Finite Group Databasebeta

← #29649228

Subgroups — #29649228

Order 15616.

572 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454936C211yesmaximal, characteristic
2#21454463C211yesmaximal, characteristic
3#21444610C211yesmaximal, characteristic, complemented
4#21444607C211yesmaximal, characteristic, complemented
5#21444605C211yesmaximal, characteristic, complemented
6#21444602C211yesmaximal, characteristic, complemented
7#21444600C211yesmaximal, characteristic, complemented
8#21444597C211yesmaximal, characteristic, complemented
9#21444595C211yesmaximal, characteristic, complemented
10#21444593C211yesmaximal, characteristic, complemented
11#21444587C211yesmaximal, characteristic, complemented
12#21444584C211yesmaximal, characteristic, complemented
13#21444580C211yesmaximal, characteristic, complemented
14#21444577C211yesmaximal, characteristic, complemented
15C61×#2989C211yesmaximal, characteristic
16#16839893—21no—
17#16839840—21no—
18#16839834—21no—
19#16839834—21no—
20#16839823C412yes—
21#16839823C412yes—
22#16839819C2211yescharacteristic
23#16839819C2211yescharacteristic
24#16839815C2211yescharacteristic
25#16839815C2211yescharacteristic
26#16839815C2211yescharacteristic
27#16839815C2211yescharacteristic
28#16839815C2211yescharacteristic
29#16839789C412yes—
30#16839786C2211yescharacteristic
31#16839786C2211yescharacteristic
32C2×C4⋊#92418C2211yescharacteristic
33#16839729C412yes—
34C4×#11758194C2211yescharacteristic
35C2×C4×#92418C2211yescharacteristic
36#16839514C2211yescharacteristic
37#16839514C2211yescharacteristic
38#16839514C2211yescharacteristic
39#16839514C2211yescharacteristic
40#16839514C2211yescharacteristic
41#16839514C2211yescharacteristic
42#16839514C2211yescharacteristic
43#16839514C2211yescharacteristic
44#16839514C2211yescharacteristic
45#16839514C2211yescharacteristic
46#16839512C2211yescharacteristic
47#16839512C2211yescharacteristic
48#16839512C2211yescharacteristic
49#16839512C2211yescharacteristic
50#16839512C2211yescharacteristic
51#16839512C2211yescharacteristic
52C4×#41×C61C2211yescharacteristic
53C61×#446—21no—
54C61×#436—21no—
55C61×#435—21no—
56C61×#435—21no—
57C61×#432C2211yescharacteristic
58C61×#432C2211yescharacteristic
59C61×#431C2211yescharacteristic
60C61×#423C2211yescharacteristic
61C61×#423C2211yescharacteristic
62C2×C4⋊C8×C61C2211yescharacteristic
63C2×#11758194—21no—
64C2×#11758194—21no—
65C2×#11758194C2×C412yes—
66C22×#92418—21no—
67C22×#92418C2×C412yes—
68C4⋊#92418—21no—
69C4⋊#92418—21no—
70C4⋊#92418—21no—
71C4⋊#92418C2×C412yes—
72C4⋊#92418C2×C412yes—
73C4⋊#92418C2×C412yes—
74C4⋊#92418C2×C412yes—
75C4⋊#92418C2311yescharacteristic
76C4⋊#92418C2311yescharacteristic
77C4⋊#92418C2311yescharacteristic
78C4⋊#92418C2311yescharacteristic
79C22⋊#92418—21no—
80C22⋊#92418—21no—
81C22⋊#92418—21no—
82C22⋊#92418C2×C412yes—
83C22⋊#92418C2×C412yes—
84C22⋊#92418C2×C412yes—
85C22⋊#92418C2×C412yes—
86#14519688—21no—
87#14519688—21no—
88#14519688C2×C412yes—
89C4×#92418—21no—
90C4×#92418C2×C412yes—
91C4×#92418C2311yescharacteristic
92C4×#92418C2311yescharacteristic
93C4×#92418C2311yescharacteristic
94C4×#92418C2311yescharacteristic
95C2×#41×C61C2×C411yescharacteristic
96C2×M16×C61—21no—
97C2×M16×C61—21no—
98C22×C8×C61—21no—
99C4×Q8×C61D411yescharacteristic
100C4×Q8×C61Q811yescharacteristic
101C4×D4×C61D411yescharacteristic
102C4×D4×C61D411yescharacteristic
103C4×D4×C61D411yescharacteristic
104C4×D4×C61Q811yescharacteristic
105C4×D4×C61Q811yescharacteristic
106C4×D4×C61Q811yescharacteristic
107#117×C61C2×C411yescharacteristic
108#117×C61C2×C411yescharacteristic
109#117×C61C2×C411yescharacteristic
110C2×C42×C61C2311yescharacteristic
111C2×C42×C61C2311yescharacteristic
112C2×C42×C61C2311yescharacteristic
113C4⋊C8×C61—21no—
114C4⋊C8×C61—21no—
115C4⋊C8×C61—21no—
116C4⋊C8×C61C2311yescharacteristic
117C4⋊C8×C61C2311yescharacteristic
118C4⋊C8×C61C2311yescharacteristic
119C4⋊C8×C61C2311yescharacteristic
120C22⋊C8×C61—21no—
121C22⋊C8×C61—21no—
122C22⋊C8×C61—21no—
123#97×C61—21no—
124#97×C61—21no—
125C4×C8×C61—21no—
126#41×C61—42no—
127C2×Q8×C61C4⋊C411yescharacteristic
128C2×D4×C61C4⋊C411yescharacteristic
129C2×D4×C61C4⋊C411yescharacteristic
130C2×D4×C61C4⋊C411yescharacteristic
131C22×C4×C61C22×C411yescharacteristic
132C22×C4×C61C22×C411yescharacteristic
133C22×C4×C61C22×C411yescharacteristic
134C22×C4×C61C2×D411yescharacteristic
135C22×C4×C61C2×D411yescharacteristic
136C22×C4×C61C2×D411yescharacteristic
137C22×C4×C61C2×Q811yescharacteristic
138C22×C4×C61C2×Q811yescharacteristic
139C22×C4×C61C2×Q811yescharacteristic
140M16×C61—81no—
141M16×C61—81no—
142C2×C8×C61—21no—
143C2×C8×C61—21no—
144C2×C8×C61—21no—
145C2×C8×C61—21no—
146C2×C8×C61—81no—
147C4⋊C4×C61C4⋊C411yescharacteristic
148C4⋊C4×C61C4⋊C411yescharacteristic
149C4⋊C4×C61C4⋊C411yescharacteristic
150C4⋊C4×C61C4⋊C411yescharacteristic
151C4⋊C4×C61C4⋊C411yescharacteristic
152C4⋊C4×C61C4⋊C411yescharacteristic
153C22⋊C4×C61C4⋊C411yescharacteristic
154C22⋊C4×C61C4⋊C411yescharacteristic
155C22⋊C4×C61C4⋊C411yescharacteristic
156C22⋊C4×C61C4⋊C411yescharacteristic
157C22⋊C4×C61C4⋊C411yescharacteristic
158C22⋊C4×C61C4⋊C411yescharacteristic
159C42×C61C22×C411yescharacteristic
160C42×C61C22×C411yescharacteristic
161C42×C61C22×C411yescharacteristic
162C42×C61C2×D411yescharacteristic
163C42×C61C2×D411yescharacteristic
164C42×C61C2×D411yescharacteristic
165C42×C61C2×Q811yescharacteristic
166C42×C61C2×Q811yescharacteristic
167C42×C61C2×Q811yescharacteristic
168C42×C61C2411yescharacteristic
169#11758194—42no—
170#11758194—81no—
171#11758194—81no—
172C2×#92418—21no—
173C2×#92418—21no—
174C2×#92418—21no—
175C2×#92418—21no—
176C2×#92418—42no—
177C2×#92418—81no—
178C2×#92418C22×C412yes—
179C2×#92418C22×C412yes—
180C2×#92418C22×C412yes—
181C2×#92418C22×C412yes—
182C23×C61C2×C4⋊C411yescharacteristic
183C23×C61C2×C4⋊C411yescharacteristic
184C23×C61C2×C4⋊C411yescharacteristic
185Q8×C61—41no—
186D4×C61—41no—
187D4×C61—41no—
188D4×C61—41no—
189C2×C4×C61—22no—
190C2×C4×C61—22no—
191C2×C4×C61—22no—
192C2×C4×C61—21no—
193C2×C4×C61—21no—
194C2×C4×C61—21no—
195C2×C4×C61—21no—
196C2×C4×C61—21no—
197C2×C4×C61—21no—
198C2×C4×C61—41no—
199C2×C4×C61—41no—
200C2×C4×C61—41no—
201C2×C4×C61C2×C4⋊C411yescharacteristic
202C2×C4×C61C2×C4⋊C411yescharacteristic
203C2×C4×C61C2×C4⋊C411yescharacteristic
204C2×C4×C61C2×C4⋊C411yescharacteristic
205C2×C4×C61C2×C4⋊C411yescharacteristic
206C2×C4×C61C2×C4⋊C411yescharacteristic
207C2×C4×C61C2×C4⋊C411yescharacteristic
208C2×C4×C61C2×C4⋊C411yescharacteristic
209C2×C4×C61C2×C4⋊C411yescharacteristic
210C2×C4×C61C23×C411yescharacteristic
211C2×C4×C61C22×D411yescharacteristic
212C2×C4×C61C22×Q811yescharacteristic
213C8×C61—41no—
214C8×C61—41no—
215C8×C61—41no—
216C8×C61—41no—
217#92418—22no—
218#92418—22no—
219#92418—22no—
220#92418—22no—
221#92418—41no—
222#92418—41no—
223#92418—41no—
224#92418—41no—
225#17825—611nomaximal, Sylow
226C22×C61—21no—
227C22×C61—21no—
228C22×C61—21no—
229C22×C61—21no—
230C22×C61—21no—
231C22×C61—21no—
232C22×C61—21no—
233C22×C61—21no—
234C22×C61—21no—
235C22×C61C22×C4⋊C411yescharacteristic
236C4×C61—21no—
237C4×C61—21no—
238C4×C61—21no—
239C4×C61—21no—
240C4×C61—21no—
241C4×C61—21no—
242C4×C61—21no—
243C4×C61—21no—
244C4×C61—21no—
245C4×C61—21no—
246C4×C61#56812yes—
247C4×C61#57611yescharacteristic
248C4×C61#57811yescharacteristic
249#2989—611no—
250#2989D6111yescharacteristic
251#2922—611no—
252#1574—611no—
253#1574—611no—
254#1573—611no—
255#1573—611no—
256#1572—611no—
257#1572—611no—
258#1571—611no—
259#1571—611no—
260#1569—611no—
261#1569—611no—
262#1568—611no—
263#1567—611no—
264C2×C61—41no—
265C2×C61—41no—
266C2×C61—41no—
267C2×C61#290511yescharacteristic
268C2×C61#291311yescharacteristic
269C2×C61#291611yescharacteristic
270C4×#41C2×D6111yescharacteristic
271#446—21no—
272#446—1221no—
273#436—21no—
274#436—1221no—
275#435—21no—
276#435—21no—
277#435—1221no—
278#435—1221no—
279#433—612no—
280#433—612no—
281#432—611no—
282#432—611no—
283#432C2×D6111yescharacteristic
284#432C2×D6111yescharacteristic
285#431—611no—
286#431—611no—
287#431—611no—
288#431—611no—
289#431—611no—
290#431C2×D6111yescharacteristic
291#424—612no—
292#423—611no—
293#423—611no—
294#423C2×D6111yescharacteristic
295#423C2×D6111yescharacteristic
296C2×C4⋊C8—611no—
297C2×C4⋊C8C2×D6111yescharacteristic
298#408—612no—
299C4×M16—611no—
300C2×C4×C8—611no—
301#335—611no—
302#335—611no—
303#335—611no—
304#335—611no—
305#335—611no—
306#335—611no—
307#335—611no—
308#335—611no—
309#335—611no—
310#335—611no—
311#334—611no—
312#334—611no—
313#334—611no—
314#334—611no—
315#334—611no—
316#334—611no—
317C61#1782511yescharacteristic, complemented, Sylow
318C2×#41C4×D6111yescharacteristic
319C2×M16—21no—
320C2×M16—21no—
321C2×M16—612no—
322C2×M16—1221no—
323C2×M16—1221no—
324C22×C8—21no—
325C22×C8—612no—
326C22×C8—1221no—
327C4×Q8Dic12211yescharacteristic
328C4×Q8C22⋊D6111yescharacteristic
329C4×D4Dic12211yescharacteristic
330C4×D4Dic12211yescharacteristic
331C4×D4Dic12211yescharacteristic
332C4×D4C22⋊D6111yescharacteristic
333C4×D4C22⋊D6111yescharacteristic
334C4×D4C22⋊D6111yescharacteristic
335#117C4×D6111yescharacteristic
336#117C4×D6111yescharacteristic
337#117C4×D6111yescharacteristic
338C2×C42C22×D6111yescharacteristic
339C2×C42C22×D6111yescharacteristic
340C2×C42C22×D6111yescharacteristic
341C4⋊C8—21no—
342C4⋊C8—21no—
343C4⋊C8—21no—
344C4⋊C8—612no—
345C4⋊C8—612no—
346C4⋊C8—612no—
347C4⋊C8—612no—
348C4⋊C8—611no—
349C4⋊C8—611no—
350C4⋊C8—611no—
351C4⋊C8—611no—
352C4⋊C8—1221no—
353C4⋊C8—1221no—
354C4⋊C8—1221no—
355C4⋊C8C22×D6111yescharacteristic
356C4⋊C8C22×D6111yescharacteristic
357C4⋊C8C22×D6111yescharacteristic
358C4⋊C8C22×D6111yescharacteristic
359C22⋊C8—21no—
360C22⋊C8—21no—
361C22⋊C8—21no—
362C22⋊C8—612no—
363C22⋊C8—612no—
364C22⋊C8—612no—
365C22⋊C8—612no—
366C22⋊C8—1221no—
367C22⋊C8—1221no—
368C22⋊C8—1221no—
369#97—21no—
370#97—21no—
371#97—612no—
372#97—1221no—
373#97—1221no—
374C4×C8—21no—
375C4×C8—612no—
376C4×C8—611no—
377C4×C8—611no—
378C4×C8—611no—
379C4×C8—611no—
380C4×C8—1221no—
381#41—42no—
382C2×Q8#1175819611yescharacteristic
383C2×D4#1175819611yescharacteristic
384C2×D4#1175819611yescharacteristic
385C2×D4#1175819611yescharacteristic
386C22×C4C2×Dic12211yescharacteristic
387C22×C4C2×Dic12211yescharacteristic
388C22×C4C2×Dic12211yescharacteristic
389C22×C4C2×C4×D6111yescharacteristic
390C22×C4C2×C4×D6111yescharacteristic
391C22×C4C2×C4×D6111yescharacteristic
392C22×C4C2×C22⋊D6111yescharacteristic
393C22×C4C2×C22⋊D6111yescharacteristic
394C22×C4C2×C22⋊D6111yescharacteristic
395M16—81no—
396M16—81no—
397M16—4881no—
398M16—4881no—
399M16—2442no—
400C2×C8—21no—
401C2×C8—21no—
402C2×C8—21no—
403C2×C8—21no—
404C2×C8—81no—
405C2×C8—612no—
406C2×C8—612no—
407C2×C8—612no—
408C2×C8—612no—
409C2×C8—1221no—
410C2×C8—1221no—
411C2×C8—1221no—
412C2×C8—1221no—
413C2×C8—4881no—
414C2×C8—2442no—
415C4⋊C4#1175819611yescharacteristic
416C4⋊C4#1175819611yescharacteristic
417C4⋊C4#1175819611yescharacteristic
418C4⋊C4#1175819611yescharacteristic
419C4⋊C4#1175819611yescharacteristic
420C4⋊C4#1175819611yescharacteristic
421C22⋊C4#1175819611yescharacteristic
422C22⋊C4#1175819611yescharacteristic
423C22⋊C4#1175819611yescharacteristic
424C22⋊C4#1175819611yescharacteristic
425C22⋊C4#1175819611yescharacteristic
426C22⋊C4#1175819611yescharacteristic
427C42C2×Dic12211yescharacteristic
428C42C2×Dic12211yescharacteristic
429C42C2×Dic12211yescharacteristic
430C42C2×C4×D6111yescharacteristic
431C42C2×C4×D6111yescharacteristic
432C42C2×C4×D6111yescharacteristic
433C42C2×C22⋊D6111yescharacteristic
434C42C2×C22⋊D6111yescharacteristic
435C42C2×C22⋊D6111yescharacteristic
436C42C23×D6111yescharacteristic
437C23C2×#1175819611yescharacteristic
438C23C2×#1175819611yescharacteristic
439C23C2×#1175819611yescharacteristic
440Q8—41no—
441D4—41no—
442D4—41no—
443D4—41no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—22no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4C2×#1175819611yescharacteristic
457C2×C4C2×#1175819611yescharacteristic
458C2×C4C2×#1175819611yescharacteristic
459C2×C4C2×#1175819611yescharacteristic
460C2×C4C2×#1175819611yescharacteristic
461C2×C4C2×#1175819611yescharacteristic
462C2×C4C2×#1175819611yescharacteristic
463C2×C4C2×#1175819611yescharacteristic
464C2×C4C2×#1175819611yescharacteristic
465C2×C4C22×C4×D6111yescharacteristic
466C2×C4C22×C22⋊D6111yescharacteristic
467C2×C4C22×Dic12211yescharacteristic
468C8—41no—
469C8—41no—
470C8—41no—
471C8—41no—
472C8—1222no—
473C8—1222no—
474C8—1222no—
475C8—1222no—
476C8—2441no—
477C8—2441no—
478C8—2441no—
479C8—2441no—
480C22—21no—
481C22—21no—
482C22—21no—
483C22—21no—
484C22—21no—
485C22—21no—
486C22—21no—
487C22—21no—
488C22—21no—
489C22C22×#1175819611yescharacteristic
490C4—21no—
491C4—21no—
492C4—21no—
493C4—21no—
494C4—21no—
495C4—21no—
496C4—21no—
497C4—21no—
498C4—21no—
499C4—21no—
500C4#1684052812yes—
501C4#1684056511yescharacteristic
502C4#1684057711yescharacteristic
503C2—41no—
504C2—41no—
505C2—41no—
506C2#2145438211yescharacteristic
507C2#2145441711yescharacteristic
508C2#2145442811yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#2989C2
socleC22×C61C22×C4⋊C4
prime radicalC2×#41×C61C2×C4
cosocleC42×C61C24
hypercenter#2989D61
hypocenterC61#17825
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #2989

Complements

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

NH ≅ G/Ntype
3. #21444610C2semidirect
4. #21444607C2semidirect
5. #21444605C2semidirect
6. #21444602C2semidirect
7. #21444600C2semidirect
8. #21444597C2semidirect
9. #21444595C2semidirect
10. #21444593C2semidirect
11. #21444587C2semidirect
12. #21444584C2semidirect
13. #21444580C2semidirect
14. #21444577C2semidirect
317. C61#17825semidirect

Maximal subgroups

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

subgroupindex
#214549362
#214544632
#214446102
#214446072
#214446052
#214446022
#214446002
#214445972
#214445952
#214445932
#214445872
#214445842
#214445802
#214445772
C61×#29892
#1782561