Finite Group Databasebeta

← #29651414

Subgroups — #29651414

Order 15616.

566 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455856C211yesmaximal, characteristic
2#21454917C211yesmaximal, characteristic
3#21454905C211yesmaximal, characteristic
4#21444713C211yesmaximal, characteristic, complemented
5#21444691C211yesmaximal, characteristic, complemented
6#21444689C211yesmaximal, characteristic, complemented
7#21444667C211yesmaximal, characteristic, complemented
8#21444667C211yesmaximal, characteristic, complemented
9#21444639C211yesmaximal, characteristic, complemented
10#21444623C211yesmaximal, characteristic, complemented
11#21444596C211yesmaximal, characteristic
12#21444290C211yesmaximal, characteristic
13#21444212C211yesmaximal, characteristic
14#21444120C211yesmaximal, characteristic
15C61×#1593C211yesmaximal, characteristic, complemented
16#16840316C2211yescharacteristic
17C4×Q8×D61C2211yescharacteristic
18#16840099C411yescharacteristic
19#16840096C411yescharacteristic
20#16840056C411yescharacteristic
21#16840055C411yescharacteristic
22#16839971C411yescharacteristic
23#16839970C411yescharacteristic
24#16839919C411yescharacteristic
25#16839916C411yescharacteristic
26#16839893C2211yescharacteristic
27#16839891—21no—
28#16839890—21no—
29#16839890—21no—
30#16839889C2211yescharacteristic
31Q8×#92418C2211yescharacteristic
32C8×Dic122C2211yescharacteristic
33C8×Dic122C2211yescharacteristic
34#16839886—21no—
35#16839886C2211yescharacteristic
36C4×Dic244C2211yescharacteristic
37C4×#11758202C2211yescharacteristic
38C4×#11758202C2211yescharacteristic
39#16839824—21no—
40#16839822—21no—
41#16839818C2211yescharacteristic
42#16839817—21no—
43#16839814—21no—
44#16839814C2211yescharacteristic
45#16839813C2211yescharacteristic
46#16839813C2211yescharacteristic
47#16839813C2211yescharacteristic
48#16839514C2211yescharacteristic
49#16839514C2211yescharacteristic
50#16839513C2211yescharacteristic
51#16839494C2211yescharacteristic
52#16839494C2211yescharacteristic
53Q8⋊#92418C2211yescharacteristic
54Q8⋊#92418C2211yescharacteristic
55#16839492C2211yescharacteristic
56#16839492C2211yescharacteristic
57#16839484C2211yescharacteristic
58#16839483C2211yescharacteristic
59C8×#92418C2211yescharacteristic
60C61×#446C2211yescharacteristic
61C61×#446C2211yescharacteristic
62C4×Q16×C61C2211yescharacteristic
63C61×#334C2211yescharacteristic
64C61×Q8⋊C8C2211yescharacteristic
65C61×Q8⋊C8C2211yescharacteristic
66C61×#322C2211yescharacteristic
67C2×Q8×D61C2×C411yescharacteristic
68C2×Dic244C2×C411yescharacteristic
69C2×#11758202C2×C411yescharacteristic
70C2×#11758202C2×C411yescharacteristic
71#14519776C2×C411yescharacteristic
72#14519775C2×C411yescharacteristic
73#14519767—21no—
74#14519757C2×C411yescharacteristic
75#14519755—21no—
76#14519753C2×C411yescharacteristic
77Q8×Dic61C2×C411yescharacteristic
78C4×Dic122—21no—
79C4×Dic122—21no—
80C4×Dic122C2311yescharacteristic
81C4×Dic122C2311yescharacteristic
82#14519742—21no—
83#14519742C2×C411yescharacteristic
84#14519734—21no—
85C4⋊C4×D61—21no—
86C4⋊C4×D61C2×C411yescharacteristic
87C42×D61—21no—
88C42×D61C2311yescharacteristic
89#14519711C2×C411yescharacteristic
90#14519710C2×C411yescharacteristic
91#14519710C2×C411yescharacteristic
92C4⋊#92418—21no—
93C4⋊#92418—21no—
94C4⋊#92418C2311yescharacteristic
95C4⋊#92418C2311yescharacteristic
96#14519706—21no—
97#14519706—21no—
98#14519706—21no—
99#14519706—21no—
100#14519706—21no—
101#14519706C2×C411yescharacteristic
102#14519706C2×C411yescharacteristic
103#14519706D411yescharacteristic
104#14519706D411yescharacteristic
105#14519702C2×C411yescharacteristic
106#14519702C2×C411yescharacteristic
107#14519701C2×C411yescharacteristic
108#14519701C2×C411yescharacteristic
109#14519700C2×C411yescharacteristic
110#14519700C2×C411yescharacteristic
111#14519689—21no—
112#14519689—21no—
113#14519689—21no—
114#14519689C2×C411yescharacteristic
115#14519689C2×C411yescharacteristic
116#14519689D411yescharacteristic
117#14519689D411yescharacteristic
118#14519688—21no—
119#14519687—21no—
120#14519687—21no—
121C4×#92418—21no—
122C4×#92418C2311yescharacteristic
123C4×#92418C2311yescharacteristic
124C4×#92418C2311yescharacteristic
125C8×Dic61—21no—
126C8×Dic61—21no—
127C8×Dic61—21no—
128C8×Dic61—21no—
129C2×Q16×C61C2×C411yescharacteristic
130C4×Q8×C61C2311yescharacteristic
131C4×Q8×C61C2311yescharacteristic
132#107×C61C2×C411yescharacteristic
133C4⋊C8×C61—21no—
134C4⋊C8×C61—21no—
135C4⋊C8×C61C2311yescharacteristic
136C4⋊C8×C61C2311yescharacteristic
137#103×C61C2×C411yescharacteristic
138#103×C61C2×C411yescharacteristic
139#97×C61—21no—
140#97×C61—21no—
141C4×C8×C61C2311yescharacteristic
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C2×Q8×C61C22×C411yescharacteristic
145C2×Q8×C61C22×C411yescharacteristic
146Q8×D61—22no—
147Q8×D61—41no—
148C2×C4×D61—21no—
149C2×C4×D61—21no—
150C2×C4×D61C22×C411yescharacteristic
151C2×C4×D61C2×D411yescharacteristic
152C2×C4×D61#4111yescharacteristic
153C2×Dic122—21no—
154C2×Dic122—21no—
155C2×Dic122C22×C411yescharacteristic
156C2×Dic122C22×C411yescharacteristic
157Q16×C61—41no—
158C2×C8×C61—21no—
159C2×C8×C61—21no—
160C2×C8×C61—21no—
161C2×C8×C61C22×C411yescharacteristic
162C2×C8×C61C22×C411yescharacteristic
163C2×C8×C61C2×D411yescharacteristic
164C2×C8×C61C2×D411yescharacteristic
165C4⋊C4×C61—21no—
166C4⋊C4×C61—21no—
167C4⋊C4×C61C22×C411yescharacteristic
168C4⋊C4×C61C22×C411yescharacteristic
169C42×C61—21no—
170C42×C61—21no—
171C42×C61C2411yescharacteristic
172#11758202—22no—
173#11758202—41no—
174#11758198—21no—
175#11758198—21no—
176C4⋊Dic61—21no—
177C4⋊Dic61—21no—
178C4⋊Dic61C22×C411yescharacteristic
179C4⋊Dic61C22×C411yescharacteristic
180#11758196—21no—
181#11758196—21no—
182#11758196—21no—
183#11758196—21no—
184#11758196—21no—
185#11758196—21no—
186#11758196—21no—
187#11758196—21no—
188C4×Dic61—21no—
189C4×Dic61—21no—
190C4×Dic61—21no—
191C4×Dic61—21no—
192C4×Dic61C22×C411yescharacteristic
193C4×Dic61C2×D411yescharacteristic
194C4×Dic61#4111yescharacteristic
195C2×#92418—21no—
196C2×#92418—21no—
197C2×#92418—21no—
198C2×#92418C22×C411yescharacteristic
199C2×#92418C22×C411yescharacteristic
200C2×#92418C2×D411yescharacteristic
201C2×#92418C2×D411yescharacteristic
202Dic244—22no—
203C22×D61C4×D411yescharacteristic
204Q8×C61—21no—
205Q8×C61—21no—
206Q8×C61—21no—
207Q8×C61—21no—
208C2×C4×C61—21no—
209C2×C4×C61—21no—
210C2×C4×C61—21no—
211C2×C4×C61—21no—
212C2×C4×C61C23×C411yescharacteristic
213C2×C4×C61C22×D411yescharacteristic
214C2×C4×C61C2×#4111yescharacteristic
215C2×Dic61—21no—
216C2×Dic61—21no—
217C2×Dic61—21no—
218C2×Dic61—21no—
219C2×Dic61C4×D411yescharacteristic
220C2×Dic61C4×D411yescharacteristic
221C2×Dic61C4×D411yescharacteristic
222C4×D61—21no—
223C4×D61—21no—
224C4×D61—21no—
225C4×D61—21no—
226C4×D61—41no—
227C4×D61—42no—
228C4×D61—42no—
229Dic122—21no—
230Dic122—21no—
231Dic122—21no—
232Dic122—42no—
233Dic122—42no—
234Dic122#13112yes—
235C8×C61—21no—
236C8×C61—21no—
237C8×C61—21no—
238C8×C61—21no—
239C8×C61—41no—
240C8×C61—41no—
241C8×C61—41no—
242#92418—21no—
243#92418—21no—
244#92418—21no—
245#92418—21no—
246#92418—41no—
247#92418—41no—
248#92418—41no—
249#18032—611nomaximal, Sylow
250C22×C61C2×C4×D411yescharacteristic
251C2×D61—21no—
252C2×D61—21no—
253C2×D61—21no—
254C4×C61—21no—
255C4×C61—41no—
256C4×C61—41no—
257C4×C61—41no—
258C4×C61—41no—
259C4×C61C2×#13111yescharacteristic
260C4×C61#56811yescharacteristic
261C4×C61#57811yescharacteristic
262C4×C61#57811yescharacteristic
263Dic61—22no—
264Dic61—21no—
265Dic61—21no—
266Dic61—21no—
267Dic61—41no—
268Dic61—41no—
269Dic61—41no—
270#3104—611no—
271#2986—611no—
272#2984—611no—
273#1593D6111yescharacteristic, complemented
274#1591—611no—
275#1587—611no—
276#1587—611no—
277#1584—611no—
278#1584—611no—
279#1579—611no—
280C8×Q16—611no—
281#1572—611no—
282#1497—611no—
283#1479—611no—
284#1454—611no—
285C2×C61#293311yescharacteristic
286C2×C61#295011yescharacteristic
287C2×C61#295511yescharacteristic
288D61—41no—
289#533—611no—
290C2×C4×Q8—611no—
291#484—611no—
292#484—611no—
293#477—611no—
294#477—611no—
295#462—611no—
296#462—611no—
297#451—611no—
298#451—611no—
299#446—611no—
300#446—611no—
301#446—1221no—
302#446—1221no—
303#446—1221no—
304#446C2×D6111yescharacteristic
305#446C2×D6111yescharacteristic
306C8×Q8—611no—
307C8×Q8—611no—
308C8×Q8—611no—
309C8×Q8—611no—
310C8×Q8—1221no—
311C4×Q16—611no—
312C4×Q16—611no—
313C4×Q16—611no—
314C4×Q16C2×D6111yescharacteristic
315#433—1221no—
316#433—1221no—
317#432—611no—
318#432—1221no—
319#431—611no—
320#431—611no—
321#431—611no—
322#431—611no—
323#431—1221no—
324#335—611no—
325#335—611no—
326#334—611no—
327#334C2×D6111yescharacteristic
328Q8⋊C8—611no—
329Q8⋊C8—611no—
330Q8⋊C8—611no—
331Q8⋊C8—611no—
332Q8⋊C8—611no—
333Q8⋊C8—611no—
334Q8⋊C8C2×D6111yescharacteristic
335Q8⋊C8C2×D6111yescharacteristic
336#322—611no—
337#322—611no—
338#322C2×D6111yescharacteristic
339C82—611no—
340C61#1803211yescharacteristic, complemented, Sylow
341C22×Q8—611no—
342C2×Q16—611no—
343C2×Q16—611no—
344C2×Q16—611no—
345C2×Q16C4×D6111yescharacteristic
346C4⋊Q8—611no—
347C4⋊Q8—611no—
348#125—1221no—
349C22⋊Q8—611no—
350C22⋊Q8—611no—
351C22⋊Q8—1221no—
352C4×Q8—611no—
353C4×Q8—611no—
354C4×Q8—611no—
355C4×Q8—611no—
356C4×Q8—1221no—
357C4×Q8—1221no—
358C4×Q8—1221no—
359C4×Q8C22×D6111yescharacteristic
360C4×Q8C22×D6111yescharacteristic
361#117—1221no—
362C2×C4⋊C4—611no—
363C2×C4⋊C4—1221no—
364C2×C42—611no—
365C2×C42—1221no—
366#107—611no—
367#107—611no—
368#107—611no—
369#107C4×D6111yescharacteristic
370C4⋊C8—21no—
371C4⋊C8—21no—
372C4⋊C8—611no—
373C4⋊C8—611no—
374C4⋊C8—611no—
375C4⋊C8—611no—
376C4⋊C8—611no—
377C4⋊C8—611no—
378C4⋊C8—1221no—
379C4⋊C8—1221no—
380C4⋊C8—1221no—
381C4⋊C8—1221no—
382C4⋊C8—1221no—
383C4⋊C8—1221no—
384C4⋊C8—1221no—
385C4⋊C8C22×D6111yescharacteristic
386C4⋊C8C22×D6111yescharacteristic
387#103—611no—
388#103—611no—
389#103—611no—
390#103—611no—
391#103—611no—
392#103—611no—
393#103C4×D6111yescharacteristic
394#103C4×D6111yescharacteristic
395C22⋊C8—611no—
396C22⋊C8—611no—
397C22⋊C8—611no—
398C22⋊C8—611no—
399C22⋊C8—1221no—
400C22⋊C8—1221no—
401C22⋊C8—1221no—
402#97—21no—
403#97—21no—
404#97—1221no—
405#97—1221no—
406#97—1221no—
407C4×C8—611no—
408C4×C8—611no—
409C4×C8—611no—
410C4×C8—1221no—
411C4×C8—1221no—
412C4×C8—1221no—
413C4×C8—1221no—
414C4×C8—1221no—
415C4×C8C22×D6111yescharacteristic
416C4×C8C22×D6111yescharacteristic
417C4×C8C22×D6111yescharacteristic
418C2×Q8—611no—
419C2×Q8—611no—
420C2×Q8—1221no—
421C2×Q8—1221no—
422C2×Q8—1222no—
423C2×Q8—2441no—
424C2×Q8C2×C4×D6111yescharacteristic
425C2×Q8C2×C4×D6111yescharacteristic
426C22×C4—611no—
427C22×C4—611no—
428C22×C4—611no—
429C22×C4—1221no—
430C22×C4—1221no—
431Q16—41no—
432Q16—1222no—
433Q16—1222no—
434Q16—2441no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—611no—
439C2×C8—611no—
440C2×C8—611no—
441C2×C8—611no—
442C2×C8—1221no—
443C2×C8—1221no—
444C2×C8—1221no—
445C2×C8C2×C4×D6111yescharacteristic
446C2×C8C2×C4×D6111yescharacteristic
447C2×C8D4×D6111yescharacteristic
448C2×C8D4×D6111yescharacteristic
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—611no—
452C4⋊C4—611no—
453C4⋊C4—1221no—
454C4⋊C4—1221no—
455C4⋊C4—1221no—
456C4⋊C4—1221no—
457C4⋊C4—1221no—
458C4⋊C4—1221no—
459C4⋊C4—1221no—
460C4⋊C4—1221no—
461C4⋊C4—1221no—
462C4⋊C4—1221no—
463C4⋊C4C2×C4×D6111yescharacteristic
464C4⋊C4C2×C4×D6111yescharacteristic
465C22⋊C4—1221no—
466C22⋊C4—1221no—
467C42—21no—
468C42—21no—
469C42—611no—
470C42—611no—
471C42—611no—
472C42—1221no—
473C42—1221no—
474C42—1221no—
475C42—1221no—
476C42C23×D6111yescharacteristic
477C23—611no—
478Q8—21no—
479Q8—21no—
480Q8—21no—
481Q8—21no—
482Q8—612no—
483Q8—1221no—
484Q8—1221no—
485Q8—1221no—
486Q8—2442no—
487Q8—2442no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—611no—
493C2×C4—611no—
494C2×C4—611no—
495C2×C4—1221no—
496C2×C4—1221no—
497C2×C4—1221no—
498C2×C4—1221no—
499C2×C4—1221no—
500C2×C4—1221no—
501C2×C4—1221no—
502C2×C4—1221no—
503C2×C4—2441no—
504C2×C4—2442no—
505C2×C4—2442no—
506C2×C4C22×C4×D6111yescharacteristic
507C2×C4C2×D4×D6111yescharacteristic
508C2×C4#41×D6111yescharacteristic
509C8—21no—
510C8—21no—
511C8—21no—
512C8—21no—
513C8—41no—
514C8—41no—
515C8—41no—
516C8—1221no—
517C8—1221no—
518C8—1221no—
519C8—1221no—
520C8—2441no—
521C8—2441no—
522C8—2441no—
523C22—1221no—
524C22—1221no—
525C22—1221no—
526C22C4×D4×D6111yescharacteristic
527C4—21no—
528C4—41no—
529C4—41no—
530C4—41no—
531C4—41no—
532C4—1221no—
533C4—1221no—
534C4—1221no—
535C4—1222no—
536C4—2441no—
537C4—2441no—
538C4—2441no—
539C4#131×D6111yescharacteristic
540C4#1684052811yescharacteristic
541C4#1684057811yescharacteristic
542C4#1684057811yescharacteristic
543C2—2441no—
544C2#2145454811yescharacteristic
545C2#2145468411yescharacteristic
546C2#2145471911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1593C2
socleC22×C61C2×C4×D4
prime radicalC22×D61C4×D4
cosocleC42×C61C24
hypercenter#1593D61
hypocenterC61#18032
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1593

Complements

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

NH ≅ G/Ntype
4. #21444713C2semidirect
5. #21444691C2semidirect
6. #21444689C2semidirect
7. #21444667C2semidirect
8. #21444667C2semidirect
9. #21444639C2semidirect
10. #21444623C2semidirect
15. C61×#1593C2semidirect
273. #1593D61semidirect
340. C61#18032semidirect

Maximal subgroups

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

subgroupindex
#214558562
#214549172
#214549052
#214447132
#214446912
#214446892
#214446672
#214446392
#214446232
#214445962
#214442902
#214442122
#214441202
C61×#15932
#1803261