×C61—21no—
170C23×C61—21no—
171C23×C61—41no—
172C23×C61—41no—
173C23×C61—42no—
174C23×C61—41no—
175C23×C61—41no—
176C23×C61—81no—
177C23×C61C4×D411yescharacteristic
178C23×C61#12111yescharacteristic
179C23×C61#12311yescharacteristic
180Q8×C61—21no—
181Q8×C61—21no—
182Q8×C61—21no—
183Q8×C61—42no—
184Q8×C61#9912yes—
185D4×C61—24no—
186D4×C61—21no—
187D4×C61—21no—
188D4×C61—21no—
189D4×C61—42no—
190D4×C61—42no—
191D4×C61—42no—
192D4×C61—42no—
193D4×C61#9912yes—
194C2×C4×C61—24no—
195C2×C4×C61—21no—
196C2×C4×C61—21no—
197C2×C4×C61—21no—
198C2×C4×C61—21no—
199C2×C4×C61—21no—
200C2×C4×C61—21no—
201C2×C4×C61—21no—
202C2×C4×C61—21no—
203C2×C4×C61—41no—
204C2×C4×C61—41no—
205C2×C4×C61—41no—
206C2×C4×C61—42no—
207C2×C4×C61—42no—
208C2×C4×C61—42no—
209C2×C4×C61—42no—
210C2×C4×C61—42no—
211C2×C4×C61—81no—
212C2×C4×C61—81no—
213C2×C4×C61C2×C22⋊C411yescharacteristic
214C2×C4×C61C4×D411yescharacteristic
215C2×C4×C61#12011yescharacteristic
216C2×C4×C61#12111yescharacteristic
217C2×Dic61—41no—
218C2×Dic61—41no—
219C2×Dic61—41no—
220C2×Dic61—41no—
221C2×Dic61—81no—
222Dic122—41no—
223Dic122—41no—
224Dic122—81no—
225C8×C61—81no—
226#92418—41no—
227#92418—42no—
228#92418—41no—
229#92418—41no—
230#92418—41no—
231#9239—611nomaximal, Sylow
232C22×C61—21no—
233C22×C61—21no—
234C22×C61—21no—
235C22×C61—21no—
236C22×C61—21no—
237C22×C61—21no—
238C22×C61—22no—
239C22×C61—21no—
240C22×C61—21no—
241C22×C61—41no—
242C22×C61—41no—
243C22×C61—41no—
244C22×C61—41no—
245C22×C61—41no—
246C22×C61—81no—
247C22×C61—81no—
248C22×C61—82no—
249C22×C61—82no—
250C22×C61#38611yescharacteristic
251C22×C61#44311yescharacteristic
252C22×C61#44411yescharacteristic
253C4×C61—21no—
254C4×C61—21no—
255C4×C61—21no—
256C4×C61—22no—
257C4×C61—41no—
258C4×C61—82no—
259C4×C61C2×#9911yescharacteristic
260C4×C61C2×#9911yescharacteristic
261Dic61—81no—
262Dic61—81no—
263C2×#452—611no—
264#2880—611no—
265#1789D6111yescharacteristic
266#1508—611no—
267#1472—611no—
268#1293—611no—
269#1282—611no—
270C2×C61—21no—
271C2×C61—21no—
272C2×C61—41no—
273C2×C61—41no—
274C2×C61—42no—
275C2×C61—81no—
276C2×C61#187611yescharacteristic
277C2×C61#189811yescharacteristic
278C2×C61#190211yescharacteristic
279C22×#41C2×D6111yescharacteristic
280C22×Q16—611no—
281C22×SD16—611no—
282C2×#131—1221no—
283C2×C22⋊Q8—611no—
284#452—1221no—
285#452—1221no—
286#452—1221no—
287#452—1221no—
288C2×#104—21no—
289C2×#104—21no—
290C2×#103—611no—
291C2×#102—611no—
292#408—1222no—
293#408—1221no—
294#407—611no—
295#407—1221no—
296#407C2×D6111yescharacteristic
297C2×C22⋊C8—611no—
298C2×C22⋊C8—611no—
299C2×C22⋊C8—1221no—
300C4×C22⋊C4C2×D6111yescharacteristic
301#328—1222no—
302#324—1221no—
303#324—1221no—
304C61#923911yescharacteristic, complemented, Sylow
305C2×#41—21no—
306C2×#41—21no—
307C2×#41—42no—
308C2×#41—42no—
309C2×#41D24411yescharacteristic
310C2×#41D24411yescharacteristic
311C2×#41C22⋊D6111yescharacteristic
312C2×#41C22⋊D6111yescharacteristic
313C22×Q8—611no—
314C22×Q8C4×D6111yescharacteristic
315C22×D4—21no—
316C22×D4C4×D6111yescharacteristic
317C23×C4—21no—
318C23×C4C22×D6111yescharacteristic
319C2×Q16—1221no—
320C2×Q16—1221no—
321C2×Q16—2442no—
322C2×SD16—1221no—
323C2×SD16—1221no—
324C2×SD16—2442no—
325#131—2442no—
326#131—2442no—
327C2×M16—21no—
328C2×M16—1222no—
329C2×M16—1221no—
330C22×C8—611no—
331C22×C8—611no—
332C22×C8—1222no—
333C22×C8—1221no—
334C22⋊Q8—1221no—
335C22⋊Q8—1221no—
336C22⋊Q8—1221no—
337C22⋊Q8—1221no—
338C2×C4⋊C4—611no—
339C2×C4⋊C4—1221no—
340C2×C22⋊C4—21no—
341C2×C22⋊C4—1221no—
342C2×C42—21no—
343#104—42no—
344#104—42no—
345#103—1221no—
346#103—1221no—
347#102—1221no—
348#102—1221no—
349C22⋊C8—21no—
350C22⋊C8—21no—
351C22⋊C8—611no—
352C22⋊C8—611no—
353C22⋊C8—612no—
354C22⋊C8—1222no—
355C22⋊C8—1222no—
356C22⋊C8—1221no—
357C22⋊C8—1221no—
358C22⋊C8—1221no—
359C22⋊C8—1221no—
360#95—21no—
361C24—21no—
362C24#1175822411yescharacteristic
363#41—22no—
364#41—22no—
365#41—22no—
366#41—22no—
367#41—41no—
368#41—41no—
369#41—41no—
370#41—41no—
371#41—44no—
372#41—44no—
373C2×Q8—21no—
374C2×Q8—22no—
375C2×Q8—41no—
376C2×Q8—1221no—
377C2×Q8—1221no—
378C2×Q8—2441no—
379C2×Q8—2441no—
380C2×Q8#1175819811yescharacteristic
381C2×Q8#1175819811yescharacteristic
382C2×D4—21no—
383C2×D4—22no—
384C2×D4—21no—
385C2×D4—21no—
386C2×D4—21no—
387C2×D4—21no—
388C2×D4—41no—
389C2×D4—44no—
390C2×D4#1175819811yescharacteristic
391C2×D4#1175819811yescharacteristic
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—41no—
398C22×C4—41no—
399C22×C4—44no—
400C22×C4—41no—
401C22×C4—1221no—
402C22×C4—1221no—
403C22×C4C2×C4×D6111yescharacteristic
404C22×C4C2×D24411yescharacteristic
405C22×C4D4×D6111yescharacteristic
406C22×C4D4×D6111yescharacteristic
407C22×C4#1175822411yescharacteristic
408C22×C4C2×C22⋊D6111yescharacteristic
409Q16—2442no—
410Q16—2442no—
411SD16—2442no—
412SD16—2442no—
413M16—41no—
414M16—41no—
415M16—2444no—
416M16—2441no—
417M16—2441no—
418C2×C8—41no—
419C2×C8—1221no—
420C2×C8—1221no—
421C2×C8—1221no—
422C2×C8—1221no—
423C2×C8—1222no—
424C2×C8—2444no—
425C2×C8—2441no—
426C2×C8—2441no—
427C2×C8—2441no—
428C2×C8—2441no—
429C4⋊C4—1221no—
430C4⋊C4—1221no—
431C4⋊C4—2441no—
432C4⋊C4—2441no—
433C22⋊C4—22no—
434C22⋊C4—41no—
435C22⋊C4—2441no—
436C22⋊C4—2441no—
437C42—41no—
438C42—41no—
439C23—21no—
440C23—21no—
441C23—21no—
442C23—21no—
443C23—41no—
444C23—41no—
445C23—42no—
446C23—41no—
447C23—41no—
448C23—81no—
449C23#1451973711yescharacteristic
450C23#1451974911yescharacteristic
451C23#1451976111yescharacteristic
452Q8—21no—
453Q8—21no—
454Q8—21no—
455Q8—42no—
456Q8—4881no—
457Q8—2441no—
458Q8—2441no—
459Q8#1451969112yes—
460D4—24no—
461D4—21no—
462D4—21no—
463D4—21no—
464D4—42no—
465D4—42no—
466D4—42no—
467D4—42no—
468D4#1451969112yes—
469C2×C4—24no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—42no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—42no—
485C2×C4—42no—
486C2×C4—81no—
487C2×C4—81no—
488C2×C4—4881no—
489C2×C4—2441no—
490C2×C4—2441no—
491C2×C4—2441no—
492C2×C4—2441no—
493C2×C4C2×#1175819811yescharacteristic
494C2×C4#1451973711yescharacteristic
495C2×C4#1451974711yescharacteristic
496C2×C4#1451974911yescharacteristic
497C8—81no—
498C8—2441no—
499C8—2441no—
500C8—2442no—
501C8—2441no—
502C8—2441no—
503C22—21no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—22no—
510C22—21no—
511C22—21no—
512C22—41no—
513C22—41no—
514C22—41no—
515C22—41no—
516C22—41no—
517C22—81no—
518C22—81no—
519C22—82no—
520C22—82no—
521C22#1683963911yescharacteristic
522C22#1683987611yescharacteristic
523C22#1683988111yescharacteristic
524C4—21no—
525C4—21no—
526C4—22no—
527C4—21no—
528C4—41no—
529C4—82no—
530C4—4881no—
531C4—4881no—
532C4C2×#1451969111yescharacteristic
533C4C2×#1451969111yescharacteristic
534C2—21no—
535C2—21no—
536C2—41no—
537C2—41no—
538C2—42no—
539C2—81no—
540C2#2144614411yescharacteristic
541C2#2144627011yescharacteristic
542C2#2144629011yescharacteristic
subgroupG/H
centerC22#16839639
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1789C2
socleC22×C61#386
prime radicalC22×#41×C61C22
cosocleC23×C4×C61C23
hypercenter#1789D61
hypocenterC61#9239
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1789

Complements

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

NH ≅ G/Ntype
3. #21444338C2semidirect
4. #21444184C2semidirect
5. #21443695C2semidirect
6. #21443667C2semidirect
8. C22×#11758202C4semidirect
9. C22×#11758200C4semidirect
16. C2×#14519701C4semidirect
17. C2×#14519698C4semidirect
304. C61#9239semidirect

Maximal subgroups

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

subgroupindex
C2×#168399242
#214542682
#214443382
#214441842
#214436952
#214436672
C61×#17892
#923961