Finite Group Databasebeta

← #29649233

Subgroups — #29649233

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#21454933C211yesmaximal, characteristic
2#21454932C211yesmaximal, characteristic
3#21454458C211yesmaximal, characteristic
4#21444609C211yesmaximal, characteristic, complemented
5#21444604C211yesmaximal, characteristic, complemented
6#21444601C211yesmaximal, characteristic, complemented
7#21444597C211yesmaximal, characteristic, complemented
8#21444596C211yesmaximal, characteristic, complemented
9#21444595C211yesmaximal, characteristic, complemented
10#21444592C211yesmaximal, characteristic, complemented
11#21444585C211yesmaximal, characteristic, complemented
12#21444583C211yesmaximal, characteristic, complemented
13#21444579C211yesmaximal, characteristic, complemented
14#21444576C211yesmaximal, characteristic, complemented
15C61×#1574C211yesmaximal, characteristic, complemented
16C4×#11758222C2211yescharacteristic
17#16839892—21no—
18#16839891—21no—
19#16839841—21no—
20#16839838—21no—
21#16839832—21no—
22#16839831—21no—
23#16839830—21no—
24#16839830—21no—
25#16839822C412yes—
26#16839820C412yes—
27#16839819C2211yescharacteristic
28#16839818C2211yescharacteristic
29#16839818C2211yescharacteristic
30#16839818C2211yescharacteristic
31#16839815C2211yescharacteristic
32#16839814C2211yescharacteristic
33#16839813C2211yescharacteristic
34#16839813C2211yescharacteristic
35#16839787C412yes—
36#16839784C2211yescharacteristic
37#16839784C2211yescharacteristic
38#16839784C2211yescharacteristic
39C2×C4⋊#92418C2211yescharacteristic
40C4⋊C8×D61C2211yescharacteristic
41#16839727C412yes—
42C4×#11758189C2211yescharacteristic
43C4×C8×D61C2211yescharacteristic
44#16839515C2211yescharacteristic
45#16839515C2211yescharacteristic
46#16839514C2211yescharacteristic
47#16839514C2211yescharacteristic
48#16839514C2211yescharacteristic
49#16839514C2211yescharacteristic
50#16839514C2211yescharacteristic
51#16839514C2211yescharacteristic
52#16839513C2211yescharacteristic
53#16839513C2211yescharacteristic
54#16839512C2211yescharacteristic
55#16839512C2211yescharacteristic
56C61×#431C2211yescharacteristic
57C61×#431C2211yescharacteristic
58C61×#423C2211yescharacteristic
59C61×#335C2211yescharacteristic
60C61×#335C2211yescharacteristic
61C61×#334C2211yescharacteristic
62C61×#334C2211yescharacteristic
63C2×#11758222C2×C411yescharacteristic
64C2×#11758189—21no—
65C2×#11758189—21no—
66C2×#11758189—21no—
67C2×#11758189C2×C412yes—
68C22×#92418—21no—
69C2×C8×D61—21no—
70C2×C8×D61C2×C412yes—
71C4×Dic122D411yescharacteristic
72C4×Dic122Q811yescharacteristic
73C4×D244D411yescharacteristic
74C4×D244Q811yescharacteristic
75C4×C22⋊D61D411yescharacteristic
76C4×C22⋊D61D411yescharacteristic
77C4×C22⋊D61Q811yescharacteristic
78C4×C22⋊D61Q811yescharacteristic
79#14519736C2×C411yescharacteristic
80#14519734C2×C411yescharacteristic
81#14519734C2×C411yescharacteristic
82C42×D61C2311yescharacteristic
83C42×D61C2311yescharacteristic
84C4⋊#92418—21no—
85C4⋊#92418C2×C412yes—
86C4⋊#92418C2311yescharacteristic
87C4⋊#92418C2311yescharacteristic
88C4⋊#92418C2311yescharacteristic
89C4⋊#92418C2311yescharacteristic
90#14519706—21no—
91#14519706—21no—
92#14519706—21no—
93#14519706—21no—
94#14519706C2×C412yes—
95#14519706C2×C412yes—
96C22⋊#92418—21no—
97C22⋊#92418C2×C412yes—
98#14519689—21no—
99#14519689—21no—
100#14519689—21no—
101#14519689—21no—
102#14519689C2×C412yes—
103#14519689C2×C412yes—
104#14519688—21no—
105#14519687—21no—
106#14519687—21no—
107#14519687—21no—
108#14519687C2×C412yes—
109C4×#92418C2311yescharacteristic
110C4×#92418C2311yescharacteristic
111C8×Dic61—21no—
112C8×Dic61C2×C412yes—
113C2×M16×C61—21no—
114C2×C42×C61C2311yescharacteristic
115C4⋊C8×C61—21no—
116C4⋊C8×C61C2×C412yes—
117C4⋊C8×C61C2311yescharacteristic
118C4⋊C8×C61C2311yescharacteristic
119C4⋊C8×C61C2311yescharacteristic
120C4⋊C8×C61C2311yescharacteristic
121C22⋊C8×C61—21no—
122C22⋊C8×C61C2×C412yes—
123C4×C8×C61—21no—
124C4×C8×C61C2311yescharacteristic
125C4×C8×C61C2311yescharacteristic
126C22×C4×C61C22×C411yescharacteristic
127C22×C4×C61C2×D411yescharacteristic
128C22×C4×C61C2×Q811yescharacteristic
129C2×C22⋊D61C4⋊C411yescharacteristic
130C2×C22⋊D61C4⋊C411yescharacteristic
131#11758222—42no—
132C2×D244C4⋊C411yescharacteristic
133C2×C4×D61C22×C411yescharacteristic
134C2×C4×D61C22×C411yescharacteristic
135C2×C4×D61C2×D411yescharacteristic
136C2×C4×D61C2×D411yescharacteristic
137C2×C4×D61C2×Q811yescharacteristic
138C2×C4×D61C2×Q811yescharacteristic
139C2×Dic122C4⋊C411yescharacteristic
140M16×C61—81no—
141C2×C8×C61—21no—
142C2×C8×C61—21no—
143C2×C8×C61—21no—
144C2×C8×C61—21no—
145C2×C8×C61C22×C412yes—
146C2×C8×C61C22×C412yes—
147C42×C61C22×C411yescharacteristic
148C42×C61C2×D411yescharacteristic
149C42×C61C2×Q811yescharacteristic
150C42×C61C2411yescharacteristic
151C22⋊Dic61C4⋊C411yescharacteristic
152C22⋊Dic61C4⋊C411yescharacteristic
153#11758198C4⋊C411yescharacteristic
154#11758198C4⋊C411yescharacteristic
155#11758198C4⋊C411yescharacteristic
156#11758198C4⋊C411yescharacteristic
157C4⋊Dic61C4⋊C411yescharacteristic
158C4⋊Dic61C4⋊C411yescharacteristic
159#11758196C4⋊C411yescharacteristic
160#11758196C4⋊C411yescharacteristic
161#11758196C4⋊C411yescharacteristic
162#11758196C4⋊C411yescharacteristic
163C4×Dic61C22×C411yescharacteristic
164C4×Dic61C22×C411yescharacteristic
165C4×Dic61C2×D411yescharacteristic
166C4×Dic61C2×D411yescharacteristic
167C4×Dic61C2×Q811yescharacteristic
168C4×Dic61C2×Q811yescharacteristic
169C2×#92418—21no—
170C2×#92418—21no—
171C2×#92418—21no—
172C2×#92418—21no—
173C2×#92418—81no—
174C2×#92418C22×C412yes—
175C2×#92418C22×C412yes—
176#11758189—42no—
177#11758189—81no—
178#11758189—81no—
179#11758189—81no—
180C8×D61—42no—
181C8×D61—81no—
182C23×C61C2×C4⋊C411yescharacteristic
183C22×D61C2×C4⋊C411yescharacteristic
184C22×D61C2×C4⋊C411yescharacteristic
185C2×C4×C61—22no—
186C2×C4×C61—21no—
187C2×C4×C61—21no—
188C2×C4×C61—41no—
189C2×C4×C61C2×C4⋊C411yescharacteristic
190C2×C4×C61C2×C4⋊C411yescharacteristic
191C2×C4×C61C2×C4⋊C411yescharacteristic
192C2×C4×C61C23×C411yescharacteristic
193C2×C4×C61C22×D411yescharacteristic
194C2×C4×C61C22×Q811yescharacteristic
195C22⋊D61—41no—
196C22⋊D61—41no—
197C2×Dic61C2×C4⋊C411yescharacteristic
198C2×Dic61C2×C4⋊C411yescharacteristic
199C2×Dic61C2×C4⋊C411yescharacteristic
200C2×Dic61C2×C4⋊C411yescharacteristic
201C2×Dic61C2×C4⋊C411yescharacteristic
202C2×Dic61C2×C4⋊C411yescharacteristic
203D244—41no—
204C4×D61—22no—
205C4×D61—22no—
206C4×D61—21no—
207C4×D61—21no—
208C4×D61—21no—
209C4×D61—21no—
210C4×D61—41no—
211C4×D61—41no—
212Dic122—41no—
213C8×C61—22no—
214C8×C61—22no—
215C8×C61—41no—
216C8×C61—41no—
217C8×C61—41no—
218C8×C61—41no—
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×C61C22×C4⋊C411yescharacteristic
230C2×D61—21no—
231C2×D61—21no—
232C2×D61—21no—
233C2×D61—21no—
234C2×D61—21no—
235C2×D61—21no—
236C4×C61—21no—
237C4×C61—21no—
238C4×C61—21no—
239C4×C61—21no—
240C4×C61#56812yes—
241C4×C61#57611yescharacteristic
242C4×C61#57811yescharacteristic
243Dic61—21no—
244Dic61—21no—
245Dic61—21no—
246Dic61—21no—
247Dic61—21no—
248Dic61—21no—
249#2989—611no—
250#2989—611no—
251#2922—611no—
252#1574—611no—
253#1574D6111yescharacteristic, complemented
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#290511yescharacteristic
266C2×C61#291311yescharacteristic
267C2×C61#291611yescharacteristic
268D61—41no—
269D61—41no—
270C4×#41—611no—
271#446—1221no—
272#446—1221no—
273#436—1221no—
274#436—1221no—
275#435—1221no—
276#435—1221no—
277#435—1221no—
278#435—1221no—
279#433—612no—
280#433—612no—
281#432—611no—
282#432—611no—
283#432—611no—
284#432—611no—
285#431—611no—
286#431—611no—
287#431—611no—
288#431—611no—
289#431C2×D6111yescharacteristic
290#431C2×D6111yescharacteristic
291#424—612no—
292#423—611no—
293#423—611no—
294#423—611no—
295#423C2×D6111yescharacteristic
296C2×C4⋊C8—611no—
297C2×C4⋊C8—611no—
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#335C2×D6111yescharacteristic
310#335C2×D6111yescharacteristic
311#334—611no—
312#334—611no—
313#334—611no—
314#334—611no—
315#334C2×D6111yescharacteristic
316#334C2×D6111yescharacteristic
317C61#1782511yescharacteristic, complemented, Sylow
318C2×#41—611no—
319C2×M16—21no—
320C2×M16—612no—
321C2×M16—1221no—
322C2×M16—1221no—
323C2×M16—1221no—
324C22×C8—612no—
325C22×C8—1221no—
326C22×C8—1221no—
327C4×Q8—611no—
328C4×Q8—611no—
329C4×D4—611no—
330C4×D4—611no—
331C4×D4—611no—
332C4×D4—611no—
333C4×D4—611no—
334C4×D4—611no—
335#117—611no—
336#117—611no—
337#117—611no—
338C2×C42—611no—
339C2×C42—611no—
340C2×C42C22×D6111yescharacteristic
341C4⋊C8—21no—
342C4⋊C8—612no—
343C4⋊C8—612no—
344C4⋊C8—612no—
345C4⋊C8—611no—
346C4⋊C8—611no—
347C4⋊C8—611no—
348C4⋊C8—611no—
349C4⋊C8—1221no—
350C4⋊C8—1221no—
351C4⋊C8—1221no—
352C4⋊C8—1221no—
353C4⋊C8—1221no—
354C4⋊C8C4×D6112yes—
355C4⋊C8C22×D6111yescharacteristic
356C4⋊C8C22×D6111yescharacteristic
357C4⋊C8C22×D6111yescharacteristic
358C4⋊C8C22×D6111yescharacteristic
359C22⋊C8—21no—
360C22⋊C8—612no—
361C22⋊C8—612no—
362C22⋊C8—612no—
363C22⋊C8—1221no—
364C22⋊C8—1221no—
365C22⋊C8—1221no—
366C22⋊C8—1221no—
367C22⋊C8—1221no—
368C22⋊C8C4×D6112yes—
369#97—612no—
370#97—1221no—
371#97—1221no—
372#97—1221no—
373#97—1221no—
374C4×C8—21no—
375C4×C8—612no—
376C4×C8—611no—
377C4×C8—611no—
378C4×C8—1221no—
379C4×C8C22×D6111yescharacteristic
380C4×C8C22×D6111yescharacteristic
381#41—2442no—
382C2×Q8—611no—
383C2×D4—611no—
384C2×D4—611no—
385C2×D4—611no—
386C22×C4—611no—
387C22×C4—611no—
388C22×C4—611no—
389C22×C4—611no—
390C22×C4—611no—
391C22×C4—611no—
392C22×C4C2×C4×D6111yescharacteristic
393C22×C4D4×D6111yescharacteristic
394C22×C4Q8×D6111yescharacteristic
395M16—81no—
396M16—4881no—
397M16—4881no—
398M16—4881no—
399M16—2442no—
400C2×C8—21no—
401C2×C8—21no—
402C2×C8—21no—
403C2×C8—21no—
404C2×C8—612no—
405C2×C8—612no—
406C2×C8—1221no—
407C2×C8—1221no—
408C2×C8—1221no—
409C2×C8—1221no—
410C2×C8—4881no—
411C2×C8—4881no—
412C2×C8—2442no—
413C2×C8C2×C4×D6112yes—
414C2×C8C2×C4×D6112yes—
415C4⋊C4—611no—
416C4⋊C4—611no—
417C4⋊C4—611no—
418C4⋊C4—611no—
419C4⋊C4—611no—
420C4⋊C4—611no—
421C22⋊C4—611no—
422C22⋊C4—611no—
423C22⋊C4—611no—
424C22⋊C4—611no—
425C22⋊C4—611no—
426C22⋊C4—611no—
427C42—611no—
428C42—611no—
429C42—611no—
430C42—611no—
431C42—611no—
432C42—611no—
433C42C2×C4×D6111yescharacteristic
434C42D4×D6111yescharacteristic
435C42Q8×D6111yescharacteristic
436C42C23×D6111yescharacteristic
437C23—611no—
438C23—611no—
439C23C4⋊C4×D6111yescharacteristic
440Q8—2441no—
441D4—2441no—
442D4—2441no—
443D4—2441no—
444C2×C4—22no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—41no—
448C2×C4—611no—
449C2×C4—611no—
450C2×C4—611no—
451C2×C4—611no—
452C2×C4—611no—
453C2×C4—611no—
454C2×C4—1222no—
455C2×C4—1222no—
456C2×C4—1221no—
457C2×C4—1221no—
458C2×C4—1221no—
459C2×C4—1221no—
460C2×C4—2441no—
461C2×C4—2441no—
462C2×C4C4⋊C4×D6111yescharacteristic
463C2×C4C4⋊C4×D6111yescharacteristic
464C2×C4C4⋊C4×D6111yescharacteristic
465C2×C4C22×C4×D6111yescharacteristic
466C2×C4C2×D4×D6111yescharacteristic
467C2×C4C2×Q8×D6111yescharacteristic
468C8—22no—
469C8—22no—
470C8—41no—
471C8—41no—
472C8—41no—
473C8—41no—
474C8—1222no—
475C8—1222no—
476C8—2441no—
477C8—2441no—
478C8—2441no—
479C8—2441no—
480C22—21no—
481C22—21no—
482C22—21no—
483C22—1221no—
484C22—1221no—
485C22—1221no—
486C22—1221no—
487C22—1221no—
488C22—1221no—
489C22C2×C4⋊C4×D6111yescharacteristic
490C4—21no—
491C4—21no—
492C4—21no—
493C4—21no—
494C4—1221no—
495C4—1221no—
496C4—1221no—
497C4—1221no—
498C4—1221no—
499C4—1221no—
500C4#1684052712yes—
501C4#1684056611yescharacteristic
502C4#1684057811yescharacteristic
503C2—41no—
504C2—2441no—
505C2—2441no—
506C2#2145438011yescharacteristic
507C2#2145441811yescharacteristic
508C2#2145442711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1574C2
socleC22×C61C22×C4⋊C4
prime radicalC2×#11758222C2×C4
cosocleC42×C61C24
hypercenter#1574D61
hypocenterC61#17825
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1574

Complements

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

NH ≅ G/Ntype
4. #21444609C2semidirect
5. #21444604C2semidirect
6. #21444601C2semidirect
7. #21444597C2semidirect
8. #21444596C2semidirect
9. #21444595C2semidirect
10. #21444592C2semidirect
11. #21444585C2semidirect
12. #21444583C2semidirect
13. #21444579C2semidirect
14. #21444576C2semidirect
15. C61×#1574C2semidirect
253. #1574D61semidirect
317. C61#17825semidirect

Maximal subgroups

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

subgroupindex
#214549332
#214549322
#214544582
#214446092
#214446042
#214446012
#214445972
#214445962
#214445952
#214445922
#214445852
#214445832
#214445792
#214445762
C61×#15742
#1782561