Finite Group Databasebeta

← #29595468

Subgroups — #29595468

Order 15616.

904 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840527C211yesmaximal, characteristic
2#21447448C211yesmaximal, characteristic, complemented
3#21447447C211yesmaximal, characteristic, complemented
4#21447446C211yesmaximal, characteristic, complemented
5C2×#16839543C211yesmaximal, characteristic, complemented
6C2×#16839543C211yesmaximal, characteristic, complemented
7C61×#2117C211yesmaximal, characteristic, complemented
8C2×#41×D61C411yescharacteristic
9#16840527—22no—
10#16840527—22no—
11#16840527—22no—
12#16840527—22no—
13C2×#14519785—21no—
14C2×#14519785C411yescharacteristic
15C2×#14519784C411yescharacteristic
16C2×#14519783—21no—
17C2×#14519783C2211yescharacteristic
18C22×#11758189—21no—
19C22×#11758189C2211yescharacteristic
20C2×M16×D61—21no—
21C2×M16×D61C411yescharacteristic
22C2×#14519717C2211yescharacteristic, complemented
23C2×#14519717C2211yescharacteristic, complemented
24#16839547—22no—
25#16839546—22no—
26#16839545—22no—
27#16839543—21no—
28#16839543—21no—
29#16839543—21no—
30#16839543—21no—
31C2×#131×C61C2211yescharacteristic
32C2×M32×C61C2211yescharacteristic, complemented
33C2×M32×C61C2211yescharacteristic, complemented
34C61×#350—22no—
35C2×#11758226C811yescharacteristic
36C2×#11758222—21no—
37C2×#11758222C2×C411yescharacteristic
38C2×#11758224—21no—
39C2×#11758224C811yescharacteristic
40#41×D61—22no—
41#41×D61—22no—
42#41×D61—22no—
43#41×D61—22no—
44C2×Q8×D61C811yescharacteristic
45C2×D4×D61—21no—
46C2×D4×D61C811yescharacteristic
47C22×C4×D61—21no—
48C22×C4×D61C2×C411yescharacteristic
49#14519785—24no—
50#14519785—24no—
51#14519785—22no—
52#14519785—22no—
53#14519784—22no—
54#14519784—22no—
55#14519783—24no—
56#14519783—24no—
57#14519783—21no—
58#14519783—21no—
59#14519783D412yes—
60#14519783D412yes—
61C2×#11758194—21no—
62C2×#11758194C2×C411yescharacteristic
63C2×#11758189—24no—
64C2×#11758189—24no—
65C2×#11758189—21no—
66C2×#11758189—21no—
67C2×#11758189—21no—
68C2×#11758189—21no—
69C2×#11758189—21no—
70C2×#11758189—21no—
71C2×#11758189—21no—
72C2×#11758189D411yescharacteristic
73C2×#11758189D411yescharacteristic
74C2×#11758189D411yescharacteristic
75C2×#11758189D411yescharacteristic
76M16×D61—24no—
77M16×D61—24no—
78M16×D61—22no—
79M16×D61—22no—
80C22×#92418—21no—
81C22×#92418C2×C411yescharacteristic
82C2×C8×D61—21no—
83C2×C8×D61—21no—
84C2×C8×D61—21no—
85#14519717—21no—
86#14519717—21no—
87#14519717—21no—
88#14519717—21no—
89C2×#11758185—21no—
90C2×#11758185—21no—
91C2×#41×C61C2×C411yescharacteristic
92#131×C61—21no—
93#131×C61—21no—
94#131×C61D412yes—
95#131×C61D412yes—
96C2×M16×C61—21no—
97C2×M16×C61C2×C411yescharacteristic
98C22×C8×C61—21no—
99C22×C8×C61C2311yescharacteristic
100M32×C61—21no—
101M32×C61—21no—
102M32×C61—21no—
103M32×C61—21no—
104C2×C16×C61—21no—
105C2×C16×C61—21no—
106C23×D61—21no—
107C23×D61M1611yescharacteristic
108#41×C61—21no—
109#41×C61—21no—
110#41×C61C22⋊C412yes—
111#41×C61M1612yes—
112C2×Q8×C61C2×C811yescharacteristic
113C2×D4×C61—21no—
114C2×D4×C61C2×C811yescharacteristic
115C22×C4×C61—21no—
116C22×C4×C61C22×C411yescharacteristic
117C2×C22⋊D61—21no—
118C2×C22⋊D61—21no—
119C2×C22⋊D61—21no—
120C22×Dic61—21no—
121C22×Dic61M1611yescharacteristic
122#11758226—22no—
123#11758226—22no—
124Q8×D61—22no—
125Q8×D61—22no—
126#11758224—24no—
127#11758224—24no—
128#11758224—22no—
129#11758224—22no—
130D4×D61—24no—
131D4×D61—24no—
132D4×D61—22no—
133D4×D61—22no—
134#11758222—24no—
135#11758222—24no—
136#11758222—21no—
137#11758222—21no—
138#11758222C22⋊C412yes—
139#11758222M1612yes—
140C2×D244—21no—
141C2×D244C2×C811yescharacteristic
142C2×C4×D61—24no—
143C2×C4×D61—24no—
144C2×C4×D61—21no—
145C2×C4×D61—21no—
146C2×C4×D61—21no—
147C2×C4×D61—21no—
148C2×C4×D61—21no—
149C2×C4×D61—21no—
150C2×C4×D61—21no—
151C2×C4×D61C22⋊C411yescharacteristic
152C2×C4×D61C22⋊C411yescharacteristic
153C2×C4×D61C2×C811yescharacteristic
154C2×C4×D61C2×C811yescharacteristic
155C2×Dic122—21no—
156C2×Dic122C2×C811yescharacteristic
157M16×C61—21no—
158M16×C61—22no—
159M16×C61—22no—
160M16×C61C22⋊C412yes—
161C2×C8×C61—21no—
162C2×C8×C61—22no—
163C2×C8×C61—22no—
164C2×C8×C61C2×D411yescharacteristic
165C2×C8×C61C2×D411yescharacteristic
166C2×C8×C61C2×D411yescharacteristic
167C2×C8×C61C2×D411yescharacteristic
168C2×C8×C61C2×D411yescharacteristic
169C2×C8×C61C2×D411yescharacteristic
170#11758194—24no—
171#11758194—21no—
172#11758194C22⋊C412yes—
173C2×#92418—24no—
174C2×#92418—21no—
175C2×#92418—21no—
176C2×#92418—21no—
177C2×#92418C22⋊C411yescharacteristic
178C2×#92418C22⋊C411yescharacteristic
179#11758189—24no—
180#11758189—24no—
181#11758189—21no—
182#11758189—21no—
183#11758189—21no—
184#11758189—21no—
185#11758189—22no—
186#11758189—22no—
187#11758189—21no—
188#11758189—21no—
189#11758189—21no—
190#11758189—21no—
191C8×D61—24no—
192C8×D61—24no—
193C8×D61—22no—
194C8×D61—22no—
195C16×C61—41no—
196C16×C61—41no—
197#11758185—41no—
198#11758185—41no—
199C23×C61—21no—
200C23×C61C2×M1611yescharacteristic
201C22×D61—21no—
202C22×D61—24no—
203C22×D61—21no—
204C22×D61—21no—
205C22×D61—82no—
206C22×D61—81no—
207C22×D61C22⋊C811yescharacteristic
208C22×D61C22⋊C811yescharacteristic
209Q8×C61—21no—
210Q8×C61C22⋊C812yes—
211D4×C61—22no—
212D4×C61—22no—
213D4×C61—21no—
214D4×C61C22⋊C812yes—
215C2×C4×C61—21no—
216C2×C4×C61—22no—
217C2×C4×C61—22no—
218C2×C4×C61C2×C22⋊C411yescharacteristic
219C2×C4×C61C2×C22⋊C411yescharacteristic
220C2×C4×C61C2×C22⋊C411yescharacteristic
221C2×C4×C61C22×C811yescharacteristic
222C2×C4×C61C2×M1611yescharacteristic
223C2×C4×C61C2×M1611yescharacteristic
224C22⋊D61—24no—
225C22⋊D61—24no—
226C22⋊D61—22no—
227C22⋊D61—22no—
228C2×Dic61—24no—
229C2×Dic61—21no—
230C2×Dic61—21no—
231C2×Dic61—21no—
232C2×Dic61C22⋊C811yescharacteristic
233C2×Dic61C22⋊C811yescharacteristic
234D244—24no—
235D244—21no—
236D244C22⋊C812yes—
237C4×D61—24no—
238C4×D61—24no—
239C4×D61—22no—
240C4×D61—21no—
241C4×D61—21no—
242C4×D61—21no—
243C4×D61—21no—
244C4×D61—21no—
245C4×D61—21no—
246C4×D61—21no—
247C4×D61—22no—
248C4×D61—21no—
249Dic122—24no—
250Dic122—21no—
251Dic122C22⋊C812yes—
252C8×C61—22no—
253C8×C61#12011yescharacteristic
254C8×C61#12011yescharacteristic
255C8×C61#12011yescharacteristic
256C8×C61#12011yescharacteristic
257#92418—22no—
258#92418—21no—
259#92418—21no—
260#12686—611nomaximal, Sylow
261C22×C61—22no—
262C22×C61—41no—
263C22×C61—42no—
264C22×C61C2×C22⋊C811yescharacteristic
265C22×C61#40711yescharacteristic
266C22×C61#40711yescharacteristic
267C2×D61—21no—
268C2×D61—21no—
269C2×D61—22no—
270C2×D61—42no—
271C2×D61—41no—
272C2×D61—41no—
273C2×D61—81no—
274C2×D61—81no—
275C2×D61—84no—
276C4×C61—22no—
277C4×C61#37911yescharacteristic
278C4×C61C2×C22⋊C811yescharacteristic
279C4×C61C2×C22⋊C811yescharacteristic
280C4×C61#40711yescharacteristic
281Dic61—21no—
282Dic61—22no—
283Dic61—21no—
284C2×#568—611no—
285#2117—611no—
286#2117—611no—
287#2117—611no—
288#2117D6111yescharacteristic, complemented
289C2×#349—611no—
290C2×#349—611no—
291C2×C61—21no—
292C2×C61—21no—
293C2×C61—21no—
294C2×C61—42no—
295C2×C61#177911yescharacteristic
296D61—42no—
297D61—41no—
298D61—41no—
299C22×#41—611no—
300#568—1222no—
301#568—1222no—
302#568—1222no—
303#568—1222no—
304C2×#131—611no—
305C2×#131—611no—
306C2×#131—611no—
307C2×#131—1221no—
308C2×#131—1221no—
309C2×#131C2×D6111yescharacteristic
310C22×M16—611no—
311C22×M16—611no—
312C22×M16—1221no—
313C22×M16—1221no—
314C2×M32—611no—
315C2×M32—611no—
316C2×M32C2×D6111yescharacteristic, complemented
317C2×M32C2×D6111yescharacteristic, complemented
318#350—22no—
319#350—1222no—
320#350—1222no—
321#350—1222no—
322#349—1221no—
323#349—1221no—
324#349—1221no—
325#349—1221no—
326C61#1268611yescharacteristic, complemented, Sylow
327C2×#41—611no—
328C2×#41—611no—
329C2×#41—611no—
330C2×#41—1221no—
331C2×#41—1221no—
332C2×#41—1222no—
333C2×#41—1222no—
334C2×#41—1222no—
335C2×#41—1222no—
336C2×#41C4×D6111yescharacteristic
337C22×Q8—611no—
338C22×D4—611no—
339C22×D4—1221no—
340C23×C4—611no—
341C23×C4—1221no—
342#131—21no—
343#131—21no—
344#131—612no—
345#131—612no—
346#131—1224no—
347#131—1224no—
348#131—1222no—
349#131—1224no—
350#131—1224no—
351#131—1222no—
352#131—1222no—
353#131—1222no—
354#131—1221no—
355#131—1221no—
356#131D24412yes—
357#131C22⋊D6112yes—
358C2×M16—21no—
359C2×M16—611no—
360C2×M16—611no—
361C2×M16—611no—
362C2×M16—611no—
363C2×M16—611no—
364C2×M16—1221no—
365C2×M16—1221no—
366C2×M16—1224no—
367C2×M16—1224no—
368C2×M16—1221no—
369C2×M16—1222no—
370C2×M16—1224no—
371C2×M16—1224no—
372C2×M16—1222no—
373C2×M16—1221no—
374C2×M16—1221no—
375C2×M16—1221no—
376C2×M16—1221no—
377C2×M16—1221no—
378C2×M16C4×D6111yescharacteristic
379C22×C8—21no—
380C22×C8—611no—
381C22×C8—1221no—
382C22×C8—1221no—
383C22×C8—1221no—
384C22×C8—1221no—
385C22×C8C22×D6111yescharacteristic
386M32—21no—
387M32—21no—
388M32—21no—
389M32—21no—
390M32—1221no—
391M32—1221no—
392M32—1221no—
393M32—1221no—
394C2×C16—21no—
395C2×C16—21no—
396C2×C16—1221no—
397C2×C16—1221no—
398C24—611no—
399C24—1221no—
400#41—21no—
401#41—21no—
402#41—612no—
403#41—612no—
404#41—1224no—
405#41—1224no—
406#41—1222no—
407#41—1224no—
408#41—1224no—
409#41—1222no—
410#41—1222no—
411#41—1222no—
412#41—1221no—
413#41—1221no—
414#41#1175818912yes—
415#41#1175819812yes—
416C2×Q8—611no—
417C2×Q8—1221no—
418C2×Q8—1222no—
419C2×Q8—1222no—
420C2×Q8C8×D6111yescharacteristic
421C2×D4—21no—
422C2×D4—611no—
423C2×D4—1221no—
424C2×D4—1221no—
425C2×D4—1222no—
426C2×D4—1224no—
427C2×D4—1224no—
428C2×D4—1221no—
429C2×D4—1221no—
430C2×D4—1222no—
431C2×D4C8×D6111yescharacteristic
432C22×C4—21no—
433C22×C4—611no—
434C22×C4—611no—
435C22×C4—611no—
436C22×C4—611no—
437C22×C4—611no—
438C22×C4—1221no—
439C22×C4—1221no—
440C22×C4—1224no—
441C22×C4—1224no—
442C22×C4—1221no—
443C22×C4—1221no—
444C22×C4—1221no—
445C22×C4—1221no—
446C22×C4—1221no—
447C22×C4—1221no—
448C22×C4C2×C4×D6111yescharacteristic
449M16—21no—
450M16—22no—
451M16—22no—
452M16—612no—
453M16—1224no—
454M16—1224no—
455M16—1224no—
456M16—1221no—
457M16—1221no—
458M16—1221no—
459M16—1221no—
460M16—1221no—
461M16—1222no—
462M16—1221no—
463M16—1221no—
464M16—1221no—
465M16—1221no—
466M16—1222no—
467M16#1175819812yes—
468C2×C8—21no—
469C2×C8—22no—
470C2×C8—22no—
471C2×C8—611no—
472C2×C8—611no—
473C2×C8—1224no—
474C2×C8—1224no—
475C2×C8—1224no—
476C2×C8—1221no—
477C2×C8—1221no—
478C2×C8—1221no—
479C2×C8—1222no—
480C2×C8—1222no—
481C2×C8C2×D24411yescharacteristic
482C2×C8D4×D6111yescharacteristic
483C2×C8D4×D6111yescharacteristic
484C2×C8D4×D6111yescharacteristic
485C2×C8D4×D6111yescharacteristic
486C2×C8C2×C22⋊D6111yescharacteristic
487C16—41no—
488C16—41no—
489C16—2441no—
490C16—2441no—
491C23—21no—
492C23—611no—
493C23—611no—
494C23—1224no—
495C23—1221no—
496C23—1221no—
497C23—1221no—
498C23—4882no—
499C23—4881no—
500C23M16×D6111yescharacteristic
501Q8—21no—
502Q8—612no—
503Q8—1224no—
504Q8—1221no—
505Q8#1451968912yes—
506D4—22no—
507D4—22no—
508D4—21no—
509D4—612no—
510D4—1224no—
511D4—1224no—
512D4—1224no—
513D4—1222no—
514D4—1222no—
515D4—1221no—
516D4#1451968912yes—
517C2×C4—21no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—611no—
521C2×C4—611no—
522C2×C4—1224no—
523C2×C4—1224no—
524C2×C4—1224no—
525C2×C4—1221no—
526C2×C4—1221no—
527C2×C4—1221no—
528C2×C4—1221no—
529C2×C4—1221no—
530C2×C4—1221no—
531C2×C4—1221no—
532C2×C4—1221no—
533C2×C4—1221no—
534C2×C4—1222no—
535C2×C4—1221no—
536C2×C4—1222no—
537C2×C4—1221no—
538C2×C4C22⋊C4×D6111yescharacteristic
539C2×C4C22⋊C4×D6111yescharacteristic
540C2×C4C2×#1175819811yescharacteristic
541C2×C4C2×C8×D6111yescharacteristic
542C2×C4M16×D6111yescharacteristic
543C2×C4C2×#1175818911yescharacteristic
544C8—22no—
545C8—1221no—
546C8—1221no—
547C8—1222no—
548C8#1451974511yescharacteristic
549C8#1451974511yescharacteristic
550C8#1451974711yescharacteristic
551C8#1451974711yescharacteristic
552C22—22no—
553C22—41no—
554C22—42no—
555C22—1221no—
556C22—1222no—
557C22—1221no—
558C22—4881no—
559C22—4881no—
560C22—4884no—
561C22—2441no—
562C22—2441no—
563C22—2442no—
564C22C22⋊C8×D6111yescharacteristic
565C22#1683972411yescharacteristic
566C22#1683972511yescharacteristic
567C4—22no—
568C4—1221no—
569C4—1221no—
570C4—1222no—
571C4#1683961711yescharacteristic
572C4C22⋊C8×D6111yescharacteristic
573C4C2×#1451968911yescharacteristic
574C4#1683972411yescharacteristic
575C2—21no—
576C2—21no—
577C2—21no—
578C2—42no—
579C2—2441no—
580C2—2442no—
581C2—2441no—
582C2#2144572811yescharacteristic
subgroupG/H
centerC4#16839617
commutatorC2×C4×C61C22×C8
FrattiniC22×C8C22×D61
FittingC61×#2117C2
socleC2×C61#1779
prime radicalC2×#41×D61C4
cosocleC22×C8×C61C23
hypercenter#2117D61
hypocenterC61#12686
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C22×C8 ◁ #2117

Complements

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

NH ≅ G/Ntype
2. #21447448C2semidirect
3. #21447447C2semidirect
4. #21447446C2semidirect
5. C2×#16839543C2semidirect
6. C2×#16839543C2semidirect
7. C61×#2117C2semidirect
22. C2×#14519717C22semidirect
23. C2×#14519717C22semidirect
32. C2×M32×C61C22semidirect
33. C2×M32×C61C22semidirect
288. #2117D61semidirect
316. C2×M32C2×D61semidirect
317. C2×M32C2×D61semidirect
326. C61#12686semidirect

Maximal subgroups

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

subgroupindex
C2×#168405272
#214474482
#214474472
#214474462
C2×#168395432
C61×#21172
#1268661